Locke on Truths of Reason

And here is Locke on the distinction between truths of reason and truths of fact, from Bk 4 ch xi, 13 ' Of our Knowledge of the Existence of Other Things'

13. Only particular propositions concerning concrete existences are knowable. By which it appears that there are two sorts of propositions:—(1) There is one sort of propositions concerning the existence of anything answerable to such an idea: as having the idea of an elephant, phoenix, motion, or an angel, in my mind, the first and natural inquiry is, Whether such a thing does anywhere exist? And this knowledge is only of particulars. No existence of anything without us, but only of God, can certainly be known further than our senses inform us. (2) There is another sort of propositions, wherein is expressed the agreement or disagreement of our abstract ideas, and their dependence on one another. Such propositions may be universal and certain. So, having the idea of God and myself, of fear and obedience, I cannot but be sure that God is to be feared and obeyed by me: and this proposition will be certain, concerning man in general, if I have made an abstract idea of such a species, whereof I am one particular. But yet this proposition, how certain soever, that “men ought to fear and obey God” proves not to me the existence of men in the world; but will be true of all such creatures, whenever they do exist: which certainty of such general propositions depends on the agreement or disagreement to be discovered in those abstract ideas.

The distinctions that Locke makes (see previous post) are therefore as follows:

1. propositions which are truths of reason, but merely trifling or verbal;

2. propositions which are truths of reason, but where the predicate is not actually contained in the subject, but is a necessary consequence of it;

3. propositions which are simply matters of fact, not deducible by reason alone.