Online research in philosophy

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.

The first section (§1) of this essay defends reliance on truth values against those who, on nominalistic grounds, would uniformly substitute a truth predicate. I rehearse some practical, Carnapian advantages of working with truth values in logic. In the second section (§2), after introducing the key idea of auxiliary parameters (§2.1), I look at several cases in which logics involve, as part of their semantics, an extra auxiliary parameter to which truth is relativized, a parameter that caters to special kinds of sentences. In many cases, this facility is said to produce truth values for sentences that on the face of it seem neither true nor false. Often enough, in this situation appeal is made to the method of supervaluations, which operate by “quantifying out” auxiliary parameters, and thereby produce something like a truth value. Logics of this kind exhibit striking differences. I first consider the role that Tarski gives to supervaluation in first order logic (§2.2), and then, after an interlude that asks whether neither-true-nor-false is itself a truth value (§2.3), I consider sentences with non-denoting terms (§2.4), vague sentences (§2.5), ambiguous sentences (§2.6), paradoxical sentences (§2.7), and future-tensed sentences in indeterministic tense logic (§2.8). I conclude my survey with a look at alethic modal logic considered as a cousin (§2.9), and finish with a few sentences of “advice to supervaluationists” (2.10), advice that is largely negative. The case for supervaluations as a road to truth is strong only when the auxiliary parameter that is “quantified out” is in fact irrelevant to the sentences of interest—as in Tarski’s definition of truth for classical logic. In all other cases, the best policy when reporting the results of supervaluation is to use only explicit phrases such as “settled true” or “determinately true,” never dropping the qualification.

Chrysippus claims that some propositions perish. including some true conditionals whose consequent is impossible and antecedent is possible, to which he appeals against Diodorus?s Master Argument. On the standard interpretation. perished propositions lack truth values. and these conditionals are true at the same time as their antecedents arc possible and consequents impossible. But perished propositions are false, and Chrysippus?s conditionals are true when their antecedent and consequent arc possible, and false when their antecedent is possible and consequent impossible. The claim of the Master Argument that Chrysippus rejects, then, is stronger ihan usually supposed.

More than a century ago, G. E. Moore famously offered an extended inference to reject what are in effect two substantially different types of ethical naturalism. Although some naturalistic doctrines targeted by that inference make semantic claims that, if true, would entail certain metaphysical claims, it is also possible that those semantic doctrines could be false and the metaphysical ones true at the same time. For if semantic naturalism is true, then moral terms and sentences are reducible, by an analysis of what they mean, into some purely descriptive terms and sentences. But, if metaphysical naturalism is true, then the moral properties and propositions expressed by moral terms and sentences are reducible to purely natural properties and propositions. By conflating claims about meaning with claims about reference, Moore‟s original inference proved vulnerable to a number of well known objections. But we believe there is a revised Moorean inference that can succeed, and we offer that argument here. Its scope is restricted to semantic reductivist forms of ethical naturalism: those that rest on theses claiming the reducibility of expressions in the moral vocabulary to expressions in a non-moral one. A not uncommon philosophical view in Moore‟s day, such theses remain live options in metaethics (as we‟ll presently show). Although our inference is run for some putative equivalences between moral and purely descriptive terms, it could easily be adapted against ethical naturalist theses 1 involving moral concepts and thoughts as well as sentences. Like Moore, we take the successful inference to consist in an open question argument („OQA’) followed by the naturalistic-fallacy charge („NFC‟). But, unlike Moore, we identify semantic naturalism as the only naturalistic doctrine vulnerable to the inference, and we offer adequate support for the inference‟s premises. Naturalism in ethics is thus undermined, though not refuted in all its forms: semantical naturalism comes out false, but metaphysical naturalism might still be true..

In recent work on context­dependency, it has been argued that certain types of sentences give rise to a notion of relative truth. In particular, sentences containing predicates of personal taste and moral or aesthetic evaluation as well as epistemic modals are held to express a proposition (relative to a context of use) which is true or false not only relative to a world of evaluation, but other parameters as well, such as standards of taste or knowledge or an agent. Thus, a sentence like chocolate tastes good would express a proposition p that is true or false not only at a world of evaluation, but relative to the additional parameter as well, such as a parameter of taste or an agent. I will argue that the sentences that apparently give rise to relative truth should be understood by relating them in a certain way to the first person. More precisely, such sentences express what I will call first­person­based genericity, a form of generalization that is based on or directed toward an essential first­person application of the predicate. The account differs from standard relative truth account in crucial respects: it is not the truth of the proposition expressed that is relative to the first person; the proposition expressed by a sentence with a predicate of taste rather has absolute truth conditions. Instead it is the propositional content itself that requires a first­personal cognitive access whenever it is entertained. This account, I will argue, avoids a range of problems that standard relative truth theories of the sentences in question face and explains a number of further peculiarities that such sentences display.

