 The main arguments against platonic realism turn on the idea that the platonist position precludes a satisfactory epistemology of arithmetic. For the classic exposition of the doubt that platonism can square its claims to accommodate knowledge of arithmetical truth with its conception of the subject matter of arithmetic as causally inert, see Benacerraf (1973). Benacerraf argued that platonism faces difficulties in squaring its conception of the subject-matter of arithmetic with a general causal constraint on knowledge (roughly, that a subject can be said to know that P only if she stands in some causal relation to the subject matter of P). In response, platonists have attacked the idea that a plausible causal constraint on ascriptions of knowledge can be formulated (Wright 1983 Ch.2, Hale 1987 Ch.4). In response, Hartry Field, on the side of the anti-platonists, has developed a new variant of Benacerraf’s epistemological challenge which does not depend for its force on maintaining a generalised causal constraint on ascriptions of knowledge. Rather, Field argues that ‘we should view with suspicion any claim to know facts about a certain domain if we believe it impossible to explain the reliability of our beliefs about that domain’ (Field 1989: 232–3). Field’s challenge to the platonist is to offer an account of what such a platonist should regard as a datum—i.e. that when ‘p’ is replaced by a mathematical sentence, the following schema holds in most instances: