By Roger Teichmann (auth.)
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Wherein the difficulties lie, and not in the task of paraphrase as such. Let us turn now to another important question, namely, does the alleged paraphrasability of abstract terms necessarily threaten realism 42 The General Problem and its Solution about abstract entities? Might not some sufficient basis for such realism simply ignore the paraphrasability question? Bob Hale, in his book Abstract Objects, has argued in favour of realism about abstract objects by appeal to the existence of abstract singular terms.
Answers available to the realist will have their counterparts for the nominalist. Thus, both sides may go in for 'stonewalling'. The realist may assert that it is simply the fact that all colours are colours which explains why they form a kind, what they have in common being simply self-evident; while the nominalist may say (for example) that 'A Abstract Terms 39 is red, so, and in virtue of this, A is coloured' is a truth in which the role of the phrase 'in virtue of this' is simply self-evident.
The resulting taxonomy will form the basis of a 'categorial grammar'. In 'A Program for Syntax', Geach adopts the above sort of method in his programme for defining the syntactic categories, a programme whose ancestry, as he says, is to be found in the work respectively of Frege and of the Polish logicians (in particular Ajdukiewicz). The more precise characterisation of 'combining' is in terms of the Fregean distinction between functor and argument. An expression (for example, a predicable) acts as a functor in taking another expression (for example, a name) as argument, thus yielding (as 'value') a sentence.