Epistemic possibilities are relative to bodies of information, or perspectives. To claim that something is epistemically possible is typically to claim that it is possible relative one’s own current perspective. We generally do this by using bare, unqualified epistemic possibility (EP) sentences, ones that don’t mention our perspective. The fact that epistemic possibilities are relative to perspectives suggests that these bare EP sentences fall short of fully expressing propositions, contrary to what both contextualists and relativists take for granted. Although they rightly reject propositional invariantism, the implausible view that a bare EP sentence expresses the same classical (absolutely true or absolutely false) proposition in any context, they maintain that a change in perspective shifts either the sentence’s propositional content (to a proposition involving a different perspective) or its truth-value (the same perspectivally neutral proposition now evaluated from a different perspective). I deny that the semantic contents of bare EP sentences shift at all. But I also deny that these contents have truth-values. Rather, according to the radical invariantism I defend, these contents are not full-fledged propositions but merely propositional radicals. Only explicitly relativized EP sentences manage fully to express propositions, and these perspective-involving propositions are the only EP propositions there are. Nevertheless, bare EP sentences are perfectly capable of being used to assert EP propositions, because utterances of them implicitly allude to the relevant perspective. Various problem cases challenge radical invariantism to explain pragmatically which perspective is read into the utterance of a given bare EP sentence. Unlike contextualism and relativism, it can do this without having to resort to any semantic bells and whistles..

Relativism has dominated many intellectual circles, past and present, but the twentieth century saw it banished to the fringes of mainstream analytic philosophy. Of late, however, it is making something of a comeback within that loosely configured tradition, a comeback that attempts to capitalize on some important ideas in foundational semantics. Relativism and Monadic Truth aims not merely to combat analytic relativism but also to combat the foundational ideas in semantics that led to its revival. Doing so requires a proper understanding of the significance of possible worlds semantics, an examination of the relation between truth and the flow of time, an account of putatively relevant data from attitude and speech act reporting, and a careful treatment of various operators. Throughout, Herman Cappelen and John Hawthorne contrast relativism with a view according to which the contents of thought and talk are propositions that instantiate the fundamental monadic properties of truth simpliciter and falsity simpliciter. Such propositions, they argue, are the semantic values of sentences (relative to context), the objects of illocutionary acts, and, unsurprisingly, the objects of propositional attitudes.

Kaplan (drawing on Montague and Prior, inter alia) made explicit the idea of world and time neutral propositions, which bear truth values only relative to world and time parameters. There was then a debate over the role of time. Temporalists sided with Kaplan in maintaining time neutral propositions with time relative truth values, while eternalists claimed that all propositions specify the needed time information and so bear the same truth value at all times. But there never was much of a parallel debate over the role of worlds. Let contingentism be the view (parallel to temporalism) that sides with Kaplan in maintaining world neutral propositions with world relative truth values, and let necessitarianism be the view (parallel to eternalism) that propositions specify the needed world information and so bear the same truth value at all worlds. This is the story of how the debate between the contingentists and the necessitarians might begin.

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 ..

It is a widely held view in philosophy that propositions perform a plethora of different theoretical roles. Amongst other things, they are believed to be the semantic values of sentences in contexts, the objects of attitudes, the contents of illocutionary acts, and the referents of that-clauses. This assumption is often combined with the claim that propositions have their truth-values eternally. In this paper I aim to show that these two assumptions are incompatible: propositions cannot both fulfill the mentioned roles and be eternally true or false. Following Kaplan and Lewis’s Operator Argument, I argue that compositional semantic values of sentences in contexts do not correspond to eternal propositions. Thus, either we regard the non-eternal entities that in fact realize the semantic role of propositions as also fulfilling the remaining propositional roles, or we abandon the assumption that there is a unique realizer of all the roles. The Operator Argument has recently come under attack, mainly for its tense-logical assumptions. However, rejecting these assumptions is not a sufficient defense of the compatibility of the two claims, since the extensional alternative to the tense-logical framework does not allow us to universally retain eternal propositions as compositional semantic values of sentences either.