Front Page Titles (by Subject) CHAP. XIII.: The difference between the Demonstration and Science of a thing's Nature and those of its Cause - Posterior Analytics
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CHAP. XIII.: The difference between the Demonstration and Science of a thing’s Nature and those of its Cause - Aristotle, Posterior Analytics 
Aristotle’s Posterior Analytics, trans. E.S. Bouchier, B.A. (Oxford: Blackwell, 1901).
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The difference between the Demonstration and Science of a thing’s Nature and those of its Cause
There are two classes of demonstration, one giving the Fact, the other the Cause of the fact; such demonstrations being effected either by the same or separate sciences. If the former, the propositions may be immediate and convertible, when we have the demonstration of the cause, or mediate and inconvertible, when we have only the demonstration of the fact. If different sciences are employed, and one is subordinate to the other, the superior gives the Cause, the inferior the Fact.
A difference exists between knowing that a fact is and knowing its cause. This may be considered firstly in connection with the same science and from two points of view, viz. (1) in the case where the syllogism is not deduced from ultimate propositions (for here the primary cause is not expressed, while knowledge of the cause goes back to the primary cause). (2) The second aspect of the distinction is seen when the propositions from which the conclusion is drawn are ultimate and reciprocal, but the middle employed is not the cause but the better known effect. Nothing in fact prevents in the case of reciprocating terms, that term which is not the cause being better known to us, so that our demonstration will be through this as a middle. E. g. Planets are proved to be near the earth from the fact that they do not twinkle, as follows. Let
C designate Planets.
B Not twinkling.
A Being near.
Here B may rightly be predicated of C, for planets do not twinkle. Also A is true of B, for that which does not twinkle is near,—a truth to be arrived at by induction or observation. A then must be true of C, so that we have now demonstrated that the planets are near.
This syllogism then does not deal with the cause of the phenomenon but with the fact; for the planets are not really near because they do not twinkle, but do not twinkle because they are near. It is also possible to prove the first fact by means of the second, and the demonstration will then be of the cause. Thus:—
Let C be the Planets.
B Being near.
A Not twinkling.
Here B is true of C, and A (‘not twinkling’) of B. Therefore A is true of C. Thus the syllogism is a syllogism of the cause, for it comprehends the primary cause. Another instance is the method by which the moon is proved to be spherical by a reference to its regular increases. It proceeds thus:—If that which increases in this particular way be spherical, and if the moon do so increase, it is clear that the moon is spherical. As thus expressed the syllogism demonstrates only the fact, but when the middle term is transposed it is a demonstration of the cause. The moon is not spherical in consequence of its increases, but undergoes these particular increases because it is spherical. Let C be the Moon; B spherical form; A the method of increase. In cases, however, where the middle terms are not interchangeable, and where the effect is better known than the cause, the fact may be proved but not the cause. This is also the case when the middle term is wider than the other two terms. Here too the demonstration is of the fact, not of the cause, for the primary cause is not stated. E. g. To the question ‘why does not a wall breathe’? suppose the answer to be given ‘because it is not an animal.’ Now if this negative quality be the cause of its not breathing, the corresponding affirmative ‘is an animal’ ought to be the cause of this phenomenon, just as granting that a negation of a quality be the cause why something does not exist, the affirmation of it is the cause why it does exist. E. g. If a want of balance between heat and cold be the cause of the absence of health, a due balance between them must be the cause of its presence. So conversely, if the affirmation be the cause of the presence of a quality the negation is the cause of its absence. But in the first instance quoted this does not hold good. Not every animal in fact does breathe. The syllogism which demonstrates a cause of this kind belongs to the second figure. E. g. Let A be Animal; B Breathing; C Wall. Now A is true of all B (for everything which breathes is an animal), but of no C. Hence B is true of no C, and therefore no wall breathes. Such statements of cause resemble hyperbolical expressions, for one is guilty of a kind of hyperbole if one depart from the proximate cause and take the more remote as one’s middle term. Of such a nature is the inference of Anacharsis that the Scythians have no flute-players because they have no vines.
Such are the differences between the syllogism of the fact and that of the cause, as regards the same science and the position of the middle terms; but from another point of view the fact sometimes differs from the cause in that each is examined by a different science. This is the case when the sciences are of such a nature that one is subordinate to the other, as optics to geometry, mechanics to the measurement of solids, harmonics to arithmetic and records of observation to astronomy. Some of these subordinate sciences have almost similar names; e.g. mathematical and nautical astronomy, mathematical and acoustic harmonics. In these cases the fact depends on the observational sciences, the cause on the mathematical sciences; for the mathematician can demonstrate the causes though he often does not know the fact, just as those who are aware of a universal law, through want of observation, are often ignorant of some of the particular facts. These superior sciences will be such as differ in essence from the subordinate sciences, and deal merely with abstract forms. Thus mathematics are concerned with forms, and do not deal with any concrete subject; and even if the propositions of geometry happen to be true of a concrete subject they are true of it not as concrete. Now there is a science which bears the same relation to optics as optics to geometry; e.g. knowledge about the rainbow. The fact that there is such a thing falls within the province of the natural philosopher, the cause within that of the optician, either as such or in so far as he is a mathematician.
Many sciences which are not subordinate one to another, yet sometimes have similar interrelations: e.g. medicine and geometry. Thus the fact that circular wounds heal more slowly must be learned by the surgeon, the cause of it by the geometrician.