# Dictionary of Arguments

Philosophical and Scientific Issues in Dispute

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The author or concept searched is found in the following 7 entries.
Disputed term/author/ism Author
Entry
Reference
Arithmetics Thiel Thiel I 225
Arithmetics/Lorenzen/Thiel: Arithmetics is the theory in which the infinite occurs in its simplest form, it is essentially nothing more than the theory of the infinite itself. Arithmetics as the theory of the set of signs (e.g. tally-list) is universal in the sense that the properties and relations of any other infinite set of signs can always be "mapped" in some way.
The complexity of matter has led to the fact that a large part of the secondary literature on Gödel has put a lot of nonsense into the world on metaphors such as "reflection", "self-reference", etc.
I 224
The logical arithmetic full formalism is denoted with F. It contains, among other things, inductive definitions of the counting signs, the variables for them, the rules of quantifier logic and the Dedekind-Peanosian axioms written as rules.
I 226
The derivability or non-derivability of a formula means nothing other than the existence or non-existence of a proof figure or a family tree with A as the final formula. Therefore also the metamathematical statements "derivable", respectively "un-derivable" each reversibly correspond unambiguously to a basic number characterizing them. > Theorem of incompleteness > Gödel.
Terminology/Writing: S derivable, \$ not derivable.
"\$ Ax(x)" is now undoubtedly a correctly defined form of statement, since the count for An(n) is uniquely determined. Either \$An(n) is valid or not.
Thiel I 304
The centuries-old dominance of geometry has aftereffects in the use of language. For example "square", "cubic" equations etc. Arithmetics/Thiel: has today become a number theory, its practical part degraded to "calculating", a probability calculus has been added.
I 305
In the vector and tensor calculus, geometry and algebra appear reunited. A new discipline called "invariant theory" emerges, flourishes and disappears completely, only to rise again later.
I 306
Functional analysis: is certainly not a fundamental discipline because of the very high level of conceptual abstraction.
I 307
Bourbaki contrasts the classical "disciplines" with the "modern structures". The theory of prime numbers is closely related to the theory of algebraic curves. Euclidean geometry borders on the theory of integral equations. The ordering principle will be one of the hierarchies of structures, from simple to complicated and from general to particular.

T I
Chr. Thiel
Philosophie und Mathematik Darmstadt 1995

Deflationism Field I 91
Deflationism/knowledge/Field: Thesis: we do not know the consistency of the axioms e.g. The quantity theory or the theory of the real numbers. - For this would require mathematical entities - Conditional possibility principle/Field: (this would also admit Frege): if non-modal form, then knowledge alone from thinking about the logical form. - Deflationism/Field/(s): leads to that, that we have no mathematical knowledge as far as mathematical entities (m.e.) are concerned, since they do not exist.
I 108
VsDeflationism/model theory/proof theory/Field: Problem: because there are no mathematical entities (m.e.) the (platonistic) schemes (MTP) If there is a model for "A", then MA - and (MS). If there is a proof of "~A" in F) then ~ MA - only trivially true - solution: modal surrogates or schemes: (MTP #) If N(NBG > there is a model for "A"), then MA - and (MS#) If N(NBG > there is a proof for "~A" inF) then ~MA - (F: here language) - "A" a sentence - NBG: Neuman/Bernays/Gödel - MA: "possibly A" -
I 110
Conclusion: the deflationism has no problem with the model theory if it is about to find out something about possibility and impossibility.
I 113
Deflationism/Field: deflationism does not say that the mathematical statements mean something different, but that what they mean cannot be literally known. Deductivism: always asserts that what AQ means is that which follows A from another statement. Deflationism: must not isolate statements - here other statements are not relevant to the meaning of A.

