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Entry
Reference
Abstraction Bigelow
 
Books on Amazon
I 380
Abstractions/Figures/Armstrong/Bigelow/Pargetter: Numbers are causally inactive. Mathematics/Realism/Bigelow/Pargetter: some mathematical entities are even observable.
---
I 381
Causation/Mathematics/BigelowVsArmstrong/Bigelow/Pargetter: in fact, people are not causes, but they are involved in causal processes. Numbers: they are also involved in causal processes. If objects did not instantiate the quantities they instanced, other changes would have occurred. Thus at least proportions are causally involved. ((s) FieldVsNumbers as causal agents, but not Vs proportions).
---
I 382
Counterfactual dependence/Bigelow/Pargetter: one can again set up consequences of counterfactual conditionals, e.g. For the lever laws of Archimedes. This also provides why-explanations. ---
I 383
Numbers/causality/Bigelow/Pargetter: this shows that numbers play a fundamental role in causal explanations. BigelowVsField: (a propos Field, Science without numbers): he falsely assumes that physics first starts with pure empiricism, in order to convert the results into completely abstract mathematics.
Field/Bigelow/Pargetter: wants to avoid this detour.
BigelowVsField: his project is superfluous when we realize that mathematics is only a different description of the physical proportions and relations and no detour.

Big I
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990

Best Explanation Bigelow
 
Books on Amazon
I 341
Best explanation/BE/Bigelow/Pargetter: behind it different kinds of realism are concealed. (> realism) ---
I 344
Explanation/BE/Bigelow/Pargetter: if we accept the realism due to conclusions on the best explanation, we must ask what kind of explanation it is. It may e.g. be about various kinds of (Aristotelian) causes (see above). The most convincing are surely those which are concerned with "efficient" causes: e.g. Cartwright, Hacking: Realism/Cartwright/Hacking: is best supported by causal explanations.
Quine/Two Dogmas/Bigelow/Pargetter: Quine has caused many philosophers not only to stay in the armchair, but also to question the experiments that scientists have carried out in real terms. We reject this.
Realism/Bigelow/Pargetter: but we also reject the other extreme that realism would have to arise solely from causal explanations.
---
I 345
There can also be formal reasons (formal causes/Aristotle) for realism. Modality/Bigelow/Pargetter: so it is also a legitimate question as to what modalities are constituted in science. Modal realism is the best explanation here for such matters.
Metaphysics/Platonism/Universals/Bigelow/Pargetter: can be supported by the best explanation: by means of conclusions on the best explanation we show that we need modalities and universals in the sciences.
Modality/Bigelow/Pargetter: their primary source is mathematics.
Mathematics/Bigelow/Pargetter: our metaphysics allows a realistic view of mathematics (BigelowVsField).

Big I
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990

Causal Theory of Reference Field
 
Books on Amazon
Horwich I 490
Field early: per Harman: there is a single causal relation in the world -> Correspondence Theory -> physicalism -> causal theory of reference - no non-physical connection between words and the world. - I 491 Field / M. Williams: metaphysical approach: how semantic properties fit in a physical world. LeedsVsField: Talk about truth can not be physically explained - Solution: truth must not play any explanatory role - otherwise we are back to the problems with acceptability and justification.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980


Hor I
P. Horwich (Ed.)
Theories of Truth Aldershot 1994
Language Field
 
Books on Amazon
Avr I 113
Belief/Meaning/FieldVsReductionism: (VsReductive Griceans): it is circular, to want to explain the semantic properties by believe. (This also says the reductionism.) - Field like Grice: one can explain believe without reference to the sentence. - Solution: what makes a symbol a symbol for Caesar is the role in my learning. - Field: then there can be no inner language without a public language. SchifferVsField: no problem: Grice (intention based semantics, IBS) does not need to assume that propositional attitudes have been acquired before the public language. - Both goes hand in hand - only there is no logical dependence between them (and to competence). - Armstrong: both are logically connected. ((s) This is stronger than Schiffer's thesis.). ---
Horwich I 481
Language/Truth-Definition/Field/Soames: when truth is defined non-semantically (i.e., speaker-independent, i.e. non-physical), language becomes an abstract object. - It has its characteristics essentially. - With other properties, it would be a different language - that is, it could not have been shown that the expressions could have denoted anything else. - Then it is still contingent on language, which language a person speaks. - But the semantic properties (truth, reference, applying) are not contingent.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980


Hor I
P. Horwich (Ed.)
Theories of Truth Aldershot 1994
Loewenheim Putnam
 
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V 54 ff
Loewenheim/Reference/PutnamVsTradition: tries to fix the intension und extension of single expressions via the determination of the truth values for whole sentences. ---
V 56f
PutnamVsOperationalism: E.g. (1) "E and a cat is on the mat." - Reinterpretation with cherries and trees so that all truth values remain unchanged. - cat* to mat*: a) some cats on some mats and some cherries on some trees, b) ditto, but no cherry on a tree - c) none of these cases - Definition cat* x is a cat* iff. a) and x = cherry, or b) and x = cat or c) and x = cherry - Definition mat*: x = mat* iff. a) and x = tree or b) and x = mat or c) and x = quark - ad c) here all respective sentences become false. - ((s) "cat* to mat*" is the more comprehensive (disjunctive) statement and therefore true in all worlds a) or b).) - Putnam: by the reinterpretation cat will be enhanced to cat* - then there might be infinitely many reinterpretations of predicates that will always attribute the right truth value - then we might even hold "impression" constant as the only expression. - The reference will be undetermined because of the truth conditions for whole sentences (>Gavagai). ---
V 58
We even can reinterpret "sees" (as sees*) so that the sentence "Otto sees a cat" and "Otto sees* a cat" have the same truth values in every world. ---
V 61
Which properties are intrinsic or extrinsic is relative to the decision, which predicates we use as basic concepts, cat or cat*. - Properties are not in themselves extrinsic/intrinsic. ---
V 286ff
Loewenheim/Putnam: Theorem: be S a language with predicates F1,F2,...Fk. Be I an interpretation in the sense that each predicate if S gets an intension. Then there will be a second interpretation J that is not concordant with I but will make the same sentences true in every possible world that are made true by I. - Proof: Be W1, W2, all possible worlds in a well-ordering, be Ui the set of possible individuals existing in world Wi - be Ri the set, forming the extension of the predicate Fi in the possible world Wj - the structure [Uj;Rij(i=1,2...k)] is the "intended Model" of S in world Wj relative to I (i.e. Uj is the domain of S in world Wj, and Rij is (with i = 1,2,...k) the extension of the predicate Fi in Wj) - Be J the interpretation of S which attributes to predicate Fi (i=1,2,...k) the following intension: the function fi(W), which has the value Pj(Rij) in every possible worlds Wj. - in other words: the extension of Fi in every world Wj under interpretation J is defined such, that it is Pj(Rij). - Because[Uj;Pj(Rij)(i=1,2...k)] is a model for the same set of sentences as [Uj;Rij(i=1,2...k)] (because of the isomorphism), in every possible world the same sentences are true under J as under I. - J is distinguished from I in every world, in which at least one predicate has got a non-trivial extension. ---
V 66
Loewenheim/Intention/Meaning/Putnam: this is no solution, because to have intentions presupposes the ability to refer to things. - Intention/Mind State: is ambigue: e.g. "pure": pain, E.g. "impure": whether I know that snow is white does not depend on me like pain (> twin earth) - non-bracketed belief presupposes that there really is water. (twin earth) - Intentions are no mental events that evoke the reference. ---
V 70
Reference/Loewenheim/PutnamVsField: a rule like "x prefers to y iff. x is in relation R to y" does not help: even when we know that it is true, could relation R be any kind of a relation (while Field assumes that it is physical). ---
II 102ff
E.g. the sentence: (1) ~(ER)(R is 1:1. The domain is R < N. The range of R is S). - Problem: when we replace S by the set of real numbers (in our favourite set theory). Then (1) will be a theorem - then our set theory will say that a certain set ("S") is not countable - then S must in all models of our set theory (e.g. Zermelo-Fraenkel, ZF) be non-countable. - Loewenheim: his sentence now tells us, that there is no theory with only uncountable models - contradiction. - But this is not the real antinomy - Solution: (1) "tells us" that S is non-countable only, if the quantifier (ER) is interpreted such that is goes over all relations of N x S.
---
II 103
But if we choose a countable model for the language of our set theory, then "(ER)" will not go over all relations but only over the relations in the model. - Then (1) tells us only, that S is uncountable in a relative sense of uncountable: "finite"/"Infinite" are then relative within an axiomatic set theory. - Problem: "unintended" models, that should be uncountable will be "in reality" countable - ...+ descending ... Skolem shows, that the whole use fo our language (i.e. theoretical and operational conditions) will not determine the "uniquely intended interpretation". - Solution: Platonism: postulates "magical reference". - Realism: has no solution. ---
II 105
At the end the sentences of set theory have no fixed truth value. ---
II 116
Solution: Thesis: we have to define interpretation in another way than by models.

Pu I
H. Putnam
Von einem Realistischen Standpunkt Frankfurt 1993

Pu II
H. Putnam
Repräsentation und Realität Frankfurt 1999

Pu III
H. Putnam
Für eine Erneuerung der Philosophie Stuttgart 1997

Pu IV
H. Putnam
Pragmatismus Eine offene Frage Frankfurt 1995

Pu V
H. Putnam
Vernunft, Wahrheit und Geschichte Frankfurt 1990

Logic Field
 
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I 34
Logic/Theory/Field: concepts such as negation, conjunction, implication do not require any theoretical access (like e.g. "light is electromagnetic radiation") - because they are logical concepts. ---
I 73
Logic/mathematics/mathematical entities/m.e./VsField: one needs mathematical entities in logic, albeit not in science. - FieldVsVs: this is a confusion of logic and meta-logic. - E.g. for definitions in model theory. ---
I 74
In logic, which is simple reasoning, we need only the entities that occur in the premises, the intermediate steps, and the conclusions, but because we ultimately draw nominalistic conclusions, we need no mathematical entities in the conclusions. - We are talking about the predictions of empirical consequences. ---
I 76
Definition Logic/Field: is the science of the possible.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980

Logical Possibility Field
 
Books on Amazon
I 86
Logical possible/possibility/diamond/KripkeVsField: "it is possible that" is not a logical truth. - FieldVsKripke: yes it is, this is due to Kripke's model-theoretical definition. - It should not be read "mathematically" or "metaphysically possible". ---
I 87
E.g. Carnap: "He is a bachelor and married": is logically wrong - (> meaning postulates) - FieldVsCarnap: Meaning relations between predicates should not belong to logic. - Then the sentence is logically consistent. - consistency operator/Field: MEx (x is red & x is round) - should not only be true, but logical. - ((s) Even without meaning postulates. Meaning postulate/(s): this is about the extent of the logic.) ---
I 118
Logical possible/FieldVsKripke: "It is possible that there is an electron": is true in all models, therefore logically true. (> Logical possibility is itself logically true).

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980

Mathematical Entities Armstrong
 
Books on Amazon
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990
Big I 380
Numbers/Armstrong/Bigelow/Pargetter: Armstrong Thesis: Numbers are causally inactive. (Field ditto). Mathematics/Realism/Bigelow/Pargetter: some mathematical entities are even observable!
I 381
Causation/Mathematics/BigelowVsArmstrong/Bigelow/Pargetter: Numbers: even they are involved in the causal processes. If objects did not instantiate the quantities they instantiate, other changes would have occurred. Thus at least proportions are causally involved. (s) FieldVsNumbers as causal agents, but not FieldVsProportions).
I 382
Counterfactual Dependence/Bigelow/Pargetter: thus we can again set up sequences of counterfactual conditionals, e.g. for the lever laws of Archimedes. This also provides why explanations.
I 383
Numbers/Causality/Bigelow/Pargetter: this shows that numbers play a fundamental role in causal explanations. BigelowVsField: (a propos Field, Science without numbers): he falsely assumes that physics first starts with pure empiricism to then convert the results into completely abstract mathematics.
Field/Bigelow/Pargetter: wants to avoid this detour.
BigelowVsField: his project is superfluous if we realize that mathematics are only a different description of the physical proportions and relations and no detour.

AR II = Disp
D. M. Armstrong

In
Dispositions, Tim Crane, London New York 1996

AR III
D. Armstrong
What is a Law of Nature? Cambridge 1983

Mathematics Bigelow
 
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I VII
Mathematics/BigelowVsField: can be understood realistically when viewed as a study of universals, properties and relations, of patterns and structures of things that can be in different places at the same time. ---
I 346
Mathematics/Realism/Bigelow/Pargetter: Pro Realism of Mathematics. ((s) The thesis that numbers exist as objects. And thus also sets, and all possible mathematical objects or entities. (FieldVs.)
We agree with the antirealists that there are human creations:
For example, words, ideas, diagrams, images, terms, theories, texts, academic departments, etc.
Realism/Bigelow/Pargetter: of mathematics: is well compatible with modal realism.
Science/Bigelow/Pargetter: no one believes that everything in science is real. There must be (useful) fictions. Therefore, one can in principle be a realist in relation to everyday things and at the same time a mathematical antirealist. For example, Field:
Field/Bigelow/Pargetter: is at the same time a realist regarding space-time, particles and fields.
---
I 347
Realism/Antirealism/Mathematics/Bigelow/Pargetter: nevertheless, there is something wrong with this marriage: mathematics is not a small element of science but a very large one. It is also not easy to isolate. Example: Galileo/Bigelow/Pargetter: did not know about instantaneous speed yet. For him, speed was simply a course divided by time. A falling object then had an average speed, although Galileo was not aware of this either.
Therefore, he made the following mistake: if two bodies are dropped together and one of them continues to fly, they both have exactly the same speed until the first one stops.
Galileo: but had to assume that this body was slower, because the other body needed less than twice as much for the eventual double distance.
---
I 348
Rate of fall/Bigelow/Pargetter: therefore the average velocity cannot be proportional to the distance. Realism/Bigelow/Pargetter: if anything is evidence for realism, it is this: an object that falls twice as far does not have twice the average velocity. If you find out, you are a realist in terms of how long it takes for an object to reach a given distance. This makes us realists in terms of velocity, time and distance.
((s) The problem arose from the fact that Galileo was forced to adhere to the definitions he had set up himself, otherwise he would have had to change his theory.).
Average/VsRealism/Bigelow/Pargetter: one could argue that average is only an abstraction.
VsVs: we do not need the average here at all: it is simply true that the object falls faster in the second section, and that simply means that the average velocity cannot be the same.
Velocity/Galileo/Bigelow/Pargetter: he respects that it is physically real. And caused by forces and proportional to these forces, so velocity was causally effective for him.
Velocity/today/Bigelow/Pargetter: we think today that it is the instantaneous speed which is causally effective, never the average velocity.
---
I 349
Realism/Mathematics/Bigelow/Pargetter: the equations we use to describe the relations between different falling objects are human inventions, but not the relations themselves. Rate of fall/fall law/Galileo/Bigelow/Pargetter: the distance is proportional to the square of the time traveled. How is this abstract law based on concrete physical facts?
Galileo: in the first unit of time the body falls a certain distance, in the second unit not double, but triple of this distance, in the third five units, and so on.
Predecessor/Bigelow/Pargetter: this had already been anticipated in the Middle Ages.
---
I 350
Middle Ages/Thesis: an increment has been added to each section. One, three, five, seven... Now the sum of the first n odd numbers is n².
Then it seems to be based on nothing but rules for the use of symbols that
(1 + 3 +... + (2n - 1) = n².
But this is a mistake:
Numbers/Number/Bigelow/Pargetter: may be abstract, but they are present in an important sense in the physical objects: in a collection of objects that have this number, they are the common thing. For example, a collection of objects which has the number n².
---
I 350
You can just see that the pattern has to go on like this. ---
I 351
And so it is in Galileo's case. Realism/Mathematics/Bigelow/Pargetter: the differences to physical bodies should not blind us for the similarities. If objects instantiate the same numbers, the same proportions will exist between them. (>Instantiation).
Instantiation/Bigelow/Pargetter/(s): For example, a collection of 3 objects instantiates the number three.
---
I 352
Equation/Bigelow/Pargetter: (e.g. Galileo's fall rate, which was wrong) is a description of real relations between real objects. Platonism/Bigelow/Pargetter: this view can roughly be called Platonist.
Bigelow/Pargetter: pro Platonism, but without the usual Platonic doctrines: we do not assume forms or ideals taken from an earlier existence that we cannot see in our world, and so on.
Realism/Universal Realism/Universals/Bigelow/Pargetter: our realism is closer to Aristotle: the universals are here in our world, not in an otherworldly.
BigelowVsAristotle: we disapprove of his preference for quantitative versus quantitative characteristics of objects.
---
I 377
Mathematics/Bigelow/Pargetter: (...) ---
I 378
Patterns unfold patterns. The structures of mathematics show up not only in the hardware of physics, but also in the "mathware", through properties and relations in different areas of mathematics. For example, not only objects, but also numbers can be counted. Proportions, for example, stand in proportions to each other. This is the reflexivity within mathematics.

Big I
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990

Metaphysical Possibility Field
 
Books on Amazon
I 86
Logically possible/possibility/diamond/KripkeVsField: "it is possible that" is not a logical truth - FieldVsKripke: that is only due to Kripke's model-theoretical definition. - It should not be seen as "mathematically" or "metaphysically possible". ---
I 87
E.g. Carnap: "He is a bachelor and married": is logically wrong - (> meaning postulates) - FieldVsCarnap: Meaning relations between predicates should not belong to logic. - Then the sentence is logically consistent. Consistency operator/Field: MEx (x is red & x is round) - should not only be true, but logically true. - ((s) Even without meaning postulates - (meaning postulate/(s): this is about the scope of logic.)

