Methods of inquiry
Recentest significant change: December 30, 2010.

Charles Sanders Peirce defined inquiry as any struggle to move from troublesome doubt to a secure belief, and outlined four methods.

See "The Fixation of Belief" (1877): via peirce.org; via Arisbe; via Google

The following bulleted paragraphs are taken mostly from the summary that I wrote at Wikipedia in various articles there:

• The method of tenacity (policy of sticking to initial belief) — which brings comforts and decisiveness but leads to trying to ignore contrary information and others' views as if truth were intrinsically private, not public. The method goes against the social impulse and easily falters since one may well notice when another's opinion seems as good as one's own initial opinion. Its successes can be brilliant but tend to be transitory.
• The method of authority — which overcomes disagreements but sometimes brutally. Its successes can be majestic and long-lived, but it cannot regulate people thoroughly enough to withstand doubts indefinitely, especially when people learn about other societies present and past.
• The method of congruity or the a priori or the dilettante or "what is agreeable to reason" — which promotes conformity less brutally, but depends on taste and fashion in paradigms and can go in circles over time, along with barren disputation. It is more intellectual and respectable but, like the first two methods, sustains capricious and accidental beliefs, destining some minds to doubts.
• The method of science — the method wherein inquiry supposes a discoverable reality independent of particular opinion — the method, then, wherein inquiry can, by its own account, go wrong (fallibilism) as well as right and thus purposely tests itself and criticizes, corrects, and improves itself. No destined doubts of the scientific method as such arise from its practice.

The method of authority, as outlined by Peirce, is the method of power and coercion. Extortion is a kind of coercion, but shades into bribery, corruption, and expedience or convenience. From force-ism to materialism. Then there is the fashionable, the glamorous, the charming or charismatic, in the swing - this seems to include Peirce's method of congruity. Finally there is the status-oriented, the standing-based - sophistic, often cocksure, self-deceptive and sometimes consciously deceptive.

Inquiry method:	Applying it to oneself, to others, consciously or unconsciously:
Method of authority, power, coercion.	Power-enhancing belief. Joining or submitting to the power in order to be powerful. Recruiting or coercing others.
Method of wealth, means, the "financial method."	Affluent belief. Seeking, taking, or offering, giving the bribe, the funding, etc. Extortion from opponents.
Method of fashion, wattage, opulence.	Fashionable belief. Manipulating oneself. Seeking to be manipulated, seduced. Manipulating and luring others. Rhetoric in the bad sense. Manipulative taunting and ridicule of opponents.
Method of status, standing.	Status-enhancing belief. Deceiving oneself. Cocksureness. Sophistry. Seeking to be deceived and to deceive others. Fraud. Fraudulant demotion of opponents to low status and obscurity.

Thus the familiar force/fraud twofold becomes a fourfold, on the pattern of other fours.

	Wrongs.	Causal terms of intelligent beings.	Realms of nature.	Tetrazed principles of the Four Causes.
1.	Force (coercion).	Will.	Forces.	Agent.
2.	Corruption (bribery, etc.)	Ability.	Matter.	Bearer.
3.	Manipulation (luring, incitement, lulling).	Affectivity.	Life.	Act.
4.	Fraud.	Cognition.	Mind.	Borne.

- posted by The Tetrast @ 12/13/2010 04:10:00 PM 0 comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Nontrivia
Recentest significant change: June 19, 2010.

In my previous post "Unsettlings" I discussed a double opposition, or "double chiasm" as I called it, among the (cognitive) lights in which a given phenomenon would seem (1) simpler or (2) more usual or normal or (3) clearer, more clarificatory, more significant or informative, or (4) deeper, less trivial:

1. Simplicity, optimality, etc. 2. Likeliness, probability, etc.

3. Informativeness, significance, etc. 4. Nontriviality, depth, etc.

The first three correlate pretty obviously to mathematics of optimization, mathematics of probability, and mathematics of information. The fourth (nontriviality, depth, etc.) seems to me to correlate to mathematical logic.

Inverseness between probability and information. A message's quantity of information, its amount of informativeness or "newsiness," reflects the improbability of that message before it was sent. The information quantity is not simply 1 minus the message's erstwhile probability (e.g., 100% minus 30% probability equals 70% improbability), but still it's pretty simple, the logarithm of the reciprocal of the erstwhile probability, and we can think of information as a kind of inverse of probability. It goes up when the erstwhile probability goes down, vice versa, and so on. Well, actually it's a little more complex than that. The information is measured as a logarithm to a given base. If the base is not specified, then the logarithm is telling you something like message length, e.g., how many (instances of) symbols. Four quaternary units of information are 16 times more information than four bits (binary units) - but same message length. In amount of information, four bits (binary units) of information equal two quaternary units of information. In Peircean terms, the message length corresponds to the number of individual instances (or individual "replicas") of symbols; the base corresponds to the number of general "replicas" of symbols on which the message depends (binary 0 and 1, trinary 0, 1, and 2, etc.). That said, onward.

So, inverseness between optimality and nontriviality? If one puts, as I do, optimality and nontriviality/depth likewise into an opposition, one might expect a similar kind of inverseness. Lloyd's and Pagels's idea of thermodynamic depth is "the entropy of the ensemble of possible trajectories leading to the current state" (from Cosma Shalizi's notebook on complexity measures) and gets us the idea of some sort of opposite or inverse of the shortest path (simple, optimal, etc.). Then there is the idea of algorithmic complexity, the shortest program capable of obtaining a given result, which complexity is uncomputable because of the halting problem, and anyway the general idea that you can't get a ten-pound theorem out of five pounds of axioms (as discussed by Chaitin). So by merely looking for "big-picture" patterns (and roving through things like the Mathematical Subject Classification), I seem, despite my amateurish ignorance, to have found myself in the right neighborhood.

Shalizi, with a bluntness that is helpful to the general reader, starts out his above-linked notebook "Complexity Measures" with this striking paragraph:

C'est magnifique, mais ce n'est pas de la science. (Lots of 'em ain't that splendid, either.) This is, in the word of the estimable Dave Feldman (who taught me most of what I know about it, but has rather less jaundiced views), a "micro-field" within the soi-disant study of complexity. Every few months seems to produce another paper proposing yet another measure of complexity, generally a quantity which can't be computed for anything you'd actually care to know about, if at all. These quantities are almost never related to any other variable, so they form no part of any theory telling us when or how things get complex, and are usually just quantification for quantification's own sweet sake.

Now, one may note that there also seems no general quantification of "optimality," either — instead, one seeks specific optima (idempotency of probability measures is involved in optimization, I guess that that's what one gets instead of a variable "amount" of optimality). As for a quantity of feasibility, it might just be a roundabout way of locating an optimum (a located feasible solution getting characterized, say, by a distance and direction from the optimum). If it's just lowness of cost (compared to a highest feasible cost) or size of net benefit (minus some lowest feasible net benefit, I guess) or some unifying generalization of those ideas (I don't know what), it still isn't like a ratio, comparable across disparate cases. If we set the optimum to unity in order to get that comparability, then can feasibility come out like probability? There's a duality between optimization and probability where cost corresponds to probability. (One would think it more intuitive that cost would correspond to improbability formulated as 1 minus probability, but I don't know whether that leads to problems or is merely less convenient for expositing the duality. Here's a paper (PDF) of which I understood maybe three sentences and one formula.)

Anyway, so maybe it's the same for the nontrivial as for the optimal. One doesn't typically seek an amount of nontriviality, instead one typically seeks nontrivia, complexuses, etc. Now, it's not so hard to understand what constitutes an optimal case, a probable case, and an informative or "newsy" case. But, if nontrivia are to be considered as being on some sort of par with optima, probabilities, and information, then what constitutes a nontrivium, a nontrivial case?

Now, there are some other big-picture considerations here. I'm thinking philosophically, analogically, so please bear with me. There are temporal issues involved with the conceptions of optima, probabilities, and information.

1. Optima and feasibles are, for lack of a better word, potentialities (with the optima as "debentialities," lowest or most efficient potential expenditures, what would really be owed) for what could happen or be done given things as they stand; the impact of directly revealing or acting if one were to reveal or act now (the moment of decision); correlated more or less to the surface of the future light cone.

2. Probabilities pertain to what is going to happen in the course of a future in virtue of repetitions; that which does happen thereby reaches 100% probability.

3. Information is newsiness and pertains to what is coming to light or being actualized (correlated more or less to the surface of the past light cone) but not already settled; if the message's information is already known, then the information is zero.

So we have this pattern (of characterizations, not definitions):

1. Optima, most feasible, simplest, most efficient, etc. — things worth supposing, imagining, etc.
2. Probabilities — things worth expecting.
3. Information — things worth noticing.

Ergo (by completing the analogy):

4. Nontrivia — things worth remembering. This associates the nontrivial or deep with truth or fact in some sense, as well as with the complex, the complicated, etc. Some mazy and labyrinthine complications have a kind of triviality when they don't teach real lessons, still they can be worth remembering — ask any lab rat. The idea of that which offers lessons worth learning, remembering, etc., that which is "educational" in some sense, that from which lessons or more or less secure conclusions can be drawn, is another thing which distinguishes the nontrivial from the distinctive, informative, etc. We learn from the past; experience is the great teacher. But can it be that the nontrivial case is simply that datum, fact, or basis (e.g., some postulates) from which one can draw conclusions? What is the complexity in it - simply that it is non-tautologously true? This seems to be missing something in that which mathematicians mean by "nontrivial" and "deep."

