The aim of the present book is to give a comprehensive account of the ‘state of the art’ of substructural logics, focusing both on their proof theory and on their semantics (both algebraic and relational. It is for graduate students in either philosophy, mathematics, theoretical computer science or theoretical linguistics as well as specialists and researchers.

The lottery paradox has been discussed widely. The standard solution to the lottery paradox is that a ticket holder is justified in believing each ticket will lose but the ticket holder is also justified in believing not all of the tickets will lose. If the standard solution is true, then we get the paradoxical result that it is possible for a person to have a justified set of beliefs that she knows is inconsistent. In this paper, I argue that the (...) best solution to the paradox is that a ticket holder is not justified in believing any of the tickets are losers. My solution avoids the paradoxical result of the standard solution. The solution I defend has been hastily rejected by other philosophers because it appears to lead to skepticism. I defend my solution from the threat of skepticism and give two arguments in favor of my conclusion that the ticket holder in the original lottery case is not justified in believing that his ticket will lose. (shrink)

The logician's central concern is with the validity of argument. A logical theory ought, therefore, to provide a general criterion of validity. This book sets out to find such a criterion, and to describe the philosophical basis and the formal theory of a logic in which the premises of a valid argument are relevant to its conclusion. The notion of relevance required for this theory is obtained by an analysis of the grounds for asserting a formula in a proof.

We introduce a logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side. The propositional version of BI arises from an analysis of the proof-theoretic relationship between conjunction and implication; it can be viewed as a merging of intuitionistic logic and multiplicative intuitionistic linear logic. The naturality of BI can be seen categorically: models of propositional BI's proofs are given by bicartesian doubly closed categories, i.e., categories which freely combine the semantics of propositional intuitionistic (...) logic and propositional multiplicative intuitionistic linear logic. The predicate version of BI includes, in addition to standard additive quantifiers, multiplicative (or intensional) quantifiers ∀ new and ∃ new which arise from observing restrictions on structural rules on the level of terms as well as propositions. We discuss computational interpretations, based on sharing, at both the propositional and predicate levels. (shrink)

Jim buys a ticket in a million-ticket lottery. He knows it is a fair lottery, but, given the odds, he believes he will lose. When the winning ticket is chosen, it is not his. Did he know his ticket would lose? It seems that he did not. After all, if he knew his ticket would lose, why would he have bought it? Further, if he knew his ticket would lose, then, given that his ticket is no different in its chances (...) of winning from any other ticket, it seems that by parity of reasoning he should also know that every other ticket would lose. But of course he doesn’t know that; in fact, he knows that not every ticket will lose. (shrink)

In this new book, Foley defends an epistemology that takes seriously the perspectives of individual thinkers. He argues that having rational opinions is a matter of meeting our own internal standards rather than standards that are somehow imposed upon us from the outside. It is a matter of making ourselves invulnerable to intellectual self-criticism. Foley also shows how the theory of rational belief is part of a general theory of rationality. He thus avoids treating the rationality of belief as a (...) fundamentally different kind of phenomenon from the rationality of decision or action. His approach generates promising suggestions about a wide range of issues--e.g., the distinction between epistemic and non-epistemic reasons for belief; the question of what aspects of the Cartesian project are still worth doing; the significance of simplicity and other theoretical virtues; the relevance of skeptical hypotheses; the difference between a theory of rational belief and a theory of knowledge; the difference between a theory of rational belief and a theory of rational degrees of belief; and the limits of idealization in epistemology. (shrink)

Definite descriptions, I shall argue, have two possible functions. 1] They are used to refer to what a speaker wishes to talk about, but they are also used quite differently. Moreover, a definite description occurring in one and the same sentence may, on different occasions of its use, function in either way. The failure to deal with this duality of function obscures the genuine referring use of definite descriptions. The best known theories of definite descriptions, those of Russell and Strawson, (...) I shall suggest, are both guilty of this. Before discussing this distinction in use, I will mention some features of these theories to which it is especially relevant. (shrink)

In some lottery situations, the probability that your ticket's a loser can get very close to 1. Suppose, for instance, that yours is one of 20 million tickets, only one of which is a winner. Still, it seems that (1) You don't know yours is a loser and (2) You're in no position to flat-out assert that your ticket is a loser. "It's probably a loser," "It's all but certain that it's a loser," or even, "It's quite certain that it's (...) a loser" seem quite alright to say, but, it seems, you're in no position to declare simply, "It's a loser." (1) and (2) are closely related phenomena. In fact, I'll take it as a working hypothesis that the reason "It's a loser" is unassertable is that (a) You don't seem to know that your ticket's a loser, and (b) In flat-out asserting some proposition, you represent yourself as knowing it.1 This working hypothesis will enable me to address these two phenomena together, moving back and forth freely between them. I leave it to those who reject the hypothesis to sort out those considerations which properly apply to the issue of knowledge from those germane to that of assertability. Things are quite different when you report the results of last night's basketball game. Suppose your only source is your morning newspaper, which did not carry a story about the 1 game, but simply listed the score, "Knicks 83, at Bulls 95," under "Yesterday's Results." Now, it doesn't happen very frequently, but, as we all should suspect, newspapers do misreport scores from time to time. On several occasions, my paper has transposed a result, attributing to each team the score of its opponent. In fact, that your paper's got the present result wrong seems quite a bit more probable than that you've won the lottery of the above paragraph. Still, when asked, "Did the Bulls win yesterday?", "Probably" and "In all likelihood" seem quite unnecessary. "Yes, they did," seems just fine.. (shrink)

1 Knowledge and Justification This book is an investigation of one central problem which arises in the attempt to give a philosophical account of empirical ...

This paper criticizes the epistemological doctrine of moderate rationalism that has been defended in recent years by such writers as Laurence BonJour, Alvin Plantinga, and George Bealer. It is argued that this new form of rationalism is really no better than the old one and that the key claim common to both---that intuition or rational insight provides a satisfactory basis for a priori knowledge---is untenable. Most of the criticism is directed specifically against Laurence BonJour’s recent “dialectical” defense of the doctrine. (...) Since BonJour’s defense is essentially an attempt to show how a priori knowledge is possible, an alternative, empiricist view of a priori knowledge is presented that eludes his objections and is supported by the criticism brought against moderate rationalism. (shrink)

This paper criticizes the epistemological doctrine of moderate rationalism that has been defended in recent years by such writers as Laurence BonJour, Alvin Plantinga, and George Bealer. It is argued that this new form of rationalism is really no better than the old one and that the key claim common to both---that intuition or rational insight provides a satisfactory basis for a priori knowledge---is untenable. Most of the criticism is directed specifically against Laurence BonJour’s recent “dialectical” defense of the doctrine. (...) Since BonJour’s defense is essentially an attempt to show how a priori knowledge is possible, an alternative, empiricist view of a priori knowledge is presented that eludes his objections and is supported by the criticism brought against moderate rationalism. (shrink)