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980

Possibility Field
 
Books on Amazon
I 86
Logically possible/possibility/diamond/KripkeVsField: "it is possible that" is not a logical truth. - FieldVsKripke: yes it is, this is only due to Kripke's model-theoretical definition. - It should not be read "mathematically" or "metaphysically possible". ---
I 87
E.g. Carnap: "He is bachelor and married": is logically wrong. (> Meaning postulates) - FieldVsCarnap: Meaning relations between predicates should not count to logic. - Then the sentence is logically consistent. - Consistency operator/Field: MEx (x is red & x is round) - should not only be true, but logically true. - ((s) also without meaning postulates.) ((s) Meaning postulate/(s): here it is about the extent of the logic.) ---
I 203
Geometric Possibility/Field: instead of logical possibility: there are different geometries. - Precondition: there are empirical axioms which differentiate the possibility from impossibility. - However, the existence quantifier must be within the range of the modal operator. ---
I 218
Problem of Quantities/mathematical entities/me/Field: For example, it is possible that the distance between x and y is twice as long as the one between x and w, even if the actual distance is more than twice as long. - Problem: extensional adequacy does not guarantee that the defined expression is true in every non-actual situation - that is, that we must either presuppose the substantivalism or the heavy duty Platonism. - That is what we do in practice.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980

Realism Bigelow
 
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I VII
Realism/Bigelow/Pargetter: thesis: pro scientific realism. Logic can also be understood best in this way. Modal Realism/Bigelow/Pargetter: pro: a scientific realist should be a modal realist. ((s) I.e. he/she should assume the existence of possible worlds).
---
I 38
Realism/Bigelow/Pargetter: our realism is neutral in relation to reductionism. ---
I 275
Metaphysical realism/Bigelow/Pargetter: pro metaphysical realism, which does not simply interpret the causal relation as a predicate, or as a set of ordered pairs, but as a universal. ---
I 341
Best explanation/BE/Bigelow/Pargetter: behind it are different kinds of realism. ---
I 342
Realism/Bigelow/Pargetter: many of his varieties are based on a best explanation. Since we are assuming there is something to explain in the explanation. Foundation/fundamental realism/Bigelow/Pargetter: a fundamental class of entities is assumed. These do not explain anything themselves, but provide the material to be explained.
Vs: the raw material should be sensations (perception, experience).
Appearance/Bigelow/Pargetter: if we start with it, we can reach the best explanation for any kind of realism by concluding. But it is not "realism about phenomena". Realism always accepts objects.
BigelowVsTradition: erroneously assumes that we ourselves are in some way outside and not in the midst of reality.
Realism/Explanation/Bigelow/Bigelow/Pargetter: not everything we assume to be real does contribute to explanations at all!
((s) For example redundancies and repetitions are not unreal, tautologies are not unreal either, nor boring stuff. So we cannot assume from the outset that reality is a valid explanation. Neither would we deny the existence of boring stuff.).
Reality/Bigelow/Pargetter: it is also doubtful whether all things should explain appearances.
---
I 343
Definition direct realism/Bigelow/Pargetter: thesis: we perceive objects "directly". I. e. without deducing their existence from anything fundamental by inference. There is some truth in it! (pro: Armstrong 1961, discussion in Jackson 1977b). BigelowVsDirect realism: even if we could keep object and appearances apart through reflection, it would be questionable whether the material thing would be the better explanation!
Appearance/Bigelow/Pargetter: dealing with it is tricky. It seems as if we have to find out something about our inner states first. The normal case, however, is the extroverted perceiver. The situation of extroverted perception must also precede introverted reflection.
Best Explanation/Bigelow/Pargetter: nonetheless, if we are realists, we will understand material objects as the best explanation of our appearances (or perception).
Realism/Bigelow/Pargetter: now it shows that there is a hierarchy of two realisms
((s) a) direct, naive, b) reflected, by deduction from appearances)
and how this hierarchy is destroyed in practice: we begin with a realism and come to the conclusion of the best explanation to the second realism, and these merge into one and the same reality. The hierarchical order does not remain in things, but becomes an extrinsic characteristic of their relation to us as perceivers.
There is also a feedback: the inverse conclusion from the reflected realism on the unreflected.
---
I 344
Holism/Bigelow/Pargetter: that leads to some kind of epistemic holism that we accept. It does not threaten realism. Explanation/Best Explanation/Bigelow/Pargetter: if we accept realism on the basis of conclusions drawn from the best explanation, we must ask what kind of explanation is at issue. It can be about different kinds of (Aristotelian) causes (see above). The most convincing ones are certainly those that are concerned with "efficient" causes: e.g. Cartwright, Hacking:
Realism/Cartwright/Hacking: is best supported by causal explanations.
Quine/Two Dogmas/Bigelow/Pargetter: Quine has caused many philosophers not only to sit in the armchair, but also to question the experiments that scientists have carried out in real. We reject that.
Realism/Bigelow/Pargetter: but we also reject the other extreme, that realism would have to arise solely from causal explanations.
---
I 345
There may also be formal reasons (formal causes/Aristotle) for realism. Modality/Bigelow/Pargetter: it is also a legitimate question as to what constitutes modalities in science. Modal realism is the best explanation here for such matters.
Metaphysics/Platonism/Universals/Bigelow/Pargetter: can be supported by the Best Explanation: by inferences on the best explanation we show that we need modalities and universals in the sciences.
Modality/Bigelow/Pargetter: their primary source is mathematics.
Mathematics/Bigelow/Pargetter: our metaphysics allows a realistic understanding of mathematics (BigelowVsField).

Big I
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990

Relation-Theory Bigelow
 
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I 55
Quantity/relational theory/Bigelow/Pargetter: Quantities are general relations between objects. They seem to be consequences of the intrinsic properties of objects. But one would not have to postulate an intrinsic relation "greater than", but only e.g. the size. Greater than/relational property/problem/Bigelow/Pargetter: one might wonder if there really is an intrinsic property to be that and that big.
Relational property/Bigelow/Pargetter: one might be tempted to assume that everything is based on relational properties, rather than vice versa. But we are not going to go into that here.
Intrinsic property/Bigelow/Pargetter: we think that in the end they can be defended against relational properties as a basis. Nevertheless, we certainly need relational properties, e.g. for the order of events. These do not just stand in time. So we definitely need relations.
Relations/Bigelow/Pargetter: we definitely need relations. Because events never stand for themselves.
---
I 56
Also for expressions such as "twice the size" etc. Quantity/Bigelow/Pargetter: Quantities cannot be based on properties alone, but need relations. For example, having this or that mass is then the property of being in relation to other massive objects.
Participation/BigelowVsPlato: Plato has all things in a more or less strong relation to a single thing, the form. We, on the other hand, want relations between things among themselves.
BigelowVsPlato: we can then explain different kinds of differences between objects, namely that they have different relational properties that other things do not have. E.g. two pairs of things can differ in different ways.
---
I 57
Relational Theory/Bigelow/Pargetter: can handle differences of differences well. Question: can it cope well with similarities? For example, explain what mass is at all?
Problem: we need a relation between a common property and many relations to it. There are many implications (entailments) which are not yet explained.
Property/Bigelow/Pargetter: 1. in order to construct an (intrinsic) property at all, we must therefore specify the many possible relations it can have to particalur.
Solution: one possibility: the sentence via the property of the 2nd level.
2. Problem: how can two things have more in common than two other things?
Ad 1. Example Mass
Common/Commonality/Bigelow/Pargetter: must then be a property of relations (of the many different relations that the individual objects have to "mass"). ---
I 58
Solution: property of the 2nd level that is shared by all massive things. For example, "stand in mass relations". Entailment/N.B.: this common (2nd level property) explains the many relations of the entailment between massive objects and the common property of solidity.
Problem/Bigelow/Pargetter: our relational theory is still incomplete.
Problem: to explain to what extent some mass-relations are closer (more similar) than others.
Relations/common/Bigelow/Pargetter: also the relations have a common: a property of the 2nd level. Property 2.
Level/difference/differentiation/problem/Bigelow/Pargetter: does not explain how two things differ more than two other things.
It also does not explain how, for example, differences in masses relate to differences in volume.
For example, compare the pairs
"a, b"
"c, d"
"e, f"
between which there are differences in thicknesses with regard to e.g. length.
Then two of the couples will be more similar in important respects than two other pairs.
---
I 59
Solution/Bigelow/Pargetter: the relation of proportion. This is similar to Frege's approach to real numbers. Real numbers/Frege: as proportions between sizes (Bigelow/Pargetter corresponds to our quantities).
Bigelow/Pargetter: three fundamental components
(1) Individuals
(2) Relations between individuals (3) Relations of proportions between relations between individuals.
Proportions/Bigelow/Pargetter: divide the relations between individuals into equivalence classes:
Mass/Volume/Proportions/N.B./Bigelow/Pargetter: all masses are proportional to each other and all volumes are proportional to each other, but masses and volumes are not proportional to each other.
Equivalence classes/Bigelow/Pargetter: arrange objects with the same D-ates into classes. So they explain how two things ((s) can be more similar in one respect, D-able) than in another.
Level 1: Objects
Level 2: Properties of things Level 3: Proportions between such properties.
Proportions/Bigelow/Pargetter: are universals that can introduce finer differences between equivalence classes of properties of the 2nd level.
Different pairs of mass relations can be placed in the same proportion on level 3. E.g. (s) 2Kg/4kg is twice as heavy as 3Kg/6Kg.
N.B.: with this we have groupings that are transverse to the equivalence classes of the mass relations, volumetric relations, velocity relations, etc.
Equal/different/Bigelow/Pargetter: N.B:: that explains why two relations can be equal and different at the same time. E.g. Assuming that one of the two relations is a mass relation (and stands in relation to other mass relations) the other is not a mass relation (and is not in relation to mass relations) and yet...
---
I 60
...both have something in common: they are "double" once in terms of mass, once in terms of volume. This is explained on level 3. Figures/Bigelow/Pargetter: this shows the usefulness of numbers in the treatment of quantities. (BigelowVsField).
Real numbers/Frege: Lit: Quine (1941, 1966) in "Whitehead and the Rise of Modern Logic")
Measure/Unit/Measuerment Unit/To Measure/Bigelow/Pargetter:"same mass as" would be a property of the 2nd level that a thing has to an arbitrary unit.
Form/Plato/Bigelow/Pargetter: his theory of forms was not wrong, but incomplete. Objects have relations to paradigms (here: units of measurement). This is the same relation as that of participation in Plato.
---
I 61
Level 3: the relations between some D-ates can be more complex than those between others. For mass, for example, we need real numbers, other terms are less clear. Quantities/Bigelow/Pargetter: are divided into different types, which leads to interval scales or ratio scales of measurement, for example.
Pain/Bigelow/Pargetter: we cannot compare the pain of different living beings.
Level 3: not only explains a rich network of properties of the 2nd level and relations between objects,...
---
I 62
...but also explain patterns of entailments between them. NominalismVsBigelow: will try to avoid our apparatus of relations of relations.
BigelowVsNominalism: we need relations and relations of relations in science.
Realism/Bigelow/Pargetter: we do not claim to have proven it here. But it is the only way to solve the problem of the same and the different (problem of the quantities with the 3 levels).
Simplicity/BigelowVsNominalism: will never be as uniform as our realistic explanation. Nominalism would have to accept complex relational predicates as primitive. Worse still, it will have to accept complex relations between them as primitive.

Big I
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990

Representation Field
 
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II 55
Representation/Field: if they were only related to public language, why then internal? - Solution: distinction type/token - question: why then referring to public language: because one can only speak with respect to types of tokens. ---
II 58
Representation: their syntax can be determined without regard to the meanings - if we have laws for body movements from wishes, etc. (narrow psychological theory). ---
II 58
Semantics/Representation: We can make truth superfluous: if we have 1. laws of beliefs from stimuli - 2. laws for body movements from beliefs and desires - that would be the "narrow psychological theory": then we do not need to assume meanings in representation. ---
II 59
But if representation should be true, it must be correlated with meanings. ---
II 60
Representation without meaning: E.g. for all sentences S1 and S2 in a system: if a person believes [S1 > S2] and desires S2, then he also wants S1. - Field: Meanings not because the believed sentences can all be wrong. - E.g. Radical Interpretation: the native raises his rifle: a reason to believe that a rabbit is nearby - (even if he is deceived). ---
II 61
Representation/semantics/psychology: for their psychological explanations, we do not need the semantic notions like "true" and "refers to", which usually sets sentences in relation to the world - belief/truth: nothing compels me to assume of a person that she has believes that are true of rabbits. - ((s) It is enough when he lifts his rifle.) - Truth: (of internal representations) we only need this if we assume that they are reliable indicators about the world. - E.g. a child behaves guiltily - For example, if a mathematician believes in a theory, it is a reason for me to believe it, too. (> Reliability). ---
II 66
Language/representation/Schiffer: early: (1972): The meaning of a sentence can be explained only by the notions of believe and desire. For example, to know the meaning of "Caesar was egoistic," one must know that the proposition is conventionally correlated with believe that Caesar was egoistic. - Everything goes through inner representations and these can be explained without further reference to language. - FieldVsSchiffer: the symbols in my representation system have gained their role by appropriation of e.g. a name in the public language. - Animals/Field: although they are likely to have representations, meanings and therefore truth, cannot be applied to them. ---
II 69
Representation/Field: one could also assume this as neither linguistic nor pictoral: E.g. "light bulb model" - that would be uninterpreted and could not explain behavior. ---
II, 77f
Representation: representative terms can replace properties - most psychology can do without them. - Advantages? - Intentional terms are projective - E.g.: "He raised his rifle ..." - the truth conditions (tr.cond.) do not matter then - The advantage of representations lies in the combination of explanation and predictions. ---
II 94
Representation/StalnakerVsField: the basic relation is between words rather than between sentences or "morphemes" (the thought language). Not even between whole states. - Field: that could be correct. ---
II 154
Representation/truth conditions/translation: one can accept representation without translation and without truth conditions: solution: one accepts reactions to his believe and a corresponding threshold for his reaction - crazy cases: e.g. the person believes that something quite different is represented . Solution: the role cannot be specified exactly, but the objective core is that there is a role. - Explanation 2nd class: "sufficient similarity to our own representation" E.g. "Khrushchev blinked" as an explanation for Kennedy's action. - Problem: our own representations are not objective. - Deflationism: for it this is not a problem - truth conditions: we only need them if we do not know how the details of the explanation are.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980

Satisfaction Putnam
 
Books on Amazon
I 91
Satisfaction/Tarski: is the terminus for reference. - Putnam: relation between words and things, more precisely, between formulas and finite sequences of things. - Tarski; "The sequence of length one only existing of x, satisfies the formula "electron (y)" iff x is an electron". - The sequence Abraham: Isaac meets the formula "x is the father of y". - If there are more binary relations one does not speak of Reference. -> Correspondence theory -> picture theory - Putnam: Tarski's theory is not suitable for the correspondence theory because satisfaction is explained by a list. - (Instead> meaning postulates: "electron" refers to electrons, etc.) - "true" is the zero digit case of fulfillment: a formula is true if it has no free variables and if it meets the zero sequence. ---
I 92
Zero digit relation: E.g. Tarski: "true" is the zero digit case of satisfaction: that means, a formula is true if it has no free variables and if the zero sequence is met. - Zero sequence: converges to 0. Example 1;, 1/4, 1/9, 1/16, ... ---
I 92
Satisfaction/Putnam: criterion T can be extended to the criterion E: (E) an adequate definition of fulfilled-in-S must generate all instances of the following scheme as theorems: "P(x1 ... xn) is only fulfilled by the sequence y1. ..yn when P (y1 .... yn) - reformulated: "electron (x)" is then and only then fulfilled by y1 when y1 is an electron - This is determined by truth and reference (not determined by provability) and is therefore even preserved in intuitionistic interpretation. PutnamVsField: his objection fails: for the realists the Tarski schema is correct - FieldVsTarski: similar to a "definition" of chemical valence by enumeration of all elements and their valence. The causal involvement in our explanations is lacking - PutnamVsField: truth and reference are not causally explanatory terms, we still need them for formal logic, even if scientific theories are wrong.

