Tag: Precision

Infinity, Finitude, and the Good

Plato and Aristotle both attribute great significance to the reality, goodness, and importance for reasoning of limits. Aristotle staunchly opposes assertions of really existing infinity, or of an infinite regress of reasons.

(Despite the opinions of some mathematicians, all that modern mathematics truly requires is “potential” infinity — the ability to construct something arbitrarily large or small through arbitrarily many definite acts of extending, dividing, or whatever of some definite thing. This is consistent, for instance, with the modern grounding of the infinities of calculus in analysis based on the concept of limits. On the frontiers of mathematical research, homotopy type theory and univalent foundations allow the most extravagant “classical” mathematics of higher infinities to be expressed in terms of definite constructions.)

Aristotle’s position on this is closely tied to his central concepts of ends and the good (see also Aristotle on Explanation).

“And since that for the sake of which something is is an end, and this sort of thing is what is not for the sake of anything else, but they are for the sake of it, then if there is any such last thing, there will not be an infinity, but if there is no such thing, there will be nothing for the sake of which it is. But those who make there be an infinite are unaware that they abolish the nature of the good. (Yet no one would make an effort to do anything if he were not going to come to a limit.) And there would not be intelligence among beings; for what has intelligence always acts for the sake of something, and this is a limit” (Metaphysics book small Alpha (II), ch. 2, Sachs tr., p. 31).

This is also central to his argument for the existence of a first cause.

The emphasis on a kind of finitude here should not be taken to imply any dogmatic attachment to particular formulations or representations, such as Hegel for instance objected to. In the following chapter, in part echoing the beginning of the Nicomachean Ethics, Aristotle notes, “Some people expect everything to be said with precision, while others are annoyed by precision, either because they can’t keep the connections straight or because of its hairsplitting pettiness. For precision does have something of this sort about it, so that, just as in business agreements, so also in reasoning it seems to people to be ungenerous. For this reason one must have been trained in how one ought to receive each kind of argument, since it is absurd to be searching at the same time for knowledge and for the direction to knowledge; and it is not possible to get either of the two easily” (ch. 3, pp. 32-33).

“Courses of lectures go along with one’s habits; for in the way that we are accustomed, in that way we think it fitting for something to be said, and what departs from this does not seem the same, but through lack of acquaintance seems too obscure and alien. For we are used to what is familiar. And what great strength the customary has, the laws show, in which mythical and childish things are of greater strength than knowing about them, because of custom” (p. 32).

This last remark clearly shows that Aristotle’s emphasis on the shareability and actual sharedness of values does not at all mean he assumes that what is held to be authoritative by one’s own community or society is always right. Unlike Socrates, who after his eloquent defense meekly accepted his city’s ignorant condemnation, Aristotle at one point fled Athens “lest the Athenians sin against philosophy twice”. This lesson is crucial to the understanding of Hegel as well.

Next in this series: Aporias

The Knowledge Sought

Following the emphasis of al-Farabi on demonstrative “science”, the Latin scholastic tradition treated “metaphysics” as a completed science. Some writers attributed such a completed science to Aristotle, while others, following in the wake of Avicenna, put forward their own improvements.

With respect to being, Aristotle himself speaks of knowledge sought rather than possessed. In inquiring about being “as such”, he is exploring a question given prominence by others. Far from claiming to have final knowledge of being as such, he highlights the ambiguity of “being”. There can be no “as such” — and hence no final knowledge — of an ambiguous thing.

This is not the end of the story, however. The very first sentence of the Metaphysics is “All human beings by nature stretch themselves out toward knowing. A sign of this is our love of the senses; for even apart from their use, they are loved on their own account (book capital Alpha (I), ch. 1, Sachs tr., p. 1).

We are after knowledge of something. It is just not clear that that something would be accurately characterized as “being”, full stop.

“[A] sign of the one who knows and the one who does not is being able to teach, and for this reason we regard the art, more than the experience, to be knowledge” (p. 2).

“Further, we consider none of the senses to be wisdom, even though they are the most authoritative ways of knowing particulars; but they do not pick out the why of anything” (ibid).

“[T]he person with experience seems wiser than those who have any perception whatever, the artisan wiser than those with experience, the master craftsman wiser than the manual laborer, and the contemplative arts more so than the productive ones. It is apparent, then, that wisdom is a knowledge concerned with certain sources and causes” (p. 3).

This concern with sources and causes, with the why, is the true subject matter of the Metaphysics. This is emphasized again at length in book Epsilon (VI).

