Dictionary of Arguments


Philosophical and Scientific Issues in Dispute
 
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The author or concept searched is found in the following 1 entries.
Disputed term/author/ism Author
Entry
Reference
Platonism Field I 8
Platonism/Field: his only argument is the applicability of mathematics.
---
I 14
FieldVsPlatonism: has to answer the fictionalist in his language - cannot rely on his "initial plausibility". ---
I 152
Definition Priority thesis/PT/Wright: Thesis: the priority of the syntactic over the ontological categories. - Platonism/Wright: that allows Frege to be a Platonist. - Definition Gödelian Platonism/Wright: in addition: the thesis that mathematical knowledge must be explained by a quasi-perceptual relation - FregeVsGödel - WrightVsGödel: we do not need that. ---
I 153
Definition weak Priority thesis/PT: that each syntactic singular term also works automatically in a semantical way as a singular term. ---
l 159
Equivalence/Platonism/Nominalism/Field: Question: In which sense is a Platonist statement (e.g. "direction 1 = direction 2") and a nominalistic statement equivalent (c1 is parallel to c2)? Problem: if there are no directions, the second cannot be a sequence of the first. ---
I 186
Definition Moderate Platonism/mP/Field: the thesis that there are abstract objects like numbers. - Then there are probably also relations between numbers and objects. - Moderate Platonism: these relations are conventions, derived from physical relations. - Definition Heavy Duty Platonism/HDP/Field: takes relations between objects and numbers as a bare fact. ---
l 189
Strong moderation condition/(Field (pro): it is possible to formulate physical laws without relation between objects and numbers. ---
I 192
Heavy Duty Platonism/Field: assumes size relationships between objects and numbers. - FieldVs: instead only between objects. ---
II 332
Platonism/Mathematics/VsStructuralism/Field: isomorphic mathematical fields do not need to be indistinguishable. ---
II 334
Quinish Platonism/Field: as a basic concept a certain concept of quantity, from which all other mathematical objects are constructed. So natural numbers and real numbers would actually be sets. ---
III 31
Number/Points/Field: no Platonist will identify real numbers with points on a physical line. - That would be too arbitrary ( "What line?") - What should be zero point - What should be 1? ---
III 90
Platonistic/Field: are terms such as e.g. gradient, Laplace Equation, etc. ---
III 96
1st order Platonism/Field: accepts abstract entities, but no 2nd order logic - Problem: but he needs these (because of power quantifiers).

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

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

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

Field IV
Hartry Field
"Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67
In
Theories of Truth, Paul Horwich Aldershot 1994


The author or concept searched is found in the following 8 controversies.
Disputed term/author/ism Author Vs Author
Entry
Reference
Artificial Intelligence Gödel Vs Artificial Intelligence Dennett I 603
Library of BabelGodel / Turing: showed that this set belongs to a different set in the Library of Babel: the set of all possible computers.   Each Turing machine in which happens to be a consistent algorithm runs for evidence of mathematical truths is associated with a Godel s theorem, an arithmetic truth that they can not prove. Dennett: So what?
Mind / Godel: it shows that the mind can not simply be like machines. People can do things which machines can t. DennettVs!
DennettVsGödel: problem: how can you find out, whether a mathematician proved a theorem, or has only made ​​a noise like a parrot? (> Behavior).

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

Dennett I
D. Dennett
Darwin’s Dangerous Idea, New York 1995
German Edition:
Darwins gefährliches Erbe Hamburg 1997

Dennett II
D. Dennett
Kinds of Minds, New York 1996
German Edition:
Spielarten des Geistes Gütersloh 1999

Dennett III
Daniel Dennett
"COG: Steps towards consciousness in robots"
In
Bewusstein, Thomas Metzinger Paderborn/München/Wien/Zürich 1996

