MCMP – Logic

Karolina Krzyżanowska (MCMP) gives a talk at the MCMP Colloquium (13 May, 2015) titled "What is Wrong with the Ramsey Test". Abstract: According to an influential idea of Frank Ramsey, known as the Ramsey Test, evaluating an indicative conditional, “If A then C,” amounts to evaluating the conditional’s consequent, C, on the supposition of its antecedent, A. This idea inspired a popular view among contemporary philosophers and psychologists that the only thing we learn when someone asserts a conditional is that the speaker believes the conditional’s consequent to be highly probable on the supposition that its antecedent holds. Though prima facie intuitively appealing and to a great extent supported by empirical data, theories of conditionals based on the Ramsey Test alone fail to account for the connection between a conditional’s antecedent and its consequent, forcing us to yield acceptable and assertable conditionals as bizarre as “If Shakespeare did not write Anna Karenina, then raccoons are American mammals noted for their intelligence.” I will argue for a theory that takes the connection between conditionals' antecedents and their consequents seriously.

Hartry Field (NYU) gives a talk at the MCMP Colloquium (21 May, 2015) titled "Caie's Paradox of Credence". Abstract: Call a sentence ‘contradictory’ if it together with acceptable assumptions entails absurdities, and ‘paradoxical’ if it and its negation are both contradictory in this sense. There are plausible examples of paradoxical sentences: e.g. Liar sentences that assert their own untruth. What should our credence be in paradoxical sentences? There is a seemingly compelling argument that it should be interval-valued: in the case of non-empirically paradoxical sentences, our credence should be the full unit interval [0,1]. But Michael Caie has raised the issue of how to handle doxastic paradoxes. These paradoxes raise problems for the above view about appropriate credence. I’m not sure how best to deal with Caie’s examples; the talk will be a somewhat inconclusive exploration of this issue.

Teresa Kouri (Ohio State) gives a talk at the MCMP Colloquium (21 May, 2015) titled "Connective Meanings in Beall and Restall's Logical Pluralism". Abstract: I will show that there is a problem with the meanings of the connectives as presented in Beall and Restall's Logical Pluralism. In their system, they claim that $\neg$ in constructive logic and $\neg$ in relevant logic are one and the same. I show this cannot be, given how they have defined the meaning of a logical connective. I suggest that this type of problem is typical of a certain way of thinking about the meanings of connectives, and gesture towards an alternate route to logical pluralism which does not encounter such problems.

Hartry Field (NYU) gives a talk at the MCMP Colloquium (20 May, 2015) titled "Indicative Conditionals, Restricted Quantification, Naïve Truth". Abstract: Truth is "naive" if for eternal sentences S, the attribution of truth to S is equivalent to S. Kripke’s theory of truth (the Kleene based version) shows how to get naive truth for very simple languages. After some motivation, I will sketch how to extend a broadly Kripkean approach to a language with a variably strict conditional operator, of the kind that Stalnaker and others have used to represent ordinary indicative conditionals of English. Also, to show how to combine this with a different conditional operator to handle restricted quantification. Previous attempts at logics for restricted quantification compatible with naive truth have mostly led to very impoverished logics. The only exception is a 2014 paper by me, but it was based on an ad hoc and unmotivated construction. This talk shows how to get a good logic for naive truth and restricted quantification in a much better-motivated way.

Karolina Krzyżanowska (MCMP) gives a talk at the MCMP Colloquium (13 May, 2015) titled "What is Wrong with the Ramsey Test". Abstract: According to an influential idea of Frank Ramsey, known as the Ramsey Test, evaluating an indicative conditional, “If A then C,” amounts to evaluating the conditional’s consequent, C, on the supposition of its antecedent, A. This idea inspired a popular view among contemporary philosophers and psychologists that the only thing we learn when someone asserts a conditional is that the speaker believes the conditional’s consequent to be highly probable on the supposition that its antecedent holds. Though prima facie intuitively appealing and to a great extent supported by empirical data, theories of conditionals based on the Ramsey Test alone fail to account for the connection between a conditional’s antecedent and its consequent, forcing us to yield acceptable and assertable conditionals as bizarre as “If Shakespeare did not write Anna Karenina, then raccoons are American mammals noted for their intelligence.” I will argue for a theory that takes the connection between conditionals' antecedents and their consequents seriously.