Pu I
H. Putnam
Von einem Realistischen Standpunkt Frankfurt 1993

Pu II
H. Putnam
Repräsentation und Realität Frankfurt 1999

Pu III
H. Putnam
Für eine Erneuerung der Philosophie Stuttgart 1997

Pu IV
H. Putnam
Pragmatismus Eine offene Frage Frankfurt 1995

Pu V
H. Putnam
Vernunft, Wahrheit und Geschichte Frankfurt 1990

Singular Terms Field
 
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I 147
Singular Term/Field: since an expression does not denote, it does not prevent it from being a real singular term. - e.g. "the number 4"/Field: does not denote any object. - But even with real singular terms, the question is whether the corresponding theorem is true. - The fact that a predicate has no extension does not prevent it from being a sortal: E.g. Homer E.g. "natural number". - FregeVsField: no singular term can stand for a concept. - (Wright pro Frege). ---
I 148
Sortal/Wright: syntactically, you cannot create statements of identity that contain a sortal like "well-being" (from "the well-being of children"). ---
I 149
Singular: E.g. "2" in "2 + 3 = 5" - different: "there are two apples in the room": no singular term, but part of a quantifier - analyzed: numeric functor "the number of" plus singular term "three". ---
I 150
If "the direction of c1 = direction of c2" - logically equivalent: "c1 and c2 are parallel" - then expressions like "the direction of" cannot function semantically as a singular term. - If syntactically and semantically singular term, then they are without ontological commitment to other entities than lines. (no direction(s)). ---
III
Singular term/Field: we reject a singular term like e.g. "87" - solution: quantifier E87: "there are exactly 87" - quantifiers are not singular terms. ---
III 22
"87" does not appear as a name but as part of an operator.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980

Tarski Field
 
Books on Amazon
I 33f
Tarski/Field: According to him the following two sentences are a contradiction because he needs quantities for his definition of implication: a) "snow is white" does not imply logically "grass is green". - b) There are no mathematical entities (m.e.) like quantities. - ((s) Therefore, Field must be independent of Tarski.) Solution Field: Implication as a basic concept. ---
II 124
Tarski/Truth: unlike disquotational truth: only for a fragment. - Unrestricted quantifiers and semantic concepts must be excluded. Problem: we cannot create infinite conjunctions and disjunctions with that. - (Tarski-Truth is not suitable for generalization). DeflationsimVsTarski/QuineVsTarski. - Otherwise, we must give up an explicit definition. - Deflationism: uses a generalized version of the truth-schema. - TarskiVsDeflationism: pro compositionality. (Also Davidson) - Tarski: needs recursion to characterize e.g."or".
---
II 125
Composition principle/Field: E.g. A sentence consisting of a one-digit predicate and a referencing name is true, iff the predicate is true of what the name denotes. - This goes beyond logical rules because it introduces reference and denotation. - Tarski: needs this for a satisfying Truth-concept. Deflationism: it is not important for it. - (> Compositionality). ---
II
Truth-Theory/Tarski: Thesis: we do not get an adequate Truth-theory if we take only all instances of the schema as axioms. - This does not give us the generalizations we need, e.g. that the modus ponens receives the truth. ---
II 142
Deflationism/Tarski/Field. Actually, Tarski's approach is also deflationistic. ---
Horwich I 477
FieldVsTarski/Soames: hides speech behavior. - Field: introduces primitive reference, and so on. -> language independence. - SoamesVsField: his physicalist must reduce every single one of the semantic concepts. - For example, he cannot characterize negation as a symbol by truth, because that would be circular. E.g. he cannot take negation as the basic concept, because then there would be no facts about speakers (no semantic facts about use) that explain the semantic properties. - FieldVsTarski: one would have to be able to replace the semantic terms by physical terms.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980


Hor I
P. Horwich (Ed.)
Theories of Truth Aldershot 1994
Truth Putnam
 
Books on Amazon
Rorty I 309
Concept of Truth/Truth/Putnam/Rorty: the concept of truth has certain properties. Putnam: if a statement is true, then its logical consequences are also true, when two statements are true, then their conjunction is also true. If a statement is now true, then it is always. ---
Horwich I 394
Truth: ... has to do with speaker-use (success), not with what is going on "in the head" - (> verification degrees, confirmation degrees). - Meaning/Putnam: is also a function of the reference (not only in the head). - Reference/Putnam: is determined by social practices and actual physical paradigms. ---
Horwich I 431
Truth/Putnam: the only reason one can have to deny that truth is a property would be that one is physicalist or phenomenalist (= reductionist) or cultural relativist. ---
Horwich I 456
Truth/Putnam: if it was not a property, the truth conditions were everything you could know about them - (((s) Putnam pro truth as a property -> PutnamVsField?) - Putnam: Then our thoughts would not be thoughts. ---
Putnam III 96f
Truth/Deconstructivism/PutnamVsDerrida: (Derrida: "The concept of truth itself is inconsistent but indispensable") - PutnamVs: the failure of a large number of contradictory statements is something else than a failure of the concept of truth itself - Truth/Putnam. Not "what I would believe if I continue researching". - Putnam: the philosophy of language got only troubled because they believed that they could clear out the normative. ---
II 204f
Truth/PutnamVsRorty: when some ideas "pay out", then there is the question of the nature of this accuracy.

Pu I
H. Putnam
Von einem Realistischen Standpunkt Frankfurt 1993

Pu II
H. Putnam
Repräsentation und Realität Frankfurt 1999

Pu III
H. Putnam
Für eine Erneuerung der Philosophie Stuttgart 1997

Pu IV
H. Putnam
Pragmatismus Eine offene Frage Frankfurt 1995

Pu V
H. Putnam
Vernunft, Wahrheit und Geschichte Frankfurt 1990


Ro I
R. Rorty
Der Spiegel der Natur Frankfurt 1997

Ro II
R. Rorty
Philosophie & die Zukunft Frankfurt 2000

Ro III
R. Rorty
Kontingenz, Ironie und Solidarität Frankfurt 1992

Ro IV
R. Rorty
Eine Kultur ohne Zentrum Stuttgart 1993

Ro V
R. Rorty
Solidarität oder Objektivität? Stuttgart 1998

Ro VI
R. Rorty
Wahrheit und Fortschritt Frankfurt 2000

Hor I
P. Horwich (Ed.)
Theories of Truth Aldershot 1994
Truth Rorty
 
Books on Amazon:
Richard Rorty
Truth/Rorty: love of truth not as love for something non-human, but as relation to the fellow human beings. Love of truth as affable willingness to talk made the quasi-object as the target of a search (Platonic idea of ​​the natural order or universally valid convictions, Habermas) entirely superfluous. II 116f
Truth/Art/ethics/Rorty: with Davidson, I believe that the distinction true/false can also be applied to sentences of the type "Yeats was a great poet" and "democracy is better than tyranny". III 84 ff
Semantic theory of truth/Tarski: Truth leads back to justification. V 26ff
Truth: absolute concept: in the following sense: true for me, but not for you... in my culture, but not in yours, true back then, but not today such statements are strange and pointless.
It makes more sense: justified for me but not for you.
Justification: relative! Justification is a criterion for truth.
Truth: not a goal of research! A goal is something of which you can know if you are heading towards or coming away from it. VI 7
Truth: Property of sentences!
Truth/existence/Rorty: Of course it was true in the past that women should not be suppressed, just like the planetary orbits were true! Truth is ahistorical, but this is not so because true statements are made true by ahistorical entities! Vi 327
Horwich I 444
Pragmatism/James/Davidson/Rorty: 1) Truth is not used explanatorily. - 2) beliefs are explained by causal relation. - 3) There are no true-makers. - 4) If no true-makers, then no dispute between realism and anti-realism that accepts this true-makers.
Horwich I 454
Truth/DavidsonVsTarski/Rorty: can therefore not be defined in terms of satisfaction or something else. - We can only say that the truth of a statement depends on the meaning of the words and the arrangement of the world. - So we are rid of the correspondence theory.
Horwich I 456
Truth/Putnam: if they were not a property, the truth conditions would be everything you could know about them - (Putnam pro truth as a property - (PutnamVsField?). - Putnam: Then our thoughts would not be thoughts.

Ro I
R. Rorty
Der Spiegel der Natur Frankfurt 1997

Ro II
R. Rorty
Philosophie & die Zukunft Frankfurt 2000

Ro III
R. Rorty
Kontingenz, Ironie und Solidarität Frankfurt 1992

Ro IV
R. Rorty
Eine Kultur ohne Zentrum Stuttgart 1993

Ro V
R. Rorty
Solidarität oder Objektivität? Stuttgart 1998

Ro VI
R. Rorty
Wahrheit und Fortschritt Frankfurt 2000


Hor I
P. Horwich (Ed.)
Theories of Truth Aldershot 1994
Truth Theory Field
 
Books on Amazon
II 21
Truth-Theory/Truth-Definition/TarskiVsField: semantic concepts are not necessary and not philosophically interesting for a T-theory. - - 2. FieldVsTarski: has only lists for denotation: (e)(a) (e is a name which denotes a) ⇔ (e is "c1" and a is c1) or (e is "c2" and a is c2) or ...
---
II 24
Truth-Theory/utterance conditions/Truth/T-theory/Quine: (1953b, p. 138) the conditions of expression are all that is needed to make the concept "true" clear. - (Field dito) - E.g. Alabama-Example: a friend says that in the southern state of Alabama is snow which is a foot high. - Therefore, utterance conditions are important. - Question: why do we need causal theories of the reference beyond the Truth-schema? - That does not work anyway, since we are on Neurath's ship ((s). That is, meanings change in the course of language development). - Still: Solution/Field: psychological models about the (inner) connection to reality. - (Do not attach a theory from the outside). - This psychological connection is still physical.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980


The author or concept searched is found in the following 31 controversies.
Disputed term/author/ism Author Vs Author
Entry
Reference
Anti-Platonism Resnik Vs Anti-Platonism
 
Books on Amazon
Field I 45
ResnikVsAnti Platonismus/ResnikVsField: (1985a und 1985b): ist nicht "echt nominalistisch"! Field erlaubt Begriffe, die der Nominalismus nicht erlauben kann. Nämlich solche, die die Logik 1. Stufe übersteigen. FieldVsResnik: das ist ganz uninteressant.
1. Bsp
Raumzeit/Ontologie/Field: (1980): ich habe dort gezeigt, daß physikalische Theorien ohne mathematische Entitäten gegeben werden können:
I 46
Theorien der Gravitation, des Elektromagnetismus usw. Die Zentralität der RZ hier ist nichts Neues. Beweistheorie: Essay 3: Bsp man kann eine "nominalistische" Redeweise vorstellen, die sagt, daß es kein Problem damit gibt, die Standard Beweisheorie zu akzeptieren als ein Korpus von Wahrheiten: man kann ungeschriebene Ableitungen als "ableitungsförmige Raumzeit Regionen" auffassen. FieldVs: das finde ich aber gar nicht attraktiv.
2.
Field: die meisten Autoren, die dagegen sind, eine Raumzeit Ontologie gegen den Anti Platonismus anzuführen,
I 47
stützen sich auf einen veralteten Begriff der Physik.

Resn I
M. D. Resnik
Oxford 2000

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980
Antirealism Field Vs Antirealism
 
Books on Amazon
Field I 64
Indispensability: if it is true that mathematics does not only facilitate inferences, it would be theoretically indispensable. How can indispensability be represented in terms of conservatism? Quine-Putnam Argument/VsAnti-Realism: (see above): only through truth! We must assume the truth of mathematics for its usefulness in the non-mathematical realm.
FieldVs: that is certainly an exaggeration. Part of the benefit may also be explained by conservatism (but not only).
I 65
Ultimately, I try to show that mathematics is not indispensable after all.
Field I 66
Realism/Mathematics/Gödel: ("What is Cantor’s Continuum Problem?", 1947) (Per Quine-Putnam argument VsField, GödelVsAnti-Realism): even with a very narrow definition of the concept of "mathematical data" (only equations of the theory of numbers ) we can justify very abstract parts by explanation success: Gödel: even without assuming the need for a new axiom, and even if it has no intrinsic necessity, a decision about its truth is possible by studying its "explanation success" with induction. The fruitfulness of its consequences, in particular the "verifiable" ones, i.e. those that are demonstrable without the new axiom, but which are easier to prove with the new Axiom. Or if this allows us to combine several proofs into one.
E.g. axioms about the real numbers, which are rejected by the intuitionists.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989
Carnap, R. Field Vs Carnap, R.
 
Books on Amazon
I 118
FieldVsCarnap: although my approach is similar to that of Carnap in Meaning and Necessity, 1) it does not refer to meaning at all. I.e. no "meaning relations between predicates" ((s)> meaning postulates).
2) my treatment of free variables does not require the introduction of "individual concepts" and is consistently anti-essentialist. (FieldVsEssentialism): no formula of the form "MB" is true in a model with view to an attribution function if it is not also true in the model in relation to any other attribution function. Nino Cocchiarella/Carnap/Field: Cocchiarella: ("On the Primary and Secondary semantics of logical necessity"): an approach similar to Carnap: FieldVsCocchiarella/FieldVsRamseyFieldVsCarnap: leads to Ramsey’s bizarre conclusion that E.g. "it is possible that there are at least 10 to the power of 10 to the power of 10 objects" is logically false if the world happens to contain fewer objects (empirical).
FieldVsCarnap: 3) his idea that modal concepts are derived from semantic concepts should be modified, Field: Just the other way around! (QuineVsField).
II 186
Referential Indeterminacy/Reference/Theory Change/Reference Change/Semantic Change/Field: we now have all the components for the indeterminacy of reference: Only (HR) and (HP) remain, but are mutually exclusive. (HP) Newton’s word "mass" denoted net mass.
(HR) Newton’s word "mass" denoted relativistic mass.
In fact there is no fact on the basis of which you could opt for one of two. Vs: it could be argued that we only lack additional information. FieldVsVs: but then it should be possible already to say what kind of information that is supposed to be. And we have already found that there can be no fact here. "Mass"/Newton/Denotation/Reference/Field: the issue is not that we do not know what Newton’s "mass" denotes, but that Newton’s word was referentially indeterminate. (Because we do not know which of the two, HP or HR should be excluded.) II 187 The truth and falsity of (4R) and (5P) cannot be explained on the basis of what Newton referred to. FieldVsReferential Semantics/FieldVsCarnap: this is excluded by this indeterminacy of reference.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie III
H. Field
Science without numbers Princeton New Jersey 1980
Devitt, M. Rorty Vs Devitt, M.
 
Books on Amazon:
Richard Rorty
Horwich I 463
Making True/True Maker/Davidson: the totality of evidence makes sentences or theories true. But no thing, no experience, no surface stimuli, not even the world makes sentences true. Rorty: I interpret this so that the inferential relations between beliefs have nothing in particular to do with the relation of "being about something" (aboutness relation) to objects. ((s) >holism).
Reference/Empiricism/Evidence/Davidson/Rorty: the lines of the confirmation (evidential force) are not parallel to those of reference. That is due to the epistemic holism. Knowledge of the former is knowledge of the language, knowledge of the latter is an empirical theory about meaning in language use. This is also a story about the causal roles within language behavior in the interaction with the environment.
Confirmation/Justification/Causality/Wittgenstein/Davidson/Rorty: linking justification (by confirmation, evidence) with the causal story is the old metaphysical urge Wittgenstein helped to overcome by warning against "meanings" as entities.
I 464
"Meanings" as entities: were then to play a double role as a cause and at the same time as justification. (>Explanation). E.g. sense data, e.g. surface stimuli. ((s) reductionism: question: does every reductionism assume double roles?)
RortyVsDevitt/RortyVsField: Devitt succumbs to the pre-Wittgensteinean temptation if he follows Field by saying that we the "intuitive idea of ​​a correspondence to an outside world" by wanting to make truth dependent on "true reference relations between words and objective reality". (DavidsonVsDevitt, DavidsonVsField, WittgensteinVsField: "real reference" pre-Wittgenstein).
RortyVsDummett: he succumbs to the same temptation if he thinks that a state of the world can verify ((s) make true) a conviction. This corresponds to the idea rejected by Davidson that pieces of the world make beliefs true. ((S) Contradiction to the above: I 461: here relation with inferential relations: "piece by piece", "stone by stone", Davidson pro?).
Realism/Semantics/Devitt/Rorty: Devitt is right when he says that if we give up on Dummett's anti-holism, the question of "realism" is de-semanticized.
RortyVsDevitt: it is thus also trivialized. Because then you cannot distinguish realism from the banal anti-idealistic thesis that physical objects exist independently of mind. Devitt thinks that this is an interesting and controversial thesis.

Ro I
R. Rorty
Der Spiegel der Natur Frankfurt 1997

Ro II
R. Rorty
Philosophie & die Zukunft Frankfurt 2000

Ro III
R. Rorty
Kontingenz, Ironie und Solidarität Frankfurt 1992

Ro IV
R. Rorty
Eine Kultur ohne Zentrum Stuttgart 1993

Ro V
R. Rorty
Solidarität oder Objektivität? Stuttgart 1998

Ro VI
R. Rorty
Wahrheit und Fortschritt Frankfurt 2000

Hor I
P. Horwich (Ed.)
Theories of Truth Aldershot 1994
Feynman, R. Platonism Vs Feynman, R.
 
Books on Amazon
Field III 105
Is the Peano arithmetic weaker than arithmetic in the context of 1st stage set theory. Nevertheless, Peano is expressive enough for all normal arithmetic consequences. (more/less). Field: Thesis: I would expect that this also applies to N0. It is more than expressive enough for all normal developments of the normal gravitational theory.
PlatonismVsField: may object that nominalism is in trouble despite the expressiveness: because N0 is weaker in nominalistic consequences than the Platonic P0. Then it does not have all nominalistic consequences we should want. Because we should wish all nominalistic consequences of P0! Even the "recherché" consequences that include the Gödel sentence.
FieldVsVs: there is something to it. But it seems to me that this cannot be used to support P0 itself. Because even P0 has a Gödel sentence (if we assume ZF). And if we add this sentence to P0, we will get "recherché" consequences that we do not get from P0 alone.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie III
H. Field
Science without numbers Princeton New Jersey 1980
Field, H. Fraassen Vs Field, H.
 
Books on Amazon
I 9
Accept/Belief/Truth/Fraassen: if accepting a theory involves belief in its truth, then tentative acceptance involve tentative belief, etc. If belief is gradual, then acceptance is also. So partial belief: "the theory is true."
This must, however, be distinguished from the belief that the theory is approximately true.
I 216 FN 2
Accept/Field: Thesis: every reason to believe that a part of the theory is not true is one reason not to accept it. FraassenVsField: this leaves open which epistemic attitude accepting involves. Plus problem: how long do we speak of full acceptance instead of partial acceptance?

Fr I
B. van Fraassen
The Scientific Image Oxford 1980
Field, H. Gödel Vs Field, H.
 
Books on Amazon
Field I 66
Realismus/Mathematik/Gödel: ("Was ist Cantors Kontinuum Problem?", 1947) (Pro Quine Putnam Argument, VsField, VsAnti Realismus):selbst bei sehr enger Definition des Begriffs "mathematischer Daten" (nur Gleichungen der Zahlentheorie) können wir ganz abstrakte Teile durch Erklärungserfolg rechtfertigen: Gödel: auch ohne die Notwendigkeit eines neuen Axioms annehmen zu müssen, und sogar, wenn es gar keine intrinsische Notwendigkeit hat, ist eine Entscheidung über seine Wahrheit möglich, indem wir mit Induktion seinen "Erklärungserfolg" untersuchen. Die Fruchtbarkeit seiner Konsequenzen, insbesondere der "verifizierbaren", d.h. jener, die ohne das neue Axiom demonstrierbar sind, deren Beweise aber durch das neue Axiom leichter sind. Oder wenn man damit mehrere Beweise zu einem zusammenziehen kann.
Bsp die Axiome über die reellen Zahlen, die von den Intuitionisten abgelehnt werden.
I 67
FieldVsGödel: wenn keinerlei mE unverzichtbar sind, dann muß man auch nicht die sogenannten "mathematischen Daten" nicht als wahr bezeichnen. Aber anfangs hatte ich gesagt, daß es kein anderes Ziel der Mathematik als Wahrheit geben kann.