Dennett IV
Daniel Dennett
"Animal Consciousness. What Matters and Why?", in: D. C. Dennett, Brainchildren. Essays on Designing Minds, Cambridge/MA 1998, pp. 337-350
In
Der Geist der Tiere, D Perler/M. Wild Frankfurt/M. 2005
Disquotation Putnam Vs Disquotation Putnam VII 431
Truth/Putnam: the only reason one can have to deny that truth is a property would be that one is physicalist or phenomenalist. Or maybe a culture-relativist. Truth/property/Putnam: only reductionist theories deny that truth is a property. (PutnamVsDisquotationalism: >Disquotationalism).
Truth/Putnam: is a property - >PutnamVsDeflationism - Rorty: (R. Rorty, The Mirror of Nature): truth is no property.
---
Horwich I 455
Divine perspective/outside/PutnamVsGods perspective/Rorty: Putnam is amused as James and Dewey about such attempts. Rorty: but he has a problem when it comes to PutnamVsDisquotationalism: this one is too reductionist, to positivistic, to "behaviorist" for him ("transcendental Skinnerism").
Truth/Putnam: if a philosopher says, truth is something other than electricity because there is probably room for a theory of electricity but not for a truth theory,
Horwich I 456
and that the knowledge of the truth conditions was everything what one could know about the truth, then he denies that truth is a property. Thus, there is then no property of the correctness or accuracy ((s)> Deflationism, PutnamVsDeflationism, PutnamVsGrover. PutnamVs: that is, to deny that our thoughts are thoughts and our assertions assertions.
Theory/existence/reduction/Putnam/Rorty: Putnam assumes here that the only reason to deny is that one needs a theory for an X, to say that the X is "nothing but Y". ((s) eliminative reductionism).
PutnamVsDavidson: Davidson must show that assertions can be reduced to noise. Then the field linguist must reduce acts on motions.
Davidson/Rorty: but he does not say that assertions were nothing but noise.
Instead:
Truth/explanation/Davidson: unlike electricity truth is no explanation for something. ((s) A phenomenon is not explained that a sentence which it claims, is true).
Richard Rorty (1986), "Pragmatism, Davidson and Truth" in E. Lepore (Ed.) Truth and Interpretation. Perspectives on the philosophy of Donald Davidson, Oxford, pp. 333-55. Reprinted in:
Paul Horwich (Ed.) Theories of truth, Dartmouth, England USA 1994
---
Horwich I XIV
VsDeflationism/Horwich: provides no explicit truth-definition, but is only based on a scheme (disquotational scheme).
Horwich I XVI
Truth/simple/unanalysable/Russell/Moore/Cartwright/Horwich: if truth is unanalysable basic concept (VsDeflationism), then it is completely independent of awareness. That is, truth gets something metaphysical. Problem: then we cannot assume that the propositions which we believe, have this property. Then the skepticism follows.
---
Horwich I 457
Correctness/PutnamVsDavidson: although he shares his distaste for intentionalist terms, (and therefore does not consider truth as an explanation), he nevertheless wishes a representation of what kind of statement it is, to be correct. Putnam/Rorty: he wants that because he is afraid that the "inside view" of the language game where "true" is an appreciative term - is weakened, if it is not philosophically supported. Because:
If language is only production of noise - without normative element - then the noises that we utter are nothing but "an expression of our subjectivity".
Normativity/standard/language/Putnam: why should there be no normative elements in the language game? That would be the inside view of the language game.
RortyVsPutnam: thus it still depends on a synoptic God's perspective to be brought together in the inner view and outside view of the language game.
Norm/JamesVsPutnam/DeweyVsPutnam: we cannot take such a God's perspective. That is, we cannot solidify our standards in that we support them metaphysically or scientifically.
Truth/appreciation/PragmatismVsPlato/DeweyVsPlato/RortyVsPutnam: we should not repeat Plato's error, and interpret expressions of appreciation as the names of esoteric entities.
---
Williams II 497
Belief/PutnamVsDavidson: that most are true, is not guaranteed by the methodology of interpretation, because the stock of beliefs is constantly changing. Therefore, we can only give a sense (ii) if we explain the reliability of learning and that can only do the realism. Causal theory/correspondence/Putnam: the reliability of learning: would represent us as reliable signal transmitters. What would the truth theory add? It announced that the sentence is true iff the condition exists. This is the correspondence, which is involved in the causal theory, it is precisely the correspondence that is established by the truth definition.
Deflationism/correspondence/M. Williams: the minimal correspondence is also available for him. That is, Putnam's argument does not guarantee physical correspondence or another substantive theory.
Williams II 502
Truth/Putnam: must be substantial ((s) explanatory role, truth as a property, PutnamVsDeflationism). Otherwise it leads to cultural relativism. PutnamVsCultural relativism: an extreme culture-relativist may himself not even consider a thinker or speaker, as opposed to a mere noise maker. ((s) speaking not distinguishable from sound). This is mental suicide.
PutnamVsDisquotationalism: has no explanatory power, unless something is said about the concept of assertion.
M. WilliamsVsPutnam: do we need that?
Putnam: to be able to view ourselves as thinkers, speaking must be more than noise-making and then we must be able to explain to ourselves what it means to understand a sentence.
PutnamVsmetaphysical Realism/M. Williams: although Putnam finds this picture sympathetic, he prefers to explain meaning in terms of situation appropriate use.
Problem: that we do not stop that there are various inguistic practices ((s) different communities) and therefore different ways of justification.
Solution: ideal justification. And that is how Putnam understands truth.
Truth/PutnamVsDisquotationalism: if we say nothing about the truth in terms of assertibility conditions, we do not get a concept of objective truth, which allows the cultural relativism to escape. Then we identified truth implicitly with assertibility relative to the norms of a particular community.

