Doubt Truth to be a Liar

Abstract

The Law of Non-Contradiction has been high orthodoxy in Western philosophy since Aristotle. The so-called Law has been the subject of radical challenge in recent years by dialetheism, the view that some contradictions are indeed true. Many philosophers have taken the Law to be central to many of our most important philosophical concepts. This book mounts the case against this view. Starting with an analysis of Aristotle on the Law, it discusses the nature of truth, rationality, negation, and logic itself, and argues that the Law is inessential to all of these things. The book develops Priest’s earlier ideas in In Contradiction.

Truth Without Contra(di)ction

“…ω has thus all the hallmarks of Boolean negation (see Priest [2006b] for a good critical discussion of this notion).…”

The inexpressibility of validity

“…However, the dialectic here is a familiar one: intuitively invalid inferences such as Leslie was a US president ∴ Leslie was a man , and intuitively invalid sentences such as 'There are at least two numbers', would thereby be declared logically valid (Etchemendy, 1990). 8 Whether rules such as x is water x is H 2 O are valid is perhaps less clear, but the examples, I hope, suffice to establish my point: logical validity is one kind of validity (see also Priest, 2006a). 9 Second, as hinted in the above McGee quote, validity arguably has a role to play in our epistemic lives.…”

Vagueness and Uncertainty

“…Firstly, I am only going to be considering uncertainty in the context of theories of vagueness that endorse classical logic. I think that the role of uncertainty in non-classical logics is a central and fascinating topic, but it is well discussed, for example, in the works of Hartry Field [9][8] and Graham Priest [16] [15], and some of the topics are tangential to the main thrust of this thesis. However, many of the issues raised here have direct analogues in the non-classical setting.…”