There's another big-picture issue — what you might call that of subjective nontriviality versus objective nontriviality but which would better be called aspectual nontriviality versus transpectual nontriviality. This could be a newsy distinction, since I haven't found any notice of it as a possible source of confusion. Take a nontrivial equivalence between mathematical propositions — its nontriviality is a nontriviality in outward aspect for the same reason as that behind mathematicians' joke that anything proven is trivial. I don't want to call it "subjective" since that would imply incorporating a subjective judgment into the reasoning itself about a mathematical structure, just as "subjective probability" suggests trying to quantify one's subjective expectation in a specific case. As for "transpectual," I just mean that as the opposite to "aspectual": if two statements are different in form but logically (or as it is sometimes said, "formally") equivalent, then they are different aspectually but the same transpectually (i.e., when you look through them enough). The difference between a good deductive proof and a circular deductive proof that assumes what it purports to prove is transpectual, not aspectual (even though in a good deductive proof the conclusion is in the premisses in a sense), because, unlike the good deductive proof, the circular deductive proof includes unestablished information (its conclusion in some form) in its premisses, while the good deductive proof includes only established information (including its conclusion in some form) in its premisses. Update: Now I think that the difference is neither aspectual nor transpectual, and that the aspectual-transpectual dichotomy is not so general as I had supposed. One's actual knowledge or ignorance of what is already implied does not depend simply on what is already implied, and one's actual knowledge or igorance does not lend the conclusion an "aspect" in the same sense as the notably persistent novel aspect of "Therefore Socrates is mortal" as deduced from its usual premisses. Equipollence (equivalence between propositions) is a transpectual simplicity; mutual non-implication is a transpectual complexity. Independence (or as some express it, independence and consistency) among axioms or postulates is a transpectual complexity. Nontriviality as a criterion of value of equipollential inferences is ironic, and is ironic and aspectual in the same way as analogous criteria for other modes of inference. (The ironic aspectual criteria may be used merely intuitively in devising methods of reasoning; whether one employs a method of incorporating specific subjective judgments of amount of likelihood or whatever into reasoning is another question, one which I'm not really addressing.) Examination of the pattern may lend some subjective probability to my claim.

Mode of inference:	Automatically preserves:	Adds or removes info or otherwise:	Ironic aspectual criterion:		More irony. Some typical uses in science:
Surmise.	Neither truth nor falsity.	Adds & removes info.	Naturalness, simplicity, facility. What's worth supposing. (Surface of the future.)		Explaining (most simply) what has happened.
Induction.	Not truth, but still falsity.	Adds & doesn't remove info.	Likeliness. What's worth expecting. (Future.)		Analyzing (likely) what is happening.
Forward-only deduction.	Truth, but not falsity.	Removes & doesn't add info.	Novelty, noteworthiness. What's worth noticing. (Surface of the past.)		Predicting (distinctively) what is going to happen.
Equipollential deduction.	Truth & falsity.	Neither removes nor adds info.	Nontriviality, depth, complexity. What's worth remembering. (Past.)		Conditionally predicting (nontrivially) what would happen (reproducibility & more, not merely repeatability). The lesson, getting learned and applied.

(Note: mathematical conclusions are often through equipollential deduction. For a common example, the induction step in mathematical induction is equipollential: the conjunction of the ancestral case and the heredity is equipollent to the conclusion. The conclusion is a universal hypothetical (in form) while the ancestral case is an existential particular, but the equipollence is intact because the existence of the well-ordered set to whose elements the hypothetical conclusion refers is already assumed and usually actually already proven. In a simpler case than mathematical induction, in a nonempty universe "whatever there is, is blue" (hypothetical in form) validly implies the existential "there is something blue." Proofs of the ancestral case and the heredity are often through equipollential deductions, though sometimes not so, especially when greater-than or less-than statements get involved.)

Modern science has been builded after the model of Galileo, who founded it on il lume naturale. That truly inspired prophet had said that, of two hypotheses, the simpler is to be preferred; but I was formerly one of those who, in our dull self-conceit fancying ourselves more sly than he, twisted the maxim to mean the logically simpler, the one that adds the least to what has been observed, in spite of three obvious objections: first, that so there was no support for any hypothesis; secondly, that by the same token we ought to content ourselves with simply formulating the special observations actually made; and thirdly, that every advance of science that further opens the truth to our view discloses a world of unexpected complications. It was not until long experience forced me to realise that subsequent discoveries were every time showing I had been wrong, while those who understood the maxim as Galileo had done, early unlocked the secret, that the scales fell from my eyes and my mind awoke to the broad and flaming daylight that it is the simpler Hypothesis in the sense of the more facile and natural, the one that instinct suggests, that must be preferred; for the reason that unless man have a natural bent in accordance with nature's, he has no chance of understanding nature at all. Many tests of this principal and positive fact, relating as well to my own studies as to the researches of others, have confirmed me in this opinion; and when I shall come to set them forth in a book, their array will convince everybody. Oh no! I am forgetting that armour, impenetrable by accurate thought, in which the rank and file of minds are clad! They may, for example, get the notion that my proposition involves a denial of the rigidity of the laws of association: it would be quite on a par with much that is current. I do not mean that logical simplicity is a consideration of no value at all, but only that its value is badly secondary to that of simplicity in the other sense. — Charles Sanders Peirce, "A Neglected Argument for the Reality of God."

1. A surmise to a best or "optimal" explanation seeks a kind of aspectual optimality, one for which we do not expect a deductive standard optimization algorithm. Such a surmise, seeking simplicity, is actually complex, and usually both adds and removes information (or data, or howsoever you wish to think of it). That's ironic. It's as if such surmise were seeking to compensate for its own complexity by seeking simplicity. Some speak in this connection of parsimony in hypothesis-formation, but the desirable simplicity should not be confused with "logical simplicity" as Peirce notes (see sidebar) — rather it's an idea of that which is most natural, "facile" as Peirce says or feasible. This is not only for hypotheses in the usual sense. Insofar as any theory's bad match to experimental results (in physical, material, and biological sciences and in human and social studies) can be explained away by additional hypotheses, there's always a role for the simplest expanation — the simplest "hypothesis" to account for a theory's persistent bad results is that the theory is wrong.

2. An induction to a trend seeks a kind of aspectual probability, one for which one does not expect a deductive standard probability measure (well, maybe in Bayesian probability, which I don't understand well enough to discuss; but those "priors" are not arrived at deductively). A lot of statistical inference seems to involve avoiding the pitfalls of reliance on subjective probability, while still giving us something aspectually probable that satisfies our desire for something like it; a frequentist might say that good statistical inference attempts not to formulate our expectations but rather to tell us what, if anything, is worth expecting, to the extent that that's just a way of talking about the light (if any) cast upon the future by objective ratios among cases. Actually an induction (adding but not removing information) increases not probability but information. That's ironic. It's as if induction were seeking to compensate for its informativeness by seeking likeliness.

3. A syllogistic or other "forward-only" deduction seeks to bring information to light — but it doesn't really increase information, it reduces it. That's ironic. There's little that I can find about efforts to quantify the "psychological novelty" (as various folks have called it) or "new aspect" (as Peirce called it) or seeming informativeness of a forward-only deduction's conclusion. It's aspectual. (Maybe there's a Bayesian way!) Another way to look at it is that a forward-only deduction increases probability (if the premisses are assigned probabilities beween 0% and 100%); in order to be true, it doesn't absolutely need all (or sometimes any) of the premisses to also be true. Anyway, it's as if forward-only deduction were seeking to compensate for its decrease of information (or increase of probability) by seeking newsiness.

4. So, continuing the pattern, the nontriviality of a deduction through equivalences or equipollences will be aspectual and ironic. Equipollential deduction neither adds nor removes data, and it's as if it were seeking to compensate for that simplicity with a kind of complexity in the sense here called aspectual. The transpectual complexity or complexus will involve independences, mutual non-redundancies, etc. It is surmise (by which I mean inference that both adds and removes information) that is transpectually nontrivial, even though surmise ironically seeks a kind of aspectual simplicity, naturalness, etc. Now, an aspectual informativeness (psychological novelty, new aspect, whatever one wishes to call it) is sought through a syllogistic or other forward-only deduction — an extrication of information by removing some of the clutter, so to speak, of the premisses. That (aspectual) informativeness is not to be confused with its kin, the (aspectual) nontriviality that is sought through equipollential deduction; that nontriviality consists (as far as I can tell) in the outward disparities of things bridged by a proven equipollence, a bridge which one may wish to cross and recross in either direction.

But can't I do better than that? Here I'm describing as aspectual the typical sense of "nontrivial" in mathematical talk but, but what makes something "transpectually" nontrivial? Is that kind of nontrivial simply a set of independent facts or truths or givens, i.e. they couldn't have proven or disproven one another? Do they have to be "facts or givens worth remembering" or is it enough that their interrelations are facts or givens worth remembering? Are such complexuses really the core of logical ideas such that logic should have been named for them ("nontrivium theory" or "complexus theory" or whatever), just as probability theory is named for probability, and so on? They may be optimal or otherwise (or more precisely, perhaps, they may be such that they would have been optimal or otherwise); but they are the paths which have been traveled, the structures which have been built. Is that it? Is a "transpectually nontrivial" statement simply one that is consistent and materially true, just not tautologously true? But isn't logic about formal truth, not material truth?

Actually that's not what bothers me. Basic deductive logic is about deducing material truths from other material truths - more or less, facts from facts, be the basal facts postulated or established observationally or merely supposed as premisses for the sake of argument. In that sense deductive logic is about material or nontautologous truths in the same sense that probability theory is about probabilities (and optimization theory is about optima, and information theory is about information). I like that idea of transpectual nontriviality: it avoids suggesting that lengthy convolution of an argument is the essence of nontriviality or depth and somehow logically "better," more "logicful," when in real life such an argument is riskier, less likely to escape a weakest-link problem. Such convolution increases aspectual nontriviality (sometimes only in a superficial way, to boot), not transpectual nontriviality, much less security or factuality.

The conclusion of a probability is not the probability of that conclusion, and the same goes for the conclusion of a nontriviality and the nontriviality (or lack thereof) of that conclusion as a conclusion. A syllogistic deduction does not turn its concluding proposition into a formal truth (or a logical truth, if you prefer). The fact that Socrates is mortal is a material truth even if deduced from other material truths, even if deduced from a postulate or axiom that Socrates is mortal. If it is postulated that Socrates is mortal in advance of premisses, a premissual proposition "Socrates is mortal" is part of the tautology "Socrates is mortal by the postulate that Socrates is mortal", but the fact, the datum, that Socrates is mortal is not tautologously true. The nontrivium is that basis on which conclusions - further bases - can be drawn. This is a kind of basality which is not the same thing as basicness or fundamentality. A set of such postulates, or, say Euclid's five postulates, independent (and consistent), have more transpectual nontriviality or depth than any single such postulate. So, if nontriviality can't be usefully quantified, maybe it can at least be ordered. Add a postulate, enrich or deepen the system - transpectually if not aspectually. (Should one say that Gödel statements are transpectually nontrivial but aspectually trivial in the mathematical system in which they are true but unprovable?) Even an axiom of propositional logic is not completely trivial, when it is introduced as an axiom, though from it by itself there follows little if anything. Those considerations may seem a bit slippery but they're not what bother me.

