Greg Restall's publications on logic and philosophy Greg Restall Greg Restall greg@consequently.org Philosophy, Logic, mathematics, pdf, research, University, Greg Restall, Melbourne, Australia, Victoria no http://consequently.org/writing/ Publications from Greg Restall. Philosopher, at the University of Melbourne. en greg@consequently.org 2008-07-16T11:28:49+10:00 hourly 1 2000-01-01T12:00+00:00 http://consequently.org/writing/ptm-second-order/index.php Second order quantification is puzzling. The second order quantifiers have natural and compelling inference rules, and they also have natural models. These do not match: the inference rules are sound for the models, but not complete, so either the proof rules are too weak or the models are too strong. Some, such as Quine, take this to be no real problem, since they take “second order logic”l to be a misnomer. It is not logic but set theory in sheep’s clothing, so one would not expect to have a sound and complete axiomatisation of the theory. I think that this judgement is incorrect, and in this paper I attempt to explain why. I show how on Nuel Belnap’s criterion for logicality, second order quantification can count as properly logic so-called, since the quantifiers are properly defined by their inference rules, and the addition of second order quantification to a basic language is conservative. With this notion of logicality in hand I then diagnose the incompleteness of the proof theory of second order logic in what seems to be a novel way. 836@http://consequently.org/writing/ Published Article 16 Jul 2008 11:28:49 EST Greg Restall http://consequently.org/writing/adcei/index.php In this short paper, I compare and contrast the kind of symmetricalist treatment of negation favoured in different ways by Huw Price (in “Why ‘Not’?”) and by me (in “Multiple Conclusions”) with Robert Brandom’s analysis of scorekeeping in terms of commitment, entitlement and incompatibility. Both kinds of account provide a way to distinguish the inferential significance of “A” and “A is warranted” in terms of a subtler analysis of our practices: on the one hand, we assert as well as deny; on the other, by distingushing downstream commitments from upstream entitlements and the incompatibility definable in terms of these. In this note I will examine the connections between these different approaches. 678@http://consequently.org/writing/ Article Accepted for Publication 24 Jun 2008 22:57:22 EST Greg Restall http://consequently.org/writing/logic_in_australasia/index.php This is an idiosyncratic history of philosophical logic in Australia and New Zealand, highlighting two significant points of research in Australasian philosophical logic: modal logic and relevant/paraconsistent logic. 844@http://consequently.org/writing/ Article Accepted for Publication 24 Jun 2008 21:59:04 EST Greg Restall http://consequently.org/writing/ten2008/index.php 840@http://consequently.org/writing/ Article Accepted for Publication 21 Mar 2008 00:11:17 EST Greg Restall http://consequently.org/writing/yo-lo-appendix/index.php The appendix to Kukla and Lance’s book is the preliminary development of a score-keeping semantics that begins with the broader field of vision opened up when we eschew the declarative fallacy and make use of abstract versions of the pragmatic distinctions developed in the body of the book. I haven’t posted the preprint of this appendix, as it really makes sense only in the context of the whole book. For that, you need to wait until Harvard University Press publishes it. 839@http://consequently.org/writing/ Article Accepted for Publication 14 Mar 2008 21:45:01 EST Rebecca Kukla, Mark Lance and Greg Restall http://consequently.org/writing/costing/index.php I point out that non-classical “solutions” the paradoxes of self-reference are non-particularly easy to give. Curry’s paradox is very very hard to avoid, if you wish to give a semantically cohrerent picture. 676@http://consequently.org/writing/ Published Article 14 Mar 2008 12:00:00 EST http://consequently.org/writing/antirealist/index.php I sketch an application of a semantically anti-realist understanding of the classical sequent calculus to the topic of mathematics. The result is a semantically anti-realist defence of mathematical realism. In the paper, I develop the view and compare it to orthodox positions in the philosophy of mathematics. 