Find counter arguments by entering NameVs… or …VsName.

The author or concept searched is found in the following 15 entries.

Disputed term/author/ism | Author |
Entry |
Reference |
---|---|---|---|

Consistency | Bigelow | I 182
Consistency/Bigelow/Pargetter: a way to guarantee that a description is consistent is to show that something meets this description.
>Satisfaction.Def Principle of instantiation/Bigelow/Pargetter: we can call this the principle of instantiation (instantiation principle). Contradiction-free/Bigelow/Pargetter: is essential for mathematics, for other areas it is more like housekeeping. >Instantiation. Consistency/Hilbert: precedes existence. A mathematical proof exists only if it is non-contradictory. >Consistency/Hilbert, >Existence/Hilbert, >Mathematics/Hilbert, >Proofs, >Provability. Consistency/FregeVsFormalism/FregeVsHilbert/Bigelow/Pargetter: Existence precedes the consistency. Consistency requires the existence of a consistently described thing. If it exists, the corresponding description is consistent. If it does not exist, how do we guarantee consistency? >Existence, >Mathematics. I 183
Frege/Bigelow/Pargetter: thinks here epistemically, in terms of "guarantees". But his view can be extended: if there is no object, there is no difference between a consistent and a contradictory description.
>G. Frege, >Foundation, >Formalism/Frege, >Truth/Frege, >Existence/Frege. Frege/Bigelow/Pargetter: pro Frege: this is the basis for modern mathematics. This is also the reason why quantum theory is so important: it provides examples of everything that mathematicians wish to investigate (at least until recently). >Sets, >Set theory. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |

Definitions | Frege | I 15
Definition/Frege: you cannot define: "The number one is a thing" because there is a definite on the one side of the equation and an indefinite article on the other.
>Equations, >Articles, >Definability.I 78
Definition/Frege: specifying a mode of operation is not a definition. I 99
Definition/Object/Introduction/Frege: the way in which an object was introduced is not a property of the object. >Introduction.
The definition of an object only specifies the use of a sign, it says nothing about the object. ((s) Here: introduction of an object in the speech = definition) Introduction/Frege: after the introduction, the definition turns into a judgment about the object. I 130
FregeVsFormalism: formalism only gives instructions for definitions, not definitions as such. >Formalism. I 131
E.g. Number i/Frege: you have to re-explain the meaning of "sum".
FregeVsFormalism/FregeVsHilbert: it is not enough to demand only one meaning. >Foundation.IV 100ff
Definition/Object/Frege: the definite article must be on both sides here. Defining an object only specifying the use of a sign. More interesting are definitions of properties. IV 100ff
Indefinable/Frege: truth and identity are indefinable as simple basic concepts. Other AuthorsVs. > truth theories, > theories of meaning.
>Truth theories, >Meaning theories. |
F I G. Frege Die Grundlagen der Arithmetik Stuttgart 1987 F II G. Frege Funktion, Begriff, Bedeutung Göttingen 1994 F IV G. Frege Logische Untersuchungen Göttingen 1993 |

Excluded Middle | Lorenzen | Berka I 271
Sentence of the excluded middle/Dialogical Logic/intuitionistic/logical constants/Lorenzen: If the particle is given its dialogical meaning also in the meta-language, then one can no longer generally prove the only classical valid A v i A.
>Dialogical logic, >Provability, >Metalanguage, >Logical particles, >Intuitionism.Solution/Gentzen: one considers the sequences with additional infinite rules: (n)A > B(n) v C > A > (x)B(x) v C (n)A u B(n) > C > A u (Ex)B(x) > C which are allowed for derivation. Axiom: all sequences are allowed as axioms A u p > q v B for false or true constant prime formulas p or q. >G. Gentzen. LorenzenVsRecursiveness/LorenzenVsFormalism: this is no longer a formalism in the sense of a definition of a recursive enumeration, but a "semi-formalism" (concept by Schütte). >Recursion, >Recursivity. Trivially, this is consistent. Any formula that can be derived from Peano's arithmetic is it also here. >Consistency. This is a "constructive" consistency proof, if the dialogical procedure is recognized as constructive. >Constructivism. I 272
Infinity/premisses/dialogical logic/Lorenzen: one can state a step number l < e0 to each formula that can be derived in the Peano formalism with the following:
e0 = ω to the power of ω to the power of ω to the power of ... P can thus first calculate an ordinal number e >Recursion. The statements that are used in the consistency proof are generally not recursive. ^{(1)}1. P. Lorenzen, Ein dialogisches Konstruktivitätskriterium, in: Infinitistic Methods, (1961), 193-200 |
Lorn I P. Lorenzen Constructive Philosophy Cambridge 1987 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |

