Monday, October 31, 2011

Thinking about thinking about physics, part 2...

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In my introductory post of this series, I noted how Roger G. Newton is what I call a "chaste realist" (C.R.) and that, as such, his instinctive realism is at odds with his crypto-Kantian idealism. As I noted in the introductory post, Newton's thinking about physics is largely deflationary, in the sense that, at the end of the day, even the strangest scientific discoveries and theories can and should be reconciled as closely as possible with common sense (i.e. realism about the world and our knowledge of it). The following are informal characterizations, but I think they will make my basic point.

A C.R. is someone that, so to speak, wants realism to be true, but who is also aware of how far from reality scientific theories can be and are. Secretly, a C.R. knows science is on the right path and that normal science tells us important, lasting things about the real, mind-independent world. A C.R. cannot bring himself to subscribe to scientism, since he admits the ontological limitations of scientific claims are tied up with their origin in human cognition. C.R.s recognize that idealization, pragmatic selectivity, aesthetic bias, and so on, effect scientific paradigms, but they insist the general thrust of scientific inquiry tracks reality better than most, if not all other, methods of reasoning. On the other hand, a C.R. rejects constructivism and most of the non-progressive, anti-realist theory of science (as espoused by Duhem, Carnap. Hempel, Quine, Kuhn, Feyerabend, Van Fraassen, Giere, et al.). Scientific standards and conceptions may be relative to human "users" of science, but that does not entail the former are relativistic and fictional. In effect, C.R.s say to the regnant anti-realist regime in the philosophy of science, "If we promise not to claim too much for science as a 'truth engine', can we be allowed to accept scientific findings as 'true enough'?"

So, I'm calling Newton a chaste realist. I'll begin by noting his realism. First of all, Newton has i) ambitious aims for scientific explanation (Se). Se must not be mere description. For instance, Newton argues, even if we discovered that physical constants changed, as Paul Dirac and others have suggested based on the expansion of the universe, "we would still have to search for an underlying time-independent law that would account for the specific way in which these constants vary with time. Physics never regards history itself as a sufficient explanation of any fundamental change" (Thinking About Physics [TP], p. 10).

Likewise, ii) Se is about more than the pragmatic success of science. "What justifies our confidence in the basis soundness of the entire [scientific] structure," Newton writes, "is its coherence, an intellectual coherence that includes consistency with all the experiences and expectations founded on it, the fulfillment of precise, far-reaching predictions implied by it, and the functioning of all the technology built on its basis" (p. 19, my italics). Newton's claim contains a number of overly realist quantificational implications, which ultimately are at odds with the chastity of his realism, about which more later.

In any case, Newton continues with a point which strikes, wittingly or unwittingly, against a main pillar of the crude scientism prevalent in much of Western society, namely, the 'argument' that "Science Works, Bitch!" As Newton says, however, "[t]o point out that science works, in the sense that we readily watch television..., is, of course, the most banal of the answers we can give to those who question the truth of science... [though] it is an important component of the coherence of physics" (p. 19). These claims indicate how, for Newton, scientific truth is not merely a matter of technical success or "better living through science," but rather derives from the ambition of making sense of the world by way of science itself. Coherence, as Newton describes it in "the broad sense above... is the basis for claiming truth as the goal of physics-- not as an attainment, but as an aim" (p. 20). Lawrence Sklar, in Theory and Truth, makes almost exactly the same claim, so I hope to discuss both authors in tandem at some point.

Lest the above seem too theoretical, I should note that "the philosophy of science" is not Newton's focus. Rather, his focus is largely on how to reconcile the oddity of quantum theory (QT) with the mainstream of historical scientific claims. For instance, he denies that QT undermines good ole fashioned Newtonian determinism in the popular "spooky" way many people think, since "[q]uantum mechanics is as deterministic as classical mechanics" and that the truly weird things about QT--namely, entanglement--"originates in the wave-particle duality" (pp. 22-23). Indeed, "while part of what is meant by entanglement would obtain for any probabilistic theory... other parts [of QT] go further and are caused by phase correlations" (p. 23). Such entanglement, free of the wave-particle duality, does not strike us as odd for wave dynamics proper, so, as I mentioned in the introductory post, it is Newton's implicit aim to demystify the weirdness of QT by situating it in the larger context of physical statistics as such. A crucial premise in Newton's deflationary QT, is that "reality at the everyday level has to be distinguished from reality at the submicroscopic level" (p. 26).

