Find counter arguments by entering NameVs… or …VsName.
The author or concept searched is found in the following 10 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Connectives | Logic Texts | Read III 268 ff Tonk/Prior/Read: Do not introduce the link first and then assign meaning. - That cannot have the consequence that another pair of statements is equivalent. >Definition, >Definability, >"Tonk", >Belnap-Prior debate. Important argument: analytic validity cannot show that. Re III 269 The meaning, even that of logic links, must be independent of and be prior to the determination of the validity of the inference structures. - BelnapVsPrior: (pro analytical validity): Must not define into existence, first show how it works. Re III 271 Classical negation is illegitimate here. >Negation- Negation-free fragment. - Peirce's law: "If P, then Q, only if P, only if P". Re III 273 ReadVsBelnap: the true disagreement lies beyond constructivism and realism. - Belnap's condition (conservative extension) cannot show that the classical negation is illegitimate. >Negation. Hoyningen-Huene II 56 Connectives/Hoyningen-Huene: You sometimes read that the truth tables would define the conncetives, i.e. clearly specify them. This is correct if one interprets the connectives in a very specific mathematical sense (namely as illustrations of two statements in the set true, false). If, on the other hand, one understands the connectives as extensional statement links, i.e. as operators that form a new statement from two statements, then the truth tables do not define the connectives. II 66 Binding strength of the connectives: increases in the following order: ,>, v, ∧. II 113 It makes sense to attribute equality and difference to the propositional logical form, because the compelling force of propositional logical inference depends on them. For the same reason, it makes sense to assign the connectives to the propositional logical form. |
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 St. Read Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press German Edition: Philosophie der Logik Hamburg 1997 |
| Conservativity | Brandom | I 199 Conservativity/Extension/Language/Tonk/Brandom: pro conservative extension: if the rules are not inferentially conservative, they allow new material inferences and can change the contents that were associated with the old vocabulary - expressive logic/Brandom: requires that no new inferences that contain only old vocabulary are rendered appropriate (if they have not been previously). I 200 E.g. "boche"/Dummett: non-conservative extension: statements that do not contain the expression (!) could be inferred from others that do not contain the expression either - E.g. conclusion from German nationality to cruelty. BrandomVsDummett: this is not about non-conservativity: it only shows that the expression "boche" has a content which is not contained in the other expressions - e.g. the term "temperature" has also changed with the methods of measurement - it s not about the novelty of a concept, but about unwanted conclusions. I 204 Especially the material content of concepts is lost when the conceptual content is identified with the truth-conditions. >Content, >Conceptual content, >Truth conditions. |
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 |
| Definitions | Logic Texts | Hoyningen-Huene II 56 Def/truth value table/junctor/Hoyningen-Huene: the tables define the junctors only if they are understood mathematically - not if they are understood extensionally. >Extensionality, >Truth table, >Connective, >Logical constant. Hoyningen-Huene II 93 Definition/Hoyningen-Huene: Synthetic: here a concept is created (abbreviation) - it cannot be true/false. Analytical: descriptive or lexical definition: here, an existing concept is analyzed - e.g. bachelor/ unmarried man. Explication: is between analytical and synthetic definition - This can be more fruitful. >Explanation, >Analytic/synthetic. --- Read III 40 The definition of truth is different from the adequacy conditions. III 265 Prior: "tonk": does not define connections first and then meaning. >tonk- Then it cannot cause another pair of statements to be equivalent. - N.B.: "analytical validity" cannot show this - BelnapVsPrior: (pro analytical validity): should not get mixed with the definition of existence, it first has to show how it works -> classical negation is illegitimate here. - Negation-free fragment - > Peirce's law: "If P, then Q, only if P, only if P": --- Salmon I 252 Some words must be defined in non-linguistic ways. I 254 Context definition: many logical words are explained by context definition. E.g. "All F are G" is equal to "Only F are G" This is a definition of the word "only". |
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 St. Read Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press German Edition: Philosophie der Logik Hamburg 1997 Sal I Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 German Edition: Logik Stuttgart 1983 Sal II W. Salmon The Foundations Of Scientific Inference 1967 SalN I N. Salmon Content, Cognition, and Communication: Philosophical Papers II 2007 |