Formalism | Bigelow | I 176
Symbol/blackening/Bigelow/Pargetter: some authors say that symbols are mere blackening on paper (e.g. numbers) or mere noises.
>Blackening of the paper.BigelowVsFormalism: Problem: on the one hand there are too many symbols then, on the other hand, too little. Too little: for very large numbers there is no corresponding blackening or noise. Too many: for smaller numbers there are too many different ways of representation, more than numbers are distinguished. E.g. "4", "four", "IV". >Stronger/weaker, >Strength of theories, >Numbers, >Numerals, >Inscriptions, >Universals. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |

Formalism | Frege | I 127
Sign/FregeVsFormalism: blank signs are only a blackening of the paper. Their use would be a logical error. Blank signs do not solve any task, e.g. x + b = c: if b > c, there is no natural number x, which can be used. To accept the difference (c - b) as an artificial new sign is no solution. Sign/Frege: where a solution is possible, it is not the sign that is the solution, but the meaning of the sign. I 130
FregeVsFormalism: formalism only offers instructions for definitions - not the definition itself. I 131
E.g. Number i: one has to re-explain the meaning of "sum" - FregeVsHilbert: it is not enough just to call for a sense.
Cf. >Foundation, >Content, >Sense, >Signs, >Symbols, >Equations, >Definitions, >Formalization, cf. >Introduction, >"tonk"/Belnap-Prior debate. |
F I G. Frege Die Grundlagen der Arithmetik Stuttgart 1987 F II G. Frege Funktion, Begriff, Bedeutung Göttingen 1994 F IV G. Frege Logische Untersuchungen Göttingen 1993 |

Formalism | Heyting | I 62
Formalism/Carnap/Heyting: there always remains the doubt, which conclusions are correct, and which are not (Carnap, 1934^{(1)}, S. 44; 1937^{(2)}, S. 51). I 66
"Letter"/darkness of the paper/formalism/Heyting: thesis of the "pragmatism" of mathematics: mathematics is a very simple thing, I take a few signs and give some rules how they are combined. Why should I prove them? They are made with regard to applications.
>Blackening of the paper, >Formalism, >Evidence, >Proofs, >Provability, >VsFormalism, cf. >Foundation.1. R. Carnap, Logische Syntax der Sprache, Wien 1934, p. 44. 2. R. Carnap, Testability and Meaning, in: Philosophy of Science 4, 1937, p. 51. |
Heyting I Arend Heyting "Disputation", in: Intuitionism, Amsterdam 1956 German Edition: Streitgespräch InKursbuch 8/1967, H. M. Enzensberger Frankfurt/M. 1967 Heyting II Arend Heyting Intuitionism: An Introduction (Study in Logic & Mathematics) 1971 |

Formalism | Lanier | I 42
Formalism/Code/Lanier: Bits do not mean anything as long as they are not interpreted by a person in the context of his culture.
>Code, >Interpretation, >Meaning, >Computer programming, >Software, >Computer, >Foundation, >VsFormalism. |
Lanier I Jaron Lanier You are not a Gadget. A Manifesto, New York 2010 German Edition: Gadget: Warum die Zukunft uns noch braucht Frankfurt/M. 2012 |

