At Dr. Feser's blog, in the post alerting his readers to my posting "Immaterial Aspects of Thought" at FCA, a reader, David Brightly (DB), objected and I replied.
DB: "Isn't Ross, in his section II, really making an epistemological point? … we can see that every output will be the perfectly determinate sum of the inputs, provided the device operates within its design range of ambient conditions. … He's saying that it's indeterminate what the device is doing. I'm afraid I flatly disagree."
As Dr. Feser replied, the epistemological point hinges on an ontological difference between a plus- and a quus-machine (pm and qm). To wit, that the latter is “informed” in a way formally incompatible with how the latter is informed. In fact, the argument about physical indeterminacy wouldn’t even require differentiating outputs, since the outputs for the pm could be triggered by auditory inputs of the form “five,” “fünf,” “cinco,” etc., whereas the identical outputs on the qm could be triggered by—and therefore represent—auditory inputs of the form “John,” “Mary,” etc. Let us then imagine that the outputs for the pm were recorded by a digital video camera and set off fireworks, whereas the outputs of the qm triggered a video camera to shut off an idling engine down the street. In this way, both pm and qm would be “doing different things,” even though their physical composition and input/output array were identical.
I imagine the objector will say pm and pm are, on my hypothesis, actually just parts of larger physical systems—call them S(pm) and S(qm)—which are determinate in their own ways. The problem is that this objection already grants the essential point, namely, that, in and of themselves in purely physical terms, pm and qm are formally indeterminate. For all we know—and literally, for all their doing physically—they could always be running different functions. Indeed, even if we established the “forms” of S(pm) and S(qm), we could just rig one of them to a new video camera system and trigger some different physical outcome, in which case, even the larger systems would be indeterminate with respect to their endless formal possibilities. It’s not just that we don’t know which function a physical/material system is “running”; the problem is that nothing about the systems themselves in purely physical/material terms restricts—determines—their being instances of a single formal operation. Pure functions, however, can never be indeterminate in this way, and therefore crucially differ from physical systems. A pure function—say, addition—can never even possibly be “running” a different incompossible operation than what it is, nor can it even possibly “mutate” to alter its formal parameters without ceasing to be the same formal operation. Add to this that pure functions exhaustively include every possible instance of themselves, whereas any single case of a function in purely physical terms is just that—a single case of some function—and therefore the single-physical case is intrinsically formally-incommensurate with the instance-exhaustion of any pure function.
Presumably, the objector would claim that all physical functions are determinate in the sense that they all “tie in” to the entire cosmos. In this way, all physical systems would be like massive Rube Goldberg devices (e.g., S(qm) triggers a video camera to shut off a car, which traps a chicken inside, which kills the chicken and release noxious fumes, which float into the atmosphere, which deflect photons back into space, which eventually get sucked into a black hole, etc.”). The problem is, no matter how Byzantine one made his Goldberg cosmos, it would still be intrinsically formally-indeterminate, since it could suddenly advert to running an incompossible somewhere down the spatiotemporal road (“amplified grueness”). For that matter, the cosmos could collapse and cease to be—would we then be justified in saying any formal functions also ceased to exist? Purely formal functions cannot ever advert to running a different function, nor can they be limited to a subset of their instances. Hence, even the cosmos as a purely physical system is intrinsically indeterminate in a way formal operations cannot be. If the human mind is a purely physical system, it follows that our minds are always just as intrinsically indeterminate with respect to cases of formal truth, which means we never actually and formally-determinately perform pure functions, which is absurd. That is Ross’s argument.
13 comments:
Mr. Brightly has posted two additional comments arguing that pm and qm would necessarily have different internal physical organizations in order to perform different functions (plus and quus, respectively)--e.g., qm would need a circuit that makes an explicit comparison of the inputs with the threshold value (57 or whatever). If this is right, then there would be a (physical) fact of the matter about which machine was performing which function. If this is wrong--i.e., if pm and qm have physically identical structures--how can it be said that they are performing different functions? Is it somehow "cheating" to peek inside the machines, rather than treating them as black boxes and only looking at their inputs and outputs?
It’s not just that we don’t know which function a physical/material system is “running”; the problem is that nothing about the systems themselves in purely physical/material terms restricts—determines—their being instances of a single formal operation.
This suggests to me that the unquestionable versatility of computers may be evidence for the indeterminacy of the physical, since different operating systems and software programs can cause the same machine to perform vastly different functions. Am I right? Even if so, the question remains whether the same can be said of machines that are "hard wired" to perform a single function.
aletheist,
I'm very much out of my league here, but I'd like to take a stab at this just to see if I understand what Cog is arguing here on behalf of Ross. In part, anyway.