What bothers me is that in a sense I'm saying that "transpectual" nontrivia are basically data, givens, facts, i.e., such that one can draw conclusions from them (well, that's the good part), but data are often quantified just like information, in bits, bytes, etc.; so, are data really something different from information or are they merely information such that one doesn't demand that they be new, previously unknown, etc.?

Maybe I shouldn't make a big deal about it, and I already fear that this is one of the most ignorance-parading posts that I've ever written. After all, as I mentioned, there's a duality between optimization and probability where cost (a kind of lowness of feasibility) corresponds to probability. (To repeat myself: one would think it more intuitive that cost would correspond to improbability formulated as 1 minus probability, but I don't know whether that leads to problems or is merely less convenient for expositing the duality.) An amount of information depends in a sense on what question was asked. Did a given horse win a race? Yes or no? That's one bit of information, as if the probability of the horse's winning had been 50% when it almost certainly was not. So maybe I shouldn't worry about data's seeming like information any more than about feasibility's seeming like probability. Now, as to a datum qua datum, we're concerned not with how newsy it is, how improbable it was before it happened, given that which was already known, etc., but with the complication or complexification that it brings (what would have been its "suboptimal" character before it happened) and what conclusions can be drawn from it. Some say that information is a difference that makes a difference. Perhaps one could say that a nontrivium is a basis for a further basis.

It also bothers me that this reduces complexity/complication to a kind of randomness. It's as if, in going conceptually from optima to probabilities to information to facts, one settles into a kind of heat death of material or non-logical truths. All I can think of at the moment is that the randomness is real in a sense, but that it's why it matters that the data be data, facts, givens in some sense, not just newsy announcements, or probables, or optima or feasibles.

Looking back at optima for a hint — maybe there's no standard way to quantify optimality, but one can often think of an optimum as a distance with a direction or directions — a shortest path for instance, or the location of a minimum of a curve, etc. Even if it's only a rough idea, still one discerns a pattern, one that I've noticed before:

optimum — difference
probability — ratio
information — logarithm
(Note that this blog's title does include the phrase "Speculation Lounge"!)

So one might expect, simply on the superficial appearance of the pattern, that for the nontrivial one might be able to think of it as the next in the series "difference, ratio, logarithm." As to the ordering "optimum, probability, information," I didn't reach that from considering the pattern "difference, ratio, logarithm." Instead I got it as part of a broad pattern (see table on right).

Some sort of proportion or analogy here.
Optima. Decision processes.	Motion, forces.
Probability. Stochastic processes.	Matter.
Information. Communication processes.	Life.
Data, nontrivia, bases (for further conclusions). Logic, learning processes.	Mind.

Well, it's hard to decide the next term after "logarithm" with confidence, when one expects only a four-term series (I expect it for various reasons including the fourfold correlations outlined earlier in this post). Now, subtraction (finding a difference) is the inverse of addition, and division (finding a quotient or ratio) is the inverse of multiplication. Yet, finding a logarithm is one of two inverses of exponentiation (raising to a power); the other being to find a root or base. A root with a direction? (Now I'm thinking of complex roots). A base? Multi-valued logic? MVL has not been a big, thriving field, so far as I can tell, but on the other hand fuzzy logic is a kind of MVL, so maybe I shouldn't speak so fast. Anyway, if you have a higher numeric base, a larger alphabet, a larger lexicon, etc., you can express things with more concision, in a sense you have increased memory capacity too, do you have an increase in some sense in that which is worth remembering (learn the ABCs, expand your vocabulary, etc.)? (I resist this in part because of the terminological coincidence between a numeric base and a basis for a conclusion. Is it just a pun of ideas?) The other alternative seems to be the hyperlogarithm, or maybe an endless series (hyperlog, hyper-hyperlog, etc.), some sort of orders of nontriviality; one starts thinking of powersets and so on. Now, all that I'm seeking here is an idea in terms of which we can think merely roughly of the nontrivial, but this sort of thing leaves me shaking my head as usual.

So I have to leave it here for the time being as it stands. It's a difficult question that has me taking shots in the dark.

(Note on the double-chiasm image near post's top: I've given Hyatt Carter total permission to use the image freely as he pleases, for example here.) - posted by The Tetrast @ 3/31/2010 11:22:00 AM 0 comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Unsettlings
Recentest change: March 26, 2010.

I can see four general inquiry-stimulating “unsettlings” at least:

1. Bafflement, perplexity, at the complex or complicated. E.g.: What has happened?

2. Surprise at the anomalous, the seemingly unlikely. E.g: What is happening?

3. Suspense, impatience, over the vague. E.g.: What’s going to happen?

4. Hesitancy, inagency, about the unfamiliar, the uncolligated, that whose lessons have not been learnt. E.g.: What would happen (if…)?

And searches for at least four kinds of answer: In what light would the unsettling phenomenon seem (1) simpler? (2) more usual or normal? (3) clearer, more clarificatory, more significant or informative? and (4) deeper, less trivial? – each of which can be helpful in any of the above questions.

Note the conceptual opposition or tension between (1) simpler and (4) deeper, less trivial. And also that between (2) more usual or normal and (3) more significant or informative. A kind of double chiasm.

1. Simplicity, optimality, etc. 2. Likeliness, probability, etc.

3. Informativeness, significance, etc. 4. Nontriviality, depth, etc.

C. S. Peirce says that all inquiry begins with irritation by doubt as a result of surprising observations and that it struggles toward belief - a fixation of belief, which is to say, a settlement of belief (a settlement at least for the time being). (See his 1877 "The Fixation of Belief"). So it seems to me appropriate to think of inquiry as beginning with an unsettling. But Peirce is more specific. Yet that word "irritation" irritates me there, it sounds unnecessarily negative. One could say that at least some inquiry begins with temptation by doubt.

Is curiosity merely a kind of irritation? Some people regard all desires as irritations. Desire is the positive version of averseness, while pleasure is the positive version of pain. Yet desire - as we say, the pangs of desire - correlates also with pain, desire as a pain of lacking something that one would like. There's something negative or privative about the would-be in contrast to the is, whether one responds with desire or averseness. Averseness, as opposite of desire, could suggest a pleasure of lacking something that one would dislike. The idea of averseness doesn't particularly suggest that to me, except when I consider the idea of contentment and satiety, but those aren't the same thing as positive pleasure. Of course, the idea of desire doesn't always bring the idea of pain strongly to mind, but still, something seems not quite symmetrical here. Looking it up, I find pang defined as an ache or twinge, and its antonym given as tingle. A tingle of aversion or disgust? A pleasurable tingle of aversion? A delighted scorn? There are threads of sense in all this but somehow they don't come together as truistically as I'd like. Maybe one of these days I'll figure it out. Anyway, since curiosity is a desire to know, one can see it as involving desire's pain and irritation, yet desire is not merely pain and irritation, the feeling of actual ill. Instead it's to feel drawn toward the potential positive presence of something that would be pleasing. Desire and pain logically involve each other but are not flatly equivalent.

Now, Peirce frames inquiry generally in terms which do not portray the inquirer as searching for truth per se, just for truth's sake, as if in some sort of idleness. Peirce holds that genuine inquiry is struggle and that inquiry based on merely verbal doubts is normally fruitless. He wants to show inquiry as a struggle driven by strong motivations yet capable of eventually attaining considerable objectivity. Quoting myself from a few articles at Wikipedia: "Starting from the idea that people seek not truth per se but instead to subdue doubt's irritation, Peirce shows how this can lead some to submit to truth." One does often notice that people are concerned to maintain beliefs in which they are invested by practices built upon those beliefs - so, doubts irritate them. But suspicions also excite people, so that many a person seeks to dampen such distracting suspicions, excitements, sneaking hopes in himself or herself, or in others, i.e., tries to keep eyes on the ball. So, I think that "irritation" is too negative a word there. Unfortunately I can't think of a more general word that covers both irritation and excitement. It's like trying to think of a word that means specifically both desire and averseness, that is to say, a word that has the meaning of the phrase affectivity oriented toward the would-be.

I disagree with Peirce's claim that surprise is the universal occasion of inquiry. Some sort of unsettling, yes, but not always surprise. Inquiry does not always begin with the improbable, the unlikely, the anomalous, as if a person had a plenum of beliefs or expectations for all occasions. Instead one is sometimes aware of things about which one has no particular expectations, things which are standing mysteries. How did some island get where it is? Etc. One is puzzled or baffled, the puzzling thing complicates one's understanding of things. One seeks a simplifying explanation. Peirce tries to account for such things as "passive" surprises, things that happen in the absence of expectations specifically of their happening. (For Peirce, "active" surprises are things that happen in the presence of expectations specifically of their not happening.) I don't think that it's a simplification to regard bafflement as passive surprise. That's like regarding fancy or supposition as passive expectation. The anomalous goes against particular expectations. Not only does the baffling complexity or complication elude particular expectations, it more actively goes against fancies or suppositions about what most simply would be.

From the start the claim of surprise as occasion for all inquiry involves idea of expectations about the future, the probable, the likely. So, from the start, in order to check that claim, one should consider whether other time ideas and modality ideas can also be found as occasions of inquiry. One such is bafflement, defiance of simplifying supposition about what most simply would be. Here the time is the would-be and the modality is simpleness, facility (to the point where it's hard not to do it), a kind of optimality. Note that surprise occurs when that which comes to light defies expectations, and bafflement, perplexity occurs when that which is (more or less) familiar defies suppositions and simplifying fancies.

So there are two other times right there to consider: the present in its coming to light, and the past. The two correlated modalities are informativeness and nontriviality, depth. Sometimes currently gained information is insufficiently clarifying as to what is going to happen, what is "coming down the pike." One becomes impatient. And sometimes one's established facts, one's remembered past, aren't deep enough to offer lessons, conclusions to be drawn, about what in a current case would happen if one were to do certain things - so that one hesitates, for instance to walk across a log bridge, or to build a bridge out of some curious material.

So, once more from the top, unsettlements that stimulate inquiry:

1. Bafflement, perplexity, at the seemingly complex or complicated, defying one's best simplifying suppositions. E.g.: What has happened?

