Paul P. Mealing

Check out my book, ELVENE. Available as e-book and as paperback (print on demand, POD). 2 Reviews: here. Also this promotional Q&A on-line.

Friday, 23 July 2010

The enigma we call time

The June 2010 edition of Scientific American had an article called Is Time an Illusion? The article was written by Craig Callendar, who is a ‘philosophy professor at the University of California, San Diego’, and explains how 20th Century physics has all but explained time away. In fact, according to him, some scientists believe it has. It reminds me of how many scientists believe that free will and consciousness have been explained away as well, or, if not, then the terms have passed their use-by-date. I once had a brief correspondence with Peter Watson who wrote A Terrible Beauty, an extraordinarily well-researched and well-written book that attempts to cover the great minds and great ideas of the 20th Century, mostly in art and science, rather than politics and history. He contended that words like imagination and mind were no longer meaningful because they referred to an inner state of which we have no real understanding. He effectively argued that everything we contemplate as ‘internal’ is really dependent on our ‘external’ world, including the language we used to express it. But I’m getting off the track before I’ve even started. My point is that time, like consciousness and free will, and even imagination, are all experiences that we all have, which makes them as real as any empirically derived quantity that we know.

But isn’t time an empirically derived quantity as well? Well, that’s effectively the subject of Callendar’s essay. Attempts to rewrite Einstein’s theory of general relativity (gravity) in the same form as electromagnetism, as John Wheeler and Bryce De-Witt did in the late 1960s, resulted in an equation where time (denoted as t) simply disappeared. As Callendar explains, time is the real stumbling block to any attempt at a theory for quantum gravity, which attempts to combine quantum mechanics with Einstein’s general relativity. According to the theory of relativity, time is completely dependent on the observer, where the perceived sequence of events can differ from one observer to another depending on their relative positions and velocities, though causality is always conserved. On the other hand, quantum mechanics, through entanglement, can defy Einstein’s equations altogether (see my post on Entanglement, Jan 2010).

But let’s start with our experience of time, since it entails our entire life, from the moment we start storing memories up to our death. And this storing of memories is a crucial point, otherwise we’d have no sense of time at all, no sense of past or future, just a continuous present. Oliver Sacks, in his book, The Man Who Mistook his Wife for a Hat, tells the story of a man who suffered retrograde amnesia (The lost mariner) through excessive alcoholism, and in the 1970s when Sacks met him, still thought he was living in 1949 or thereabouts when he left the navy after WW2. The man was unable to create new memories so that he was effectively stuck in time, at least psychologically.

Kant famously argued in his Critique of Pure Reason, that both time and space were projections of the human mind. Personally, I always had a problem with Kant’s thesis on this subject, because I contend that both time and space exist independently of the human mind. In fact, they are the very fabric of the universe, but I’m getting ahead of myself again.

Without memory we would have no sense of the past and without imagination, no sense of the future. Brian Boyd, in his book The Origin of Stories (see my review called Storytelling, July 2009) referenced neurological evidence to explain how we use the same parts of the brain when we envisage the past as we do when we envisage the future. In both cases, we create the scenario in our mind, so how do we tell the difference?

Raymond Tallis, who writes a regular column in Philosophy Now (Tallis in Wonderland), wrote a very insightful essay in the April/May 2010 edition (the Is God really Dead? issue) ‘on the true mystery of memory’, where he explains the fundamental difference between memory in humans and memory in computers. It is impossible for me to do justice to such a brilliant essay, but effectively he questions how does the neuron or neurons, that supposedly store the memory, know or tell us when the memory was made in a temporal sense, even though it is something that we all intuitively sense. On the other hand, memory in a computer simply has a date and time stamp on it, a label in effect, but is otherwise physically identical to when it was created.

In the case of the brain, it’s in the hippocampus, where long term memories are generated, new neurons are created when something eventful happens which ties events together. Long term memory is facilitated by association, and so is learning, which is why analogies and metaphors are so useful for comprehending new knowledge, but I’m getting off the track again.

The human brain, and any other brain, one expects, recreates the memory in our imagination so that it’s not always accurate and certainly lacks photographic detail, but somehow conjures up a sense of past, even distance in time. Why are we able to distinguish this from an imaginary scenario that has never actually happened? Of course we can’t always, and false memories have been clinically demonstrated to occur.