Göd II
Kurt Gödel
Collected Works: Volume II: Publications 1938-1974 Oxford 1990

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie III
H. Field
Science without numbers Princeton New Jersey 1980
Field, H. Kripke Vs Field, H.
 
Books on Amazon
Nonfactualism/Field: Usually we say that there is no fact which causes isomorphism as the cross world identity.
Crossworldidentity/KripkeVsField: Kripke (1972) (S.A. Kripke, Naming and Necessity, in D. Davidson and G. Harman (eds.), Semantics of Natural Language, 2nd edition, pp. 253-355; Addenda pp. 763-769, Dordrecht, 1972): may raise doubts as to whether this qualitative aspect is our normal convention for cross world identity.
Field: I think these examples show that cross world identity can only be determined at a point in time.
Kripke:
E.g. A possible world just like ours until the birth of Nixon, but deviating from it at that point. In this possible world person X, who is born to people who are qualitatively identical with Nixon’s parents, looks different and has a different career than Nixon in the actual world Somebody else, Y on the other hand develops like Nixon and looks like him.
Individuation/Cross world identity/Kripke: We individuate things in worlds in such a way that.
I 41
The isomorphisms of the worlds’ beginning segments (until the birth of Nixon) count as identity. This results in X being Nixon and not Y!.

K I
S.A. Kripke
Name und Notwendigkeit Frankfurt 1981

K III
S. A. Kripke
Outline of a Theory of Truth (1975)
In
Recent Essays on Truth and the Liar Paradox, R. L. Martin (Hg), Oxford/NY 1984
Field, H. Lewis Vs Field, H.
 
Books on Amazon
Schwarz I 75
Ontology/Science/Mathematics/Lewis: Philosophy needs to accept the results of established sciences. It would be absurd to reject mathematics because of philosophical reasons. LewisVsField. Lewis: It is about a systematic description, which should be as simple as possible, of the mathematical part of reality. Solution: Reduction on set theory.
Set Theory/Mereology/Lewis: (Parts of Classes, 1991): Are sets simply mereological sums? As such ML manifests itself as mereologically expanded arithmetic, with successor relation, a set relation between object A and its singleton {A}.
[Dabei erweist sich ML als mereologisch erweiterte Arithmetik, mit Nachfolgerrelation, eine Mengenbeziehung zwischen Ding A und seiner Einermenge {A}.]
With a structural analysis of this relation, Lewis establishes the thesis: All mathematics are based on the assumption that there many objects.


LW I
D. Lewis
Die Identität von Körper und Geist Frankfurt 1989

LW II
D. Lewis
Konventionen Berlin 1975

LW IV
D. Lewis
Philosophical Papers Bd I New York Oxford 1983

LW V
D. Lewis
Philosophical Papers Bd II New York Oxford 1986

LwCl I
Cl. I. Lewis
Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991

Schw I
W. Schwarz
David Lewis Bielefeld 2005
Field, H. Putnam Vs Field, H.
 
Books on Amazon
Horwich I 405
Internal realism/metaphysical/Putnam/Field: (ad Putnam: Reason, Truth, and History): FieldVsPutnam: the contrast between internal realism and metaphysical realism is not defined clearly enough.
Metaphysical realism/Field: comprises three theses, which are not separated by Putnam.
1. metaphysical realism 1: thesis, the world is made up of a unity of mentally independent objects.
2. metaphysical realism 2: thesis, there is exactly one true and complete description (theory) of the world.
Metaphysical realism 2/Field: is not a consequence of the metaphysical realism 1 ((s) is independent) and is not a theory that any metaphysical realist would represent at all.
Description/world/FieldVsPutnam: how can there only be a single description of the world ((s) or of anything)? The terms that we use are never inevitable; Beings that are very different from us, could need predicates with other extensions, and these could be totally indefinable in our language.
---
I 406
Why should such a strange description be "the same description"? Perhaps there is a very abstract characterization that allows this, but we do not have this yet. wrong solution: one cannot say, there is a single description that uses our own terms. Our current terms might not be sufficient for a description of the "complete" physics (or "complete" psychology, etc.).
One could at most represent that there is, at best, a true and complete description that uses our terms. However, this must be treated with caution because of the vagueness of our present terms.
Theory/world/FieldVsPutnam: the metaphysical realism should not only be distinguished from his opponent, the internal realism, by the adoption of one true theory.
3. Metaphysical realism 3/Field: Thesis, truth involves a kind of correspondence theory between words and external things.
VsMetaphysical Realism 3/VsCorrespondence Theory/Field: the correspondence theory is rejected by many people, even from representatives of the metaphysical realism 1 (mentally independent objects).
---
I 429
Metaphysical realism/mR/FieldVsPutnam: a metaphysical realist is someone who accepts all of the three theses: Metaphysical realism 1: the world consists of a fixed totality of mentally independent objects.
Metaphysical realism 2: there is only one true and complete description of the world.
Metaphysical realism 3: truth involves a form of correspondence theory.
PutnamVsField: these three have no clear content, when they are separated. What does "object" or "fixed totality", "all objects", "mentally independent" mean outside certain philosophical discourses?
However, I can understand metaphysical realism 2 when I accept metaphysical realism 3.
I: is a definite set of individuals.
---
I 430
P: set of all properties and relations Ideal Language: Suppose we have an ideal language with a name for each element of I and a predicate for each element of P.
This language will not be countable (unless we take properties as extensions ((s) intensions would not be countable > Language infinite because intensions are infinite) and then only countable if the number of individuals is finite. But it is unique up to isomorphism (but not further, unique up to isomorphism).
Theory of World/Putnam: the amount of true propositions in relation to each particular type (up to any definite type) will also be unique.
Whole/totality/Putnam: conversely, if we assume that there is an ideal theory of the world, then the concept of a "fixed totality" is (of individuals and their properties and relations) of course explained by the totality of the individuals which are identified with the range of individual variables, and the totality of the properties and relations with the region of the predicate variables within the theory.
PutnamVsField: if he was right and there is no objective justification, how can there be objectivity of interpretation then?
Field/Putnam: could cover two positions:
1. He could say that there is a fact in regard to what good "rational reconstruction" of the speaker's intention is. And that treatment of "electron" as a rigid designator (of "what entity whatsoever", which is responsible for certain effects and obeys certain laws, but no objective fact of justification. Or.
2. He could say that interpretation is subjective, but that this does not mean that the reference is subjective.
Ad 1.: here he must claim that a real "rational reconstruction" of the speaker's intention of "general recognition" is separated, and also of "inductive competence", etc.
Problem: why should then the decision that something ("approximately") obeys certain laws or disobeys, (what then applies to Bohr's electrons of 1900 and 1934, but not for phlogiston) be completely different by nature (and be isolable) from decisions on rationality in general?
Ad 2.: this would mean that we have a term of reference, which is independent of procedures and practices with which we decide whether different people in different situations with different background beliefs actually refer on the same things. That seems incomprehensible.
Reference/theory change/Putnam: We assume, of course, that people who have spoken 200 years ago about plants, referred, on the whole, to the same as we do. If everything would be subjective, there would be no inter-theoretical, interlinguistic term of reference and truth.
If the reference is, however, objective, then I would ask why the terms of translation and interpretation are in a better shape than the term of justification.
---
Putnam III 208
Reference/PutnamVsField: there is nothing that would be in the nature of reference and that would make sure that the connection for two expressions would ever result in outcomes by "and". In short, we need a theory of "reference by description".
---
V 70
Reference/FieldVsPutnam: recently different view: reference is a "physicalist relationship": complex causal relationships between words or mental representations and objects. It is a task of empirical science to find out which physicalistic relationship this is about. PutnamVsField: this is not without problems. Suppose that there is a possible physicalist definition of reference and we also assume:
(1) x refers to y if and only if x stands in R to y.
Where R is a relationship that is scientifically defined, without semantic terms (such as "refers to"). Then (1) is a sentence that is true even when accepting the theory that the reference is only determined by operational or theoretical preconditions.
Sentence (1) would thus be a part of our "reflective equilibrium" theory (see above) in the world, or of our "ideal boundaries" theory of the world.
---
V 71
Reference/Reference/PutnamVsOperationalism: is the reference, however, only determined by operational and theoretical preconditions, the reference of "x is available in R y" is, in turn, undetermined. Knowing that (1) is true, is not of any use. Each permissible model of our object language will correspond to one model in our meta-language, in which (1) applies, and the interpretation of "x is in R to y" will determine the interpretation of "x refers to y". However, this will only be in a relation in each admissible model and it will not contribute anything to reduce the number of allowable models. FieldVs: this is not, of course, what Field intends. He claims (a) that there is a certain unique relationship between words and things, and (b) that this is the relationship that must also be used when assigning a truth value to (1) as the reference relation.
PutnamVsField: that cannot necessarily be expressed by simply pronouncing (1), and it is a mystery how we could learn to express what Field wans to say.
Field: a certain definite relationship between words and objects is true.
PutnamVsField: if it is so that (1) is true in this view by what is it then made true? What makes a particular correspondence R to be discarded? It appears, that the fact, that R is actually the reference, is a metaphysical inexplicable fact. (So magical theory of reference, as if referring to things is intrinsically adhered). (Not to be confused with Kripke's "metaphysically necessary" truth).
----
Putnam I 93
PutnamVsField: truth and reference are not causally explanatory terms. Anyway, in a certain sense: even if Boyd's causal explanations of the success of science are wrong, we still need them to do formal logic.

Pu I
H. Putnam
Von einem Realistischen Standpunkt Frankfurt 1993

Pu II
H. Putnam
Repräsentation und Realität Frankfurt 1999

Pu III
H. Putnam
Für eine Erneuerung der Philosophie Stuttgart 1997

Pu IV
H. Putnam
Pragmatismus Eine offene Frage Frankfurt 1995

Pu V
H. Putnam
Vernunft, Wahrheit und Geschichte Frankfurt 1990

Hor I
P. Horwich (Ed.)
Theories of Truth Aldershot 1994
Field, H. Quine Vs Field, H.
 
Books on Amazon:
Willard V. O. Quine
Field I 128
Quine Putnam Argument/VsField: (see introduction above): we must assume the truth of mathematical statements in order to be able to do academic work. FieldVs: the only way around this: show that the nominalistic resources for good science are adequate. This is not a consequence of conservatism.

Field II 202
Partial Signification/Field: is not so unusual: we often apply it implicitly in the case of vague expressions. Ex what is the extension of the term e.g. "big man" in German? There is no fact which decides whether 185 or 180 cm. Solution: "big man" partially signifies a set and partially other sets. Namely, the sets of shape
{xI x is a person taller than h}.
FieldVsQuine: that is quite unlike in Quine.
QuineVsField: it is not necessary to abandon the normal semantic concepts of denotation and signification. Instead, we can make them relative.
(1) for a foreign language: here we do not have to refrain from talking about the signification of a foreign word. But we must say that relative to the obvious translation manual ...
FieldVsQuine: but apparently that makes no sense. (1) seems to suggest that we could explain relative signification as:
(2) saying that a term T used in one language signifies the amount of rabbits, relative to a ÜH M, actually means that M translates T as "rabbit".
FieldVs: that is not sufficient.

Q I
W.V.O. Quine
Wort und Gegenstand Stuttgart 1980

Q II
W.V.O. Quine
Theorien und Dinge Frankfurt 1985

Q III
W.V.O. Quine
Grundzüge der Logik Frankfurt 1978

Q IX
W.V.O. Quine
Mengenlehre und ihre Logik Wiesbaden 1967

Q V
W.V.O. Quine
Die Wurzeln der Referenz Frankfurt 1989

Q VI
W.V.O. Quine
Unterwegs zur Wahrheit Paderborn 1995

Q VII
W.V.O. Quine
From a logical point of view Cambridge, Mass. 1953

Q VIII
W.V.O. Quine
Bezeichnung und Referenz
In
Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982

Q X
W.V.O. Quine
Philosophie der Logik Bamberg 2005

Q XII
W.V.O. Quine
Ontologische Relativität Frankfurt 2003

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie III
H. Field
Science without numbers Princeton New Jersey 1980
Field, H. Tarski Vs Field, H.
 
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Tarski II 142
T-Theory/TarskiVsField: seine Variante ist dagegen rein axiomatisch. FieldVsTarski/FefermanVsTarski: Ansatz mit Schemabuchstaben statt reinen Axiomen: Vorteile:
1. wir haben denselben Vorteil wie Feferman für die schematische disquotation und schematische meta language: Erweiterungen der Sprache werden automatisch berücksichtigt.
2. der Gebrauch von ""p" ist wahr iff p" (jetzt als Schema-Formel als Teil der Sprache statt als Axiom) scheint den Begriff der Wahrheit besser zu fassen.
3. (am wichtigsten) ist nicht abhängig von einem kompositionalen Zugang des Funktionierens der anderen Teile der Sprache. Zwar ist das wichtig, aber es wird von meinem Ansatz auch nicht ausgelassen.
FieldVsTarski: eine axiomatische Theorie ist für Glaubenssätze schwer zu bekommen.

Horwich I 484
TarskiVsField/Soames: dass Tarski’s semantische Eigenschaften nicht von Tatsachen über Sprecher abhängig sind, dadurch geht nichts verloren. Man sollte die Semantik abstrakt angehen und der Pragmatik die Interpretation des Sprecherverhaltens überlassen. Vorteil: so erhält man ein T-predicate für metatheoretische Diskussion, und behält die Möglichkeit philosophische Fragen in anderen Bereichen zu stellen.

Tarsk I
A. Tarski
Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983

Hor I
P. Horwich (Ed.)
Theories of Truth Aldershot 1994
Field, H. Wright Vs Field, H.
 
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Field I 43
Anti-Platonismus/AP/WrightVsField: (Hale, 1987): behauptet, daß modale Überlegungen meine Version des AP untergraben. Weil ich Mathematik und die Existenz von mathematischen Entitäten (mE) als konsistent, und Konsistenz als modalen Grundbegriff (Möglichkeit) nehme, wäre ich darauf festgelegt, daß ich es für falsch halte, daß es mE gibt daß die Existenz von mE "kontingent falsch" sei. ((s)"Es hätte genauso gut auch mE geben können, also empirische Frage").
kontingent/Wright/HaleVsField: ist nicht logisch, und also etwas anderes als "weder logisch wahr noch logisch kontradiktorisch". Und das macht Fields Position absurd.
WrightVsField: worauf soll Fields "Kontingenz" kontingent sein? Bsp nach Field enthält die WiWe keine Zahlen aber sie hätte welche enthalten können. Aber gibt weder eine Erklärung dafür warum nicht, noch gäbe es eine Erklärung, wenn es doch Zahlen gäbe.
FieldVsVs: wenn das Argument gut wäre, gälte es genauso gegen den (nicht logischen) Platonismus, für den Mathematik hinter die Logik zurückreicht. Dann wäre die Leugnung der ganzen Mathematik logisch konsistent und daher "kontingent". Aber das ist eine Verwechslung der verschiedenen Bedeutungen von "möglich". Analog:
Bsp wenn die Existenz von Gott logisch konsistent ist, und es keinen gibt, so ist es kontingent falsch, daß es einen gäbe.
Problem: der Atheist hat keinen Zugang dazu, worauf das kontingent sein soll. Es gäbe weder eine Erklärung für die Existenz noch für die Nichtexistenz. Es gibt keine für Gottes Existenz günstigen Bedingungen und keine ungünstigen. (>Anselm, 2. ontologisches Argument).
WrightVsField: hat aber noch interessantere Argumente: 1. ohne die Annahme, daß die Mathematik aus notwendigen Wahrheiten besteht, ist die Sichtweise, daß Mathematik konservativ (konservierend, s.o.) sei, ungerechtfertigt.
I 44
analog: ohne die Annahme, daß die Mathematik wahr ist, sei die Annahme, daß sie konsistent sei, ungerechtfertigt. Rechtfertigung/FieldVsWright: man kann jeden Glauben durch einen stärkeren Glauben rechtfertigen, aus dem er folgt. (>stärker/schwächer).
Wright und Hale müßten zeigen, daß der Platonismus bessere Gründe für die notwendige Wahrheit der Mathematik hat als der Anti Platonismus für die Annahme hat, daß Mathematik konservativ (oder konsistent) ist. Und es ist nicht sicher, daß das stimmt.
WrightVsField: 2. jeder, der beides vertritt:
a) daß die Existenz von mE "kontingent falsch" ist und
b) daß Mathematik konservativ ist,
kann keinen Grund angeben, nicht an mE zu glauben!
Def Konservativität/Mathematik/Field: bedeutet, daß jede intern konsistente Kombination von nominalistischen Aussagen auch konsistent mit der Mathematik ist. DF Ordnung.
Dann kann keine Kombination nominalistischer Aussagen ein Argument gegen den Glauben an Mathematik (Ontologie) liefern.
WrightVsField: wie kann es dann überhaupt einen Grund geben, nicht an Mathematik zu glauben? Er hat keinen Beweis für seinen eigenen Nominalismus. Daraus folgt, daß Field nicht Nominalist sein kann, sondern Agnostiker sein muß.
FieldVsWright: dieser verkennt die Relevanz, die ich der Frage der Verzichtbarkeit und Unverzichtbarkeit zubillige.
Konservativität: zeigt nicht von sich aus, daß es keinen Grund geben kann, an Mathematik zu glauben.
Um VsPlatonismus Erfolg zu haben, müssen wir auch zeigen, These daß Mathematik verzichtbar ist in Wissenschaft und Metalogik. Dann haben wir Grund, nicht buchstäblich an Mathematik glauben zu müssen.
I 45
Wenn das gelingt, können wir hinter den Agnostizismus gelangen.