Formalism | Quine | XIII 63
Formalism/Quine: deduction is useful if you have previously doubted the truth of the result. XIII 64
For example, you can test a hypothesis by looking at the consequences of it.
Euclid: had difficulties to prove theorems, the truth of which nobody doubted anymore. Elegance/Science/Euclid: he already tried, for reasons of simplicity, to limit his postulates. Deduction/Problem/Quine: how can we prevent our already existing knowledge (about the objects ("what is true")) from creeping into the evidence? One tries to simulate ignorance, but what is the point? Knowledge/Truth/Quine/(s): To "know what is true" is more a knowledge of objects than of logic (see below). Disinterpretation/Reinterpretation/Interpretation/Tradition/Quine: one possibility was reinterpretation: in which it was assumed that the logical constants retained their meaning, but the other terms were merely regarded as provisional. And that in the theorem to be proved as well as in its consequences ((s) thus practically then in everyday use, everyday language). Pure Mathematics/Quine: this led many authors to regard their object as intrinsically uninterpreted. Pure Mathematics/Formalism/Russell: here we never know what we are talking about or if what we are saying is true. QuineVsFormalism/QuineVsRussell: in his favour, he has quickly forgotten that again. XIII 65
Pure Mathematics/Science/Quine: seems to be on a par with the other sciences. Pure arithmetic, for example, has to do with pure numbers that count objects, but also electrons in the economy.
Variables: go over numbers as well as over objects.Example: speed of light: here a relation is determined between a pure number (300,000) and light waves. Thereby not the number is emphasized as special, but the relation. Example: price: here the number is formed neither by the object, nor by the currency. ((s) Solution/((s): Relation instead of predicate.) Quine: relation instead of pure numbers and "pure object". QuineVsDisinterpretation/Disinterpretation/Quine: the purity of pure mathematics is not based on reinterpretation! Arithmetic/Quine: is simply concerned with numbers, not with objects of daily life. Abstract Algebra/Quine: if it exists, it is simply the theory of classes and relations. But classes and relations of all possible things, not only abstract ones. XIII 66
Logic/Quine: there was a similar problem as before with deduction, where we had to suspend our previous knowledge about objects: how can we suspend our previous knowledge about conclusions?
Solution/Frege/Tradition: again through disinterpretation, but this time of the particle. (>Formalism). Formalism/Quine: ironically, it spares us from ultimate disinterpretation. We can extend the conclusions allowed by our signs. We can be sure that they are not altered by the meanings of the signs. Frege/Russell/Principia Mathematica/Quine: the Principia Mathematica ^{(1)} was a step backwards from Frege's conceptual writing in terms of formalistic rigor.1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. |
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 InFrom a Logical Point of View, Cambridge, MA 1953 Quine VII (b) W. V. A. Quine Two dogmas of empiricism InFrom a Logical Point of View, Cambridge, MA 1953 Quine VII (c) W. V. A. Quine The problem of meaning in linguistics InFrom a Logical Point of View, Cambridge, MA 1953 Quine VII (d) W. V. A. Quine Identity, ostension and hypostasis InFrom a Logical Point of View, Cambridge, MA 1953 Quine VII (e) W. V. A. Quine New foundations for mathematical logic InFrom a Logical Point of View, Cambridge, MA 1953 Quine VII (f) W. V. A. Quine Logic and the reification of universals InFrom a Logical Point of View, Cambridge, MA 1953 Quine VII (g) W. V. A. Quine Notes on the theory of reference InFrom a Logical Point of View, Cambridge, MA 1953 Quine VII (h) W. V. A. Quine Reference and modality InFrom a Logical Point of View, Cambridge, MA 1953 Quine VII (i) W. V. A. Quine Meaning and existential inference InFrom 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 InZur 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 |

Identity | Brandom | I 619
Identity/FregeVsPeano/FregeVsFormalism: (axioms): identities as "1 = successor to the number 0" are trivial. >Formalism, ((s) For informative identity see identity between >intensions.) |
Bra I R. Brandom Making it exlicit. Reasoning, Representing, and Discursive Commitment, Cambridge/MA 1994 German Edition: Expressive Vernunft Frankfurt 2000 Bra II R. Brandom Articulating reasons. An Introduction to Inferentialism, Cambridge/MA 2001 German Edition: Begründen und Begreifen Frankfurt 2001 |

Intuitionism | Heyting | I 59ff
Intuitionism/Heyting: Brouwer studied the conceptual mathematical construction as such, without questioning the nature of things, for example, whether these things exist independently of our knowledge of them.
>L. Brouwer.I 60
Sentence of the excluded middle: e.g. the invalidity of the sentence of the excluded middle: if we compare the definitions of two natural numbers, k and l then:
(A) k is the largest prime number such that k 1 is also a prime number, if there is no such number, k = 1.(B) l is the largest prime number such that l 2 is also a prime number, if there is no such number, l = 1. Intuitionists reject (B) as a definition of an integer. K can be really calculated (k = 3), while we have no method of determining l, since it is not known whether the sequence of the prime number twins is infinite or not. The intuitionists regard something as well-defined only when a method of determination is given. >Law of the Excluded Middle, >Numbers. Classical mathematics: one can argue that the extent of our knowledge about the existence of the last twin is purely coincidental. And completely irrelevant in questions of mathematical truth. Existence/intuitionism/Heyting: the argument of the representative of classical mathematics is of a metaphysical kind. If existing does not mean "constructible", it must have a metaphysical meaning. Cf. >Constructivism. I 61
Classical mathematics/VsIntuitionism/Heyting: assuming that on January 1st, 1970, it is proved that there are infinitely many twins, l is equal to 1. Was that not already the case before the date (Menger, 1930)?
Intuitionism/Heyting: a mathematical assertion states that a certain construction is possible. Before the construction exists, the construction is not there. Even the intuitionists are convinced that mathematics is based on eternal truths in some sense, but when one attempts to define this meaning one gets entangled in metaphysics.>Metaphysics. I 62
Formalism/Carnap/Heyting: there always remains the doubt, which conclusions are correct, and which are not (Carnap, 1934^{(1)}, S. 44; 1937^{(2)}, S. 51).
>Correctness.I 63
Intuitionism: we are not interested in the formal side, but precisely in the nature of inferences in meta-mathematics. There is a fundamental ambiguity in the language.
Classical mathematics: the semanticists are even worse relativists than the formalists and intuitionists.Cf. >Semantic truth, >Truth conditions. I 65
Intuitionism: there is an intuitionist logic, e.g. transitivity. Conclusion: logic is a part of mathematics and therefore cannot be taken as its basis.
>Blackening of the paper, >Formalism, >Evidence, >Proofs, >Provability, >VsFormalism, cf. >Foundation. 1. R. Carnap, Logische Syntax der Sprache, Wien 1934, p. 44. 2. R. Carnap, Testability and Meaning, in: Philosophy of Science 4, 1937, p. 51. 3. Karl Menger. Der Intuitionismus. Blätter Für Deutsche Philosophie 4:311--325 (1930) |
Heyting I Arend Heyting "Disputation", in: Intuitionism, Amsterdam 1956 German Edition: Streitgespräch InKursbuch 8/1967, H. M. Enzensberger Frankfurt/M. 1967 Heyting II Arend Heyting Intuitionism: An Introduction (Study in Logic & Mathematics) 1971 |

