Self-Identity, Infinite Regress

Identity is unity or union; either because the things which are said to be the same are plural in their being, and yet are called the same insofar as they agree in some one factor; or because they are one in their being, but the intellect treats them as though they are plural in order to think a relation. For a relation can only be thought to obtain between two extremes, as when something is said to be the same as itself; for then the intellect treats what is one in reality as though it were two; otherwise it could not designate a relation of something to itself. Wherefore it is clear that if a relation always requires two extremes, and in relations of this sort there are not two extremes in reality but only in the mind, the relation of identity is not a real relation but only a relation of reason . . . for if the relation of identity were some thing besides that which is called the same, that thing which is a relation, since it is the same as itself, for the same reason would have another relation which would be identical with itself, and on to infinity. But it is impossible to go to infinity in things. But in matters of the intellect nothing prohibits it. For when the intellect reflects on its acts it understands that it understands, and it can understand this as well, and so on to infinity.

--St Thomas Aquinas, Commentary on the Metaphysics, Lib.V, lectio XI, par.912, my translation

A couple of thoughts about this passage. First, it's a good example of the fact that some of the "problems" that modern philosophy finds the most challenging and fascinating, such as the nature of self-identity, are for the classical and scholastic mind non-starters (the converse is also true, of course). In fact this disconnect between what modern thinkers find interesting or worth spilling gallons of ink on and what I find interesting and worth reading and thinking about is part of what makes reading much modern philosophy so difficult for me (it's rather like my reluctance to read contemporary fiction rather than classical and medieval poetry). Not only are modern philosophers frequently preoccupied with issues that to the classical mind seem rooted in silly misunderstandings, but those - to us - misunderstandings also seem to breed contempt for the kinds of thinking that I and the scholastics do find worthwhile. In any case, Aquinas is not alone here in finding nothing mysterious or profound about identity, since it's a mere relation of reason: what's difficult is understanding the being and the essence of a thing, not how that being is the same as itself. But, as I've claimed on this blog before, it seems to me that a lot of the absurdities of modern philosophers stem ultimately from an inability to tell the difference between real being and beings of reason.

A second, related, thought is that Thomas' point here not only makes use of an infinite regress argument, but is important for understanding infinite regress arguments in general. Anyone who's read much of the modern literature on arguments for the existence of God will know that the denial of the impossibility of an infinite regress is a favorite way for moderns to wiggle out of them. St Thomas' comments suggest that the reason an infinite regress, so obviously absurd to the scholastics, is unproblematic to the moderns, is (again) because moderns are not used to carefully distinguishing between real relations and relations of reason. And this is unsurprising, given that so much modern philosophy (and "science"), being born of Cartesian mathematicism, has been accustomed to axiomatically assuming that mathematical techniques are paradigmatic for philosophical (and "scientific") knowledge. But mathematical objects are indifferently divided between purified (i.e. denuded of what the Thomists always call material conditions) formal abstractions from experience and mere relations of reason, which happily sit on the number line together. Mathematics itself doesn't care about the distinction, but metaphysics must.

I believe this thought is suggested by Thomas here but it jumped out at me because it reminded me of a passage in John Deely's recent Medieval Philosophy Redefined, which I read a couple of months ago (the following is from page 268):

This contrast between relations in the physical order which depend upon actual characteristics of actual individuals (upon "subjective accidents of substances" in Aristotle's terms) and relations in the objective order which are not tied to actual subjective characteristics but may be founded upon whatever other relations happen to exist within a given cognition was the reason why Aristotle, and the Latin logicians after him, rejected arguments which led to an infinite regress. An infinite regress is actually possible only in the mind, because only in the mind can relations be founded upon relations. So any argument that involves an actual infinite regress, to the extent that it involves one, is an argument that has lost touch with the order of physical being as something to be explained through proper causes. For proper causes are found only within the physical interactions of finite substances, and these, as finite, are always determinate within the order of moved movers. . . .

Deely gives a further reference to his book The Human Use of Signs, which I have not read. In any case it's interesting to note that modern thinkers so often take the rejection of infinite regress as an arbitrary ad hoc principle whose only purpose is to force one to accept a First Cause, when the scholastics themselves not only see it as completely necessary and self-evident but also use it constantly in a host of nontheological contexts.