Wri I
Cr. Wright
Wahrheit und Objektivität Frankfurt 2001

WriGH I
G. H. von Wright
Erklären und Verstehen Hamburg 2008

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie III
H. Field
Science without numbers Princeton New Jersey 1980
Field, H. Verschiedene Vs Field, H. Field I 51
Unendlichkeit/Physik/Essay 4: selbst ohne "Teil von" Relation brauchen wir nicht wirklich den Endlichkeits Operator für Physik. VsField: viele haben mir vorgeworfen, daß ich jede Extension der Logik 1. Stufe brauche. Aber das ist nicht der Fall.
I 52
Ich nehme eher an, daß das Nominalisierungsprogramm (nominalization) noch nicht weit genug vorangetrieben worden ist, um sagen zu können, was die beste logische Basis ist. Letztlich werden wir nur wenige natürliche Mittel wählen, die über die Logik 1. Stufe hinausgehen, Möglichst solche, die der Platonist auch brauchen würde. Aber das können wir nur durch Ausprobieren erfahren.
I 73
Unverzichtbarkeits Argument/Logik/VsField: wenn mE in der Wissenschaft verzichtbar sein mögen, so sind sie es doch nicht in der Logik! Und Logik brauchen wir in der Wissenschaft. logische Folgebeziehung/Konsequenz/Field: wird normalerweise in Begriffen der Modelltheorie definiert: (Modelle sind mE, semantisch: ein Modell ist wahr oder nicht wahr.
Auch wenn man sie beweistheoretisch formuliert ("es gibt eine Ableitung", syntaktisch, bzw. beweisbar in einem System) braucht man mE bzw. abstrakte Objekte: willkürliche Zeichen Sequenzen von Symbol Tokens und deren willkürliche Sequenzen.
I 77
VsField: manche haben eingewendet, daß nur wenn wir eine Tarski Theorie der Wahrheit akzeptieren, wir mE in der Mathematik brauchen. FieldVsVs: das führte zum Mißverständnis, daß Mathematik ohne Tarskische Wahrheit keine epistemischen Probleme hätte.
Mathematik/Field: impliziert in der Tat selbst mE, (bloß, wir brauchen nicht immer Mathematik) und zwar ohne Hilfe des Wahrheitsbegriffs, z.B. daß es Primzahlen > 1000 gibt.
I 138
Logik der Teil-von-Relation/Field: hat kein vollständiges Beweisverfahren. VsField: wie können semantische Folgebeziehungen daraus dann von Nutzen sein?
Field: sicher, die Mittel, mit denen wir wissen können, daß etwas aus etwas anderem folgt, sind in einem Beweisverfahren kodifizierbar, und das scheint zu implizieren, daß kein Appell an irgend etwas Stärkeres als einen Beweis von praktischem Nutzen sein kann.
FieldVsVs: aber man braucht gar keinen epistemischen Zugang zu mehr als einem abzählbaren Teil davon anzunehmen.
I 182
Feldtheorie/FT/Relationalismus/Substantivalismus/einige AutorenVsField: begründen die Relevanz von Feldtheorien für den Streit zwischen S/R gerade umgekehrt: für sie machen FT es leicht, eine relationalistische Sicht zu begründen: (Putnam, 1981, Malament 1982): sie postulieren als Feld ein einziges riesiges (wegen der Unbegrenztheit physikalischer Kräfte) und einen korrespondierenden Teil davon für jede Region. Variante: das Feld existiert nicht an allen Orten! Aber alle Punkte im Feld sind nicht null.
FieldVsPutnam: ich glaube nicht, daß man auf Regionen verzichten kann.

Field II 351
Unbestimmtheit/Unentscheidbarkeit/Mengenlehre/ML/Zahlentheorie/ZT/Field: These: nicht nur in der ML auch in der ZT haben viele unentscheidbare Sätze keinen bestimmten WW. Viele VsField: 1. Wahrheit und Referenz sind im Grunde disquotational.
disquotationale Sicht/Field: wird manchmal so gesehen, als schlösse sie Unbestimmtheit für unsere gegenwärtige Sprache aus.
FieldVsVs: das ist nicht so :>Kapitel 10 zeigte das.
VsField: selbst wenn es Unbestimmtheit in unserer gegenwärtigen (current) Sprache auch für den Disquotationalismus gibt, sind die Argumente für sie aus dieser Perspektive weniger überzeugend.
Bsp die Frage nach der Mächtigkeit des Kontinuums ((s) ist unentscheidbar für uns, die Antwort könnte aber (aus objektivistischer Sicht (FieldVs)) einen bestimmten WW haben.
Unbestimmtheit/ML/ZT/Field: in jüngster Zeit haben einige namhafte Philosophen Argumente für eine Unmöglichkeit jeglicher Unbestimmtheit in ML und ZT hervorgebracht, die mit dem Disquotationalismus nichts zu tun haben: Zwei Varianten:
1. Angenommen, ML und ZT sind in voller Logik 2. Stufe (d.h. Logik 2. Stufe, die modelltheoretisch verstanden wird, mit der Forderung, daß jede legitime Interpretation
Def „voll“ ist in dem Sinne, daß die Quantoren 2. Stufe über alle Teilmengen des Bereichs der Quantoren 1 Stufe gehen.
2. Angenommen, ZT und ML seien in einer Variante der vollen Logik 2. Stufe formuliert, die wir „volle schematische Logik 1. Stufe“ nennen könnten.

II 354
volle schematische Logik 1. Stufe/LavineVsField: bestreitet, daß sie eine Teiltheorie der (nichtschematischen!) Logik 2. Stufe ist. Field: wir vergessen jetzt lieber die Logik 2. Stufe zugunsten der vollen schematischen Theorien. Dabei bleiben wir ei der ZT um Komplikationen zu vermeiden. Wir nehmen an, daß die Bestimmtheit der ZT nicht in Frage steht, außer was den Gebrauch von vollen Schemata anbetrifft.





Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie III
H. Field
Science without numbers Princeton New Jersey 1980
Field, H. Bigelow Vs Field, H.
 
Books on Amazon
I 345
Mathematics/Bigelow/Pargetter: our metaphysics allows a realistic conception of mathematics (BigelowVsField).
I VII
Mathematics/BigelowVsField: can be understood realistically, if it is understood as studying the universals, properties and relations, patterns and structures of things that can be at different places at the same time.
I 59
Equivalence class/equ.set/Bigelow/Pargetter: sort objects with the same D-ates (determinates) into classes. THis is how they explain how two things can be more similar in one way than in another.
Level 1: objects
Level 2: properties of things Level 3: proportions between such properties.
Proportions/Bigelow/Pargetter: are universals that can introduce subtle differences between equ.sets of properties on tier 2nd level.
Equal/different/Bigelow/Pargetter: Important argument: This explains why two relations can be the same and different at the same time. E.g. Suppose one of the two relations is a mass relation (and stands in relation to other mass-relations) and the other is not a mass relation (and is not in relation to mass relations), and yet
I 60
both have something in common: they are "double" once in relation to mass, and then in terms of volume. This is explainedon level 3. Numbers/Bigelow/Pargetter: this shows the usefulness of numbers in the treatment of quantities. (BigelowVsField).
I 383
BigelowVsField: (a propos science without numbers): he wrongly assumes that physics begins with pure empiricism in order to then convert the results into completely abstract mathematics. Field/Bigelow/Pargetter: wants to avoid this detour.
BigelowVsField: his project is superfluous if we accept that mathematics is just a different description of the physical proportions and relations instead of a detour.

Big I
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990
Field, H. Schiffer Vs Field, H.
 
Books on Amazon:
Stephen Schiffer
I 105
SchifferVsField: wrong is his suggestion: physical relations as an explanation for the reference relation would also cover relations to things of which they are not true. (E.g. "Arthrite"> shmarthrite, E.g. "Addition"> Quaddition - FieldVsPhysicalism). Conclusion: no functional relation, which operates without disquotation scheme will be appropriate for the "true-of" relation. ((s) Anyway not the relation, but the theory works, if at all with the disquotation scheme.).
I 109
Def Conceptual Role/c.r./Field: (Field 1977): the subjective conditional probability-function of an agent Two mental representations S1 and S2 have the same cr for one person, iff. their (the person’s) subjective conditional prblty-function is so that s for any mental representation, given the subjective probability of s1 s is the same as that of s2 where s. SchifferVsField: This is of little use, because not two people have the same conditional probability function. But Field is anyway pessimistic with respect to a precise concept of intersubjective sameness of mental content that goes beyond sameness of referential significance.

Schi I
St. Schiffer
Remnants of Meaning Cambridge 1987
Field, H. Stalnaker Vs Field, H.
 
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Field II 28
Equality of the inferential role/Field: must be defined only in relation to an idiolect here. This solves the problem that we otherwise might incorporate the meaning of the token in what the reference comes from. ((s) circular). VsField: (Wallace 1977, Davidson 1977, 1979, McDowell 1978 Stalnaker 1984): the reduction of the truth conditions on the semantics of the basic concepts were too atomistic. It takes too little account that the proposition itself is a unit of meaning.
FieldVsVs: I should understand reduction a bit "wider".

Field II 94
StalnakerVsField: would argue 1. that the causal theories of reference require the public language intentional concepts: what a word means depends on the attitude of the language user. ((s) Problem: >Humpty Dumpty theory VsVs: is this about the speech community? >attitude semantics?). Field: then a non-intentional causal theory would be more successful for the "morphemes" of a thought language than words for a public language.
A non-intentional theory for the public language seems irrelevant.
StalnakerVsField. 2. (deeper): Field's access was too atomistic: he thinks the basic representation exists between words instead of between propositions or "morphemes" of the thought language instead of whole states.
Field: he might be right with this. Two points about this:
FieldVsStalnaker: 1. he thinks for me the "name-object-" or "predicate-property"-relations come first. The sentence-proposition-relation is then derived. Does that mean that people first invented names and predicates and then awesomely put them together? I have never claimed that.
Rather, truth conditions are characterized by "name-object" - or "predicate property"-relations.
2. an atomistic theory can explain much of the interaction between the atoms.
Stalnaker's theory is not atomistic enough.

Sta I
R. Stalnaker
Ways a World may be Oxford New York 2003

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie III
H. Field
Science without numbers Princeton New Jersey 1980
Field, H. Nominalism Vs Field, H.
 
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Field III 92
Nominalism/VsField: one could doubt that everything is purely nominalistic because we would partly need 2nd stage logic. 1) Question: could we make do with 1st stage logic? 2) Question: If not, is nominalism threatened? Ad 1: we can probably do that for the theory of gravity, but that would be beyond the scope. Ad 2: We have 2nd stage logic at two locations: 2nd Stage Logic/Field: We have it in two places: 1) in the axiomatization of space-time geometry and the scalar order of space-time points we have III 93 The "full logic of the part-whole relation" (see above Chapter 4) or the "full logic of the Goodman sums"
2) (in section B, chapter 8): the binary quantifier "less than". But we do not need this if we have Goodman sums:
Goodman Sum/Field: its logic is sufficient to provide comparisons of widths. For heuristic reasons we want to keep an extra logic for widths ("less than").

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989
Field, H. Resnik Vs Field, H.
 
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Field I 47
Field: Raumzeit-Regionen sind bekannt als kausal aktiv: Bsp Feldtheorien wie der klassische Elektromagnetismus oder AR oder Quantenfeldtheorie. Eigenschaften/Struktur/ResnikVsField: (1985): die Frage des Physikers war nie "welche Eigenschaften der RZ Punkte sind verantwortlich für dieses Phänomen?" sondern eher: "was ist die Struktur der Raumzeit?".
FieldVsResnik: das ist falsch: die Theorie des elektromagnetischen Felds ist genau die Theorie der Eigenschaft auch der Teile der Raumzeit, die nicht von physikalischen Objekten besetzt sind. ((s) Frage: ist Field nun pro oder VsSubstantivalismus?).
VsField: man könnte das nun (Field: rein verbal) umdrehen und sagen, daß Felder dann eben eher Entitäten als Moden seien.
FieldVs: aber das bringt nichts: was ich mit Raumzeit Region meine, ist dann genau das, was der andere mit "Teil eines Felds" meint.
3.
VsField: einige haben eingewendet, daß meine Annahme von Punkten als Regionen der Größe Null falsch sei, selbst wenn man eine anti platonistische Perspektive einnimmt. Denn Regionen sind einfach Mengen von Punkten.

Resn I
M. D. Resnik
Oxford 2000

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie III
H. Field
Science without numbers Princeton New Jersey 1980
Field, H. Boolos Vs Field, H.
 
Books on Amazon:
George Boolos
Field I 190
Science without numbers/SwN/Nominalisierungsstrategie/Nominalisierung//Field: (Versuch, Physik rein nominalistisch (ohne mathematische Entitäten (mE)) zu betreiben: hatte zwei Forderungen gestellt: 1. ich brauchte Logik 2. Stufe, aber die war nicht verfügbar, weil sie über Mengen quantifizierte.
2. Mereologie sollte als Logik betrieben werden: Field: heute Vs),
BoolosVsField: Lösung: Logik 2. Stufe sollte mit "pluralen Quantoren" konstruiert werden, die selbst Einzeldinge in ihrem Bereich haben.
Field: dann brauchen die Quantoren Einheitsprädikate als ihre Substituenden.
SwN: dort war ich gezwungen, die Quantoren 2. Stufe über Regionen als (klassisch) über Punktmengen zu konstruieren. Nach Boolos wäre es dann auch möglich, über Klassen von Regionen zu quantifizieren. Aber das war für die Nominalisierung der klassischen Feldtheorien nicht notwendig.

Boolo I
G. Boolos
Computability and Logic Fifth Edition Cambridge 2007

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie III
H. Field
Science without numbers Princeton New Jersey 1980
Field, H. Shapiro Vs Field, H.
 
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Field I 125
Stewart ShapiroVsField: (Conservativeness and incompleteness").
I 126
Konservativität/ShapiroVsField: sollte man entweder a) semantisch oder
b) beweistheoretisch (syntaktisch) nehmen. je nachdem, ob man die Folgebeziehung (Konsequenz) semantisch oder als Ableitbarkeit versteht.
Die Unterscheidung ist wichtig, weil wir bald Logiken höherer Stufe betrachten, die keine vollständigen Beweisverfahren haben.
Logik 2. Stufe/SwN/Field: hier gibt es kein Vollständigkeits Theorem: wir müssen uns die ganze Zeit an semantische Begriffe halten.
Wir können platonistische Argumente für semantische Konservativität der Mengenlehre im Kontext der Logik 2. Stufe geben, aber keine beweistheoretische.
ShapiroVsField: die Wahl der semantischen statt der beweistheoretischen Konservativität war philosophisch falsch:
1. Field sagt, daß die Nützlichkeit der Mathematik in der Erleichterung und Verkürzung von Deduktionen liegt. Nichtsdestotrotz können längere Deduktionen gegeben werden.
I 127
ShapiroVsField: 1. das verträgt sich nicht mit dem Anspruch, daß es um semantische Folgebeziehung geht. (Field pro Shapiro). Field: ich hätte sagen sollen, daß Mathematik nützlich ist, weil es oft leichter zu sehen ist, daß eine nominalistische Aussage aus einer nominalistischen Theorie plus Mathematik folgt, als zu sehen, daß sie aus der nominalistischen Theorie alleine folgt.
ShapiroVsField: 2. (tiefer): zweiter Grund, warum Beweistheorie wichtiger als semantische Folgebeziehung ist: der Nominalismus hat Schwierigkeiten, logische Folgerungen (Konsequenzen) zu verstehen, die über das hinausgehen, was beweistheoretisch erklärbar ist.
FieldVsShapiro: 1. die Folgebeziehung kann modal erklärt werden, und die Modalität kann ohne Erklärung in Begriffen platonistischer Entitäten verstanden werden.
2. die gleichen Schwierigkeiten bestehen für die Beweistheorie, d.h. Ableitbarkeit: die Erklärung müßte über die Existenz abstrakter Sequenzen abstrakter Ausdruckstypen erfolgen, von denen kein Token jemals gesprochen oder geschrieben wurde.
I 133
ShapiroVsField: (nach Gödels 2. Unvollständigkeits Theorem): Field: Anwendung von Mathematik auf physikalische Theorien ist unterminiert, wenn die physikalischen Theorien als 1. Stufe aufgefaßt werden.
FieldVsShapiro: Abschnitt 5 und 6.

Shap I
St. Shapiro
Philosophy of Mathematics: Structure and Ontology Oxford 2000

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie III
H. Field
Science without numbers Princeton New Jersey 1980
Field, H. McGee Vs Field, H.
 
