Online research in philosophy

This book is about one of the most baffling of all paradoxes--the famous Liar paradox. Suppose we say: "We are lying now." Then if we are lying, we are telling the truth; and if we are telling the truth we are lying. This paradox is more than an intriguing puzzle, since it involves the concept of truth. Thus any coherent theory of truth must deal with the Liar. Keith Simmons discusses the solutions proposed by medieval philosophers and offers his own solutions and in the process assesses other contemporary attempts to solve the paradox. Unlike such attempts, Simmons' "singularity" solution does not abandon classical semantics and does not appeal to the kind of hierarchical view found in Barwise's and Etchemendy's The Liar. Moreover, Simmons' solution resolves the vexing problem of semantic universality--the problem of whether there are semantic concepts beyond the expressive reach of a natural language such as English.

The aim of this paper is to show that Graham Priest's dialetheic account of semantic paradoxes and the paraconsistent logics employed cannot achieve semantic universality. Dialetheism therefore fails as a solution to semantic paradoxes for the same reason that consistent approaches did. It will be demonstrated that if dialetheism can express its own semantic principles, a strengthened liar paradox will result, which renders dialetheism trivial. In particular, the argument is not invalidated by relational valuations, which were brought into paraconsistent logic in order to avoid strengthened liar paradoxes.

The vast majority of approaches to the liar paradox generate new paradoxes that are structurally similar to the liar (often called revenge paradoxes). There is a complex group of issues surrounding revenge paradoxes, the expressive powers of natural languages, and the adequacy of approaches to the liar. My goal is to provide a precise framework against which these issues can be formulated and discussed. The centerpiece of this framework is the notion of internalizability: a semantic theory is internalizable for a language if and only if there exists an extension of the language such that (i) the theory is expressible in that extended language, and (ii) the theory assigns meanings to all the relevant sentences of that extended language. The framework is applied to three examples from the literature: Reinhardt and McGee on theories that require expressively richer metalanguages, Field on revenge-immunity, and Gupta on semantic self-sufficiency.

There are some seemingly small points to be made, first of all, about usemention confusions in Stephen Read’s paper ‘The Truth Schema and the Liar’. But underlying them is a grammatical point that has much wider repercussions. For it generates, on its own, a more straightforward way of understanding what gets people into a tangle with Liar and Strengthened Liar sentences, and that leads to a much fuller, critical assessment of the line of approach to these matters that Read derives from Bradwardine.

I revisit my earlier arguments for the (trivial) inconsistency of natural languages, and take up the objection that no such argument can be established on the basis of surface usage. I respond with the evidential centrality of surface usage: the ways it can and can't be undercut by linguistic science. Then some important ramifications of having an inconsistent natural language are explored: (1) the temptation to engage in illegitimate reductio reasoning, (2) the breakdown of the knowledge idiom (because its facticity isn't comfortable with every sentence being true and false). Restoring the utility of the knowledge idiom motivates regimentation - the consistentist reinterpretation of natural language inferences (as they occur in real time). It's then sketched how to give the semantics of a natural language despite its inconsistency: Necessary and sufficient truth conditions are dropped in favor of necessary truth conditions and sufficient truth conditions.

The Liar Paradox is an argument that arrives at a contradiction by reasoning about a Liar Sentence. The classical Liar Sentence is the self-referential sentence “This sentence is false.”.

In the Tarskian theory of truth, the strengthened liar sentence is a theorem. More generally, any formalized truth theory which proves the full, self-applicative scheme True(“f”) f will prove the strengthened liar sentence. (This scheme is sometimes called (T-Out).).

“To this day, partiality approaches to the paradox have been dogged by the so-called ‘Strengthened Liar’. .... The Strengthened Liar observes that if we follow a partiality theorist and declare the Liar sentence* neither true nor false (or failing to express a proposition,. or suffering from some sort of grave semantic defect), then the paradox is only pushed back. For we can go on to conclude that whatever this status may be, it implies that the Liar sentence is not true. This claim is true, but it is just the Liar sentence again.* We are back in paradox.” (Glanzberg 2002, p. 468, bold emphasis added.) Cf.: “We are back in our contradiction,”(Glanzberg 2001, p. 222). *The Liar sentence intended is evidently the sentence ‘the Liar sentence is not true’, and, the Liar sentence = ‘the Liar sentence is not true’. Cf.: “Consider a Liar sentence: ...let us take a sentence l which says l is not true. We can, informally, reason as..

We show how to construct certain L M, T -type interpreted languages, with each such language containing meaningfulness and truth predicates which apply to itself. These languages are comparable in expressive power to the L T -type, truth-theoretic languages first considered by Kripke, yet each of our L M, T -type languages possesses the additional advantage that, within it, the meaninglessness of any given meaningless expression can itself be meaningfully expressed. One therefore has, for example, the object level truth (and meaningfulness) of the claim that the strengthened Liar is meaningless.

A view often expressed is that to classify the liar sentence as neither true nor false is satisfactory for the simple liar but not for the strengthened liar. I argue that in fact it is equally unsatisfactory for both liars. I go on to discuss whether, nevertheless, Kripke''s theory of truth represents an advance on that of Tarski.