II 104
Inflationism: Frege/Russell/Tractatus/Ramsey: truth conditions are central for meaning and content. - Vs: Deflationism: does not need truth conditions.
II 108
Deflationism/Field: Main point: that the deflationism does not need truth condtions. - He also does not need any verificationism. Deflationism must also exclude the possibility of a physical reduction of truth conditions.
II 114
Logical connection/Deflationism: one main advantage seems to be that deflationism does not have to make the choice between facts. Solution: one can easily explain in his own words what it is that "or" the truth table obeys: It follows from the truth functional logic together with the logic of the disquotational truth-predicate, without mentioning any facts about the use. "P" is true iff p follows by conceptual necessity through the cognitive equivalence of the right and left side.
Problem: conceptual necessity is not sufficient to show that "or" the truth table is sufficient. - We still need generalization.
II 116
Deflationism/Gavagai: for deflationism there is nothing to explain here - it is simply part of the logic of "refers" that "rabbit" refers to rabbits.
II 117
Reference/Deflationism: if truth conditions are unimportant, then reference cannot play a central role. Solution: not reference is the basis but observations about our practice of concluding. - Then reference is purely disquotational - E.g.: "Gödel does not refer to the discoverer of the incompleteness sentence" but "Gödel is not the discoverer ..." - then semantic ascent.
II 118
Causal theoryVsDeflationism: the deflationism cannot say that all we need for that, that my word for Hume refers to Hume, is the disquotation scheme. Nevertheless, the deflationist can accept that the causal network that explains what else would be mysterious: the correlation between believe and facts about Hume.
II 119
Deflationism: the border to the inflationism is blurred because we have to construct something that could be considered as an inflationist relation "S has the truth conditions p", or not.
II 127
VsDeflationism: 1. He cannot distinguish between "Either he is a hairdresser or not a hairdresser" and - "Either he is a fascist or not a fascist". 2. It cannot explain the explanatory power of the truth conditions - (E.g. For behavior and success)
3. It cannot distinguish between vague and non-vague discourse
4. It cannot deal with truth attribution in other languages
5. It gives "true" false modal properties ((s) "necessarily true" or "contingent true")
6. It cannot deal with ambiguity, indices, and demonstrativa
7. It cannot explain learning.
---
Deflationism/Nonfactualism/Conclusion/Field/(s): the deflationism (disquotationalism) does not accept any facts which, for example, are relevant why a word refers to a thing. - For deflationism, it is senseless to ask why "entropy" refers to entropy. - ((s)(use/(s): would be such a fact.) >Disquotationalism, >Minimalism, >Quote/Disquotation.

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 Numbers Godel number: natural number that encodes mathematical and logical statements by a certain method. The symbols such as +, -, =,(, etc. are in turn encoded by primes and subsequently multiplied, so they can be uniquely reconstructed by prime factorization. Gödel numbers make it possible to create directories of formulas and perform proofs of completeness or incompleteness.

Incompleteness Logic Texts Read III 61
Incompleteness Theorem/Gödel/Read: the compact inference produces too little: there are intuitively valid inferences that mark it as invalid. For example, the most famous example is the Omega theory: assuming a formula is true for any natural number. Then "for every n, A(n) is true". This is not a classical logical conclusion from them, because it does not follow from any finite subset of any set. The Omega rule would allow us to deduce from the premises A(0),A(1)... etc. "for every n A(n)." But this is a rule that could never be applied, it would require that a proof be an infinite object.
Def Omega model: the natural numbers, as well as the zero, with the operations of the successor, addition, multiplication and exponentiation.
The Omega rule is not accepted as a rule of orthodox classical proof theory. How can I do this? According to classical representation, a rule is valid if it is not possible to make the premises true and the conclusion false by any interpretation over any range of definition. How can the premises A(0),A(1) etc. was, but be false for each n,A(n)?
III 61/62
The explanation lies in the limitation of the expressiveness. >Compactness/Logic texts, >2nd order logic.
III 64
The Omega rule requires an extra premise: "and these are all numbers". This extra premise is arithmetically true, but the non-standard models show that, as far as logic is concerned, it has to be formulated explicitly (in 1st level terms, i.e. logical terms).
III 65
Two ways to see that this answer is not appropriate as a defense of classical logic and its compactness. >Compactness/Logic texts. 1. the extra provision "and these are all numbers " cannot be expressed in terms of 1st level terms.
2. a proposal by Wittgenstein: a long conjunction for "each F is G": "this is G and that is G and that other is G...
RussellVs: these two statements are not equivalent, because the long conjunction needs a final clause "and these are all F's".
ReadVsRussell: Error: if a conjunction is exhaustive, then the two statements are equivalent. If not, the extra clause has no effect, because it is wrong. It does not do extra work. >Second order logic.
Logic Texts
Me I Albert Menne Folgerichtig Denken Darmstadt 1988
HH II Hoyningen-Huene Formale Logik, Stuttgart 1998
Re III Stephen Read Philosophie der Logik Hamburg 1997
Sal IV Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 - German: Logik Stuttgart 1983
Sai V R.M.Sainsbury Paradoxes, Cambridge/New York/Melbourne 1995 - German: Paradoxien Stuttgart 2001

