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Our actions are a product of mental states that represent how the world is, how we want it to be, and so forth. Such is central to our conception of ourselves as rational agents. I suppose it is possible that this conception is simply wrong. Perhaps there are, as eliminativists have argued, no such things as beliefs and desires. Or perhaps there are, but these states are merely relations to uninterpreted formulae in some internal computational system. I am going to set such questions aside here and assume that our ordinary conception of our ourselves is not wholly mistaken. The question I want to discuss concerns the role played in this conception by the notion of representation, that is, by representational content. The question is: How must we understand the contents of mental states such as beliefs and desires if those states are to play the causal and explanatory roles envisaged for them? 1 The question can be illustrated as follows. According to Frege (1984b, pp. 144-5), the reference of a sentence is its truth-value. Frege did not, however, take the content of a sentence to be its truth-values and, relatedly, he did not regard beliefs as relations between thinkers and truth-values. Such a view would widely be regarded as patently absurd. But why?One answer is that such an account fits poorly with our intuitions about the truth-values of sentences that attribute beliefs. If beliefs were relations to truthvalues, it might be said, then "N believes that S" and "N believes that P" would have the same truth-value whenever S and P had the same truth-value. Since each of us surely has at least one belief that is true and one belief that is false, every sentence of the form "N believes that S" would then be true. That does not accord with intuition.

As is well-known, the formal system in which Frege works in his Grundgesetze &r Arithmetik is formally inconsistent, Russell's Paradox being derivable in it. This system is, except for minor differences, 111 secondorder logic, augmented by a single non-logical axiom, Frege's Axiom V. It has been known for some time now that the bt-order fragment of the theory is consistent. The present paper establishes that both the simple &the ramifiedpredicative second-order fragments arc consistent, and that Robinson arithmetic, Q, is relatively interpretable in the simple predicative fragment. The philosophical signiiicance of the result is discussed.

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