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 |
|---|---|---|---|
| Articles | Russell | Cresswell I 179 Definite Article/theory of descriptions/Russell: requiring that a sentence e.g. "the φ is ψ" provided that "the φ" has a wide range, entails that there exists a unique φ. >Scope, >Narrow scope, >Wide Scope. Russell I X Russell/Gödel: (K.Gödel, Preface to Principia Mathematica) Russell avoids any axioms about the particular articles "the", "the", "that". - Frege, on the other hand, must make an axiom about it! The advantage for Russell, however, remains only as long as he interprets definitions as mere typographical abbreviations, not as the introduction of names. >Proxy, >Names, >Logical proper names, >Axioms, Typographical abbreviation: >"blackening of the paper", >Formalism. |
Russell I B. Russell/A.N. Whitehead Principia Mathematica Frankfurt 1986 Russell II B. Russell The ABC of Relativity, London 1958, 1969 German Edition: Das ABC der Relativitätstheorie Frankfurt 1989 Russell IV B. Russell The Problems of Philosophy, Oxford 1912 German Edition: Probleme der Philosophie Frankfurt 1967 Russell VI B. Russell "The Philosophy of Logical Atomism", in: B. Russell, Logic and KNowledge, ed. R. Ch. Marsh, London 1956, pp. 200-202 German Edition: Die Philosophie des logischen Atomismus In Eigennamen, U. Wolf (Hg) Frankfurt 1993 Russell VII B. Russell On the Nature of Truth and Falsehood, in: B. Russell, The Problems of Philosophy, Oxford 1912 - Dt. "Wahrheit und Falschheit" In Wahrheitstheorien, G. Skirbekk (Hg) Frankfurt 1996 Cr I M. J. Cresswell Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988 Cr II M. J. Cresswell Structured Meanings Cambridge Mass. 1984 |
| Calculus | Bernays | Thiel I 20 Formalism ("linguistic turnaround"): a) calculus-theoretical variant/Bernays: what is the mathematician's work? b) Structure-theoretical variant/Hilbert: different systems can be interpreted as valid in the same object area. >Formalism, cf. >FregeVsHilbert, >Formalism/Frege, cf. >Blackening of the paper. |
T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 |
| Definitions | Gödel | Berka I 367 Definition/Goedel: all definitions are abbreviations and therefore in principle superfluous.(1) >Concepts, >Meaning, >Terms, >Expressions, >Formulas, >Formalism, >Blackening of the paper, >Symbols, >Signs, >Distinctions. 1. K. Gödel: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Mh. Math. Phys. 38 (1931), pp. 175-198. |
Göd II Kurt Gödel Collected Works: Volume II: Publications 1938-1974 Oxford 1990 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
| Entailment | Geach | I 174 Entailment/Quine/Geach: Quine used "implies" instead of "entails". >Implication. Geach: Entailment requires nouns. Quotes are nevertheless noun-similar. >Quote. Entailment requires quotes to include sentences. >Quotation marks. GeachVsPropositions: "entails": is an artificial word; instead you can also use "an if". Example: "A. if Russell is a brother, Russell is male" That avoids looking at partial sentences as a blackening of the paper (letters). - (Otherwise "The proposition that Russell is a Brother ..."). >Blackening of the paper, >Proposition. I 180 Entailment/Geach: truth conditions: thesis: "p entails q" if and only if there is an a priori possibility to know that Cpq, which is not to find out whether either p or q is true. >Truth conditions. Problem: that implies a possibility that we have: "p" is false and "it is possible to find out that p" is true. One can know necessary things without facts and without conceptual analysis. >Necessity. Lewy's First Paradox: Entailment cannot be fully transitive. >Transitivity. I 183 Entailment/Lewy's 1. Paradox: Summary: 1. One can know a priori that Cpq without knowing p v q. 2. one can know a priori that Cqr without knowing p v r. We can conclude from these premises: Conclusion: one can know a priori that Cpr. N.B.: but we cannot add safely: without knowing ("which is not a way to find out") whether p v r. We have the a priori way of finding out that Cpr, derived from our a priori knowledge that Cpq and that Cqr. But that does not allow to answer if p, and figure out that Cqr allows not to figure out whether r. If the truth table provides the same truth values anyway, you cannot speak of a link. There is no reason to believe that we have any knowledge a priori that both Cp(Kpq) and C(Kpq)r, and such that Cpr, with the exception of a priori knowledge, that r. Therefore, there is no reason to believe p entails r. I 184 Transitivity/Geach: Entailment is not transitive, but validity of evidence is transitive. >Validity, >Evidence. FitchVs: Evidence is not transitively valid in order to solve paradoxes of set theory. >Paradoxes, >Set theory. |
Gea I P.T. Geach Logic Matters Oxford 1972 |
| 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 | Geach | I 173 Characters/Geach: a mere coloring of the paper (Graphic occurrence) can not be true or false. >Blackening of the paper, >Formalism, >Foundation, >Truth value, >FregeVsHilbert. |
Gea I P.T. Geach Logic Matters Oxford 1972 |
| 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 In Kursbuch 8/1967, H. M. Enzensberger Frankfurt/M. 1967 Heyting II Arend Heyting Intuitionism: An Introduction (Study in Logic & Mathematics) 1971 |
