'As to the history of this axiom, I suspect it to have taken its rise from what Descartes laid down as the criterion of truth, which he maintained to be clear and distinct conception. Quidquid clare et distincte concipio esse verum, id est verum. Cudworth seems to have followed him in this, making the criterion of verity to be clear, self-consistent intelligibility. Those who came after, judging it difficult to maintain that everything is true which is clearly conceivable or intelligible, have maintained that everything that can be clearly conceived is at least possible. This seemed to be the proper correction of Descartes’ maxim, and it has passed from one hand to another without strict examination.
'Whatever is true or false, whatever is possible or impossible, may be expressed by a proposition. Now, what do we mean when we say that we conceive a proposition? I think no more is meant, if we speak properly, than that we understand what is meant by that proposition. If this be so, it must surely be granted that we may understand the meaning of a proposition which expresses what is impossible. He who understands the meaning of this proposition, “Two and two make four,” must equally understand the meaning of this other, “Two and two do not make four.” Both are equally understood; that is, the conception of both is equally clear; yet the first is necessarily true, and the second impossible.
'Perhaps it will be said, that we may not merely conceive the meaning of a proposition, but we may conceive it to be a true proposition, and that it is our being able to conceive it to be true that gives us ground to think it possible. In answer to this, I beg you would attend very carefully to the meaning of these words—“Conceiving a proposition to be true.” I can put no other meaning upon them but judging it to be true, that is, giving some degree of assent to it. Judgment or assent admits of various degrees, from the slightest suspicion to the most deliberate conviction; from the most modest and diffident assent to the most pertinacious and dogmatical. I conceive there may be inhabitants in the moon; that is, my judgment leans a little that way. I would not use that expression unless the probability, however small, seemed to be on that side of the question.
'If this be the meaning of conceiving a proposition to be true, then the meaning of the axiom will be, that a proposition