meaning of the known. Constructive hypotheses are simply guesses at unknown principles. Their great function is as an instrument in discovery.
Illustrative hypotheses and constructive hypotheses are subject to different conditions. And once more it will be found that the conditions that attach to the suppositions under discussion arise from the ends they respectively subserve.
Illustrative hypotheses, because they aim merely at illustration, may not only go beyond truth, but even against truth, or against possibility. In the teaching of physical science, for example, untrue and impossible suppositions are freely used. Thus, in explaining the principle of the pendulum, a teacher might say if the pendulum is swung under certain conditions, in a perfect vacuum, and so that there is no friction, it will swing for ever, though the complete removal of air, and the complete removal of friction are alike physically impossible. Again, the present writer has heard Sir Robert Ball, in an astronomical lecture, when speaking of the fact that the transmission of light is not instantaneous, but takes a certain time, make the supposition that if an observer were to recede from the earth more rapidly than the rate at which light travels, that observer would see the events of the earth's history repeat themselves but repeat themselves in an order the reverse of actual occurrence, in other words, backwards. This couple of examples will sufficiently remind the reader how little regard to truth or practicability illustrative hypotheses need pay. An illustrative hypothesis is not limited even by the metaphysical conditions of the possible. Thus in a treatise on Ethics written from the scholastic standpoint, the student may find an illustrative hypothesis of this sort: If God had not commanded men to do what is right, what obligation would attach to the natural law? The 'if' here introduces a supposition that the writer of the treatise regards as at variance with metaphysical possibility. But this in no way prejudices it as an illustration. An illustration, if it is to illustrate, should be quite clear and definite, but it need not be and is no better for being a fact. There may be much virtue in an "if" even if that virtue is not truth.
Constructive hypotheses, the second subdivision of suppositions that have truth as their end, are subject to much more stringent conditions. A constructive hypothesis is a guess at the truth. It is a tentative assumption made in the hope that it will turn out to be true. And from this arise the conditions of a valid hypothesis as they are laid down in logical text-books. Truths must be in harmony with themselves and with each other; they must be, as it has been put, internally and externally consistent. A constructive hypothesis unlike an illustrative cannot be at variance with possibility. What is impossible cannot be even provisionally taken as true. A constructive hypothesis unlike an illustrative cannot be at variance with fact: truth must be in harmony with truth. A supposition made in the hope that it will turn out to be a truth
