Philosophical Hunting

Book II, Chapter 13 of the Posterior Analytics begins, “Now we have already said how what a thing is is set out in the terms, and in what way there is or is not demonstration or definition of it; let us now say how one should hunt out what is predicated in what a thing is.” That the hunt for what belongs to a thing in what it is does not differ from a hunt for the demonstrative middle is not immediately obvious, but follows from the fact that what belongs in what a thing is does not differ from what is necessary. The discussion which follows makes clear that the hunt here has the purpose of discovering what something is, that is, of finding out of the demonstrative middle what it is. The things which are predicated in what it is are hunted out, sorted, and sifted with a view to the substance of the object. Aristotle says this explicitly: “such things must be taken up to the first point at which just so many are taken that each will belong further but all of them together will not belong further; for necessarily this will be the substance of the object.”

The question about how things predicated in what it is are to be hunted out is not a question of by what means these things may be identified. Rather it is a question of the context proper to such a pursuit: “How?” here has the sense of “In what way? Along what path?” None of these attributes inhering necessarily in a thing is of scientific interest on its own account, as the stopping point of an inquiry. Rather, they have the character of an “if it is.” Knowledge of them imparts knowledge that there is a demonstrative middle. The satisfaction of the inquiry in pursuit of the that is not a stopping point, but opens on a further inquiry, in pursuit of what it is. Aristotle is not here articulating a methodology for turning up attributes which belong necessarily to something. Indeed, his position here would caution against the very notion of such a methodology in abstraction from inquiry proper, which directs itself to a middle term to learn what it is. Such a pedantic, disinterested manner of “hunting out” would differ from the “hunting out” here recommended as a sportsman's weekend out putting bullets in things differs from the patient, urgent incursions into the wild of a man who hunts for his sustenance. That is to say, it differs in failing, however many trophies it may accrue, to be the hunt—the genuine, high human activity of science which runs through and unifies our intellectual capacities, and gives them their meaning.

The Humane Critique, c't'd

Because the principle of purposiveness must be open-ended in its range of applicability, the possibility always remains open to judgment of construing all of nature in mechanistic terms, and indeed given the option, the intentional direction of our cognitive powers is such that they will always lead us to prefer such an interpretation, since we will prefer what brings all of nature within our ambit. If we follow this inclination, which is so deeply rooted in our nature that it grows together with and indeed gives life to our scientific activity, then we give free rein to our cognitive powers and simply let their own self-born orientation direct us in our relation to things. However reckless this might seem, if all the same this is the direction which comes to us through the unimpeded activity our most characteristic powers, would this not be most human?

But this ramification of the principle of purposiveness has a companion growing almost invisibly alongside it: namely, the critical power which retrospectively reflects on and clarifies the origin of science. And this power begins with a presupposition contrary to that which judgment wishes to arrogate to itself: that the cognitive powers are limited, and that these limitations present themselves to view purposively for the ordering of cognitive ambition, rather than for meeting its intention. This presupposition will be found in no one of the powers into which Kant divides cognition, as though he were doing so exhaustively—and this is perhaps the strangest feature of Kant's thought, that he omits to provide or even look for conditions of possibility for that mode of attention which facilitates his entire project. Whether this silence is a failure of self-consciousness or rather a supreme tact of the true charioteer seems to be the question, although perhaps it is no question at all—since it is at least suggestive of the highest human condition if not true to say that failure of self-consciousness is the essence of tact, just as Douglas Adams has imagined the secret of flight as consisting in being able to throw oneself at the ground, and miss.

Part 2: The Geo-Logical Foundations of Techno-Logic According to Wall-E

So what is an axiom?

Axiom, as no doubt you are aware, is the name of the great space station on which mankind draws out its centuries-long vacation from the planet as the movie Wall-E opens. It seems to have been named in the confidence that it could supply the complete conditions for human life without any need of its being supported, and this confidence would seem seem to be confirmed by the fact that so many generations later, humans still live on the ship, with not even a memory of any other place to live. However, we learn that the Axiom has according to its own intelligence reached such an estimation of its self-sufficiency that it rebels against that part of its directive which it interprets as a threat to its autonomy--namely, the directive to seek a return to ground. Being themselves aliens to ground, men have no resource to question this claim.

