Plumb down he dropped, ten thousand fathoms deep.’
Whether our power of conceiving is so far a test of possibility, as that what is distinctly conceived must be concluded to be possible, and what cannot be conceived impossible, was a question which interested Reid. It is discussed in the Essays on the Intellectual Powers, and also in the draft of a letter to Dr. Price, preserved among the manuscripts at Birkwood; in which it is argued that our power of conception cannot be a criterion of what is possible. The argument turns much on the meanings of ‘conception,’ ‘possibility,’ and ‘impossibility.’ He thus addresses Dr. Price:—
‘I would willingly suggest some subject on which I might have the favour of your thoughts when you have leisure and are disposed for such correspondence. What occurs to my thoughts just now is a metaphysical axiom very generally adopted, and, I think, occasionally adopted by you in your Review of the Principal Questions in Morals—That what we distinctly conceive is possible. From this axiom D. Hume infers that it is possible that an universe may start into existence without a cause, and other like extravagancies. The use he makes of it led me to consider it a good many years ago, and I have a strong suspicion that there is some fallacy in it, which has imposed on men’s understandings, owing to the ambiguity of the word conceive.
‘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 maybe 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 which appears to us to have any degree of probability, however small, must at least be possible. But the axiom, taken in this sense, is surely false. It would be superfluous to give instances of this to a mathematician.
‘If it should be said that conceiving a proposition to be true means, neither barely to understand the meaning of the proposition, nor the giving any degree of assent to it, I would be glad to know what it really does mean. For I am at a loss to know what power of the understanding we mean by the conceiving a proposition to be true, if it is neither simple apprehension, by which we barely understand the meaning of a proposition, nor judgment, by which we assent to the proposition or dissent from it. I know of no power of the understanding intermediate between these two. And if there is none, I think the axiom must be false.
‘There are many propositions which, by the faculties God has given us, we perceive to be not only true, but necessarily true; and the contradictions of these must be impossible. So that our knowledge of what is impossible keeps pace with our knowledge of necessary truth.