it certainly does not follow that
'If a man wins a race, he sometimes does not run it.'
§ 716. There is a common but erroneous notion that all conditional propositions are to be regarded as affirmative. Thus it has been asserted that, even when we say that 'If the night becomes cloudy, there will be no dew,' the proposition is not to be regarded as negative, on the ground that what we affirm is a relation between the cloudiness of night and the absence of dew. This is a possible, but wholly unnecessary, mode of regarding the proposition. It is precisely on a par with Hobbes's theory of the copula in a simple proposition being always affirmative. It is true that it may always be so represented at the cost of employing a negative term; and the same is the case here.
§ 717. There is no way of converting a disjunctive proposition except by reducing it to the conjunctive form.
§ 718. Permutation of Complex Propositions.
(A) If A is B, C is always D.
.'. If A is B, C is never not-D. (E)
(E) If A is B, C is never D.
.'. If A is B, C is always not-D. (A)
(I) If A is B, C is sometimes D.
.'. If A is B, C is sometimes not not-D. (O)
(O) If A is B, C is sometimes not D.
.'. If A is B, C is sometimes not-D. (I)
§ 719.