THE LOGIC OF THE CATUSKOTI

In early Buddhist logic, it was standard to assume that for any state of affairs there were four possibilities: that it held, that it did not, both, or neither. This is the catuskoti (or tetralemma). Classical logicians have had a hard time making sense of this, but it makes perfectly good sense in the semantics of various paraconsistent logics, such as First Degree Entailment. Matters are more complicated for later Buddhist thinkers, such as Nagarjuna, who appear to suggest that none of these options, or more than one, may hold. The point of this paper is to examine the matter, including the formal logical machinery that may be appropriate

On An Error In Grove's Proof

Nearly a decade has past since Grove gave a semantics for the AGM postulates. The semantics, called sphere semantics, provided a new perspective of the area of study, and has been widely used in the context of theory or belief change. However, the soundness proof that Grove gives in his paper contains an error. In this note, we will point this out and give two ways of repairing it

The nature of philosophy and its place in the university

Inaugural lecture delivered at the University of Queensland 18 October 1989

Inconsistent models of artihmetic Part II : The general case

The paper establishes the general structure of the inconsistent models of arithmetic of [7]. It is shown that such models are constituted by a sequence of nuclei. The nuclei fall into three segments: the first contains improper nuclei: the second contains proper nuclei with linear chromosomes: the third contains proper nuclei with cyclical chromosomes. The nuclei have periods which are inherited up the ordering. It is also shown that the improper nuclei can have the order type of any ordinal. of the nationals. or of any other order type that can be embedded in the rationals in a certain way

無: paradoks in praznina

Nothingness is a tantalizing concept. It appears in the thinking of many major philosophers—East and West—where it plays a profound role in their thinking concerning the nature of the world (that is, the beings that constitute it). However, nothingness is implicated in contradiction and paradox right from the start. It is something and, well, nothing. This essay has three themes. The first is the role of nothingness in Mahāyāna Buddhist philosophy. The second is the paradoxical nature of nothingness. The third is a mereological account of the nature of nothingness which does justice to the paradox. Though the themes are distinct, they are interconnected in important ways, as the essay will show.Nič je mamljiv koncept. Pojavlja se v mišljenju mnogih pomembnih filozofinj ter filozofov – tako Vzhoda kot Zahoda – in sicer igra pomembno vlogo v njihovih razmišljanjih o naravi sveta (torej bitij, ki ga sestavljajo). Vendar je nič že od samega začetka vpet v protislovje in paradoks. Je nekaj in hkrati – nič. Ta esej ima tri teme. Prva je vloga niča v budistični filozofiji mahāyāna. Druga je paradoksna narava niča. Tretja tema je mereološki opis narave niča, ki ustrezno prikaže paradoks. Četudi gre za različne teme, so med seboj povezane v pomembnih vidikih, kakor bo razvidno iz eseja

Logical Theory Choice: The Case of Vacuous Counterfactuals

There is at present a certain dispute about counterfactuals taking place. What is at issue is whether counterfactuals with necessarily false antecedents are all true. Some hold that such counterfactuals are vacuously true, appearances notwithstanding. Let us call such people vacuists. Others hold that some counterfactuals with necessarily false antecedents are true; some are false: it just depends on their contents. Let us call such people non-vacuists. As a notable representative of the vacuists, I will take Tim Williamson. On the other side, I will take the position defended by Berto, French, Priest, and Ripley. I will argue (unsurprisingly) that the better choice is Non-Vacuism. That, however, is a subsidiary aim of this paper. The main point is to illustrate the method of theory-choice

Logical Pluralism Hollandaise

Johan van Benthem compares and contrasts two research programmes, which he calls logical pluralism and logical dynamics, stating his ‘preference’ for the second of these ‘alternatives’. In this note I want to put the matter into a slightly different perspective

Old Wine in (Somewhat Leaky) New Bottles: Some Comments on Beall

Dialetheists concerning the paradoxes of self-refrence have often argued that the phenomeonon provides a choice between inconsistency and expressive incompleteness, and that inconsistency is the correct choice. In a recent paper (`Trivialising Sentences and the Promise of Semantic Completeness', Analysis (2015) 75: 573-84), JC Beall attacks this argument. This paper analyses his arguments, and argues that his paper simply provides a new spin on matters well known

Logical Theory Choice: The Case of Vacuous Counterfactuals

There is at present a certain dispute about counterfactuals taking place. What is at issue is whether counterfactuals with necessarily false antecedents are all true. Some hold that such counterfactuals are vacuously true, appearances notwithstanding. Let us call such people vacuists. Others hold that some counterfactuals with necessarily false antecedents are true; some are false: it just depends on their contents. Let us call such people non-vacuists. As a notable representative of the vacuists, I will take Tim Williamson. On the other side, I will take the position defended by Berto, French, Priest, and Ripley. I will argue (unsurprisingly) that the better choice is Non-Vacuism. That, however, is a subsidiary aim of this paper. The main point is to illustrate the method of theory-choice