Have you ever noticed that in dreams (see previous post), we experience a continuous present? Our dreams never have a history and never a future, they just happen, and often morph into a new scenario in such a way that any dislocation in time is not even registered, except when we wake up and try to recall them. Sometimes in a dream, I have a sense of memory attached to it, like I’ve had the dream before, yet when I wake up that sense is immediately lost. I wonder if this is what happens when people experience déjà vu (when they’re awake of course). I’ve had episodes of TGA (Transient Global Amnesia) where one’s thoughts seem to go in loops. It’s very disorienting, even scary, and the first time I experienced this, I described it to my GP as being like ‘memories from the future’, which made him seriously consider referring me to a psychiatrist.

So time, as we experience it, is intrinsically related to memory, yet there is another way we experience time, all the time, at least while we are conscious. And it is this ‘other way’ that made me challenge Kant’s thesis, when I first read it and was asked to write an essay on it. All animals, with sight, experience time through their eyes, because our eyes record the world quite literally as it passes us by, in so many frames a second. In the case of humans it’s twenty something. Movies and television need to have a higher frequency (24 from memory) in order for us to see movement fluidly. But many birds have a higher rate than us, so they would see a TV as jerky. When we see small birds flick their heads about in quick movement, they would see the same movement as fluid, which is why they can catch insects in mid-flight and we haven’t got Buckley’s. The point is that we literally see time, but different species see time at different rates.

We all know that our very existence in this world, on a cosmic scale, is just a blink, and a subliminal blink at that. On the scale of the universe at large, we barely register. Yet think upon this: without consciousness, time might as well not exist, because without consciousness the idea of a past or future is irrelevant, arguably non-existent. In this sense, Kant was right. It is only consciousness that has a sense of past and future; certainly nothing inanimate has a sense of past and future, even if it exists in a causal relationship with something else.

But of course, we believe that time does exist without consciousness, because we believe the universe had a cosmic history long before consciousness even evolved and will continue to exist long after the planet, upon which we are dependent for our very existence, and the sun, upon which we are dependent for all our needs, both cease to exist.

There has been one term that keeps cropping up in this dissertation, which has time written all over it, and it’s called causality. Causality is totally independent of the human mind or any other mind (I’m not going to argue about the ‘mind of God’). Causality, which we not only witness every day, but is intrinsic to all physical phenomena, is the greatest evidence we have that time is real. Even Einstein’s theories of relativity, which, as Callendar argues, effectively dismisses the idea of a universal time (or absolute time) still allow for causality.

David Hume famously challenged our common sense view of causality, arguing that it can never be proven; only that one event has followed another. John Searle gives the best counter-argument I’ve read, in his book, Mind, but I won’t digress as both of their arguments are outside the scope of this topic. However, every animal that pursues its own food believes in causality, even if they don’t think about it the way philosophers do. Causality only makes sense if time exists, so if causality is a real phenomenon then so is time. I might add that causality is also a lynch pin of physics, otherwise conservation of momentum suddenly becomes a non sequitur.

My knowledge of relativity theory and quantum mechanics is very rudimentary, to say the least, nevertheless I believe I know enough to explain a few basic principles. In a way, light replaces time in relativity theory; that’s because, for a ray of light, time really does not exist. For a photon, time is always zero – it only becomes a temporal entity for an observer who either receives it or transmits it. That is why light is always the shortest distance between 2 events, whether you want to travel between them or send a message. Einstein’s great revelation was to appreciate that this effectively turned time into a dimension that was commensurate with a spatial dimension. Equations for space-time include a term that is the speed of light multiplied by time, which effectively gives another dimension in addition to the other 3 dimensions of space that we are familiar with. You can literally see this dimension of time when you look at a night sky or peer through an astronomical telescope, because the stars you are observing are not only separated from us by space but also by time – thousands of years in fact.

But quantum mechanics is even more bizarre and difficult to reconcile with our common-or-garden view of the world. A lot of quantum weirdness stems from the fact that under certain conditions, like quantum tunneling and entanglement, time and space seem to become irrelevant. Entanglement implies that instantaneous connections are possible, across any distance, completely contrary to the restraints of relativity that I described above (see addendum below). And quantum tunneling also disregards relativity theory, where time can literally disappear, albeit temporarily and within energy constraints (refer my post, Oct.09).

