Jc Beall

Spandrels of truth

1. The Basic Picture 2. Suitable Conditional 3. Just True 4. A Look at the Field 5. Objections and Replies 6. Appendix Overlap Without Inconsistency? References

On the Ternary Relation and Conditionality

One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley–Meyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions of conditionality. We close by briefly discussing a general conception of conditionality that may unify the three given conceptions.

On Mixed Inferences and Pluralism about Truth Predicates

A familiar view concerning sentences about the ethical or comical is that they are not truth-apt – not capable of being true or false. Against this view Peter Geach famously noted that such sentences may figure in true (or false) conditionals and so must thereby be truth-apt. In response to Geachs argument, Crispin Wright proposed a pluralism about truth predicates, a pluralism which sees Geachs conditional clauses as being true in a sense that avoids realism about the entities involved. I defend Wrights proposal against an interesting recent attack by Christine Tappolet, and show that, pace Tappolet, Wrights proposed pluralism is compatible with the Tarskian idea that validity is necessary truth-preservation.

Multiple-conclusion LP and default classicality

Philosophical applications of familiar paracomplete and paraconsistent logics often rely on an idea of ‘default classicality’. With respect to the paraconsistent logic LP (the dual of Strong Kleene or K3), such ‘default classicality’ is standardly cashed out via an LP-based nonmonotonic logic due to Priest (1991, 2006a). In this paper, I offer an alternative approach via a monotonic multiple-conclusion version of LP.

Relevant Restricted Quantification

The paper reviews a number of approaches for handling restricted quantification in relevant logic, and proposes a novel one. This proceeds by introducing a novel kind of enthymematic conditional.

Looking for contradictions

There has been considerable debate recently on whether there are true contradictions. A very natural and interesting question arises in the context of this debate: Why don’t we observe contradictions? The obvious answer is that there aren’t any true contradictions— observable or otherwise—so little wonder we don’t see any. Many philosophers would be happy to leave the matter there, but for those like Graham Priest who believe that there are true contradictions, the question of why we don’t observe contradictions is potentially embarrassing. Priest, however, does have an answer ready to hand [11]; he argues that the observable world is consistent. We suggest that Priest is a bit quick in drawing this conclusion. There are, we believe, a couple of reasons to doubt it. First, it is not clear that we would recognise a contradiction if we saw one; so, it does not follow from the lack of evidence for observable true contradictions that there are no observable contradictions. Second, we make a tentative case for the stronger claim that we do in fact see contradictions. If this latter claim is right, the observable world is inconsistent.

A neglected deflationist approach to the liar

(1) is the simple liar; (2) is the strengthened liar; and (3) is the truth-teller. That these sentences engender paradox is familiar enough – so much so that no review is required. What do these familiar paradoxes teach us about our (English) language? To this question there are many different answers. The answer at issue in this paper is a common one; it is, perhaps, the most common initial response to the given paradoxes.1 The response in question is one according to which none of (1), (2), or (3) are meaningful; each of the given sentences, according to the going response, is meaningless – they ‘say nothing’, ‘express no proposition’, or so on. The trouble with the given response, and perhaps the reason that it tends to be only an initial response, is that it appears to be ad hoc, in addition to being implausible. The implausibility of the response arises from the fact that nobody has trouble reasoning about (1), (2), or (3); indeed, it is such effortless reasoning that leads one to recognize that the sentences are, alas (allegedly) meaningless. But this is puzzling; for one would think that such apparently successful reasoning is possible only if the given sentences are meaningful. For this reason the appearance of ad hocery is difficult to avoid; the only way of avoiding it is to provide independent reason for thinking that (1), (2), and (3) are meaningless; but this task, as is familiar, has not been an easy one.

LP + , K3 + , FDE + , AND THEIR ‘CLASSICAL COLLAPSE’

Abstract. This paper is a sequel to Beall (2011), in which I both give and discuss the philosophical import of a ‘classical collapse’ result for the propositional (multiple-conclusion) logic LP+. Feedback on such ideas prompted a spelling out of the first-order case. My aim in this paper is to do just that: namely, explicitly record the first-order result(s), including the collapse results for K3+ and FDE+.

Should Deflationists Be Dialetheists

Our answer to the title question is affirmative: deflationists should be dialetheists, where dialetheists hold that some truths have true negations. (We discuss dialetheism further below.) Why should deflationists be dialetheists? The answer rests on the Liar (and related) paradox. In his comparative study of disquotational and correspondence truth [10] Marian David completely neglects the Liar paradox. Why? Davids answer is clear:

A SIMPLE APPROACH TOWARDS RECAPTURING CONSISTENT THEORIES IN PARACONSISTENT SETTINGS

Abstract. 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 forLP-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.