Ross gets some play!

[From a thread at Philosophy Forums, via Dr. Feser. Go here to read "Immaterial Aspects of Thought" itself. I realize this post keeps growing (see the glosses ADDED 20., 21., 23., 25.12.09 below), but it's all eventually going into a book, so I need the raw material together at some point. ;) ]

Seeing as I think I might have been the one to spur aletheist to read Ross's essay, via Dr. Feser's link to my posting the essay at my blog –– veniaminov.blogspot.com/200...s-of-thought-by-james.html –– I feel behooved to chime in on the discussion so far.

First of all, Ross doesn't mean judgment is ratiocination, as someone suggested by saying a judgment is a weighing of probabilities, etc. This is why Ross specifies in note 2 that "thinking" means judgmental understanding, and cites Aristotle in _De Anima_ (bk. 111, ch. 4, 429b, 30): "Mind is in a sense potentially whatever is thinkable, though actually it is nothing until it has thought." Because a single act of intellection––formal judgment––is necessarily incompossibly determinate, whereas a physical system is in principle always subject to differing formal determinations––descriptions––the actuality of the intellect gives shape to the potency of matter, not vice versa.

Second, plus/quus is hardly the linchpin of Ross's argument. It is a case in point, like grueness, amplified grueness, gavagai, points on a curve, rule-following, etc. Further, others have reached the same conclusions by different means, such as Plato, Aristotle, St. Thomas Aquinas, Mortimer Adler in _Mind Over Matter_, David Braine in _The Human Person_, John DePoe, Norman Malcolm (mutatis mutanids), Victor Reppert, et alii.

Now, some of the nitty gritty.

Contrarian, and perhaps others, have referred to idealizations (and self-models) as counters to Ross's argument, but Ross explicitly addresses the place of nomic/mathematical idealizations in the essay. A falling ball does not exhaustively and exclusively perform a = dt^2. Its action and composition could equally well descriptively perform an infinite number of incompossible functions. The physical does not in se manifest itself prescriptively to us, but it is only manifest to us under formal descriptions. F = ma is a formal idealization on OUR part, which is why empirical variations from it now and then (including the inescapable errors of friction, measurement indeterminacy, etc.) don't call for a whole new law in every case. Is the Law of Inertia really a determinately physical happening? (I.e., Has any physical object ever moved without the influence of any other and in a perfect vacuum?) Physical science works because natural objects conform well enough to our formal abstractions, and vice versa; but physical science doesn't work as well as we might like because there is in principle an infinite gap between what any formal ratio accomplishes in a single case and what a physical system (on any order of magnitude) accomplishes in a single case. Is the Bode-Titius law a genuine law of nature? Under certain conditions, yes. But obviously it's just an obscure limiting case of sounder Newtonian physics, which themselves are but limiting cases of Einsteinian relativity, and so on. The history––and, yes, future––of science is nothing more than humans saying, "Oh, so nature wasn't actually doing ____ but ____* instead!" If a physical system WERE as determinate as formal description of it, scientific progress would halt there. (Just imagine if a physical system, once subsumed by a formal-mathematical principle, could NEVER be defined otherwise in the way addition or modus ponens cannot be redefined.) The very fact that differing data can be used to support different formal theories is based again on the underdetermination of the physical as such. The physical data DO fit differing theories, but differing theories, if sufficiently formalized, don't fit each other. In this (among other things) the physical and the formal (as primary content of the intellect) differ in-principle. That's the heart of the matter.

A physical object in any instance is subsumable to a myriad of formal operations, whereas the grasp we display of any one of those formal operations––however obscure or limited it might be empirically or computationally––is incompatible in a single case with any other function, and in a way in-principle beyond the myriad of law-like simulations on display in physical nature at any instant. What a physical system is "really doing" depends on our grasp of what is a formally coherent description of it. As Ross notes, there are no (prescriptive) logical relations in physical nature because physical phenomena are never under only one quantitative relation. That is how and why the physical is underdetermined in a way qualitatively unlike determinate intellection.