| Formalism | Wittgenstein | VI 119 Formalism/Substitute/Sign/Symbol/WittgensteinVsFrege: Frege: characters are either mere blackening or signs of something - then what they represent, is their meaning - Wittgenstein: false alternative - E.g. chess pieces: represent nothing. Solution: use like in the game instead of representation of something. - ((s) Use is more than mere blackening of the paper and less than representation of an object). Wittgenstein: formalism is not entirely unjustified. >Blackening of the paper, >Mathematics, >Representation, >Rules; cf. >FregeVsHilbert. |
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 |
| 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 In Kursbuch 8/1967, H. M. Enzensberger Frankfurt/M. 1967 Heyting II Arend Heyting Intuitionism: An Introduction (Study in Logic & Mathematics) 1971 |
| Knowledge | Kosslyn | I 264 Knowledge/Kosslyn/Pomerantz: it only makes sense to speak of knowledge in a context in which there is any processing of internal representations, - Paper with characters has no knowledge itself. >Representation, >Knowledge representation, >Presentation, cf. >Blackening of the paper, >Code. Stephen M. Kosslyn/James R. Pomerantz, Imagery, Propositions and the Form of Internal Representations”, Cognitive Psychology 9 (1977), 52-76 |
Kosslyn I Stephen M. Kosslyn James R. Pomerantz "Imagery, Propositions, and the Form of Internal Representations", in: Cognitive Psychology 9 (1977), 52-76 In Kognitionswissenschaft, Dieter Münch Frankfurt/M. 1992 |
| Language | Prior | I 106 Def well-organized language/Prior: here the overall sentence has no meaning if a clause has no meaning. >Clauses, >Sentences, >Meaning, >Reference. E.g. The name "Baf" shall specify the blackening of the paper: (clause) "something that means x is true" if that does not mean that it is wrong, then it means nothing at all. Solution: a set must be able to have multiple meanings at the same time. >Buridan: truth. |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 |
| 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 |
| Theoretical Entities | Craig | Field III 43 Theoretical Entities/Craig/Field: Re-interpretation of the sciences without theoretical entities. >Theoretical entities. FieldVsCraig: in contrast to numbers, these can very well be causally relevant, e.g. electrons. >Causality, >Causal relation, >Causation, >Measurements. Fraassen I 206 Craig/Craig's Theorem: we eliminate theoretical entities and replace a theory T by a description of an infinitely complex regularity which contains all the observation consequences of the original theory. >Regularities, >Description. The original theory is then finally axiomatized. Craig's transformation is infinitely axiomatized. >Axioms, >Axiom systems. SmartVsCraig: if the theory were only blackening, it would be a cosmic coincidence if the transformation were to work with names of theoretical entities instead of the theoretical entities themselves. >Blackening of the paper, >Cosmic coincidence. So the alleged recourse would only be the postulation of a coincidence. This means we do not need to go to infinity. >Regress, >Infinity, >Randomness. |
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 Fr I B. van Fraassen The Scientific Image Oxford 1980 |
| Word Meaning | Deacon | I 59 Word Meaning/Deacon: it is not the case that words differ from other signals by chance or conventionally. I 60 Tradition: assumes that there are two kinds of referential or meaningful relations: a) transparent: here a similarity between the signal (word, picture, sign) and the object addressed (icon) works >Icons. b) opaque: this resemblance is missing here. Instead, additional knowledge about the code is required. >Symbol. Icon: Refers to similarity characteristics between the sign (word, sound, image) and the object. (Transparency). >Similarity. Symbol: refers without such similarity, instead a code has to be learned. (Opacity). Signal: is simply a sign that is physically correlated with other objects without considering the semantics. >Signal, >Semantics. >Index, >Petrol gauge example, Dretske. I 62 Reference: Examples such as the > twin earth show that reference does not generally need something like meaning to be determined. >Twin Earth, >Reference, >H. Putnam. Reference/Solution/DeaconVsPutnam: what makes inanimate things such as blackening of the paper or a sign on the screen meaningful is an interpretation of which a crucial part really... I 63 (even if not everything) happens „in the head“. Reference is not intrinsic "in the" word (noise, gesture), but reference is formed by a kind of response to it. Cf. >"Meanings are not in the head"/Putnam. >Reference/Deacon, > Interpretation/Deacon, >Intrinsicness, >Words, >Subsententials, cf. >Sentences. |
Dea I T. W. Deacon The Symbolic Species: The Co-evolution of language and the Brain New York 1998 Dea II Terrence W. Deacon Incomplete Nature: How Mind Emerged from Matter New York 2013 |
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| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| 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 |
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