2. Surprise at the anomalous, the seemingly unlikely, defying one's expectations. E.g: What is happening?

3. Suspense, impatience, over the vague, the seemingly uninformative, defying one's discernment. E.g.: What’s going to happen?

4. Hesitancy, inagency, about the unfamiliar, the uncolligated, the seemingly trivially-connected, that whose lessons have not been learnt, defying one's remindedness. E.g.: What would happen (if…)?

Note: I understand the would-be, in those contexts, as corresponding roughly to the surface of the future light cone, in a sense the present, but the present to which one appears and into which one acts directly. That present, one's presence to others, is the surface of one's future. This is as opposed to the present as it comes to light to one - that coming-to-light present is the surface of one's past (corresponding roughly to the surface of the past light cone). I say "roughly" because, for example regarding the analogy to the future light cone's surface, one's outgoing most-feasible, optimal or extremal, or best "shots" don't always travel at lightspeed, yet the difference between such and the later future, the future as probabilities, parallels the difference between the future light cone's surface and the future light cone's inside. Thus a difference between desire and trying for what is almost now, on the one hand, and hope and pursuit toward a later goal on the other hand. In that sense, where one is distinguishing between that which has happened, that which is happening, that which is going to happen, and that which would happen, I'd like a conditional participle, so that it's clear that I'm talking about a would-be based in the concrete situation. (Informal Esperanto would allow it - tio, kio estas pasunta.) - posted by The Tetrast @ 3/25/2010 01:10:00 PM 0 comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Symbols
I discussed kinds of sign (index, semblance, symbol, proxy) in terms of some broadened notion of Jakobson's syntagmatic-paradigmatic distinction in my recent post "Rosen, Saussure, Peirce". Of course I went too far in that broadening - I was reaching for an analogy that might be a bridge or shortcut to a better understanding of what a symbol would be in my four-fold division of signs. I was whizzing along there, using words like "homology" rather too loosely. Anyway, I wish to gain an idea of symbol that seems consistent with my ideas of index, semblance, and proxy, and also seems as simple as them. As to consistency, for instance, since I allow of concrete individual natural indices, semblances, and proxies, I need to conceive of a concrete individual natural symbol. I thought I might need to broaden the idea of symbol somehow. Obviously I'm going against Peirce in various ways here, but that's for another discussion.

Underlying my ideas of index, semblance, symbol, and proxy, are four categories:
1. 'Substance' or object. Primary substance is this man, this horse, etc. But it could be abstract, a mathematical structure for example.
2. 'Accident' or attribute or quality.
3. Modality, logical quality ('indeed', 'not'), probability, novelty (information), feasibility, optimality, etc. By those I mean mode in its original definition though not usage (see Peirce, CP 2.382 and DPP p. 89) as referring to any qualification of a proposition or its copula, and I expand the idea to include straightforward logical quality - affirmative and negative. Update (3/17/2010). I just found that Peirce leaned that way about modality and logical quality. See "Prolegomena to an Apology for Pragmaticism" (1906) The Monist, v. XVI, n. 4, pp. 492-546, footnote on page 525 (last footnote of CP 4.552). End of update. Obviously I need a distinct technical term for it but I'll make do with "modality" for the time being, though, again, I do not mean it only in the usual sense (necessity, possibility, impossibility, unnecessariness). It is something like a conduit of comprehension (intension) which may qualify the comprehension in terms of fulfillment in some portion or totality of cases, the distribution of the associated denotation, etc.
4. Mathematical relationship ('double of', 'inverted order of', 'indefinite integral of', etc.), particularly as conceived of as object(s)-to-object(s) relationships. In a way, it's like a router or re-router of denotation (or maybe I should say, denotational relationships).

The index represents an object by being connected to it (in the same larger object).
The semblance represents an object by sharing characteristics or qualities with it.
The symbol represents its object by having the same modal properties/relationships.
The proxy represents its object by having the same mathematical relationships in some sense, anyway by making the same "decisions," following the same rules under ongoing observation and experimentation.

So, consider a property which has a 50-50 chance of belonging to any given object in a total population. One side (it could be either side) of a fair coin symbolizes that property in its frequency. Surprising winners symbolize each other, in a sense, irrespectively of resemblance or connection or proxyhood to each other. There is something in common about their situations - not their locations or times, but about the alternatives in which they are involved. Again, not proxyhood: you can't use a fair coin to determine the outcome of an evenly matched two-horse race, but you can consider the fair coin in order to deduce horses' odds on the assumption that the race is evenly matched. And so on. Sometimes the odds overwhelmingly favor a given outcome. Two masses of particles can be proxies for each other if they make the same "decisions" thanks to the law of large numbers when their respective particles are not proxies for each other. These relationships of attribution, distribution, etc., are matters of interpretation, but are not always subjective or matters of mere convention. Implication itself depends on structures or processes of alternatives among cases; meaning is a phenomenon, if you will, of modality. The modalities lead to an effect on interpretation. Sometimes, habitual implications are translated into conventional symbols which have the same value as (are equivalent to) their objects despite disconnection and dissimilarity.

(At one time, Peirce distinguished comprehension or intension from implication; at later times, he seemed to hold that they're more or less the same thing. I need to look further into that. The problem is that comprehension is of characteristics, but Peirce does not seem to take resemblance as a kind of comprehension. And if one either denotes objects ("Seconds") or comprehends characters ("Firsts"), then, in Peirce's system, what mode of sign relation is there to "Thirds" - representation, sign relation, attribution, etc., themselves? It appears that, early on, Peirce would have said implication, but not later on.)

As regards Jakobson's paradigm, it is an alternative among words that could be used in a given place and time. It is not the expression of such an alternative, e.g., "The horse cantered or galloped." Such disjunctive compounds, as well as conjunctive compounds, are alternates forming an alternative or paradigm (if there's some flexibility about the length of the phrase to be chosen). Moreover, logical conjunctions and alternatives all express basically "paradigmatic" rather than syntagmatic relationships, insofar as paradigmatic relations reflect relations of logical quality and modality. (Note: the polyadized variables expression "xyz" is not a logical conjunction like the conjunct propositions expression "pqr", instead it is something else.) When we speak in a second-order way about the first order, then the "and" versus "or" distinction is like that of syntagmatic versus paradigmatic - you use one word (or phrase) AND another AND another, etc., in the syntagmatic relation, and one word (or phrase) OR another OR another in the paradigmatic relation, but the resultant sentence does not thereby express relations of conjunction and alternation. Expressions of logical relations - "She wore a blue or green dress" - "She wore a blue and green dress" - etc., are expressions, explicitations, of options about things, options that also also underlie and help determine paradigmatic relations among words. That said, I'm unsure how best to analogize paradigm (to process? to function?) as I've analogized syntagma to structure. I guess it's not such a shortcut after all.

Do I feel that my idea of symbol is comfortably simple and consistent with my ideas of the other sign kinds yet? Not quite yet. - posted by The Tetrast @ 3/14/2010 11:52:00 AM 0 comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Rosen, Saussure, Peirce
(Recentest significant change: December 30, 2010).

In Peirce's semiotic, an irreducible triadic relationship defines object (subject matter), sign, and interpretant. I've argued the need for a fourth element, which I've called a recognizant. Trying to get away from such a psychological-sounding term and to follow the word pattern of "interpretant", I've also called the recognizant the verificant but that's misleading, because I mean not the verificatory evidence but instead that of which the content is the verified or established or corroborated, etc., the lesson learned. As the interpretant is, in a sense, an aspect or moment of an interpreter, so the recognizant is an aspect or moment of the recognizer (who in a sense is a verifier or corroborator, etc. - recognizing or acknowledging a legitimation). In the analogy of semiotic to Shannon's information-theoretic scenario: As interpretant stands to decoding, so recognizant stands to recipient.

Now, among kinds of sign, Peirce's most famous trichotomy is that of icon, index, symbol. The three are defined by how they stand for their objects: icon by its own characters, as resembling its object; the index by factual connection to its object; and the symbol by interpretive norm or habit of reference to its object. The point to notice is that the index represents in virtue its object-connection which it has had; the icon in virtue of its own representative characters as now presented; and the symbol in virtue of how it will be interpreted, i.e., in virtue of its interpretant. You see the pattern:

index : object :: icon : sign :: symbol : interpretant.

So I thought that to complete the pattern for my version of semiotic I would need a fourth kind of sign, one defined by some sort of relationship to the recognizant. The pattern seemed to generate the idea of a sign which represents in virtue of the case that it would be recognized to stand for its object by one observing the object if the object were available. Such would be a sign which stands for its object for observational and experimentational purposes. This I called a proxy. I distinguished proxy from mere surrogate by this consideration: a proxy can make decisions on somebody's or something's behalf, by following some sort of rules for the decisions that that person or thing would make. Of course, in a corporate election, if you have somebody's proxy, you can vote howsoever you want. But I was thinking of things like power-of-attorney, a lawyer representing somebody by acting on that person's behalf according to the rules of that person's best interest, making the decisions that that person would make if they were conscious and present, grasped the law, etc. Eventually it occurred to me that that which Peirce calls diagrams are also proxies. Now, Peirce classes the diagram as a kind of icon. The diagram is subject to the same transformabilities as its object. Peirce holds that the study of mathematics proceeds through experimentation with diagrams, observation of them, etc. Such diagrams may consist in geometric forms or in arrays of algebraic expressions, etc. They need not outwardly resemble their objects at all. So, I speak of semblances, not icons, and class diagrams as proxies, not as semblances. It occurred to me that some physical objects can be proxies for others - electrons can be proxies in experiments for any electrons, they're all the same and follow the same rules. A statistical correlation between two things, on the other hand, may be a mere resemblance independent of underlying sameness of structure, rules, etc. It's the kind of relationship which conduces to inductive generalizations, subject to testing. Anyway, as signs, proxies are no more infallible than semblances and still need to be checked.

I've noticed that the word "proxy" is currently used to refer to surrogate indices, such as tree rings as so-called "proxies" for thermometers. I'm doubtful that that is a good use of the word "proxy." They are alternate indices for the same phenomena. Any, the scientific currency of the word "proxy" in such a sense is certainly inconvenient for me, but there's little that I can do about it.