This is a striking claim, and one with profound philosophical implications. Since, as always, my time is running short before I must head to class, I will close this post without getting any deeper into Newton's own claims in TP. In the next post I will connect Newton's premise about the macro-/microscopic cleft in reality (or the MMC) with its larger philosophical implications from an Aristotelian perspective (mainly by citing Wolfgang Smith's The Quantum Enigma and David Oderberg's Real Essentialism).

Stay tuned.

Saturday, October 22, 2011

Thinking about thinking about physics…

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The following are some observations derived from some of my recent reading materials, mainly Roger G. Newton's Thinking about Physics (TP), as well as Nick Huggett's Everywhere and Everywhen (EE).

The first thing to note is that Huggett's and Newton's approaches to "the philosophy of physics" are very similar, while their methods of exposition are very different. Both authors show a strong bias in favor of letting "normal science" reign over philosophizing about "science per se". For both authors, physical results can be dispositive of metaphysical questions. Newton plainly states in his preface that he will stick as close to physical data and methods as possible, but does defend metaphysics as the arena for honest disputes between intelligent people about those data and methods. At the end of nearly every chapter in EE, Huggett shows how physical discoveries can shed light (even decisive light) on classic philosophical queries.

Huggett's book is much broader than Newton's, and much more accessible to "the intelligent lay reader." Indeed, three or four times while reading EE, I realized Huggett had explained matters so well that it felt like the first time I had really grasped the issue, despite countless previous exposures on my part. Newton is also a very lucid writer, but, as he points out in the first sentence, TP is addressed to "readers with a good undergraduate education in physics", so, if, like me, you lack such an education, TP will be rough sledding. One deficit of EE, is its relative (!) lack of discussion of quantum mechanics, whereas TP discusses quantum theory in great detail. A good book to read in conjunction with TP, is Wolfgang Smith's The Quantum Enigma. Another good companion book is Lawrence Sklar's Theory and Truth, not the least because both authors qua "chaste realists" evince the same weaknesses in what I would call Kantian or critical realism.

It is in this vein that we can begin to discuss what I think is a substantive philosophical disparity between EE and TP. As a professional and highly awarded physicist, Newton is much more inclined to "let the physics do the thinking," as it were. In this way, he is very much a realist about scientific truth, since he writes as if we can read reality from the very face of science. His form of realism is, however, burdened by serious complications, which I shall discuss presently. Huggett, by contrast, is a professional philosopher with training in physics, and so he is much better at situating various physical questions in their broader philosophical context. Even so, Huggett strikes me as even more of a realist than Newton, and this, precisely in inverse proportion to their respective rejection of, or kinship with, Kantian idealism. Huggett locks horns with Kant on a few occasions to refute him in EE. As far as I can tell, Newton only refers to Kant once in TP, and dismissively, but certain statements he makes show how he is unwittingly a disciple of Kant, a connection which I shall also have to discuss later.

In any case, to focus on TP, Newton writes in his preface that he wants "to demystify quantum mechanics as much as possible." This is a key admission, since TP is very much a philosophically deflationary book. Time and again in TP, to philosophers of quantum reality, and physicists who would like to imagine they are philosophers of their trade, Newton effectively say, "Simmer down." Quantum theory (QT) tends to make people say and propose wacky theories, a tendency which Newton does not entirely gainsay, nor repudiate, but one that he insists can and should be toned down with a more reasonable interpretation of basic physics. His key tactic for demystifying QT, in express disagreement with Feynman and Heisenberg, is to shift focus from the particle as the most fundamental reality to the field as being most fundamental. It is only because people instinctively treat QT as a particle-based theory that QT seems to bizarre. An extension of this tactic is to undermine the crazy-making focus on indeterminacy in (Copenhagen-interpretation) QT, and treat quantum indeterminacy as just one mode of the larger, rather pedestrian issue of probabilistic physics altogether. Hearing that QT is indeterministic, Newton basically shrugs, and points out that so is, for example, classical thermodynamics. Get over it. Simmer down.

