This volume includes a target paper, taking up the challenge to revive, within a modern (formal) framework, a medieval solution to the Liar Paradox which did ...

I examine the theory of consequentia of the medieval logician, John Buridan. Buridan advocates a strict commitment to what we now call proposition-tokens as the bearers of truth-value. The analysis of Buridan's theory shows that, within a token-based semantics, amendments to the usual notions of inference and consequence are made necessary, since pragmatic elements disrupt the semantic behaviour of propositions. In my reconstruction of Buridan's theory, I use some of the apparatus of modern two-dimensional semantics, such as two-dimensional matrices and (...) the distinction between the context of formation and the context of evaluation of utterances. (shrink)

In this paper, I consider the question of whether or not the deflationist about truth can respond to the Liar and allied paradoxes by taking sentences such as the following: (1) (1) is false (2) (2) is not true (3) (3) is true to be meaningless. Let's call this strategy for dealing with the Liar and Liar-like phenomena the Meaningless Strategy. This strategy is intuitively satisfying: it captures many people's initial response to the paradoxes; and it is theoretically important: if (...) successful, it might allow the deflationist to avoid the revenge problem that plagues so many putative solutions to the Liar. Moreover, owing to the austerity of their theory, deflationists have very few resources to deploy in attempting to accommodate the Liar, which means that if the deflationist is in a good position to employ the Meaningless Strategy, so much the better for deflationism. (shrink)

This book was designed primarily as a textbook; though the author hopes that it will prove to be of interests to others beside logic students. Part I of this book covers the fundamentals of the subject the propositional calculus and the theory of quantification. Part II deals with the traditional formal logic and with the developments which have taken that as their starting-point. Part III deals with modal, three-valued, and extensional systems.

The general verificationist thesis says that What is true can be known or formally: φ → ◊Kφ VT Fitch's argument trivializes this principle. It uses a weak modal epistemic logic to show that VT collapses truth and knowledge, by taking a clever substitution instance for φ: P ∧ ¬KP → ◊ K(P ∧ ¬KP) Then we have the following chain of three conditionals (a) ◊ K(P ∧ ¬KP) → ◊ (KP ∧ K¬KP) in the minimal modal logic for the knowledge (...) operator K, (b) ◊ (KP ∧ K¬KP) → ◊ (KP ∧¬KP) in the modal logic T, and finally (c) ◊ (KP ∧¬KP) → ⊥ in the minimal modal logic for. (shrink)

Mental language, According to ockham, Consists of mental acts or capacities for performing mental acts. Its structure is analogous to that of spoken or written language and is the structure of a logically ideal language. Hence its study is useful for philosophy. Ockham's concern about the apparent closeness of the analogy is also considered with reference to his discussion of the possibility of angelic (and hence nonphysical) language.

The ?no???no? paradox (so-called by Sorensen) consists of a pair of propositions each of which says of the other that it is false. It is not immediately paradoxical, since it has a solution in which one proposition is true, the other false. However, that is itself paradoxical, since there is no clear ground for determining which is which. The two propositions should have the same truth-value. The paper shows how a proposal by the medieval thinker Thomas Bradwardine solves not only (...) the Liar paradox, but also symmetric paradoxes like the ?no???no?, the descending ?no???no?, and the Truth-teller paradoxes. (shrink)

A textual and philosophical study of the claim that according to ockham there is no synonymy or equivocation in mental language. It is argued that ockham is committed to both claims, Either explicitly or in virtue of other features of his doctrine. Nevertheless, Both claims lead to difficulties for ockham's theory.

A view often expressed is that to classify the liar sentence as neither true nor false is satisfactory for the simple liar but not for the strengthened liar. I argue that in fact it is equally unsatisfactory for both liars. I go on to discuss whether, nevertheless, Kripke''s theory of truth represents an advance on that of Tarski.

In what follows, I analyze Ralph Strode's treatise on obligations. I have used a hitherto unpublished edition of the text (based on 14 manuscripts) made by Prof. E.J. Ashworth. I first give a brief description of Strode's text, which is all the more necessary given that it is not available to the average reader; I also offer a reconstruction of the rules proposed by Strode, following the style of reconstruction used in my analysis of Burley's and Swyneshed's rules elsewhere—that is, (...) essentially based on the idea that obligationes can be viewed as logical games. In the second part, I address Strode's explicit arguments contra Swyneshed. In the third part, I discuss Strode's epistemic and pragmatic approach to obligationes. (shrink)

I argue that the medieval form of dialectical disputation known as obligationes can be viewed as a logical game of consistency maintenance. The game has two participants, Opponent and Respondent. Opponent puts forward a proposition P; Respondent must concede, deny or doubt, on the basis of inferential relations between P and previously accepted or denied propositions, or, in case there is none, on the basis of the common set of beliefs. Respondent loses the game if he concedes a contradictory set (...) of propositions. Opponent loses the game if Respondent is able to maintain consistency during the stipulated period of time. The obligational rules are here formalised by means of familiar notational devices, and the application of some game-theoretical concepts, such as (winning) strategy, moves, motivation, allows for an analysis of some crucial properties of the game. In particular, the primacy of inferential (syntactic) relations over semantic aspects and the dynamic character of obligations are outlined. (shrink)

A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.

It is argued that Yablo’s Paradox is not strictly paradoxical, but rather ‘ω-paradoxical’. Under a natural formalization, the list of Yablo sentences may be constructed using a diagonalization argument and can be shown to be ω-inconsistent, but nonetheless consistent. The derivation of an inconsistency requires a uniform fixed-point construction. Moreover, the truth-theoretic disquotational principle required is also uniform, rather than the local disquotational T-scheme. The theory with the local disquotation T-scheme applied to individual sentences from the Yablo list is also (...) consistent. (shrink)

In this paper, I examine a solution to the Liar paradox found in the work of Ockham, Burley, and Pseudo-Sherwood. I reject the accounts of this solution offered by modern commentators. I argue that this medieval line suggests a non-hierarchical solution to the Liar, according to which ?true? is analysed as an indexical term, and paradox is avoided by minimal restrictions on tokens of ?true?. In certain respects, this solution resembles the recent approaches of Charles Parsons and Tyler Burge; in (...) other respects, it is related to a suggestion of Gödel. But, as a whole, it suggests an original solution to the Liar paradox, quite unlike any current proposals. (shrink)

The paper highlights a certain kind of self-falsifying utterance, which I shall call antiperformative assertions, not noted in speech-act theory thus far. By taking such assertions into account, the old question whether explicit performatives have a truth-value can be resolved. I shall show that explicit performatives are in fact self-verifyingly true, but they are not related to propositions the way ordinary assertions are; antiperformatives have the same unusual relation to propositions, but are self-falsifyingly false. Explicit performatives are speech acts performed (...) in situations where it is important that the speaker is self-reflectively aware of what he is doing in the speech act. Antiperformatives, on the other hand, are speech acts performed in situations where lack of direct self-reflectiveness is required. In order to situate performatives and antiperformatives, the analysis is embedded within a more general discussion of self-falsifying and self-verifying assertions. (shrink)