Rosen

Somebody who has read my Websites contacted me in late 2008 and, in our subsequent correspondence, mentioned Robert Rosen's modeling relation and gave me this link: http://www.panmere.com/?page_id=18. I read that and another page at the linked Website http://www.panmere.com/?p=56. The distinction which Rosen made between simulacrum and model is much like mine between semblance and proxy, except that I was unsure that Rosen models could be concrete and not only abstract. Later I learned from a comment by Rosen's daughter Judith that for Rosen a model could be an individual concrete object (http://www.panmere.com/rosen/mhout/msg02147.html), so, as far as I can tell, my proxy is Rosen's model; and my semblance is Rosen's simulacrum. Well, I'm glad that Rosen beat me to it! It suggests that the idea is not just my whimsical notion. He worked it out in terms of considerations of scientific thinking, especially in biology. I arrived at it through consideration of Peircean semiotic, an area in philosophical logic. I've mentioned this fit of my ideas to Rosen's a couple of times on peirce-l, in a May 17, 2009 post and in a July 14, 2009 post. (My earliest peirce-l discussion of proxies that I can find is this December 2, 2004 post.) So which is the better word, proxy or model? Well, a lawyer can be a proxy for, or of, his/her client. But you wouldn't say that the lawyer is or acts as a model for the client, because that suggests that the lawyer's function is to set an example for the client to emulate. On the other hand, as I've noted, the word "proxy" has taken on a specialized and weakened meaning in science. Well, I'll go on speaking of proxies rather than of models, so that it's clear that I'm speaking about the idea of proxy as I've been working on it, not Rosen's idea of model as he worked on it, howsoever they may coincide.

Anyway, for Rosen, a model has that which he calls a synonymy of structure of entailment with the thing or process that is modeled. I'm not sure what is the point of the word "synonymy" in that context. It suggests that the structure itself is some sort of word or symbol. Instead it's enough that the structures of entailment be the same, or isomorphic, or homologous, or whatever, between model and modeled thing, without calling those structures "synonymous." To have the same meaning is to reflect the same norms or parameters, to make the same difference; not necessarily to teach the same lessons through experimentational structural transformations. The reader may think that I'm splitting hairs but I'm dealing with four kinds of sign (index, semblance, symbol, proxy) and they involve meaning in various ways. I need to maintain some sort of careful distinctions, at least sometimes.

A symbol is a kind of sign that has the same value or import as its object even when they have neither a connection nor a resemblance nor a structural sameness (the kind of sameness that allows for parallel transformations). Now, since I can think of concrete objects which are natural indices, natural semblances, and natural proxies, why not symbols? So I have to broaden the idea of the symbol, to that of a sort of functional surrogate or functional equivalent for something, such that it serves as a sign about that thing, irrespectively of connection, resemblance, or homology. Wish I could think of an already existent name for this broadened idea of symbol.

Saussure

In trying to regularize this tetrachotomy of index, semblance, broadened symbol, and proxy, thinking (as always) of Aristotle's four causes, and so on, I recently started considering the syntagmatic-versus-associative dichotomy of Saussure and, more specifically, Jakobson's refined version, the syntagmatic versus the paradigmatic. The syntagmatic has to do with the way things are compounded or connected in an orderly way; it's a broadening of the idea of syntax. The paradigmatic has to do with sets of options which exclude each other in some sense, anyway involving at least an alternative among words if not among things, as in "She wears a..." scarf or jacket or blouse, etc. They don't have to exclude each other literally, though they can. Paradigmatic relations involve differentiation.

1. Index - thing which represents its object by being in the same syntagm, so to speak, with its object - it is connected to its object. (This involves broadening the idea of syntagm.) 2. Semblance - thing which represents its object by having the same differentiae, the same qualities, differentiating respective parts or stages. (Here a sequence is seen not as a temporal syntagm but as a paradigm going through its alternatives, its various phases, in time). A very simple semblance is when two things simply have the same single quality across respective parts or stages.

3. Broadened symbol - thing which repesents its object by being an alternative to it, but still having the same value, still making (as opposed to having) the same difference. 4. Proxy - thing which represents its object by having the same syntagm, in some sense same structure, following the same rules, and teaching the same lessons.

- posted by The Tetrast @ 3/03/2010 02:19:00 PM 0 comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Lyric, epic, dramatic, orphic, hermetic, peithic
Recentest significant change or addition: March 15, 2009.

There seem four poles in art: the subject matter, the artist, the art work, and the audience. Four genres (aside from intermediate genres) of art may be distinguishable accordingly.

James Joyce focuses on two of those poles - (A) the artist and (B) others (the subject matter) - in defining forms or genres of literary art, and adopts the three-way lyric-epic-dramatic distinction. The artist, expressing personal emotion, is at the heart of the lyrical form, while the dramatized world of others, with the artist refined out of existence as it were, is at the heart of the dramatic form. The epic form is intermediate between the two.

Gerald L. Bruns in Modern Poetry and the Idea of Language (1974, 2001, praised by Gilbert Sorrentino) divides the poem into two genres - the orphic, focused on emotion and the artist as singer calling the world into existence, uniting with it; and the hermetic, focused on ability or technique, on form in the formalist sense, and on the art work itself to the exclusion of the outside world.

Following the pattern of object (subject matter), sign, interpretation, and establishment or recognition, I've usually distinguished and ordered art's poles as (1) subject matter, (2) artist, (3) artwork, (4) audience. In terms of the dependence of signs and observations on the real, such conceptions of those series are fallibilist but not relativist. Following the similar pattern of agent, bearer, act, borne, I've usually distinguished and ordered the human powers (or human causal principles) as (1) will & conation, (2) dealing, ability, (3) affectivity, and (4) cognition. In the case of the forms or genres of art, the two series come to seem aligned in opposite orders.

Putting these ideas together (but omitting the intermediate form (epic) for simplicity's sake since we have more than two poles now):

(3) Artwork.	(2) Ability, dealing.	Hermetic, 'formalist', etc.
(2) Artist.	(3) Affectivity.	Lyric.
(1) Subject matter.	(4) Cognition.	Dramatic.

It turns out to be easy to extrapolate to a fourth genre, a genre that actually exists and is focused on the two remaining elements: will (& conation) and the audience. Artist's will, the audience? The artist trying exert his will on the audience? Always, in a sense. But when does it stand out? Isn't that "impure" art? Anyway it's when the artist preaches or aims to influence, in one sense or another. There's been a lot of that. The idea seems to work, so the orderings and their systematically "inverse" alignment seem to work. They also align nicely with inter-behaviors as I usually order them. I gleaned the inter-behaviors, also on the pattern of agent, bearer, act, borne, from a systematic consideration of kinds of human concerns.

Focus on which pole of art.	Focus on which human power (of the artist).	Artistic genre.	Correlated inter-behavior.
(4) Audience.	(1) Will & conation.	"Peithic,"* persuasional, hortatory, sermonic, critical, argumentative, seductive, proselytic, etc.	(1) Vying (conflict, competition, rivalry, contention, etc.), arenas, etc.
(3) Artwork.	(2) Ability, Dealing.	Hermetic, 'formalist', etc.	(2) Practices, cooperation, tolerance, minding one's (own) business, occupational spheres & concourses (e.g., workaholic Hephaistos focused on work to exclusion of external concerns).
(2) Artist.	(3) Affectivity.	Lyric.	(3) (Valuational) community, distinctive unitings.
(1) Subject matter.	(4) Cognition.	Dramatic.	(4) Disciplines, checks & balances, supports, etc.

* Note: I made the word "peithic" up just now from Ancient Greek peitho meaning "persuasion," "persuasiveness," or the goddess "Persuasion." The idea of which I'm thinking seems to include, but be broader than, the idea of rhetoric.

Why post this in the Speculation Lounge? I just thought of this division of genres the day before yesterday I think it was. It seems right but who knows and maybe I'll change my mind.

Here's a way to look at it in a two-by-two square (skip):

1. Peithic, hortatory, etc. Will & conation. Vying, conflict, competition, rivalry, contention, arenas. 4. Audience. 2. Hermetic. Ability, dealing, handling. Practices, cooperation, toleration, minding one's business. 3. Art work.

3. Lyric. Affectivity. Community, distinctive unitings. 2. Artist. 4. Dramatic. Cognition. Disciplines, supports, checks & balances. 1. Subject matter.

It is to be noted that the foci on various human powers are notwithstanding that art generally is a kind of cognition regarding the affective; more particularly it could be characterized as understanding in what effects one feels things; works of art are embodiments of such understanding. It is not systematic, scientific knowledge, which is knowing in or on what light or basis one knows things. There cognition is featured at both levels of the definition. With art, cognition is featured at one level and affectivity at the other. Such definitions use the same style as some use in order to define the economic realm as that of decision-making about means. For a four-by-four of 16 areas so definable, see "A periodic table of aspects of humanity which lend themselves to social compartmentalization."

Problem. I take as a problem an irregularity in such structures, and try to see such an irregularity as reflecting an underlying regularity, an ordering, whatever. The four poles of art seem irregular in regard to which ones can or must be persons. The artist is a person or people. The audience (which can include and even be limited to the artist) is a person or people. The subject matter could be persons or non-persons, even abstract objects. How can the artwork be a person at all? Should one distinguish (fictional or non-fictional) people as subject matter from (fictional or non fictional) people as they end up being shown in the artwork? When art involves performers, does that count as the artwork's being people? - and, when one reads a book, is one, like a musician reading a musical score, "performing" the book in one's mind? - doing some kind of double duty as artwork (performer) and audience? One has to get science-fictional in order to think of an artist making actual living persons for artistic purposes (I don't even mean architecture of persons and souls; I mean making actual people for the same reasons that one would make a poem, a painting, a drama, a song, etc.). If the artist "merely" modifies rather than makes actual people, - again, for artistic rather than merely cosmetic ends - it seems somewhat less science-fictional, though still morally awful. Well, I'll have to think about all those things.

End of main discussion.

From Chapter 5 of A Portrait of the Artist as a Young Man by James Joyce, his young persona Stephen Dedalus speaking:

The image, it is clear, must be set between the mind or senses of the artist himself and the mind or senses of others. If you bear this in memory you will see that art necessarily divides itself into three forms progressing from one to the next. These forms are: the lyrical form, the form wherein the artist presents his image in immediate relation to himself; the epical form, the form wherein he presents his image in mediate relation to himself and to others; the dramatic form, the form wherein he presents his image in immediate relation to others.

