Find counter arguments by entering NameVs… or …VsName.
The author or concept searched is found in the following 6 entries.
| Disputed term/author/ism | Author |
Entry |
Reference |
|---|---|---|---|
| Connectives | Brandom | II 87 Connectives/Gentzen/Brandom: connectives are defined according to their inferential role. (Epoch-making): Definition Introduction rules: sufficient conditions for the use of the connective - Definition elimination rules: necessary consequences of the use (of the connective). E.g. in order to define the inferential role of "&" in Boole you indicate that everyone who is defined on p and q thus has to be regarded as defined on p&q as well - the first part without the connective specifies the circumstances, i.e. the sets of the premises. >Cf. >Logical constants. --- II 88 Dummett transferred this to sentences, singular terms and predicates - it may be that we do not overlook all connections - conservative extension: by these two rules. Dummett |
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 |
| 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 |
| Equivalence | Field | l 159 Equivalence/Platonism/Nominalism/Field: Question: in what sense are platonist (E.g. "Direction1 = direction2") and nominalistic statements (c1 is parallel to c2) equivalent? >Platonism, >Nominalism. Problem: if there are no directions, the second cannot be a consequence of the first. - They are only equivalent within a directional theory. Cf. >Definition/Frege, >Consequence. Solution/Field: one can regard the equivalences as important, even if the theories are wrong. Problem: for the meaning one should be able to accept truth. >Meaning. Solution: conservative extension (does not apply to the ontology) - this is harmless for consequences that do not mention directions. >Conservativity/Field, >Mention. I 228 Def cognitively equivalent/Field: equivalent by logic plus the meaning of "true". >Truth. Disquotational true/Deflationism: means that the propositions in the Tarski scheme should be cognitively equivalent. - ((s) Plus meaning of true here: the same understanding of true.) >Disquotationalism/Field, >Deflationism. --- II 16 Extensional equivalence/Field: Problem: if we assume extensional equivalence and abstract it from the size, there are infinitely many entities to which a simple theory, such as the chemical valences applies: For example, the number 3 not only applies to molecules but also to larger aggregates etc. >Reference classes. II 106 Redundancy theory/Field: an utterance u and the assertion that u is true (as the speaker understands it) are cognitively equivalent. >Redundancy theory, >Utterance. N.B.: the assertion that an utterance is true, has an existential obligation (ontological commitment): there must be something that is true. >Ontological commitment. While the utterance u itself does not provide an ontological obligation. Therefore, the two are not completely cognitively equivalent. Relatively cognitively equivalent: here: u and the assertion of the truth of u are cognitively equivalent relative to the existence of u. II 106 E.g. "Thatcher is so that she is self-identical and snow is white" is cognitively equivalent to "snow is white" relative to the existence of Thatcher - the verification conditions are the same. N.B.: we do not need any truth conditions. >Verification conditions, >Truth conditions. II 252 Material Equivalence/Field: means that A > B is equivalent to ~ A v B. Problem: most authors do not believe the conclusion of e.g. "Clinton will not die in office" on "When Clinton dies in office, Danny de Vito becomes President". Therefore equivalence does not seem to exist. Solution/Lewis: the truth conditions for indicative conditionals must be radically index-dependent to maintain the surface logic. >Conditionals. Lewis: thesis: the surface logic should not be respected. Lewis: thesis: E.g. Clinton/Vito: truth-maintaining despite absurdity. Solution: probability function: P (Vito I Clinton). >Probability function. II 253 In the case of the indicative conditional, the premise is always presupposed. Adams: intuitively, conclusions with conditionals are correct. >Conditional/Adams. Problem: then they will say less about the world. >Empiricism. |
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 |
| 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 |
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 |
| Dummett, M. | Brandom Vs Dummett, M. | I 202 BrandomVsDummett: if he see the problematic aspect of the concept "boche" in that it causes a non-conservative extension of the remaining language, it is not right. The non-conservativity merely shows that the concept has a substantial content which was not already included in other concepts. E.g. Temperature: was introduced with certain criteria, with the introduction of new measurement methods, the complex inferential definition developed that determines the significance of today (> Measuring). Introduction: it is not to be asked if the conclusions were already accepted, but whether this conclusion is one that should be accepted! The problem with "boche" and "nigger" is not the novelty, but the unwanted conclusions. Brandom II 173 But there are other ways of justification than showing that we’ve already been on them determined implicitly, even before the term was introduced. Background of material inferential practices. Frege, late: sentences are singular terms! Predicates: frames. (DummettVsFrege: this disregards the specific nature of the sentences of being able to be moves in the language game BrandomVsDummett:. As if Frege had no idea about Fregian power). |
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 |
| Field, H. | Burgess Vs Field, H. | Field I 133 BurgessVs Field: a Gödel’s construction can not be performed in N0. This means that there is a nominalist sentence that is undecidable in N0, but at the same provable in P0. Therefore, N0 cannot be a conservative part theory of P0. And this also shows that P0 can never have any nominalistic part theories as conservative extensions. |
Burgs I J. P. Burgess Logic, Logic, and Logic Boston 1999 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 |
| 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 |
| Quine, W.V.O. | Field Vs Quine, W.V.O. | I 129 Nominalism/Philosophy of Science/FieldVsQuine-Putnam Argument: An argument to show that nominalistic resources are adequate for good science would be: (E) For each Platonic scientific theory there is a nominalist theory to which the Platonic one is a conservative extension. But this is trivial if there are no restrictions regarding which sets of sentences that have been completed under a logical entailment count as theories. Of course, any Platonic theory T is a conservative extension of the "theory" which consists of nominalistic inferences from T. We have to reinforce (E) so that uninteresting nominalistic theories are excluded. Science Without Numbers: here I did not argue with (E). (E) or any amplifying extension is an existence assertion of a sufficiently wide variation of nominalist theories, and that goes beyond the assertion of the conservatism of mathematical theory. I 241 Conservatism/Mathematics/Field: Truth does not require conservatism! True empirical theories are obviously not conservative! But conservatism is certainly also recognized by most realists for mathematics. For they say that good mathematics is not only true, but necessarily true! Conservatism/Field: (see above) conservative mathematics has the properties of necessary truth, without having to be true itself! Quine: is a realist in terms of mathematics. He wants to nip talk of mathematical necessity in the bud. But for that he needs conservatism. FieldVsQuine: for that he would have to make a major renovation to his thesis that mathematics continuously flows into the rest of the other sciences. Logic/Empiricism/Quine: Thesis: logic could be empirically refuted. Conservatism/Field: The fact that mathematics is empirically refuted is consistent with that, while the logic remains intact. IV 407 Internal Realism/IR/Existence/Ontology/Property/Putnam: what kind of objects exist can only be decided within a theory, according to the IR. FieldVsPutnam: I’m not sure I understand what he means. I suppose he thinks there are several correct theories that answer the question of ontology differently. But this is too trivial. sharper: (Put p 72 74.) two equally correct theories may have different ontologies. PutnamVsRedundancy Theory: does not offer an explanation of our understanding. FieldVsPutnam: this implied neither mind-independence nor theory-dependence, however! And it does not refute the correspondence theory. E.g. you can explain the behavior of electrically charged bodies with or without the assumption of fields. Ontology/Existence/Field: most of us would say that there is more than we are forced to assert. FieldVsQuine: E.g. is rarely critical to assert the existence of unseparated rabbit parts in addition to the existence of rabbits. FieldVsPutnam: if this is clear, then you can hardly draw anti-realistic conclusions from the fact that two equally good theories may differ in ontology. |
Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
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