METAPHYSICS the universe If God created the world, then mechanistic explanation is underpinned by teleological explanation; the fundamental explanation of the existence and operation of any creature is the purpose of the creator If there is no God, but the universe is due to the operation of necessary laws upon blind chance, then it is the mechanistic level of explanation that is fundamental So far as I know, no one, whether scientist or philosopher, has provided a definitive answer to this question Realism vs Nominalism Throughout the history of philosophy one metaphysical problem recurs again and again, presented in different terms This is the question whether, if we are to make sense of the world we live in, there must exist, outside the mind, entities of a quite different kind from the fleeting individuals that we meet in everyday existence In the ancient world, Plato and Aristotle discussed whether or not there were Ideas or Forms existing independently of matter and material objects Throughout the Middle Ages, realist and nominalist philosophers disputed whether universals were realities or mere symbols In the modern era philosophers of mathematics have conducted a parallel debate about the nature of mathematical objects, with formalists identifying numbers with numerals, and realists asserting that numbers have an independent reality, constituting a third world separate from the world of mind and the world of matter The most vociferous defender of realism in modern times is Frege In a lecture entitled ‘Formal Theories of Arithmetic’ (CP 112–21) he attacks the idea that signs for numbers, like ‘ 12⁄ ’ and ‘ð’, are merely empty signs designating nothing Even calling them ‘signs’, he says, already suggests that they signify something A resolute formalist should call them ‘shapes’ If we took seriously the contention that ‘ 12⁄ ’ does not designate anything, then it is merely a splash of printer’s ink or a splurge of chalk, with various physical and chemical properties How can it possibly have the property that if added to itself it yields 1? Shall we say that it is given this property by definition? A definition serves to connect a sense with a word; but this sign was supposed to have no content Sure, it is up to us to give a signification to a sign, and therefore it is partly dependent on human 178