Re III
Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press
German Edition:
Philosophie der Logik Hamburg 1997
Incompleteness Debray Sokal I 200
Incompleteness/Gödel/Debray/Bricmont/Sokal: (R. Debray, Critique de la raison politique, Paris, 1981): Debray makes an allusion to Gödel's incompleteness theorem and explains that "collective insanity finds its final reason in a logical axiom that itself is not justified: incompleteness". (1981, p. 10). (1981, p. 256): The "mystery of our collective misery, the a priori condition of every political history in the past, present and future, can be expressed in a few simple, even childlike words. When one realizes that more work and the unconscious are to be defined in a single sentence (...),...
---
Sokal I 201
...there is no danger of confusing simplicity with exaggerated simplification. The mystery takes the form of a logical law, an extension of Gödel's theorem: there can be no organized system without closure, and no system can be closed by elements that belong to only this system.
SokalVsDebray: There is simply no logical relationship between this sentence and sociological questions.
Note: in a more recent text (R. Debray, "L'incomplétude logique du religieux", Bulletin de la societé francaise de philosophie 90, 1996 pp. 1-25), Debray admits that "Gödelitis... is a common disease" and that the "transfer of a scientific knowledge and its generalisation outside its specific valid domain can lead to great mistakes (p. 7). In addition, he explains that his use of the sentence is only meant "metaphorical or isomorphic". (1996, S. 7).

Debr I
Régis Debray
Critique de la raison politique ou l’Inconscient religieux Paris 1987

Sokal I
Alan Sokal
Jean Bricmont
Fashionabel Nonsense. Postmodern Intellectuals Abuse of Science, New York 1998
German Edition:
Eleganter Unsinn. Wie die Denker der Postmoderne die Wissenschaften missbrauchen München 1999

Sokal II
Alan Sokal
Fashionable Nonsense: Postmodern Intellectuals’ Abuse of Science New York 1999
Incompleteness Serres Sokal I 203
Incompleteness/Society/Debray/Serres/Bricmont/Socal: (M. Serres,"Paris 1800" in: M. Authier (Ed.) Elemente einer Geschichte der Wissenschaften, Frankfurt/M. 1994, p, 636f): according to Debray... societies organize themselves only under the explicit condition that they are based on something different from them, something that is beyond their definition or boundary. They cannot satisfy themselves. He describes the foundation as religious. With Gödel he completes Bergson....
SokalVsSerres: the so-called "Gödel-Debray principle" is just as irrelevant to the history of science as it is to politics.

Serres I
M. Serres
The Five Senses: A Philosophy of Mingled Bodies

Sokal I
Alan Sokal
Jean Bricmont
Fashionabel Nonsense. Postmodern Intellectuals Abuse of Science, New York 1998
German Edition:
Eleganter Unsinn. Wie die Denker der Postmoderne die Wissenschaften missbrauchen München 1999