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Field II 274
Logische Konstanten/Verknüpfung/Unbestimmtheit/McGeeVsField: (McGee 2000): McGeeVsUnbestimmtheit logischer Konstanten: Bsp materielles Konditional: ist bestimmt von zwei Regeln: Einführungs- und Eliminationsregel. Aber irgendwelche zwei Verknüpfungen >1 und >2 in unserer Sprache, die von diesen zwei Regeln bestimmt werden, sind beweisbar äquivalent: Das Argument dafür ist einfach: A, A >1 B I- B, durch >1-Elimination
So
A > 1 B I- A >2 B, B durch >2- Einführung. (Sonderzeichen spitze Klammern)
Und analog für die Konverse.
Field. pro: es ist korrekt, daß wir keine zwei verschiedenen Konditionale in unserer Sprache haben können, die von denselben unbeschränkten Regeln der >-Einführung und >-Elimination bestimmt werden. (Unbeschränkt: soll hier heißen, sogar für Sätze, die das jeweils andere Konditional enthalten).
FieldVsMcGee: aber daraus kann man nicht eine der beiden folgenden Konklusionen schließen:
(i) daß die Tatsache, daß jemand eine Verknüpfung - genannt „>“ - anwendet, die beiden Regeln genügt, für uns hinreichend ist zu schließen, daß er dasselbe mit „>“ meint wie wir
(ii) daß unser Wort „>“ bestimmt ist.
McGee: behauptet (ii) , Field: (i) könnte hier die Brücke schlagen.
Ad (i): scheint klar falsch: Bsp ein Intuitionist und ein Vertreter der klassischen Logik akzeptieren beide die Einführungs- und Eliminationsregel für „>“ aber ihre Begriffe von > unterscheiden sich.
Wenn wir nun das klassische und das intuitionistische > in einer Sprache kombinieren, müssen wir wenigstens eine der Regeln für eine Verknüpfung beschränken, wenn sie auf Sätze angewendet wird, die die andere Verknüpfung enthalten.
Aber das zeigt nicht, daß der uneingeschränkte Gebrauch durch Leute, die nur einen der beiden Begriffe haben, den Begriff völlig bestimmt.
Bsp Angenommen, jemand der wenig Verständnis von Logik hat, insbesondere keinen Begriff der klassischen Negation (sonst wäre der Intuitionismus bei ihm ausgeschlossen):
II 276
Nichts in seinen informellen Erklärungen wird zeigen, ob er ein Intuitionist oder ein Vertreter der klassischen Logik ist. Field: das ist ein klarer Fall von Unbestimmtheit logischer Konstanten.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989
Field, H. Leeds Vs Field, H.
 
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Field II 304
Indeterminacy/Set Theory/ST/Leeds/Field: e.g. somebody considers the term "set" to be undetermined, so he could say instead: The term can be made "as large as possible". (Leeds 1997,24) (s) "everything that is included in the term"). As such the term can have a wider or narrower definition. Cardinality of the continuum/Indeterminacy/Field: This indeterminacy should at least contain the term set membership.
LeedsVsField: It is not coherent to accept set theory and to qualify its terms as indetermined at the same time. And it is not coherent to then apply classical logic in set theory.
Field: It could also look like this: the philosophical comments should be separated from mathematics. But we do not need to separate theory from practice, e.g. if the belief in indeterminacy is expressed in whether the degree of the mathematician's belief in the continuum hypothesis and his "doubt degree" adds up to 1 ((s) So that there is no space left for a third possibility).
Problem: A mathematician for whom it adds up to 1 could ask himself "Is the continuum hypothesis correct?" and would look for mathematical proof. A second mathematician, however, whose degree of certainty adds up to 0 ((s) since he believes in neither the continuum hypothesis nor its negation) will find it erroneous to look for proof. Each possibility deserves to be analyzed.
The idea behind indeterminacy however is that only little needs to be defined beyond the accepted axioms. ((s) no facts.)
Continuum Hypothesis/Field: Practical considerations may prefer a concept over one another in a particular context and a different one in another context.
Solution/Field: This is not a problem as long as those contexts are hold separate. But is has been shown that its usefulness is independent from the truth.
II 305
Williamsons/Riddle/Indeterminacy/Leeds/Field: (LeedsVsField): (e.g. it must be determined whether Joe is rich or not): Solution/Leeds: i) we exclude the terms in question, e.g. rich (in this example) from the markup language which we accept as "first class"
and
ii) the primary (disquotional) use of "referred" or "is true of" is only used for this markup language.
Indeterminacy/Leeds: Is because there is no uniform best way to apply the disquotional scheme in order to translate into the markup language.
Field: This is genius: To reduce all indeterminacy on the indeterminacy of the translation.
FieldVsLeeds: I doubt that a meaning can be found.
Problem: To differentiate between undetermined termini and those which are only different regarding the extension of the markup language. Especially if we have a number of translations which all have different extensions in our markup language.
Solution/Disquotationalism: It would integrate the foreign terms in its own language. We would then be allowed to cite.(Quine, 1953 b, 135. see above chap. IV II 129-30).
Problem: If we integrate "/" and "", the solution which we obtained above may disappear.
FieldVsLeeds: I fear that our objective - to exclude the indeterminacy in our own language- will not be reached.It even seems to be impossible for our scientific terms!
e.g. the root –1/√-1/Brandom/Field: The indeterminacy is still there; We can simply use the "first class" markup language to say that -1 has two roots without introducing a name like "i" which shall stand for "one of the two".
FieldVsLeeds: We can accept set theory without accepting its language as "first class". ((s) But the objective was to eliminate terms of set theory from the first class markup language and to limit "true of" and "refer" to the markup language.)
Field: We are even able to do this if we accept Platonism (FieldVsPlatonism) :
II 306
e.g. we take a fundamental theory T which has no vocabulary of set theory and only says that there is an infinite number of non-physical eternally existing objects and postulates the consistency of fundamental set theory. Consistency is then the basic term which is regulated by its own axioms and not defined by terms of set theory. (Field 1991). We then translate the language of set theory in T by accepting "set" as true of certain or all non-physical eternally existing objects and interpret "element of" in such a way that the normal axioms remain true.
Then there are different ways to do this and they render different sentences true regarding the cardinality of the continuum. Then the continuum hypothesis has no particular truth value. (C.H. without truth value).
Problem: If we apply mathematical applications to non-mathemtical fields, we do not only need consistency in mathematics but in other fields as well. And we should then assume that the corresponding theories outside mathematics can have a Platonic reformulation.
1. This would be possible if they are substituted by a nominal (!) theory.
2. The Platonic theorie could be substituted by the demand that all nominal consequences of T-plus-set theory are true.
FieldVs: The latter looks like a cheap trick, but the selected set theory does not need to be the one deciding the cardinality of the continuum.
The selected set theory for a physical or psychological theory need not to be compatible with the set theory of another domain. This shows that the truth of the ML is not accepted in a parent frame of reference. It's all about instrumental usefulness.
FieldVsLeeds: We cannot exclude indeterminacy - which surpasses vagueness- in our own language even if we concede its solution. But we do not even need to do this; I believe my solution is better.

Horwich I 378
Truth/T-Theory/T-concept/Leeds: We now need to differentiate between a) Truth Theory (T-Theory) ((s) in the object language) and
b) theories on the definition of truth ((s) metalinguistic, ML) .
Field: (1972): Thesis: We need a SI theory of truth and reference (that a Standard Interpretation is always available), and this truth is also obtainable.
(LeedsVsStandard Interpretation/VsSI//LeedsVsField).
Field/Leeds: His argument is based on an analogy between truth and (chemical)valence. (..+....)
Field: Thesis: If it would have looked as if the analogy cannot be reduced, it would have been a reason to abandon the theory of valences, despite the theory's usefulness!
Truth/Field: Thesis: (analogous to valence ): Despite all we know about the extension of the term, the term also needs a physicalistic acceptable form of reduction!
Leeds: What Field would call a physicalistic acceptable reduction is what we would call the SI theory of truth: There always is a Standard Interpretation for "true" in a language.
Field/Leeds: Field suggests that it is possible to discover the above-mentioned in the end.
LeedsVsField: Let us take a closer look at the analogy: Question: Would a mere list of elements and numbers (instead of valences) not be acceptable?
I 379
This would not be a reduction since the chemists have formulated the law of valences. Physikalism/Natural law/Leeds: Does not demand that all terms can be easily or naturally explained but that the fundamental laws are formulated in a simple way.
Reduction/Leeds: Only because the word "valence" appears in a strict law there are strict limitations imposed on the reduction.
Truth/Tarski/LeedsVsTarski: Tarski's Definitions of T and R do not tell us all the story behind reference and truth in English.
Reference/Truth/Leeds: These relations have a naturalness and importance that cannot be captured in a mere list.
Field/Reduction/Leeds: If we want a reduction à la Field, we must find an analogy to the law of valences in the case of truth, i.e. we need to find a law or a regularity of truth in English.
Analogy/Field: (and numerous others) See in the utility of the truth definition an analogy to the law.
LeedsVsField: However, the utility can be fully explained without a SI theory. It is not astonishing that we have use for a predicate P with the characteristic that"’__’ is P" and "__"are always interchangeable. ((s)>Redundancy theory).
And this is because we often would like to express every sentence in a certain infinite set z (e.g. when all elements have the form in common.) ((s) "All sentences of the form "a = a" are true"), > Generalization.
Generalization/T-Predicate/Leeds: Logical form: (x)(x e z > P(x)).
Semantic ascent/Descent/Leeds: On the other hand truth is then a convenient term, same as infinite conjunction and disjunction.
I 386
Important argument: In theory then, the term of truth would not be necessary! I believe it is possible that a language with infinite conjunctions and disjunctions can be learned. Namely, if conjunctions and disjunctions if they are treated as such in inferences. They could be finally be noted.
I 380
Truth/Leeds: It is useful for what Quine calls "disquotation" but it is still not a theory of truth (T-Theory). Use/Explanation/T-Theory/Leeds: In order to explain the usefulness of the T-term, we do not need to say anything about the relations between language and the world. Reference is then not important.
Solution/Leeds: We have here no T-Theory but a theory of the term of truth, e.g. a theory why the term is seen as useful in every language. This statement appears to be based solely on the formal characteristics of our language. And that is quite independent of any relations of "figure" or reference to the world.

Reference/Truth/Truth term/Leeds: it shows how little the usefulness of the truth term is dependent on a efficient reference relation!
The usefulness of a truth term is independent of English "depicts the world".
I 381
We can verify it: Suppose we have a large fragment of our language, for which we accept instrumentalism, namely that some words do not refer. This is true for sociology, psychology, ethics, etc. Then we will find semantic ascent useful if we are speaking about psychology for example. E.g. "Some of Freud's theories are true, others false" (instead of using "superego"!) Standard Interpretation/Leeds: And this should shake our belief that T is natural or a standard.
Tarski/Leeds: This in turn should not be an obstacle for us to define "T" à la Tarski. And then it is reasonable to assume that "x is true in English iff T (x)" is analytic.
LeedsVsSI: We have then two possibilities to manage without a SI:
a) we can express facts about truth in English referring to the T-definition (if the word "true" is used) or
b) referring to the disquotional role of the T-term. And this, if the explanandum comprises the word "true" in quotation marks (in obliqua, (s) mentioned).

Acquaintance/Russell/M. Williams: Meant a direct mental understanding, not a causal relation!
This is an elder form of the correspondence theory.
I 491
He was referring to RussellVsSkepticism: A foundation of knowledge and meaning FieldVsRussell/M. WilliamsVsRussell: das ist genau das Antackern des Begriffsschemas von außen an die Welt.
Field/M. Williams: His project, in comparison, is more metaphysical than epistemic. He wants a comprehensive physicalistic overview. He needs to show how semantic characteristics fit in a physical world.
If Field were right, we would have a reason to follow a strong correspondence theory, but without dubious epistemic projects which are normally linked to it.
LeedsVsField/M. Williams: But his argument is not successful. It does not give an answer to the question VsDeflationism. Suppose truth cannot be explained in a physicalitic way, then it contradicts the demand that there is an unmistakable causal order.
Solution: Truth cannot explain (see above) because we would again deal with epistemology (theory of knowledge).(>justification, acceptancy).

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie III
H. Field
Science without numbers Princeton New Jersey 1980

Hor I
P. Horwich (Ed.)
Theories of Truth Aldershot 1994
Field, H. Pollock Vs Field, H.
 
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Field II 384
Rules/Standards/Evaluation/PollockVsRelativism/PollockVsField: even tries to avoid the weak relativism: Thesis: the concepts of each person are so shaped by the system of epistemic rules which applies them that there can be no real conflict between people with different systems. I.e. the systems themselves cannot be considered as being in conflict. FieldVsPollock: that is quite implausible: sure, it may be that someone with slightly different rules of induction has a slightly different concept e.g. of ​​ravens. But not so much that one would say that there is no conflict between his belief: "The next raven will be black" and my belief "... not black ...".
Concept/Pollock: at the object level, our concepts are determined by our rule system.
Concept/FieldVsPollock: more plausible: our epistemic concepts like "reasonable" are determined like this: "reasonable means" "reasonable in terms of our rules."

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie III
H. Field
Science without numbers Princeton New Jersey 1980
Field, H. Soames Vs Field, H.
 
