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Here’s an analysis of the argument against the thesis at III.2 of Ibn Sina’s Danishnameh-ye Ala’i. Before presenting the argument though, let me briefly lay down a few preliminary points relevant to better understanding what the argument purports to establish.All change (taghayyur), both substantial and accidental, is said to be the actualization of a potential. As such, change is divided into either gradual (tadriji) or instantaneous (daf’i). Now motion (harakah), properly speaking, only refers to the former kind. This kind of change in distinguished from latter kind by the fact that it possess intermediate states between the initial and final states the mobile traverses. As the Shaykh explains:

Motions are sub-distinguished as follows: given a thing that is potentially such and such i.e., a body that is potentially black, either (1) there exists between its initial state of potency and its final actual state another state[DD1] or (2) there is no such intermediate state. In the latter case, the object in question, [when it changes], changes instantly (daf’atan) from potentiality to actuality.[DD2] An example of the first motion (1.a) is a continual[DD3] blackening of a body until it has reached the maximum[DD4] shade of blackness and remains in such a state. An example of the second motion (2.a) is an immediate blackening or whitening. In (2.a), there is no state between the initial state of potentiality and the final actual state. Regarding (1.a), we further say: so long as the body has not attained its full potential blackness[DD5], it is in motion and in a state that is neither entirely and purely potential, nor completely actual, because the changing body is neither purely white nor has it reached the blackness toward which it is progressing.

[DD1]E.g., X, in its motion from state A to state C passes through state B.
[DD2]If in the motion from state A to state C there is not middle state B, then X will make the transition from A to C instantly.
[DD3]The Shaykh says “continual” as in there is no disruption in the motion of X from A to B to C. More generally, in this sense the gradations of anything that is graded are not discontinuous with each other, as they are in changes which happen instantly.
[DD4]Notions of ‘maximum’ and ‘minimum’ involve degrees and gradations.
[DD5]That is, so long as it has not become fully black, it is in a sate between pure potency and act while it is changing.

With respect to the the issue at hand then, the question is about whether or not there is gradual change (motion) in the very substance of an object in the same way as there is gradual change in its various accidents. For example, locomotion, i.e., a substance’s movement from place to place, is gradual; quantitative motion, i.e., a substance’s growth, is also gradual. And etc. The important point to keep in mind is that if it is proved that change in substance occurs in an instant, then it follows that it isn’t gradual. And if that is the case, then we’ve established that there is no motion in substance since, as we saw, gradual change just is motion. Having said all that, here then is the Shaykh’s argument:

However, a thing can change from one substance to another, like [the change] from water to fire, only if it does so [instantaneously], because substantiality, unlike accidentality, does not admit of less and more [i.e., degrees]. Indeed, one black entity can be blacker than another, but one human cannot be more human than another. A man at once leaves off his humanity; he is either fully human or not at all human. Suppose, though, his humanity could be diminished; then, either his species form survives or does not survive [the change]. If it survives, the change is in accidents, not in the genus and difference, i.e., in the whole definition; if his species form disappears, his humanity also disappears and is not merely deficient [or diminished]. [ …].

Put syllogistically, the above argument is as follows:

What does not admit of degrees does not change gradually but instantly
Substance does not admit of degrees
Therefore, substance does not change gradually but instantly

Proof of the major: this is so because what does not admit of degrees possess no intermediate states. In fact, to not be graded is just what it means to lack intermediate states. Hence, in any motion in which there are no intermediate states between its beginning (i.e., potency) and end (i.e., actuality), the transition from one to the other, as was said, is instantaneous. This last point is confirmed by experience, as e.g., when a black object is changed into a white object. Proof of the minor: the Shaykh provides a reductio: suppose, he argues, Zayd’s ‘humanity’ could decrease or increase [i.e., admit of degrees or intermediate states]; then, when it does so, either his specific form (i.e., of humanity), survives or disappears i.e., after each transition. If it survives, the change involves accidents, not (specific differences) between genera and so this isn’t motion in the substance of Zayd but in his accidents. If his specific form disappears, then, obviously enough, his ‘humanity’ also disappears and is not merely decreased or increased. And the conclusion would then follow; that is, there is no motion in substance. Rather, substantial change occurs instantly.

Shubha: the argument at hand presupposes that a substance is an independent, fixed, ontological entity and not, as per the Sadrian, a degree of (one unified) existence. Assuming the latter account is true, to be human then would mean something like to have a degree of existence anywhere between degree x and y. This is would not only explain Zayd’s being human but also allow his being more (literally!) human than Amr, depending how we conceptualize the hierarchical relation between x, y, and their intermediate degrees.

Response: granted that the Sadrians hold that to be a substance is to be a particular degree of existence. Still, the Shaykh’s argument, it seems to me, goes through: for suppose that anything which has a degree of existence anywhere between degrees x and y is a human h. Now, suppose further h changes; then, either h is still between x and y or not. If so, then given that h is still a human, the change, by definition, is merely accidental. If not, then given that h is outside degrees x and y, h is no longer human strictly and not just a deficient, i.e., a lower degree of, human. Therefore, there is no motion in substance.

The above I think is the gist of Ibn Sina’s argument against motion in substance as contained in III.2 of the Physics of his Daneshnameh. In the next post, I’ll provide two arguments for the thesis by the Sadrian philosopher Sayyid Hussaini Qazwini.