Sokal II
Alan Sokal
Fashionable Nonsense: Postmodern Intellectuals’ Abuse of Science New York 1999
Truth Tarski K.Glüer Davidson zur Einführung Hamburg, 1993 p. 22
The defined T-predicate in the metalanguage can be translated back into the object language and the state before the elimination of the true can be restored. - Object and metalanguage should contain the predicate true - Davidson, however, can evade the dilemma by not giving a definition. He calls it a definition of truth in Tarski's style, hereafter referred to as T-theory.
---
Rorty IV (a) 22
True/Tarski: the equivalences between the two sides of the T-sentences do not correspond to any causal relationship. Davidson: there is no way to subdivide the true sentences so that on the one hand they express "factual", while on the other side they do not express anything. ---
Berka I 396
Truth/Tarski: we start from the classical correspondence theory.
I 399
We interpret truth like this: we want to see all sentences as valid, which correspond to the Tarski scheme - these are partial definitions of the concept of truth. - Objectively applicable: is the truth definition, if we are able, to prove all the mentioned partial definitions on the basis of the meta language.(1)
1. A.Tarski, „Grundlegung der wissenschaftlichen Semantik“, in: Actes du Congrès International de Philosophie Scientifique, Paris 1935, Vol. III, ASI 390, Paris 1936, pp. 1-8
---
Berka I 475
Truth-Definition/truth/Tarski: wrong: to assume that a true statement is nothing more than a provable sentence. - This is purely structural - Problem: No truth-definition must contradict the sentence definition - N.B.: but this has no validity in the field of provable sentences - E.g. There may be two contradictory statements that are not provable - all provable statements are indeed content-wise true. The truth definition must also contain the non-provable sentences.
Berka I 482
Definition true statement/Tarski: x is a true statement, notation x e Wr iff. x ε AS (meaningful statement) and if every infinite sequence of classes satisfies x. - That does not deliver a truth criterion - no problem: nevertheless the sense of x ε Wr (x belongs to the class of true statements) gets understandable and unambiguous.
I 486
Relative Truth/accuracy in the range/Tarski: plays a much greater role than the (Hilbertian) concept of absolute truth, which was previously mentioned - then we modify Definition 22 (recursive fulfillment) and 23 (truth). - As derived terms we will introduce the term of the statement that a) in a domain of individuals with k elements is correct and - b) of the statement that is true in every domain of individuals.(2)
2. A.Tarski, Der Wahrheitsbegriff in den formalisierten Sprachen, Commentarii Societatis philosophicae Polonorum. Vol. 1, Lemberg 1935
---
Horwich I 111
Truth/Tarski: is a property of sentences - but in the explanation we refer to "facts". - ((s) Quotation marks by Tarski).
Horwich I 124
Truth/true/eliminability/Tarski: cannot be eliminated with generalizations - If we want to say that all true sentences have a certain property. - E.g. All consequences of true sentences are true. - Also not eliminable: in particular statements of the form "x is true": E.g. the first sentence that Plato wrote, is true. - Because we do not have enough historical knowledge. - ((s) The designation "the first sentence..." is here the name of the sentence.) - This cannot be converted into the sentence itself. Eliminability: from definition is quite different from that of redundancy.(3)

3. A. Tarski, The semantic Conceptions of Truth, Philosophy and Phenomenological Research 4, pp. 341-75
---
Skirbekk I 156
Definition Truth/Tarski: a statement is true when it is satisfied by all objects, otherwise false.
Skirbekk I 158
Truth/Tarski: with our definition, we can prove the (semantic, not the logical) sentence of contradiction and the sentence definition. - The propositional logic does not includes the term true at all. - Truth almost never coincides with provability. - All provable statements are true, but there are true statements that cannot be proved. - Such disciplines are consistent but incomplete (>Incompleteness/Gödel). - There's even a pair of contradictory statements, neither of which is provable.(4)
4. A.Tarski, „Die semantische Konzeption der Wahrheit und die Grundlagen der Semantik“ (1944) in: G. Skirbekk (ed.) Wahrheitstheorien, Frankfurt 1996

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

Berka I
Karel Berka
Lothar Kreiser
Logik Texte Berlin 1983

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

Skirbekk I
G. Skirbekk (Hg)
Wahrheitstheorien
In
Wahrheitstheorien, Gunnar Skirbekk Frankfurt 1977