Jack Woods (Bilkent) gives a talk at the MCMP Colloquium (23 April, 2015) titled "Revision and Logical Neutrality (or, a Plea for Ecumenical Reasons)". Abstract: What reasons are there for revising our logic? One natural suggestion is that we should move from a logical theory L to L′ when L′ does “better” than L in terms of “simplicity, ontological leanness (Occam’s razor), explanatory power, a low degree of ad hocness, unity, [and] fruitfulness.” (Priest 2006, 147) This is to apply relatively familiar standards of scientific theory choice, such as inference to the best explanation, to the case of logic. There are special difficulties in the case of logic, however, since our choice of a logical theory impacts the background theory in which we carry out theory choice. It is by no means obvious that we can have a logically neutral account of how L and L′ meet these criteria. Certain ways of developing these criteria are not logically neutral as I show. And, given that they are not, there is a serious epistemic worry about the permissibility of using such reasons. Or, anyways, so I shall argue.

Alexander Paseau (Oxford) gives a talk at the MCMP Colloquium (23 April, 2015) titled "Capturing Consequence". Abstract: What reasons are there for revising our logic? One natural suggestion is that we should move from a logical theory L to L′ when L′ does “better” than L in terms of “simplicity, ontological leanness (Occam’s razor), explanatory power, a low degree of ad hocness, unity, [and] fruitfulness.” (Priest 2006, 147) This is to apply relatively familiar standards of scientific theory choice, such as inference to the best explanation, to the case of logic. There are special difficulties in the case of logic, however, since our choice of a logical theory impacts the background theory in which we carry out theory choice. It is by no means obvious that we can have a logically neutral account of how L and L′ meet these criteria. Certain ways of developing these criteria are not logically neutral as I show. And, given that they are not, there is a serious epistemic worry about the permissibility of using such reasons. Or, anyways, so I shall argue.

Peter Verdée (Université catholique de Louvain) gives a talk at the MCMP Colloquium (16 April, 2015) titled "On Relevance of Entailment in a Classical Logic Context". Abstract: In this talk I present a logic that aims to determine whether implications in a classical logic context express a relevant connection between antecedent and consequent. Just like in the relevance logic tradition, the connective '->' is added to the language of classical logic as a formalisation of the relevant entailment relation in the object language (without nesting restrictions). The recursively enumerable set of theorems of the logic is defined by a set of axioms closed under a number of rules and the principle of uniform substitution. Unlike the logics in the relevance logic literature, the presented logic leaves classical negation intact in the sense that the law of non-contradiction can be used to obtain relevant implications, as long as there is a connection between antecedent and consequent. In order to realise this strengthening of traditional relevance logics, the traditional requirement that a theory of relevance should also define a new standard of deduction is given up. I present and argue for a list of requirements such a logical theory of relevant entailment in classical contexts needs to meet. I then formulate the system by presenting its axiomatisation and an algebraic semantics and demonstrate that it respects each of these requirements. This system is conceived by means of a translation into the relevant logic R and by presupposing an asymmetric treatment of symbols that occur in antecedents and symbols that occur in consequents. I moreover will give a philosophical motivation for our non-standard relevant implication and the asymmetric interpretation of antecedents and consequents. Finally I argue that there is no a priori reason to require that a successful formal theory of relevant entailment should also be a successful formal theory of (the standard of) deduction.

Alexander Paseau (Oxford) gives a talk at the MCMP Colloquium (23 April, 2015) titled "Capturing Consequence". Abstract: What reasons are there for revising our logic? One natural suggestion is that we should move from a logical theory L to L′ when L′ does “better” than L in terms of “simplicity, ontological leanness (Occam’s razor), explanatory power, a low degree of ad hocness, unity, [and] fruitfulness.” (Priest 2006, 147) This is to apply relatively familiar standards of scientific theory choice, such as inference to the best explanation, to the case of logic. There are special difficulties in the case of logic, however, since our choice of a logical theory impacts the background theory in which we carry out theory choice. It is by no means obvious that we can have a logically neutral account of how L and L′ meet these criteria. Certain ways of developing these criteria are not logically neutral as I show. And, given that they are not, there is a serious epistemic worry about the permissibility of using such reasons. Or, anyways, so I shall argue.

Jack Woods (Bilkent) gives a talk at the MCMP Colloquium (23 April, 2015) titled "Revision and Logical Neutrality (or, a Plea for Ecumenical Reasons)". Abstract: What reasons are there for revising our logic? One natural suggestion is that we should move from a logical theory L to L′ when L′ does “better” than L in terms of “simplicity, ontological leanness (Occam’s razor), explanatory power, a low degree of ad hocness, unity, [and] fruitfulness.” (Priest 2006, 147) This is to apply relatively familiar standards of scientific theory choice, such as inference to the best explanation, to the case of logic. There are special difficulties in the case of logic, however, since our choice of a logical theory impacts the background theory in which we carry out theory choice. It is by no means obvious that we can have a logically neutral account of how L and L′ meet these criteria. Certain ways of developing these criteria are not logically neutral as I show. And, given that they are not, there is a serious epistemic worry about the permissibility of using such reasons. Or, anyways, so I shall argue.