Putnam I
Hilary Putnam
Von einem Realistischen Standpunkt
In
Von einem realistischen Standpunkt, Vincent C. Müller Frankfurt 1993

Putnam I (a)
Hilary Putnam
Explanation and Reference, In: Glenn Pearce & Patrick Maynard (eds.), Conceptual Change. D. Reidel. pp. 196--214 (1973)
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam I (b)
Hilary Putnam
Language and Reality, in: Mind, Language and Reality: Philosophical Papers, Volume 2. Cambridge University Press. pp. 272-90 (1995
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam I (c)
Hilary Putnam
What is Realism? in: Proceedings of the Aristotelian Society 76 (1975):pp. 177 - 194.
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam I (d)
Hilary Putnam
Models and Reality, Journal of Symbolic Logic 45 (3), 1980:pp. 464-482.
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam I (e)
Hilary Putnam
Reference and Truth
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam I (f)
Hilary Putnam
How to Be an Internal Realist and a Transcendental Idealist (at the Same Time) in: R. Haller/W. Grassl (eds): Sprache, Logik und Philosophie, Akten des 4. Internationalen Wittgenstein-Symposiums, 1979
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam I (g)
Hilary Putnam
Why there isn’t a ready-made world, Synthese 51 (2):205--228 (1982)
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam I (h)
Hilary Putnam
Pourqui les Philosophes? in: A: Jacob (ed.) L’Encyclopédie PHilosophieque Universelle, Paris 1986
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam I (i)
Hilary Putnam
Realism with a Human Face, Cambridge/MA 1990
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam I (k)
Hilary Putnam
"Irrealism and Deconstruction", 6. Giford Lecture, St. Andrews 1990, in: H. Putnam, Renewing Philosophy (The Gifford Lectures), Cambridge/MA 1992, pp. 108-133
In
Von einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993

Putnam II
Hilary Putnam
Representation and Reality, Cambridge/MA 1988
German Edition:
Repräsentation und Realität Frankfurt 1999

Putnam III
Hilary Putnam
Renewing Philosophy (The Gifford Lectures), Cambridge/MA 1992
German Edition:
Für eine Erneuerung der Philosophie Stuttgart 1997

Putnam IV
Hilary Putnam
"Minds and Machines", in: Sidney Hook (ed.) Dimensions of Mind, New York 1960, pp. 138-164
In
Künstliche Intelligenz, Walther Ch. Zimmerli/Stefan Wolf Stuttgart 1994

Putnam V
Hilary Putnam
Reason, Truth and History, Cambridge/MA 1981
German Edition:
Vernunft, Wahrheit und Geschichte Frankfurt 1990

