In other words...

"The speed of truth is faster than the speed of light."

And:

"General Relativity: It's Funny Cuz It's True."

-- Elliam Fakespeare

(That's the thesis of these two related posts.)

Talk to me...

"I've been praying for years now, literally years, for God to talk to me."

"Talk to you?"

"Yes, like a real person! Like a real voice."

"How do you know He hasn't been talking to you?"

"That's my point: why should I have to wonder? Why should the voice of God--of God!--be so hard to hear?"

"Well maybe it's like asking, 'Why are diamonds so precious?' Because they're so rare. Maybe this world isn't a very good 'medium' for God's voice to 'carry in,' for now at least. Then again, maybe our hearts aren't very good media for God's voice to travel in. So maybe when we really do hear Him, it's like finding a diamond. If we heard from Him all the time--like wearing a divine iPod--I think we'd start to suffer spiritual 'inflation'--'Oh, it's God again. That guy never shuts up. I'm more in the mood for hip hop right now, God, can you call back later?'"

"Good point, but our God is a God of love--He is love!--and doesn't He want to reach all people? So shouldn't He go out of His way to be heard more clearly?"

"You raise a good point. Answering it is above my pay grade."

"But it doesn't bother you. I mean...."

"Why am I not upset about it too? Why don't I want to hear from God, too?"

"Yeah. I mean, don't you want to hear God for once in your life? So you could tell all non-believers you had total proof, total confidence, that God is real?"

"Who says I haven't heard from God? I mean, I wouldn't even have faith in the first place, let alone after all this time, if God were wholly silent."

"I see your point, but it seems like a such a small favor--just, I don't know, to whisper in my ear or something. I just want a little something more from God, just once."

"All right, well, how do you want Him to talk to you?"

"Like a friend, like a normal person."

"Well, that right there--don't you think that's a little odd--to want God to be just like a normal person? I mean, what if part of a relationship with Him means He is shrouded in the mystery of His own glory? Sort of like, no matter how well we know them, we never really know the inner life of our family members and friends. There's always 'something more,' some deeper reality behind their actions and words. Like they say, still waters run deep. A waterfall is loud, but all froth and impermanence. Maybe that's the problem of knowing God, only a thousand times deeper. He's too much of a person for us to just take in like any other person."

"But He's God! Can't He overcome those psychological obstacles?"

"Who says they're psychological? I'm suggesting they might be intrinsic to the possibility of our knowing God at all. If we were the kinds of beings that could hear God clearly, like you want, on a regular basis, I don't know if we would be ourselves anymore."

"But God talked to Moses and Elijah like a normal person, so why not to me?"

"That's a question only God can answer. But I find it interesting that nearly all the people God spoke to most directly--in a really 'Hollywood' way--never asked for it. In fact, Moses and Elijah and Jeremiah and Jonas all saw God's direct attention as a burden."

"Hmm, that's a good point."

"Plus, look at the Israelites: they had tons of 'close encounters' with God, but that didn't mean they were especially devout or thankful in the long run."

"Wow, that's pretty depressing, thanks!"

"I guess my basic point is just that God is a person, and you can't just force a person to do what you want in a relationship. Who's to say that hearing from Him like you want would 'cure' your faith anyway?"

"Of course it would! It's the only thing I want. Some kind of immediate proof, or contact with God. The rest would all fall into place."

"Like I just said: Elijah, Jeremiah, Moses, and Jonas probably see things very differently. Be careful what you wish for. Job asked for a face-to-face with God, got it, and only ended up regretting his folly. Before He got a taste of God 'up close and personal,' at least he could savor his suffering as a possible bargaining chip against God. But once he saw how, well, godlike God is, and how low he was, he had no excuses, no leverage with God: he could only see God as the Almighty and love him that much more deeply in his suffering."

"Well, I'm just glad I'm not Job either. I think I get your point."

"Think about this, too: Once you got that special 'word' from God, who says you wouldn't want another and another, more and more? If loving God as He usually is for most believers, isn't enough for you after all these years, maybe after enough time, you'd get just as addicted to some higher and higher contact with God. Eventually nothing would be good enough."

"Okay, I see your point... but is one time really too much to ask?"

"Well, let me ask you: why do you what God to speak to you?"

"I told you--"

"I know. I'm asking so you can really look at the question in the first place. I mean, so you can look at your desire for some 'word' perhaps more, uh, objectively."

"Meaning?"

"What if you asked me to communicate better with you."

"'Kay."

"And you saw I was trying."

"'Kay, sure."

"But then what if we reached an issue, or just some 'mood,' in which we couldn't seem to bridge the gap? Like if I disagreed with something you were doing but didn't want to argue, or I was trying to explain a new idea, or some new plan, but wasn't sure how to explain so you could really get it. So, for whatever reason, our coomunication reached a deadlock, but we were still friends."

"Well, I guess, we'd just have to be patient. Stay friends and hang out, but just kind of bracket that problem for the time being."

"Right. Do you think you could force me to communicate with you in some way you preferred, just so you sensed I was 'still there'?"

"No."

"I can only really communicate myself to you by communicating in my own way, right? And if there are times when we can't say everything we want, and times we can't even hear what the other person is trying and trying to say, doesn't it stand to reason that there are depths or 'moments' in our life with God which simply defy either our efforts to hear Him clearly or for Him to say what He wants in a way we can really grasp?"

"Fair enough. But can't God give me a break?"

"You remember when I used to teach English in Asia?"

"Sure."

"Well, one thing I learned is that you can't force communication if the cultural divide is too big."

"'Kay. Go on."

"I can't tell you how many times I wanted to pull my hair out in class when I'd ask a question, prompt a response, and just get blank looks. Or I'd try to explain a new topic and, while some students would try, it was just beyond them at first, so communication simply halted."

"'Kay. So?"

"So, no matter how much I wanted my students, and sometimes even my friends, to communicate with me in the way I wanted, at some point, I had to respect that we were simply talking across too big a cultural divide."

"So what did you do?"

"Well, I either changed the topic and gave them more time for the English to 'settle in,' or, more importantly for the point I'm trying to make, I broke into their language. There was a limit at which I could either stop communicating or sacrifice my own preferences for communication and adapt myself to the culture I had chosen to abide in."

"So you're saying...."

"I'm saying maybe there's a limit in our faith-life, when we need to get over certain 'highs' and 'lows', as psychological bonuses or losses, and adapt ourselves--adapt our own sense of communication--to God's own 'culture.' So many times people would ask me, 'How do you say this or that in English, or this and that in Chinese?' and it was really hard, because sometimes, there are things you can only say in one language. Obviously, you can translate the idea nehind some phrase or joke, but outside that original language and its culture, you just can't say it other than just saying it in the original. It's like I would always ask people, 'How do you say "cool" in Chinese?'"

"How?"

"You don't--you just say 'ku'."

"Uhh, I think you lost me. Try again."

"My point is that maybe across the 'cultural divide' between us and God, Jesus is the only complete translation, but there are still 'phrases' in our lives, based on very specific things in our own lives, which just can't be 'translated' as clearly as we want. In human life as well as in life with God, there are some things which can be said only by silence."

"Whoa, that's very Zen. Unpack it for me."

"Well, the Gospel, the Good News, is that God has spoken definitively to humankind in Christ. Therefore, if we believe the Gospel, we shouldn't expect some 'better' or 'clearer' word from Him. According to the Gospel, anything more than the Incarnation and anything less than it would 'garble' the message God is conveying. Jesus Christ is God's best word to us, to each of us in the Church because Christ is the very Word of God. Demanding or expecting some 'improvement' on the voice of God in Christ is just basically to deny the voice of God, His own whole life, is truly in Christ."

"What you're saying is beautiful, but frankly, it sounds kind of harsh. Are you saying I just need to 'be tough' and ignore my desires for some special word from God?"

"Not exactly, no. I'm saying that you need to ask yourself why you want a special word from Jesus in the first place. I walk past dozens of people every day, but I don't necessarily want to hear what they have to say. Only if I already believe someone is a great figure will I want a special, personal word from him. Christians are fundamentally concerned with wanting to know what Jesus says about life and death and all the rest."

"That's a cool way of saying it."

"I say it like that because we need to always remember that Jesus Himself is the Word we want, not necessarily some secondary word from, or even about, Him. Think about it: you say you want a special word from God because you care about Him above all else, right?"

"Well, yeah."

"But if you care about Him so much, you have to care about how He Himself authentically expresses Himself to us, to you. The hard, but good, truth, according to the Gospel, is that God has said all He can really say to us at this point in creation in Jesus Christ. If you think that's not good enough--if, in other words, you think the Incarnation, and its continuation in the sacraments, needs a 'boost,' or some 'extras'--then you're just not a Christian. And why would a non-Christian want a special word from Jesus? Only if you already believe Jesus is, so to speak, the only one you have ears for, then you should be able to find some peace that how He has spoken to you all this time is part of His wisdom and His worth. In fact, I think the fundamental question is: do we want God or do we want some benefit of knowing God?"

The court rules...

