Jc Beall

Weber, Colyvan, and Priest have advanced glutty approaches to the sorites, on which the truth about the penumbral region of a soritical series is inconsistent. The major benefit of a glut-based approach is maintaining the truth of all sorites premisses while none the less avoiding, in a principled fashion, the absurdity of the sorites conclusion. I agree that this is a major virtue of the target glutty approach; however, I think that it can be had without gluts. If correct, this result weighs heavily against the proposed glutty approach, at least given the default-consistency principle that all target glutty philosophers accept: posit gluts only if there is no consistent theory that enjoys the same virtues as the would-be glutty solution

My aim here is a modest one: to note another example in which the theory of validity and the theory of ‘inference’ naturally come apart. The setting is multiple-conclusion logic. At least on one philosophy of multiple-conclusion logic, there are very clear examples of where logic qua validity and logic qua normative guide to inference are essentially different things. On the given conception, logic tells us only what follows from what, what our ‘choices’ are given a set of premises; it is simply silent on which, of the given ‘choices’, we select from the (conclusion) set of options

I believe that, for reasons elaborated elsewhere (Beall, 2009; Priest, 2006a, 2006b), the logic LP (Asenjo, 1966; Asenjo & Tamburino, 1975; Priest, 1979) is roughly right as far as logic goes.1 But logic cannot go everywhere; we need to provide nonlogical axioms to specify our (axiomatic) theories. This is uncontroversial, but it has also been the source of discomfort for LP-based theorists, particularly with respect to true mathematical theories which we take to be consistent. My example, throughout, is arithmetic; but the more general case is also considered

When physicists disagree as to whose theory is right, they can (if we radically idealize) form an experiment whose results will settle the difference. When logicians disagree, there seems to be no possibility of resolution in this manner. In Paradox and Paraconsistency John Woods presents a picture of disagreement among logicians, mathematicians, and other “abstract scientists” and points to some methods for resolving such disagreement. Our review begins with (very) short sketches of the chapters. Following the sketches, we respond to a few of Woods’ arguments.

In "Semantic paradoxes and abductive methodology", Williamson presents a new Quinean argument based on central ingredients of common pragmatism about theory choice (including logical theory, as is common). What makes it new is that, in addition to avoiding Quine's unfortunate charge of mere terminological squabble, Williamson's argument explicitly rejects at least for purposes of the argument Quine's key conservatism premise. In this paper I do two things. First, I argue that Williamson's new Quinean argument implicitly relies on Quine's conservatism principle. Second, by way of answering his charges against nonclassical logic I directly defend a particular subclassical account of logical consequence.

“Curry’s paradox”, as the term is used by philosophers today, refers to a wide variety of paradoxes of self-reference or circularity that trace their modern ancestry to Curry (1942b) and Löb (1955). The common characteristic of these so-called Curry paradoxes is the way they exploit a notion of implication, entailment or consequence, either in the form of a connective or in the form of a predicate. Curry’s paradox arises in a number of different domains. Like Russell’s paradox, it can take the form of a paradox of set theory or the theory of properties. But it can also take the form of a semantic paradox, closely akin to the Liar paradox. Curry’s paradox differs from both Russell’s paradox and the Liar paradox in that it doesn’t essentially involve the notion of negation. Common truth-theoretic versions involve a sentence that says of itself that if it is true then an arbitrarily chosen claim is true, or—to use a more sinister instance—says of itself that if it is true then every falsity is true. The paradox is that the existence of such a sentence appears to imply the truth of the arbitrarily chosen claim, or—in the more sinister instance—of every falsity. In this entry, we show how the various Curry paradoxes can be constructed, examine the space of available solutions, and explain some ways Curry’s paradox is significant and poses distinctive challenges.

A very natural and philosophically important subclassical logic is FDE. This account of logical consequence can be seen as going beyond the standard two-valued account to a four-valued account. A natural question arises: What account of logical consequence arises from considering further combinations of such values? A partial answer was given by Priest in 2014; Shramko and Wansing had also given a partial result some years earlier, although in a different context. In this note we generalize Priest’s result to show that even if one considers ordinal-many combinations of the previous values, for any ordinal, the resulting consequence relation remains FDE.

Traditional monotheism appears to many to involve contradiction in basic 'omni' properties (e.g. omnipotence and too-heavy stones, etc.). A glut-theoretic account of such problems treats them as gluts (dual to familiar truth-value gaps): 'omnipotence' is both true of and false of God. Many philosophers, glut theorists and otherwise, acknowledge that such a glut-theoretic account of at least some traditional omni-god problems is natural, at least in the abstract. But what about the problem of evil? The unanimous view even among glut theorists (including myself until now) has long been clear: gluts have nothing to offer in response to the problem of evil even if they are involved in true theology elsewhere. This paper refutes said view by advancing a simple glut-theoretic response to the target problem of evil on the assumption that gluts are involved in the theology elsewhere (notably, at 'omnipotent' or 'omniscient' or both).

Extensively classroom-tested, Possibilities and Paradox provides an accessible and carefully structured introduction to modal and many-valued logic. The authors cover the basic formal frameworks, enlivening the discussion of these different systems of logic by considering their philosophical motivations and implications. Easily accessible to students with no background in the subject, the text features innovative learning aids in each chapter, including exercises that provide hands-on experience, examples that demonstrate the application of concepts, and guides to further reading.

The following are some preliminary remarks that will set the stage for my individual replies to Timothy Pawl, Thomas McCall, A. J. Cotnoir, and Sara L. Uckelman’s responses to my paper ‘Christ – A Contradiction’. In that paper I advance and defend a contradictory Christology which solves the fundamental ‘problem’ of Christology by holding that Christ is a contradictory being: it is true that Christ is mutable and it is false that Christ is mutable; it is true that Christ is immutable and it is false that Christ is immutable; and so on for other fundamental-problem properties. Familiarity with ‘Christ – A Contradiction’ is assumed.