(I should mention in passing that the issue does not just pertain to science. Why/How did the unitary physical constitution of, say, "Piss Christ" strike some as a brave work of art and others as a rank abomination? "Piss Christ" qua physical system is simply indeterminate, like any physical system, with respect to possible formal definitions, whereas as those formal judgments are mutually incompossible. [And as for the objection that they might be synthesized or reconciled in a 'higher reading', that just underscores the point: "Piss Christ" qua physical system is but soft wax to the firmness of formal determinations in the intellect.] The fecundity of creative art presupposes the indeterminacy of the physical compared to the actuality of a formal vision.)

A very fine rejoinder referred to binary voltage readings in a CPU. Yet, this fails too, since even the binary voltage readings computers make in their time cycles are only intelligible to us as a determinate algorithm because WE program them to do so as we already grasp the operation.

(Digression: This is why the reference to a program's source code also just begs the question. Who shapes the potency of binary code into a definite formal algorithm if not the programmer by the actuality of his/her intellect? [As for the rejoinder that Darwinian algorithms {à la Steve Grand's a-life, etc.} could and do spin out novel algorithms as they go, and thereby trump our intellectual grasp in a physically determinate, albeit idiosyncratic, way, actually this just reinforces the point. Viewed purely physical from the outside, we'd have no real way of saying, "This program has evolved to follow ____ function," since at any instant it could evolve along new lines, and only at the end of the evolution drill could we, looking back, intellectualize just what it had done all along. Until its outputs are subsumed to a formal ratio, by the intellect, the algorithm's physical constitution is literally indeterminate in and of itself. But, again, so is any physical system in and of itself.])

If we looked at the input/outputs of the voltage readings only, from the outside, as it were, we would have no purely physical way of determining in a formally pure way what the machine is doing. For all we know in purely physical terms, the machine could be running (at LEAST) one the following two algorithms:

"F(V): 10 t>1 min<60 mins read voltage V 20 V = 1 GOTO 30; 30 reset V to 0 GOTO 10; … 20 V = 0 GOTO 40; 40 go to 10"

or

"F(V'): 10 t>1 min<60 mins read voltage V 20 V = 1 GOTO 30; 30 reset V to 0 GOTO 10; … 20 V = 0 GOTO 40; 40 go to 10 … 20 V = 1 on forty-billionth cycle GOTO 50; 50 shut down".

We would see the same results and the machine would just as easily be simulating F(V) as F(V'). No one denies that machines simulate the functions we desire and grasp; as Ross says, machines add like puppets walk. Leaves "add" by piling up on a windy day, but that is hardly addition. The argument really is as simple as asking, "COULD this computer/machine be performing––indeed, COULD it at all perform––a different formal operation and still produce the same detectable results?" The answer is yes, in every case, and this shows the difference: we simply can't grasp operations like "addition," "modus ponens," etc. without concomitantly grasping that no other function fulfills the same formal criteria. We can certainly fathom that, at a moment's notice down the line, we might slip and start performing a brave new function called "mantraddition" (define it as you like), but once we grasped WHAT each function is, we would admit that they are incompossible, no matter how closely they simulate each other in their physical outputs. For that matter, a mathematician someday might discover a genuine law that says addition becomes mantraddition under certain very abstruse geometric conditions, and any instances of addition previously (unknowingly, for centuries) done under those conditions would not have been "addition" all along. We'd be humbled and amazed, but we'd still see at least that the two functions are incompossible, even if performing either one makes no practical difference in real life.

Further, waving at Occam's razor is a red herring, since nothing in purely physical terms logically prescribes us to use it, and a case of petitio principii, since Occam's principle itself is just another formal judgment which we impose on, not derive "raw" from, physical reality. Occam's razor doesn't help here, since the skepticism of mentation ON A PHYSICALIST READING is endemic to any rule-usage, even linguistic ("Occam's razor stipulates…").

Without such an in-principle cleft between the actuality of formal operations and the potency of the physical, we would be reduced to something like a man asked to measure inches in inches. We need at least a stereoscopic metaphysics to give coherence to the physical as potential surd.]