Now I want to begin discussing what I think are crucial defects in Newton's philosophical handling of his own beloved subject. I will have to bracket a discussion of Huggett for now, not only because this post is getting largish, but also because his book requires more codgitating (and a re-reading) on my part. In fact, since I need to go to class soon, I will leave this post as an introduction to the more detailed critiques to come.

Sunday, October 16, 2011

The halting halting halting halting halting halting…

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This an argument I think I devised while teaching this morning. I say I think I devised it, since it is still so tentative that I need to present what the strands to see if it is even an argument, or rather just an observation, sprung, like so much, from my endless ignorance.


I was thinking about the halting problem (HP) (I'll save you the click):

In computability theory, the halting problem can be stated as follows: Given a description of a computer program, decide whether the program finishes running or continues to run forever. This is equivalent to the problem of deciding, given a program and an input, whether the program will eventually halt when run with that input, or will run forever. Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist.

(Here is a delightful proof of the halting problem, for those of you seeking reading materials for your children.)

Now, here was my wondering:

Assuming that "the mind is the brain and the brain is a computer"––a thesis which I do not accept (cf. e.g. Schulman, Searle, Tallis, Dreyfus, Ross, Bougis, et al.)––, but for argument's sake, say that the thesis of the computational mind (TCM) is true.

If TCM is true, then there is nothing in the brain itself qua algorithmic engine, to halt its own computations. A stop would only come from outside influences, say, if all sensory input were blocked, or if so many portions of the brain were mangled that the brain simply shut down.

Which brings us to a second prong of the inquiry: the modularity of the mind (MoM).

I think that TCM nearly goes hand in hand with MoM these days, since it is a lemma of TCM that the "programmer" of the mind is blind natural selection, and therefore there is no "central programmer" for making a unified mind. This lemma is extended in research programs about the modality of the mind. What biological sub-systems still exist in the human nervous system and comprise the modular mind? Apart from the different lobes of the brain (visual, somatic, motor, etc.), there are also cognitive modules that are all vestiges of earlier cognizant organisms, and just happen to be confined in one space––the human cranium––by natural selection. The mind is a "kludge", as some would put it. The mind is actually just a quilt of neural-cognitive modules which have tended to increase reproductive success in humanoid populations over time.

Fine. We'll take TCM and MoM as true for the purpose of argument. What follows?

If the mind is the brain and the mind is a computer, then the mind:brain is subject to HP.

If the modules of the human brain:mind are themselves kids-of-minds by virtue of being algorithmic engines, differing from "the human brain" on in degree, then human neural-cognitive modules (hNCM) are subject to HP. This is modus ponens.

If, however, the brain, either as an agglomerate of hNCM or as any one hNCM, is subject to HP, it (or they) should never halt in any algorithmic state. hNCM do/does not, however, endlessly "fail to halt", therefore…. This modus tollens, but I must elaborate on some conditional conclusions.

Since human cognition does not endlessly fail-to-halt––otherwise, how do we perform any action?––, but our behavior is governed by hNCM, then something peculiar is happening in our mind:brain. Enter my hypothesis.

Even if we grant humans are governed wholly by hNCM, we can see why humans have free will. If each hNCM is its own little non-halting Turing machine (á la TCM), then none of them should ever halt in a concrete decision. Halting is a function of decidability, but purely algorithmic halting is undecidable. So, how does/do our hNCM ever halt? From MoM, we must treat each hNCM as an external environment to every other hNCM. It is because our hNCM mutually interact that they can halt in ways that produce our unified-modular behavior.

The upshot is that there is a radical indeterminacy in the total hNCM nexus known as our consciousness, yet one that does not generate simple randomness––and this is the basic meaning of free will: non-random indeterminacy. The competing pre-halting computations of our hNCM lead to a dynamic series of non-random but non-deterministic actions aka our selves. Interestingly, even research into the irrational biases of hNCM itself relies on a standard of rationality that surpasses those very biases: we are not determined by our modular biases, although our modular mind is wholly physically deterministic. Even the mind:brains of cognitive scientists defending TCM indicate the non-random, non-deterministic nature of human consciousness.