But relativity and quantum mechanics are not the end of the story of time in physics; there is another aspect, which is perhaps even more intriguing, because it gives us the well-known arrow of time. Last year I wrote a review of Erwin Schrodinger’s book, What is Life? (Nov.09), a recommended read to anyone with an interest in philosophy or science. In it, Schrodinger reveals that one of his heroes was Ludwig Boltzmann, and it was Boltzmann, who elucidated for us, the second law of thermodynamics, otherwise known as entropy. It is entropy that apparently drives the arrow of time, as Penrose, Feynman and Schrodinger have all pointed out in various books aimed at laypeople, like myself. But it was Penrose who first explained it to me (in The Emperor’s New Mind) that whilst both relativity theory and quantum mechanics allow for time reversal, entropy does not.

Callendar, very early in his Scientific American article, posits the idea that time may be an emergent property of the universe, and entropy seems to fit that role. Entropy is why you can’t reconstitute an egg into its original form after you’ve dropped it on the floor, broken its shell and spilled all its contents into the carpet. You can run a film backwards showing a broken egg coming back together and rising from the floor with no trace of a stain on the carpet, but we immediately know it’s false. And that’s exactly what you would expect to see if time ran backwards, even though it never does. The two perceptions are related: entropy says that the egg can’t be recovered from its fall and so does the arrow of time; they are the same thing.

But Penrose, in his exposition, goes further, and explains that the entire cosmos follows this law, from the moment of the Big Bang until the death throes of the universe – it’s a universal law.

But this in itself begs another question: if a photon experiences zero time and the early universe (as well as its death) was just entirely radiation, where then is time? And without time, how did the universe evolve into a realm that is not entirely radiation. Well, there is a clue in the radiation itself, because all radiation has a frequency and from the frequency it has an energy, defined by Planck’s famous equation: E = hf. Where f is frequency and h is Planck’s constant. So the very equation, that gives us the energy of the universe, also entails time, because frequency is meaningless without time. But if photons have zero time, how is this possible? Also, if any particle approaches the same velocity as the photon, so does its time approach zero. And this happens when something falls into a black hole, so it becomes frozen in time to an external observer. Perhaps there is more than one type of time. A relativistic time that varies from one observer to another (this is a known fact, because the accuracy of GPS signals transmitted from satellites are dependent on it) and an entropic time that drives the entire universe and stops time from running backwards, thus ensuring causality is never violated. And what of time in quantum mechanics? Well, quantum mechanics hints that there is something about our universe that we still don’t know or understand, and to (mis)quote Wittgenstein: Of that which one does not know, one should not speak.

Addendum: Timmo, who is a real physicist, has pointed out that my comment on entanglement could be misconstrued. Specifically, entanglement does not allow faster-than-light communication. For a more comprehensive discussion on entanglement, I refer you to an earlier post.

Addendum 2: I revisited this topic in Oct. 2011 with a post, Where does time go? (in quantum mechanics).

33 comments:

J. Hamlyn said...

Another wonderful and inspiring post.

I often listen to the excellent Philosophy Bites podcasts and the one I've probably listened to most is Hugh Mellor on Time. I kept getting lost in the convolutions, but after reading your post I listened again and it makes much more sense now.

Just a small point: LW was talking aboutSpeaking not 'knowing". Very tempting though isn't it to speak of that which we do not know and especially to 'think' of it - essential, unavoidable even?

One final thing: do you really think the future is a product of our imagination? I'm inclined to agree but I saw a bird out my window just a moment ago and I realised that it had anticipated an event and avoided it. Does anticipation therefore require imagination in some form?

Best

Jim

Paul P. Mealing said...

Hi Jim,

Glad you liked it. Yes, I took a bit of licence with Wittgenstein. The exact wording is: What we cannot speak about we must pass over in silence.

Yes, I believe animals do imagine the future, even if it's only in the short term, otherwise they would not be able to anticipate outcomes or develop hunting strategies, which, of course, many do.

I wrote a post on imagination in 2008. It covers some of what I wrote here, with particular reference to my brief correspondence with Peter Watson, amongst other things. Not surprisingly, I do repeat myself over time.

Regards, Paul.

Mary Anne said...

A topic that has been occupying much of my thinking lately. I am thinking that Einstien is correct. Time is just an illusion. Its entanglement with space gives us a clue and our limited left brain functioning another. Memories are all left-brain. We are trapped inside a spacetime warp of our own making. We create and use time to organize the ever present Now. Granted time is another word for entropy, but entropy is a word that decribes our brain's inability to accurately perceive spacetime. I found the ideas expressed in Barbour's The End of Time most interesting.