Books on Amazon
Horwich I 467
W Theorie/Wahrheitstheorie/WT/Tarski/Soames: zwei Status: a) als mathematische Theorie mit vielen reichen Resultaten
b) philosophisch signifikant für den Begriff der Wahrheit.
WT/Soames: es gibt Streit drüber, was eine WT sein sollte, allgemein sollte sie eins der folgenden drei Dinge tun:
(i) die Bedeutung des T-predicate für natürliche Sprachen geben.
(ii) diese W Prädikate reduktionistisch ersetzen
(iii) einen schon vorher verstandenen T-concept zur Erklärung von Bedeutung oder für andere metaphysische Zwecke gebrauchen.
Proposition/Soames: für folgende Zwecke braucht man eher Propositionen als Sätze oder Äußerungen: Bsp
(1) a. die Proposition, dass die Erde sich bewegt, ist wahr.
b. Churchs Theorem ist wahr
c. Alles was er sagte, ist wahr.
I 468
SoamesVsPropositionen. T-predicate/Verallgemeinerung/Quine/Soames: Bsp zur Charakterisierung des Realismus:
(5) Es gibt einen Doppelgänger der Sonne in einer entfernten Raumregion, aber wir werden niemals hinreichende Belege dafür finden, dass es ihn gibt.
Soames: natürlich kann man Realist sein, ohne (5) zu glauben. ((s) (5) ist zu speziell, es ist nur ein Beispiel).
Anti Realismus/Soames: was unterschiedet ihn dann vom Realismus? Man ist versucht zu sagen:
(6) Entweder gibt es einen Doppelgänger unserer Sonne.... oder keinen.... und wir werden jeweils keine Belege....
I 470
SoamesVs: das führt zu einer unendlichen Liste, die wir vermeiden sollten. Lösung: semantischer Aufstieg:
(7) Es gibt wenigstens einen Satz S, so dass S wahr ist (auf Deutsch) aber wir werden niemals (hinreichende) Belege für S finden.
I 472
W Def/Field: besteht aus zwei Teilen: 1. "primitive Denotation": Bsp (s) „Cäsar“ bezieht sich auf Cäsar.
2. die T-Def in Begriffen primitiver Denotation.
Das Resultat ist ein Satz der Metasprache:
(8) Für alle Sätze S von L, S ist wahr gdw. T(S).
FieldVsTarski/Soames: (Field: „Tarskis W Theorie“ (diese Zeitschrift, I XIX, 1972): diese Annahme (dass Wahrheit, Zutreffen und Referenz bei Tarski physikalistisch akzeptabel seien) ist falsch!
Field: die vorgeschlagenen Ersetzungen für die Begriffe der primitiven Denotation sind nicht physikalistisch akzeptable Reduktionen
I 474
unserer vortheoretischen Begriffe der Referenz und des Zutreffens. Soames: das gilt nur unter der Voraussetzung, dass Field annimmt, dass Tarski Wahrheit auf primitive Denotation reduziert hat.
T-Def/Korrektheit/Tarski/Field/Soames: Field bestreitet nicht, dass die T-Def extensional korrekt ist.
FieldVsTarski: aber extensionale Korrektheit ist nicht hinreichend.
"Cb" sei ein Satz und die semantische n Tatsachen über ihn sind in (9) gegeben:
(9) a. "b" referiert (in L) auf Boston
b. "C" trifft (in L) auf Städte (und nur Städte) zu
c. "Cb" ist wahr (in L) gdw. Boston eine Stadt ist. (Sprecher abhängig)
Problem: man kann jetzt nicht einfach die Tatsachen aus (10) mit den Tatsachen aus (9) identifizieren.
semantische Eigenschaft/Field: haben Ausdrücke einer Sprache nur Kraft der Weise, wie sie durch Sprecher gebraucht werden (Sprachgebrauch).
Problem: die Tatsachen aus (9) hätten gar nicht bestanden, wenn das Sprachverhalten (im weitesten Sinn) anders gewesen wäre!
Pointe: die Tatsachen aus (10) sind nicht sprecher abhängig. Daher sind sie keine semantischen Tatsachen. Daher kann Tarski sie nicht auf physikalistische Tatsachen reduzieren.
T-predicate/FieldVsTarski: es ist sowohl physikalistisch als auch koextensiv mit "wahr in L", aber es ist dennoch kein physikalistischer T-concept.
Problem: die Inadäquatheit erbt die Charakterisierung der Wahrheit aus den Pseudo Reduktionen die die "base clauses" (s) rekursiven Definitionen?) ((s) u.a. für und, oder usw. (base clauses) konstituieren.
I 475
Lösung/Field: wir müssen echte Reduktionen für die Begriffe der primitiven Denotation finden oder etwas wie ein Modell der Kausaltheorie der Referenz. Field/Soames: das sind wieder zwei Stadien:
1. Tarskis Reduktion von Wahrheit auf primitive Denotation ((s) wie oben)
2. eine vorgestellte, Kausaltheorie artige Reduktion der Begriffe der Referenz von Namen und des Zutreffens von Prädikaten.
Sprachunabhängigkeit/Field/Soames: wenn die physikalischen Tatsachen die die Denotation in einer Sprache bestimmen, dies für alle Sprachen tun, dann gilt die Denotation für alle Sprachen. Wenn logische Konstanten und Syntax konstant gehalten werden, erhalten wir einen W Begriff der sprachunabhängig
Problem: 1. Referenz auf abstrakte Objekte ((s) für diese gibt es keine semantischen Tatsachen).
2. ontologische Relativität und Unterbestimmtheit der Referenz.
SoamesVsField: dieser hat seine Kritik an Tarski (FieldVsTarski) sogar noch untertrieben!
Tarski/Soames: denn wenn Tarski primitive Denotation nicht auf physikalische Tatsachen reduziert hat, dann hat er auch Wahrheit gar nicht auf primitive Denotation reduziert ((s) also Punkt 1 verfehlt).
Bsp zwei Sprachen L1 und L2 die identisch sind außer:
L1: hier trifft „R“ auf runde Dinge zu
L2: hier auf rote Dinge.
truth cond.: sind dann für einige Sätze in beiden Sprachen verschieden:
(11) a. "Re" ist wahr in L1 gdw. die Erde rund ist
b. "Re" ist wahr in L2 gdw. die Erde rot ist.
Tarski/Soames: in seiner W Def wird dieser Unterschied in die Instanzen (base clauses) der beiden T-Def für die einzelnen Sprachen zurückverfolgbar sein. denn hier werden die Anwendungen der Prädikate in einer Liste dargestellt.
FieldVsTarski: seine T-Def teilt korrekt mit (reports), dass "R" auf verschiedene Dinge zutrifft in den zwei Sprachen, aber sie erklärt nicht, wie der Unterschied aus dem Sprachgebrauch durch Sprecher zustanden kommt.
SoamesVsField/SoamesVsTarski: Field sagt aber nicht, dass derselbe Vorwurf VsTarski gemacht werden kann
I 476
in Bezug auf logisches Vokabular und Syntax im rekursiven Teil seiner Definition. Bsp L1: könnte [(A v B)] als wahr behandeln, wenn A oder wenn B wahr ist,
L2: ...wenn A und B wahr sind.
FieldVsTarski: dann ist es nicht hinreichend für die Charakterisierung von Wahrheit, bloß "mitzuteilen" dass die truth conditions verschieden sind. Sie müsste durch das Sprachverhalten in den zwei verschiedenen Sprachen ((s) > Sprecherbedeutung) erklärt werden.
FieldVsTarski: weil dieser nichts über Sprachverhalten (Sprecherbedeutung in einer Gemeinschaft) sagt, erfüllt er nicht die Forderungen des Physikalismus ((s) physikalische Tatsachen des Verhaltens) zu erklären.
Soames: das bedeutet, dass Fields Strategie, eine echte Reduktion von Wahrheit zu erhalten, indem man Tarski mit nichttrivialen Definitionen primitiver Denotation ergänzt, nicht funktionieren kann. Denn Tarski hat nach Field Wahrheit nicht auf primitive Denotation reduziert. Er hat sie bestenfalls auf Listen reduziert von semantischen Grundbegriffen:
(13) der Begriff eines Namens, der auf ein Objekt referiert
der Begriff eines Prädikats, das auf ein Objekt zutrifft
der Begriff einer Formel, die die Anwendung eines n stelligen Prädikats auf ein n Tupel von Terme ist
...
I 477
Soames: das erfordert aber eine Reformulierung jeder Bedingung (clause) in Tarskis rekursiver Definition. Bsp alt: 14 a, neu: 14.b: (14) a. wenn A = [~B] , dann ist A wahr in L (im Hinblich auf eine Sequenz s) gdw. B nicht wahr ist in L (im Hinblick auf s).
b. Wenn A eine Negation einer Formel B ist, dann ist A ....
Soames: die resultierende Abstraktion dehnt die Allgemeinheit der W Def auf Klassen von Sprachen 1. Stufe aus. Diese Sprachen unterscheiden sich willkürlich in Syntax, plus logischem und nichtlogischem Vokabular.
SoamesVsField: Problem: diese Allgemeinheit hat ihren Preis.
Alt: die Originaldefinition stipulierte einfach, dass [~A) eine Negation ist ((s) >Symbol, Festlegung).
Neu: die neue Definition gibt keinen Hinweis darauf, welche Formeln in diese Kategorien fallen.
SoamesVsField: sein Physikalist muss nun jeden einzelnen der semantischen Begriffe reduzieren.
Logische Verknüpfung/Konstanten/logische Begriffe/Soames: wir können sie entweder
a) über Wahrheit definieren, oder
b) festlegen, dass bestimmte Symbole Instanzen dieser logischen Begriffe sein sollen.
SoamesVsField: ihm steht nun keiner dieser beiden Wege offen!
a) er kann nicht Negation als Symbol charakterisieren, dass einer Formel angehängt wird, um eine neue Formel zu bilden, die wahr ist, wenn die ursprüngliche Formel falsch wahr, weil das zirkulär wäre.
b) er kann nicht einfach Negation als Grundbegriff (primitiv) nehmen und festlegen, dass [~s] die Negation von s sei. Denn dann würde es keine Tatsachen über Sprecher geben, ((s) Sprachverhalten, physikalistisch), die die semantischen Eigenschaften von [~s] erklären.
Soames: es gibt Alternativen, aber keine ist überzeugend.
Truth functional operator/Quine: (Wurzeln d. Referenz) werden charakterisiert als Dispositionen in einer Gemeinschaft für semantischen Aufstieg und Abstieg.
Problem/Quine: Unbestimmtheit zwischen klassischen und intuitionistischen Konstruktionen der Verknüpfungen sind unvermeidlich.
SoamesVsField: Reduktion von primitiver Denotation auf physikalische Tatsachen ist schwierig genug.
I 478
sie wird noch viel schwieriger für logische Begriffe. SoamesVsField: das liegt daran, dass semantische Tatsachen auf physikalischen Tatsachen über Sprecher supervenieren müssen. ((s) >Sprecherbedeutung, Sprachverhalten).
Problem: das beschränkt adäquate Definitionen auf solche, die das Einsetzen für semantische Begriffe in Kontexten wie (15) und (16) legitimieren. ((s) (15) und (16) sind in Ordnung, die späteren nicht mehr).
(15) Wenn L Sprecher sich anders verhalten hätten hätte "b" (in L) nicht auf Boston und "C" nicht Städte refereiert und .....((s) Kontrafaktische Konditionale).
(16) Die Tatsache, dass L Sprecher sich so verhalten, wie sie sich verhalten, erklärt, warum „b“ (in L) auf Boston referiert usw.
((s) Beide Male Referenz)
Soames: FieldVsTarski ist überzeugt, dass es eine Möglichkeit gibt, (15) und (16) so zu
entziffern, dass sie wahr werden, wenn die semantischen Terme durch physikalistische ersetzt werden und die Anfangs Teilsätze (initial clauses) so konstruiert werden, dass sie kontingente
physikalische Möglichkeiten ausdrücken. Das ist nicht der Charakter von Tarski’s T-Def.
I 481
primitive Referenz/sprachunabhängig/SoamesVsField: Bsp ein Name n referiert auf ein Objekt o in einer Sprache L iff FL(n) = o. FL: ist dabei ein rein mathematisches Objekt: eine Menge von Paaren vielleicht. D.h. sie beinhaltet keine undefinierten semantischen Begriffe.
T-predicate/Wahrheit/Theorie/Soames: das resultierende T-predicate ist genau das, was wir brauchen, um die Natur, Struktur und Reichweite einer vielfältigen Zahl von Theorien metatheoretisch zu untersuchen.
T-Def/Sprache/Soames: was die T-Def uns nicht sagt, ist etwas über die Sprecher der Sprachen, auf die sie angewendet wird. Nach dieser Auffassung sind Sprachen abstrakte Objekte.
((s) Die ganze Zeit muss man hier zwischen Sprachunabhängigkeit und Sprecherunabhängigkeit unterscheiden).
Sprache/primitive Denotation/sprachunabhängig/Wahrheit/SoamesVsField: nach dieser Auffassung sind Sprachen abstrakte Objekte, d.h. sie können so aufgefasst werden, dass sie ihre semantischen Eigenschaften wesentlich haben ((s) nicht abhängig von Sprachverhalten oder Sprechern, (Sprecher Bedeutung), nicht physikalistisch. D.h. mit anderen Eigenschaften wäre es eine andere Sprache).
D.h. es hätte sich nicht herausstellen können, dass Ausdrücke einer Sprache etwas anderes denotiert haben könnten, als das was sie tatsächlich denotieren. Oder dass Sätze einer Sprache andere truth conditions hätten haben können.
I 483
SoamesVsField: auch dieser wird diese Aufteilung kaum vermeiden können. Indexwörter/Mehrdeutigkeit/Field: (:S. 351ff) Lösung: Äußerungen werden durch den Kontext eindeutig gemacht (contextually disambiguated). Semantische Begriffe: sollten auf eindeutige Entitäten angewendet werden.
D.h. alle Bedingungen (clauses) in einer T-Def müssen so formuliert werden, dass sie auf Tokens angewendet werden. Bsp
Negation/Field
(21) Ein Token von [~e] ist wahr (im Hinblick auf eine Sequenz) iff das Token von e das es beinhaltet, nicht wahr ist (im Hinblick auf diese Sequenz).
SoamesVsField: das funktioniert nicht. Denn Field kann keine W Def akzeptieren, in der irgendeine syntaktische Form einfach nur als Negation festgelegt ist . ((s) Symbol, stipuliert, dann unabhängig von physikalischen Tatsachen).
Soames: denn dies würde keine Tatsachen über Sprecher erklären, kraft derer negative Konstruktionen die semantischen Eigenschaften haben, die sie haben.
semantische Eigenschaft/(s): nicht etwa Negation selbst, sondern, dass die Negation eines bestimmten Ausdruckes, in einer Situation wahr ist oder zutrifft. Bsp "Cäsar" referiert auf Cäsar: wäre völlig unabhängig von Umständen, Sprechern, wenn auch nicht von der Sprache, letzteres betrifft aber eigentlich nur die Metasprache.
Lösung/Soames:
(22) Ein Token einer Formel A, die eine Negation einer Formel B ist, ist wahr (im Hinblick auf eine Sequenz) gdw. ein bezeichnetes (designated) Token von B nicht wahr ist (im Hinblick auf diese Sequenz).
"designated"/(s) : heißt hier: explizit mit einem truth value versehen.

Soam I
S. Soames
Understanding Truth Oxford 1999

Hor I
P. Horwich (Ed.)
Theories of Truth Aldershot 1994
McGee, V. Field Vs McGee, V.
 
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II 351
Second Order Number Theory/2nd Order Logic/HOL/2nd Order Theory/Field: Thesis (i) full 2nd stage N.TH. is - unlike 1st stage N.TH. - categorical. I.e. it has only one interpretation up to isomorphism.
II 352
in which the N.TH. comes out as true. Def Categorical Theory/Field: has only one interpretation up to isomorphism in which it comes out as true. E.g. second order number theory.
(ii) Thesis: This shows that there can be no indeterminacy for it.
Set Theory/S.th.: This is a bit more complicated: full 2nd order set theory is not quite categorical (if there are unreachable cardinal numbers) but only quasi-categorical. That means, for all interpretations in which it is true, they are either isomorphic or isomorphic to a fragment of the other, which was obtained by restriction to a less unreachable cardinal number.
Important argument: even the quasi-categorical 2nd order theory is still sufficient to give most questions on the cardinality of the continuum counterfactual conditional the same truth value in all interpretations, so that the assumptions of indeterminacy in ML are almost eliminated.
McGee: (1997) shows that we can get a full second order set theory by adding an axiom. This axiom limits it to interpretations in which 1st order quantifiers go above absolutely everything. Then we get full categoricity.
Problem: This does not work if the 2nd order quantifiers go above all subsets of the range of the 1st order quantifiers. (Paradoxes) But in McGee (as Boolos 1984) the 2nd order quantifiers do not literally go above classes as special entities, but as "plural quantifiers". (>plural quantification).
Indeterminacy/2nd Order Logic/FieldVsMcGee: (see above chapter I): Vs the attempt to escape indeterminacy with 2nd order logic: it is questionable whether the indeterminacy argument is at all applicable to the determination of the 2nd order logic as it is applicable to the concept of quantity. If you say that sentences about the counterfactual conditional have no specific truth value, this leads to an argument that the concept "all subsets" is indeterminate, and therefore that it is indeterminate which counts as "full" interpretation.
Plural Quantification: it can also be indeterminate: Question: over which multiplicities should plural quantifiers go?.
"Full" Interpretation: is still (despite it being relative to a concept of "fullness") quasi-unambiguous. But that does not diminish the indeterminacy.
McGeeVsField: (1997): he asserts that this criticism is based on the fact that 2nd order logic is not considered part of the real logic, but rather a set theory in disguise.
FieldVsMcGee: this is wrong: whether 2nd order logic is part of the logic, is a question of terminology. Even if it is a part of logic, the 2nd order quantifiers could be indeterminate, and that undermines that 2nd order categoricity implies determinacy.
"Absolutely Everything"/Quantification/FieldVsMcGee: that one is only interested in those models where the 1st. order quantifiers go over absolutely everything, only manages then to eliminate the indeterminacy of the 1st order quantification if the use of "absolutely everything" is determined!.
Important argument: this demand will only work when it is superfluous: that is, only when quantification over absolutely everything is possible without this requirement!.
All-Quantification/(s): "on everything": undetermined, because no predicate specified, (as usual E.g. (x)Fx). "Everything" is not a predicate.
Inflationism/Field: representatives of inflationist semantics must explain how it happened that properties of our practice (usage) determine that our quantifiers go above absolutely everything.
II 353
McGee: (2000) tries to do just that: (*) We have to exclude the hypothesis that the apparently unrestricted quantifiers of a person go only above entities of type F, if the person has an idea of ​​F.
((s) i.e. you should be able to quantify over something indeterminate or unknown).
Field: McGee says that this precludes the normal attempts to demonstrate the vagueness of all-quantification.
FieldVsMcGee: does not succeed. E.g. Suppose we assume that our own quantifiers determinedly run above everything. Then it seems natural to assume that the quantifiers of another person are governed by the same rules and therefore also determinedly run above everything. Then they could only have a more limited area if the person has a more restricted concept.
FieldVs: the real question is whether the quantifiers have a determinate range at all, even our own! And if so, how is it that our use (practices) define this area ? In this context it is not even clear what it means to have the concept of a restricted area! Because if all-quantification is indeterminate, then surely also the concepts that are needed for a restriction of the range.
Range/Quantification/Field: for every candidate X for the range of unrestricted quantifiers, we automatically have a concept of at least one candidate for the picking out of objects in X: namely, the concept of self-identity! ((s) I.e. all-quantification. Everything is identical with itself).
FieldVsMcGee: Even thoguh (*) is acceptable in the case where our own quantifiers can be indeterminate, it has no teeth here.
FieldVsSemantic Change or VsInduction!!!.
II 355
Schematic 1st Stage Arithmetic/McGee: (1997, p.57): seems to argue that it is much stronger than normal 1st stage arithmetic. G. is a Godel sentence
PA: "Primitive Arithmetic". Based on the normal basic concepts.
McGee: seems to assert that G is provable in schematic PA ((s) so it is not true). We just have to add the T predicate and apply inductions about it.
FieldVsMcGee: that’s wrong. We get stronger results if we also add a certain compositional T Theory (McGee also says that at the end).
Problem: This goes beyond schematic arithmetics.
McGee: his approach is, however, more model theoretical: i.e. schematic 1st stage N.TH. fixes the extensions of number theory concepts clearly.
Def Indeterminacy: "having non-standard models".
McGee: Suppose our arithmetic language is indeterminate, i.e. It allows for unintended models. But there is a possible extension of the language with a new predicate "standard natural number".
Solution: induction on this new predicate will exclude non-standard models.
FieldVsMcGee: I believe that this is cheating (although some recognized logicians represent it). Suppose we only have Peano arithmetic here, with
Scheme/Field: here understood as having instances only in the current language.
Suppose that we have not managed to pick out a uniform structure up to isomorphism. (Field: this assumption is wrong).
FieldVsMcGee: if that’s the case, then the mere addition of new vocabulary will not help, and additional new axioms for the new vocabulary would help no better than if we introduce new axioms simply without the new vocabulary! Especially for E.g. "standard natural number".
Scheme/FieldVsMcGee: how can his rich perspective of schemes help to secure determinacy? It only allows to add a new instance of induction if I introduce new vocabulary. For McGee, the required relevant concept does not seem to be "standard natural number", and we have already seen that this does not help.
Predicate/Determinacy/Indeterminacy/Field: sure if I had a new predicate with a certain "magical" ability to determine its extension.
II 356
Then we would have singled out genuine natural numbers. But this is a tautology and has nothing to do with whether I extend the induction scheme on this magical predicate. FieldVsMysticism/VsMysticism/Magic: Problem: If you think that you might have magical aids available in the future, then you might also think that you already have it now and this in turn would not depend on the schematic induction. Then the only possible relevance of the induction according to the scheme is to allow the transfer of the postulated future magical abilities to the present. And future magic is no less mysterious than contemporary magic.
FieldVsMcGee: it is cheating to describe the expansion of the language in terms of its extensions. The cheating consists in assuming that the new predicates in the expansion have certain extensions. And they do not have them if the indeterminist is right regarding the N.Th. (Field: I do not believe that indeterminism is right in terms of N.Th.; but we assume it here).
Expansion/Extenstion/Language/Theory/FieldVsMcGee: 2)Vs: he thinks that the necessary new predicates could be such for which it is psychological impossible to add them at all, because of their complexity. Nevertheless, our language rules would not forbid her addition.
FieldVsMcGee: In this case, can it really be determined that the language rules allow us something that is psychologically impossible? That seems to be rather a good example of indeterminacy.
FieldVsMcGee: the most important thing is, however, that we do not simply add new predicates with certain extensions.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie III
H. Field
Science without numbers Princeton New Jersey 1980
Operationalism Field Vs Operationalism
 