Logic | Brandom | I 164
Logic/Brandom: is not only restrict to formally valid inferences.
BrandomVsFormalism: one should assume silent premises and implicit logic rules with everyone - Dummett: one should not define logical consequences in concepts of logical truth.I 167
Achilles and the tortoise/Carroll: however, some inferential definitions must be implied. - There must be rules, not only truths. >Rules.
---II 47
Tells us something about the conceptual contents task: not proving something - the formal accuracies are derived from the material accuracies, which contain much more non-logical vocabulary.
---I 175
Logic/Frege/Brandom: the task is an expressive one: not to prove something, but to say it - even in science concepts are formed arbitrarily - Goal: not a certain kind of truth but of inferences. I 176
Conceptual contents are considered to be identified through their inferential role - which requires that one can speak meaningfully about consequences, even before a specific logical vocabulary is introduced. >Inferential role. I 542
Logic/Brandom: the use of identity and quantifiers requires the use of singular terms and predicates.
>Quantifiers, >Singular terms, >Predicates.Terms (symmetric) must be interchangeable (identity) - predicates (asymmetric) must provide the frame for expressing incompatibilities - BrandomVsFormalism: Accuracies of inference are not always the same as logical correctness. --- II 24
Logic/tradition: bottom-up: from the analysis of the meanings of the singular terms to the judgments. II 25
Brandom, New: top-down: Pragmatism: first, the use of terms - ((s) always in complete sentences.) |
Bra I R. Brandom Making it exlicit. Reasoning, Representing, and Discursive Commitment, Cambridge/MA 1994 German Edition: Expressive Vernunft Frankfurt 2000 Bra II R. Brandom Articulating reasons. An Introduction to Inferentialism, Cambridge/MA 2001 German Edition: Begründen und Begreifen Frankfurt 2001 |

