Value

Book Symposium: Dunin-Kozicka Commentary and Reply

Monika Dunin-Kozicka (née Chylinska) is a lecturer in philosophy and cognitive science at the John Paul II Catholic University of Lublin, Poland. Her areas of research include pretense, creativity, imagination and counterfactuals. This week at The Junkyard we’re hosting a symposium on Piotr Kozak’s recent book: Thinking in Images: Imagistic Cognition and Non-propositional Content. On Monday, we began with an introduction from Piotr Kozak. Commentaries follow Tuesday through Thursday.* * *Can we be creative in using rulers and thinking in images?And why even ask such an odd question? First, any time when we use rulers we recreate an old simple procedure — we apply the ruler to the thing to be measured and read the standardized measurement results. We are substantially uncreative then. Second, when we think in images our chances to come up with something new are good — for not only can we operate with images in many ways (e.g. rotating them, combining them, seeing them from a different perspective) but we can also arrive at a new image as a result of such operations. Indeed, we can be original when thinking in images. Why even put rulers and images together in this question then?For those already familiar with Piotr Kozak’s Thinking in Images, collating a ruler (or a balance) with an image should not be such an eccentricity, for the author of the book — a proponent of the so-called measurement-theoretic account of thinking with images — directly says: “…thinking with images is a skill in using... -

Comparing Rules for Identity in sequent systems and natural deduction

Abstract: It is straightforward to treat the identity predicate in models for first order predicate logic. Truth conditions for identity formulas are given by a natural clause: a formula s = t is true (or satisfied by a variable assignment) in a model if and only if the denotations of the terms s and t (perhaps relative to the given variable assignment) are the same. On the other hand, finding appropriate rules for identity in a sequent system or in a natural deduction proof setting leaves a number of questions open. Identity could be treated with introduction and elimination rules in natural deduction, or left and right rules, in a sequent calculus, as is standard for familiar logical concepts. On the other hand, since identity... -

Collection Frames for Distributive Substructural Logics

We present a new frame semantics for positive relevant and substructural propositional logics. This frame semantics is both a generalization of Routley–Meyer ternary frames and a simplification of them. The key innovation of this semantics is the use of a single accessibility relation to relate collections of points to points.... -

Structural Rules in Natural Deduction with Alternatives

Natural deduction with alternatives extends Gentzen–Prawitz-style natural deduction with a single structural addition: negatively signed assumptions, called alternatives. It is a mildly bilateralist, single-conclusion natural deduction proof system in which the connective rules are unmodified from the usual Prawitz introduction and elimination rules–the extension is purely structural. This framework is... -

Recent Sites Posting In Value

All Posts in Value

Structural Rules in Natural Deduction with Alternatives Natural deduction with alternatives extends Gentzen–Prawitz-style natural deduction with a single structural addition: negatively signed assumptions, called alternatives. It is a mildly bilateralist, single-conclusion natural deduction proof system in which the connective rules are unmodified from the usual Prawitz introduction and elimination rules–the extension is purely structural. This framework is general: it can be used for (1) classical logic, (2) relevant logic without distribution, (3) affine logic, and (4) linear logic, keeping the connective rules... Consequently.org -

Collection Frames for Distributive Substructural Logics We present a new frame semantics for positive relevant and substructural propositional logics. This frame semantics is both a generalization of Routley–Meyer ternary frames and a simplification of them. The key innovation of this semantics is the use of a single accessibility relation to relate collections of points to points. Different logics are modeled by varying the kinds of collections used: they can be sets, multisets, lists or trees. We show that collection frames on... Consequently.org -

Questions, Justification Requests, Inference, and Definition In this paper, I examine connections between the speech acts of assertion, denial, polar questions and justification requests, and the common ground. When we pay attention to the structure of norms governing polar questions, we can clarify the distinction between strong and weak denial, together with the parallel distinction between strong and weak assertion, and the distinct way that these speech acts interact with the common ground. In addition, once we pay attention to the... Consequently.org -

Comparing Rules for Identity in sequent systems and natural deduction Abstract: It is straightforward to treat the identity predicate in models for first order predicate logic. Truth conditions for identity formulas are given by a natural clause: a formula s = t is true (or satisfied by a variable assignment) in a model if and only if the denotations of the terms s and t (perhaps relative to the given variable assignment) are the same. On the other hand, finding appropriate rules for identity in... Consequently.org -