Putnam VI
Hilary Putnam
"Realism and Reason", Proceedings of the American Philosophical Association (1976) pp. 483-98
In
Truth and Meaning, Paul Horwich Aldershot 1994

Putnam VII
Hilary Putnam
"A Defense of Internal Realism" in: James Conant (ed.)Realism with a Human Face, Cambridge/MA 1990 pp. 30-43
In
Theories of Truth, Paul Horwich Aldershot 1994

SocPut I
Robert D. Putnam
Bowling Alone: The Collapse and Revival of American Community New York 2000

Horwich I
P. Horwich (Ed.)
Theories of Truth Aldershot 1994

WilliamsB I
Bernard Williams
Ethics and the Limits of Philosophy London 2011

WilliamsM I
Michael Williams
Problems of Knowledge: A Critical Introduction to Epistemology Oxford 2001

WilliamsM II
Michael Williams
"Do We (Epistemologists) Need A Theory of Truth?", Philosophical Topics, 14 (1986) pp. 223-42
In
Theories of Truth, Paul Horwich Aldershot 1994
Field, H. Gödel Vs Field, H. Field I 66
Realism/Mathematics/Gödel: ("What is Cantor's Continuum Problem?", 1947) (Pro Quine Putnam Argument, VsField, VsAnti Realism): even with a very narrow definition of the term "mathematical data" (only equations of number theory) we can justify quite abstract parts by explanatory success: Gödel: even without having to accept the necessity of a new axiom, and even if it has no intrinsic necessity at all, a decision about its truth is possible by examining its "explanatory success" with induction.
The fertility of its consequences, especially the "verifiable" ones, i.e. those which can be demonstrated without the new axiom, but whose proofs are made easier by the new axiom. Or if one can combine several proofs to one.
For example the axioms about the real numbers, which are rejected by the intuitionists.
I 67
FieldVsGödel: if no mathematical entities are indispensable, then one does not have to call the so-called "mathematical data" true. But at the beginning I had said that there can be no other goal of mathematics than truth.

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

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

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

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

Field IV
Hartry Field
"Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67
In
Theories of Truth, Paul Horwich Aldershot 1994
Goedel, K. Dennett Vs Goedel, K. I 603
Gödel number/Dennett: Goedel numbers make it possible to arrange all possible axiom systems in alphabetical order. Goedel/Turing: showed that this set belongs to a different set in the Library of Babel: the set of all possible computers.
Each Turing machine in which happens that a consistent algorithm runs for proving mathematical truths is associated with a Godel s theorem - with an arithmetic truth that it can not prove. Dennett: So what?
Mind/Goedel: it shows that the mind can not simply be like machines. People can do things which may not be performed by machines. DennettVs!
DennettVsGödel: problem: how can you find out, whether a mathematician has proved a theorem, or has only made ​​a noise like a parrot? (> Proofs).

Dennett I
D. Dennett
Darwin’s Dangerous Idea, New York 1995
German Edition:
Darwins gefährliches Erbe Hamburg 1997

Dennett IV
Daniel Dennett
"Animal Consciousness. What Matters and Why?", in: D. C. Dennett, Brainchildren. Essays on Designing Minds, Cambridge/MA 1998, pp. 337-350
In
Der Geist der Tiere, D Perler/M. Wild Frankfurt/M. 2005
Goedel, K. Deutsch Vs Goedel, K. I 233
Proof: proof theory is not a branch of mathematics, but a science. Proofs are not abstract!   In the proof theory nothing is a matter of logic alone.
DeutschVsGödel: his assumption was, for example, that evidence must always have a finite number of steps. Since the proof of the four-color theorem by computer, however, we know that evidence can at least have so much sentences that they cannot be viewed by any person in his lifetime .... But what is a "step" and what is "at last "?
DeutschVsGödel: At least one of Gödel s insights into evidence turned out to be faulty. (Source: where in D. Deutsch?)