Paul P. Mealing said...

Hi Mary Anne,

Thanks for taking an interest in my post. I have to admit I haven't read Barbour's The End of Time. Is it a philosophical treatise or a novel?

Regards, Paul.

J. Hamlyn said...

Hi again Paul,

I forgot to mention - when you mentioned Oliver Sachs I was reminded of an essay he wrote in An Anthropologist on Mars about the experience of the blind. He wrote that blind people experience space through time (it takes time to move through space) whereas sighted people experience space instantaneously. Unfortunately I can't find the book to quote him for you but I thought it was an interesting point about different perceptions of time and space.

Best

Jim

Paul P. Mealing said...

Hi Jim,

I haven't read that book, though I heard a radio interview with him when it came out. He used to visit Oz quite a lot once, though not for a while, as far as I know.

I do know of a guy who makes clicking sounds and quite literally echo-locates.

Regards, Paul.

larryniven said...

A question occurs: have you read anything, Paul, about a minimum time interval or lack thereof? There's a question, of course, about whether the universe is smooth* like the real numbers or if it's broken up like the integers (although on a much smaller scale, of course). Theoretically this has philosophical consequences and stuff, but I'm just interested cause it's a neat question.

Also, would that, I guess, be related to a minimum spatial interval? I feel like yes, but...this is kinda complicated.

*Not the technical word, but it's not coming to me at the moment.

Paul P. Mealing said...

Hi Larry,

Earlier in the year I read a really good book, called On Space and Time which is a collection of dissertations by physicists: Alain Connes, Andrew Taylor, Shahn Majid and Roger Penrose. It also includes a couple of essays by theologians: Michael Heller and John Polkinghorne; but don't let that put you off.

I have to admit it got a bit esoteric, even for me, which is probably why I haven't written anything on it yet, though I'd like to.

But, in answer to your question, there is something called the Planck scale where quantum physics and gravity meet, or so people believe. It's 1.62 x 10(-35) metres, or 5.3 x 10(-44) seconds, converting by the speed of light, c. It's believed that at this scale spacetime should acquire a foam-like structure called 'quantum foam', but it's purely conjecture.

There is no reason why space-time might not become fractal, and I'm sure that's been investigated as well (at least theoretically), but this stuff is a bit out of my league.

Regards, Paul.

Timmo said...

Larry asks whether space and time are continuous or discrete. To date, the geometry of the universe has been described using continuous "manifolds," and this has proved adequate over almost all of physics. As you mention, Paul, there are conjectures that at distances approaching the so-called Planck length scale some other geometry may be required. (There is also an associated Planck time.) But, the idea that time is discrete is not new; there were medieval scholars who asserted that an hour consists of exactly 22,560 indivisible instants. I would add the cautionary remark that, really, we have no better reason to believe that space and time are discrete than those medieval scholars. We can't, at present, even seriously dream about directly exploring those small distances. Other observable consequences are not forthcoming. As an experimentalist, I'm hard-headed and want theories to make predictions we can test.

There's an old joke. A man finds a drunk beneath a street lamp searching the floor. The drunk says, "I'm looking for my keys. I lost them across the street." "But, if you lost them across the street, why are you looking here?" To which the wise drunk replies, "Because this is where the light is." Similarly, there may be problems you want to work on, but unless you're laboring beneath the light, you're only speculating.

Timmo said...

Entanglement implies that instantaneous connections are possible, across any distance, completely contrary to the restraints of relativity that I described above.

I must strongly protest! The non-classical correlations between observables of entangled systems are strange and interesting, but they do not violate the theory of relativity. One can show that you cannot use an entangled particles to send faster-than-light signals even if they are arbitrarily far apart. If the principles of quantum mechanics really were inconsistent with the theory of relativity, then it wouldn't have been possible to develop relativistic quantum field theory. But, as I recall, we may have explored this ground before...

Paul P. Mealing said...

Thanks Timmo for your response to Larry's question and your protest. I knew that if I made a faux pas you would let me know.

I know that entanglement doesn't breach causality (and you can't send a message with it) but doesn't it lie at the heart of the EPR paradox, which Einstein originally formulated to challenge what he called 'spooky action at a distance'?