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III 3
Nominalism/Field: I use some means which the nominalist rejects: E.g. finitism and operationalism reject the way in which I formulate physical theories: FieldVsFinitism/FieldVsOperationalism: I will say that between two points (E.g. of a light beam) there is always a third point (FinitismVsField). The objections (VsField) stem from considerations that have nothing to do with the nature of the physical entities. Physics/Field: I make strong assumptions about the nature and structure of physical objects (also about subatomic particles). Also about postulated unobservables. ((s) In return, he avoids strong assumptions about the mathematics that deals with it).
III 36
Region/Field: do we need it together with the sp.z. points? Not necessarily, we can quantify on any small open region instead of on points. That’s still nominalistic. But we must not do without points. III 37 Finitism/Field: the purist desire to make do without points is a quasi-finitistic one, not nominalistic. FieldVsFinitism. Region/Field: reverse question: can nominalism have something against regions? Is there a problem with them? III 114 Solution: Individuals Calculus/Goodman/Field: if we accept Goodman’s individuals calculus, there is no problem with regions: we simply regard them as sums of points. Then, namely with the introduction of points, the concept of region is simultaneously introduced (as the sum of points). Empty Region/Individuals Calculus/Sum/Goodman/Field: it then also follows that there can be no empty region. III 37 Region/Goodman/Field: (as sum) does not need not be connected or measurable. There are very "unnatural" collections of points that can count as regions.
Point/Field: even without individuals calculus entities can be assumed that can be regarded as a "sum" of points. Then points can be seen as a special case of the regions (very small ones). That’s nominalistically acceptable.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989
Operationalism Putnam Vs Operationalism
 
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V 50
Operationalism: clumsy agreement: when the needle of the voltmeter is deflected, current flows. PutnamVsOperationalism:
1. The connections between theory and experience (read) are probabilistic and cannot be properly formalized as perfect correlations. (Background noise, etc.).
2. Even these probabilistic connections are not simple semantic correlations but depend on the empirical theory, which is exposed to the revision. According to the naive operationalism the terms undergo each time a change of meaning when a new test procedure is developed.
There is an operational notion after which theories are tested sentence after sentence.
---
V 51
Solution: one can formulate the class of permissible to be accepted interpretations so that the sentence S is mostly true. (Attenuation). The ideal set of operational preconditions is what we gradually approach in the course of empirical research, and not something that we just agree on. E.g. a "permissible interpretation" is such that different effects always have different causes.
---
V 70
Re-interpretation/language/PutnamVsOperationalism: the whole problem only arises when the permissible interpretations are only picked out by operational or theoretical preconditions. The embarrassing thereto is that operational plus theoretical preconditions represent the natural process. What remains is the looseness of the relationship between truth conditions and reference.
---
V 71
Reference/Reference/PutnamVsOperationalism: is the reference, however, only determined by operational and theoretical preconditions, the reference of "x is in R y" is, in turn, undetermined. Knowing that (1) is true, is not useful. Each permissible model of our object language will correspond to one model in our meta-language, in which (1) applies, and the interpretation of "x is in R to y" will determine the interpretation of "x refers to y". However, this will only be a relation in each permissable model and it will nothing contribute to reduce the number of permissable models. FieldVs: this is not, of course, what Field intends. He claims (a) that there is a certain unique relationship between words and things, and (b) that this is the relationship that must also be used when assigning a truth value to (1) as the reference relation.
PutnamVsField: but this cannot necessarily be expressed in that you simply pronounce (1), and it is a mystery how we could learn to express what Field wants to say.
Field: a certain definite relationship between words and objects is true.
PutnamVsField: if it is so that (1) is true in this view, whereby is it then made true? How is a particular correspondence R discarded? It appears, the fact that R is really the reference, should be a metaphysical inexplicable fact. (So magical theory of reference, as if reference to things is intrinsically adhered). (Not to be confused with Kripke 'metaphysically necessary' truth).

Pu I
H. Putnam
Von einem Realistischen Standpunkt Frankfurt 1993

Pu V
H. Putnam
Vernunft, Wahrheit und Geschichte Frankfurt 1990
Possibilia Lewis Vs Possibilia
 
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Schwarz I 87
Possibilia/MöWe/mögliche Welten/possibilistischer Strukturalismus/Lewis/Schwarz: (1991,1993d) hier ging Lewis davon aus, These: dass es deutlich weniger Bewohner von MöWe (Possibilia) gibt als Mengen. ML: für sie mussten also zusätzliche Entitäten neben den Possibilia angenommen werden. Diese zusätzlichen Entitäten sollten dann gerade die Mengen (und Klassen), wie die 5. Bedingung (s.o.) verlangt.
Lewis später: akzeptiert, dass es mindestens so viele Possibilia wie Mengen (s.o. Abschnitt 3.2). Dann könnte man auf die zusätzlichen mathematischen Entitäten verzichten (Lewis pro). Dann streichen wir die 5. Bedingung. Dann müssen „viele“ Bewohner von MöWe Mengen sein.
Schw I 88
Denn Lewis setzt voraus, dass es mehr Mengen als Individuen gibt. Denn wenn es „viele“ Individuen gibt, dann auch „viele“ individuelle Atome, Atome von Individuen. Es gibt aber mehr Summen individueller Atome als individuelle Atome. Dann gibt es auch mehr Individuen als Atome überhaupt und dann nach Bedingung (1) und (3) auch mehr Einermengen als Atome, im Widerspruch zu (2). Possibilia/Lewis/Schwarz: wenn sie keine Kardinalität haben, können nicht alle Possibilia Individuen sein.
Def possibilistischer Strukturalismus/Lewis/Schwarz: mathematische Aussagen handeln ohnehin nicht nur von mathematischen Entitäten, sondern teilweise auch von Possibilia. Warum dann nicht nur von diesen?
Pro: er kommt nicht nur ganz ohne primitives mathematisches Vokabular, sondern auch ohne primitive mathematische Ontologie aus. Damit erledigen sich Fragen nach deren Herkunft und unserem epistemischen Zugang. Handeln mathematische Aussagen von Possibilia, ergibt sich ihr
modaler Status aus der Logik unbeschränkter Modalität: Für unbeschränkt
modale Aussagen fallen Wahrheit, Möglichkeit und Notwendigkeit zusammen
(s.o. Abschnitt 3.6).
Lewis: kann aber die mathematische Entitäten nicht einfach streichen. (LewisVsField): Problem: gemischte Summen. Bsp wenn einige Atome in Cäsars Gehirn als Einermengen und andere als Individuen eingestuft werden, dann ist Cäsar eine gemischte Summe.
Gemischte Summe/Mereologie/Lewis: ist aber selbst weder Individuum noch Klasse.
Klasse: Summe von Einermengen.
Schw I 89
gemischte Summen: sind in Lewis’ Originalsystem auch keine Elemente von Mengen. Schwarz: das ist mengentheoretisch unmotiviert: nach der iterativen Auffassung hat absolut alles eine Einermenge. Lewis ignoriert gemischte Summen sowieso meist.
Problem: nicht unter jeder Einermengenbeziehung gibt es eine Einermenge von Cäsar.
Lösung: a) auch gemischten Summe eine Einermenge zugestehe. Vs: es gibt mehr gemischte Summen als Einermengen, das funktioniert also nicht.
b) Forderung: dass alle „kleinen“ gemischten Summen eine Einermenge haben.
c) eleganter: gemischte Summe dadurch erledigen, dass man Individuen verbietet. Wenn man Klassen mit gewöhnlichen Possibilia identifiziert, könnte man jedes Atom als Einermenge behandeln. Bsp Cäsar ist dann immer eine Klasse, seine Einermenge Gegenstand der reinen Mengenlehre.
LewisVs: das funktioniert in seiner ML (anders als bei ZFC) nicht. Denn wir brauchen mindestens ein Individuum als leere Menge.
Einermenge/Lewis/Schwarz: da ein einziges individuelles Atom dazu aber ausreicht, könnte man an Stelle von (1) (3) Einermengenbeziehungen auch als beliebige eineindeutige Abbildungen von kleinen Dingen in alle Atome außer einem bestimmen. Dieses eine Atom ist dann die leere Menge relativ zur jeweiligen Einermengen Beziehung. (> QuineVsRussell: mehrere leere Mengen, dort je nach Typ).
Lösung/Daniel Nolan: (2001, Kaß 7, 2004): VsLewis, VsZermelo: leere Menge als echter Teil von Einermengen:
Def „Esingleton“ von A /Nolan: {A} besteht aus 0 und einem Ding {A} – 0 . (Terminologie: „Singleton“: einzige Karte einer Farbe).
Esingleton/Nolan: für sie gelten ähnliche Annahmen wie bei Lewis für Einermengen.
Gemischte Summe/Nolan: dieses Problem wird zu dem von Summen aus 0 und Atomen, die keine Esingletons sind. Diese sind bei Nolan nie Elemente von Mengen.
Gegenstand/Nolan: (2004.§4):nur gewisse „große“ Dinge kommen als 0 in Frage. Also werden alle „kleinen“ Dinge als Elemente von Klassen erlaubt.
Individuum/Nolan: viele „kleine“ Dinge sind bei ihm unter allen Esingleton Beziehungen Individuen.
Leere Menge/Schwarz: alle diese Ansätze sind nicht makellos. Die Behandlung der leeren Menge ist immer etwas künstlich.
Schw I 90
leere Menge/Lewis/Schwarz: Menge aller Individuen (s.o.): Das hat einen guten Grund! ((s) Also gibt es keine Individuen und die leere Menge wird gebraucht, um das auszudrücken.). Teilmenge/Lewis/Schwarz: ist dann disjunktiv definiert: einmal für Klassen und einmal für die leere Menge.
possibilistischer Strukturalismus/Schwarz: ist elegant. Vs: er verhindert mengentheoretische Konstruktionen von MöWe (etwa als Satzmengen).
Wenn man Wahrheiten über Mengen auf solche über Possibilia reduziert, kann man Possibilia nicht mehr auf Mengen reduzieren.

LW I
D. Lewis
Die Identität von Körper und Geist Frankfurt 1989

LwCl I
Cl. I. Lewis
Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991
Reductionism Field Vs Reductionism
 
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Avramides I 113
FieldVsReductionism/VsReductive Griceans: the reductive Gricean approach says that one can explain what it means to believe that Caesar was selfish, without somehow referring to the semantic properties of the sentence "Caesar was selfish". Because explaining the semantic properties of the sentence with belief would be circular. The question is whether the Gricean presupposition is true that you can explain belief without reference to the sentence. (84).
((s) This is not the argument of Pieter Seuren that one could not explain linguistic meaning linguistically. ((s)> Evans/McDowellVsSeuren)).
Field: I believe that the presupposition is correct. In a typical case, that which in my system makes a symbol a symbol that stands for Caesar that this symbol has acquired its role in my representation system as a result of my learning a name.
I 114
Which stands for Caesar in the public language. (85). Meaning/Language/Field: if that’s right, then ... Avramides: then there can be no inner language without public language, according to Field.
SchifferVsField: there is no incompatibility. Intention-based Semantics (IBS, Grice) does not need to assume that you have propositional attitude before you have acquired public language.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie III
H. Field
Science without numbers Princeton New Jersey 1980

Avr I
A. Avramides
Meaning and Mind Boston 1989
Tarski, A. Field Vs Tarski, A.
 
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Brendel I 68
T-Def/FieldVsTarski: does not do justice to physicalistic intuitions. (Field 1972). Semantic concepts and especially the W concept should be traceable to physical or logical-mathematical concepts. Tarski/Brendel: advocates for a metalinguistic definition himself that is based only on logical terms, no axiomatic characterization of "truth". (Tarski, "The Establishment of Scientific Semantics").
Bre I 69
FieldVsTarski: E.g. designation: Def Designation/Field: Saying that the name N denotes an object a is the same thing as stipulating that either a is France and N is "France" or a is Germany and N is "Germany"... etc.
Problem: here only an extensional equivalence is given, no explanation of what designation (or satisfiability) is.
Bre I 70
Explanation/FieldVsTarski/Field: should indicate because of which properties a name refers to a subject. Therefore, Tarski’s theory of truth is not physicalistic. T-Def/FieldVsTarski/Field/Brendel: does not do justice to physicalistic intuitions - extensional equivalence is no explanation of what designation or satisfiability is.
Field I 33
Implication/Field: is also in simpler contexts sensibly a primitive basic concept: E.g. Someone asserts the two sentences.
a) "Snow is white" does not imply logically "grass is green".
b) There are no mathematical entities such as quantities.
That does not look as contradictory as
Fie I 34
John is a bachelor/John is married FieldVsTarski: according to him, a) and b) together would be a contradiction, because he defines implication with quantities. Tarski does not give the normal meaning of those terms.
VsField: you could say, however, that the Tarskian concepts give similar access as the definition of "light is electromagnetic radiation".
FieldVsVs: but for implication we do not need such a theoretical approach. This is because it is a logical concept like negation and conjunction.
Field II 141
T-Theory/Tarski: Thesis: we do not get an adequate probability theory if we just take all instances of the schema as axioms. This does not give us the generalizations that we need, for example, so that the modus ponens receives the truth. FieldVsTarski: see above Section 3. 1. Here I showed a solution, but should have explained more.
Feferman/Field: Solution: (Feferman 1991) incorporates schema letters together with a rule for substitution. Then the domain expands automatically as the language expands.
Feferman: needs this for number theory and set theory.
Problem: expanding it to the T-theory, because here we need scheme letters inside and outside of quotation marks.
Field: my solution was to introduce an additional rule that allows to go from a scheme with all the letters in quotation marks to a generalization for all sentences.
Problem: we also need that for the syntax,... here, an interlinking functor is introduced in (TF) and (TFG). (see above).
II 142
TarskiVsField: his variant, however, is purely axiomatic. FieldVsTarski/FefermanVsTarski: Approach with scheme letters instead of pure axioms: Advantages:
1) We have the same advantage as Feferman for the schematic number theory and the schematic set theory: expansions of the language are automatically considered.
2) the use of ""p" is true iff. p" (now as a scheme formula as part of the language rather than as an axiom) seems to grasp the concept of truth better.
3) (most important) is not dependent on a compositional approach to the functioning of the other parts of language. While this is important, it is also not ignored by my approach.
FieldVsTarski: an axiomatic theory is hard to come by for belief sentences.
Putnam I 91
Correspondence Theory/FieldVsTarski: Tarski’s theory is not suited for the reconstruction of the correspondence theory, because fulfillment (of simple predicates of language) is explained through a list. This list has the form
"Electron" refers to electrons
"DNS" refers to DNS
"Gene" refers to genes. etc.
this is similar to
(w) "Snow is white" is true iff....
(s)> meaning postulates)
Putnam: this similarity is no coincidence, because:
Def "True"/Tarski/Putnam: "true" is the zero digit case of fulfillment (i.e. a formula is true if it has no free variables and the zero sequence fulfills it).
Def Zero Sequence: converges to 0: E.g. 1; 1/4; 1/9; 1/16: ...
Criterion W/Putnam: can be generalized to the criterion F as follows: (F for fulfillment):
Def Criterion F/Putnam:
(F) an adequate definition of fulfilled in S must generate all instances of the following scheme as theorems: "P(x1...xn) is fulfilled by the sequence y1...yn and only if P(y1...yn).
Then we reformulate:
"Electron (x)" is fulfilled by y1 iff. y1 is an electron.
PutnamVsField: it would have been formulated like this in Tarskian from the start. But that shows that the list Field complained about is determined in its structure by criterion F.
This as well as the criterion W are now determined by the formal properties we desired of the concepts of truth and reference, so we would even preserve the criterion F if we interpreted the connectives intuitionistically or quasi intuitionistically.
Field’s objection fails. It is right for the realist to define "true" à la Tarski.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie III
H. Field
Science without numbers Princeton New Jersey 1980

Bre I
E. Brendel
Wahrheit und Wissen Paderborn 1999

Pu I
H. Putnam
Von einem Realistischen Standpunkt Frankfurt 1993

Pu V
H. Putnam
Vernunft, Wahrheit und Geschichte Frankfurt 1990

The author or concept searched is found in the following disputes of scientific camps.
Disputed term/author/ism Pro/Versus
Entry
Reference
Logicism/Math. Pro Field II 331
KreiselVsPutnam / KreiselVsField: These mathematical objectivity is transcended logical objectivity - FieldVsKreisel: logical objectivity is all we have.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie III
H. Field
Science without numbers Princeton New Jersey 1980

The author or concept searched is found in the following 3 theses of the more related field of specialization.
Disputed term/author/ism Author
Entry
Reference
Language Field, Hartry
 
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Avramides I 114
Field: no inner language without public language. SchifferVsField: since there is no incompatibility. Intention-based semantics (Grice) does not need to assume that one has propositional attitudes before one has acquired public language.
Thesis: the two go hand in hand.

Avr I
A. Avramides
Meaning and Mind Boston 1989
Standardinterpr. Leeds, St.
 
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Horwich I 378
Field: (1972): These: wir brauchen eine SI-Theorie der Wahrheit und der Referenz (daß eine Standard-Interpretation immer verfügbar ist), und diese Theorie ist auch erhältlich. (LeedsVsSI/LeedsVsField).
Wahrheit/Field: These (in Analogie zur Valenz): trotz allem was wir über die Extension des Begriffs wissen, auch für ihn gibt es noch die Notwendigkeit einer physikalistisch akzeptablen Reduktion!
Leeds: was Field eine physikalistisch akzeptable Reduktion nennen würde, wäre das, was wir die SI-Theorie der Wahrheit nennen: daß es immer eine Standard-Interpretation für -žwahr-œ für eine Sprache gibt.

Hor I
P. Horwich (Ed.)
Theories of Truth Aldershot 1994
Vs Relativism Pollock, J.
 
Books on Amazon
Field II 384
Rules /Standards /Sssessment / PollockVsRelativism / PollockVsField: he even tries to avoid the weak relativism thesis, that the terms of each person are shaped by the system of epistemic rules, that there can be no real conflict between people with different systems.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie III
H. Field
Science without numbers Princeton New Jersey 1980