[ADDED 21.12.09:

Jedaisoul asked: "+ is a physical entity???" Do you mean to say that + is a non-physical entity? The + can and does perform a multitude of functions; as such it is, in and of itself qua (mini) physical system, as indeterminate as any other (midi or mega) physical system. It is precisely because the abstractions behind symbols are determinate in a way that asymmetrically "dominates" their physical representations (e.g., + for addition, etc.) that we see the ontological asymmetry between the formal and the physical.

Further, do you claim that computers use numbers, or merely coded representations of numbers? We use numbers; computers don't. They use simulations of actual numbers, which is one more reason why they simulate actual functions without performing them as we do.

You seem to dislike Ross's use of the word judgment. But he explains how he means it and why it is essential to intellection. Again, give the essay at least one more reading. The reason Ross looks to thinking as judgmental understanding, and why it must be determinate in the way no physical state can be, is because a pure function is "truth-preserving" in a single case and in every case. But physical functions are truth-preserving of one and the same function only within particular parameters. (Put differently, they are truth-preserving for too many incompatible functions, and therefore essentially unlike pure functions as truth-preserving forms.) It is the inherent contingent parameter-particularity of physical functions which separates them decisively from the exhaustive parameter-universality of formal operations as such.

In any case, Ross is not the one who demonstrated physical underdetermination. Take it up with Duhem and Quine, inter alia. Cf. e.g. Nancy Cartwright and Ian Hacking. Ross just happens, in typical fashion, to have connected modern analytic advances with ancient insights.

Contrarian: You're getting warmer. You said that Ross needs to show that an "indeterminate system cannot generate a determinate one." This is not the issue, actually. The issue is whether any PHYSICALLY determinate state is ever adequately and exclusively determinate in the way our intellect is via formal operations. Whatever determinate state S(d) an indeterminate physical state S(~d) terminates in at time t is perfectly well subsumable to and describable by countless other functions. But a pure function is not so hetero-subsumable and counter-describable.

Contrarian said: "Doesn't matter whether its behavior is intelligible to us."

Again, warmer, but not seeing the bridge. The problem is not whether a physical system is intelligible to us, but that it is overly intelligible to us. There is an inverse proportion between a thing's essential determinateness and its "understood-flexibility." It is precisely because we can ascribe all kinds of incompatible but competitively coherent formalizations of a physical system that it is indeterminate in a way no formal reality can be. The point is not––I repeat NOT––that the physical is indeterminate as such. The point is that concrete versus abstract entities are determinate in totally different ways, a difference Ross elaborates in _Thought and World_ by reference to the "transcendent determinateness" of the concrete versus the abstract. The endless number of physical particular predicates which pertain to any physical object––its "overflow" predicates––simply surpass the ability of the intellect to tie down under one formal statement. By contrast, no purely formal entity CAN be transcendentally determinate, since if its determinateness transcended the intellect, like the overflow de re necessities of any physical object do, it would not BE an object of the intellect. Ross is not an idealist trying to subvert the physical to the immaterial. He is simply delineating how each form of being has its own proper mode of existence, giving each domain its proper due. The issue is that, insofar as they possess crucially different determining factors, the physical and the immaterial are not identical.

You grant the real cleft that exists between idealized physical functions (e.g., F = ma, etc.), but still fail to see how decisive that is here. Physics says a falling rock behaves as if it is obeying F = ma. But because a falling rock does not perfectly and exclusively (let alone always) conform to F = ma, but just as easily behaves "as if" it is behaving innumerable variants of F = ma, the falling rock––like any physical system––is determinate with respect to a limitless range of competing variant functions. Admitting the rock is formally determinate in infinitely differing ways is just another way of saying the rock qua physical system is infinitely indeterminate. Which is Ross's point. Anything which in a single case coherently instantiates an infinite number of incompossible functions doesn't actually instantiate any one of them. Potentially, yes, but formally determinately, no.

Contrarian said: "If we knew nothing about the machine, we would still see it behaving consistently in one way given a 0 input, and in a different way given a 1 input. There are many such binary "switches" in Nature, too. Though the system as a whole may be non-determinate, it has determinate features."

