|Disputed term/author/ism||Author Vs Author
|Field, H.||Leeds Vs Field, H.||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.
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"
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) :
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 metalanguage 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.
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) .
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.
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?
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.
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.
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".
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.
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, acceptability).
"Theories of Reference and Truth", Erkenntnis, 13 (1978) pp. 111-29
Truth and Meaning, Paul Horwich Aldershot 1994
Realism, Mathematics and Modality Oxford New York 1989
Truth and the Absence of Fact Oxford New York 2001
Science without numbers Princeton New Jersey 1980
"Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67
Theories of Truth, Paul Horwich Aldershot 1994
|Leeds, St.||Field Vs Leeds, St.||II 281
Indeterminacy/Own Language/Theory Change/Leeds/Field: (Leeds, Steven 1997), Section IV) LeedsVs indeterminacy within a theory (within one language): Field: Leeds view seems to be disquotational, i.e. the reference of our own expressions should be determined according to the following scheme: (R) if b exists, then "b" refers to b and nothing else. Foreign Language/Theory Change: In this case, it only makes sense relative to a correlation between the concept of the two theories. More Moderate View/Field: we might as well have an unrelativized concept of reference that extends beyond our own concepts, this will, however, be very vague. FieldVsLeeds: it seems very reasonable to assume that the concepts of our currently best theories are vague. Simply because many aspects still have room for improvement. E.g. Ricci tensor: will probably not just refer directly to something, but it will not be without any reference either. Falseness/Theory/False Theory/Field: E.g. "mass"/"weight" makes it clear that if a theory is false, it is often because of the vagueness of terms.
Correctness/Translation/Theory/Field: the concept of a "correct translation" is nonsense:
E.g. root -1, "i"/"-i" "/" / "" (see above). This is not about an epistemic limitation. There is no "subtle fact" that we cannot know, it is rather the case that there is no certain fact that makes a difference. The example is interesting in the context of Leeds: it seems as if also our own terms "i" and "-i" would be indeterminate, because: Chauvinism/Theory/Theory Change/Asymmetry/Field: it would be chauvinistic to assume that our own theory is determined if we attest indeterminacy to the other theory. FieldVsLeeds: he cannot avoid the accusation of chauvinism, because he denies our own theory indeterminacy.
Solution: In the process of language acquisition (learning, use) we learn to accept (R) and that creates no connection between "refers" as applied to "/" and "i". Asymmetry/Chauvinism/Field: we get this asymmetry without chauvinism: our term "i" is as indeterminate as the foreign term "/", it is just that the indeterminacy is "hidden" in our normal semantic statements, because these semantic concepts contain a compensating indeterminacy! (f..o.th. compensation).
Indeterminacy/FieldVsLeeds: this dissolves the doubts regarding the indeterminacy of our own language.
The fact that "i" refers to i does not show that "i" is determined, it is therefore compatible with the fact that "i" and "refers disquotationally" are both indeterminate.
Caution: This only shows how a prior indeterminacy of "i" would lead to an indeterminacy of "refers disquotationally".
Indeterminacy/Own Language/FieldVsLeeds: the possibility of indeterminacy of our own language can also be shown regardless of the theory of reference, and thus also of disquotationality: surely, vagueness is a kind of indeterminacy, and that is everywhere. Vagueness: it can also be problematic itself:
Vagueness/Williamson’s Riddle/Field: (Williamson 1994): there are people who consider the riddle to be so serious that it would be doubtful whether II 283 the phenomenon of vagueness (or, more generally, of indeterminacy) would be a real phenomenon.
Realism, Mathematics and Modality Oxford New York 1989
|Leeds, St.||Verschiedene Vs Leeds, St.||Horwich I 381
Standard Interpretation/Truth/SI/Leeds: if that is true, we do not need standard interpretation, but maybe sometimes we do? Perhaps some statements about truth that are denied by naturalistic instrumentalism (NI), for example the idea that a truth theory is necessary to explain why our theory works. Theory/Success/Function/Truth: For example, the idea that a truth theory is necessary to explain why our theories work.
Explanation/Leeds: the Explanandum must be formulated in such a way that it is clear that it must be explained systematically. For example, it is not enough to simply read "our theory works" as "our theories contain truth-sentences".
Observation/Truth/Theory/Leeds: the agreement with observation must come into play. For example, we can say in a clear sense that humans are superior to animals because their predictions are more precise and more often apply.
Theory/Success/Leeds: Success consists in having expectations that are fulfilled.
Next: we might find that many sentences of our language are associated with certain stimulus patterns, so whoever believes these sentences will expect a certain stimulus type. Success/Theory: then we can say that our theories work because they have correct O consequences (observation consequences). Then we want to explain why they have these consequences.
Observation consequence(s): For example "if I have observed this, this and that will happen afterwards".
VsLeeds: the sharp distinction between theory and observation that I have made here is, of course, controversial. ((s) > Theoryladenness of observation).
Leeds: but our thesis does not depend on this distinction.
P. Horwich (Ed.)
Theories of Truth Aldershot 1994