LECTURE 8 (204 b 4-205 a 6)

AN INFINITE IN ACT IN SENSIBLE THINGS CANNOT BE GRANTED. THIS IS SHOWN FIRST WITH LOGICAL ARGUMENTS, SECONDLY WITH NATURAL ARGUMENTS, ON THE SUPPOSITION THAT THE ELEMENTS OF BODIES ARE FINITE IN NUMBER

             349. After the Philosopher has refuted the opinion of the ancients who did not speak of the infinite as natural philosophers, inasmuch as they separated it from sensible things, he shows here that there is no infinite, as the natural philosophers held.

             He shows this first with logical arguments, and secondly, with natural arguments, where he says, 'If, on the other hand . . .' (204 b 10).

             The first arguments are called logical arguments not because they proceed logically from logical terms, but because they proceed according to a logical method, i.e., from the common and the probable, which is proper to the dialectical syllogism.

             350. He sets forth two logical arguments. In the first argument it is shown that there is no infinite body.

             A body is defined as that which is determined by a surface, just as a line is defined as that whose termini are points. However, no body determined by a surface is infinite. Therefore, no body is infinite--neither a sensible body, which is a natural body, nor an intelligible body, which is a mathematical body.

             The word 'rationally' must be understood to mean 'logically'. For logic is called rational philosophy.

             351. The second argument shows that there is no infinite in multitude. For everything numerable is numbered, and consequently is passed through by being numbered. But every number and every thing which has a number is numerable. Therefore, everything of this sort is passed through. Therefore, if any number, whether separated or existing in sensible things, is infinite, it would follow that it is possible to pass through the infinite, which is impossible.

             352. It must be noted, however, that these arguments are probable and proceed from things which are commonly said. They do not conclude of necessity. For one who holds that some body is infinite would not concede that it is of the nature [ratio] of a body to be terminated by a surface, except perhaps in potency, even though this is probable and generally accepted.

             Likewise one who would say that some multitude is infinite would not say that it is a number or that it has number. For number adds to multitude the notion [ratio] of a measure. For number is a multitude measured by one, as is said in Metaphysics, X. And because of this number is placed in the species of discrete quantity, whereas multitude is not. Rather multitude pertains to the transcendentals.

             353. Next where he says, 'If on the other hand . . .' (204 b 10), he sets forth natural arguments to show that there is no infinite body in act.

             Concerning these arguments it must be noted that since Aristotle has not yet proven that a celestial body has an essence other than the four elements and since the common opinion of his time was that a celestial body has the nature of the four elements, he proceeds in these arguments, according to his custom, as if there were no sensible body other than the four elements. For before he proves his own opinion, he always proceeds from the supposition of the common opinion of others. Hence after he has proven in De Caelo et Mundo, I, that the heavens have a nature other than the elements, he brings his consideration of the infinite to the certitude of truth by showing universally that no sensible body is infinite.

             Here, then, he shows first that there is no infinite sensible body on the supposition that the elements are finite in multitude. Secondly, he shows the same thing universally, where he says, 'The preceding consideration . . .' (205 a 7).

             He says, therefore, first that by proceeding naturally, i.e., from the principles of natural science, it can be more certainly understood from what will be said that there is no infinite sensible body. For every sensible body is either simple or composite.

             354. First he shows that there is no infinite composite sensible body on the supposition that the elements are finite in multitude. For it cannot be that one of these elements is infinite and the others finite. For the composition of any mixed body requires that the elements be many and that contraries be in some way balanced. Otherwise the composition could not endure, because that which would be altogether stronger would destroy the others, since the elements are contraries. If, however, one of the elements were infinite and the others were finite, there would be no equality. For the infinite exceeds the finite beyond every proportion. Therefore, it cannot be that only one of the elements which enter into the mixture is infinite.

             However, one might say that the infinite element would be weak in the power to act, and so not able to suppress the others, i.e., the finite elements, which are stronger in power. For example, let the infinite be air and the finite fire. And so to preclude this, he says that no matter how much the power of the infinite body falls short of the power of the finite body (as if fire were finite and air infinite), it is necessary to say that air is equal to fire in power according to some multiple of number. For if the power of fire is one hundred times greater than the power of the same quantity of air, then if the air is multiplied one hundred fold in quantity, it will be equal to fire in power. And yet air multiplied one hundred fold is multiplied by some determined number and is exceeded by the power of the whole infinite air. Hence it is clear that the power of fire will be destroyed by the power of infinite air. And so the infinite exceeds and corrupts the finite, however more powerful in nature the latter should seem.

             355. In like manner it cannot be that all of the elements of which a mixed body is composed are infinite. For the nature [ratio] of body is to have dimensions in every direction, not in length only, like a line, nor in length and breadth only, like a surface. However, the nature [ratio] of the infinite is to have distances or dimensions which are infinite. Hence the nature [ratio] of an infinite body is to have infinite dimensions in every direction. And thus one thing cannot be composed of many infinite bodies. For each body would occupy the whole world, unless one says that two bodies exist together, which is impossible.

             356. Thus, having shown that a composite body cannot be infinite, he shows further that a simple body also cannot be infinite, i.e., neither one of the elements nor some intermediate between them, such as vapour is an intermediate between air and water, is infinite. For some have held that this latter is a principle, saying that other things are generated from it. And they said that this intermediate is infinite, but air, or water, or one of the other elements is not infinite, because it would happen that the other elements would be corrupted by whichever of them was held to be infinite. For the elements have contrariety among themselves, since air is humid, water is cold, fire is hot and earth is dry. Hence, if one of them were infinite, it would corrupt the other, since a contrary is naturally disposed to be corrupted by a contrary. And so they say that something other than an element is infinite, from which the elements are caused as from a principle.

             However, he says that this position is impossible insofar as it claims that such an intermediate body is infinite, because with respect to this a certain common argument relative to fire and air and water and also to an intermediate body will be given below. The position stated above is also impossible because it posits some elementary principle other than the four elements.

             For there is no sensible body other than those which are called the elements, i.e., air, water and the like. But this would be necessary if something other than the elements were to enter into the composition of bodies. For every composite is resolved into the things of which it is composed. If, therefore, something other than these four elements should enter into the composition of bodies, it would follow that by resolving them into their elements, there should be found here among us some simple body other than these elements. Therefore it is clear that the above position is false insofar as it posits a simple body other than these known elements.

             357. Further, he shows with a common argument that none of the elements could be infinite. For if one of the elements were infinite, it would be impossible for the whole universe to be other than that element. And it would be necessary for all the elements to be converted into it, or else they would already have been converted into it because of the excellence of the power of the infinite element over the others. Thus, Heraclitus says that at some time all things will be converted into fire because of the excelling power of fire. The same argument applies both to one of the elements and to the other body which some natural philosophers set up beyond the elements. For that other body must be contrary to the elements, since other things are held to be generated from it. Moreover, change occurs only from contrary to contrary, as from hot to cold, as was pointed out above. Therefore, that intermediate body would destroy the other elements because of its contrariety.