If determinism is true and all my actions are reducible to more basic causal sequences in my organs, tissues, molecules, the enveloping physical conditions, etc., then I genuinely wonder how we select the crucial causal element in assigning responsibility to "persons." I ask this toothlessly, wonderingly.

If, for example, I bump a flower vase and it shatters on the floor, both a determinist and a libertarian can assuage my guilt by saying it wasn't my "fault." Accidents do happen. For the determinist, however, my bumping the vase is not a pure accident--far from it. Rather, on determinism, it was an inevitable occurrence derived from my total lower-level causal constitution at the moment I bumped the vase. It was a metaphysical necessity, but not my personal fault. "You didn't really break the vase," my determinist friend might explain, "your elbow did. It was bound to happen. Don't be too hard on yourself." Not I but my arm is to blame. On this it seems both the determinist and the libertarian can agree: not being a personal action, my bumping off (heheh) the vase does not belong in the realm of personal responsibility. (If, however, elbows and hard floors could be penalized...!)

Now suppose I aim a gun at my neighbor's house and fire a bullet, whereupon it kills my neighbor. Along come my determinist and libertarian friends, if not to assuage my guilt, at least to ascertain what happened. This time I am clearly to blame for my neighbor's death. Or so says my libertarian friend: "Your elbow didn't do it this time, you did. You've done a bad thing." Distressed, I turn to my determinist friend for some Lucretian counsel. "Did not," I ask, "my finger pull the trigger in the same way that my elbow bumped the vase? Wasn't my firing of the gun 'bound to happen' in the same way my bumping of the vase was? Why am I culpable now but not then?" I won't put words in his mouth, because I genuinely wonder what the determinist's appropriate reply ought to be.

Assuming, arguendo, that both my bumping the vase (and, not insignificantly, its falling to shatter on the floor), as well as my firing the gun (and, again, not insignificantly, its striking my neighbor), are wholly determined by antecedent causal conditions, what differentiates them in a morally significant way? How do we decide where along the total causal line of some event "my" responsibility comes in? Does the difference emerge if my volitional consciousness is added to an action? Seeing as I had no intention or desire to bump the vase (itself a wholly determined lack of volition), but that I did have a conscious desire or intention to shoot my neighbor (likewise a wholly determined volition), am I thus morally responsible for firing the gun but not for breaking the lamp? This sort of reply seems unsatisfactory for two reasons.

First, it seems that volition is not intrinsic to moral responsibility. Were I a truck driver, imagine that one night I negligently fall asleep while driving and crash into another car, killing the family of four inside. Certainly I had no volition to kill them, nor to fall asleep, but I am no less responsible for my negligence at the wheel. Recall that I had no volition to break the vase (and let's add that it was a priceless heirloom handed to my wife by her mother on her death bed, such that breaking it seems like a genuine moral failure on my part). Allegedly, my causally determined lack of volition in that case morally differentiates my bumping the vase from my causally determined firing of the gun plus a volition to murder. But my point now is that a presence of volition, determined or not, is not a necessary condition for moral culpability (such as falls to a negligent driver). Whence, then, arises the moral gravitas of crashing into a family on the road which bumping a vase lacks? Both events were, assuming determinism, wholly precipitated by antecedent causal factors, yet one is morally culpable, while the other is only dimly and analogously so. Volition is usually relevant to assigning guilt, but not intrinsically.

Second, my volitions, or lack thereof, were as deterministically incipient in the causal progression as were the events themselves. My volition to shoot my neighbor, that is, was just as deterministically incipient as the clutching of my finger around the trigger--and yet only the former is morally significant. Why? Indeed, my bumping the vase was just as deterministically incipient in its own causal sequence as shooting my neighbor was in its causal complex. Yet, only the latter is morally significant deterministic eventuality. Why? It seems that moral significance does not arise from the mere 'tightness' of causal antecedents prior to an event, otherwise both my bumping the vase and pulling the trigger would be equally deterministically "moral." Willing to shoot my neighbor and pulling the trigger--as well as the bullet's flight into his body--are equally determined eventualities, yet oddly I am only culpable when they are paired, not when they are determined separately. (I.e., if I were causally subjected to a desire to kill him but not causally subjected to pulling the trigger, I would not be culpable, and, presumably, were I only subjected to a random pull of the trigger, minus a subjection to a desire to kill, I would not be culpable.) Whereas my libertarian friend had said, "You've done a bad thing," I wonder if my determinist friend would be magnanimous enough to say, "A bad thing has been done by way of you."

What we have are four circumstantially 'quasi-events'--not-willing, bumping, willing, shooting--which mysteriously become moral only when determined in certain pairs. What accounts for this? There appears to be no morally significant difference between the incipient emergence of one event minus an emergent volition and another event that happens to have been paired deterministically with a volition. After all, the pairing or decoupling of volitions-and-actions is but a deterministic function of the larger causal sequence in which they occur. Just as my determinist friend consoled me that "accidents happen" (like bumping vases) and that it was "bound to happen," so he might console me in jail by saying that "volitions happen" and that my homicidal urge was "bound to happen." My homicidal intention--in whatever sense it could even be ascribed to me--is no more or less a brute causal 'efflux' of a deterministic world than my lack of such an intention, or my elbow's collision with a vase, or my finger's pressure on a trigger, or your eyes moving over the screen to read this post. And so on.

This is why I said above that it was not insignificant that the fall of the vase and the flight of the bullet were determined events. Their significance lies in showing how difficult it is to assign personal, moral responsibility on determinism alone. My volition, or lack of it, and my bumping or firing are significantly like the falling of the vase the motion of the bullet. And this suggests a dilemma: either we regard all concatenated sub-events in some larger event as trivially determined--and thus as void of moral significance in their own right as the falling and flying of a vase and bullet are, respectively, as pure causal alterations in spacetime--or we inexplicably elevate all such (sub)events to a quasi-moral status just so we can bestow the "sum" of their quasi-moral value on the larger event itself, which we hope to treat as a morally culpable action. For let us not forget that a deterministic moral ascription must be taken as a whole. If, ex hypothesi, the laws of nature had altered radically (and very locally) as the vase fell and the bullet flew, such that it never hit the floor (or struck my neighbor), or landed on a suddenly soft floor (or ricocheted off my suddenly adamantine neighbor), or swooped back up to safety (or returned harmlessly into my gun), etc., etc.--if the posterior sub-events in my vase- and gun-scenarios had not obtained with as much deterministic 'completion' as they did, then even despite having possessed a volition to do wrong, I would not be culpable. The vase would be unbroken and my neighbor still alive, so for what could I be blamed? My volition (or lack thereof) would be wholly irrelevant to the ultimate moral status of the macro-event, since its moral value was ultimately "decided" by deterministic sub-events after it. Astoundingly, it seems determinism means that my prior determined volition (or lack thereof) itself only assumes a moral status by virtue of posterior sub-events, which themselves lack a moral dimension. Thus in a twofold way, it is not at all up to me to commit a moral act on determinism, since I not only did not generate that intention myself, but also cannot be assured it will "follow through" to complete a moral (or immoral) action. Amoral or quasi-moral sub-events. Either way, volitions seem the odd man out in a deterministic morality. Why are they alone regarded as truly moral, whereas other equally determined sub-events in conjunction with them are not? I believe this inconsistency arises from an inveterate impulse on our part as agents to stress the peculiar metaphysical--and thus moral--significance of volition as opposed to mere mechanism and chance. The problem, however, is that this seemingly reasonable, and certainly untiring, impulse seems to have no place in determinism.

Hence, if I trust my determinist friend, I shouldn't be too hard on myself for killing my neighbor, since the co-incidence of my determined volition with my determined firing were never really up to me. The coincidence of a homicidal intention with the flexing of my trigger finger is not a moral statement about me; it is a factual description of the causal sequence to which I belong. For a determinist, it seems no more coherent (and no less incoherent) to ascribe moral significance to my volitions or lack of volitions than to ascribe moral weight to the bumping and flexing of my elbows and fingers, respectively.

And so I reiterate my quandary: what 'determines' (if you'll excuse the pun) exactly which 'node' in a deterministic causal sequence bears moral weight? Insofar as my volition to commit a crime is metaphysically inextricable from and incipient in all prior conditions, it seems just as void of moral significance as my bumping the vase. If, however, volition is an intrinsic property of moral fault, this seems to depend on the particular case, which in turn depends on the agent himself--which of course relocates responsibility within the agent himself, in contradistinction to locating "morality" in the 'mere' totality of causal conditions in which (on determinism) he finds himself trapped. If, by contrast, it really is "up to us" to decide where to assign blame, this suggests we at least have a kind of "judicial" freedom in analyzing our own allegedly determined actions.

[It dawned on a couple days later to add to the picture the idea that my responsibility might not even obtain unless it were also coincidentally determined that the judge convicted me of homicide. Failing that, at the end of the whole ordeal, I would not be guilty––despite the facts of my intentions and actions!]

Way back when...

Buddhists and Hindus claim we are what we are because of who we were in previous eons.

Christians and Jews claim we suffer what we suffer and do what we must because of a primordial deformation of creation by our ancestors, our earliest nature.

