MCMP – Logic

Michael Friedman (Stanford) gives a talk at the MCMP workshop "Carnap on Logic" (3-6 July, 2013) titled "From Intuition to Tolerance in Carnap's Philosophy of Mathematics". Abstract: I plan to discuss the evolution of Carnap's views on arithmetic and geometry from Der Raum, through the Aufbau period, to Logical Syntax and the semantic period. I will concentrate on the way in which he consistently distinguished the two cases -- where geometry, in Der Raum, is explicitly tied to spatial intuition, and then, even though it remains distinguished from arithmetic, its ties to spatial intui- tion become empirical rather than a priori. The character of Carnap's generally tolerant attitude towards philosophical disputes in the foundations of mathematics thereby changes as well. Carnap's attitude towards intuition in the arithmetical case, finally, becomes clarified in his exchange with E. W. Beth in the Schilpp volume -- and this clarifies his application of the principle of tolerance in this case as well.

Bjørn Jespersen (TU Ostrava) gives a talk at the MCMP Colloquium (24 October, 2013) titled "Qualifying quantifying-in". Abstract: If you know that Munich is a city, does it follow that there is an individual x and a property f such that you know that x is an f? Similarly, if you find the millionth digit of the decimal expansion of π, does it follow that there is a number y such that you find y? It does, provided the rule of existential generalization extends to so-called non-extensional contexts like those involving attitudes and modalities. I argue that EG must apply to all contexts, since the rule essentially serves to make explicit ontological commitments already implicit in the premise. Nor do non-extensional contexts cripple the rule of substitution of identicals. The law is universally valid, but its substituends must be chosen more carefully. This talk presents an extensional logic of hyperintensions that validates quantifying into hyperintensional contexts and quantifying over hyperintensions and intensions (functions from possible worlds), though not always also over extensions, due to non-factive attitudes. The talk also explains how to obtain universal transparency, i.e. a context-invariant theory of meaning and reference, by universalizing Frege’s semantics for oblique contexts. The background theory is Transparent Intensional Logic, formally a hyperintensional, partial, typed λ-calculus. TIL conceptualizes hyperintensions as structured procedures detailing how to produce an extension or intension, or even another hyperintension. My focus will be on hyperintensional attitudes, i.e. those whose complements are individuated finer than up to logical equivalence. The talk summarizes the latest results on the details of the logic of quantifying-in.

Michael Dunn (Bloomington) gives a talk at the MCMP Colloquium (25 June, 2013) titled "Arrows, Relevance, and Relations*". Abstract: The van Benthem-Venema "arrow logics" are abstractly well-motivated and have epistemic applications, e.g., to the logic of information flow and information update. I explore the relationships between the van Benthem-Venema semantics for arrow logics and the Routley-Meyer semantics for relevance logics, and show that there is a translation between the two. I will also briefly discuss the relationship to Barwise’s (1993) logic of "channels." I compare van Benthem’s version of the semantics for arrow logic aimed at relation algebras with my own generalization of the Routley-Meyer semantics aimed at the same target. I use my (1993, 2001) representation of relation algebras based on Routley-Meyer frames to give an equivalent representation of relation algebras based on frames for arrow logic. A philosophical interpretation is given to this representation as showing that each element of a relation algebra can be interpreted as a set of relations (not as a single relation –Lyndon showed this is impossible). This interpretation is thus a type level higher than the natural interpretation of an element as just a relation, and can be viewed in terms of interpreting each element as a relational database. The operations of a relation algebra can then be interpreted as operations combining relational databases.

Martin Fischer (MCMP/LMU) gives a talk at the MCMP workshop "Truth and Paradox" (24-25 May, 2013) titled "Truth and Speed-up".

Thomas Schindler (MCMP/LMU) gives a talk at the MCMP workshop "Truth and Paradox" (24-25 May, 2013) titled "Truth and Paradox".

David Ripley (Melbourne) gives a talk at the MCMP workshop "Truth and Paradox" (24-25 May, 2013) titled "Contractions of noncontractive consequence".

Lionel Shapiro (Connecticut) gives a talk at the MCMP workshop "Truth and Paradox" (24-25 May, 2013) titled "Naive Sequent Structure, Contraction and Paradox".

Johannes Stern (MCMP/LMU) gives a talk at the MCMP workshop "Truth and Paradox" (24-25 May, 2013) titled "Necessities and Necessary Truths. A Proof-Theoretic Addendum".

Thomas Schindler (MCMP/LMU) gives a talk at the MCMP workshop "Truth and Paradox" (24-25 May, 2013) titled "Truth and Paradox".

Sebastian Lutz (MCMP/LMU) gives a talk at the MCMP workshop "Carnap on Logic" (3-6 July, 2013) titled "On Carnap on Empirical Significance".