Let's imagine a really simplified system: A calculator that could only do addition, could only use whole numbers, and could only handle outputs as high as 2. So you're limited to 0+0=0, 0+1=1, 1+0=1, and 1+1=2.
Let's imagine another equally simplified system: A device used as a memory aid for what dinner to serve to mixes of carnivores and vegans. If two carnivores show up, they get the carnivore meal. If a carnivore and a vegetarian show up, they get the vegetarian meal. If two vegetarians show up, they get the vegan meal. No other combination is considered.
It seems to me that the same exact machine could satisfy both uses. Same hardware, same programming, etc. Mentally, I'd just be interpreting the inputs and outputs differently while changing nothing about the machine. So is the machine adding / is it programmed to add? Is the machine showing proper dinner service instructions / is it programmed to do this? Is "two vegetarians get meal C" exactly the same thing as "1+1=2"? None of the above?
Either way, I'd like Cog to tell me if what I wrote above is on the right track with this 'indeterminacy of the physical' thing. Another way to put it would be that even with the exact same physical system, we could come up with multiple 'equivalent' descriptions (mathematical and perhaps otherwise?) of the system. Meaning more than one description or formula or elsewise that perfectly matches what we're seeing, but is nevertheless distinct.
Thanks, Crude. If I understand you correctly, you seem to be suggesting that the meaning of the physical inputs and outputs is indeterminate and must be assigned to them by an immaterial mind in order for what happens in the machine to correspond to a formally truth-preserving pure function. Dr. Feser made a similar point in chapter 6 of TLS, using addition and deductive syllogism as his examples.
One response that I have seen is to define the differences in output as the "meaning" of the differences in input, or to claim that a response to a stimulus is "meaningful" as long as it is non-random. Any thoughts on how to deal with those objections? My initial approach was an appeal to intentionality ("aboutness").
One quibble with your "simplified systems" here is that 2+0=2 and 0+2=2 would also be possible for the calculator. With this in mind, how would you map the six different mathematical operations of the first device to the three different combinations of diners such that "the same exact machine could satisfy both uses"?
aletheist,
I knew I was forgetting something simple! Thanks.
0+2 and 2+0 could fulfilled as saying that if a vegan and a carnivore show up, serve the vegan meal. Simple enough.
As for the response, I actually have a couple questions of my own.
First, if someone insists that there is really some kind of "meaning" or "meaningfulness" in a 'purely physical operation' - isn't that what Ed would call a return to a broadly Aristotlean metaphysic anyway? In other words, how is this an objection against formal and final causality? I'm an amateur here, so I could be missing something. And it does seem that if the fallback is to "some kind of meaning", then the argument really is that whatever the purely physical system is doing, it can't be adding - so we're back to "so does that mean we're not adding either?" question with Ross, if I'm right.
Second, I wonder how much blurriness is being played up on with 'internal' versus 'external'. If I type '2+2=4' into a calculator, how do I know "2+2=4" is being instantiated, and not "2+2=4 until 2012"? The response here seems to be "If you completely examine the computer's hardware and software, you will have a physically fixed machine and a completely determinate set of operations." But, the hardware and software is just part of another "physical system", so the exact same questions seem to be lingering.
aletheist and Curde:
Thanks for your contributions. I might be too buzzed on coffee to reply as precisely and as thoroughly as I should, but I've also got some reading to do; and I don't think I'll get much stuff done online over the weekend, so I don't want this weighing on me without getting a few points across. (Venting is good for the soul?)
1. I have not seen Brightly's two additional comments, since it looks like even my comments at Dr. Feser's have not shown up yet. Maybe it's just my server or something. aletheist, are you retro-fitting my pm and qm into his initial objections?
Anyway, the problem with saying pm and qm (as well as S(pm) and S(qm), etc.) "differ" commensurately with their differing formal processes, is that, apart from an antecedent FORMAL division of just WHAT pm and qm are, we have no PURELY PHYSICAL way of distinguishing them. That is, how do we know in PURELY MATERIAL terms exactly (determinately) where pm and qm begin and end in spacetime? Moreover, how do we know they are even independent systems and not actually parts of a larger (but perhaps inscrutably complex) super-system which runs a totally different function based on the sub-operations of pm and qm? How do we know pm does not crucially depend on negative ion concentration in the air but qm does not? Those ions would then "count" as parts of pm. And this is not just an epistemological fault on our part: it's an endemic indeterminacy of the purely physical as such. The epistemological skepticism/confusion is a function of the ontological indeterminacy/potency, not vice versa. If physicalism/materialism is true, a species of monism is true, and if monism is true, then we have no way “outside” the formal constraints of that monism to analyze reality.