Materialists and fatalists claim we do what we do and are what we are because prior causal conditions leave us no other choice.

Thus it seems one transcendent aspect of humanness is our inability to shake the burdens of 'anticity'.

Perhaps the only way "out" is to reorient our anticity into the vivacity of Christ ever-present in the Eucharist, not as a mere historical anamnesis, but as the formal agent of what we have come to call "history" itself. We ought not then look "ahead" nor "behind" for Utopia, but simply "Behold!" hic et nunc Him Who Is in the Gift of Bread and Wine.

The news of late...

The good news is that, even under adverse conditions, you can find a way to be yourself.

The bad news is that, even under ideal conditions, you can find a way to be yourself.

The Good News is that, whether under adverse or ideal conditions, you can find a way to be like Jesus Christ with the Father in the Holy Spirit.

When and where can materialism be true?

[The following considerations carry over into a third post, which you should read after reading the first installment and this post.]

I would like to expand on my previous post about certain epistemological and metaphysical problems vis-à-vis Einsteinian relativity (ER, special and general, ESR and EGR). In that post, I argued that, inasmuch as ESR is construed as a realist theory, it entails inherent contradictions in purely materialistic (Minkowskian) terms. Specifically I argued (1) that the nature of analytic truths transcend the limitations of four-dimensional spacetime (4DST), inasmuch as they are true everywhere and 'everywhen', which is impossible on a realist-materialist reading of ESR; and (2) that our grasp of ESR as a cosmic truth defies the limitations of 4DST by virtue of the fact that we simultaneously 'deflate' naïve phenomenological observations in light of the reality of cosmic behind 'behind the phenomena' in a different frame of reference. Now I would like to clarify just why these claims present a challenge to materialism.

According materialism, there are no immaterial realities (such as abstract thought or angels or immanent forms). One way or another, everything we know, do, and are, is fundamentally material, and thus limited to 4DST. Specifically, every instance of thought is itself a material phenomenon with hypothetically measurable proportions in 4DST. My memory of my seventh birthday, then, just is the constellation of spacetime in the larger constellation of spacetime known as my brain. Likewise, my grasp of analytic truths (e.g., no part is greater than its corresponding whole) just is a segment of spacetime. When many people grasp the same (part-whole) truth, they are just instancing a sufficiently similar constellation of spacetime in their brains. Thought is not, then, a mental event, but one physical occurrence among many others. Indeed, events, far from being abstract entities, just are concrete rearrangements of spacetime. Any truth is what I shall call 'occurrent-true' in 4DST just by deforming 4DST in a way proportionate to the sameness of the propositional content in question.

But this should immediately alert us to the problem I am raising: if there is no 'all at once' (or “absolute time”) in which diverse things can happen, as ESR stipulates, then no identical event can happen in more than one frame of reference. Specifically, it is impossible, on a materialist reading of ESR, for one and the same constellation of spacetime (aka 'the same idea') to occur in more than one segment of 4DST. Yet, the entire point is that by instantiating analytic truths, and a the truth of ESR itself, we are instantiating entities which are identically true, and thus identical, in countless frames of reference all at once.

For a materialist, my memory of my seventh birthday can only occur at disparate times, because the so-called mental event of remembering it is limited by 4DST. The reason why no one can have my memory of my birthday party at the same time as I do, is because no one is coterminous with my aggregated share of spacetime. So, obviously, my memory cannot transcend spacetime, by, say, being entertained at once in my head and in a neutral simulator on a planet light years away, since my memory intrinsically happens in and by me. Of course, admitting this sort of limitation to “mental” events (phantasmata), like memories and sensations, is compatible with Aristhomism, since Thomistotelians grant that phantasmata are material, somatic events.

The real conflict comes in, however, when we speak of abstract truths. For if we deny these truths, as real events, can be perfectly and identically true everywhere and all at the same time, then we are exploding their intrinsic truthfulness. If I say my grasp of the unmarriedness of bachelors cannot be instantiated in an identically true fashion at all points in 4DST, then I am simply denying the truth that bachelors are unmarried. For, if in my frame of reference fr1 it is a true event (in my brain) that bachelors are unmarried, but in some distant frame of reference fr2 near Alpha Centauri the exact same mental event (about bachelors) cannot be occur at the same time, then I am just saying the proposition “bachelors are unmarried” (P-bu) is not always true, which of course completely misses the point of what an analytic truth is: namely, one that is always and everywhere true. If a materialist argues that analytic truths can't be true in more than one brain, like my memories of my childhood can't be in more than one place than in my head, then they are, again, just violating the meaning of analytic truth, reducing its universality to contingent occurrences in this or that place at this or that time. Analytic truths, as a class of abstract thought, are not subject to the same somatic limitations as phantasmata; otherwise they simply cease to be analytic. Denying the truth of analytic truths may be a way out for the materialist, but it seems a very high price to pay.

Nonetheless, it seems that not even the high price of denying analytic truths is sufficient to redeem materialism. For consider the claim of materialism itself (calling it proposition P-M): “Materialism is true, not only as we see things, but everywhere in the universe. It is true all over the cosmos that there are no immaterial realities.” That's easy enough to claim, but it once more raises the specter of incoherence in 4DST. If P-M is a material event in our frame of reference fr1, it automatically surpasses the bounds of fr1 by being 'occurrent-true' in all frames of reference frN. This is just what Aristhomism means by “spiritual” or “immaterial” reality: it is not subject to material limitations. Materialism may claim its truth holds at every point in the cosmos, but it thereby attains an immaterial transcendence of matter itself.

In the same way, ESR can only be true, despite our phenomenological failure to see empirically outside our frame of reference fr1, if at the same instant in which it is deployed an 'occurrent-truth' about corresponding realities in a different frame of reference frX grounds the deflationary impact ESR has on empirical phenomena in fr1. Whatever the empirical truth-making conditions tm-C (in frX) might be in order for a deflation of phenomena in fr1 to be true (based on ESR), we are simply unable to know them empirically in fr1––and yet we must simultaneously know that tm-C do ground ESR-deflations in fr1, otherwise ESR no longer really holds in fr1. In the same way that the occurrent-truth value of P-M entails its occurrent-truth in all frames of reference, so likewise the omni-spatiotemporal breadth of ESR (when combined with EGR) as a theoretical confinement to 4DST in and of itself entails transcendence of 4DST.

(As an aside, if a materialist retreated into a constructivist, as opposed to realist, reading of ESR-EGR, he would thereby undercut the empirical support materialism has traditionally invoked from ESR-EGR. If ESR-EGR is just a convenient series of operations which we use in fr1, devoid of any objective truth value in the cosmos as such, then materialism cannot draw upon the empirical findings of ESR-EGR to ground a materialistic confinement to 4DST based on ESR-EGR.)

Meanwhile, an Aristhomist can reconcile the seeming paradoxes of 4DST-transcendent abstraction by invoking at least some immaterial reality. ESR and EGR can be true “all at once” since their nature qua abstract truths never takes place “over time.” The truth of ESR-EGR are instantaneous truths about non-instantaneous entity-events. If they were not true “the whole world over,” then they would ipso facto no longer pose a threat to the omnitemporality of abstract thought, and thus post no threat to immateriality as such. Abstract truth is not a physically coherent, quantifiable reality limited to 4DST––but no less real for being superphysical. Reality, in other words, is not simply physical and thus not simply material. Ergo, on a realist reading of ESR-EGR, materialism is false.

An infinitely thin knife cuts no ice…

How we know infinity, and thus eternity, is not a natural concept. Or a reductio of Spinoza.

[The following link HERE presents an earlier stab at this same point.]

AXIOM 1: A characteristic which cannot be instantiated in nature should not be presumed to hold for nature as such.

POSTULATE 1: An object A cannot be in more than one place P at one time T. If A were in more than one place P at T, it would eo ipso cease to be a single object A. That is just what we mean by A being an object as opposed to two objects B and C. This is a basic characteristic of what it means to be a physically delimited (and thus quantifiable) object. A's objective unity allows for compossible, internal margins, but not noncontiguous, external boundaries.

CONSEQUENT 1 from AXIOM 1 + POSTULATE 1: Nature as a whole cannot be in two places at once, if for no other reason that there is no larger “space” in which nature can exist at this or that location. A further reason why nature as a whole can no more be in one place P than A can at a single T, is that A's objective existence in a presumed whole-nature at T would require A to be as objectively existent in some other whole-nature* at T, which, again, violates POSTULATE 1 and the unity of corporeal objects.

OBJECTION 1: Perhaps nature is infinite (and eternal) and therefore at all places (and all times) at once.

REPLY 1: An infinite quantity is a contradiction in terms, since a quantity is only possible by being physically, or even just conceptually, distinct from and delimited by some other quantity.

CONSEQUENT 2 from REPLY 1: Nature as a whole is not infinite and eternal. If it is, then it is no longer a physical reality, subject to quantification-mensuration.