Natural Deduction with Alternatives: on structural rules, and identifying assumptions Abstract: In this talk, I will introduce natural deduction with alternatives, explaining how this framework provides a simple, well-behaved, single conclusion natural deduction system for a range of logical systems, including classical logic, (classical) linear logic, relevant logic and affine logic, in addition to the familar intuitionistic restrictions of these systems. Each of these proof systems have identical connective rules. As we expect in substructural logics, different logical systems are given by varying the structural rules in play. The distinctly... Consequently.org -

Platonism, Nominalism, Realism, Anti-Realism, Reprentationalism, Inferentialism and all that My usual talk (a close-up view of the Old Quad and Arts West at the University of Melbourne). Abstract: In this talk, I will place contemporary research in philosophical logic in a wider historical and philosophical context, showing how recent work in logic connects to the rivalry between Platonism and Nominalism, or realism and anti-realism in metaphysics, and between representationalism and inferentialism in the the philosophy of language. Along the way, I will touch on... Consequently.org -

Comparing Rules for Identity in Sequent Systems and Natural Deduction Abstract: It is straightforward to treat the identity predicate in models for first order predicate logic. Truth conditions for identity formulas are straightforward. On the other hand, finding appropriate rules for identity in a sequent system or in natural deduction leaves many questions open. Identity could be treated with introduction and elimination rules in natural deduction, or left and right rules, in a sequent calculus, as is standard for familiar logical concepts. On the other... Consequently.org -

Generics: Inference & Accommodation In this talk, I aim to give an account of norms governing our uses of generic judgements (like “kangaroos have long tails”, “birds lay eggs”, or “logic talks are boring”), norms governing inference, and the relationship between generics and inference. This connection goes some way to explain why generics exhibit some very strange behaviour: Why is it, for example, that “birds lay eggs” seems true, while “birds are female” seems false, despite the fact that... Consequently.org -

Collection Frames for Substructural Logics Abstract: In this talk I present a new frame semantics for positive substructural and relevant propositional logics. This frame semantics is both a generalisation of Routley–Meyer ternary frames and a simplification of them. The key innovation is the use of a single accessibility relation to relate collections of points to points. Different logics are modelled by varying the kinds of collections featuring in the relation: for example, they can be sets, multisets, lists or trees.... Consequently.org -

Assertions, Denials, Questions, Answers, and the Common Ground Abstract: In this talk, I examine interconnections between norms governing assertion, denial, questions and answers, and the common ground of a discourse. When we pay attention to the structure of norms governing polar (yes/no) questions, we can clarify the distinction between strong and weak denials, together with the parallel distinction between strong and weak assertion, and the way that these speech acts interact with the common ground. With those connections established, I respond to two... Consequently.org -

Generality and Existence I: Quantification and Free Logic In this paper, I motivate a cut free sequent calculus for classical logic with first order quantification, allowing for singular terms free of existential import. Along the way, I motivate a criterion for rules designed to answer Prior’s question about what distinguishes rules for logical concepts, like ‘conjunction’ from apparently similar rules for putative concepts like ‘tonk’, and I show that the rules for the quantifiers—and the existence predicate—satisfy that condition. Consequently.org -

Accommodation, Inference, Generics and Pejoratives Abstract: In this talk, I aim to give an account of norms governing our uses of generic judgements (like “kangaroos have long tails”, “birds lay eggs”, or “logic talks are boring”), norms governing inference, and the relationship between generics and inference. This connection goes some way to explain why generics exhibit some very strange behaviour: Why is it, for example, that “birds lay eggs” seems true, while “birds are female” seems false, despite the fact... Consequently.org -

Defining Rules, Proofs and Counterexamples Abstract: In this talk, I will present an account of defining rules, with the aim of explaining these rules they play a central role in analytic proofs. Along the way, I’ll explain how Kreisel’s squeezing argument helps us understand the connection between an informal notion of validity and the notions formalised in our accounts of proofs and models, and the relationship between proof-theoretic and model- theoretic analyses of logical consequence. This is a talk for... Consequently.org -

What Proofs are For Abstract: In this short talk, I present a new account of the nature of proof, with the aim of explaining how proof could actually play the role in reasoning that it does, and answering some long-standing puzzles about the nature of proof. Along the way, I’ll explain how Kreisel’s Squeezing argument helps us understand the connection between an informal notion of of validity and the notions formalised in our accounts of proofs and models, and... Consequently.org -