Possibility of Deductive Reasoning.
As the truth of an hypothesis is to be proved by its conformity with fact, the first condition is that we be able to apply methods of deductive reasoning, and learn what should happen according to such an hypothesis. Even if we could imagine an object acting according to laws hitherto wholly unknown it would be useless to do so, because we could never decide whether it existed or not. We can only infer what would happen under supposed conditions by applying the knowledge of nature we possess to those conditions. Hence, as Boscovich truly said, we are to understand by hypotheses “not fictions altogether arbitrary, but suppositions conformable to experience or analogy.” It follows that every hypothesis worthy of consideration must suggest some likeness, analogy, or common law, acting in two or more things. If, in order to explain certain facts, a, a′, a″, &c., we invent a cause A, then we must in some degree appeal to experience as to the mode in which A will act. As the laws of nature are not known to the mind intuitively, we must point out some other cause, B, which supplies the requisite notions, and all we do is to invent a fourth term to an analogy. As B is to its effects b, b′, b″, &c., so is A to its effects a, a′, a″, &c. When we attempt to explain the passage of light and heat radiations through space unoccupied by matter, we imagine the existence of the so-called ether. But if this ether were wholly different from anything else known to us, we should in vain try to reason about it. We must apply to it at least the laws of motion, that is we must so far liken it to matter. And as, when applying those laws to the elastic medium air, we are able to infer the phenomena of sound, so by arguing in a similar manner concerning ether we are able to infer the existence of light phenomena corresponding to what do occur. All that we do is to take an elastic substance, increase its elasticity immensely, and denude it of gravity and some other properties of matter, but we must retain sufficient likeness to matter to allow of deductive calculations.
The force of gravity is in some respects an incomprehensible existence, but in other respects entirely conformable to experience. We observe that the force is proportional to mass, and that it acts in entire independence of other matter which may be present or intervening. The law of the decrease of intensity, as the square of the distance increases, is observed to hold true of light, sound, and other influences emanating from a point, and spreading uniformly through space. The law is doubtless connected with the properties of space, and is so far in agreement with our necessary ideas.
It may be said, however, that no hypothesis can be so much as framed in the mind unless it be more or less conformable to experience. As the material of our ideas is derived from sensation we cannot figure to ourselves any agent, but as endowed with some of the properties of matter. All that the mind can do in the creation of new existences is to alter combinations, or the intensity of sensuous properties. The phenomenon of motion is familiar to sight and touch, and different degrees of rapidity are also familiar; we can pass beyond the limits of sense, and imagine the existence of rapid motion, such as our senses could not observe. We know what is elasticity, and we can therefore in a way figure to ourselves elasticity a thousand or a million times greater than any which is sensuously known to us. The waves of the ocean are many times higher than our own bodies; other waves, are many times less; continue the proportion, and we ultimately arrive at waves as small as those of light. Thus it is that the powers of mind enable us from a sensuous basis to reason concerning agents and phenomena different in an unlimited degree. If no hypothesis then can be absolutely opposed to sense, accordance with experience must always be a question of degree.
In order that an hypothesis may allow of satisfactory comparison with experience, it must possess definiteness and in many cases mathematical exactness allowing of the precise calculation of results. We must