This is akin to Robert Kane's account of free will, in that at any moment of conscious decision (note that MoM-TCM accounts for unconscious decision processes), we are literally an indeterminate, yet wholly physical, complex of unhalted, unweighted decision variables. Once the mutual interference among hNCM generates a halting state which propagates non-centrally but uniformly through the mind:brain, we act freely. We act because hNCM halt; we act freely because there is nothing deterministic about hNCM qua computational algorithm engines. The understanding of chance qua the overlapping of otherwise disparate causal chains goes back to Aristotle, and it is that sense of indeterminate causality which I invoke here. We are free because––assuming TCM-MoM––there is an intrinsically indeterminate congeries of hNCM which could not function unless they mutually limited each other. A jumble of indeterminate rational engines produces a stream of rational action.

So, I propose that free will is intelligible even on a materialist account of the brain, and certainly intelligible on a non-materialist account of human existence. Regardless which ontology of persons is true, the doctrine of rational, human free will is true.

Various and sundry…

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Strive to learn at least one new prëmbil every day.

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Everyone is happy until they are not. Therefore, no one is happy. No one can be made unhappy if they are already truly unhappy. Therefore, everyone is happy.

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Telling yourself over and over again that "telling yourself something over and over again makes it true" doesn't make it true. Or so I am told.

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If time increases (or "slows") at higher speeds, and time increases in speed (or "flies"), when you're having fun, then having-fun is a slower activity, and therefore closer to the immobility of the divine.

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‎"The gravity at the CERN site where the neutrinos left, for example, is actually slightly greater than the gravity at the OPERA detector site. As a consequence, time would appear to move more slowly at CERN from the vantage point of the OPERA detector. Failing to take this into account, Contaldi contends, means that '[t]he resulting measurement that the neutrino velocity differs from c is not only unsurprising but should be expected in their setup.'"
–– cf. Gravity May Have Thrown Off Faster-Than-Light Neutrino Calculations - Forbes

“'From the perspective of the clock [on the GPS satellite], the detector is moving towards the source and consequently the distance travelled by the particles as observed from the clock is shorter….' Which is to say: it is shorter than the distance measured in the reference frame on the ground. [It seems] the OPERA team failed to take this into account––indeed, that they thought of the clocks as on the ground, not in orbit. Van Elburg argues once you take the changing distances between the GPS clocks and the neutrino detectors into account, it cancels out the 60 nanoseconds by which the neutrinos seemed to exceed the speed of light."

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Hilarous cuz it's verdicial. 

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Class, make sense of this prop. 

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"Sean Connery's best line ever." 

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"Haters gonna hate." 
"Never give up." 
Pick your caption. 

Friday, October 14, 2011

STR notes for future reference...

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I've read x about STR but not only still feel like I've read x minus x about it... and I also find it harder to grasp than GTR, which is odd, since the former is but a subset of the latter.

Notes on TSR...

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It doesn't seem to matter how much I ingest about STR, it's still a mindbender.

Part 2

~2:30 : Since all observers will see the same laws of physics hold, and since the speed of light (c) is a part of the laws of physics, all observers will see c the same, regardless of their state of motion. c is constant. In order to agree on the speed of light, observers may need to disagree about distance and time.

As I was trying to explain to my wife (my weakness, not hers), the reason classic relativity (CR) says object move with different speeds in different reference frames, is actual because the equations work only by keeping c constant. (That this was not known, but that the equations still worked, raises an interesting point about counterfactuals and scientific theory.) A pitcher P on a moving truck will see his pitched ball B move at 100mph, whereas an observer O of the truck-ball system TB would see the ball B moving at 150mph (cf. part 1 of video series). Since the time of measurement is the same for both P and O, and since c must remain constant, the speeds must rise as the relative distances increase. O is removed from TB to an extent that speed will rise in order to keep the ratio between distance and speed constant relative to c. P is closer to TB, so the speed decreases to preserve the c-ratio. In fact, P is "inside" TB so that he will detect no motion (unless he pitches B), which just means that as distance (between P and TB) shrinks to 0, the speed of B in TB shrinks to zero--all the while c is constant.