Two points.

1) By admitting the physical system as a whole is non-determinate, you're just restating Quine's insight and Ross's thesis.

2) Again, the issue is not whether we CAN detect pockets of real determinateness in nature and define them in some formal way. We can. We do. Which is just the problem: we can and we do and we can and can and can ad infinitum. Let me put it this way: Ross is not saying that physical reality is not determinate, but that it is overly determinate. The problem is not that physical nature is not amenable to any formal determinations, but that it is amenable to all too many. The issue is that, even in the act of defining S(d) as "actually performing" F(S(d)), we can easily––and without limit––incorporate S(d) under other formally incompossible functions. The data points F(s(d)) leans on in S(d) really can fit an infinitude of other functions (or curves), even though any and all of the competing function/curve are mutually incompossible. Because S(d) "fits" F(S(d)) just as "perfectly" as it fits F'(S(d)), F''(S(d)), … F^n(S(d)), it doesn't exhaustively-formally fit F(S(d)). Precisely because S(d) is really determinate with respect to ANY AND ALL of its coherentized functions––or has "determinate features," as you put it––, thus it is indeterminate with respect to any one of them (at the exclusion of all the others contenders). F(S(d)) is always perfectly F(S(d)), and incompatible with divergent functions, but S(d) is not––cannot be––determinate in a single case in the same way (viz., incompatibly with other encompassing curves/functions), since it really is coherently determinate via F'(S(d)), etc.]

[ADDED 22.12.09:

Contrarian wrote: "...you'll have to show that [a.] the indeterminate physical system cannot, consistently with its own laws, generate a determinate formal system. I.e., that [b.] there is no logically available path from the physical to the formal."

Contra a.: The challenge is not to show that an "indeterminate physical system cannot ... generate a determinate formal system," since the point is that a physical system generates a myriad of formal operations in any case. A single physical "point" S(d1) at time t is coherently an instance of infinitely many incompossible functions: it fits on any curve: like any physical constellation, it is formally indeterminate in and of itself. Its physical parameters are subsumable to countless variant formal systems, and therefore it is indeterminate in the way no formal operation ever is. The issue, again, is not (i) whether a physical system can be formally determined, and therefore determinate. The issue is that (ii) a physical system is overly formally determined, and therefore indeterminate unlike any act of (formal) intellection. Duhem, Quine, Kripke, Goodman, Ross, Feser, Braine, Machuga, I, et alii, accept (i) as truism, and accept (ii) as a sort of modal restriction against (i)'s being affirmed in physicalist terms. (i) is true, but not to the benefit of physicalism.

Contra b.: Again, the problem is not that there is "no logically available path" from S(d) to F(S(d)), but that there are too many such paths. Being coherently "open" to innumerable functional ascriptions, a physical system is indeterminate as just one of them. But this is not the case whenever we perform an actual, specific function. If it were--i.e., if addition were possibly also quaddition in the very act of performing addition in a single case--we could never actually "run" a pure function. But we do, ergo, etc. A function is what it is and nothing else. A physical emulation of a function is what it is, too, in its de re necessities, but these necessities are simply incommensurate with the truth-preserving capacity of a pure function (just as the essential formal 'austerity' of a function is incommensurate with the limitless overflow actualities of a physical object). Any physical system S(d) (and any "slice" of the physical system S(t1(d1)), S(t2(d2)), etc.) is simultaneously "running" a limitless number of variant functions. But we don't run any more than one pure function when we do a single function in a single case. That's the insuperable divide.

If you want a sound bite, here it is: A function actually contains every possible instance of it in a single case without remainder, whereas as a physical system potentially contains every possible function in a single case. That's the decisive difference.

Also, Ross addresses the issue of sufficiently higher levels of generality (e.g., modus ponens is a true case of an otherwise invalid form "If C then P"). Even in just a single case, a particular pure function is what it is in its own particular way, whereas increasing or decreasing levels of physically generality are never determinately true in the same way.]

[ADDED 23.12.09:

Contrarian said: "By "physicalism" I mean simply the doctrine that the universe of experience, including "mental experience" (Kant's phenomenal realm) is explicable in terms which lend themselves to empirical investigation."

