First posted April 17, 2014. Recentest significant edit: October 14, 2016. Since this is the first new post in years, I'll let it sit on the home page for a while.

• "Quadruple Object, The" at Zero Books: a set of reviews, quotes, and diagrams.
• Graham Harman's blog Object-Oriented Philosophy.
• Harman's recent professional home page at the American University in Cairo and versions at older URL.
• Harman's new professional home page at the Southern California Institute of Architecture (SCI-Arc).

Harman in his book The Quadruple Object says that an object has four poles — real object (inexhaustible object in itself, unknowable), sensual object, real quality, sensual quality.

Harman characterizes four pairings of those poles as involving 'tensions':

1. Time is the tension between sensual object and sensual quality.
2. Space is the tension between real object and sensual quality.
   
3. Husserlian eidos is the tension between sensual object and real quality.
4. Essence is the tension between real object and real quality.

I have read quotes from The Quadruple Object in reviews and perused passages from it via Google Books. Harman's quadruple object seems unlike my fourfolds, since I hold that object and quality (or characteristic) form a fourfold with modality (in a broad sense, including feasibility, probability, information, and givenness) and mathematical relation. His fourfold of tensions seems unlike my fourfolds.

The following material on page 79 is of a kind probably more interesting to me than to many:

The number one is the password of monism. Despite its comforting promise of holistic unity, it tends to be too sanguine in its implicit assertion that difference and strife are less real than a primal harmony in things. The number two seems to announce a conflict of two opposed principles. But such dualism turns out to be paradoxically monotonous, since usually nothing occurs but a constant struggle back and forth across the divide. The number three seems more sophisticated [...].

Then we come to a passage at which cognoscenti of Charles Sanders Peirce may wince or scoff:

The number three seems more sophisticated, with its claim to unify two opposed principles in a dynamic third term that both preserves and transcends the crucial features of the two opposite terms; it is essentially dualism with the introduction of a mediator, as in Hegel's dialectic and Heidegger's own repetitive threes. But the frequent danger of threefold structures is that of false happy endings that neuter the tragic force of opposition, uniting all opposites in a place too easily accessible to human resolution.

Harman goes on to mention famous fourfolds in philosophy, notes that they tend to result from the crossing of two given axes, and offers two criteria for a good fourfold — its axes must be "well-chosen," not merely incidental to each other, and it must offer a "useful account" of how the fourfold's members interrelate, an account in which the four parts don't just sit "in static co-existence".

To one like me who hasn't read widely enough in philosophy to have a good sense of how the various-numbered philosophical divisions have worked out, it will somewhat seem cloud-talk, not that I myself don't try to talk it occasionally. As they say, here goes. My sense of it is that, when a duality involves positive conflict, the conflict is between two vying to be the one, the first — first, not in Peirce's sense of the fresh, novel, etc., but in the sense of the determinative, the beginning qua leader, arché, not beginner qua neophyte (to originate is not exactly the same as to be originated). Yet, when two meet and harmonize to some end-as-a-third, then to the extent that, of the first two, one leads and the other follows, the follower (secundum) is the mediator, the harmonizer. In other words, instead of thesis-antithesis-synthesis, we have:

• a beginning or impetus (or maybe two or more vying together), dynamic;
• a middle or means, harmonizing, rhythmicizing; and
• an end or culmination, synergizing, radiant — which is where the element, not of mediation, but of novelty, freshness, bloom, rejuvenation, reproduction, etc., comes in. I mean, while we're talking cloud-talk.
• Yet, that's not all, since, likewise as (1) a beginning is related to (2) a middle or continuation, so, in a parallel manner, (3) a culmination is related to (4) a final state. The final state in this idealized story is a stabilism, an integrity, checked, balanced, established, confirmed. (Bet you thought I was going to omit the first of Aquinas's three requisites of the beautiful — I put it fourth; to spell the revision out, with apologies to Aquinas and Joyce: 1st, due force, due directed magnitude, arresting; 2nd, harmony or due proportion, fascinating; 3rd, radiance, enchanting; 4th, wholeness, i.e., integritas or perfectio, producing attachment, devotion.)

The only picture at all like this of which I know in past philosophy is that of Aristotle's four causes — efficient, material, final (as telos), and formal (as entelechy, having in completeness, being at an end, as Joe Sachs put it). This works better when one conceives of form as structure — rather than of form as appearance or look (original meaning of Greek eidos and Latin species).

So, (third-phase) false happy endings, of which Harman warns, and unhappy endings more generally, are often to some extent avoided or corrected by consideration, anticipation, recognition, etc., of (fourth-phase) completenesses, end states, entelechies — consideration of aptness of means, unintended consequences, clashes of values, and so on.

I add a third criterion for a good fourfold: meaningful pattern via verticals, horizontals, and diagonals:

Both 1 & 2 (along the left vertical) involve the earlier.
Both 3 & 4 (along the right vertical) involve the later.

Both 1 & 3 (along the top horizontal) involve change and suggest external relations.
Both 2 & 4 (along the bottom horizontal) involve non-change and suggest internal relations.

Both 1 & 4 (along the downward-sloping diagonal) are more space-like in that sense in which they are directional opposings (those in dynamism and those in structural integrity).
Both 2 & 3 (along the upward-sloping diagonal) are more time-like in that sense in which they are not directional opposings (either in endurance or in vigor).

(Those are three sets of pairs, where is the fourth, if any? Insofar as those sets reflect potential inversions or 'flips' of the square, there is a fourth flip-related operation, the one which leaves the square the same as before, equivalent to doing any of the other flippings twice. One could think of it as involving the square's each quadrant's pairing with itself.)

I vote for a fourth criterion awarding extra points if a four-fold's four items are also ordered. And a fifth criterion awarding more extra points if the ordering can recur nicely enough in a loop.

- posted by The Tetrast @ 10:14 AM [top of post] [top of page] Copyright © BenjaminðA.ðUde11.