Paul Boghossian defends a meaning‐based approach to the apriority of the propositions of logic. His model is based on the idea that the logical constants are implicitly defined by some of the axioms and inference rules in which they are involved, thereby offering an alternative to those theories that deny that grasp of meaning can contribute to the explanation of a thinker's entitlement to a particular type of transition or belief.

It seems obvious that I could have failed to exist. My parents could easily never have met, in which case I should never have been conceived and born. The like applies to everyone. More generally, it seems plausible that whatever exists in space and time could have failed to exist. Events could have taken an utterly different course. Our existence, like most other aspects of our lives, appears frighteningly contingent. It is therefore surprising that there is a proof of my (...) necessary existence, a proof that generalizes to everything whatsoever. I will explain the proof and discuss what to make of it. A first reaction is that a ‘proof’ of such an outrageous conclusion must contain some dreadful fallacy. Yet the proof does not collapse under scrutiny. Further reflection suggests that, suitably interpreted, it may be sound. So interpreted, the conclusion is not outrageous, although it may not be the view you first thought of. (shrink)

In this paper I will offer a novel understanding of a priori knowledge. My claim is that the sharp distinction that is usually made between a priori and a posteriori knowledge is groundless. It will be argued that a plausible understanding of a priori and a posteriori knowledge has to acknowledge that they are in a constant bootstrapping relationship. It is also crucial that we distinguish between a priori propositions that hold in the actual world and merely possible, non-actual a (...) priori propositions, as we will see when considering cases like Euclidean geometry. Furthermore, contrary to what Kripke seems to suggest, a priori knowledge is intimately connected with metaphysical modality, indeed, grounded in it. The task of a priori reasoning, according to this account, is to delimit the space of metaphysically possible worlds in order for us to be able to determine what is actual. (shrink)

Hartry Field; XV*—The A Prioricity of Logic, Proceedings of the Aristotelian Society, Volume 96, Issue 1, 1 June 1996, Pages 359–380, https://doi.org/10.1093/ar.

A stellar line-up of leading philosophers from around the world offer new treatments of a topic which has long been central to philosophical debate, and in ...

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

Zeno argued that since at any instant an arrow does not change its location, the arrow does not move at any time, and hence motion is impossible. I discuss the following three views that one could take in view of Zeno's argument:(i) the "at-at" theory, according to which there is no such thing as instantaneous velocity, while motion in the sense of the occupation of different locations at different times is possible,(ii) the "impetus" theory, according to which instantaneous velocities do (...) exist but these are only contingently and causally related to the temporal developments of positions,(iii) the "no instants" theory, according to which instants in time do not exist, and hence instantaneous velocities do not exist, while motion, in the sense of different areas occupied during different time intervals, is possible.I argue that, despite the fact that there have been interesting and relevant developments in mathematics and physics since the time of Zeno, each of these views still has serious drawbacks. (shrink)

Such a conception, says Dummett, will form "a base camp for an assault on the metaphysical peaks: I have no greater ambition in this book than to set up a base ...

The Law of Non-Contradiction - that no contradiction can be true - has been a seemingly unassailable dogma since the work of Aristotle, in Book G of the Metaphysics. It is an assumption challenged from a variety of angles in this collection of original papers. Twenty-three of the world's leading experts investigate the 'law', considering arguments for and against it and discussing methodological issues that arise whenever we question the legitimacy of logical principles. The result is a balanced inquiry into (...) a venerable principle of logic, one that raises questions at the very centre of logic itself. The aim of this volume is to present a comprehensive debate about the Law of Non-Contradiction, from discussions as to how the law is to be understood, to reasons for accepting or re-thinking the law, and to issues that raise challenges to the law, such as the Liar Paradox, and a 'dialetheic' resolution of that paradox. The editors contribute an introduction which surveys the issues and serves to frame the debate, and a useful bibliography offering a guide to further reading. This volume will be of interest to anyone working on philosophical logic, and to anyone who has ever wondered about the status of logical laws and about how one might proceed to mount arguments for or against them. (shrink)

E. J. Lowe, a prominent figure in contemporary metaphysics, sets out and defends his theory of what there is. His four-category ontology is a metaphysical system which recognizes four fundamental categories of beings: substantial and non-substantial particulars and substantial and non-substantial universals. Lowe argues that this system has an explanatory power which is unrivalled by more parsimonious theories and that this counts decisively in its favour. He shows that it provides a powerful explanatory framework for a unified account of causation, (...) dispositions, natural laws, natural necessity and many other related matters, thus constituting a full metaphysical foundation for natural science. (shrink)

The doctrine of semantic dialetheism is set out and contrasted with metaphysical dialetheism. We find that there is a lot to be said in favour of semantic dialetheism. Semantic dlaietheism is given credence by the doctrine of partially defined predicates. To make sense of a partially defined predicate, Tappenden and Soames suggest that the seman tics of predicates should be given in terms of a set of conditions under which the predicate can be applied to things and a set of (...) conditions under which its negation can be applied. If Tappenden and Soames are correct that many predicates are partially defined then it is also plausible that some are 'overdefined'. We say that a predicate is overdefined if and only if it is possible that its negative and positive conditions pick out some of the same objects at the same time. Some examples of overdefined predicates are discussed and it is suggested that a semantic dialetheist treatment of some folk theories (such as the folk theory of identity and the folk theory of belief) is appropriate. (shrink)

Approaches to paraconsistency can be arranged on a spectrum similar to the way in which approaches to vagueness are often understood. On the left are the metaphysical realists; those who think that there are real contradictory facts, that are mind and language independent. On the right are those who think that although we can have inconsistent beliefs and inconsistent theories — and we need a paraconsistent logic to deal with them — the world itself is perfectly consistent. In the middle (...) are the semantic dialetheists, who claim that there are true contradictions, but that these come about because of particular features of our use of language. This chapter outlines a particular version of semantic dialetheism based on a four-valued logic. It contends that although we need such a logic to deal with our current language, we could regiment our uses of predicates (and other expressions) to eliminate all true contradictions. (shrink)

A common response to those who question the Law of Non-Contradiction is that it is impossible to debate such a fundamental law of logic. The reasons for this response vary, but what seems to underlie them is the thought that there is a minimal set of logical resources without which rational debate is impossible. This chapter argues that this response is misguided. First, it defends non-apriorism in logic: the view that logic is in the same epistemic boat as other scientific (...) theories. It then offers an account of logical theory change in terms of this epistemology. The LNC is discussed in terms of this account of logical theory change, and it is shown that rational debate over this law can, and does, proceed. Finally, arguments for and against the LNC are discussed, and how and where non-a priori considerations arise in these arguments are illustrated. (shrink)