Wittgenstein on Mathematics, Minds and Mental Machines

This an historical analysis of the three main topics of Wittgenstein's work. Part 1 deals with the universal "game" of mathematics, it covers the early background to Wittgenstein's writings on mathematics and his doctrines in the Tractatus concerning the "limit of language" as well as the "metaphysical subject". Comparisons with Martin-Lof are made and Brouwer's institutionistic view is contrasted with Wittgenstein's early operationalistic view, bringing together a summary of his pre-1929 view of pure mathematics. Part II discusses "Thought, Language and Philosophy" with Wittgenstein's development up to 1930. This includes his co-operation with Ramsay, the problem of "intention", the "private language" arguments and its consequences for the understanding of "cognitivism". Wittgenstein's view is also compared and contrasted with the Anti-Realist and Realist doctrines of philosophy as well as "rules-of-theory" illusion.
Part III looks at explicit philosophical problems concerning mathematical calculations, conceptual problems in the meta-mathematical writings in the formal sciences and the philosophical problems of psychology arising from the possiblity of the existence of strong artificial intelligence. The author concludes with a synopsis of Wittgenstein's treatment concerning the impossibility of there existing a genuine artificial intelligence indepenently from human thought.