The author or concept searched is found in the following 7 controversies.
Disputed term/author/ism Author Vs Author
Entry
Reference
Bundle Theory Newen Vs Bundle Theory New I 233
Def Reference/Newen: Relation between the occurrence of a singular term and the object thus designated. ((s) i.e. general terms do not refer?).
Names/Proper Names/Newen: two problems:
1) Reference definition: how is the reference determined
2) Meaning: what is the meaning of a name.
Names/Description Theory/Newen: E.g. "Aristotle": the meaning would then be "student of Plato".
Vs: Problem: it could be that someone does not know that Aristotle was a student of Plato, but otherwise uses the name correctly.
Bundle Theory/Solution/Searle/Newen/(s): it should not happen that a single failure refutes the entire theory, therefore, a bundle of descriptions should be decisive, not a single description.
I 234
Bundle Theory/Reference Definition/Searle/Newen: Searle's bundle theory simultaneously regards itself as a theory of reference definition. Names/Proper Names/KripkeVsBundle Theory/KripkeVsDescription Theory/KripkeVsSearle/Kripke/Newen: (modal argument): there is a necessary condition for Def meaning equality/Kripke:

(meaning equality) if two expressions a1 and a2 have the same meaning, they are mutually replaceable in sentences that are introduced by the modal operator "It is necessary that", without changing the truth value.
I 235
E.g. It is necessary that Aristotle is K. Here, "student of Plato" is not usable. Hence the name "Aristotle" (quotation marks by Newen) cannot have the same meaning as "student of Plato".
Description Theory/Meta-Linguistic/Names/Newen: special case description theory of proper names: the so-called meta-linguistic description theory:
E.g. the meaning of the name Aristotle can be specified with the description "The bearer of the name "Aristotle"."
Point: this description captures the context-independent knowledge of a speaker with respect to the name.
KripkeVs/Newen: if the modal argument is also true for the meta-linguistic theory, it cannot be right: it is indeed necessary that Aristotle is Aristotle, but not necessary that Aristotle is
I 236
the bearer of the name "Aristotle". He could have been given a different name. Object Theory/Meaning/Names/Proper Names/Newen: Thesis: The meaning of a name is the designated object.
A variation of this theory is Russell's theory of the meaning of logical proper names. ("dis", etc.)
Epistemology/VsRussell/Newen: Russell's epistemology proved untenable.
Solution/Newen: Reference definition by a description: "The only object that satisfies the description associated with the concept "E" (quotation marks by Newen)".
Frege: was the first to specify this (in his theory of sense and meaning)
Names/Frege/Newen: the Fregean meaning of a name is the designated object.
Reference Definition/Frege/Newen: through description. This is Frege's theory of sense.
Sense/Frege/Newen: through description (= reference definition for proper names).
Names/Frege/Newen: Frege combines an object theory of meaning with a description theory of reference definition.
I 237
((s) KripkeVsFrege/KripkeVsDescription Theory/Newen/(s): Kripke also criticized the description theory of reference definition: E.g. Schmidt was the discoverer of the incompleteness theorem, not Gödel. Nevertheless, we refer with "Gödel" to Gödel, and not to an object which is the singled out with a description that can be true or not.) Solution/Kripke: causal theory of proper names.

New II
Albert Newen
Analytische Philosophie zur Einführung Hamburg 2005

Newen I
Albert Newen
Markus Schrenk
Einführung in die Sprachphilosophie Darmstadt 2008
Description Theory Kripke Vs Description Theory Evans I 310/311
Reference/Description/Acquaintance/Kripke: Although the reference is set by the standard meter of Paris, not every speaker must know it or even know that it exists (according to Evans). Strawson: "the mean of different opinions".
KripkeVsDescription Theory/Evans: His attacks were only directed against the first variant (speaker designation). They ignore the social character of naming.