A bit further on:

Even in literature, the highest and most spiritual art, the forms are often confused. The lyrical form is in fact the simplest verbal vesture of an instant of emotion, a rhythmical cry such as ages ago cheered on the man who pulled at the oar or dragged stones up a slope. He who utters it is more conscious of the instant of emotion than of himself as feeling emotion. The simplest epical form is seen emerging out of lyrical literature when the artist prolongs and broods upon himself as the centre of an epical event and this form progresses till the centre of emotional gravity is equidistant from the artist himself and from others. The narrative is no longer purely personal. The personality of the artist passes into the narration itself, flowing round and round the persons and the action like a vital sea. This progress you will see easily in that old English ballad TURPIN HERO which begins in the first person and ends in the third person. The dramatic form is reached when the vitality which has flowed and eddied round each person fills every person with such vital force that he or she assumes a proper and intangible esthetic life. The personality of the artist, at first a cry or a cadence or a mood and then a fluid and lambent narrative, finally refines itself out of existence, impersonalizes itself, so to speak. The esthetic image in the dramatic form is life purified in and reprojected from the human imagination. The mystery of esthetic, like that of material creation, is accomplished. The artist, like the God of creation, remains within or behind or beyond or above his handiwork, invisible, refined out of existence, indifferent, paring his fingernails.

Tetrastic patterns

	1. AGENT.	2. BEARER.	3. ACT.	4. BORNENESS.
Requisites for beauty (augmented Aquinas).	Due magnitude & direction.	Harmony, due proportion, due rhythm.	Radiance, vibrance.	(Structural) wholeness, integrity.
Aesthetic stages (augmented Joyce).	Arrest.	Fascination.	Enchantment.	Attachment, devotion.
Art's four poles.	Subject matter (mastering it from an artistic standpoint).	Artist (materials, technique, sensibility).	Art work (the point, the artistic effect; publishing it, performing it).	Audience (target audience, reception, etc. The audience isn't always right but then what is?)
Artistic genres (Some Joyce, some Gerald L. Bruns plus what):	Foci: volition & audience. "Peithic," critical, contentional, persuasional, seductive, proselytic, etc. Cf. vyings (below).	Foci: ability & artwork. Hermetic, formalist, etc. Cf. cooperation, tolerance, minding one's (own) business (below). Workaholic Hephaistos's focus on work to exclusion of world.	Foci: affectivity & artist. Lyric. Cf. community, distinctive unitings (below).	Foci: cognition & subject matter. Dramatic. Cf. checks & balances (below).
Broader correlations
Kinetic / mechanical correlatives.	Net momentum, impulse, force.	Rest mass, rest energy, internal work & power.	(Non-rest) energy, work, power.	Internal, balanced momenta (potential & kinetic), impulses, forces.
Tetradic semiosic stages (augmented Peirce).	Objectification.	Representation.	Interpretation.	Establishment.
Creative process (Helmholtz & Poincaré).	Saturation (getting handles on a problem).	Incubation.	Illumination (e.g., as in "eureka!").	Verification.
Disciplines	Ruling or governing arts.	Know-how, productive arts/sciences.	Affective arts.	Mathematics & sciences.
Bahavioral phases / foci.	Adoption, appropriation, assumption, control.	Processing, adaptation, production.	Consumption, expression, conversion.	Rumination, assimilation, learnings.
Inter-behaviors.	Vying — conflict, competition, rivalry, contention.	Cooperation, tolerance, minding one's (own) business.	Community, distinctive unitings.	Checks & balances.
Human causal principles.	Will, conation. Character. Virtues, vices, etc.	Ability, dealing. Competence. Métiers, etc.	Affectivity. Sensibility. Values, etc.	Cognition. Intelligence. Knowledgeability, etc.
Causes as rational characters.	The strong has the rational character of a beginning or leading.	The apt has the rational character of a middle or means.	The good has the rational character of an end.	The true, real, genuine has the rational character of a check, entelechy.
Static or quasi-static causes.	Essential tensions, pressures (of a thing especially as in its environment but also internally).	Composition, material (of a thing but also of its external relations, environment, media, etc.).	Differentiation, diversification (of a thing especially as a system among others in its environment, but also as among its parts, organs).	Unitary structure (of a thing especially but also of its external relations, environment, etc.).
Existence (consistently extreme version).	Efficient cause.	Sustainer.	Consumer, exhauster.	Assimilator / suppressor.
Causes as stages.	Impetus.	Development, process.	Culmination.	Settlement, establishment.
Causes as turns of becoming.	Beginning.	Middle, means.	End (-ing), teleiosis.	Check, entelechy, standing finished.

- posted by The Tetrast @ 3/12/2009 11:21:00 AM 2 comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Logical quantity & the problem of universals
Recentest (mildly) significant change: January 2, 2009 (third such change since August 6, 2007). This post is much less speculative in style than the others on this blog. But my other blog "feels" filled up, I can't quite say why. Still, maybe I'll eventually move this post to there.

We tend to consider the logical quantity of the term and not only that of the proposition, especially when a logical quantity such as the singular gets involved. Yet tradition has kept the spotlight on propositions (or sentences, etc.) because of the interest in valid argumentation involving them. That seems to be why logical quantity from the term's viewpoint has lain largely unexplored by philosophy. Philosophy hasn't stopped and smelt the roses long enough to see what vistas might spread thence. Given a term "H" predicated (truly or purportively truly) of something (call it "x"), the question of its logical quantity then depends on quantification over the rest of the universe of discourse: Is there something which isn't that thing x and of which the term "H" is also true? -- and -- Is there something which isn't that thing x and of which the term "H" is instead false? The twin questions stand mutually independent and resolve into four answers, conjoinable in four ways (notwithstanding issues of term purport which multiply relevant options). For the polyadic case, incorporate criteria requiring one-to-one correspondences as needed and slackening as needed to compensate for sequence variety. None of the four conjunctions enframes a blind or almost blind window as long as we class the singular and the singulars-in-a-polyad together in logical quantity, just as we class both the monadic general and the polyadic general as general. One such conjunction, the monadic-or-polyadic singular-cum-universal, is a logical quantity corresponding to a gamut, a total population and its parameters, a universe of discourse, etc. The eventual result of a systematic approach to logical quantity from the term's viewpoint is a surrounding scene of various categories of the 'essences' -- attributes/modifications, modes of attributability, and forms of mathematical correspondence -- whereto nonsingular terms are often allied, 'essences' categorially as different each from the others as they are from the scene-completing object -- this man, this horse, etc. -- of a typical concrete singular term.

The "problem of universals" is a philosophical perennial. Now, before one does a metatheory about, say, the theory of geology, one needs first to do theory of geology. And, before that, one needs to do physical geography. The "geography" of logical quantity (singular, general, universal, etc.) seems to have lain largely unexplored by philosophers. Aristotle and C.S. Peirce are exceptions.

On July 17, 2007, I searched on Google for the two phrases problem-of-universals logical-quantity. Only two results came up, both mine -- the first version of this post and a similar thing which I posted to peirce-l some weeks ago. I searched for problem-of-universals logical-quantification and found few results, half of them mine. (My own earlier post on the topic at The Tetrast doesn't come up, and of course the problem of universals isn't always called that by name, but it still seems fair to take the paucity of Google results as significant). The lack of an adequate systematic terminology is another sign of how little attention philosophers have given to the topic of logical quantity, despite their long interest in the problem of universals.

The problem of universals gets its standard name from the noun "universal" in the sense in which one finds it used in translations of Aristotle -- that which is true of more than one object, a sense for which the word "general" is now sometimes employed as a noun in philosophical discussion and is in any case usually so employed here.

Singular and general in standard 1st-order logic
Now, in the standard terminology of first-order logic, a "general term" is a term which does not purport as to logical quantity (or has only a "default" purport to the existential particular affirmative when the term is true of something). If the monadic general term were to purport, when true of an object at all, to denote more than one object, then a proposition claiming in effect that the term were uniquely true of some given object would be formally false. Instead such a proposition is merely contingent. In other words, a so-called general term in standard first-order logic is vague in logical quantity and is 'general' from a kind of second-order viewpoint -- one might call it "general" across various possible logical quantities. On the other hand, a "singular term" in standard first-order logic is a term (and indeed a subject term rather than a predicate term) which does purport as to logical quantity, and purports to singularity, so that a proposition which claims in effect that a monadic singular term corresponds to two different objects is formally false. I am speaking of constant a.k.a. definite terms such as "blue" and "Jack." Constancy versus variability is a similar yet distinct issue or dimension which complicates an elementary discussion.

Generality more generally
In speaking philosophically of generality, not adhering to the linguistic habits of standard first-order logic, we may mean neither vagueness in logical quantity nor a purportive (or still some other de jure) generality; instead we may mean a de facto generality, for instance that of a monadic term like "blue" which happens to be true of more than one object. In speaking of singularity we may likewise mean a de facto singularity. I'm not sure what there is for all this, except to get used to the distinction between purportive and other sorts of de jure, and de facto. It seems difficult to limit one's discussion to examples of just one kind or just the other. The distinction does not seem so hard and fast to intuition. "Blue" -- as term or as idea or as quality -- is the kind of thing which one would not expect to be true of just one single object.

In order to distinguish the sense of "general" as that which corresponds to more than one object (in the monadic case), I will speak of the coaliant general. (I could just call it the "coaliant" per se but I wish it remembered that I'm speaking of a kind of general. I coin it from co- + aliud + -ant.) The coaliant general corresponds, purportively, etc., or de facto, to something but not to that thing alone but also to something else. In the polyadic case, consider it to correspond to polyads whose intersections lack objects from each polyad. (As for re-orderings or re-sequencings of the same polyad, they are another issue which complicates an elementary discussion.)

A bustling floor under generality
Since one thinks in terms of greater and lesser generality, there arises an imagery of limits. Such imagery is itself limited in usefulness but inevitable in its way.

Now, the coaliant general (monadic or polyadic) encounters something like a limit, closure, or bound, at the "low" end, in the singular or singulars in a polyad. A polyadic version of a singular is not strictly to be called "singular" in that it is not monadic, and "plural" already has specialized meanings in logic. One might say only loosely that it is a polyadic singular. The word "singular" isn't quite right for a logical quantity definable by its opposition to the general -- the mind places "singular" opposite not only to "general" but also to "plural" and thus also to "polyadic." In order to unglue term adicity a.k.a. term valence from logical quantity and instead to treat all logical quantities on the same plane, I'll call any monadic-or-polyadic singular transingular. The coaliant general encounters an excluded or external limit, at the "low" end, in the transingular. A transingular term can be a subject but also can be a predicate or other things.

