Find counter arguments by entering NameVs… or …VsName.
The author or concept searched is found in the following 3 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 |
| 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, >Connectives. 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 |
| 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 |
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Reference |
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| 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 |
| 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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