Pseudo-Thomas, Concerning Demonstration.
Translated by John Longeway
In order to have cognition of demonstration it must be known that a demonstration is a syllogism from true, primary, immediate, prior, and better known premises that express the causes of the conclusion, and this is demonstration of the most powerful sort—or it is from such as have taken the principle of their cognition from something true and primary, and this is demonstration that is not of the most powerful sort. Then it must be known that three things are needed for demonstration, namely subject, passion, and axiom. The subject is that of which the passion is proved. A passion is a per se accident convertible with its subject. It is, then, demonstration of the most powerful sort when the passion is proved of the universal subject through a middle term, which is the definition saying what it is and why it is.
Now the universal subject of a passion is what is convertible with its passion and what has the cause of its passion within it, for instance, triangle is the universal subject of its passion, having three etc., and it is convertible with its passion, for whatever is a triangle has three, and conversely, and triangle has three because it is triangle. A particular subject is what is not convertible with the passion, and does not have the cause within it of its passion, for instance, isosceles, since not everything having three is isosceles, and it does not have three because it is isosceles, but because it is triangle.
But the definition indicating what it is is the definition given through the essence and is the definition of the subject, for instance, “triangle is a plane figure contained by three lines.” But a definition indicating why it is is a definition given through the cause, and this is a definition of a passion, for the definition of a passion indicates the cause of inherence of the passion in the subject, through which the subject has this passion. For example, having three angles equal to two right angles is having an extrinsic angle equal to the two intrinsic angles opposite it, and because of this a passion is in a triangle, that is, through its definition. Now if it is asked why it has three etc., it is answered that it has an extrinsic angle equal to the two intrinsic angles opposite it.
I hold that a definition indicating what and why, which is composed from the definition of the subject and the passion, is the middle in the most powerful sort of demonstration, and through it the proper passion is proved of its universal and adequate subject. For example, “Every plane figure contained in three lines, having an extrinsic angle equal to the two intrinsic angles opposite it, has three angles, etc.” In this major premise falls the second way of speaking per se, which occurs when the defined is predicated of its definition. “But every triangle is a plane figure contained in three lines, having an extrinsic angle equal to the two intrinsic angles opposite it.” In this minor premise falls the first way of speaking per se, which occurs when a definition or part of a definition is predicated of the defined. And the conclusion follows: “Every triangle has three angles equal to to two.” Here falls the fourth way, which occurs when the passion is predicated of the subject, which occurs with a reduplication of causes, for instance, the Moon lacks light because of the interposition of the Earth, and one kills him who is killed because of the killing.
Another example of the most powerful sort of demonstration: “Every natural body illuminated by the Sun, and deprived of light by the opposition of the Earth, lacks light, the Moon is of this sort, therefore etc.” And the passion is proved here through the definition indicating what and why.
Demonstration that is not of the most powerful sort arises in a number of ways, namely when the passion is proved of a particular subject through a middle term which is the subject of that passion, since the subject is the proximate cause of the passion under the particular subject, so, for instance, if it is proved of isosceles that it has three through triangle, thus: “Every triangle has three, isosceles is triangle; therefore etc.” Hence this syllogism can be sophistical or dialectical or a particular demonstration. It is a sophistical syllogism if it is proved of the particular subject as though it were a universal and convertible subject, because of the identity in part which isosceles has with triangle. When, due to the identity in part of the subject with the predicate, one is moved to believe that whatever is said of one is also to be said of the other, it is a fallacy of accident. But it is a dialectical syllogism as a passion is proved of that, for instance of isosceles, as of a particular subject through triangle, insofar as it is a certain common predicable of several things, for the middle in a dialectical syllogism is a common predicable of several things. Again, it is a particular demonstration insofar as the passion is proved of isosceles as of a particular subject through triangle, considered as it is the proximate cause of the passion in the particular subject, for triangle is the proximate cause why isosceles has three. Isosceles does not have three, because it is isosceles, but because it is triangle.
Again, a demonstration that is not of the most powerful sort can arise otherwise, namely when the effect is proved through a remote cause, or when the cause is proved through the effect. For instance, if it is proved of isosceles that it has three not through triangle, which is the proximate and immediate case of isosceles, as has been said, but through plane figure etc., which is the definition of traingle and of its passion, indicating what and why, which is the proximate cause in respect of the universal and is the remote cause in respect of the particular subject. And the demonstration is formed through the remote cause thus: “Every plane figure by three etc., isosceles is of this sort, therefore etc.”
Again, demonstration that is not of the most powerful sort arises in another way when the cause is proved through the effect, for instance, if it proved of a planet that it is near through its not twinkling, in this way: “Every luminous body that does not twinkle is near the position of the vision <of the one for whom it does not twinkle>, but a planet is of this sort; therefore it is placed near us.” For here the cause is demonstrated through the effect, since its being placed near is the cause why it does not twinkle, and not conversely. It is not because the planet does not twinkle that it is near, but because it is near that it does not twinkle. Now if it is demonstrated through “luminous body placed nearby” that it does not twinkle, the effect will be demonstrated through its cause. It is the same when it is proved of the Moon that it is circular because it is augmented in a circular manner, in this way: “Every luminous body or one suited to be illuminated, in which it is augmented in a circular manner through light is circular, the moon is of this sort; therefore etc.” For it is not because light is augmented in the moon in a circular manner that it is circular, but because it is circular that the moon is augmented in a circular manner. Thus what we have said is made clear.