Faith is “desire (approved by the Conscience) of which we imagine the fulfilment, while putting doubt at a distance”: see the _Definitions_ at the end of the volume.
I am afraid your notions about “proof” are still rather hazy; for you quote against me a stern and self-denying dictum which passes current among some of your young friends, that “it is immoral to believe what cannot be proved.”
Have you seriously asked yourself what you mean by “proved” in enunciating this proposition? Do you mean “made sufficiently probable to induce a man to act upon the probability”? Or do you mean “absolutely demonstrated”?
If you mean the former, not so many as you suppose are guilty of this “immorality.” Give me an instance, if you can, of a man who “believes what cannot be made sufficiently probable to induce him to act upon the probability.” Of course some men _say_ they believe what they, in reality, do not believe; but you speak, not about “saying” but about “believing;” and I do not see how any man can “believe” what he does not regard as probable. I am inclined to think therefore that, in this sense of the word “prove,” your proposition is meaningless.
But perhaps by “prove,” you mean “absolutely demonstrate;” and your thesis is that “it is immoral to believe what cannot be absolutely demonstrated;” in that case I am obliged to ask you how you can repeat such cant, such a mere parrot cry, with a grave face.
Do you not see that, as soon as you conceded (as I understand you to have done) that our belief in the Laws of Nature is based upon the Imagination, you virtually conceded the validity of a kind of proof in which faith and hope play a large part, and in which demonstration is impossible. “Demonstration” applies to mathematics and to syllogisms where the premises are granted, though it is also sometimes loosely used of proof conveyed by personal observation; “proof” applies to the other affairs of life. Demonstration appeals very largely (not entirely, as I have shown above, but very largely) to Reason; proof is largely based on Faith. Having defined “angles,” “triangles,” “base,” and “isosceles,” and having been granted certain axioms and postulates, I can demonstrate that the angles at the basis of an isosceles triangle are equal to one another; but I cannot “demonstrate” that, if I throw a stone in the air, it will come down again, though I am perfectly convinced that it will come down, and though I commonly assert that I can “prove” that it will come down.