Field II 117
Reference/Deflationism/Field: Deflationism seems to make the hard work of recent years regarding the study of the reference insignificant. For if truth conditions do not play a central role, neither do the references. E.g.: KripkeVsDescription Theory/Name/Field: (Kripke 1972): This is not correct.
Field: At least if they do not use metalanguage.
Reference/Deflationism/Field: Problem: When the truth condition does not matter, then it is also valid for the reference since the relevant scheme is:
(R) if b exists, "B" refers to b and nothing else; if B does not exist, "b" refers to nothing.
Problem:
It this is all that can be said about reference, what is the meaning of Kripke’s critique on Description Theory?
Description Theory/Gödel-Schmidt Case/Kripke: e.g. Gödel = proves the "incompleteness Theorems"
Then e.g. Schmidt did actually prove it, but was murdered. Everyone would say that "Gödel" nevertheless refers to Gödel and not to Schmidt.
Deflationism/Field: Problem: If deflationism is unable to explain this, then something is wrong with it! But it is actually able to:
Reference/Deflationism/Field: The reference is not the actual basis, but observations about our practice of closing. That is actually what Kripke shows.

Stalnaker I 15
KripkeVsDescription Theory/Stalnaker: Arises from a confusion between semantics and metasemantics. Anti-Essentialism/Kripke/Stalnaker: Arises from a confusion between semantics and metaphysics.

Kripke I
S.A. Kripke
Naming and Necessity, Dordrecht/Boston 1972
German Edition:
Name und Notwendigkeit Frankfurt 1981

Kripke II
Saul A. Kripke
"Speaker’s Reference and Semantic Reference", in: Midwest Studies in Philosophy 2 (1977) 255-276
In
Eigennamen, Ursula Wolf Frankfurt/M. 1993

Kripke III
Saul A. Kripke
Is there a problem with substitutional quantification?
In
Truth and Meaning, G. Evans/J McDowell Oxford 1976

Kripke IV
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

EMD II
G. Evans/J. McDowell
Truth and Meaning Oxford 1977

Evans I
Gareth Evans
"The Causal Theory of Names", in: Proceedings of the Aristotelian Society, Suppl. Vol. 47 (1973) 187-208
In
Eigennamen, Ursula Wolf Frankfurt/M. 1993

Evans II
Gareth Evans
"Semantic Structure and Logical Form"
In
Truth and Meaning, G. Evans/J. McDowell Oxford 1976

Evans III
G. Evans
The Varieties of Reference (Clarendon Paperbacks) Oxford 1989

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

Stalnaker I
R. Stalnaker
Ways a World may be Oxford New York 2003
Description Theory Newen Vs Description Theory NS E 105
KripkeVsDescription Theory/(s): E.g. Gödel Schmidt case: we always refer to Gödel when we use the name, even if it turned out that Gödel has not found the incompleteness proposition. Newen/Schrenk: the name always designates the person, regardless of which descriptions apply to them in other hypothetical situations.
This shows that the characteristic descriptions in names are not responsible for the reference definition.

Newen I
Albert Newen
Markus Schrenk
Einführung in die Sprachphilosophie Darmstadt 2008
Field, H. Shapiro Vs Field, H. 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.

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

Varian I
Carl Shapiro
Hal Varian
Information Rules: A Strategic Guide to the Network Economy Brighton, MA 1998

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
Intuitionism Quine Vs Intuitionism VII (a) 14
Set Theory/Fraenkel: classes are discovered. (VsIntuitionism). Quine: this is more than a play on words, it is an essential question. (>Beings).

X 118
QuineVsIntuitionist Logic: it lacks manageability and familiarity. Its sentence links have no truth-functional, but an intuitive meaning which we explain using "refute" and "from ... follows". These explanations become unclear, however, if we want to maintain the difference between uttering a sentence and talking about the sentence (mention/use)! Quine: then you might as well move on to Heyting's axioms and not interpose translation, but
X 119
Apply the direct method of language teacher. Intuitionism: gained more momentum through Godel's proof of incompleteness.
Constructivism/Quine: there is not a correct definition for it.