POSTULATE 2: An infinitely thin surface cannot exist in nature. In our normal experience, the thinner something is, the sharper it is and the more easily and deeply it can cut into something else. But if we extend our mind along an infinitely thinner and thinner blade, we can quickly see that something goes wrong, as it were, in natural terms. For, while any surface asymptotically on its way towards infinity with indeed cut magnificently into physical reality, once it so to speak “reaches infinite thinness,” it will no longer cut anything, since an infinitely thin cut into something is physically equivalent to no cut at all. An infinitely small gap between two objects is actually no gap at all. When infinity is applied to nature as a presumably physical reality, we see that, to put it mildly, funny things happen.

CONSEQUENT 3 from POSTULATE 2 + AXIOM 1: Therefore, again, infinitely great––or minor––measures do not pertain to nature and natural objects, nor to nature as a whole. As such, it is illegitimate to refer to nature as a whole as both physical and infinite-eternal.

Someone can certainly refer to nature as "eternal," "infinite," and the like, but then it no longer seems the referent is nature, but supernature. The price, then, of naturalizing God is that of rendering nature incoherent for scientific, let alone naive exploratory, purposes.

"Immaterial Aspects of Thought" by James Ross

[Well, I finally got off my duff, irritated as it was that this great essay is only available here and there in PDF, and reformatted it into a revisable document. I'm sorry that my Macbook's interface with Blogger denudes it of all italics and font adjustments, but I have a nicer, more accurate version available by email if you ask. Read this essay well. And more than once, I would say. Don't be ashamed to admit you "don't get it" after a first reading. I barely did. Nonetheless, it is a philosophical time-bomb much too little recognized.]

IMMATERIAL ASPECTS OF THOUGHT
by James F. Ross

ANIMAL cognition and desire, from the appetite of a clam to the optical systems of vultures and frigate birds, is supposed to have neurobiological explanations resultant from, if not reducible to, universal laws of physics. That is a minimal and modest project for epistemology naturalized, one to be assisted by specialized sciences.1

There is a larger and bolder project of epistemology naturalized, namely, to explain human thought in terms available to physical science, particularly the aspects of thought that carry truth values, and have formal features, like validity or mathematical form. That project seems to have hit a stone wall, a difficulty so grave that philosophers dismiss the underlying argument, or adopt a cavalier certainty that our judgments only simulate certain pure forms and never are real cases of, e.g., conjunction, modus ponens, adding, or genuine validity. The difficulty is that, in principle, such truth-carrying thoughts2 cannot be wholly physical (though they might have a physical medium),3 because they have features that no physical thing or process can have at all.4

I propose to articulate that "difficulty in principle" so as to press home the point that it cannot be dismissed or evaded, or the underlying arguments or costs disregarded. First, the underlying arguments themselves are among the jewels of analytic philosophy (underdetermination considerations); and, secondly, to deny that our judgments are of definite logical forms and pure functions conflicts with our own certainty and with what we tell our logic, mathematics, and linguistics students about validity, proof, and formal syntax, and leaves us unable to explain what we do when we do mathematics, logic, or any other formal thinking.

But now let us look at the argument:

Some thinking (judgment) is determinate in a way no physical process can be. Consequently, such thinking cannot be (wholly5) a physical process. If all thinking, all judgment, is determinate in that way, no physical process can be (the whole of) any judgment at all. Furthermore, "functions" among physical states cannot be determinate enough to be such judgments, either. Hence some judgments can be neither wholly physical processes nor wholly functions among physical processes.

Certain thinking, in a single case, is of a definite abstract form (e.g., N × N = N^2), and not indeterminate among incompossible forms (see I below). No physical process can be that definite in its form in a single case. Adding cases even to infinity, unless they are all the possible cases, will not exclude incompossible forms. But supplying all possible cases of any pure function is impossible. So, no physical process can exclude incompossible functions from being equally well (or badly) satisfied (see II below). Thus, no physical process can be a case of such thinking. The same holds for functions among physical states (see IV below).

I. THE DETERMINATENESS OF SOME THOUGHT PROCESSES

Can judgments really be of such definite "pure" forms? They have to be; otherwise, they will fail to have the features we attribute to them and upon which the truth of certain judgments about validity, inconsistency, and truth depend; for instance, they have to exclude incompossible forms or they would lack the very features we take to be definitive of their sorts: e.g., conjunction, disjunction, syllogistic, modus ponens, etc. The single case of thinking has to be of an abstract "form" (a "pure" function) that is not indeterminate among incompossible ones. For instance, if I square a number––not just happen in the course of adding to write down a sum that is the square, but if I actually square the number––I think in the form "N x N = N^2."

The same point again. I can reason in the form, modus ponens ("If p then q"; "p"; "therefore, q"). Reasoning by modus ponens requires that no incompossible form also be "realized" (in the same sense) by what I have done. Reasoning in that form is thinking in a way that is truth-preserving for all cases that realize the form. What is done cannot, therefore, be indeterminate among structures, some of which are not truth preserving.6 That is why valid reasoning cannot be only an approximation of the form, but must be of the form. Otherwise, it will as much fail to be truth preserving for all relevant cases as it succeeds; and thus the whole point of validity will be lost. Thus, we already know that the evasion, "We do not really conjoin, add, or do modus ponens but only simulate them," cannot be correct. Still, I shall consider it fully below.

"Being truth preserving for all relevant cases" is a feature of the single case. The form of the reasoning that actually occurs is "truth-preserving," regardless of which case it is. Otherwise, it would not be "impossible by virtue of the form to proceed from truth to falsity" in that reasoning (especially when the premises are not true). Thus, the form of the actual "encompasses" (logically contains) all relevant counterfactual situations. In fact, it encompasses all relevant cases whatever. Without that, there is no genuine difference between valid and invalid reasoning.

Squaring, conjoining, adding. I propose with some simple cases to reinforce the, perhaps already obvious, point that the pure function has to be wholly realized in the single case, and cannot consist in the array of "inputs and outputs" for a certain kind of thinking. Does anyone doubt that we can actually square numbers? "4 times 4 is sixteen"; a definite form (N × N = N^2) is "squaring" for all relevant cases, whether or not we are able to process the digits, or talk long enough to give the answer. To be squaring, I have to be doing something which works for all the cases, something for which any relevant case can be substituted without change in what I am doing, but only in which thing is done.

Size and length of computation, for example, are external to the form of thinking, accidental to what is done. I am squaring just in case my thinking is of the form mentioned. If it is of any incompossible form, or is indeterminate among incompossible forms, it is not of the form, "N times N = N squared." It is not then squaring, however much its products may look like it, and however long a sequences of its outputs do.

The fact that I cannot process every case of modus ponens, because most of them have premises too long for me to remember, sentences too long to say, or words I do not understand, is adventitious, like my not being able to do modus ponens in Portuguese. Those are features of the functors, not of the function. The function that has to be realized in every case is the one wholly realized in the single case.

That point is to be taken literally: that the function is wholly present, not by approximation, exemplification, or simulation, but by realization in the single case. To make that distinction clearer, consider an even simpler function, "conjoining." Conjoining is the functional arrangement of an n-tuple of assertions into a single assertion that is determinately true just in case every one of the n-tuple of judgments is, and false otherwise. The truth of the whole block is the truth of all of the units ("p • q = T just in case p = T and q = T"). I can conjoin every sentence in the fourteenth edition of the Encyclopedia Britannica, or yesterday's Times. What I do in the single case is what would conjoin any string of suitable units, even ones too long for me to think of, or beyond my access to refer to. It is impossible to conjoin thoughts, if what I do is indeterminate among incompossible forms (at the same level).

Adding––genuinely adding, not estimating––is a sum-giving thought form for any suitable array of numbers.7 If I add two "elevens," I am doing what would have given "forty-four" had I been adding two "twenty-twos" (and not making mistakes), and so on for every other combination of suitable numbers. I cannot be really adding when I do something which gives the "right output" but which cannot, by its form, determine the "right outcome" for any case whatever, even one on which I make a mistake. There is a great difference between adding incorrectly and doing something else, like guessing, estimating, or following a routine or algorithm. The adding I am talking about, like conjoining, is a form of understanding.

This is not a claim about how many states we can be in. This is a claim about the ability exercised in a single case, the ability to think in a form that is sum-giving for every sum, a definite thought form distinct from every other. When a person has acquired such an ability is not always transparent from successful answers, and it can be exhibited even by mistakes.

Definite forms of thought are dispositive for every relevant case actual, potential, and counterfactual. Yet the "function" does not consist in the array of inputs and outcomes.8 The function is the form by which inputs yield outputs. The array of inputs and outputs for a function is the logical tail of the comet, not what the function is.9

The trait that determines the tail of the comet, the trait that "settles every relevant case, including all countercases," marks the contrast with any physical process: a physical process has no feature that can do that. That grounds my main argument: that a necessary consequence of even a single case of such thinking is something that is logically impossible to be a consequence of any physical process, or function among physical processes, whatever. Thus, the activity of such thinking cannot be a physical process, and the ability for such thinking cannot be a physical capacity.