| 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 |
| Introduction | Belnap | Brandom II 94 Def "tonk"/logical particle/Belnap: 1. Rule: licenses the transition from p to p tonk q for any q. 2. Rule: licenses the transition from p tonk q to q. Thus we have a "network map for inferences": any possible conclusion is allowed! >Definitions, >Definability, >Conclusions, >Inferences, >Logical constants, >Connections. II 93 Conservativity/Conservative Expansion/Dummett: If a logical constant is introduced by introduction and elimination rules, we may call it a conservative extension of language. >Conservativity. II 94 For example, this might be true of Belnaps "tonk": the introduction rule of the disjunction and the elimination rule of the conjunction. >Disjunction, >Conjunction. PriorVsBelnap/PriorVsGentzen: this is the bankruptcy of definitions in the style of Gentzen. BelnapVsPrior: if one introduces logical vocabulary, one can restrict such definitions by the condition that the rule does not allow inferences with only old vocabulary that was not already allowed before the introduction of the logical vocabulary. (Conservative expansion). Such a restriction is necessary and sufficient. >Expansion, >Sufficiency. Brandom: the expressive analysis of the logical vocabulary provides us with a deep reason for this condition: only in this way the logical vocabulary can perform its expressive function. The introduction of new vocabulary would allow new material inferences without the constraining condition (conservativity) and would thus change the contents correlated with the old vocabulary. >Vocabulary, >Content, cf. other entries for >"tonk". |
Beln I N. Belnap Facing the Future: Agents and Choices in Our Indeterminist World Oxford 2001 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 |
| Meaning | Logic Texts | Read III 269 Meaning: the meaning, even the logical connectives, must be independent of and before the determination of the validity of the concluding structures. >Validity, >Conncetive, >Logical constant. ((s) See also problems in relation to an arbitrary definition of a connective: "tonk".) III 275 It is denied that truth, understood as a prove-transcendental concept, can be the central concept in the theory of meaning. Such a cthe doncept of truth (the realist, independent of knowledge) could not play a role in the concept of meaning. We must be able to manifest it with our use. (> Anti-Realism/Dummett). |
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 St. Read Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press German Edition: Philosophie der Logik Hamburg 1997 |
| Meaning (Intending) | McGinn | I 104 Meaning/reference/McGinn: when I use the word "red", I mean something in particular, and that is different from what I mean with other words. >Reference, >Meaning, >Intention, >Intentionality. I 106 Whoever masters the meaning of the word, has never seen the vast majority of the corresponding objects. >Language acquisition. Infinity is created from the outset in the intentionality. That is just the joke of meaning. The meaning allows us to access places, times and distances that cannot be approached by the body and the senses. If one means something with a word, one does not host an isolable element in the stream of mental processes, because the intended meaning does not behave like pain. The meaning does not spread in a medium, in which the individual things are lined up. It is even more important that meaning is diffuse. I 109 It is impossible, to mean something with one word, without that it would be determined what is considered the right expression for this word. (((s) See also the problems in relation to the artificial connective > "tonk".) The intended meaning is the one instance that permits the formation of true or false statements. I 118 Tradition: we know what we mean. >Belief. McGinnVsPrivileged access/meaning: this is a mistake: it may be that we know something of a description, without being able to subordinate it to other descriptions that the immediate known in a theoretical view is perhaps not understandable to us. |
McGinn I Colin McGinn Problems in Philosophy. The Limits of Inquiry, Cambridge/MA 1993 German Edition: Die Grenzen vernünftigen Fragens Stuttgart 1996 McGinn II C. McGinn The Mysteriouy Flame. Conscious Minds in a Material World, New York 1999 German Edition: Wie kommt der Geist in die Materie? München 2001 |