QuineVsIntuitionist Logic: changes the meanings of quantification and the constants.
Solution: you can follow the constructivist procedure, and still use the orthodox logic: that is what Weyl's constructive set theory does.
Quantifier/Differing Logic/Quine: there are also variations in quantifiers: intuitionistic logic requires knowledge of the proof path.
X 120
Problem: The variables must all (be able to) have a name so that the existential quantification can correspond to the (finite) adjunction of the singular sentences that make them true (see above). Problem: with infinite existential quantification no infinite number of names can be given out.
Variations in the quantification are of course important in terms of ontology.
X 121
Ontology/QuineVsIntuitionism/VsIntuitionist Logic: we might not even see with what the intuitionist declares as existing,. Solution: We need to translate his language into ours first. And not necessarily into our logic, but into our overall language!
Then we can say what he regards as existing (and in our sense of "existing").

Quine I
W.V.O. Quine
Word and Object, Cambridge/MA 1960
German Edition:
Wort und Gegenstand Stuttgart 1980

Quine II
W.V.O. Quine
Theories and Things, Cambridge/MA 1986
German Edition:
Theorien und Dinge Frankfurt 1985

Quine III
W.V.O. Quine
Methods of Logic, 4th edition Cambridge/MA 1982
German Edition:
Grundzüge der Logik Frankfurt 1978

Quine V
W.V.O. Quine
The Roots of Reference, La Salle/Illinois 1974
German Edition:
Die Wurzeln der Referenz Frankfurt 1989

Quine VI
W.V.O. Quine
Pursuit of Truth, Cambridge/MA 1992
German Edition:
Unterwegs zur Wahrheit Paderborn 1995

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

Quine VII (a)
W. V. A. Quine
On what there is
In
From a Logical Point of View, Cambridge, MA 1953

Quine VII (b)
W. V. A. Quine
Two dogmas of empiricism
In
From a Logical Point of View, Cambridge, MA 1953

Quine VII (c)
W. V. A. Quine
The problem of meaning in linguistics
In
From a Logical Point of View, Cambridge, MA 1953

Quine VII (d)
W. V. A. Quine
Identity, ostension and hypostasis
In
From a Logical Point of View, Cambridge, MA 1953

Quine VII (e)
W. V. A. Quine
New foundations for mathematical logic
In
From a Logical Point of View, Cambridge, MA 1953

Quine VII (f)
W. V. A. Quine
Logic and the reification of universals
In
From a Logical Point of View, Cambridge, MA 1953

Quine VII (g)
W. V. A. Quine
Notes on the theory of reference
In
From a Logical Point of View, Cambridge, MA 1953

Quine VII (h)
W. V. A. Quine
Reference and modality
In
From a Logical Point of View, Cambridge, MA 1953

Quine VII (i)
W. V. A. Quine
Meaning and existential inference
In
From a Logical Point of View, Cambridge, MA 1953

Quine VIII
W.V.O. Quine
Designation and Existence, in: The Journal of Philosophy 36 (1939)
German Edition:
Bezeichnung und Referenz
In
Zur Philosophie der idealen Sprache, J. Sinnreich (Hg) München 1982

Quine IX
W.V.O. Quine
Set Theory and its Logic, Cambridge/MA 1963
German Edition:
Mengenlehre und ihre Logik Wiesbaden 1967

Quine X
W.V.O. Quine
The Philosophy of Logic, Cambridge/MA 1970, 1986
German Edition:
Philosophie der Logik Bamberg 2005

Quine XII
W.V.O. Quine
Ontological Relativity and Other Essays, New York 1969
German Edition:
Ontologische Relativität Frankfurt 2003

Quine XIII
Willard Van Orman Quine
Quiddities Cambridge/London 1987
Nagel, Th. Putnam Vs Nagel, Th. IV 151/152
PutnamVsNagel: it is a mistake to assume that Goedel would have shown that the human mind is more complicated than the most complex machine so far. >Incompleteness/Gödel.