If this is the "physicalism" you want to salvage from formal underdetermination problems, be my guest. (Sounds more like "shmysicalism" to me.) I'm baffled why you think positing immaterial abstract entities has any place in PHYSICALism/MAT(T)ERIALism. Admitting a physical/non-physical cleft in being just gives away the game. Hence, I doubt most self-respecting physicalists would grant the divide you blithely admit (Kantian style). Physicalism stipulates that ALL phenomena, perceivable or otherwise, are properly reducible (and actually reduced) to wholly physical states of affairs. But Quine, Kripke, Goodman, Ross, et alii have demonstrated that certain formal operations are determinate, in se, in a way that the physical cannot in principle exhaust/satisfy.

Let's go through this again:

Any instance of a pure function is irreducibly a formal whole and includes every possible instance of its "instance-conditions." By "instance-conditions" I mean the logical and operational criteria which congrue with the definition/form of that function in a single case. A pure function is called a "pure function" because its notionally hermetic definiteness excludes incompossible variant formality within itself (i.e., excludes "polyformal impurities" [my term of art] in its own definition). Addition can't possibly be quaddition, though a single case of "x ? y = z" could be addition or quaddition (or something else altogether, ad infinitum). So, the formal has (at least) two essential criteria: 1. instance-exhaustion and 2. variant-exclusion. Physical states simply cannot meet these criteria, and therefore differ essentially from pure functions.

Now, physicalism says that whenever we do addition and the like, all that is "really happening" is the emergence (or crystallization) of a complex pattern of physical elements. On physicalism, "formal patterning" (and everything else, for that matter) is just a complex arrangement of physical components devoid of intentionality and reason. But the point, again, is that no physical state, no matter how complex -- indeed, the more complex the worse -- ever satisfies the conditions of any single one of the functions it is simulating. The physical state is, after all, just an INSTANCE of a function, whereas a function itself is never just an instance, but actually includes all its possible instances in a formally exhaustive way. (Again, the claim is NOT that physical systems can't be [or aren't] determinate, but that they are never determinate as pure functions must be. A physical instance of a function IS determinate, only not determinate in the right way to ground pure functionality as we grasp/employ it.) "To be a function" means to be unlimited in "instance capacity," but since a physical system can be (at least) only one instance of a function, no physical system is IDENTICAL with "what a function is." If a function were just "an instance of some operation" it would cease to BE a pure (instance-exhaustive) function. Not only is every physical state just one instance of a function, but also is an instance of innumerable variant functions. "To be a pure function" entails "to be THIS function and not possibly any other one." Any instance of a physical state is subsumable to endless variant functions and therefore can never wholly instantiate the truth-preserving capacity of a pure function. F = ma is always wholly and solely F = ma, whereas objects in motion are neither purely cases of F = ma nor only cases of F = ma. A function is "all there and only that" at once, whereas a physical system is never formally "all there" or "only that" in a single case. The formal and the physical essentially differ in this respect.

I repeat: The formal has (at least) two essential criteria: 1. instance-exhaustion and 2. variant-exclusion, but physical states simply cannot meet these criteria, and therefore differ essentially from pure functions. Now here's the rub: No physical system can ever exclusively instantiate a SINGLE function in ALL its instance-capacities, and yet we undeniably encounter pure functions in reality, so real "pure functionality" must be grounded in (or generated by) a non-physical system or power. This power is classically referred to as the intellect. By grasping a pure function, in just a single case, the intellect congrues with the existential criteria of a pure function: namely, it both (1.) encompasses all possible instances and (2.) manifests a single function to the exclusion of variant forms. If no physical system can do the same, but the intellect does so, it follows that the intellect is not a physical power.

In any case, by propping up "physicalism" with a generous empiricism the "shymsicalist" is just traipsing right back into the nest where (Duhemian/Quinean) underdetermination was born. If the infinite array of physical permutations can't satisfy the existential criteria of pure functions, the tiny clumps of empirical data we have can hardly be expected to do the same. Again, if that's the (Kantian?) physicalism physicalists want, they can have it.]