II. THE INDETERMINACY OF THE PHYSICAL

Now we need reasons why no physical process or function among physical processes can determine "the outcome" for every relevant case of a "pure" function. Those considerations mark some of the most successful analytic philosophy, from W. V. Quine, to Nelson Goodman, to Saul Kripke. No physical process is so definite as to determine among incompossible abstract functions that one rather than another is realized, and thus to settle for every relevant case what the "outcome" is to be. That indeterminacy remains no matter how long the physical process is "repeated," even infinitely. In a word, with a machine it is indeterminate among incompossible functions what it is doing, no matter what it does.10 Therefore, no matter what it does, what it is doing remains formally indeterminate. Goodman's11 "grue" considerations and the plus-quus adaptations by Kripke12 suggest the form of my argument to show that. The argument is as follows.

Whatever the discriminable features of a physical process may be, there will always be a pair of incompatible predicates, each as empirically adequate as the other, to name a function the exhibited data or process "satisfies." That condition holds for any finite actual "outputs," no matter how many. That is a feature of physical process itself, of change. There is nothing about a physical process, or any repetitions of it, to block it from being a case of incompossible forms ("functions"), if it could be a case of any pure form at all. That is because the differentiating point, the point where the behavioral outputs diverge to manifest different functions, can lie beyond the actual, even if the actual should be infinite; e.g., it could lie in what the thing would have done, had things been otherwise in certain ways. For instance, if the function is x(*)y = (x + y, if y < 10^40 years, = x + y + 1, otherwise), the differentiating output would lie beyond the conjectured life of the universe.

Just as rectangular doors can approximate Euclidean rectangularity, so physical change can simulate pure functions but cannot realize them. For instance, there are no physical features by which an adding machine, whether it is an old mechanical "gear" machine or a hand calculator or a full computer, can exclude its satisfying a function incompatible with addition, say, quaddition (cf. Kripke's definition (op. cit., p. 9) of the function to show the indeterminacy of the single case: quus, symbolized by the plus sign in a circle, "is defined by: x ⊕ y = x + y, if x, y < 57, =5 otherwise") modified so that the differentiating outputs (not what constitutes the difference, but what manifests it) lie beyond the lifetime of the machine. The consequence is that a physical process is really indeterminate among incompatible abstract functions.

Extending the list of outputs will not select among incompatible functions whose differentiating "point" lies beyond the lifetime (or performance time) of the machine. That, of course, is not the basis for the indeterminacy; it is just a grue-like illustration. Adding is not a sequence of outputs; it is summing; whereas if the process were quadding, all its outputs would be quadditions, whether or not they differed in quantity from additions (before a differentiating point shows up to make the outputs diverge from sums).

For any outputs to be sums, the machine has to add. But the indeterminacy among incompossible functions is to be found in each single case, and therefore in every case. Thus, the machine never adds.

Extending the outputs, even to infinity, is unavailing. If the machine is not really adding in the single case, no matter how many actual outputs seem "right," say, for all even numbers taken pairwise (see the qualifying comments in notes 7 and 10 about incoherent totalities), had all relevant cases been included, there would have been nonsums. Kripke drew a skeptical conclusion from such facts, that it is indeterminate which function the machine satisfies, and thus "there is no fact of the matter" as to whether it adds or not. He ought to conclude, instead, that it is not adding; that if it is indeterminate (physically and logically, not just epistemically) which function is realized among incompossible functions, none of them is. That follows from the logical requirement, for each such function, that any realization of it must be of it and not of an incompossible one.

There is no doubt, then, as to what the machine is doing. It adds, calculates, recalls, etc., by simulation. What it does gets the name of what we do, because it reliably gets the results we do (perhaps even more reliably than we do) when we add by a distinct process. The machine adds the way puppets walk. The names are analogous. The machine attains enough reliability, stability, and economy of output to achieve realism without reality. A flight simulator has enough realism for flight training; you are really trained, but you were not really flying.

A decisive reason why a physical process cannot be determinate among incompossible abstract functions is "amplified grueness": a physical process, however short or long, however few or many outputs, is compatible with counterfactually opposed predicates; even the entire cosmos is. Since such predicates can name functions from "input to output" for every change, any physical process is indeterminate among opposed functions. This is like the projection of a curve from a finite sample of points: any choice has an incompatible competitor.

We have no doubt that the processes in a mechanical adding machine and in a personal computer are entirely physical. Addition cannot be identical with either of those physical processes because then it could not be done by the other. Suppose that addition is identical with a function among those processes. Then the processes would have to determine that function to the exclusion of every incompossible function. But they cannot do that, as the "quus," "grue," and "points-on-a-curve" examples show. So the machines cannot really add.

Secondly, opposed functions that are infinite (that is, are a "conversion" of an infinity of inputs into an infinity of outputs) can have finite sequences, as large as you like, of coincident outputs; they can even have subsequences that are infinitely long and not different (e.g., functions that operate "the same" on even numbers but differently on odd numbers). So for a machine process to be fully determinate, every output for a function would have to occur. For an infinite function, that is impossible. The machine cannot physically do everything it actually does and also do everything it might have done.13 That is the heart of the matter. The physical, as process, is formally vague, no matter how far you extend it, or how minutely you describe its innermost mechanisms. The conclusion is that a physical process cannot realize an abstract function. It can at most simulate it.

What Happened to Nature? Do natural processes, say, the behavior of a freely falling body, not realize pure functions like "d = 1/2gt" and, where g = 32, "d = 16t"? And is it not true that an object in empty space decreases in length in the direction it is traveling by an amount equal to √(1 – v^2/c^2) There are two reasons why such processes do not realize pure abstract functions of the sorts mentioned, only the second being relevant to the present discussion. First, these laws apply by idealization. What is "the direction" in which the object is traveling? There are no "point masses." That is an idealization, as is its rest mass (say, for photons or neutrinos, which are always moving at C). No object falling to earth is in a vacuum and under no gravitational attraction to other bodies. Physical phenomena often come close to our mathematizations which, of course, are invented to represent them. But those mathematizations are idealizations.14 That the laws are idealizations does not affect the present point.

The kind of indeterminacy I am talking about is different from that. For the incompossible functions are equally idealizations, and may differ only logically because the "manifestation phenomena" lie beyond the actual (it being presupposed that all the actual phenomena accord with each function). So it is not a consequence of this account that there are no general and mathematizable laws of nature. Rather, just because there are general and mathematizable regularities, an object falling to the earth "in a vacuum" satisfies some incompossible function just as well as it satisfies "d = 1/2gt." That is a consequence of the underdetermination arguments.

Now, to accept the overall argument, one does not need to deny that there are definite natural structures, like benzene rings, carbon crystals, or the structural (and behavior-explaining) molecular differences among procaine, novocaine, and cocaine. These are real structures realized in many things, but their descriptions include the sort of matter (atoms or molecules) as well as the "dynamic arrangement." They are not pure functions.15

A musical score, say, Mahler's 2nd Symphony, can be regarded as an analog computer that determines, from any given initial sound, the successive relative sounds and their relative lengths (within conventions of intervals and length), and thus is a function from initial sound onto successor sounds; yet, from the sounds (a performance) there is not a unique score determined among incompossible ones, except by convention. So, too, when we abstract the formal structure, without matter, the physical thing (cell, molecule, gene, enzyme) or process will satisfy a logically incompossible structure just as well.

III. RETREAT FROM PEOPLE

So, to avoid the argument, someone will say:

We do not really add, either; we just simulate addition. Pure addition is just as much an idealization as E = mc^2. Of course, we can define such pure functions but cannot realize them; that is just a case of the many functions we can define which cannot be computed by any finite automation, or any other computer either. In a word, the fact that there is no pure addition and no pure conjunction or modus ponens is no odder than the fact that there are no perfect triangles.

We cannot really add, conjoin, or do modus ponens? Now that is expensive. In fact, the cost of saying we only simulate the pure functions is astronomical. For in order to maintain that the processes are basically material, the philosopher has to deny outright that we do the very things we had claimed all along that we do. Yet our doing these things is essential to the reliability of our reasoning. Moreover, we certainly can, Platonistically, define the ideal functions, otherwise we cannot say definitely what we cannot do. That exposes a contradiction in the denial that we can think in pure functions, however; for to define such a function is to think in a form that is not indeterminate among incompossible forms. To become convinced that I can only simulate the recognition that two Euclidean right triangles with equal sides are congruent, I have to judge negatively with all the determinateness that has just been denied. Each Platonistic definition of one of the processes, and each description of the content of logical or arithmetical judgment, is as definite a form of thought as any of the processes being denied; and each judgment that we do not do such and such a function is as definite in form as is conjunction, addition, or any of the judgments that are challenged; otherwise, what is denied would be indeterminate. It is implausible enough to say we do not really add or conjoin. It is beyond credibility to say we cannot definitely deny that we add, conjoin, assert the congruence of triangles, or define particular functions, like conjunction.

The final and greatest cost of insisting that our judgments are not more determinate as to pure functions than physical processes can be, is that we can do nothing logical at all, and no pure mathematics either. Now, who believes that?