Numbers | Wittgenstein | II 32
Number/Wittgenstein: not a concept, but a logical form. II 283
Numbers/cardinal/Wittgenstein: that there are infinitely many cardinals, is a rule that one sets up. II 343
Number/Frege/WittgensteinVsFrege: a number is a property of a property. - Problem: E.g. for blue-eyed men in the room. - Then the five would be a property of a property - to be a blue-eyed man in the room - e.g. to express that Hans and Paul are two, they would then have a property in common, which not exactly belongs to the other. - ((s) each would have the property to be different from the other.) - Solution/Frege: the property of being Hans or Paul. II 344
Number/Wittgenstein: are not merely signs. - One can have two items of the form three, but only one number. - ((s) WittgensteinVsFormalism). >Formalism. II 360
Number/Definition/WittgensteinVsRussell: numerical equality is a prerequisite for a clear correspondence. - Therefore, Russell's definition of the number is useless. - ((s) Because it is circular reasoning if you want to define number via illustration). II 361
Definition/Wittgenstein: instead of a definition of "number" we must figure out the rules of usage. >Rules, >Use. II 415
Number/Russell/Wittgenstein: has claimed, 3 is a property that is common to all triads. - ((s) Frege: classes of classes - does Frege not mean objects with classes (instead of properties)?). II 416
Definition number/WittgensteinVsRussell: the number is an attribute of a function which defines a class, not a property of the extension. - E.g. Extension: it would be a tautology to say, ABC is three. - In contrast, meaingful: to say, in this room are three people. >Functions, >Extensions, >Sets.
---IV 93
Definition number/numbers/Wittgenstein/Tractatus: 6,021 - the number is the exponent of an operation.
Waismann I 66
Def Natural numbers/Wittgenstein: those to which induction can be applied in proofs. |
W II L. Wittgenstein Wittgenstein’s Lectures 1930-32, from the notes of John King and Desmond Lee, Oxford 1980 German Edition: Vorlesungen 1930-35 Frankfurt 1989 W III L. Wittgenstein The Blue and Brown Books (BB), Oxford 1958 German Edition: Das Blaue Buch - Eine Philosophische Betrachtung Frankfurt 1984 W IV L. Wittgenstein Tractatus Logico-Philosophicus (TLP), 1922, C.K. Ogden (trans.), London: Routledge & Kegan Paul. Originally published as “Logisch-Philosophische Abhandlung”, in Annalen der Naturphilosophische, XIV (3/4), 1921. German Edition: Tractatus logico-philosophicus Frankfurt/M 1960 Waismann I F. Waismann Einführung in das mathematische Denken Darmstadt 1996 Waismann II F. Waismann Logik, Sprache, Philosophie Stuttgart 1976 |

Possible Worlds | Goodman | II IX (Preface Putnam)
There are no "possible but not actual" worlds.
GoodmanVsFormalism: no formalism for the sake of formalism.>Formalism. GoodmanVsImagination: imagination is independent from our theorizing "ontological basement". >Imagination. II 78
We have become accustomed to see the real world as one of many possible. This needs to be corrected: all possible worlds are within the real.
---Putnam III 144
Versions/Goodman: it is not about different descriptions of "identical facts". Versions are unequal possible worlds and only incompatible versions must refer to different possible worlds - not different languages, so that tables sometimes as aggregates of time segments of molecules ... etc., but we decide to produce a corresponding world, e.g. "Big Dipper" was not created, but made a constellation.
PutnamsVsGoodman: this is a too daring extrapolation: that there was nothing what we have not created.III 147
PutnamVsGoodman: "Big Dipper" is not analytical: if a star perishes, we would further speak of the Big Dipper - but "star" has properties that cannot be accounted for by specifying a list - we cannot get to know this, by finding out what belongs to the Big Dipper.
Big Dipper: which stars are included, is rather answered by the linguist. PutnamVsGoodman: the term "constellation" is in the middle. The constellation remains when all the stars are light bulbs. PutnamVsGoodman: easy answer: we have not created the star Sirius ourselves. We have not made it a star and we have brought about the term star, and this term applies to Sirius. Our term of bachelor applies to "Joseph Ullian", without, however, that our language practice made him a bachelor. We create the concepts, but we do not cause them to be true. |
G IV N. Goodman Catherine Z. Elgin Reconceptions in Philosophy and Other Arts and Sciences, Indianapolis 1988 German Edition: Revisionen Frankfurt 1989 Goodman I N. Goodman Ways of Worldmaking, Indianapolis/Cambridge 1978 German Edition: Weisen der Welterzeugung Frankfurt 1984 Goodman II N. Goodman Fact, Fiction and Forecast, New York 1982 German Edition: Tatsache Fiktion Voraussage Frankfurt 1988 Goodman III N. Goodman Languages of Art. An Approach to a Theory of Symbols, Indianapolis 1976 German Edition: Sprachen der Kunst Frankfurt 1997 Putnam I Hilary Putnam Von einem Realistischen Standpunkt InVon 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) InVon 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 InVon 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. InVon 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. InVon einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (e) Hilary Putnam Reference and Truth InVon 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 InVon 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) InVon 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 InVon einem realistischen Standpunkt, Vincent C. Müller Reinbek 1993 Putnam I (i) Hilary Putnam Realism with a Human Face, Cambridge/MA 1990 InVon 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 InVon 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 InKünstliche 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 InTruth 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 InTheories of Truth, Paul Horwich Aldershot 1994 SocPut I Robert D. Putnam Bowling Alone: The Collapse and Revival of American Community New York 2000 |

