Online research in philosophy

We represent truth sets for a variety of the well known semantic theories of truth as those sets consisting of all sentences for which a player has a winning strategy in an infinite two person game. The classifications of the games considered here are simple, those over the natural model of arithmetic being all within the arithmetical class of $\Sum_{3}^{0}$.

Two-dimensional (2D) semantics is a formal framework that is used to characterize the meaning of certain linguistic expressions and the entailment relations among sentences containing them. 2D semantics has also been applied to thought contents. In contrast with standard possible worlds semantics, 2D semantics assigns extensions and truth-values to expressions relative to two possible world parameters, rather than just one. So a 2D semantic framework provides finer-grained semantic values than those available within standard possible world semantics, while using the same basic model-theoretic resources. The 2D framework itself is just a formal tool. To develop a semantic theory for someone’s language, a proponent of 2D semantics must do three things: (i) explain what exactly the two possible world parameters represent, (ii) explain the rules for assigning 2D semantic values to a person’s words and sentences, and (iii) explain how 2D semantic values help in understanding the meanings of the person’s words and sentences.

A somewhat simplified version of Jerrold J. Katz's theory of the analytic/synthetic distinction for natural languages is presented. Katz's account is criticized on the following grounds. (1) the antonymy operator is not well defined; it leaves certain sentences without readings. (2) The account of negation is defective; it has the consequence that certain nonsynonymous sentences are marked as synonymous. (3) The account of entailment is defective; it has the consequence that analytic sentences entail synthetic ones. (4) Katz's account of indeterminable sentences is criticized; it has the consequence that certain logical truths are not marked as analytic. (5) Katz's semantics provides no account of truth, so that he is unable to show that analytic sentences are true and that indeterminable sentences are not.

Cappelen and Hawthorne’s Relativism and Monadic Truth (2009) offers an extended defense of a thesis they call simplicity, which, in brief, holds that propositions are true or false simpliciter. Propositions are cast in their traditional roles as the contents of assertions, and as the semantic values of declarative sentences in contexts. Simplicity stands in sharp contrast to forms of relativism including, for instance, a form that hold that our claims are true or false only relative to a judge. This applies especially to claims of taste, which come out true or false only relative to the judge who finds things tasty (e.g. Glanzberg 2007, Lasersohn 2005). But simplicity also rejects the more widespread temporalist view that propositions are true or false only relative to a time, and it rejects the even more widely held view that propositions are true or false only relative to a world. One reason that has been advanced for temporalism, e.g. by Kaplan (1989), is that our languages seem to contain non-trivial temporal operators. Hence, the argument goes, the semantic values of sentences need to be temporally neutral, i.e. vary for truth or falsehood with time. The same goes for possible worlds and modal operators. Hence, Kaplan and many others think of the semantic values of sentences as sets of world-time pairs. It has been tempting to apply this sort of argument much more widely, to see the semantic values of sentences as varying not just with world and time, but perhaps with location and other parameters as well. Kaplan..

Millianism says that the semantic content of a name (or indexical) is simply its referent. This thesis arises within a general, powerful research program, the propositionalist approach to semantics, which sets as a goal for philosophical semantics an assignment of entities — semantic contents — to bits of language, culminating in the assignment of propositions to sentences. Communication, linguistic competence, truth conditions, and other semantic phenomena are ultimately explained in terms of semantic contents. Over 100 years ago Frege (1952/1892) pointed out the problem with Millianism: sentences containing co-referential names seem semantically inequivalent. a=a is trivial, a priori, etc.; a=b is not, even if a and b have the same referent; φ(a) and φ(b) embed differently in the scope of propositional attitude verbs.

Cappelen and Hawthorne tell us that the most basic, explanatory notion of truth is a monadic property of propositions. Other notions of truth, including those applying to sentences, are to be explained in terms of it. Among them are those found in Kripkean, Montagovian, and Kaplanean semantic theories, and their descendants – to wit truth at a context, at a circumstance, and at a context-plus-circumstance. If these are to make sense, the authors correctly maintain, they must be explained in terms of the monadic notion of truth. (1-2) I thought that this was the received view, but the authors indicate otherwise. They describe possible-worlds semantics as making it “very natural to think of the foundational mode of evaluation for propositions as truth relative to worlds.”(7) I disagree. The natural way to understand possible worlds-semantics is to take world-states to be certain kinds of properties, and to take the truth of p at w to be the fact that p would be true (i.e. would instantiate monadic truth) were the universe to instantiate w. The authors add that it is somewhat natural to take “the actual truth of a proposition as [being] a matter of the proposition getting the value ‘true’ relative to a distinguished world -- the actual world.” (7) If this means that being actually true is being true at the actual world-state @, this isn’t just natural, it is unassailable -- as long as one doesn’t erroneously identify being true with being actually true. Since Cappelen and Hawthorne don’t do this, I take us to be on more or less the same page. Others, apparently, aren’t. We are told that “a number of the participants in the relevant disputes [about relativism] seem to take it for granted that philosophical semantics has somehow shown that the semantic value of sentences cannot be evaluated for truth or falsity simpliciter, since truth and falsity hold of a proposition relative to a world.” (77-8) We are also told: 1 Contemporary Analytic relativists reason as follows: ‘Lewis and Kaplan have shown that we need to relativize truth to triples of ..

For the sentences of languages that contain operators that express the concepts of definiteness and indefiniteness, there is an unavoidable tension between a truth-theoretic semantics that delivers truth conditions for those sentences that capture their propositional contents and any model-theoretic semantics that has a story to tell about how indetifiniteness in a constituent affects the semantic value of sentences which imbed it. But semantic theories of both kinds play essential roles, so the tension needs to be resolved. I argue that it is the truth theory which correctly characterises the notion of truth, per se. When we take into account the considerations required to bring model theory into harmony with truth theory, those considerations undermine the arguments standardly used to motivate supervaluational model theories designed to validate classical logic. But those considerations also show that celebration would be premature for advocates of the most frequently encountered rival approach – many-valued model theory.

Bringing together powerful new tools from set theory and the philosophy of language, this book proposes a solution to one of the few unresolved paradoxes from antiquity, the Paradox of the Liar. Treating truth as a property of propositions, not sentences, the authors model two distinct conceptions of propositions: one based on the standard notion used by Bertrand Russell, among others, and the other based on J.L. Austin's work on truth. Comparing these two accounts, the authors show that while the Russellian conception of the relation between sentences, propositions, and truth is crucially flawed in limiting cases, the Austinian perspective has fruitful applications to the analysis of semantic paradox. In the course of their study of a language admitting circular reference and containing its own truth predicate, Barwise and Etchemendy also develop a wide range of model-theoretic techniques--based on a new set-theoretic tool, Peter Aczel's theory of hypersets--that open up new avenues in logical and formal semantics.

Millianism says that the semantic content of a name (or indexical) is simply its referent. This thesis arises within a general, powerful research program, the propositionalist approach to semantics, which sets as a goal for philosophical semantics an assignment of entities – semantic contents – to bits of language, culminating in the assignment of propositions to sentences. Communication, linguistic competence, truth conditions, and other semantic phenomena are ultimately explained in terms of semantic contents.

Soames (Philos Top 15:44–87, 1987 , J Philos Logic 37:267–276, 2008 ) has argued that propositions cannot be sets of truth-supporting circumstances. This argument is criticized for assuming that various singular terms are directly referential when in fact there are good grounds to doubt this.