Laurence Goldstein

(1947 - 2014)

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.

It is uncontroversial that, on any run through a Sorites series, a subject, at some point, switches from an ‘F’ verdict on one exhibit to a non-‘F’ verdict on the next. (Where this ‘cut-off’ point occurs tend to differ from trial to trial.) It is a fallacy to infer that there must be a cut-off point simpliciter between F items and non-F items. The transition is from firm ground to swamp. In the Sorites reasoning, some conditionals of the form ‘If Item n is F, then Item n + 1 is F’ are not false but nonsensical. This solution respects boundarylessness

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

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 …

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.

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.

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

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

A standard method for refuting a set of claims is to show that it implies a contradiction. Stephen Clark questions this method on the grounds that the Law of Non-Contradiction, together with the other fundamental laws of logic do not accord with everyday reality. He accounts for vagueness by suggesting that, for any vague predicate 'F', an ordinary object is typically to some extent both F and not-F, and that objects do not change abruptly from being F to being not-F. I challenge Clark's 'deconstruction' of logic, and show that, in characterizing vagueness and dealing with the associated Sorites paradox, we can accommodate his observation that change from being F to being not-F is ineradically continuous without tampering with any fundamental logical laws

Romane Clark has complained of the dissimilarity between Sellars’s treatment of conceptual thought and his treatment of sense impressions. For sense impressions are intrinsic to perceptions and, on Sellars’s view, both conceptual thought and perception are species of judgment. In the first section of this paper I want to raise a converse sort of complaint: Sellars offers an ‘adverbial’ theory of sense impressions and a similar account of conceptual thought. But this similarity of treatment is not justified by what Sellars says in its defence. If the adverbial theory of conceptual thought is true, as I believe it is, then a number of consequences, important for the philosophy of action, follow. Sellars traces some of these in his paper “Metaphysics and the Concept of a Person.” It would be desirable, therefore, if the adverbial theory of conceptual thought could be made secure. This is attempted in the second section and, in conclusion, the power of the theory is exhibited by directing it briefly at a long-standing problem in the philosophy of logic.