There is not some parallel evidential indeterminacy between our activities and those of a machine whereby we cannot be sure what either is doing.16 The machine cannot in principle add. We can be sure of that. And we can, and do add, and conjoin and reason syllogistically. We can be sure of that, too.

Someone rejoins, "So you say. But we might be just simulating." The rejoinder defeats itself. By its presumption, it grants the force of the argument as a whole, that there are pure functions and that, if certain thought processes were physical processes or functions among them, they would not be formally determinate. It merely asserts as a counterpossibility that I may think I am adding, etc., when I am only simulating a pure function. But to think I am adding or conjoining, with a clear idea of what that is, is to perform a pure function in that very thought, whether it is true or not.

Besides, such counterpossibilities require an ontological status for the pure functions simulated. We think of them and even define them. If that is so, then the thoughts and definitions cannot be indeterminate among incompatible functions because no definite function would then be defined by such thinking. So those function-determining thoughts cannot themselves be just simulations but have to realize pure functions, e.g., "defining addition," "conceiving modus ponens. "Hence, in order to be mistaken in a certain way, I have to think in exactly the way that cannot be entirely physically realized.

To say we may not know whether we are adding, when we are, or squaring, when we are, is actually to grant that we might perform the determinate thought function that cannot be wholly physical, and thus to grant the whole argument. Similarly, to say, "We do not know whether we ever perform a formally determinate function," is to say either (a) we are in a cognitive state, "uncertainty as to whether we are really adding, squaring, or conjoining," although we do not experience uncertainty, when we produce sums, squares, and simple arguments; or (b) we are always mistaken when we are certain we are adding, conjoining, etc., because at most we simulate.

Now, the first option also concedes the main argument because it postulates uncertainty when we actually do add, etc. The second postulates mistakes about what we are doing, and thus concedes the main argument, too: that there are such definite functions for which the only locus must be in thought. Any other answer will leave the pure function without any logical space (locus). When we are certain we are adding, we are always wrong. But that reasoning will hold for whatever we do. Thus, we are always wrong about what we think we are doing, when we think we are doing something definite enough to be a pure function. To suppose we can think definitely enough about functions to be wrong about what we are doing concedes the supposition of the argument again. Now the doubt has spread to include every pure function: asserting, questioning, objecting, stating, reporting, as well as adding, squaring, and conjoining. The doubt has even spread to include the very repeating of what I take, mistakenly, to be my argument and to make it indefinite whether you are actually denying or disputing my conclusion. Moreover, the cost extends to particular pure functions, specified by content: "adding three and three," “judging that Greeks are courageous," "doubting whether philosophy is scientific," "reading a paper," "thinking this writer is mad." Such an epidemic of doubt, without any effect on one's own certainty, must involve a mistake.

If we are always only simulating when we think we are doing something formally definite, then it is never determinate what we are doing at all. That requires that we are never doing such definite things at all. That is expensive, because there is no place for logic or mathematics or any other formal thinking at all; we cannot even "castle" in chess, but only "simulate" it, without any explanation for what "it" is or what its status is ontologically. Saint Augustine similarly objected to a "verisimilitude" account of truth in Contra Academicos. The relation of simulation will not be definable without the prior notion of pure functions.

If we can agree that either (1) we do have such definite thought processes as I described, cases of conjunction, determinate among all incompatible functions, and that they cannot wholly be physical processes (or functions among physical processes only), or (2) we never perform such processes but at most simulate them, then I am content. For I shall then wait for the counterattack to support (2), the one that explains the status of all those functions I cannot really perform and only think I can define (for to define one is to perform another one), and, in particular, explains the success of mathematics and pure logic, especially natural deduction systems and the proofs of completeness of propositional calculus, and offers a worked-out contrast between adding (which no one, apparently, can do) and simulating adding.

IV. FUNCTIONAL STATES

Kripke seemed to realize that functionalism would fail because "any concrete physical object can be viewed as an imperfect realization of many machine programs" (op. cit., pp. 36–7, n24). But it looks to me as if he was about to draw the wrong conclusion, when he said "taking a human organism as a concrete object, what is to tell us WHICH program he should be regarded as instantiating? In particular, does he compute 'plus' or 'quus'?" He should have concluded that, if a human is only a "concrete physical object," then nothing determines, at a certain level of refinement, which program it instantiates because it instantiates none; whereas humans do add, define, and so forth, and are thus not just concrete physical objects.

If a "thought process," say, adding, were a function linking actual physical states to "subsequent" physical states, then whatever the pattern of inputs to outputs, there are incompossible functions that link the states equally well. In that case, we could not really add. Nor could we deny that we add precisely. Since we can add, we know our thought process is not the same as any function among brain states because no such function is determined (the way two points determine a line) by physical states.

The very step toward generality to escape the inconveniences of identifying an abstract process with a particular physical process, say, mechanical addition (with the inconvenience that there could be no electronic addition), creates the situation where incompossible general functions equally well "explain" the succession of physico-cognitive states, and thus discloses that no one function is realized to the exclusion of all the others at the physical level, and thus no pure function is realized at all. That guarantees that functions among physical states (in a process) are not the thought states because there are no determinate functions realized among physical states, when the form of thought is determinate. No real process of adding is identical with any process that equally well realizes an incompossible function. Consequently, "adding" is not a physical process or function among physical states either. Besides, the functors in such functions are not physical either. For, of course, it is numbers we add, not numerals.

V. ALL THOUGHT IS ABSTRACT

The main argument is that some thought is determinate, among incompossible functions, the way no physical process, series of processes, or physically determined function among processes can be. The result is that such thought is never identical with any physical process or function. (Nor can it really be such a physical process or function either, though it may, for all we have said, have a material medium, like speech.)

The full generalization that all thought is determinate that way is harder to make cogent, because it rests on one's recognizing that, whatever thinking we do, whether simple assertion or hoping or wanting or intending (over the whole family of things each of those can be, according to its particular content on a particular occasion) is such that, in order to do that, we have to do what is the same for an infinity of other cases (sorted by content) that do not happen. For someone else might have thought or said or believed or felt the same in a way definite among incompossibles. So, any thinking at all is of general "form," just as is adding, conjoining, reasoning validly, and squaring.

By its nature, thinking has "other cases" and is therefore always of a definite form (which may not be articulable by us, as are mathematical and logical forms). Asserting (in any one of its senses) cannot be "halfway" between opposed forms; it would not be asserting then. And so on, for every form of thinking. But no physical process or sequence of processes or function among processes can be definite enough to realize ("pick out") just one, uniquely, among incompossible forms. Thus, no such process can be such thinking.

The conclusion is that no physical process or sequence of processes or function among physical processes can be adding, squaring, asserting, or any other thinking at all.17

JAMES ROSS
University of Pennsylvania

1 After three centuries of amazingly successful science, we do not have a successful explanation of animal cognition, not even for a spider or a fish. Probably, we have been misconceiving the project in ways that makes science both less productive and less helpful.

2 Thinking here means "judgmental understanding"––what Aristotle thought to be the actuality of the intellect (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"). There are many kinds of thinking; some thinkings are bodily doings, like my pouring a liquid. But it is only the processes of understanding that I am now trying to show cannot be wholly physical; understandings that involve feeling cannot be entirely nonphysical either, any more than my going for a walk can be a mere willing.

3 See Aristotle's argument (De Anima, bk. 111, ch. 4, 429a, 10–28; see also Aquinas's commentary in Aristotle's De Anima in the Version of William of Moerbeke and the Commentary of St. Thomas Aquinas, Kenelm Foster and Silvester Humphries, trans. (New Haven: Yale, 1959 repr.), sec. 684–6, pp. 406–7) that the understanding cannot have an organ as sight has the eye (and nowadays philosophers suppose thinking has the brain), because the limited physical states of an organ would fall short of the contrasting states of understanding that we know we can attain.

4 Philosophers should not recoil with distaste at such remarks about thought, because they attribute even odder features to propositions, e.g., being infinite in number, belonging to a tight logical network with formal features like "excluded middle," and being such that every one is determinately either logically related, by implication or exclusion, or logically independent of every other; in fact, in a system of material implication, no proposition is logically independent of any other.

5 But in part, yes, in the sense that my utterances are physical. Moreover, the thought may not even be possible apart from feeling or sense, just as a gesture is not possible without bodily movement. The target in this paper is theories that thoughts are "no more than" physical or functions determined physically; not that, for us, they are "at least physically realized."

6 I am not, of course, suggesting that a valid course of reasoning is not also a case of a variety of invalid forms, e.g., "P, therefore, C." But it must determinately be a case of some valid form.

7 Some conjunction tasks seem possible that are not: e.g., to conjoin all statements that can be expressed in English. That impossibility is not because of some fuzziness about the function "conjoin," but because the supposed totality is incoherent. You cannot add up all the even numbers, taken pairwise, just as you cannot conjoin all the sentences of English. See note 10.

8 We can even add certain nonterminating decimals, like .33333 and .66666 carrying from infinity to get 1. That is a form of understanding.

