Tag: Bad Infinite

Individuality, Community

The last sections of Hegel’s “Reason” chapter begin to introduce a notion of community, still starting from the point of view of the individual. Here he wants to suggest a broad developmental arc from the simplicity of what he calls “True Spirit” — in which personal identity is experienced as coming directly from one’s place in a traditional, “natural” face-to-face community — through the emergence of individual freedom, which he sees occurring in a necessarily “alienated” way that also tends to undermine ethical values — to Hegel’s anticipated recovery of ethical values in a future community based on something like love of one’s neighbor, that also gives the individual her due. In the course of it he discusses the limits of “law-giving Reason” and “law-testing Reason”, with Kant and Fichte in mind. Sophocles’ Antigone is used to illustrate a conflict between perspectives of family loyalty and formally instituted law.

H. S. Harris in his commentary says that from the naive perspective of True Spirit, “Individual self-consciousness just knows what is right. The laws are there” (Hegel’s Ladder II, p. 113). “These laws are ‘laws of nature’. They need no warrant” (p. 112). He characterizes this as another return to the immediacy-based logic of Sense Certainty. It will be “the determination to fulfill Apollo’s command [know thyself] that brings to pass the downfall of the Ethical Substance…. [But the] climax of the effort to ‘know ourselves’ in one another individually is the recognition that we must forgive one another for the inevitability of our failure to act with universal unselfishness” (p. 115).

“It is a logical fact that we cannot go immediately from the universal to the singular. We can only produce formal universals (non-contradictions)…. So we are left with a logical form (non-contradiction) as the form of law” (p. 116).

The “internal dialectic of justice is much more important than the fact that different standards of justice are justifiable in terms of their abstract rationality” (p. 120).

“Hegel made clear that it is the speculative sense of identity that matters. The stability and harmony of the Substance we have lost is ‘identical’ with that which we are just now in the process of regaining. Neither Antigone nor Jesus is formally a Kantian. But the piety of both requires us to ‘respect humanity as an end'” (p. 117).

“Our own law-testing procedure is a moment in the greater cycle of logical comprehension; and it has always known itself to be that. It is not formal in the sense in which Stoicism is formal; we saw at the beginning why error and ignorance are necessary in the comprehensive cycle. Those who complain that ‘dialectic and absoluteness are ultimately at loggerheads’, or that Hegel seeks to ‘close the gates of truth’, are merely expressing the Skeptic’s absolute knowledge regarding the folly of Stoic pretensions. It is precisely the justification of their own critical reason that Hegel wants to offer” (p. 121).

“[Hegel’s] criticism of Law-Testing Reason… is meant to bring home to us the fact that a long historical experience is required for the laying down of the substantial foundation that gives law-testing the sort of range and validity it can and does have” (ibid).

A feeling of spiritual “identity” with the goddess Athena motivated the Athenian to be willing to die for his city. Harris thinks this qualifies as a supra-personal motivation, but argues against those who attribute a notion of other-than-individual “consciousness” to Hegel. Rather, “certain experiences of a deeper or higher identity that every individual has, or can have, reveal the true meaning of what it is to be rational (or human)” (p. 127).

“We ought not to permit any reduction of the rhetoric of ‘Spirit’ to the rhetoric of ‘humanism’ because humanity has… two necessary sides, and it is the ‘human animal’ side that is naturally fundamental. For the human animal to go to the death in a struggle is (functionally) irrational; but that is not necessarily the case for a ‘human spirit'” (p. 128).

On the other hand, Hegelian Spirit also has nothing in it of what Hegel called the “bad infinite” or of the Sublime, which Kant associated with seemingly infinite (and definitely more-than-human) power.

“Whether we look outside or inside ourselves, the bad infinite, or the ‘more-than-individual’, is no suitable object of religious reverence. We must maintain Hegel’s ‘spiritual’ terminology because his language clarifies the religious language of tradition in a rational way. Those who use it become functionally liberated from the bad infinite or Sublime; for even as ‘believers’ they are bound to agree with Thomas Aquinas that what they are talking about is not rationally comprehensible in its ‘sublime’ aspect; and they will be morally rational in the sense that they will not try to impose their religious faith on others by the use of force (which would contradict its spiritual essence)” (p. 129).

“All that Hegel, the observer, does is talk to us about the ways in which our poets and prophets have spoken, and to show us several necessary truths that we are not usually conscious of. First, he proves that the way they spoke was necessary for the advent of morally autonomous Reason; and then he makes us see how these modes of speech form a pattern that forces us to admit that all rational speech (not just that of the poets and prophets) is the utterance of a different ‘self’ than the one who is fighting a losing battle to stay alive encased in a human skin. We all know this perfectly well. But never, until Hegel wrote, did we know how to put our rational and our natural knowledge together without speaking in ways that are not humanly interpretable and testable. A critic who accuses Hegel of speaking not as the poets and prophets speak, but in some peculiar philosophically prophetic way of his own, is committing the ultimate rational injustice of obscuring his supreme achievement. [The influential critic Charles] Taylor’s theory of a ‘self-positing Spirit’ that is somehow ‘transcendent’ is itself ‘the sin against Hegel’s Spirit'” (p. 131).

“The chapter on Reason closes into a perfect circle. It begins and ends in ‘Observation’; and the Observing Reason that goes forward is comprehensive. It does not just observe Nature as an external or found ‘objectivity’; it observes the Ethical Substance — the total unity or identity of Nature and Spirit as a harmony that has made itself. It is the Ethical Substance, seen clearly as the source of self-conscious individual Reason, that becomes the subject of the new experience.”

“True Spirit is the self-realizing consciousness that takes its own self-making to be the direct expression of nature. What True Spirit lacks is the awareness that Spirit must make itself in the radical sense of expressing a freedom that is opposed to Nature. True Spirit does not know that it must ‘create itself from nothing’.”

“This ‘nothing’ is the speculative observing consciousness” (p. 134).

“On the side of Consciousness, all pretense of a ‘difference’ between itself and its object can now be dropped…. When ‘difference’ is reborn (as it immediately will be) it is because the Object itself (the Sache selbst as a communal self-consciousness) cannot maintain itself as a living object… without an essential differentiation…. But at the moment [consciousness] has come to self-expressive identity with the Sache selbst that it merely observes” (p. 135).

Next in this series: Ethical Substance to Personhood

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.