Deutsch I
D. Deutsch
Fabric of Reality, Harmondsworth 1997
German Edition:
Die Physik der Welterkenntnis München 2000
Goedel, K. Penrose Vs Goedel, K. PenroseVsGödel: "Insight" cannot be formalized. (Source: where?)

Penr I
R. Penrose
The Road to Reality: A Complete Guide to the Laws of the Universe 2005
Hilbert Deutsch Vs Hilbert I 236
Hilbert: "Über das Unendliche": spottete über den Gedanken, dass die Forderung nach der"endlichen Anzahl von Schritten" wesentlich ist. DeutschVsHilbert: aber er irrte sich. DeutschVsGödel: Zumindest eine von Gödels Einsichten in Beweise stellte sich als fehlerhaft heraus.
I 237
Diesem Gedanken zufolge ist ein Beweis etwas besonderes, eine Reihe von Aussagen, die Beweisregeln gehorchen. Wir haben schon gesehen, dass ein Beweis besser nicht als ein Ding, sondern als ein Vorgang (Programm) gesehen werden sollte. Eine Art von Berechnung. Im klassischen Fall ist also die Umwandlung von Beweisvorgängen in Beweisdinge immer durchführbar. Wenn wir aber eine klassisch nicht auszuführende mathematische Berechnung, die ein Quantencomputer leicht machen kann betrachten: hier gibt es keine Möglichkeit all das aufzuzeichnen, was im Beweisprozess abläuft, weil das Meiste in anderen Universen passiert. Auf diese Weise kann man keinen Beweis alter Art führen.

