A syntactically correct number-specification may fail to specify any number due to underspecification. For similar reasons, although each sentence in the Yablo sequence is syntactically perfect, none yields a statement with any truth-value. As is true of all members of the Liar family, the sentences in the Yablo sequence are so constructed that the specification of their truth-conditions is vacuous; the Yablo sentences fail to yield statements. The ‘revenge’ problem is easily defused. The solution to the semantical paradoxes offered here (...) revives the mediaeval cassatio approach, one that largely disappeared due to its incomprehending rejection by influential contemporary writers such as William Shyreswood and Thomas Bradwardine. The diagnosis readily extends to the set-theoretic paradoxes. (shrink)

Consideration of a paradox originally discovered by John Buridan provides a springboard for a general solution to paradoxes within the Liar family. The solution rests on a philosophical defence of truth-value-gaps and is consistent (non-dialetheist), avoids ‘revenge’ problems, imports no ad hoc assumptions, is not applicable to only a proper subset of the semantic paradoxes and implies no restriction of the expressive capacities of language.

The Russell class does not exist because the conditions purporting to specify that class are contradictory, and hence fail to specify any class. Equally, the conditions purporting to specify the Liar statement are contradictory and hence, although the Liar sentence is grammatically in order, it fails to yield a statement. Thus the common source of these and related paradoxes is contradictory (or tautologous) specifying conditions-for such conditions fail to specify. This is the diagnosis. The cure consists of seeking and destroying (...) the deep-seated preconceptions that make almost irresistible our belief in the existence of items which provably do not exist. (shrink)

Laurence Goldstein gives a straightforward and lively account of some of the central themes of Wittgenstein's writings on meaning, mind, and mathematics.

outrageous remarks about contradictions. Perhaps the most striking remark he makes is that they are not false. This claim first appears in his early notebooks (Wittgenstein 1960, p.108). In the Tractatus, Wittgenstein argued that contradictions (like tautologies) are not statements (Sätze) and hence are not false (or true). This is a consequence of his theory that genuine statements are pictures.

The views on contradiction and consistency that Wittgenstein expressed in his later writings have met with misunderstanding and almost uniform hositility. In this paper, I trace the roots of these views by attempting to show that, in his early writings, Wittgenstein accorded a ?unique status? to tautologies and contradictions, marking them off logically from genuine propositions. This is integral both to his Tractatus project of furnishing a theory of inference, and to the enterprise of explaining the nature of the Satz (...) (statement, proposition). Wittgenstein mantained that contradictions are not false. In his early writings this surprising thesis is a consequence of his view that contradictions are not statements. In his late writings he continues to advocate the thesis, but for quite different reasons. In these late writings, I contend, Wittgenstein succeeds in making the surprising thesis plausible. (shrink)

Wittgenstein's Tractatus is widely regarded as a masterpiece, a brilliant, if flawed attempt to achieve an ‘unassailable and definitive … final solution’ to a wide range of philosophical problems. Yet, in a 1931 notebook, Wittgenstein confesses: ‘I think there is some truth in my idea that I am really only reproductive in my thinking. I think I have never invented a line of thinking but that it was always provided for me by someone else’. This disarming self-assessment is, I believe (...) accurate. The Tractatus, despite making significant advances on the logical doctrines of Frege and Russell, is essentially a derivative work—Wittgenstein, as he elsewhere acknowledges, provided a fertile soil in which the original seeds of other peoples' thought grew in a unique way. In a play of mine, published in Philosophy (1999), Wittgenstein fails a tough viva on the Tractatus because he fails to properly support some of the weak arguments in the work and because of his inadequate acknowledgment of sources. The present paper further explores some of the antecedents of Wittgenstein's early views and answers some criticisms of the play. (shrink)

The three puzzles here considered are shown to have a common structure. And in each, an agent is thrust into a cleverly contrived deliberatively unstable situation. The paper advocates a resolutely Pyrrhonian abandonment of the futile reasoning in which the agent is trapped and advocates an alternative strategy for escape.

For familiar reasons, stereotyping is believed to be irresponsible and offensive. Yet the use of stereotypes in humor is widespread. Particularly offensive are thought to be sexual and racial stereotypes, yet it is just these that figure particularly prominently in jokes. In certain circumstances it is unquestionably wrong to make jokes that employ such stereotypes. Some writers have made the much stronger claim that in all circumstances it is wrong to find such jokes funny; in other words that people who (...) laugh at such jokes betray sexist/racist attitudes. This conclusion seems false. There is, as I shall argue, a thin dividing line between being properly sensitive to the rights and feelings of women and of racial groups different from our own, and being excessively sensitive to oversensitivity. Oversensitivity is, in this context, a kind of intolerance, and there is no reason why we should pander to that. One can be opposed to the unchecked dissemination of certain kinds of racist or sexist humor without oneself being a racist or sexist for finding such humor funny. The use of various stereotypes in humor serves the linguistic purpose of facilitating brevity and punch, the cultural purpose of preserving, in a sanitized form traditional rivalries and antipathies, and the psychological purpose of discharging fears. Blanket moral condemnation is inappropriate, though there will, of course, be circumstances under which the promulgation of certain types of humor, or even its enjoyment, ought to be condemned. (shrink)

