Online research in philosophy

Hofstadter has introduced the notion of an explicit Henkin sentence. Roughly speaking, an explicit Henkin sentence not only asserts its own provability, as ordinary Henkin sentences do, but explicitly provides a detailed description of a proof. We provide, in this paper, a precise formalization of Hofstadter's notion and then show that true explicit Henkin sentences exist.

“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..

If we try to evaluate the sentence on line 1 we ¯nd ourselves going in an unending cycle. For this reason alone we may conclude that the sentence is not true. Moreover we are driven to this conclusion by an elementary argument: If the sentence is true then what it asserts is true, but what it asserts is that the sentence on line 1 is not true. Consequently the sentence on line 1 is not true. But when we write this true conclusion on line 2 we ¯nd ourselves repeating the very same sentence. It seems that we are unable to deny the truth of the sentence on line 1 without asserting it at the same time.

The Liar sentence is here the sentence ‘The Liar sentence is not true.’. “Consider a Liar sentence: ...let us take a sentence l which says l is not true. W e can, informally, reason as..

Language is used to express thoughts and to represent aspects of the world. What thought a sentence expresses depends on what the sentence means, and how it represents the world also depends on what it means. Moreover, it is ultimately arbitrary, a matter of convention, that the words of a language mean what they do. So it might seem that what they mean is a matter of how they are used. However, they need not be used in accordance with their literal meanings. One can speak nonliterally, and convey something other than what the sentence means ('The look on his face spoke volumes'), or speak indirectly, and convey something more than what the sentence means ('I wonder if you know the time'). Linguistic communication requires knowledge of linguistic meaning, on the part of both the speaker and his audience, but it requires extralinguistic knowledge as well.

I argue on three distinct grounds that the contrast between speaking and revealing is nothing like so sharp as Wolterstorff maintains in Divine Discourse. Speaking may be revealing: in speaking a person may reveal much about himself. Putative divine speaking can only be made intelligible given a background of what I refer to as INIS revelation, and in revealing, or more exactly, in having revealed, God may still speak.

According to Kent Bach (forthcoming), our book, Insensitive Semantics (IS), suffers from its 'implicit endorsement' of (1): (1) Every complete sentence expresses a proposition (this is Propositionalism, a fancy version of the old grammar school dictum that every complete sentence expresses a complete thought) (Bach (ms.)) In response (C&L, forthcoming), we claim to be unaware of endorsing (1). No argument in IS depends on (1), we say. We don't claim to have shown that that there couldn't be grammatical sentences the semantic contents of which are not propositional.

This paper defends the claim that although ‘Superman is Clark Kent and some people who believe that Superman flies do not believe that Clark Kent flies’ is a logically inconsistent sentence, we can still utter this sentence, while speaking literally, without asserting anything false. The key idea is that the context-sensitivity of attitude reports can be, and often is, resolved in different ways within a single sentence.

Once upon a time it was assumed that speaking literally and directly is the norm and that speaking nonliterally or indirectly is the exception. The assumption was that normally what a speaker means can be read off of the meaning of the sentence he utters, and that departures from this, if not uncommon, are at least easily distinguished from normal utterances and explainable along Gricean lines. The departures were thought to be limited to obvious cases like figurative speech and conversational implicature. However, people have come to appreciate that the meaning of a typical sentence, at least one we are at all likely to use, is impoverished, at least relative to what we are likely to mean in uttering it. In other words, what a speaker normally means in uttering a sentence, even without speaking figuratively or obliquely, is an enriched version of what could be predicted from the meaning of the sentence alone. This can be because the sentence expresses a “minimal” (or “skeletal”) proposition or even because it fails to express a complete proposition at all.1 Indeed, it is now a platitude that linguistic meaning generally underdetermines speaker meaning. That is, generally what a speaker means in uttering a sentence, even if the sentence is devoid of ambiguity, vagueness, or indexicality, goes beyond what the sentence means. The question is what to make of this Contextualist Platitude, as I’ll call it. It may be a truism, but does it require a radical revision of the older conception of the relation between what sentences mean and what speakers mean in uttering them? Does it lead to a major modification, or perhaps even outright rejection, of the semantic-pragmatic distinction? I think..

The only passage from Aristotle's works that seemsto discuss the paradox of the liar is within chapter 25 of Sophistici Elenchi (180a34–b7). This passage raises several questions: Is it really about the paradox of the liar? If it is, is it addressing a strong version of the paradox or some weak strain of it? If it is addressing a strong version of the paradox, what solution does it propose? The conciseness of the passage does not enable one to answer these questions beyond doubt, and commentators have offered very different replies. However, a reasonable case can be made for claiming, first, that the passage in question is about the paradox of the liar, second, that it addresses a strong version of the paradox, and, third, that it attempts to solve it by assuming that someone uttering 'I am speaking falsely' (or whatever sentence-type the paradox turns on) is neither speaking truly nor speaking falsely absolutely.