A bustling ceiling into generality
The coaliant general, if it has an upper limit in some sort of "most general," will include it in a way that it does not include the transingular, since the coaliant general is definable as the determinately non-transingular. What would non-arbitrary utmost generals be? They would be something like the Scholastic transcendentals (unity, truth, goodness) which are true of each and every thing automatically, in sheer virtue of the thing's existing at all -- the given thing is one thing, a true thing, and a good thing, at least in respect of its existence if not of its character. That seems to make of the utmost general a rather narrow window, while other logical quantities at the same level of analysis are rich and, in their way, panoramic. Is the world's symmetry really that deeply broken? A systematic understanding of logical quantity does not foster a view of the world as arranged mainly into genus-species type relations, strict inclusions, etc., with one or a few utmost generals monotonous at the top. Confronted with the Scholastic transcendentals one, true, good, one may ask, what about two things? Aren't any two things two in sheer virtue of their being things xy such that ~(x=y)? Now, if one views collections in such a way as to see othernesses and unities among selected parts as definitive attributes of the whole, then, since obviously not every such collection consists of exactly two things or of exactly one thing or of etc., in that sense such numberish predicates are not utmost generals. However, any object (in a large enough universe) will fairly belong among polyadized objects whereof "two" is true collectively. Keeping this in mind, we have a notion of universality reached by utmost generality, universality which can be extended to sequence schemata, etc., and which seems, as a "window," practical and cornucopious like the singular or transingular. If we "arbitrarily" declare a given predicate term universal, equivalent to a predicate like in "Tx" or in "Hxyz v ~Hxyz", it can be refined by formal schemata. (Via a richer formalism such as set theory or the like, mathematics can treat these universals as more or less general and even unique properties of various sets or the like, and mathematics can re-generate the world's wild variegation, while building imaginative, metamorphosic bridges of equivalences across the greatest disparities of outward appearance.) The point is that the 'accidents' or 'modifications' of the objects xyz in the above example don't matter. All that can matter is their othernesses and unities, relationships defined within the formalism (of first-order logic with equality a.k.a. ...with identity). On the other hand, with things like "blue," we're getting into modifications of objects. Such terms or ideas or qualities as "blue" and "Jack" befit (at least in a realistic universe where not everything is blue or Jack) that which I will call the special, or contraliant special to ensure clarity as to just what sense of the polysemic word "special" I mean. ("Contraliant" from contra- + aliud + -ant). The contraliant special term is (or purports to be) true of something (or things in a polyad) but decidedly not of everything.

Yet the universal can be either transingular (as in the case of a total population, its parameters, etc.) or (coaliant) general (or indeterminate about that alternative in the case of a term's de jure applicability). So the universal is better pictured as a ceiling into generality than as a ceiling in generality.

Generality's limits
The universal supplies the upper limit of the coaliant general, and is a kind of extreme to which the coaliant general reaches, like a line segment which includes its endpoint adjoinment with something else (a universal may be general or instead transingular). In the other direction, generality's "line segment" includes everything till the transingular but not the transingular itself, like when a mathematician replaces an endpoint with a little bubble. A coaliant general is either universal or contraliant special (or indeterminate about that alternative in the case of a term's purport, its de jure applicability, or the like).

- The (coaliant) general has two limits -- an excluded limit, the transingular, and a partly included limit, the universal (a universal is not necessarily general).
- The (contraliant) special has two limits -- a partly included limit, the transingular (a transingular is not necessarily special), and an excluded limit, the universal.
- Should the general-cum-special be considered a fully included "limit" of both the (coaliant) general and the (contraliant) special? Here we seem to approach a limit to the usefulness of the imagery of limits.

Singularity's options
A transingular may be universal too. If the transingular is a total population, a universe, a gamut, then it is also universal, at least in the relevant universe of discourse. When it is not the universe, the transingular is (contraliant) special. (In the case of term purport, the transingular may be indeterminate about that alternative.)

Universals & universes
Basically one ends up with two kinds of (coaliant) general and two kinds of universal. Now, in the universe of a plinker's distinct notes cdefgab, that gamut is the universe. It is both unique and universal. In its universe of discourse there's no polyad that contains notes uncontained in the gamut. "The gamut" is true of cdefgab and there's nothing else of which "the gamut" is true. In that sense it is not general. Yet it is universal, it is the universe and, in that sense, it is not (contraliant) special. A gamut, a universe of discourse, a total population is a transingular universal. Also universal is a monadic or polyadic term which does not exhaust the universe's population in a single predication yet which, like "one," is true of each object distributively or which, like "two," is such that every object is among some objects whereof the term is true collectively. Such a universal is also general, since there is more than one instantiation of it in its universe. One the other hand, "THE one" and "THE two," etc., are not general, insofar as they are true of the one object in a one-object universe, the two objects in a two-object universe, etc., respectively.

So we have two kinds of universal, one a transingular and the other a (coaliant) general. A universal which does not exhaust its universe in a single predication is (coaliant) general, not transingular, and is closer to the kind of thing which one usually has in mind with the word "universal," something like a rule, with more instances than the given one, indeed sometimes infinitely more, as with the "miraculous jar" of positive integers.

To be in the world
A transingular which does not exhaust its universe in a single predication is much closer (than the universal transingular) to the sort of thing which one usually has in mind with the word "singular," a singular or singulars-in-polyad among still more singulars in a larger world. Such a transingular is not its universe, it is not universal. It is (contraliant) special.

So a transingular may be universal or special. Likewise, a general may be universal or special. Just because a term is general, having more than one instantiation, doesn't mean that every object is covered one way or another in its instantiations. For instance, "blue" is, eclectically, true of some things and false of the others. So now we have four comparatively simple logical quantities -- universal, (coaliant) general, (contraliant) special, and transingular -- and four conjunctions nameless except for such improvised unwieldy names as "universal-cum-general," "universal-cum-transingular," "special-cum-general," and "special-cum-transingular."

To be systematic
Any pair of statements are TT, FF, FT, or TF. We define logical binary compounds in that way. Formal logic wouldn't even think of not systematizing the four mutually exclusive and collectively exhaustive cases -- the four conjunctions based on truth conditions. And we get "and," "neither-nor," "no, but," and "and not."

In the same inevitable way, any term true of something is, de facto: -- (1) universal & (coaliant) general -- or (2) universal & transingular -- or (3) (contraliant) special & (coaliant) general -- or (4) (contraliant) special & transingular. All that's being done is to answer two mutually independent logical-quantity questions, which bring us --

To the heart of it
In the monadic case, the two logical-quantity questions are:

"Given that there's a thing (call it 'x') which is H, is there a thing (call it 'y') which isn't that thing x and which also is H?" If yes, then "H" is (coaliant) general. If no, then "H" is transingular.
and
"Given that there's a thing (call it 'x') which is H, is there a thing (call it 'y') which isn't that thing x and which is not H?" If yes, then "H" is (contraliant) special. If no, then "H" is universal.

The mutual independence of the twin questions needs to be appreciated; they result in four possible conjunctions. The result is not simply two separate extremes of universal and singular with the somewhat-general somewhat-special as a third, in between. The habitual swerve of thinking of the singular only in monadic terms even while thinking of all three of its kindred logical quantities (special, general, and universal) in both monadic and polyadic terms, leads to thinking incorrectly of the universal singular as a trivial combination (if one notices it at all), a nearly blind window, confined to a one-object universe. In fact the window's vista is quite populous. A grand boat gets missed there, that of a logical quantity corresponding to a gamut, a total population and its parameters, etc., along with a whole class of research, research starting from given parameters of a total population, universe of discourse, etc., to draw deductive conclusions.

(There are even more than four options for term purport, de jure applicability, or the like, 16 including the formally false option, mostly since indeterminateness becomes an option in various alternatives. Such options for de jure applicability seem to become 2^16=65,536 if we admit options for objective indeterminateness and an option for objective inconsistency.)

Simplify?
Now, in a large enough universe, the general-cum-special will be mostly vague in range. In the monadic case it could be true of just two things or it could be true of all but one thing or it could be anywhere in between. It is so much like logic's "general term" as to be barely distinguishable except under certain near-the-limit conditions. For similar reasons, one might question at least the utility of some of the other combinations. One might say, instead of column A, why not column B?:

A	B
General-cum-special	Logic's "general," logical-quantitatively indeterminate like the predicate term letters in logical schemata.
Transingular-cum-special	"Just plain" Transingular (be it universal or (contraliant) special).
General-cum-universal	"Just plain" Universal (be it transingular or (coaliant) general).
Transingular-cum-universal	Transingular-cum-universal (a universe, total population, gamut).

A.1

B.1

Universal

(Contraliant) Special

(indeterminate)

Universal

(indeterminate)

General- cum-universal

General- cum-special

(Coaliant) General

Transingular- cum-universal

Transingular- cum-special

Transingular

Transingular- cum-universal

Transingular

Now, if we're defining kinds of terms by purportive logical quantity for the purpose of a formalism or grammar, then Column B seems the more convenient way to go. However, Column A is logically "nicer" and more consistent in its criteria; its four logical quantities are on a par with each other. In any case Column A girt by the simple logical quantities as shown in A.1 is the completed relevant picture (almost completed -- one could also devise terms for the diagonals). And if one is interested in logical quantities as characterizing typical mental perspectives distinguishing classes of research, Column A is the way to go, and even a pair of terms for A.1's diagonals would be useful. Now, I speak of the perspective as represented by the given subject matter, not the object(ive) or goal which, for instance in the special sciences, may include finding generals true of multitudes of singular objects and events.

