Being and Representation

In L’Être et représentation (1999), Olivier Boulnois documents the emergence of “metaphysics” in its distinctively non-Aristotelian modern sense among various 13th century authors, including Roger Bacon, Henry of Ghent, and Siger of Brabant, leading to its decisive formulation by the Franciscan theologian John Duns Scotus in the 14th century. Avicenna had already claimed that metaphysics is about “being in general”, whereas Aristotle himself had emphasized that “being is said in many ways”, which implies that there is no “being in general”.

Boulnois suggests that the 13th century authors just mentioned paved the way for Scotus’ innovations by already treating being as a concept. We are so used to that, that it is hard for us to grasp what Aristotle means in suggesting that “being in general” is not a proper concept at all.

Scotus argued against Aristotle that there is a unifying, logically minimal criterion of being, and it is representability. To be representable is to be “not nothing”. Unicorns and other imaginary creatures are representable, whereas Aristotle would not have called them beings. Scotus’ concept of representation seems to be purely logical; to have a representation of something is not necessarily to have understanding of it. For Scotus, God and creatures are equally representable, even though creatures, as finite, can be properly understood by the human mind and God, as infinite, cannot. Whereas Aristotle never speaks of an infinite being — only of a perfect one — Scotus’ generic concept of being is very explicitly indifferent to distinctions between finite and infinite.

It is one thing to acknowledge representation as a logical concept among others, and quite another to give it the kind of special first place status that Scotus does in his ontology, and that Locke does in his epistemology.

Boulnois says it is with Scotus that metaphysics became linked to what Kant later called ontotheology. While separating metaphysics as the account of being from theology as the separate account of God, Scotus also made God indifferently one of the objects of metaphysics, along with all the other beings. The combination of these changes actually brought metaphysics closer to revealed theology, and helped it to be perceived as the safe handmaiden of the later Latin tradition, rather than as independent philosophical theology that some found threatening.

If one speaks of a subject of representation, it could be — in a sense of “subject” closer to that of Aristotle — that in which something stands for something, or it could be — in a modern sense — the one who represents. “In the context of representation, the soul is not the content of its thought, but rather has a representation, distinct from itself” (Boulnois, op. cit., p. 152, my translation).

It seems that for both Scotus and Locke, the mind has representations. The soul in Aristotle is thoughts and feelings and capabilities, not something standing behind them. (See also Repraesentatio; Ontology; Being, Existence.)

Infinity, Finitude

Here is another area where I find myself with mixed sympathies.

Plato seems to have regarded infinity — or what he called the Unlimited — as something bad. Aristotle argued that infinity exists only in potentiality and not in actuality, a view I find highly attractive. I think I encounter a world of seemingly infinite structure but only finite actualization.

Some time in the later Hellenistic period, notions of a radical spiritual infinity seem to have appeared in the West for the first time, associated with the rise of monotheism and the various trends now commonly called Gnostic. This kind of intensive rather than extensive infinity sometimes seems to be folded back on itself, evoking infinities of infinities and more. The most sophisticated development of a positive theological infinite in later Western antiquity occurred in the more religious rethinking of Greek philosophy by neoplatonists like Plotinus, Proclus, and Damascius.

In 14th century CE Latin Europe, Duns Scotus developed an influential theology that made infinity the principal attribute of God, in contrast to the pure Being favored by Aquinas. Giordano Bruno, burned at the stake in 1600, was a bombastic early defender of Copernican astronomy and notorious critic of established religion who espoused a curious hybrid of Lucretian atomistic materialism, neoplatonism, and magic. He proclaimed the physical existence of an infinity of worlds like our Earth.

Mathematical applications of infinity are a later development, mainly associated with Newton and Leibniz. Leibniz in particular enthusiastically endorsed a speculative reversal of Aristotle’s negative verdict on “actual infinity”. Nineteenth century mathematicians were embarrassed by this, and developed more rigorous reformulations of the calculus based on limits rather than actual infinity. The limit-based formulation is what is generally taught today. Cantor seemingly went in the opposite direction, developing infinities of infinities in pure mathematics. I believe there has been another reformulation of analysis using category theory that claims to equal the rigor of 19th century analysis while recovering an approach closer to that of Leibniz, which might be taken to refute an argument against infinity based solely on lack of rigor according to the standards of contemporary professional mathematicians. One might accept this and still prefer an Aristotelian interpretation of infinity as not applicable to actual things, though it is important to recall that for Aristotle, the actual is not all there is.

The philosophy of Spinoza and even more so Leibniz is permeated with a positive view of the infinite — both mathematical and theological — that in a more measured way was later also taken up by Hegel, who distinguished between a “bad” infinite that seems to have been an “actual” mathematical infinite having the form of an infinite regress, and a “good” infinite that I would gloss as having to do with the interpretation of life and all within it. Nietzsche’s Eternal Return seems to involve an infinite folding back on itself of a world of finite beings. (See also Bounty of Nature; Reason, Nature; Echoes of the Deed; Poetry and Mathematics.)

On the side of the finite, I am tremendously impressed with Aristotle’s affirmative development of what also in a more Kantian style might be termed a multi-faceted “dignity” of finite beings. While infinity may be inspiring or even intoxicating, I think we should be wary of the possibility that immoderate embrace of infinity may lead — even if unwittingly — to a devaluation of finite being, and ultimately of life. I also believe notions of infinite or unconditional power (see Strong Omnipotence; Occasionalism; Arbitrariness, Inflation) are prone to abuse. In any case, ethics is mainly concerned with finite things.