9 Equivalent but nonsynonymous functions would give the same arrays from inputs to outputs. Besides, a device that went to an address for the answer, and took it out in an envelope (encoded), which it did not open (decode) but handed to you (displayed for you to decode), could be made to produce the same array of outputs as addition. Yet it would not be adding. Besides, look at this function: 10 Z = X*X*X, 20 Print Z; 30 X = X + 1; 40 GOTO 10. That is a machine function for an endless loop to print the cube of every number beginning with zero. You can see that no matter what outputs the machine gives, it might have been doing something other than printing successive cubes, unless it produces all cubes––which cannot be done.

10 Postulating an infinity of cases will not suitably discriminate the functions that are the same for even numbers but differ for odd numbers after N. Postulating that "all" the cases are actual involves an incoherent totality, because the machine cannot both do all that it does and all that it might have done instead. Consequently, a pure function does not reduce to a pattern of inputs and outputs.

"All the additions" is as incoherent as "all the sets." So "what" addition is cannot be explained by "all the outcomes": rather, each and every outcome is determined by what addition is. It is impossible that all cases of addition be actual, even if infinities are performed because, even if we used up all the suitable numbers, the function itself would still be repeatable, say, for the same additions, but now done in a different order. The function cannot be exhausted by its cases, however many there are.

11 See "The New Riddle of Induction," in Fact, Fiction and Forecast, 2nd ed. (Indianapolis: Bobbs-Merrill, 1968), pp. 63-86.

12 Wittgenstein on Rules and Private Language (Cambridge: Harvard,
1982), p. 9. and passim.

l3 There is a complementary line of inquiry about immateriality. Christopher Cherniak argues (Minimal Rationality (Cambridge: MIT, 1986), p. 127) that because a physical object cannot be in an infinity of states, the mind treated as a brain computer is of limited understanding. That would be an understatement, were it true. Most of what actually happens would be unintelligible to us. An infinity of English sentences would be unintelligible, as would "most" truths of arithmetic.

For even if each of the finite number of electrochemical states the brain is capable of realizing actually happened, say, 10140 different thoughts, there would be an infinity of mathematical theorems we could not even understand because there would be no brain state or function among brain states to realize them.

The opposite seems to be true: there is nothing that is in principle unintelligible insofar as it has being, as Plato and Aristotle both thought. And we are able to be in an infinity of states of understanding, not successively but qualitatively. That is, we have the active ability to understand anything (accidents of presentation and of intelligence quotient being ignored for now). Thus, there is no arithmetical theorem we cannot understand, accidents ignored for now. Nor are there any well-formed utterances of any of the conjectured 10,000 human languages (most now lost) that we would not understand in the appropriate circumstances. But any one of those languages would require more than all the brain states. Brain states would have to be vehicles for varying content, perhaps media for thought and not the same thing.

Nothing is excluded because of its subject matter. Ours is not a successive infinite capacity (if we do not exist forever) but a selective infinite capacity. That is why the brain cannot even be the organ of thought, the way the eye is the organ of sight, as Aristotle, Avicenna, Averroes, Aquinas, and many others argued; otherwise, there would be something (that might be actually) that is unintelligible. Our corporeality imposes accidental limitations on understanding, the most important of which is that our contents of judgment have to be made by dematerialization (abstraction) and our intelligence cannot directly access immaterial being (e.g., angels or God). One consequence is the indeterminacy of contingent truth (see note 17).

How the dematerialization involved in our understanding something as shape (without consideration of which thing it is, or of its particular material composition) or our understanding something as in being (without consideration of its being material) could even come about is totally beyond the resources of any known experimental or formal science.

l4 See Nancy Cartwright, How the Laws of Physics Lie (New York: Oxford, 1983); and Ian Hacking, Representing and Intervening (New York: Cambridge, 1983).

l5 General natures (e.g., structural steel) do "have" abstract forms, but are not "pure functions." Two humans, proteins, or cells are the same, not by realizing the same abstract form, but by a structure "solid" with each individual (but not satisfactorily described without resort to atomic components) that does not differ, as to structure or components, from other individuals. There can be mathematical abstractions of those structures, many of which we can already formulate (cf. Scientific Tables (Basel: CIBA-GEIGY, 1970)).

l6 I think Kripke (op. cit., pp. 21, 65, and 71) interprets what he regards as indeterminacy as to whether I meant plus or quus as the basis for alleging an indeterminacy about what I do. ("There is no fact of the matter.") I say this gets the explanatory order backward and invites mistaken conclusions.

l7 All thought, as content, is immaterial in two other ways. (1) It lacks the transcendent determinacy of the physical. A true judgment, "someone is knocking on my door," requires for its physical compliant reality a situation with an infinity of features not contained (or logically implied) in the true judgment. Thus, an infinity of determinate but incompossible physical situations could make the same statement true. (2) Any physical-object truth requires its truth-making reality to overflow the thought infinitely in the detail of what obtains. So every compliant reality is infinitely more definite then anything contingently true we can say about it. It takes a lakeful of reality for one drop of truth.

A second argument: Products of physical processes are transcendently determinate. But no product of the understanding has an infinity of content, not contained therein logically. So no physical product can ever be such a content of the understanding.

Some thinking is as much physical as it is immaterial. My walking, as an action, is as much a mode of thought as it is a mode of movement; yet no movement, however complex, could ever make a thought.

Leibniz says in section 17 of the Monadology (in Philosophical Papers and Letters, Leroy Loemker, ed. and trans. 2nd ed. (Dordrecht: Reidel, 1969), p. 644) that, if perception were supposed to be produced by a machine, we could make the machine on large scale and walk around in it like a mill; we would never find a perception, only the movements of wheels, gears, and pulleys. Similar reasoning is given in Leibniz's Conversation of Philarete and Ariste (Loemker, p. 623). I thank Margaret Wilson for pointing these passages out to me.

A third argument: The present cases concern the definiteness of the form of the thinking. A third, parallel argument can be constructed from the definiteness of the content of thought, that thought is definite among incompossible contents in a way no physical process can ever be. Similar underdetermination arguments apply.

Machines do not process numbers (though we do); they process representations (signals). Since addition is a process applicable only to numbers, machines do not add. And so on for statements, musical themes, novels, plays, and arguments.

Science is, is not…

“Science is the new religion, and healthcare one of its greatest gods. I live my life under the unsleeping benevolence of Science and show my pious devotion by supporting its advancement and perfection the world over. But at times I fall ill, incurring the wrath of my lower, prescientific inheritance and the wild assaults of a yet unbridled Nature. But I am not afraid. For all I must do is enter the medical temple nearest me, pay my offering to the god of the Healthcare System, and receive ablutions and counsel from the high priests in the scrubs and white coats. They invoke the powers of Science on my behalf and I consume the concoctions of deep wisdom. In time, all is set right within me. I am one with the Laws of Nature. If the Healthcare System fails some, which I admit having heard of, blasphemous as the idea sounds, it is only because Nature has not yet deigned to disclose her deeper secrets and our high priests are not yet pure enough to pierce of veil of Science to behold the naked face of Nature. But in time a great Savior, an all encompassing and absolutely simple Theory, will come––it has been prophesied! And then the ancient art of Prediction shall be complete––nay, obsolete, for the Theory will expose Nature's innermost essence as one unified harmony, in which prediction will be redundant because axiomatic!”

Desensitize to legitimize, and vice versa…

“Did you ever think it's the only time I'm brave enough, or maybe just unpreposssed enough, to ask these kind of questions?”

“Sure, I can see that. But did you ever think that when you ask those kind of questions has something, maybe everything, to do with why you ask those questions?”

“What do you mean?”

“Well, I mean, logically speaking, the occasion for your asking such questions is coextensive with you asking those questions.”

“Huh?”

“Again, logically speaking, I mean that the times you ask such questions is at least materially equivalent to your asking the questions.”

“Kay. So?”

“You have no way of asking questions like you do unless you also have an occasion, a suitable span of time, in which to pose the questions to yourself. So if you remove the occasions for asking the questions, you remove the asking of the questions. Don't make time for the questions, so to speak, and you won't make the questions.”

“But you're just telling me not to ask the questions. But my whole point is that maybe I only let them rise to the surface on those occasions. Not making time for them doesn't mean I don't still have them brewing, lurking, inside. So why can't I at least have times to ask myself questions like that?”

“My point is not that you shouldn't give vent to the questions, but maybe instead that the act of making time for them––setting up a stage for them, if you will––is just the reason you have the questions in the first place. What if they are just artificial effects of the times you get like that?”

“But don't my questions have validity in their own right? I mean, if I normally raised them, under normal circumstances, at normal, calmer times, wouldn't they still demand answers, or at least pondering?”

“Fair enough. But my point is that that's too hypothetical given what we know about your consistent behavior. I didn't say the questions only arise when you are like that, you did!”

“Well, yes, it's true, I only feel them, or face them, I guess, at those times, but that just tells me I normally don't face them.”

“But you don't like the questions, so if they normally don't bother you, isn't the deeper problem that you put yourself into situations, into a state of mind, that basically confabulates questions, questions which you would normally, and in a clearer state of mind, wouldn't give a hearing? If you remove the cause, you thereby remove the effects. And it seems to the questions are just effects of the cause, of you bringing yourself into that state of mind. The only reason you give them a hearing at all, perhaps, is because you get far enough from your normal self that you can't resist the absurd quandries you pose to yourself.”