| Quotation Marks | Geach | Problem: this cannot be replaced salva veritate by "Robinson", because "it" then becomes senseless. - in the original also not replaceable by "a book", because then it is also senseless. >Senseless. I 110f Fake predicate/fake token/Geach: the philosopher whose disciple (was) Plato was bald - fake: "Plato was bald" - Example: "A philosopher smoked and drank whisky": fake token: "a philosopher smoked"..."and he (or the philosopher (!)) drank... >Predicates, cf. >Pronouns, >Reference. I 110f Fake event/Geach: the philosopher, whose student was Plato, was bald. False: "Plato was bald". E.g. "A philosopher smoked and drank whiskey": false: "A philosopher smoked" - "and he (or the philosopher!) drank ... Solution: "casus": two smoking philosophers, one of which does not drink - sentence does not show which is true - but no psychologizing: ("what the speaker thought of" -) what he said is true, even if not all thoughts were true. False question: to what the subject refers to: "he" or "this philosopher" is not a subject at all. - "And" (conjunction) connects here two predicates, not two sentences. Def fake predicate: if the question is irrelevant to what it is applied to - for example, "everyone loves him or herself" can be true even if "every man loves ---" does not appeal to anyone. -> Anaphora. I 189f Equivalence/Biconditional/GeachVsBlack: "is material equivalent" is not synonymous with "iff and only if" - "three-dash" ≡ is often read as "material equivalent" - equivalence exists only between sentences, not between names of sentences. - Problem: "Tom loves Mary ↔ Mary loves Tom" is only designating when "↔" (three-dash, ≡) is read as "exactly when" and not as "material equivalent". I 199/200 Quotation marks/Geach: E.g. Carnap: If "A" is false, then for every "B" "A > B" is true (quotation marks only on the outside) - This does not contain "B", but "B" directly included in inverted commas. >Variables / >Constants. I 208 Quotation marks/Geach: not a functor that makes the name "Cicero" out of an expression, but an indicator that creates an intentional point of argument into which "Cicero" is inserted. - Thus, iterated quotes have no place in our logic: "name of a name": false. Solution: simple symbol, e.g. "tonk" for the name "Cicero". - Then e.g. for an x, [Tonk] is a name of [x] and [x] is a proper name. - Quasi-quotation: is not a name. >Quasi-Quotation. |
Gea I P.T. Geach Logic Matters Oxford 1972 |
| Validity | Logic Texts | Salmon I 41 Validity/W.Salmon: affects arguments (= groups of statements), not individual statements. Menne I 25 Menne: We become aware of laws through experience, but that does not mean that their validity is based on experience. Hoyningen-Huene II 100 Propositional logic: Validity of conclusions of propositional logic: conditions: 1. The validity of the conclusion depends on the multiple occurrence of certain (partial) statements. II 101 2. The validity is dependent on certain junction points occurring in it. 3. The validity is independent of the sense of the (partial) statements. II 102 Def Truth transfer/Hoyningen-Huene: positive: the truth of the premises guarantees the truth of the conclusion. 4. The validity of the conclusion requires truth transfer, i.e. that a true premise conjunction never occurs together with a false conclusion. >Truth transfer, Predicate logic: II 229 Adequacy conditions 1. The validity of the conclusion depends on the multiple occurrence of predicates (which refer to the same range of individuals) and possibly the logical constants (from the same range of individuals). II 230 2. The validity depends on the quantifiers and possibly the connectives that occur. 3. The validity is independent of the sense. 4. Validity requires truth transfer. >Connective, >Sense, >Quantifier, >Logical constant. Read III 71 Validity/Read: Problems: VsClassical logic: Classical logic does not succeed in including as valid those inferences whose correctness is based on the connections between non-logical expressions. If an object is round, then it follows that it is not square. But this conclusion is not valid thanks to its form, but thanks to its content. Logical Universe: Problem: one can find inferences whose invalidity can only be seen by looking at a larger universal range of definitions. ((s) See also Problems with the introduction of new connectives: >tonk.) |
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 Sal I Wesley C. Salmon Logic, Englewood Cliffs, New Jersey 1973 German Edition: Logik Stuttgart 1983 Sal II W. Salmon The Foundations Of Scientific Inference 1967 SalN I N. Salmon Content, Cognition, and Communication: Philosophical Papers II 2007 Me I A. Menne Folgerichtig Denken Darmstadt 1997 Re III St. Read Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press German Edition: Philosophie der Logik Hamburg 1997 |
