Partial Belief

Abstract

Hume’s account of partial belief is an extension in a quite natural way of his account of non-partial belief.¹ Partial belief is a consequence, on his view, of the mind’s capacity to divide its force equally among distinct alternatives. This is most simply applicable to conditional partial beliefs, of the form ’B will be consequent upon A’. The strength of such a belief will, he says, be m/k just when:

• (i) The lively conception (belief in A) is followed in the mind by the lively conceptions of some distinct C¹,. . .,C_k.

• (ii) Just m of these cases are seen to be B. Hume’s account assumes the principle of indifference. The alternatives in which B obtains are supposed to contribute equally to the strength of the belief in B. It is quite clear that this account is intended to be probabilistic, that is to conform to the laws.

• (iii) If B is a necessary consequence of A, then the strength of belief in B given A is 1.

• (iv) If B₁ and B₂ are incompatible in the presence of A, then (assuming conditional belief is defined in B₁ given A and in B₂ given A) the strength of belief in B₁ or B₂ given A is the sum of the strength of the beliefs in B₁ given A and in B₂ given A.