~7:00 : Reflected-photon clocks C1 and C2 would be precisely synchronized for an outside observer O. If C1 is stationary while C2 is in motion, O will see the time of C2 pass more slowly. why? Since both reflected-photon beams move at the same speed, and the moving clock C2 covers a farther distance than C1, the time of C2 must increase in order to keep c constant (despite other changes like increased distance).

Part 3

~1:30 : All the rulers aboard the moving ship S2 shrink just enough to keep c constant invariantly with respect to increased speed. Time dilation and length contraction.

I was trying to get length contraction clearer in my mind tonight, and here is what I thought of:

The faster object moves towards me, the faster its "trailing photons" will reach me relative to its "leading photons". In other words, when I observe a normal stationary ruler, with one end pointed at me, light from its front end reaches me at no discernibly different time than light from its rear end. But if it is moving at an appreciable fraction of the speed of light, photons from its front end will reach me at about the same time as photons from its back end, and thus it will appear that both ends are closer together (i.e. that the ruler is shrunken). I "understand" that this compression is not merely a result of my neural-observational limitations, but actually holds in a Lorentzian way (cf. Wiki). But what of non-Lorentzian relativity?

~3:30 : The faster you go through space, the slower you go through time. If you could travel at the speed of light in space, you would make no progress in time. If you could surpass c through space, you could travel back in time. If different observers must always agree on c, they must disagree on time and distance.

~5:15 : There is no single time or space on which everyone can agree. [Thus, unless the universe transcends space and time, there is no universe. There is a universe, however, in which c is constant. Therefore the universe as known by humans transcends space and time.] Velocity depends on distance (viz. from which frame of reference it is observed, i.e. how far from its center it is clocked), and time depends on velocity (viz., as velocity increases, time decreases, and distance increases). What is observed far apart in space, appears near in time. What is observed near in space, appears far apart in time (relative to something farther away).

~6:30 : The faster a particle goes, the heavier it goes. In order to maintain acceleration, as mass increases, energy must increase. E = mc^2. Once again, c must remain constant. In a given time, an object's velocity depends on the energy given to its mass.

Part 4

~0:20 : Einstein's STR says that an observer at a constant velocity Ov will observe the same laws of physics as an observer at rest Or. [I think "at rest" here could only mean "an observer moving at the speed of light (Ol). Cf. Einstein's scenario of sitting on a photon.]

~1:55 : Einstein argued that there's no way to tell a difference between being stationary under the influence of gravity versus being accelerated through space. Hence, given the universality of the laws of physics, the laws of gravity must be equivalent to (i.e. transformable into) the laws of acceleration through space.


Basic maths for time dilation

γ = 1/√(1 - (v2/c2))

This helps me make sense of the "substantial fraction of the speed of light" condition (i.e. the focus on "motion at relativistic speeds"). As v increases, the ratio of v2/c2 nears 0, and the divisor under 1 therefore nears 0, which would make γ into an increasingly large (and potentially infinite) amount. In turn, as γ increases, Δt' decreases. As observed time (t') decreases, time "flows more slowly". Time dilation at relativistic.


Time dilation with Dr Wittman

~0:00 : "Moving clocks run slowly and moving things contract in the direction of their motion. Those are two of the amazing conclusions of special relativity."

~ 2:30 : "We have to measure the same speed of light, even if the clock is moving. ... Let's see if it can get to the top of that clock." The faster the photon clock moves, the less distance it travels inside the apparatus, and therefore the less time it traverses. "Moving clocks go slower."

~ 4:05 : γ = c(1/√(1 - (v2/c2))

So as speed increases, time increases and length decreases. Anything beyond the speed of light would be eternal and sub-spatial (i.e. immaterial). And you're telling me natural theology is dead??

~6:30 : In order for the truck driver to maintain c, he must measure "our" v as vγ.

Thursday, October 13, 2011

How the future shapes the past…

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1. Retrodictively

2. Counterfactually (Retrodictively*)

3. Spatiotemporally

4. Ethically

In more detail…

1. Cf. Aristotle and Diodorus on the master argument.

What happens tomorrow makes true or false what you say today.

2. Cf. Nick Huggett's Everywhere and Everywhen, Hempel's theories, Musser's Scientific American article on free will, etc.