Not to make too much or too little of the heroic exploits by which mankind is brought back down to Earth, it will be enough for my present purposes to remind you that the same Axiom which adrift in space sustained nothing which could be called human life and therefore failed in its own directive, when grounded on the Earth does serve human life as a starting point--that is, a point of departure. And this departure (from itself) is the true being of the Axiom.

Tune in next time for the full interpretation of this allegory.

The Logical Foundations of Logic According to Wall-E

There is a prejudice abroad that an axiom is a certain sort of proposition or statement, which serves as one of a set of starting points to build the any science (construed as a set of interrelated propositions regarding a genus) through inferences from these axioms. For those who distinguish between axioms and principles--which we must if we are to countenance the notion of an empirical science (and let that be an axiom if you like)--this thesis may be refined to say that axioms serve as the most general starting points and function alongside the empirically disclosed and clarified principles of any given empirical science to govern the manner in which inference may and must proceed from those starting points.

Presumably Aristotle is somehow responsible for this state of affairs, since perhaps there are only a handful of prejudices of logic which cannot somehow be traced back to his work. I have not yet found anything of the sort asserted in the Analytics, but perhaps that will only tell you how little attention I have been able to give that text. What I do find is the fact that an axiom is never brought into a straightforward argument: e.g., "That it is not possible to affirm and deny at the same time is assumed by no demonstration--unless the conclusion too is to be proved in this form" (An Post 77a10). In other words, only if one wants to prove precisely that a certain true proposition is not to be denied, or that a certain false proposition is not to be asserted, do we appeal to the axiom known as the principle of non-contradiction. Yet, even in this case, if the principle of non-contradiction is truly an axiom in the sense of being indispensable for grasping anything whatsoever, the same principle which is made explicit as a premise must also undergird the connection of this premise through the other to the conclusion. And it cannot do this as a premise.

Okay, so what does this have to do with Wall-E? I guess all you robot-loving fools out there will just have to wait till next time to find out,

The Humane Critique

That the Critique of Judgment is Kant's most humane critique could be established on superficial grounds: for in it, he discusses those things which above all make us human, as opposed to being simply one or the other of those two terms which go together to make our definition (i.e., rational, animal). Surely art and purpose, more than logic or, say, digestion, are the fields in which we most eminently show ourselves for what we are as whole beings, beyond the elements of our composition. No doubt this proposition could be denied, but not from within the perspective properly called humanism, which is perhaps the same perspective from within which we may expect to grow a concern for the application of the term “humane.”

But in addition to this superficial reason, there is also the fact—an astonishing fact, when it appears within the context of a received notion of Kant as the philosopher who stole the real world away, walling it off from our pathetically grasping and clutching reason behind an impenetrable range of phenomena—that here he invites us to discover the real bases we have for judging nature as subjectively and objectively purposive. True: these bases are merely a set of presuppositions which enable judgment to expect to discover purposive organization in nature, and therefore enable it to reach out for universal empirical laws and structures. They cannot satisfy pure reason that the world is such and such. But is it humane to expect the world to satisfy pure reason? Is it not possible that, contrary to the parable of Plato, the seat of raving ambition is not in the horse but in the charioteer—and that it is he who must be reined in by the nobility of his horsemanship?

logical foundations of logic

Tonight I am wondering what logic is made of? In other words, if logic is a system of relatedness (through inference or deduction or whatchawannacallit), what does it relate? "Propositions" seems to be a popular answer to this question, but I don't find it particularly helpful, since it is not clear what a proposition is. Is it a kind of statement? Is it whatever is left of a statement when intentionality is subtracted out? Is it something that is done to statements?

I've got Aristotle laying it out two different ways, in the first chapter of Prior Analytics. He says a proposition is a "statement," sure enough, "affirming or denying something of something," but when he gets down to dividing propositions up into kinds, he says a demonstrative proposition is an "assumption of one of two contradictories," rather than saying that it simply is "one of two contradictories" and that a dialectical proposition is a "choice." I think either of these lines could be assimilated to other, just by pointing out that anything we do as logical practicioners we do through statements. I.e., nothing is assumed unless someone makes a statement, to himself at least, to the effect that this one of the two contradictories is the case. Or on the other hand, a proposition can be called a statement even if it isn't one, because what it does it does in a statement.