Online research in philosophy

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.

In his 1982 book Wittgenstein on Rules and Private Language, Saul Kripke develops a famous argument that purports to show that there are no facts about what we mean by the expressions of our language: ascriptions of meaning, such as “Jones means addition by ‘+’” or Smith means green by ‘green’”, are according to Kripke’s Wittgenstein neither true nor false. Kripke’s Wittgenstein thus argues for a form of non-factualism about ascriptions of meaning: ascriptions of meaning do not purport to state facts. Define semantic realism to be the view that ascriptions of meaning are apt to be assessed in terms of truth and falsity, and are, at least in some instances, true. Semantic realism, thus defined, is a form of cognitivism about semantic judgement, according to which judgements ascribing meaning express beliefs, states apt for assessment in terms of truth and falsity. Kripke’s Wittgenstein thus argues against semantic realism, and in favour of a form of semantic non-cognitivism.1 En route to semantic non-cognitivism, Kripke’s Wittgenstein argues against dispositionalist theories of meaning, which hold something roughly along the lines of the following: Jones means magpie by “magpie” if and only if Jones is disposed to apply “magpie” to magpies in ideal conditions (where the ideal conditions can be specified in terms that don’t presuppose the notion of meaning, and are such that in those conditions Jones applies “magpie” to a thing if and only if that thing is a magpie).

(Beall ed. The Revenge of the Liar, forthcoming from Oxford University Press) > The main presentation of my approach to the semantic paradoxes. I take them to show that understanding a natural language is sharing a cognitive relation to a logically false semantic theory with other speakers.

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.

Semantic holists view what one's terms mean as function of all of one's usage. Holists will thus be coherentists about semantic justification: showing that one's usage of a term is semantically justified involves showing how it coheres with the rest of one's usage. Semantic atomists, by contrast, understand semantic justification in a foundationalist fashion. Saul Kripke has, on Wittgenstein's behalf, famously argued for a type of skepticism about meaning and semantic justification. However, Kripke's argument has bite only if one understands semantic justification in foundationalist terms. Consequently, Kripke's arguments lead not to a type of skepticism about meaning, but rather to the conclusion that one should be a coherentist about semantic justification, and thus a holist about semantic facts.

The distinction between the semantic content of a sentence or utterance and its use is widely employed in formal semantics. Semantic minimalism in particular understands this distinction as a sharp dichotomy. I argue that if we accept such a dichotomy, there would be no reason to posit the existence of semantic contents at all. I examine and reject several arguments raised in the literature that might provide a rationale for assuming semantic contents, in this sense, exist, and conclude that Ockham’s razor should be applied to these postulated entities. Since the notion of “semantic content” doubles both as what a semantic theory is a priori supposed to account for and as the product of that same theory, it is methodologically unsound to appeal to this notion to fend off criticisms of and counterexamples to semantic theories.

No semantic theory satisfying certain natural constraints can identify the semantic contents of sentences (the propositions they express), with sets of circumstances in which the sentences are true–no matter how fine-grained the circumstances are taken to be. An objection to the proof is shown to fail by virtue of conflating model-theoretic consequence between sentences with truth-conditional consequence between the semantic contents of sentences. The error underlines the impotence of distinguishing semantics, in the sense of a truth-based theory of logical consequence, and semantics, in the sense of a theory of meaning.

Sententialism: An adequate semantic theory for a language assigns semantic values to complex expressions (typically on the basis of the semantic values of the syntactic parts of those complex expressions), with the assignment process culminating in the assignment of appropriate semantic values (typically propositions or truth conditions) to entire sentences. Sententialism is so-called because it takes the task of semantic theory proper to be exhausted once semantic values have been assigned to full sentences. Beyond the sentence may lay further linguistic phenomena broadly construed, such as various discourse properties and relations, but any such phenomena are relegated to the pragmatics. Sententialism thus typically goes hand-in-hand with a larger philosophical perspective according..

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.

Davidson approaches the notions of meaning and interpretation with the aim of characterizing semantic competence in the syntactically characterized natural language. The objective is to provide a truth-theory for a language, generating T-sentences expressed in the semantic metalanguage, so that each sentence of the object language receives an appropriate interpretation. Proceeding within the constraints of referential semantics, I will argue for the viability of reconstructing the notion of linguistic meaning within the Tarskian theory of reference. However, the view proposed here involves a revision of Davidson’s con-ception of the object of semantic investigation. Taking (idealized) language-theories as the proper object of semantic characterization, provides solutions to outstanding problems in Davidson’s views, better approximates the practice in standard model-theoretic semantics, and incorporates the elements of semantic competence sought for in tradi¬tional theories of lexical analysis. Sources of evidence beyond those emphasized by Davidson will be invoked in order to allow for the selection of interpre¬tive T-sentences. In the final section, possible Quinean objections will be considered.