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Scientific knowledge of a thing consists in knowing its cause demonstratively. The principles required for Demonstration. Meaning of ‘Thesis,’ ‘Hypothesis,’ ‘Axiom,’ ‘Definition.’

We suppose ourselves to know anything absolutely and not accidentally after the manner of the sophists, when we consider ourselves to know that the ground from which the thing arises is the ground of it, and that the fact cannot be otherwise. Science must clearly consist in this, for those who suppose themselves to have scientific knowledge of anything without really having it imagine that they are in the position described above, while those who do possess such knowledge are actually in that position in relation to the object.

Hence it follows that everything which admits of absolute knowledge is necessary. We will discuss later the question as to whether there is any other manner of knowing a thing, but at any rate we hold that that ‘knowledge comes through demonstration.’ By ‘demonstration’ I mean a scientific syllogism, and by ‘scientific’ a syllogism the mere possession of which makes us know.

If then the definition of knowledge be such as we have stated, the premises of demonstrative knowledge must needs be true, primary, immediate, better known than, anterior to, and the cause of, the conclusion, for under these conditions the principles will also be appropriate to the conclusion. One may, indeed, have a syllogism without these conditions, but not demonstration, for it will not produce scientific knowledge. The premises must be true, because it is impossible to know that which is not, e.g. that the diagonal of a square is commensurate with the side. The conclusion must proceed from primary premises that are indemonstrable premises, for one cannot know things of which one can give no demonstration, since to know demonstrable things in any real sense is just to have a demonstration of them. The premises must be Causal, Better known and Anterior; Causal, because we only know a thing when we have learned its cause, Anterior because anteriority is implied by causation, previously known not only in our second sense, viz. that their meaning is understood, but that one knows that they exist.

Now the expressions ‘anterior’ and ‘better known’ have each a double meaning; things which are naturally anterior are not the same as things anterior to us, nor yet are things naturally better known better known to us. I mean by things anterior, or better known, ‘to us,’ such as are nearer our sense-perception, while things which are absolutely anterior or better known are such as are more removed from it. Those things are the furthest removed from it which are most Universal, nearest to it stands the Particular, and these two are diametrically opposed.

The phrase ‘the conclusion must result from primary principles’ means that it must come from elements appropriate to itself, (for I attach the same meaning to primary principle [πρτον] and to element [ρχή]). Now the element of demonstration is an immediate proposition; ‘immediate’ meaning a proposition with no other proposition anterior to it. A premise is either of the two parts of a predication, wherein one predicate is asserted of one subject. A dialectical premise is one which offers an alternative between the two parts of the predication, a demonstrative premise is one which lays down definitely that one of them is true.

Predication is either part of a Contradiction. Contradiction is an opposition of propositions which excludes any intermediate proposition. That part of a Contradiction which affirms one thing of another is Affirmation, that which denies one thing of another is Negation.

I apply the name Thesis to an immediate syllogistic principle which cannot be proved, and the previous possession of which is a necessary condition for learning something, but not all. That which is an indispensable antecedent to the acquisition of any knowledge I call an Axiom; for there are some principles of this kind, and ‘axiom’ is the name generally applied to them.

A Thesis which embodies one or other part of a predication (that is that the subject does, or does not, exist) is a Hypothesis; one which makes no such assertion a Definition. Definition is really a kind of Thesis; e.g. the arithmetician ‘lays it down’ that Unity is indivisibility in respect to quantity, but this is not a Hypothesis, for the nature of unity and the fact of its existence are not one and the same question.

Since then belief and knowledge with regard to any subject result from the possession of a demonstrative syllogism, and since a syllogism is demonstrative when the principles from which it is drawn are true, we must not merely have a previous knowledge of some or all of these primary principles, but have a higher knowledge of them than of the conclusion.

The Cause always possesses the quality which it impresses on a subject in a higher degree than that subject; thus, that for which we love anything is dear in a higher degree than the actual object of our love. Hence if our knowledge and belief is due to its primary principles, we have a higher knowledge of these latter and believe more firmly in them, because the thing itself is a consequence of them. Now it is not possible to believe less in what one knows than in what one neither knows nor has attained to by some higher faculty than knowledge. But this will happen unless he whose belief is produced by demonstration has a previous knowledge of the primary principles, for it is more needful to believe in these principles, either all or some, than in the conclusion to which they lead.

Now in order to attain to that knowledge which comes by demonstration one must not only be better acquainted with and believe more firmly in the elementary principles than in the conclusion, but nothing must be better known nor more firmly believed in than the opposites of those principles from which a false conclusion contrary to the science itself can be educed; that is to say if he who possesses absolute knowledge is to be quite immovable in his opinions.