Perspective in typical subject matter:	Class of research:	Typical inferential character of conclusions:
Transingular-cum-special.	The special sciences a.k.a. idioscopy. Human/social, biological, material, physical.	Surmise (ampliative-cum-precisive).
General-cum-special.	Sciences of positive phenomena in general, rather than of special classes. Philosophy, cybernetic theory*, statistics, and inverse-optimization theory.	Strictly ampliative induction.**
Transingular-cum-universal.	Deductive math theories of logic, information***, probability, and optimization.	Strict (precisive) deduction.
General-cum-universal.	'Pure' mathematics. Ordering, calculation, enumeration/measure, graphing/topology.	"Reversible" deduction.****

	Kinds of INFERENCE referenced here or in related posts.	Deductive (the premisses formally imply the conclusions):		Ampliative (the premisses don't formally imply the conclusions):
	Non-precisive (the conclusions formally imply the premisses):	"Reversible" deduction (equivalents, bridging gulfs).		Strictly ampliative induction (likeness, correlation).
	Precisive (the conclusions don't formally imply the premisses):	Strict deduction (novel aspects, extrication).		Surmise (naturalness, simplicity, directness).

* Maybe I should say "communication theory" instead of "cybernetic theory." I just don't know enough in order to know.
** That's notwithstanding the internal properties of the 'domain-independent' deductive formalisms with which these fields sometimes occupy themselves.
*** Deductive mathematical theory of information considerably overlaps into 'pure' math, abstract algebra in particular, because of the pure-mathematically deep treatment of laws of information, laws which also turned out to be equivalent to some principles of group theory.
**** In mathematical induction, the minimal case and the heredity, conjoined, are equivalent to the conclusion, given the well-orderedness of the relevant set. The proof of the minimal case or of the heredity is sometimes not reversibly deductive, especially when inequalities or greater-than or less-than statements get involved. More generally, pure maths are rife with inference through equivalences and equipollencies.

Update August 6, 2007: Am I analytic?
Thank you to Enigmania for including me in the 51st Philosophers' Carnival. In answer to his implied question: Well, I don't take the analytic linguistic turn, and I went through a Merleau-Ponty phase, but I like C.S. Peirce more and don't regard science as sinister to some great extent that would distinguish science from the humanities. Indeed, as "Enigman" says, my stuff "seems to be more analytic" than Continental, "but who can say?" and this is also partly because I'm an insufficiently disciplined amateur, not a professional philosopher. If wishes were horses, and so forth. To date, I've engaged in discussion mainly with Peirceans (at peirce-l), which has been good for me and, I hope, not bad for them. I've read some of the important early papers in analytic philosophy and some books by Quine, but I haven't engaged in discussions with analytic philosophers, so I've lacked the benefit of criticism from them. I don't know how to rectify that but, if I'm lucky, the Philosophers' Carnival will help.

• I regard philosophy's best bet to be to define itself (A) as having, as its subject matter, positive phenomena in general in their inferential issues, and (B) as properly tending to draw, as its conclusions, inductive generalizations to or toward totalities -- all in all, sort of like statistical theory, but tackling the inductive inverse of the problem of deductive theory of logic rather than of probability, and thus lacking the quantitative-measurement emphasis and having multiplicity of levels, reflexivity, and so on, pursuing problems of estimating, interpolating, extrapolating the logical structure of a universe rather than the parameters of a total population, and rising to consider general processes of experience, mind, heart, society, etc., and complex inference processes including all mathematical and scientific research, to say the least. (Note: The kinship between statistical theory and philosophy isn't very close -- they're still far apart like, say, matter science and human/social studies.)

• I certainly don't oppose deductive formalisms (not to mention deductive arguments) in philosophy, any more than a statistician opposes probability formalisms. Statistics' normal curve of distribution is a way of looking at Pascal's Triangle extended indefinitely. A piece of logical formalism transits the heart of the ideas in this post.

• Still, recognition of its underlying kinship with inductive, totality-targeting fields like statistical theory could help philosophy manage and temper its own aspirations to a "God's eye view" (pace Rorty, who, complaining of its aspirations, essentially gave up on philosophy), help philosophy reduce attendant hyperbole and disillusionment, and help it be more pragmatic about vagueness, discriminate in hyperbolic doubt, fallibilistic, etc., without tending to substitute some idea of utility (not to mention power) in place of the idea of truth be it ever so slippery. My 2¢ worth. End of August 6, 2007 update (Edited, January 2, 2009).

A few informal assertions about the problem of universals.
Areas of research can be ordered according to their appeals to principles of how we know things (ordo cognoscendi, the order of learning or familiarity) and, in pretty much reverse order, to principles (entities, laws, etc.) whereby we explain things (ordo essendi, the order of being). The order of being is often preferred in the special sciences (physics first, etc.), while the order of learning and of the verificatory bases on which we know things is sometimes preferred in maths (where such preference tends to put logic and order theory first). Maybe those researches which I call "sequenced in the order of being" you would call "sequenced in the order of abstractness." Still could well be the same ordering. I'm not saying that the ontological questions are unimportant, to the intellectual climate, the human spirit, and the ultimate bearings which people take in their decisions. But for my part I generally take their involvement in questions of math and science classification as an intrusion signifying that the classification is either deficient in firm and fertile constraints or just plain nebulous. And, if people argue over whether some sciences should be ordered by increasing concreteness or increasing abstractness, and if it's essentially the same ordering forwards versus backwards,

♂♀†∞$

versus

$∞†♀♂

, then they're arguing over a shiny gewgaw, the right of some science to be called "1st" rather than "last"; the real classificational choices have already been made, and the two orderings just need to be distinctly named, so that people can specify the sense of the ordering. Sometimes one can discern little pushes and shoves over prestige. "More basic" can be a laudatory term for "prior." "Lower" can be a pejorative term for "prior." Profundus versus bathos. And so forth. Much more pertinent is to specify the sense or standard of the ordering. Various orderings can be quite compatible when distinguished by an articulated sense or standard of the ordering. Questions of ontology and questions of research-classificatory preference are often best separated. Same is true for the topic of logical quantity and any connected research-classificatory preference issues.

On various topics I prefer compatibility with a range of ontological viewpoints, but I do I have my own ontological views. Generally, when people deny the reality or ontological legitimacy of generals in any usual sense, I don't know what to think but that they regard Scholastic Realism as "secretly" believing that generalities like redness and threeness exist like lamps and chairs. As if we might expect to hear a news bulletin, "Blueness, as such, has been finally been found, orbiting a house in New Orleans." Now, if "blue" is not itself a real individual object like a blue thing, still the real individual object is really blue. So blue has really-ness. But that extrapolates to coming up with syntactically complicated words for variations of "real" and you know that sooner or later we'll find some general word for them all. I foreshorten the process and take that word to be the word "real" itself and will merrily consider in what senses and what universes Santa Claus, Planet Pluto, and Cthulhu are real. Sure, some things are "realer" than others. Indeed even with reality we can admit graduality, etc., if we don't try to live always in the armor of a flat first-order logical universe, as interesting a challenge as that can sometimes be, and as needful as it may be for those whose sense of reality is unfortunately shaky. Coarse is what it is, like that browser Safari which should instead be called Tour by Tank. Anyway, Peirce's definition of the real as that which is what it is, and indeed in some sense persists, independently of that which you or I or any finite community thinks of it and which would be discovered by research adequately prolonged, suffices for a definition of "real" which takes things like blue in and is a critically unfolded version of the common-sense interpretation of the word "real." Now, if somebody, Quine or Stuart Rankin or whoever wants to come along and define "real" as "singular object" or as "Scottish" or as whatever, they can do that, but only the Peircean kind of definition has earned the force and feeling of the everyday word "real" which everybody in the discussion prizes. I certainly don't know what would be a "naturalistic solution" to generals and mathematicals and I see no germane practical significance in the idea.

The transingular subject is a this, or a this, this, that, yon,, etc., and, as a more or less haecceitous rest point or useful stopper to analysis, is also a hook or polyad of hooks on which, to borrow Peirce's phrase, to hang the hat of a predicate, it is a point of general indetermination and freedom regarding how the predicate relates to components or sections or durations (and so forth) of the singular subject(s). For instance, it is left to the definition, context, etc., of the predicate "blue" whether "something blue" means something entirely blue or mostly blue, etc.; one is not automatically forced to quantify over parts or stuff of the described subject. Many a natural thing, through such characteristics as forcefulness, endurance, vigor, and firmness/integrity, lends itself to treatment as a singular. As Peirce argued persistently, some things impose themselves on us, whether we like it or not. The haecceitous thing may come crashing in through a hundred windows. And things could not be alike in their bare singularness -- they could not all be singulars -- but for generality. And the general would not be general but for ranging over more than one thing.

The singular seems just as mysterious as the general to me, and neither one of them makes sense without the other. I can't see anything in the limitation of the real to the singular but a kind of fetish arising from the fight against the unmoored generalities so involved with causing chaos and destruction to people and society.

To go on being systematic
Also, to be concerned with the singular and the general and not also with the universal and the special seems unsystematic, unthoroughgoing, and illogical to me. The possibilities of a term's being true or false of objects besides that of which the term is predicated in the given instance don't play such favorites.

There's plenty in all that to examine philosophically. As the transingular-cum-special term lends itself to use as a subject term, and as the general-cum-special term lends itself to use as a predicate term, so a transingular-cum-universal term lends itself to adaptation as a predicate-formative functor such as "with a probability of 75%," and a general-cum-universal term lends itself to adaptation as a subject-formative functor such as "double of". There is a parallelism which runs among logical quantity, grammatical form, and philosophical category such as substance, attribute/modification, mode of attributability (modalities and "indeed," "not," "if," "novelly," "probably," "feasibly," "optimally," etc.), and correspondences/variances (such as "another than," the combinatory "Inv," "double of," "product of," "antiderivative of," etc.) The parallelisms, as non-binding affinities, seem to help empower thought.

Parallels, Not Equalities

Logical Quantity:	Grammatical Form:	Philosophical Category:
Transingular-cum-special.	Subject.	Substance, hypostasis.
General-cum-special.	Predicate.	Modification, attribute.
Transingular-cum-universal.	Predicate-formative functor.	Mode of attributability.
General-cum-universal.	Subject-formative functor.	Mathematical correspondence/variance.

Whatever one thinks of the problem of universals, still for inquiry on the problem of universals to get off on the right foot, it's a good idea to develop more than a nodding, dozing acquaintance with logical quantity. For really what there is is not simply a problem of universals but instead, from the start, a systematic complex of issues of the (comparatively) simple logical quantities and their conjunctions.
- posted by The Tetrast @ 7/17/2007 07:03:00 PM 0 comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.