In a well-known story constructed by Saul Kripke , Pierre, a rational but monolingual Frenchman who has never visited England, acquires, on the evidence of many magazine pictures of London, the belief that London is beautiful. He is happy to declare ‘Londres est jolie’. Pierre eventually moves to England and settles in one of the seedier areas of London, travelling only to comparably shabby neighbourhoods. He learns English by immersion, though he does not realize that ‘London’ and ‘Londres’ are co-referential. (...) Naturally enough, given his current circumstances, he acquires a belief that he is only too willing to express by uttering ‘It is not the case that London is beautiful’. So apparently he now holds contradictory beliefs. But rational people do not hold contradictory beliefs ….One popular response to Kripke's puzzle is that people …. (shrink)

According to some commentators, Wittgenstein’s Tractatus is all one big joke: we plough through the text trying to extract the sense out of each spare and heroic proposition, only to be told at the end, that anyone who understands the author will realize that all of his propositions are nonsensical and so are not even propositions. The whole work is a kind of hoax; the readers are ridiculed, but, with luck, will eventually have to laugh when they come to recognize (...) that what they had taken for deep philosophy was all so much gibberish. As a result of this revelation, they will be cured for ever of the urge to philosophize. (shrink)

Brevity in conversation is a window to the workings of the mind. It is both a multifaceted topic of deep philosophical importance and a phenomenon that serves as a testing ground for theories in linguistics, psycholinguistics and computer modeling. Speakers use elliptical constructions and exploit salient features of the conversational environment, a process of pragmatic enrichment, so as to pack a great deal into a few words. They also tailor their words to theirparticular conversational partners. In Brevity, distinguished linguists, philosophers (...) and cognitive scientists shed new light on economy in discourse. The book will appeal to linguists, philosophers, and psychologists at advanced undergraduate level and above. (shrink)

Wittgenstein likened himself to a soil distinctive only in that once implanted with the seeds of great thinkers, interesting flora grew. This chapter examines the influence on him of authors he regarded as truly original, such as Bolzmann, Hertz, Schopenhauer, Frege and Russell.

There has recently been revived logical interest, particularly in the context of attempts to solve the logico-semantical paradoxes, of the idea that there are true contracistions, and of semantics accomodating the glut value both true and false. By considering some generally accepted claims about assertion. I attempt to show that this dialetheist idea is untenable.

The plausibility of the theory of evolution depends on abandoning the assumption of a unique 'big bang' ex nihilo marking the beginning of the universe.

(1983). Scientific scotism — The emperor's new trousers or has armstrong made some real strides? Australasian Journal of Philosophy: Vol. 61, No. 1, pp. 40-57.

Logicism is one of the great reductionist projects. Numbers and the relationships in which they stand may seem to possess suspect ontological credentials – to be entia non grata – and, further, to be beyond the reach of knowledge. In seeking to reduce mathematics to a small set of principles that form the logical basis of all reasoning, logicism holds out the prospect of ontological economy and epistemological security. This paper attempts to show that a fundamental logicist project, that of (...) defining the number one in terms drawn only from logic and set theory, is a doomed enterprise. The starting point is Russell's Theory of Descriptions, which purports to supply a quantificational analysis of definite descriptions by adjoining a 'uniqueness clause' to the formal rendering of indefinite descriptions. That theory fails on at least two counts. First, the senses of statements containing indefinite descriptions are typically not preserved under the Russellian translation. Second (and independently), the 'uniqueness clause' fails to trim 'some' to 'one'. The Russell–Whitehead account in Principia Mathematica fares no better. Other attempts to define 'one' are covertly circular. An ontologically non-embarrassing alternative account of the number words is briefly sketched. (shrink)

Wittgenstein discusses speakers exploiting context to inject meaning into the sentences that they use. One facet of situation comedy is context-injected ambiguity, where scriptwriters artfully construct situations such that, because of conflicting contextual clues, a character, though uttering a sentence that contains neither ambiguous words nor amphibolous contruction may plausibly be interpreted in at least two distinct ways. This highlights an important distinction between the (concise) sentence that a speaker uses and what the speaker means, the disclosure of which may (...) require considerable spelling out. Understanding this phenomenon of nonindexical contextualism is the key to solving, inter alia , problems where, puzzlingly, exchanging a singular term in a statement with a co-referential one fails to preserve truth-value. This is a rare case where there is a huge debate in the recent literature that is decisively settled by Wittgenstein’s approach. (shrink)