CONT.
The objector will say, "Just look at/in pm and qm and see how long their circuits are, where their wires lead, etc.," but this just begs the question, since WHAT pm and qm are requires a FORMAL grasp of their operative and material differences from the outset. That’s why the objector says we can see their determinateness: they were designed to BE something formally determinate. That of course just gives away the game. If on the other hand a thoroughgoing physicalist says ALL “complex” systems are the result of blind, brute physical happenstance (cf. hostility to Intelligent Design, etc.), then she ipso facto has no FORMALLY DETERMINATE REASON to assert qm and pm really and wholly perform their respective functions. They weren’t “designed” with a formal goal in mind, since nature has no mind and is no finalizing designer. Ergo, they not only did not emerge in accord with some formal truth but also do not irrefragably operate according to any formal truth.
2. The scenario about a "crude" (heheh) machine dishing out food to different animals is on track in that it relates to what I was saying about the spill-over indeterminacy of S(pm) and S(qm), and the spill all the way up to the cosmos. Who the hell knows what the machines are "supposed" (teleology!) to do without already knowing what is formally possible?
3. "2 + 2 = 4 until 2012" is just another example of Goodman's grue problem, and therefore on-track. It signals once more what I referred to as "endless formal possibilities" for any wholly material system. The (two-pronged) fact that a purely material system COULD (for all we know) be running countless incompossible functions under the exact same mechanical parameters and that it CAN at any point commence running a variant function, suffices to show that the material system is not and cannot be formally determinate. The physical is ALWAYS subsumable to a competing formal definition (points on a curve, no experimentum crucis, etc.), whereas the formal is NEVER subsumable to some incompossible function. This is an essential ontological difference. We are physical beings, yet we are able to instantiate formally complete operations. Wholly physical systems cannot do that. Ergo, we are not wholly physical systems.
If we assert that "This wholly physical machine JUST IS doing addition," we also assert that it can't even possibly do anything else, which is false, since i.) it could be part of larger incompossible function and ii.) could malfunction down the road (in which case its IDENTITY with its formal content would entail the formal operation itself malfunctioned). If the formal is possibly IDENTICAL with a physical system, the function becomes as limited and as mutable as the system itself, which of course makes mush of formal determinacy. And let no objector wiggle out from under the fact that physicalism/materialism assert the IDENTITY of any and every formal operation (all formal truth) with "subvening" the physical system(s). Also, when I said that nothing in the purely physical mode “restricts” a physical system to running only one formal operation—and thus crucially differs from formal truth in the mind—you can imagine my point like this: A wholly physical system is, on physicalism, devoid of intention, finality, will, etc., and therefore, a “formally operative” machine has no intrinsic ability or drive to abide by one formal operation. It isn’t really saying, “No, THIS is the formal operation I want to do forever.” It’s completely ‘passive’ with respect to how it is informed and therefore formally indeterminate, whereas formal realities as such are incommensurately “stubborn” about doing/being ONLY ONE function.
I may write more as it comes to mind, but let me know if the above helps for now.
Best,
Sorry, Crude, I didn't mean to call you a "Kurd" and possibly entangle FCA in a sociopolitical imbroglio. See the Coffee Buzz Proviso in my first comment. ;)
aletheist: "Mr. Brightly has posted two additional comments...."
I realize now that you mean Brightly's two other comments after Dr. Feser's reply to his first. They were about N up to 57 and differentiating outputs, i.a. I had all three of his comments on-screen when I wrote this post, so I was cognizant of the latter two comments when I wrote it. Indeed, they are what I am batting down with my S(pm) and S(qm), Rube-Goldberg-cosmos scenarios. As I said, the issue doesn't strictly hinge on there being differentiating outputs in the operations of the machines themselves, since only the larger formal context of even physically (type-) IDENTICAL machines would determine WHAT the machines are doing.
"...pm and qm would necessarily have different internal physical organizations in order to perform different functions (plus and quus, respectively)--e.g., qm would need a circuit that makes an explicit comparison of the inputs with the threshold value (57 or whatever)."
Again, the point is that pm and qm could have physically (type-) identical compositions and still be underdetermined with respect to any SINGLE pure function. Their performance can either be described under a myriad of incompossible functions or fail to generate every possible instance of a given function. In either case, the machines qua purely physical system crucially lack the identity criteria for "being a case of a determinately pure function."