Leibniz on the History of the Faith-Reason Problem

From his Theodicy, preliminary discourse, p. 76-77 (Newhaven 1952):

The question of the conformity of faith with reason has always been a great problem. In the primitive Church the ablest Christian authors adapted themselves to the ideas of the Platonists, which were the most acceptable to them, and were at that time most generally in favor. Little by little Aristotle took the place of Plato, when the taste for systems began to prevail, and when theology itself became more systematic, owing to the decisions of the General Councils, which provided precise and positive formularies. St. Augustine, Boethius and Cassiodorus in the West, and St. John of Damascus in the East contributed most towards reducing theology to scientific form, not to mention Bede, Alcuin, St. Anselm and some other theologians versed in philosophy. Finally came the Schoolmen. The leisure of the cloisters giving full scope for speculation, which was assisted by Aristotle's philosophy translated from the Arabic, there was formed at last a compound of theology and philosophy wherein most of the questions arose from the trouble that was taken to reconcile faith with reason. But this had not met with the full success hoped for, because theology had been much corrupted by the unhappiness of the times, by ignorance and obstinacy. Moreover, philosophy, in addition to its own faults, which were very great, found itself burdened with those of theology, which in its turn was suffering from association with a philosophy that was very obscure and very imperfect. One must confess, notwithstanding, with the incomparable Grotius, that there is sometimes gold hidden under the rubbish of the monks' barbarous Latin. I have therefore oft times wished that a man of talent, whose office had necessitated his learning the language of the Schoolmen, had chosen to extract thence whatever is of worth, and that another Petau or Thomasius had done in respect of the Schoolmen what these two learned men had done in respect of the Fathers. It would be a very curious work, and very important for ecclesiastical history, and it would continue the History of Dogmas up to the time of the Revival of Letters (owing to which the aspect of things has changed) and even beyond that point. For sundry dogmas, such as those of physical predetermination, of mediate knowledge, philosophical sin, objective precisions, and many other dogmas in speculative theology and even in the practical theology of cases of conscience, came into currency even after the Council of Trent.

Leibniz on the Soul-Body Relation

The following is a snippet from Leibniz.  Note Leibniz here discards a scholastic commonplace held by both Scotus and Aquinas, to wit, that the soul is present in every part of the body. Not a surprising claim, if one knows about hylemorphism, nor one that has any direct bearing on the celebrated controversy regarding the unicity of substantial form.

From Leibniz, Philosophical Essays, 326 (the letters to Clarke):

12. God is not present to things by situation but by essence; his presence is manifest by his immediate operation. The presence of the soul is quite of another nature. To say that it is diffused all over the body is to make it extended and divisible. To say it is, the whole of it, in every part of the body is to make it divisible of itself. To fix it to a point, to diffuse it all over many points, are only abusive expressions, idols of the tribe.

Leibniz's complaint is clear enough. He thinks that the scholastic claim that the soul is in every part of the body amounts to saying that the soul is extended and divisible in itself.  What is the A-T or A-S philosopher to say in response? First recall the basic hylemorphic theory: a human being is a composite of matter, generally interpreted as a potential principle, and substantial form, generally interpreted as a principle of actuality. Apart from giving actuality and being to the composite, substantial forms also support accidents. A scholastic philosopher would think of extension and divisibility as accidents, probably falling under the category of quantity. Leibniz wants to argue that since the body is divisible the soul must also, by its very nature, be divisible.  But a scholastic would deny this inference, and hold instead that for the soul to be in every part of the body means that, as the subject to the accident of quantity, it is accidentally extended and divisible.

Leibniz: Theorist of Spiritual Matter?

From a letter of Leibniz to Johann Bernoulli (Philosophical Essays, p. 169-70):

"You rightly judge that the passive is never actually separated from the active in creatures. What God could have done, I don't venture to say. The passive alone and the vacuum seem, at least, incompatible with his wisdom, even if they aren't incompatible with his power. Neither is it certain that there are intelligences completely separated from bodies except for God. Many Church Fathers have also inclined to the contrary, attributing bodies to angels."