NECESSITY, APRIORITY, AND LOGICAL STRUCTURE

Logical structure may explain the necessity and a priori knowability of such truths as that if A is red then A is either red or green. But this explanation cannot be extended to sentences that, while necessary and knowable a priori, do not wear the appropriate logical structure on their sleeves – sentences like 'if A is a point and A is red, then A is not green,' or 'if A is a sphere, then A is not a cube.' The real origin of these sentences' necessity and a priori knowability is a relationship between the meanings of their component atomic sentences – a relationship which cannot be systematically reduced to logical structure by translating those atomic sentences into any kind of 'ideal' language. Moreover, this kind of relationship is one to which any atomic sentences are susceptible if they have a classifying, or comparison-implying, content. Arguably, then, all atomic sentences are capable of being related to others in ways that are necessary and knowable a priori.