| Vocabulary | Brandom | I 199 Conservativeness/Expansion/Language/Tonk/Brandom: pro conservative expansion: if the rules are not inferentially conservative, they allow new material inferences and thus change the contents that were associated with the old vocabulary expressive logic/Brandom: requires that no new inferences that only contain old vocabulary be rendered appropriate by this (if they were not before). >Conservatity. I 200 E.g. "boche"/Dummett: non-conservative extension, statements that do not (!) contain the expression might now be inferred from others that do not contain it either E.g. inference from German nationality to cruelty BrandomVsDummett: this is not about non-conservatism: it only shows that the expression "boche" has a content which is not contained in the other expressions E.g. the cocnept "temperature" has also changed with the methods of measurement. It's not about novelty of a concept, but undesirable inferences. >Concepts, >Words. I 204 In particular the material content of concepts is lost when the conceptual content is identified with the truth conditions. >Truth conditions. I 427/8 Definition Supervenience/Brandom: one vocabulary supervenes another if and only if there could be no two situations in which true assertions (i.e. facts) would differ expressably in the supervening vocabulary, while the true assertions do not differ expressably in the vocabulary that is being supervened more neutral: if it is clear what is defined in one language, then it is clear what is defined in the other. >Supervenience. I 958 Order/Twin Earth/TE/Brandom: it does not help to speak in concepts of what can be distinguished by the individuals, because what they can react depends on which reactions are considered to be different, and then the same problem occurs with regard to the vocabulary used Problem: specifying a vocabulary that satisfies two conditions: 1) The twins are indistinguishable in different environments because of their description in that vocabulary (physical language is not sufficient for that). 2) The sub-determination of the semantic properties of their states in this limited vocabulary must point at something interesting. --- II 76 Material inference/Sellars/Brandom: from "a east of b" to "b west of a" also from flash to thunder, needs no logic. II 79 Formally valid ones can be derived from good material inferences, but not vice versa Proof: if a subset of somehow privileged vocabulary is given, such an inference is correct if it is materially good and it cannot become a bad one if non-privileged vocabulary is replaced by privileged vocabulary. If one is only interested in logical form, one must be able to distinguish a part of the vocabulary as a especially logical beforehand. E.g. if one wants to explore theological inferences, one must investigate which replacement of non-theological vocabulary with non-theological preserves the material quality of the inference. II 94 Definition "tonk"/Belnap: Rule 1): licenses the transition from p to p tonk q for any q. Rule 2): licenses the transition from p tonk q to q. With that we have a "network map" for inferences: any conclusion is thus permitted. PriorVsBelnap: Bankruptcy of all definitions in the style of Gentzen. BelnapVsPrior: Solution: Restriction: no inferences with only old vocabulary that were not allowed previously,otherwise the old contents would be changed retrospectively. |
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 |
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| Disputed term/author/ism | Author Vs Author |
Entry |
Reference |
|---|---|---|---|
| Belnap, Nuel | Prior Vs Belnap, Nuel | Brandom I 198 "Tonk": (Belnap) PriorVsBelnap: bankruptcy of definitions of the inferential roles in the style of Gentz. "Network card for arbitrary conclusions". (>"Boche"/Dummett; > conservative extension). Prior: "tonk": Do not start by introducing the link first and then the meaning - cannot have the consequence that another pair of statements is equivalent - Important Argument: "analytical validity" cannot show this - BelnapVsPrior: (per analytical validity): must not define into existence, first show how it works. Normal >negation is illegitimate - >negation-free fragment; - Peirce's law: If P,then Q or, if Q only if P, then R. Prior: thesis: it is absurd to assume an "analytical validity", a "carte blanche", to introduce a possibility link and then to give them a meaning by simply determining it. His well-known example was "tonk". Absurd: how can the simple introduction of a new link have the consequence that any pair of statements (without "tonk") is equivalent? III 269 If we learned what "tonk" meant, we would see that one or another inference is not truth-preserving. But, and that's Prior's point: the representative of the view of the analytical validity cannot say this, because he has no independent explanation of the meaning of "tonk" with respect to which he could show that the conclusions are invalid. Meaning: the meaning, even that of logic links, must be independent of and prior to the determination of the validity of the inference structures! (>BelnapVsPrior). |
Pri I A. Prior Objects of thought Oxford 1971 Pri II Arthur N. Prior Papers on Time and Tense 2nd Edition Oxford 2003 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 |