Deutsch I
D. Deutsch
Fabric of Reality, Harmondsworth 1997
German Edition:
Die Physik der Welterkenntnis München 2000
Prosentential Theory Verschiedene Vs Prosentential Theory Horwich I 344
Quote/VsProsentential Theory/Camp, Grover, Belnap/VsCGB: one accuses the prosentential theory of ignoring cases where truth of quotes, i.e. names of sentences is stated. Example (27) "Snow is white" is true.
CGB: we could say here with Ramsey that (27) simply means that snow is white.
CGBVsRamsey: this obscures important pragmatic features of the example. They become clearer when we use a foreign-language translation. Example
(28) If „Schnee ist weiß“ is true, then…
Why (28) instead of
If it’s true that snow is white, then
Or
If snow is white, then…
CGB: there are several possible reasons here. We may want to make it clear that the original sentence was written in German. Or it could be that there is no elegant translation, or we do not know the grammar of German well enough. Or example: "Snow is white" must be true because Fritz said it and everything Fritz says is true.
I 345
Suppose English* has a way of formally presenting a sentence: E.g. „Betrachte __“ („Consider____").
(29) Consider: Snow is white. This is true.
CGB: why should it not work the same as "snow is white is true" in normal English?
VsCGB: you could argue that it requires a reference to sentences or expressions because quotation marks are name-forming functors.
Quotation marks/CGB: we deviate from this representation! Quotation marks are not name-forming functors. ((s) not for CGB).
Quote/CGB: should not be considered as a reference to expressions in normal English. But we do not want to follow that up here.
I 346
VsCGB: one has accused the prosentential theory of tunnel vision: Maybe we overlooked certain grammatically similar constructions? Example (30) John: there are seven legged dogs
Mary: that's surprising, but true.
(31) John: the being of knowledge is the knowledge of being
Mary: that is profound and it is true.
Ad (30): of course the first half is "that is surprising" in no way prosentential. It is a characterization!
VsCGB: Ad (31) "is profound" expresses a quality that Mary attributes to the sentence. Why shouldn't "true" be understood in the same way?
CGB: it makes sense to take "this" here as referring to a sentence. But that would make things more complicated because then we would have to treat "that" and "it" differently in "that's true" and "it's true".
CGBVsVs: 1. it is just not true that the "that" in "that's surprising" refers to an utterance (in the sense of what was said, or a proposition).
What is surprising here? Facts, events or states of affairs.
Statement/Surprise/CGB: a statement can only be surprising as an act.
I 347
The surprising thing about the statement is the fact reported. ((s) But then the content rather than the act of testimony.)
CGBVs(s): it is not the fact that there are seven legged dogs claimed to be true in (30), because that fact cannot be true!
Proposition/CGB: (ad (31) Propositions are not profound. Acts can be profound. For example insights or thoughts.
Truth/Act/Action/Statement/CGB: but statements in the sense of action are not what is called true. ((s) see also StrawsonVsAustin, ditto).
Reference/Prosentential Theory/CGB: even if we consider "that's surprising, but it's true" as referring, the two parts don't refer to the same thing! And then the theory is no longer economic.
Reference/Prosentential Theory/CGB: are there perhaps other cases where it is plausible that a pronoun refers to a proposition? Example
(32) John: Some dogs eat grass.
Mary: You believe that, but it's not true.
Proposition: is often understood as a bearer of truth, and as an object of belief. (CGBVs).
I 348
However, if "that" is understood here as a referencing pronoun, then the speaker must be a proposition. CGBVs: we can interpret "that you believe" also differently: as prosentential anaphora (as above in the example "that is wrong", with preceding negation prefix). Then we have no pronominal reference.
N.B.: the point is that no property is attributed. Truth is not a property.
VsCGB: another objection: it is also a "tunnel vision" that we only have "that is true" but not "that is right" in view. Or the example "exaggerated" by Austin.
Example: a child says
I've got 15 logs
That is right.
I 349
Question: should this (and e.g. "This is an exaggeration!") be understood prosententially? CGBVsVs: "that is right" is here the statement that the child counted right, that it did something right. Sometimes this can overlap with the statement that a statement is true. The overlap must exist because there is no clear boundary between language learning and use.
I 349
Anaphora/Prosentential Theory/VsCGB: could not one split the prosody and take the individual "that" as an anaphora? CGBVsVs: then one would also have to split off "is true" and no longer perceive it as referencing, but as characterizing ((s) And thus attributing it as property).
CGBVs: then we would have to give up our thesis that speech about truth is completely understandable without "carrier of truth" or "truth characteristic".
Moreover:
Reference/CGB: it is known that not every nominalization has to be referencing ((s) E.g. Unicorn).
Predication/CGB: also not every predication has to be characterizing.
Divine Perspective/outside/PutnamVsGod's point of view/Rorty: Putnam amuses himself like James and Dewey, about such attempts.
Rorty: But he has a problem when it comes to PutnamVsDisquotationalism: it smells too reductionist, too positivist, too "behaviorist" ("transcendental skinnerism").
Truth/Putnam: when a philosopher says truth is something other than electricity because there is room for a theory of electricity but not for a truth theory,
I 456
and that knowledge of the truth condition is all that could be known about truth, then he denies that truth is a property. So there is also no property of correctness or accuracy ((s) >Deflationism, PutnamVsDeflationism, PutnamVsGrover.) PutnamVs: that is, to deny that our thoughts are thoughts and our assertions are assertions.
Theory/Existence/Reduction/Putnam/Rorty: Putnam here assumes that the only reason to deny is that you need a theory for an X is to say that the X is "nothing but Y" ((s) eliminative reductionism).
PutnamVsDavidson: Davidson must show that claims can be reduced to sounds. Then the field linguist would have to reduce actions to movements.
Davidson/Rorty: but this one does not say that claims are nothing but sounds.
Instead:
Truth/Explanation/Davidson: other than electricity, truth is no explanation for something. ((s) A phenomenon is not explained by the fact that a sentence that claims it is true).





Horwich I
P. Horwich (Ed.)
Theories of Truth Aldershot 1994

The author or concept searched is found in the following theses of the more related field of specialization.
Disputed term/author/ism Author
Entry
Reference
Math. Platonism Gödel, K. Field I 152
Def "priority thesis" / Wright: "thesis of the priority of syntactic over ontological categories."   Def Gödel s Platonism / Wright: in addition: the thesis that mathematical knowledge must be explained by a "quasi-perceptual relation".
  FregeVsGödel.
  WrightVsGödel: we do not need it.

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

Field IV
Hartry Field
"Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67
In
Theories of Truth, Paul Horwich Aldershot 1994