“Yeah, but what about other people, like atheists and skeptics and nonbelievers, who have the same questions in a normal, clear state of mind? Are you saying they are habitually displaying an unhealthy state of mind just by raising such worries about our faith?”

“Why not? It's just a cultural bias in favor of Freudian suspicion that we think letting out perverse inner impulses is a sign of health. Supposedly, if every time a man is on drugs he starts pondering suicide, he is doing himself a small form of therapy, of catharsis. But if he began pondering suicide without drugs, we'd instantly recognize it as a mental imbalance. So why give vent to perverse worries in one state of mind, pretending they are healthy releases, when in a different state of mind you'd recognize them as absurd and neurotic?”

“So are you really saying atheists and the like are habitually neurotic about religion?”

“Like I said, why not? If you drink and start wildly criticizing your boss and loathing your job's very existence in society because of the stress and faitgue they give you, but when you're sober you just take the stress in stride, as countless people do every day, then why should you legitimize the pessimism under a cloak of alcoholic catharsis? I can't help but pose the same kind of question about your religious worries at times like those. If it's reckless and negligent to allow a man to stoke the flames of his rage or depression my drinking and taking drugs to the point that they bleed into his mind when he's sober and clean, then how much more reckless and naïve is it to pat skeptical scruples on the head just because they've escaped the bonds of alcoholic melancholy and paranoia and become a respectable dimension of our modern society?”

“You're mad. Everyone's entitled to their own opinions.”

“Look who's talking! And that's just your opinion anyway, haha. If an otherwise good man wants to abandon his family for an illusion of freedom every time he gets drunk, then how can we condone the same desire on his part when he's sober? I can't help but see much difference between that and the established paranoia of atheism. When a man at a pub mounts his mug of tears and begins decrying the goodness and value of the world, and goes on to accuse God of great failure, we just tell him to go home and sleep it off. But when a sober man undermines the goodness of God and the world in the same way in a philosophical journal, we give him an honorary degree. A bit odd, don't you think?”

“You should have been born in the Middle Ages. We live in a pluralistic society now. Things aren't so black and white anymore.”

“I enjoy Youtube too much to have been born in the Middle Ages. You're right that we live in a pluralistic society, but that's hardly an argument for it as such. Pluralism might entail the establishment of a drunkard's society, but in a healthy society, it would be quickly abolished due to harm an organized, condoned society of walking drunks poses to society at large. Why can't we raise the same objection to irreligion based on the harm it poses to society?”

“What harm? At least no one is burned at the stake anymore these days.”

“Well, no, no one who escapes the womb in time, you're right. But the harm I'm talking about has to do with the undermining of a collective sense of brotherhood and unity based on an awareness of the transcendent fatherhood and unity of God as the one Maker of all. Once you start fracturing the unity of the heavens, the stability of the earth follows in little time. In any case, we've gotten away from the original point, which is about you.”

“What about me?”

“If you recognize that the questions in question, heheh, undermine your own inner peace and more basic sense of well-being in the world, then don't you owe it to yourself to preempt the occasions for those questions? Your state of mind at those times just infects you with despair, and it's a kind of moral duty to yourself to weed out the seeds of despair. My larger point is just that we might owe it to our neighbors as much as we owe it to ourselves to see the seeds of despair for what they are: worries stirred up by unhealthy consumption. If what you do to yourself is wrong because it undermines your well-being, like slow suicide by gas leaking in, then it seems just as wrong to legitimize and applaud collective efforts to undermine society's well-being by denying any ultimate or eternal value to its endeavors.”

“Yes, but…”

But…?

All at once or not at all?

[After reading this, please follow up with a related post for elaboration.]

According to special relativity (SR), there is no single, absolute frame of reference for all physical descriptions of phenomena. Literally, nothing happens all at the same time, since, in a bizarre sense, there is no single time. This means, to invoke a common illustration, that what we are seeing "now" in the starry skies, actually portrays celestial happenings from millions of years ago. The stars' distant "now" is still "on its way" to become our very distant future picture of the heavens. As James Ross argues in his essay on the eschatological annihilation of the world in St. Thomas' writings, the world literally could not be destroyed "all at once," not even by God, since there is no "all at once" frame of time in which the act of total annihilation could occur.

This concept raises two interesting considerations for me at "present" (heheh). Or perhaps I should say it is a single consideration with two nested elements. First, it seems that acts of intellection defy SR precisely by "actualizing" truth in a physically exhaustive way, and thus "make true" certain things which hold at all points in spacetime, and thus "all at once," albeit not in a temporal manner. Second––perhaps as just a nested example of this, let us say, Scholastic qualification of SR––it seems our own grasp of SR demands it is in some way violated if SR is construed as a realist theory of science.

In the first case, consider what we call "timeless" truths, like analytic definitions and mathematical operations. By intellectually grasping that a bachelor is always and at every moment "an unmarried male," am I not actualizing something, namely, a truth proposition, which is true "all at once" everywhere throughout the cosmos? It seems an excessively high price to pay for SR as a total metaphysical principle to say that analytic truths are not true as such just because they can't be uttered or written "all at once" in material reality. Likewise, grasping that 2 + 2 makes 4 actualizes a truth which holds eternally (and/or-at-least "omnitemporally.") Probably the most vivid example of an intellectual truth which defies SR is SR itself! To wit, as a theoretical set of truths, or even as just a single proposition (e.g., "All frames of empirical reference are relative to the constant speed of light."), SR stipulates that its truth holds at all points––and therefore at all times––in the cosmos. So, our intellectual grasp of SR as true must hold for all of spacetime, or SR itself is untrue. This feature of intellectual operations indicates that such truths, while wholly real, are not strictly physical realities. Alternatively, we might say that if they are defined as physical realities, presumably on account of some deeper commitment to, say, physicalism, then SR is not a true description of reality, since it cannot account for intellectual operations which transcend its spatiotemporal strictures by their very universality. Or to phrase it more like Wolfgang Smith does in The Wisdom of Ancient Cosmology, because intellection is not something that happens in time, it is something that can and does happen throughout time. (As Thomas More argued, not being any-place is equivalent to being every-where.) The 'verticality' of intellection both frees it from the limits of 'horizontal' spacetime and frees it to the fullness of spacetime, much like a 3D agent can access multiple points of 2D space.

In any case, to turn to the second consideration above, let us consider what it means to say the things we observe "now" are not actually happening "now," but actually represent long-past celestial phenomena. This deflationary phenomenology, if I may call it such, contains a subtle self-contradiction as soon as it is made into a realist description of the natural world. For in the very act of denying that what science observes "now" is really what is happening "now" (i.e., in the physical parameters of the objects themselves), we are simultaneously (!) acknowledging at least that something-as-yet-unobserved is happening right now in the same moment in which we qualify our naive perceptions based on SR. In other words, by deflating the phenomenological authority of our perceptions of y at time t1, based on our theoretical awareness that the phenomena at t1 correspond to events at 'pre-time' t1-n, we are simultaneously positing, in place of t1's phenomena, some as-yet-unspecified (and empirically unspecifiable) set of events happening at t1 (which future ages would perceive at time t1+n). In other words, the very idea that unobservable natural events are really happening presupposes that they are happening at the same time we make that claim. The upshot is that to uphold SR as a realist theory of nature, is to admit that parts of reality can exist actually but non-empirically. It is not––and, according to SR, can never be––an empirical truth that "x is 'really' happening behind the phenomena observed at t1." It is an empirical truth that y is happening at t1, and it may be true that "x is really happening at t1" (as scientists at t1+n might verify), but this is not even in principle an empirical claim.

Interestingly, for the purposes of this post, at t1 two things in different frames of reference are true at the same time, namely, the reality of our SR-qualified phenomenology and the undergirding events actually happening as we formulate our SR-qualified claims. Further, these two things, although in vastly disparate temporal frames of reference, must be true at the same time. If x were not actually "what's happening" at t1, then our true, deflationary claims about observables (y) at t1 would not be true. In other words, if there were not something-other-than-what-we-observe-at-t1 (i.e., something-but-not-y) really and simultaneously occurring when we make our claims, then our claims would have no basis in reality. The paradox is that, in order to say that what we observe "now" is not "really" what is happening "now," our claim must be grounded by events which, ex hypothesi, have not even happened yet in "now"! If x were not actually happening when we employ it to deflate y, then our SR-deflations of y would not be true when we utter them at t1. We would have to suspend our SR-deflations of y until we had empirical confirmation of x at t1+n. And yet, in the very moment we invoke SR to deflate, we know it is true despite a lack of empirical backing at t1.

The solution I propose to this paradox is simply that the spatiotemporally transcendent powers of the intellect enable the dual nature of truth (as being in things and as being in the mind), to synthesize polytemporal realities into a single frame of reference. This would tie the second consideration back to the first. This is just a rough draft and I need to thinker more with this. …