| Belnap, Nuel | Read Vs Belnap, Nuel | Re III 270 Belnap: we have not shown, and cannot show that there is such a link. The same applies for "tonk". Read: One problem remains: why is there ever an analogy between definitions and links. It cannot always be wrong to expand a language with new links. Calculation rules for 'conservative' extensions of languages are conceivable. The old rules must persist. Re III 271 Peirce's Law: (>Peirce): "If P, then Q, or if Q only if P, then R" is negation-free, but still not, as the constructivist claims, part of the negation-free fragment (>Gentzen). The law cannot be proved within the classical calculus without using classic negation rules. Re III 273 The crucial step in all cases is certainly that the implication "If P, then Q or R" from "If P then Q or R" (Note: the comma is missing here) is allowed. A step which foresees the establishment of the multiple conclusion, the LK, and not the establishment of the individual conclusion. (Peirce's Law: "If P, then Q or, if Q only if P, then R") The constructivist objects against such a step, because he introduces a disjunction in a way that does not guarantee that you know which member of the disjunction is the justification! ReadVsBelnap: The true disagreement lies beyond constructivism and realism. Belnap's condition (conservative extension) cannot show that the classical negation is illegitimate. |
Re III St. Read Thinking About Logic: An Introduction to the Philosophy of Logic. 1995 Oxford University Press German Edition: Philosophie der Logik Hamburg 1997 |
| Hilbert | Frege Vs Hilbert | Berka I 294 Consistency/Geometry/Hilbert: Proof through analogous relations between numbers. Concepts: if properties contradict each other, the concept does not exist. FregeVsHilbert: there is just nothing that falls under it. Real Numbers/Hilbert: here, the proof of consistency for the axioms is also the proof of existence of the continuum.(1) 1. D. Hilbert, „Mathematische Probleme“ in: Ders. Gesammelte Abhandlungen (1935) Bd. III S. 290-329 (gekürzter Nachdruck v. S 299-301) Thiel I 279 Hilbert: Used concepts like point, line, plane, "between", etc. in his Foundations of Geometry in 1899, but understood their sense in a hitherto unfamiliar way. They should not only enable the derivation of the usual sentences, but rather, in its entirety, specify the meaning of the concepts used in it in the first place! Thiel I 280 Later this was called a "definition by postulates", "implicit definition" >Definition. The designations point, line, etc. were to be nothing more than a convenient aid for mathematical considerations. FregeVsHilbert: clarifies the letter correspondence that his axioms are not statements, but rather statement forms. >Statement Form. He denied that by their interaction the concepts occurring in them might be given a meaning. It was rather a (in Frege’s terminology) "second stage concept" that was defined, today we would say a "structure". HilbertVsFrege: the point of the Hilbert’s proceeding is just that the meaning of "point", "line", etc. is left open. Frege and Hilbert might well have been able to agree on this, but they did not. Frege: Axiom should be in the classical sense a simple, sense-wise completely clear statement at the beginning of a system. Hilbert: statement forms that combined define a discipline. From this the "sloppy" figure of speech developed E.g. "straight" in spherical geometry was then a great circle. Thiel I 343 Formalism: 1) "older" formalism: second half of the 19th century, creators Hankel, Heine, Thomae, Stolz. "Formal arithmetic", "formal algebra". "Object of arithmetic are the signs on the paper itself, so that the existence of these numbers is not in question" (naive). Def "Permanence Principle": it had become customary to introduce new signs for numbers that had been added and to postulate then that the rules that applied to the numbers of the original are should also be valid for the extended area. Vs: that would have to be regarded as illegitimate as long as the consistency is not shown. Otherwise, you could introduce a new number, and E.g. simply postulate § + 1 = 2 und § + 2 = 1. This contradiction would show that these "new numbers" did not really exist. This explains Heine’s formulation that "existence is not in question". (> "tonk"). Thiel I 343/344 Thomae treated the problem as "rules of the game" in a somewhat more differentiated way. FregeVsThomae: he had not even precisely specified the basic rules of his game, namely the correlation to the rules, pieces and positions. This criticism of Frege was already a precursor of Hilbert’S proof theory, in which also mere character strings are considered without regard their possible content for their production and transformation according to the given rules. Thiel I 345 HilbertVsVs: Hilbert critics often overlook that, at least for Hilbert himself, the "finite core" should remain content-wise interpreted and only the "ideal", not finitely interpretable parts have no directly provable content. This important argument is of a methodical, not a philosophical nature. "Formalism" is the most commonly used expression for Hilbert’s program. Beyond that, the conception of formalism is also possible in a third sense: i.e. the conception of mathematics and logic as a system of action schemes for dealing with figures that are free of any content. HilbertVsFrege and Dedekind: the objects of the number theory are the signs themselves. Motto: "In the beginning was the sign." Thiel I 346 The designation formalism did not come from Hilbert or his school. Brouwer had hyped up the contrasts between his intuitionism and the formalism of Hilbert’s school to a landmark decision. |