Best,
I also wanted to add that objectors think they can say a physical system is formally determinate only by relying on a suppressed premise, to wit, a massive ceteris paribus clause. E.g., "This machine is determinately doing f(x) [...but only if the laws of the universe are exactly what we take them to be at this moment and if they don't alter at some point]." That's a decisive lemma, however, since it is precisely the ceteris paribus clause which artificially buttresses a physical system's formality from malfunction or 'impurity' in a single case. Without a unilateral ceteris paribus clause, a physical system is wide open to entering "alternate nomic conditions" and thereby performing a different function. (E.g., F = ma is only formally true of any physical system under serious, outdated Newtonian ceterus paribus qualifications.) The prophylactic ceteris paribus clause being deployed, unwittingly, I think, by many objectors, simply begs the question: for it assumes that physical nature IS and always WILL perform its 'one' super-complex function as the stabilizing background for lesser functions in this debate. If ceteris paribus does not hold, then the nomic parameters of lesser functions eo ipso deform (!) into variant functions.
Best,
Cog,
No prob on Kurd of course. :) I'm still learning a lot here, but one thing I'm curious of is that whole idea of there being actual "meaning" in nature at all. Ed recently got done with a series with the EM claim that nature cannot really have meanings, or directedness, or aboutness, etc. And one claim I've read with Ed is that if it's argued that nature really does have things like "meaning" and "aboutness" and such present in it, then what's being argued for is, in essence, a broadly Aristotlean metaphysic.
Do I have that much right?
Second, if I do have that right, then isn't all this talk of the physical determinately instantiating a single formal operation A) Still part of that broadly Aristotlean conception of nature, and therefore B) Still not physicalism?
Or am I missing something?
I appreciate all of the feedback. It is helpful, but still not as "clear and distinct" as I would like. Some explicit and precise definitions of key terms would probably clarify things further, at least for me--formal, determinate, function, pure function, operation, meaning, etc. Which of these presuppose or depend on Aristotelian metaphysics (AM)? Would someone who rejects AM define them differently? If so, would that indicate that the two sides are simply talking past each other?
Additional specific questions:
1. Why is it "absurd" to suggest that the human mind is just as formally indeterminate as a physical machine? How do we know that we really "formally-determinately perform pure functions" and "instantiate formally complete operations"? How do we know that determinately pure functions exist at all?
2. Is the indeterminacy of the physical linked to the problem of induction? We assume that today's laws of nature will remain unchanged in the future (and have been unchanged in the past), but we do not know this. Perhaps the material universe is hard-wired such that E=mc^2 until 2012, after which E=mc^2.001. Or perhaps the speed of light in a vacuum is constant until 2012, after which it is 1 m/s faster. Either way, would we notice?
3. The notion of (proper) function entails teleology, but does it (by itself) entail that there are immaterial aspects of thought? If so, how exactly?
4. Is underdetermination a central concept? Does the inherent (possibly ontological) indeterminacy of quantum phenomena have any bearing?
I realize that some of these are addressed by Ross, Feser, and/or earlier comments here, but again, I would like to have the answers spelled out more explicitly and precisely. To me, the overall argument boils down to this:
A. Some thoughts are incompossibly determinate.
B. No physical processes or functions of physical processes are incompossibly determinate.
C. Therefore, some thoughts are not physical processes or functions of physical processes.
I am looking for equally succinct and valid arguments to support both premises (A and B).
Crude: I still do not see how the six calculator operations would be mapped to the three diner combinations. Can you lay out the translations of 0, 1, and 2 to vegetarians, carnivores, vegetarian meals, and carnivore meals?
Happy New Year to all!
aletheist,
You're aware that vegan and vegetarian are distinct classes, right?
0 = Carnivore
1 = Vegetarian
2 = Vegan
So, 2 carnivores yields carnivore meal (0+0), a carnivore and a vegetarian yields a vegetarian meal (0+1, 1+0), two vegetarians yields a vegan meal (1+1), a vegan and a carnivore yields a vegan meal (2+0, 0+2).
Crude: Yes, I know that vegan and vegetarian are different; but to be honest, I am not up to speed on exactly what the differences are. Why would two vegetarians want a vegan meal, rather than a vegetarian one? Maybe I am just overthinking the whole thing at this point. :-)
aletheist,
Vegans avoid using any animal product, vegetarians avoid meat and such, I think the generality goes. Though what they'd personally want isn't really the issue here, just the rule set of what meal type to serve depending on who shows up.
But yeah, whether they like what they get isn't much a concern here. :)
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