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
Smart, J. C. Quine Vs Smart, J. C. II 118 ff
The Oxford trained philosopher today turns one ear to common sense and the other one to science. Historians who do not want to be outflanked claim that the real driving force behind development was fashion. Even quantum theorists are heard to say that they do not attribute reality so much to the tiny objects of their theory as primarily to their experimental apparatuses, i.e. to ordinary things. In refreshing contrast to that is the Australian philosopher Smart: he represents a shamelessly realistic conception of physical elementary particles. The worldview of the physicist is not only ontologically respectable, but his language gives us a truer picture of the world than common sense. (Smart mainly studies physics).
There have also been materialists who believe that living beings are indeed material, but subject to biological and psychological laws, which cannot be reduced to physical laws in principle. This was the emergence materialism.
Smart's materialism is more robust than that.
II 119
Smart Thesis: He denies that there are any laws in the strict sense in psychology and biology at all. The statements there are site-specific generalizations about some terrestrial plants of our acquaintance.
SmartVsEmergence.
They are at the same level as geography or reports on consumer behavior. That even applies to statements about cell division. They will most likely be falsified at least elsewhere in outer space, if not even here with us. (Law: explanatory force) Smart admits that statements about the small processes in biology tend to have more explanatory force. (Precisely, they come indeed closer to physicochemistry.)
Biology describes a site-specific outgrowth, while physics describes the nature of the world. Psychology then describes an outgrowth on this outgrowth.
II 120
Colors: Smart on the color concept: Color dominates our sensory experience, with its help we distinguish objects. But, that's the point of Smart's explanations: color differences rarely have an interesting connection to the laws of physics: a mixed color can appear to us as a pure one depending on contingent mechanisms inside us. It can be assumed that extraterrestrial beings have similar concepts of distance and electric charge, but hardly similar concepts of color. To view the world sub specie aeternitatis we have to avoid the concept of color and other secondary qualities. Primary: length, weight, hardness, shape, etc. are those that are easiest to incorporate in physical laws. For Smart, physicalism wins.
On the subject of "humans as machines", today's opponents of mechanistic thought refer to Godel's theorem, which states that no formal proof method can cover the entire number theory.
II 121
Smart, who represents the mechanistic view, argues against this rather gloomy application of the great Gödel theorem. The place where man defies the barriers of formal proof theory is that of the informal and largely resultless maneuvers of scientific method. Determinism: Smart agrees with Hobbes that >determinism and freedom are not antithetic to one another: deterministic action is considered free if it is in a certain way mediated by the agent.
Ethics: The differentiation of activities for which one can be responsible, and those for which this is not true, follows the social apparatus of rewarding and punishing. Responsibility is assigned a place where reward and punishment tended to work.
Disposition/Smart: This corresponds to an important element in the use of "he could have done." Smart continues to infer on "it could have" (e.g. broken). He brings this into context with the incompleteness of information relating to causal circumstances.
Quine: I welcome this thesis for modalities. These modalities are not based on the nature of the world, but on the fact that we ourselves, e.g. because of ignorance, disregard details.
There is a conception mocked by Smart, according to which the present moment moves forward through time at a velocity of sixty seconds per minute.
Furthermore, there is the idea that sentences about the future are neither true nor false. Otherwise fatalism would get the the reins in his hand. Such thoughts are widespread and confused and partially go back to Aristotle.
They have been put right with great clarity by Donald Williams et al.
As Smart puts them right again, distinctive details are added.
II 122
Incredible contrast between probability and truth. Smart: "probably" is an indicator; such as "I", "you" "now" "then" "here", "there". A word that depends on the use situation. For a specific statement of fact is, if at all, true at all times, whether we know it or not, but even then it can be more or less probable, depending on the situation. So modality concept of probability finally ends in subjective ambiguity, like the modalities. Quine: Smart is an honest writer. Smart overcomes all moral dilemmas; the materialist takes the bull by the horns and effortlessly wins over the moralists!

Quine I
W.V.O. Quine
Word and Object, Cambridge/MA 1960
German Edition:
Wort und Gegenstand Stuttgart 1980

Quine XIII
Willard Van Orman Quine
Quiddities Cambridge/London 1987