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 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 T I Chr. Thiel Philosophie und Mathematik Darmstadt 1995 |
| Prior, A. | Belnap Vs Prior, A. | Brandom I 198 BelnapVsPrior: if you introduce logical vocabulary, you must restrict such definitions by the condition that the rule does not allow inferences containing only old vocabulary. This means that the new rules must extend the repertoire conservatively. > Example "boche". Brandom: if these rules are not inferentially conservative, they allow new material inferences and thus change the contents associated with the old vocabulary. The expressive concept of logic requires that no new inferences containing only old vocabulary be made appropriate. Conservativity/Conservative Extension/Dummett: if a logical constant is introduced by introduction and elimination rules, we can call this a conservative extension of language. Brandom II 93 For example, this could apply to Belnap's "tonk": introduction rule of the disjunction and elimination rule of the conjunction: Def "tonk"/Belnap: 1. Rule: licenses the transition from p to p tonk q for any q. 2. Rule: licenses the transition from p tonk q to q. With this we have a "network card for inferences": any inference is allowed! Brandom II 94 PriorVsBelnap/PriorVsGentzen: this is the bankruptcy of definitions in Gentzen's style. BelnapVsPrior: if you introduce logical vocabulary, you can restrict such definitions by the condition that the rule does not allow inferences with only old vocabulary that were not allowed before the introduction of the logical vocabulary. Such a restriction is necessary and sufficient. Brandom: the expressive analysis of the logical vocabulary now gives us a deep reason for this condition: only in this way can the logical vocabulary perform its expressive function. The introduction of new vocabulary would allow new material inferences without the restrictive condition (conservatism) and would thus change the contents correlated with the old vocabulary. ((s) retroactive change, also of the truth values of established sentences). Read: meaning: the meaning, even the logical connections, must be independent of and prior to the determination of the validity of the consequent structures. Logic III 269 Belnap: came to the aid of the view of "analytical validity". What it lacks, he said, is any proof that there is such a connection as "tonk" at all. This is a problem for definitions in general. One cannot define into existence. First of all you have to show that there is such a thing (and only 1). Example "Pro-Sum" of two fractions. (a/b)!(c/d) is defined as (a+c)/ (b+d). If you use numbers, you will quickly come to results that produce completely wrong results. Although it is easy to find originally matching numbers, they cannot be shortened.(> Dubislav). Logic III 270 Belnap: we have not shown, and cannot show, that there is such a connection. The same applies to "tonk". Read: one problem remains: why is there any analogy at all between definitions and links? One problem remains: why is there an analogy between definitions and links at all. It cannot always be wrong to extend a language with new links. One could imagine calculation rules for "conservative" extensions of languages. The old rules must continue to exist. |
Beln I N. Belnap Facing the Future: Agents and Choices in Our Indeterminist World Oxford 2001 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 |
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The author or concept searched is found in the following theses of the more related field of specialization.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| tonk | Prior, A. | Read Logik III 268 Prior: Thesis: it is absurd to assume an "analytical validity", a "carte blanche", to introduce a possibility linkage and then to give them a meaning by simply defining them. His well-known example was "tonk". III 269 Absurd: how can the simple introduction of a new linkage result in any pair of statements (without "tonk") being equivalent? If we were to experience what "tonk" meant, we would see that one or the other conclusion is not truth-preserving. But and this is Prior's point: The analytic validity advocate cannot say that because he has no independent explanation of the meaning of "tonk" regarding which he could show that the inferences are invalid. |
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