[ADDED 25.12.09:

As St. Thomas said, "Sapientis enim est non curare nominibus (The wise man is not fussy about words)." This thread has reached a saturation point of sorts, so, while I appreciate the opportunity to elaborate on and sharpen the thrust of Ross's argument, I see no reason to keep sharpening the knife for those who will not cut their own coneptual fetters. Perhaps you can understand how disheartening it is to dialogue with some going by the name “contrarian,” since it suggests a forthcoming rebuttal to any argument or claim will be made, just to be authentically contrarian. It’s no less heartening to read another interlocutor’s replies and say to myself, Jedi-style, “These aren’t the rebuttals you’re looking for.”

An ideology gradually conforms to its content, which is why it has become apparent (esp. in this thread) that "physicalism" is as indeterminate as its object, the physical. (Once a worldview and its key elements start getting scare-quotes de rigeur, its days are numbered.) I think reading Alex Rosenberg's recent précis of his argument about "disenchanted" naturalism goes a long way towards showing how little warm-blooded physicalism can allow the abstract-concrete, empirical-formal cleft with which (1) Jedaisoul and (2) Contrarian agree.

In the first (1) case, to say that formal truths have no bearing on physical reality is not only to admit Ross's argument is correct, but also to recognize that, pace scientism, "reality" and "nature" are bigger than "the physical." (I must wonder, though, how seriously Jedaisoul-- who apparently hosts a website devoted to Einsteinian relativity et relata-- can assert that formal truth has no bearing on physical reality. A case of "Methinks the fellow doth protest too much"? Or perhaps a case of cutting off one's nose to spite one's face?) Ross says over and over again that recognizing the in-principle immateriality by which the intellect operates is not to deny or trivialize the systematically material medium in which it operates. (E.g., A wave-function is formally distinct from the particular ocean swell that manifests its form, but the wave-function is not actually materially separable from the water. Hylomorphism 101.) Ross does not deny that our thoughts occur in and through our brains-bodies, only that they occur by and as such physical systems. Acts of intellection shape our neural matter the same way a wave-function shapes water.

Recognizing the in-principle incapacity of the physical to instantiate formally true operations entails that, when we do instantiate formally true operations, it is not possibly on account of the physical matter which mediates the operations, but on account of a power commensurate with the formality of the operation. One of Aristotelianism-Thomism’s axioms is that, for sentient creatures, nihil est in intellectu quod non prius fuerit in sensu (nothing is in the intellect that is not first in the senses). A corollary is that each sense is formally proportionate to its proper object: the eye is the organ of the visible, the ear of the audible, etc. It just so happens that the brain-- or rather, the entire human nervous system including its intentional relations to the 'external' world (which I'll refer to as iHNS)-- is the analogously proportionate organ of intellection on a case by case basis. iHNS is the proper potential medium for the immaterial activity (or actuality) of intellection. But, being merely a physical medium, not even iHNS can be the generative basis for purely formal operations: for no physical system can be that. Operative formality must happen somehow, and it can’t happen by the purely physical, so it follows that we-- in our very bodies in actual spacetime-- make it happen by some not-purely-physical principle.

In the second (2) case, to say that physicalism just means a realist scientific approach to the world is just to revive classical "Aristhomism." That's exactly why Ross's argument is but a piece of-- and all of a piece with-- his broader metaphysics (esp. in Thought and World). This is hylomorphism of a very scientifically literate kind. Materialists may not care to see the inescapable value of immaterial principles in science, but for those who have eyes to see, the "stereoscopic" metaphysics of modestly realist hylomorphism just is the constitution of productive science. Aristotelian forms are what some modern philosophers of science call "structure," so if you want to see how non-physicalist realism functions in modern philosophy of science, read up on structural realism. Ross has argued numerous times that science functions on a hardware-software paradigm; formal order is real "software" everywhere in material nature, which just is what science tracks. Admitting the irreducible role of the irreducibly formal is not to undermine science-- on the contrary-- but it is to be rid of physicalism and materialism as such.]