“Since we are seeking this knowledge, this should be examined: about what sort of causes and what sort of sources wisdom is the knowledge. Now if one takes the accepted opinions we have about the wise man, perhaps from this it will become more clear. We assume first that the wise man knows all things, in the way that is possible, though he does not have knowledge of them as particulars. Next, we assume that the one who is able to know things that are difficult, and not easy for a human being to know, is wise; for perceiving is common to everyone, for which reason it is an easy thing and nothing wise. Further, we assume the one who has more precision and is more able to teach the causes is wiser concerning each kind of knowledge. And among the kinds of knowledge, we assume the one that is for its own sake and chosen for the sake of knowing more to be wisdom than the one chosen for the sake of results” (ch. 2, p. 3).

“Now of these, the knowing of all things must belong to the one who has most of all the universal knowledge, since he knows in a certain way all the things that come under it; and these are just about the most difficult things for human beings to know, those that are most universal, since they are farthest away from the senses. And the most precise kinds of knowledge are the ones that are most directed at first things, since those that reason from fewer things are more precise than those that reason from extra ones” (p. 4).

For long I struggled with this last statement. How could a knowledge of first things be the most precise of all? In the Topics, he says that first principles can only be investigated by dialectic: “[T]his task belongs properly, or most appropriately, to dialectic; for dialectic is a process of criticism wherein lies the path to the principles of all inquiries” (Collected Works, Barnes ed., p. 168).

Some commentators — influenced by al-Farabi and the subsequent tradition’s overwhelming emphasis on the place of demonstration as opposed to dialectic in Aristotle — have considered it a puzzle or a defect that the Metaphysics and other Aristotelian texts do not seem to consist in demonstrations as described in the Prior Analytics. The answer is that the Metaphysics and the others generally do follow the model of dialectic articulated in the Topics, as the Topics itself says they ought to.

Returning to the Metaphysics, Aristotle has already stressed that the most universal knowledge is also the most difficult. Also, he standardly distinguishes between how things are “in themselves” and how they are “for us”. The knowledge of first things would be most precise in itself, not necessarily for us in our relative achievement of it.

To anticipate, I think the final conclusion of the Metaphysics will be something like “All things are ultimately moved by love of the good”. The qualification “ultimately” is essential to making sense of this.

(For Aristotle himself, all becoming and terrestrial motion are grounded in — though not in detail determined by — the entelechy or entelechies of circular celestial motion. The stars are a kind of everlasting living beings endowed with superior intellect, and are directly moved by love of the first cause. This might seem quaint to modern people. I find the love part beautiful in a poetic sort of way, but think Aristotle’s theoretical astronomy in general and his views of the special status of celestial objects have relatively little impact on interpretation of the rest of his work — particularly with respect to the teleology affecting earthly things and the discussions here in the Metaphysics.)

Plato says that the Good surpasses all things in ancientness and power. He represents Socrates as provocatively arguing that all beings desire the good, regardless of how confused they may be about what the good really is. No one deliberately and self-consciously desires what they recognize as evil. That is impossible, because it is logically self-contradictory. For the same reason, there also could not be a “principle” of evil. This is a tremendously powerful thought, of unparalleled importance for ethics. It sets a fundamental tone of charitable interpretation, in diametrical contrast to the kind of point of view that says those people over there are just evil.

Aristotle, however, says that Plato does not clearly explain the mode of activity of the Good, or how it acts as a cause. According to Aristotle, when Plato does gesture in this direction, he lapses into treating the Good as either a formal cause or an efficient cause, or both. But speaking in terms of formal or efficient causality loses what is most essential about the good — what many contemporary philosophers would call its normative character.

Aristotle considered his own contribution in this area to be a thorough account of how all things are ultimately moved by that for the sake of which, and of how the Good indirectly influences things just as that for the sake of which. This, once again, is what Kant called “internal teleology”.

After the horrors of the 20th century, many people have lost faith in the fundamental goodness of life. This is basically an emotional response. The indubitable factuality of horrendous evil in the world is not an Aristotelian or Hegelian actuality, and does not touch actuality. The factuality of evil does pose a roadblock for common interpretations of particular providence or “external” teleology, but not for Aristotelian or Hegelian teleology.

But how could a knowledge of first things be exact? We certainly don’t have knowledge of the first cause in itself. But coming back to my formulation “All things are ultimately moved by love of the good”, this does meet Aristotle’s criterion of simplicity: all things are said to be ultimately moved by one thing (even though more directly, they are moved by their own love of whatever they do love, which seems good to them within the limits of their understanding).

We have exact knowledge neither of the first cause in itself nor of the particulars we encounter in life, but perhaps we can after all have exact, certain knowledge that “All things are ultimately moved by love of the good”. This is the kind of thing I think Aristotle is suggesting. (See also Aristotle on Explanation.)

Next in this series: The Four Causes Revisited