Signs | Frege | II 31
Signs/Frege: as long as e.g. the plus sign is used only between integers ("a + b"), it only needs to be explained for this purpose. If other objects are to be linked, e.g. "sun" with something else, the plus sign must be redefined.
>Definition, >Definability, >Connectives, >Equal sign, >Copula.II 41
Frege: a sign is a proxy.
>Proxy.II 88
Numeral/Frege: e.g. "2" is saturated. In contrast: the functional character, e.g. "sin" (sine, sinus) is unsaturated. >Unsaturated. II 91
Sign/Frege: signs are the requirements for conceptual thinking - they no longer refer to the individual thing, but to what several things have in common.
I 127
Sign/FregeVsFormalism: empty signs are only black spots on paper. Their use would be a logical error. Empty signs do not solve any task. E.g. x + b = c: if b > c, there is no natural number x that can be inserted - nor to accept the difference (c - b) as an artificial new sign.
Sign/Frege: and where a solution is possible, the sign is not the solution, but the meaning of the sign. Husted V 130
FregeVsFormalism: formalism only gives instructions for definitions, not definitions themselves.
>Formalism.Frege I 131
E.g. Number i: the meaning of "total" must be re-explained.
FregeVsHilbert: it is not enough just to call for a sense. |
F I G. Frege Die Grundlagen der Arithmetik Stuttgart 1987 F II G. Frege Funktion, Begriff, Bedeutung Göttingen 1994 F IV G. Frege Logische Untersuchungen Göttingen 1993 Husted I Jörgen Husted "Searle" InPhilosophie im 20. Jahrhundert, A. Hügli/P. Lübcke Reinbek 1993 Husted II Jörgen Husted "Austin" InPhilosophie im 20. Jahrhundert, A. Hügli/P. Lübcke Reinbek 1993 Husted III Jörgen Husted "John Langshaw Austin" InPhilosophie im 20. Jahrhundert, A. Hügli/P. Lübcke Reinbek 1993 Husted IV Jörgen Husted "M.A. E. Dummett. Realismus und Antirealismus InPhilosophie im 20. Jahrhundert, A. Hügli/P. Lübcke (Hg) Hamburg 1993 Husted V J. Husted "Gottlob Frege: Der Stille Logiker" InPhilosophie im 20. Jahrhundert, A. Hügli/P. Lübcke (Hg) Reinbek 1993 |

Symbols | Bigelow | I 176
Symbol/blackening/Bigelow/Pargetter: some authors believe that symbols are mere blackenings on paper (e.g. numbers) or mere noises.
>Blackening of the paper, >Numbers, >Formalism.BigelowVsFormalism: Problem: on the one hand there are too many symbols and on the other hand there are not enough. Not enough: for very large numbers there is no corresponding blackening or noise. Too many: for smaller numbers there are too many different ways of representation, more than numbers can be distinguished. Example "4", "four", "IV". >Numerals, >Names of numbers, >Representation, >Presentation. |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |

Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
---|---|---|---|

Formalism | Frege Vs Formalism | Brandom I 606
FregeVsFormalists: How can evidence be provided that something falls under a concept? Frege uses the concept of necessity to prove the existence of an object. Brandom I 609
Free Logic: "Pegasus is a winged horse" is regarded as true, although the object does not exist physically. It can serve as substituent. FregeVs. (>Read). Brandom I 620
Frege: Pegasus has "sense" but no "meaning".
FregeVsFormalism: Important argument: it is not enough merely to refer to the Peano axioms, identities such as "1 = successor to the number 0" are trivial. They do not combine two different ways of picking out an object. Solution: Abstraction: it is necessary to connect the use of the expressions of the successor numbers with the already common expressions.Frege I 130
Equation/Frege: you must not put the definite article on one side of an equation and the indefinite article on the other.
FregeVsFormalism: a purely formal theory is sufficient. It’s only an instruction for the definitions, not a definition as such.I 131
Number System/Expansion/Frege: in the expansion, the meaning cannot be fixed arbitrarily.
E.g. the meaning of the square root is not already unchangeable before the definitions, but it is determined by these. ((s) Contradiction? Anyway, Frege is getting at meaning as use).Number i/Frege: it does not matter whether a second, a millimeter or something else is to play a role in this. I 132
It is only important that the additions and multiplication sentences apply. By the way, i falls out of the equation again.
But, E.g. with "a ´bi" you have to explain what meaning "total" has in this case. It is not enough to call for a sense. That would be just ink on paper. (FregeVsHilbert).Bigelow I 182
Consistency/FregeVsFormalism/FregeVsHilbert/Bigelow/Pargetter: Existence precedes consistency. For consistency presupposes the existence of a consistently described object. If it exists, the corresponding description is consistent. If it does not exist, how can we guarantee consistency?
Frege I 125
Concept/Frege: How can you prove that it does not contain a contradiction? Not by the determination of the definition. I 126
E.g. ledger lines in a triangle: it is not sufficient for proof of their existence that no contradiction is discovered in on their concept. Proof of the disambiguity of a concept can strictly only be carried out by something falling under it. The reverse would be a mistake. E.g. Hankel: equation x + b = c: if b is > c, there is no natural number x which solves the problem. I 127
Hankel: but nothing keeps us from considering the difference (c - b) as a sign that solves the problem! Sign/FregeVsHankel/FregeVsFormalism: there is something that hinders us: E.g. considering (2 - 3) readily as a sign that solves the problem: an empty sign does not solve the problem, but is only ink on paper. Its use as such would then be a logical error. Even in cases where the solution is possible, it is not the sign that is the solution, but the content.
Wittgenstein I 27
Frege/Earlier Wittgenstein/Hintikka: ((FregeVsFormalism) in the philosophy of logic and mathematics). Frege dispensed with any attempt to attribute a semantic content to his logical axioms and rules of evidence. Likewise, Wittgenstein: "In logical syntax, the meaning of a sign must never play a role, it may only require the description of the expressions." Therefore, it is incorrect to assert that the Tractatus represents the view of the inexpressibility of language par excellence. The inexpressibility of semantics is merely limited to semantics, I 28 syntax can certainly be linguistically expressed! In a letter to Schlick, Wittgenstein makes the accusation that Carnap had taken his ideas, without pointing this out (08.08.32)! |
F I G. Frege Die Grundlagen der Arithmetik Stuttgart 1987 F II G. Frege Funktion, Begriff, Bedeutung Göttingen 1994 F IV G. Frege Logische Untersuchungen Göttingen 1993 Bra I R. Brandom Making it exlicit. Reasoning, Representing, and Discursive Commitment, Cambridge/MA 1994 German Edition: Expressive Vernunft Frankfurt 2000 Bra II R. Brandom Articulating reasons. An Introduction to Inferentialism, Cambridge/MA 2001 German Edition: Begründen und Begreifen Frankfurt 2001 Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 W II L. Wittgenstein Wittgenstein’s Lectures 1930-32, from the notes of John King and Desmond Lee, Oxford 1980 German Edition: Vorlesungen 1930-35 Frankfurt 1989 W III L. Wittgenstein The Blue and Brown Books (BB), Oxford 1958 German Edition: Das Blaue Buch - Eine Philosophische Betrachtung Frankfurt 1984 W IV L. Wittgenstein Tractatus Logico-Philosophicus (TLP), 1922, C.K. Ogden (trans.), London: Routledge & Kegan Paul. Originally published as “Logisch-Philosophische Abhandlung”, in Annalen der Naturphilosophische, XIV (3/4), 1921. German Edition: Tractatus logico-philosophicus Frankfurt/M 1960 |

Formalism | Bigelow Vs Formalism | I 176
Symbol/Blackening/Bigelow/Pargetter: some authors say that symbols are mere blackening of the paper (e.g. numbers) or mere sounds.
BigelowVsFormalism: Problem: on the one hand, there are then too many symbols, on the other hand there are too few.too few: there is no corresponding blackening or noise for very large numbers. too many: for smaller numbers, there are too many different ways of representation, more than numbers is distinguished. E.g. "4", "four", "IV". |
Big I J. Bigelow, R. Pargetter Science and Necessity Cambridge 1990 |

Formalism | Barrow Vs Formalism | Barrow I 57
VsFormalism: every mathematical sentence is true in any mathematical system. Therefore formalism is a very unsatisfactory theory of mathematics. Besides, you have to change all the structures even if only one axiom changes. |
B I John D. Barrow Warum die Welt mathematisch ist Frankfurt/M. 1996 B II John D. Barrow The World Within the World, Oxford/New York 1988 German Edition: Die Natur der Natur: Wissen an den Grenzen von Raum und Zeit Heidelberg 1993 B III John D. Barrow Impossibility. The Limits of Science and the Science of Limits, Oxford/New York 1998 German Edition: Die Entdeckung des Unmöglichen. Forschung an den Grenzen des Wissens Heidelberg 2001 |

Formalism | Waismann Vs Formalism | Waismann I 76 ff
VsFormalism: does not bring a final clarification about the nature of arithmetic, because it pays attention to the structure one-sidedly and misses the examination of the terms. |
Waismann I F. Waismann Einführung in das mathematische Denken Darmstadt 1996 Waismann II F. Waismann Logik, Sprache, Philosophie Stuttgart 1976 |

Various Authors | Brandom Vs Various Authors | I 205
The approach advocated here is critical of three views: Vs
1) that the content is construed exclusively in accordance with the model of the representation of facts.2) that the quality of the inference solely according to the model of formal validity, 3) that rationality is construed only according to the model of reasoning based on means or purposes. I 338
Brandom: VsReductionism, Brandom pro Relativism I 340
Beliefs: make a difference for what we say and do. They can only be understood in a context of social linguistic practice.
First-person reflection is the internalization of third-person reflections. (Vs "privileged access").I 542
BrandomVsFormalism: of course it is not the case, that something would be propositional in content only by virtue of its relation to accuracies in the inferential practice. Formalistic error: equals all accuracies of inference with logical correctness. I 822
VsTradition: so far, a clear distinction could be made between semantics and pragmatics only by largely overlookeding anaphoric phenomena. I 826
BrandomVsTradition: instead of non-perspective facts one must pay attention only to the structural characteristics of score keeping practices. II 13
VsBrandom: characterized as super-rationalist by others. The meaning of it all stems from the role in language use. |
Bra I R. Brandom Making it exlicit. Reasoning, Representing, and Discursive Commitment, Cambridge/MA 1994 German Edition: Expressive Vernunft Frankfurt 2000 Bra II R. Brandom Articulating reasons. An Introduction to Inferentialism, Cambridge/MA 2001 German Edition: Begründen und Begreifen Frankfurt 2001 |

Various Authors | Goodman Vs Various Authors | I 81
GoodmanVsIntrinsic/Extrinsic: this does apparently not work: because in every classification of properties in extrins./intrins. each image or each object has both internal and external poperties. II Preamble Putnam IX
GoodmanVsFormalism for the Sake of Formalism.
GoodmanVsIdea of an ontological basement independent from our theorizingII 10
It is not true that science could do without unreal conditional clauses. The tendency to dismiss the problems of unr. conditional clauses as a pseudo-problem or unsolvable is understandable considering the great difficulties (GoodmanVs.) If you drop all problems of disposition, possibility, scientific law, confirmation, etc., then you are in fact giving up the philosophy of science. II 67
The argument that one should better dispense with the definition of an expression if it was not usually defined by scientists or laymen, is similar to the argument that philosophy need not be systematic, because the reality described by it is not systematic (VsAdorno). You might as well say that philosophy should not be in German, because the reality is not written in German. II 70
(s) SalmonVsGoodman: Objects do not need to appear at all times, but places must be there at all times! ((s) GoodmanVs: Description dependence for him does not only refer to objects, but to the whole of reality. (VsKant)) Kant: space and time are not reality, but the condition for the possibility to experience reality.
III 67 Presentation/Empathy/GoodmanVsEmpathy Theory: Gestures do not need to have features in common with music.III 81
Metaphor: the general question: What does a metaphor say and what makes it true? GoodmanVsMetaphor as abridged comparison: sometimes we say a metaphor is elliptically designed and the metaphorical truth was simply understood as the literal truth of the extended statement. But the comparison cannot just result in the image of the person being similar in one respect or another. In this way, everything is similar to everything. III 224
GoodmanVs"Special Aesthetic Emotion" - GoodmanVs Theory that it does not depend on the pleasure that one has, but on a certain "objectified pleasure": Goodman: Then the pleasure would be something that the object must have, and indeed rather without causing it; ultimately it would therefore probably have to feel this pleasure itself. III 228
GoodmanVsDichotomy between the Cognitive and the Emotional. It blocks the insight that emotions work cognitively in the aesthetic experience. |
G IV N. Goodman Catherine Z. Elgin Reconceptions in Philosophy and Other Arts and Sciences, Indianapolis 1988 German Edition: Revisionen Frankfurt 1989 Goodman I N. Goodman Ways of Worldmaking, Indianapolis/Cambridge 1978 German Edition: Weisen der Welterzeugung Frankfurt 1984 Goodman II N. Goodman Fact, Fiction and Forecast, New York 1982 German Edition: Tatsache Fiktion Voraussage Frankfurt 1988 Goodman III N. Goodman Languages of Art. An Approach to a Theory of Symbols, Indianapolis 1976 German Edition: Sprachen der Kunst Frankfurt 1997 |

Disputed term/author/ism | Pro/Versus |
Entry |
Reference |
---|---|---|---|

Platonism | Pro | Quine Lauener XI 136
Platonism: Quine reluctantly, but QuineVsFormalism/QuineVsHilbert |
Q XI H. Lauener Willard Van Orman Quine München 1982 |

Formalism | Versus | Quine Lauener XI 136
Platonism: Quine reluctantly, but QuineVsFormalism/QuineVsHilbert |
Q XI H. Lauener Willard Van Orman Quine München 1982 |