783@http://consequently.org/writing/ Article in Progress 14 Mar 2008 07:36:14 EST Greg Restall http://consequently.org/writing/bradwardine-truth-tellers/index.php Stephen Read’s work on Bradwardine’s theory of truth is some of the most exciting work on truth and insolubilia in recent years. Read brings together modern tools of formal logic and Bradwardine’s theory of signification to show that medieval distinctions can give great insight into the behaviour of semantic concepts such as truth. In a number of papers, I have developed a model theory for Bradwardine’s account of truth. This model theory has distinctive features: it serves up models in which every declarative object (any object signifying anything) signifies its own truth. This leads to a puzzle: there are good arguments to the effect that if anything is a truth-teller, it is false. This is a puzzle. What distinguishes paradoxical truth-tellers from benign truth tellers? It is my task in this paper to explain this distinction, and to clarify the behaviour of truth-tellers, given Bradwardine’s account of signification. 835@http://consequently.org/writing/ Article in Progress 13 Mar 2008 02:24:55 EST Greg Restall http://consequently.org/writing/bradwardine-liars/index.php Stephen Read’s work on Bradwardine’s theory of truth is some of the most exciting work on truth and insolubilia in recent years. In this paper, I give models for Read’s formulation of Bradwardine’s theory of truth, and I examine the behaviour of liar sentences in those models. I conclude by examining Bradwardine’s argument to the effect that if something signifies itself to be untrue then it signifies itself to be true as well. We will see that there are models in which this conclusion fails. This should help us elucidate the hidden assumptions required to underpin Bradwardine’s argument, and to make explicit the content of Bradwardine’s theory of truth. 834@http://consequently.org/writing/ Article Accepted for Publication 13 Mar 2008 01:55:48 EST Greg Restall http://consequently.org/writing/mfsa/index.php This paper explores models for arithmetics in substructural logics. In the existing literature on substructural arithmetic, frame semantics for substructural logics are absent. We will start to fill in the picture in this paper by examining frame semantics for the substructural logics C (linear logic plus distribution), R (relevant logic) and CK (C plus weakening). The eventual goal is to find negation complete models for arithmetic in R. This paper is dedicated to Professor Robert K. Meyer. 824@http://consequently.org/writing/ Article Accepted for Publication 13 Mar 2008 01:08:54 EST Greg Restall http://consequently.org/writing/dlot/index.php We study the interpretation of Grzegorczyk’s Theory of Concatenation TC in structures of decorated linear order types satisfying Grzegorczyk’s axioms. We show that TC is incomplete for this interpretation. What is more, the first order theory validated by this interpretation interprets arithmetical truth. We also show that every extension of TC has a model that is not isomorphic to a structure of decorated order types. We provide a positive result, to wit a construction that builds structures of decorated order types from models of a suitable concatenation theory. This construction has the property that if there is a representation of a certain kind, then the construction provides a representation of that kind. 833@http://consequently.org/writing/ Article in Progress 12 Mar 2008 22:45:16 EST Vedran Cacic, Pavel Pudlak, Greg Restall, Alasdair Urquhart and Albert Visser http://consequently.org/writing/s5nets/index.php 743@http://consequently.org/writing/ Published Article 31 Dec 2007 23:44:03 EST Greg Restall http://consequently.org/writing/symbolic-logic/index.php 1007 words on symbolic logic – concentrating on the history of 20th Century logic, aimed at an audience of social scientists 837@http://consequently.org/writing/ Published Article 31 Dec 2007 20:44:49 EST Greg Restall http://consequently.org/writing/ptm-context/index.php I examine Belnap’s two criteria of existence and uniqueness for evaluating putative definitions of logical concepts in inference rules, by determining how they apply in four different examples: conjunction, the universal quantifier, the indefinite choice operator and the necessity in the modal logic S5. This illustrates the ways that definitions may be evaluated relative to a background theory of consequence, and the ways that different accounts of consequence provide us with different resources for making definitions. 830@http://consequently.org/writing/ Article Accepted for Publication 02 Nov 2007 03:00:35 EST Greg Restall http://consequently.org/writing/bradwardine/index.php Stephen Read has recently discussed Thomas Bradwardine’s theory of truth, and defended it as an appropriate way to treat paradoxes such as the liar. In this paper, I discuss Read’s formalisation of Bradwardine’s theory of truth, and provide a class of models for this theory. The models facilitate comparison of Bradwardine’s theory with contemporary theories of truth. 821@http://consequently.org/writing/ Article Accepted for Publication 26 Oct 2007 01:14:36 EST Greg Restall