I think Musser's invocation of the block universe to explain retroaction is probably fallacious. I'd have to re-read the article, but the problem basically is this: the whole point of the (Minkowskian) block universe is that time is static, and therefore it's illicit to say action a at time t', after time ti, alters the conditions for action C(A) at time t. In a block universe, nothing changes.

Even so, it is not all that startling a claim that we can alter prior conditions. It is a possible property of our universe at time t-alpha (the putative origin of spacetime as we know it) that from the initial conditions Ci, there will occur X number of sandwich-eatings. It is also a possible property of the universe at time t-alpha that it will contain X' number of sandwich-eating events. If tomorrow I eat a sandwich, and then at some time t-omega the universe ends and the sandwich-eatings are tallied, I'll have brought the number to X. If, however, I don't eat a sandwich, the number will end up as X'. So whatever I do , I will decide a property of the universe at time-alpha, even though I am vastly far removed from it in spacetime.

His point about the impossibility of copying oneself, due to quantum indeterminacy, was, however, extremely apt. Down with Moravec! Down with Kurzweil! The singularity will not be televised!

Further, in any case, there is this worry: if a natural law's "authority" is based on its holding good at all times (i.e. ∃x∀t(Lx(t))), then a law can only said to be lawful if it holds at all times including all future times. Therefore, a law's putative lawfulness depends now on its holding-good at any and all future times. So a law's present status depends on future conditions.

In addition, Huggett discusses how a (hypothetical) future state of affairs (SoA), accessible by a time machine, would render certain SoA in the present impossible. E.g., my going into the time portal now at time t would be rendered impossible by my future self's persuading my past self not to enter the time portal at time t–x. Likewise, my entering the time portal in a red T-shirt at t would be rendered impossible by my future self deciding and succeeding to prevent my past-self-in-a-red-T-shirt from entering the time portal at t–1.

3. Some of what makes STR true is the general theory of relativity (GTR), but what makes GTR true is the total state of the cosmos at any formulation or enunciation of GTR. Thus, the truth of GTR depends on factors in the universe to which STR says no one can have access. In other words, we know GTR is true because it extends to the STR-relative states of the universe anywhere, but knowing GTR is true in that way transcends the limits STR says we cannot transcend. To be more precise, GTR's truth-being-made depends on factors operant in the cosmos even at times beyond which we could possibly observe. On earth we never see the sun immediately (without telescopes, etc.), but are always seeing it as it was about eight minutes earlier. This means the sun's current SoA is in the future relative to us. The same holds for cosmic factors even farther removed than the sun. GTR is true in the present based on the operant actuality of future phenomena.

4. What I do now can easily be modulated or negated by its impact on the future. Being green, for example, has (perhaps) everything to do with being ethically responsible towards our progeny (i.e. towards the future as an ethical condition on the present).

Wednesday, October 12, 2011

And now back to our regularly scheduled programming…

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If whatever (B) happens actually only happens at times (t(n-1) + t(n-2) + … t (n-k)), then nothing happens at time t (i.e. ~∃x(Bx(t)). If no-thing happens at time t (i.e. ~∀x(Bx(t))), then nothing ever happens. If it is granted that "what happens at t" is B itself, then perdurantism is false. Otherwise, if there is no B, then there is no sense in speaking of parts of B.

The canonical example for (but really just "in") perdurantism qua entailment of the theory of special relativity (TSR), is a train collision, or mutatis mutandis a train passing a station. The point is supposed to be that there is no unique time in which "the train T passes the station S", rather that there are only time slices which correspond to relative observations. If so, then those observation-slices are themselves divisible into "smaller" slices, and don't exist in their own right. If it is granted that observation is instantaneous, then we're getting all Thomistic.

What is a "unique" time? There is no "singly valid" (unique) observational standpoint on perdurantism, so, by extension, there is no singly valid (unique) event. That is fallacious, however. Chalk it up to my abiding worries about woebegone simultaneity and truth-makers as a metaphysical family secret. Plus my profound dissatisfaction with perdurantist (ethical, logical, etc.) entailments.

∃ is {& exist;}
∀ is {& forall;}
↔ is {& harr;}
≡ is {& equiv;}
∴ is {& there4;}
□ is {& #9633;}
◊ is shift+alt/option v (auf 'ner deutschen Tastatur) or ◊ {& loz;}
∩ {& #x2229;} (Where members of set X are members of A both and B.)
U is… U (Where members of set X are members of either A or B.)

