Roderic Girle

In this essay a theory of proper names is developed and applied to the construction of quantified modal logics and to a discussion of problems concerning identity across possible worlds. The theory is then used to aid discussion of essentialism, empty singular terms, quantification into epistemic contexts, and Frege’ s problem with identity. In the first chapter, after a preliminary discussion of Russell’s and Frege’s theories of names, a theory is developed. It is argued that in the giving of a name a relation is established between the name and what is named. That relation is the sense of the name. It is also argued that names can be given to imaginary, fictional, and other such non-existent things. The second chapter is devoted to a discussion of Quine’s programme for eliminating singular terms. It is there argued that the programme cannot be justified. The third chapter centres around the construction of logical systems to deal with identity across possible worlds. It is assumed that once a name is given and its sense thereby established the name is a rigid designator. Quantificational systems are constructed without modal operators yet in terms of which cross world identity can be discussed. Modal operators are then introduced to facilitate a discussion of essentialism and identity. At each point the formal systems are constructed in accordance with clearly stated assumptions about constant singular terms, the domains of quantification, and the interpretation of modal operators.

In this paper we compare central elements of Dialogue Logic and Belief Revision theory. Dialogue Logic of the Hamblin/Mackenzie style, or Formal Dialectic, contains three main features. First, there is a rule governed interaction between dialogue participants—the minimal case being two participants. Second, each participant has a commitment store which changes as the dialogue progresses. Third, the changes in the commitment store are governed by rules for additions and withdrawals of material. Withdrawal of material is one major source of difficulty in proposing rules for commitment store change. The classic Belief Revision theory is the AGM theory. AGM theory is a theory about ideal rational believers who change their sets of beliefs by either expansion or contraction. Contraction is a major source of difficulty in belief revision theory. We claim that the commitment stores of dialogue logic include, in a sense, the belief sets of belief revision theory. Further, withdrawal and contraction are essentially the same process. We consider various kinds of withdrawal and contraction, and show how approaches to these processes illuminate certain of the formal fallacies.

INTRODUCTION TO LOGIC is a combined text and workbook for students beginning their study of logic. The workbook style allows students to proceed at their own pace, checking their progress in the end-of-chapter exercises. The text covers propositional logic and predicate logic with identity, the focus being on arguments. The methods of proof are truth-tables and truth-trees in the style of Jeffrey. This text is suitable for students of philosophy, computer science, mathematics and science in general.

It has been argued that consciousness might be what differentiates human from machine mentality. What then is consciousness? We discuss consciousness, particularly perception accounts of consciousness. It is argued that perception and consciousness are distinct. Armstrong's account of consciousness is rejected. It is proposed that perception is a necessary but not sufficient condition for consciousness, and that there is a distinction to be drawn between consciousness and self-consciousness. Consciousness is tightly linked to attention and to certain sorts of knowledge. Implications for machine consciousness and machine attention are discussed

Jan Łukasiewicz’s analysis of Aristotle’s syllogism drew attention to the nature of syllogisms as conditionals rather than premise-conclusion arguments. His further idea that syllogisms should be understood as theorems of an axiom system seems a step too far for many logicians. But there is evidence to suggest that Aristotle’s syllogism was to regularise some of the steps made in ‘dialogue games.’ This way of seeing the syllogism is explored in the framework of modern formal dialogue systems. A modern formal syllogistic game, DLSyll, is set out and analysed in use.

Gödel's modal ontological argument is the centerpiece of an extensive examination of intensional logic. First, classical type theory is presented semantically, tableau rules for it are introduced, and the Prawitz/Takahashi completeness proof is given. Then modal machinery is added to produce a modified version of Montague/Gallin intensional logic. Finally, various ontological proofs for the existence of God are discussed informally, and the Gödel argument is fully formalized. Parts of the book are mathematical, parts philosophical.