As to the same science then, and the position of the media, these are the differences between a syllogism of, that a thing is, and of why it is, but in another respect the why differs from the that, because each is beheld in a different science. Another explains the reason why a thing is. But since ‘the same’ is used in many senses, false and true opinions are in one sense the same, in another different. For instance, supposing that both A and B are C, if it be asserted that C is A, but C is not B, the premise CA will be true, the other premise false. But (deception) is possible, when one proposition is false, and either of them casually; for it is possible that A C may be true, but C B false; A C true, because A is not present with all beings, but C B false, In the middle figure, however, it is not possible that both propositions should be wholly false, for when A is present with every B, it will be impossible to assume any thing, which is present with every individual of the one, but with no individual of the other; but we must so assume the propositions that the (middle) may be present with one (extreme), and not be present with the other, if indeed there is to be a syllogism.

Now there are different modes of thought by means of which we attain to truth, and some of them are always infallible, while others, as Opinion and Calculation, admit of error.

We must admit only essential attributes, must arrange them in their right order, and must not omit a single one.The first of these depends on whether we are able to make an essential predication with the help of the generic notion, as we predicate accidental attributes in the syllogism. Aristotle’s Posterior Analytics is one of the most important, and difficult, works in the history of western philosophy. If then, when they are thus assumed, they are false, it is clear that, when taken contrarily, they will subsist vice versâ, but this is impossible. If however we do not at once attain some ultimate proposition, and if the middle term be found to be not one but many, then the causes also must be many.Particular effects are produced by causes which lie nearer to the particular than to the universal.Concerning the faculty which acquires knowledge of the ultimate principles of demonstration. Kindle: 160 KB: This is an E-book formatted for Amazon Kindle devices. Here necessity will be secured so long as everything falls within the division, nothing being omitted, and so long as no term is admitted which is capable of a further subdivision. For instance, a true opinion that the diagonal is commensurable with the side of a square would be absurd, but since the diagonal concerning which the opinions are held remains the same whether the opinion about it be right or wrong, the object of the two kinds of opinions is one and the same, while according to their essential nature and definition those opinions are different. If this were so number will be predicable as primary subject of all the attributes thus becoming predicable of it. If then the same occurs, as to all causes and inquiries into the why, but as to things which are so causes as that for the sake Moreover since it has been shown impossible for a syllogism to be produced with both propositions negative, but that one must of necessity be such (negative), and the other that a thing is present with, (that is affirmative,) we must in addition to this assume this, for it is necessary that affirmative (propositions) when the demonstration is increased, should become more, but it is impossible that the negatives should be more than one in every syllogism. But they are not the first conditions of such disappearance.

In definition it is easier to assert something of the particular than of the universal; one ought therefore to pass from particulars to universals. But they are hypotheses, from the existence of which, in that they are, the conclusion is produced. The same thing applies to astronomy.In short in every demonstrative science there are three elements: (1) the things whose existence it assumes, namely the subject or genus, the essential attributes of which are investigated by the science; (2) what are called ‘Common Axioms’ which the demonstration uses as its primary principles; and (3) Properties, the meaning of which is assumed.However nothing prevents some sciences from overlooking That which must needs exist and must necessarily be supposed to exist is neither Hypothesis nor Petition but Axiom.

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