Why I like perdurantism…

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Regular readers might be surprised by this post's title, since I've made it no secret how antagonistic I am to perdurantism (i.e., the metaphysical doctrine that object do not exist wholly at any given time, but are in fact comprised of innumerable time slices for each segment of the spacetime manifold). I have ethical, logical, and metaphysical objections to perdurantism, which I have voiced at FCA in a few posts, but tonight I will voice one thing the theory has going for it in my eyes.

The good thing about perdurantism is that it makes some of the hardest doctrines of Christianity quite reasonable. Note: this does not mean that the latter is so wedded to the former that a disproof of the former entails a rejection of the latter, but it does mean that the authority of the latter might give tremendous metaphysical weight to the former by making "more" intelligible some of the latter. 

Here's an example of the perdurantist-Christian alliance (PCA): if perdurantism is true, not only is Adam literally continuant in all of us, but also no one has ever died. In one swoop, PCA has secured both the literal headship of Adam, and thus the transmission of original injustice to all humans, and the immortality of humans. In the first instance, because Adam is just a "compilation" of his spatiotemporal time-slices, which include all the atoms and subatomic "particles" in any slice, then not all of Adam's atoms have disappeared in the cosmos, and are thus still perduranistically interwoven with all other humans. If at time t, Adam had a physical stature of {t,x,y,z}––which object we shall label A({t,x,y,z})––, then at time t* (say, fifty years later), due to natural growth and muscular development, Adam had a stature of {t*,x*,y*,z*}––the Adam we shall label as A({t*,x*,y*,z*}).

On perdurantism, there is a literal continuity between A({t,x,y,z}) and A({t*,x*,y*,z*}). Just because A({t*,x*,y*,z*})'s bicep's muscular tissues was {x,y,z}mm farther from his humerus than the bicep tissue of A({t,x,y,z}), does not mean they are not members of the same meta-Adam A({t_,x_,y_,z_}). By extension (!), therefore, just because the numerous components of A({t_,x_,y_,z_})'s tissue are now––at time t(p)––farther removed from each other than they were at t or t*, does not mean there is no longer A({t_,x_,y_,z_}). Indeed, it is precisely because A({t_,x_,y_,z_})'s components have "gone into" making his numerous progeny that A({t_,x_,y_,z_}) is still literally a member of our causal nexus. Adam is just as fully present in me as he was in any of his other spatiotemporal configurations (A({t:,x:,y:,z:}). 

Now it is time to make space for the matter (!) of human immortality (HI) under the PCA. Fortunately, from the above, HI falls out quite obviously. If Adam persists in "us" (qua variegated pragmatic configurations of A({t_,x_,y_,z_})), then it follows that each of us (P({t_,x_,y_,z_})) persists throughout the span of the cosmos, despite how dispersed, contracted, agglutinated, or reduced we become. 

Wednesday, October 5, 2011

Logical updates…

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Good to know, for HTML, at least: 

∃ is {& exist;}
∀ is {& forall;}
↔ is {& harr;}
≡ is {& equiv;}
∴ is {& there4;}
□ is {& #9633;}
◊ is shift+alt/option v (auf 'ner deutschen Tastatur) or ◊ {& loz;}
∩ {& #x2229;} (Where members of set X are members of A both and B.)
U is… U (Where members of set X are members of either A or B.)

[Remove space between & and the sequalia.]

Here are my poor man's HTML-free stabs at it…

$x : there is an x
A*x : for all x
<--> : iff
=* : means, is semantically entailed by
‹› : it is contingent that
[] : it is necessary that
Ω* : intersection of
∆· : therefore

All of these only work (or work best) on a German keyboard (as I have set on my Mac).

So, let's try this again…

For : "Every dog (Dx) is loved by (Lyx) at least one man (My). herefore, at least one man loves every dog (~∀y∃x(~∃x~Lyx)) loves every dog (Dx)." 

Valid or invalid? Show your work!

~(Dx --> ($y(My ^ Lyx)) ^ --> (A*x$x(Dx ^ My ^ Lyx)))