In /An Enquiry Concerning Human Understanding/, Hume made
a distinction about how subject and predicate could be related:
All the objects of human reason or enquiry may naturally be divided
into two kinds, to wit, /Relations of Ideas/, and /Matters of Fact/.
Of the first kind are the sciences of Geometry, Algebra, and
Arithmetic; and in short, every affirmation which is either
intuitively or demonstratively certain [/note:/ these are Locke’s
categories]. /That the square of the hypothenuse is equal to the
square of the two sides/, is a proposition which expresses a
relation between these figures. /That three times five is equal to
the half of thirty/, expresses a relation between these numbers.
Propositions of this kind are discoverable by the mere operation of
thought, without dependence on what is anywhere existent in the
universe. Though there never were a circle or triangle in nature,
the truths demonstrated by Euclid would for ever retain their
certainty and evidence.
Matters of fact, which are the second objects of human reason, are
not ascertained in the same manner; nor is our evidence of their
truth, however great, of a like nature with the foregoing. The
contrary of every matter of fact is still possible; because it can
never imply a contradiction, and is conceived by the mind with the
same facility and distinctness, as if ever so conformable to
reality. /That the sun will not rise to-morrow/ is no less
intelligible a proposition, and implies no more contradiction than
the affirmation, /that it will rise/. We should in vain, therefore,
attempt to demonstrate its falsehood. Were it demonstratively false,
it would imply a contradiction, and could never be distinctly
conceived by the mind. [/Enquiries/, Selby-Bigge edition, Oxford,
1902, 1972, pp.25-26]
eidetisch 