The Religion of Nature Delineated by William Wollaston (mystery books to read .txt) 📕

be known immediately and truly. For if the relation be immediate, the ideas cannot subsist without it; it is of their nature: and therefore they cannot be known adequately, but this must be known too. They are in this respect like the ideas of whole and part. The one cannot be without the other: nor either of them not discover that relation by which the one must be always bigger and the other less.

To say no more, we may satisfy ourselves of the truth of this, as well as of the foregoing propositions, from the experiences of our own minds, where we find many relations that are immediately seen, and of which it is not in our power to doubt.121 We are conscious of a knowledge that consists in the intuition of these relations. Such is the evidence of those truths, which are usually called axioms, and perhaps of some short demonstrations.

V. Those relations or respects which are not immediate, or apparent at the first view, may many times be discovered by intermediate relations, and with equal certainty. If the ratio of B to D does not instantly show itself, yet if the ratio of B to C122 does, and that of C to D,123 from hence the ratio of B to D124 is known also. And if the mean quantities were ever so many, the same thing would follow; provided the reason of every quantity to that which follows next in the series be known. For the truth of this I vouch the mathematicians:125 as I might all, that know any science, for the truth of the proposition in general. For thus theorems and derivative truths are obtained.

VI. If a proposition be true, it is always so, in all the instances and uses to which it is applicable. For otherwise it must be both true and false. Therefore

VII. By the help of truths already known, more may be discovered. For

Those inferences, which arise presently from the application of general truths to the particular things and cases contained under them, must be just. E.g. “The whole is bigger than a part”: therefore A (some particular thing) is more than half A. For it is plain that A is contained in the idea of whole, as half A is in that of part. So that if the antecedent proposition be true, the consequent, which is included in it, follows immediately, and must also be true. The former cannot be true unless the other be so too. What agrees to the genus, species, definition, whole, must agree to the species, individuals, thing defined, the part. The existence of an effect infers directly that of a cause; of one correlate that of the other; and so on. And what is said here holds true (by the preceding proposition) not only in respect of axioms and first truths, but also and equally of theorems and other general truths, when they are once known. These may be capable of the like applications; and the truth of such consequences as are made by virtue of them, will always be as evident as that of those theorems themselves.

All those conclusions which are derived through mean propositions that are true, and by just inferences, will be as true as those from which they are derived. My meaning is this: every just consequence is founded in some known truth, by virtue of which one thing follows from another, after the manner of steps in an algebraic operation; and if inferences are so founded, and just, the things inferred must be true, if they are made from true premises.

Let this be the form of an argument. M = P: S = M: ergo S = P. Here if S = M be false, nothing is concluded at all: because the middle proposition is in truth not S = M, but perhaps S = Ma, which is foreign to the purpose. If S = M be true, but M = P false, then the conclusion will indeed be a right conclusion from those premises: but they cannot show that S = P, because the first proposition, if it was expressed according to truth, would be Me = P, which is another thing, and has no place in the argument. But if these two propositions are both true, M = P, S = M, then it will not only be rightly concluded, but also true, that S = P. For the second or middle proposition does so connect the other two, by taking in due manner a term from each of them, (or to speak with the logicians, by separately comparing the predicate or major term of the conclusion with the medium in the first proposition, and the subject or minor term with it in the second), that if the first and second are true, the third must be so likewise, all being indeed no more than this: P = M = S. For here the inference is just, by what goes before, being founded in some such truth as this, and resulting immediately from the application of it, Quæ eidem æqualía sunt, et inter se sunt æqualia; or Quæ conveniunt in eodem tertio, etiam inter se conveniunt; or the like.126 Now if an inference thus made is justifiable, another, made after the same manner, when the truth discovered by it is made one of the premises, must be so too; and so must another after that; and so on. And if the last, and all the intermediate inferences, be as right as the first is supposed to be, it is no matter to what length the process is carried. All the parts of it being locked together by truth, the last result is derived through such a succession of mean propositions as render its title to our assent not worse by being long.

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