We did have this conversation before, but it was in regard to quantum tunnelling, not entanglement. You explained how Dirac's equations combined Schrodinger's equations with special relativity, which, I admit, I still struggle with.


Regards, Paul.

Timmo said...

Hi Paul,

It's hardly a faux pas -- you just happen to have an opinionated reader! There are theorists who make their careers thinking about these topics, but my attitude toward this work is on the whole negative. It's a pet peeve for me because (wild) speculations occupy so much attention, at least outside of science itself. Not too long ago, there was a piece in the New York Times about a physicist who believes that gravity doesn't exist, at least as a fundamental force. He suggests that gravity might be an entropic effect and could be reduced to something else. Maybe; just tell me where to look.

The EPR paradox was formulated with an different end in mind. Einstein was skeptical that quantum mechanics could provide a complete description of atomic phenomena in the sense that every element of reality has some counterpart in the theory. The EPR paper uses an example of two entangled particles in an attempt to show that the quantum-mechanical description of those particles, while correct, nevertheless leaves something out. Those things which are allegedly left out are commonly called "hidden variables."

It's hard to explain the EPR paradox without some exposition. But, I think I state very simply the basic principle behind Einstein's later writings on it: spatially separated objects possess their own real states. Quantum mechanics does not satisfy this principle, as quantum mechanics allows for spatially separated objects to be entangled, that is, they can only be described in a single quantum-mechanical "state." Einstein reasoned that we therefore ought to supplement quantum mechanics with another, deeper theory of Nature.

Paul P. Mealing said...

Hi Timmo,

Well, I've always tended to agree with Einstein on that point, in as much as quantum mechanics suggests that there is something about nature that we don't understand at this stage of our evolving knowledge.

Roger Penrose voices a similar opinion. That's not to say that I understand the topic as well as Penrose, not to mention Einstein, because I obviously don't.

Have you read my review of Louisa Gilder's book on this topic? There is a link in my previous comment.

Regards, Paul.

Paul P. Mealing said...

Actually, the link is at the bottom of the post, where I reference your original comment.

Regards, Paul.

Timmo said...

Hi Paul,

Your review of Gilder's book persuaded me to finally read the copy that's been chilling out at my apartment for the last half-year or so.

While I'm sympathetic to the hidden variables program, the mathematical structure of quantum mechanics places strong constraints on possible hidden variables theories. Bell's theorem shows that you can't have separability and locality. But, there are others, like the Kochen-Specker Theorem, which shows you can't be consistent with quantum mechanics and satisfy the following two principles:

(1) All observables have a definite value at all times.

(2) The properties that a system has at a particular moment in time are independent of any measurement context.

You can't have value-definiteness (1), non-contextuality (2), and quantum mechanics. The constraints that the Bell and KS theorems place on possible hidden variables theories tend to make them less attractive, at least from philosophical viewpoint that motivates the hidden variables to begin with (realism). The most famous hidden variables theory, Bohmian mechanics, has the "odd" features of being non-local and contextual, so it satisfies these theorems. But, Einstein didn't accept Bohmian mechanics or the more primordial de Broglie theory, and I suspect that if he was aware of these constraints he would have shuddered.

My own view is that we should go 'back to Bohr," but it's good not to be prejudiced about these things.

Paul P. Mealing said...

Thanks Timmo,

The impression I get, from everything I read, is that there is something missing in our knowledge. Quantum mechanics hints, to me, something akin to hidden dimensions. You get the sense that there is something happening behind the scenes, whether it be infinite pathways or hidden variables or multiple worlds, there is something going on that we don't see.

Regards, Paul.

Anonymous said...

Here's some new thinking that suggests that Time is ultimately only subjective, which challenges much of that 20th century thinking:

http://www.scribd.com/doc/32856404/The-Origin-of-Man
http://www.scribd.com/doc/32852505/Theory-of-Social-Interaction

Paul P. Mealing said...

Hi Anonymous, or is it Julian?

I assume the links are to 2 books you've written. A quick look suggests that they are about social-economics and nothing to do with time per se.

Thanks for taking an interest in my blog, but I'm not sure your links are relevant to the topic.

Regards, Paul.

Peter Kent said...

Though I could, I suppose, if subjected to some unimaginably exquisite form of epistemological torture, discuss time in terms of the usual, this-strictly-abstract-mathematical-model-behaves-in-a-way-isomorphic-to-the-universe-so-we'll-pretend-it's-indistinguishable-from-reality sort of way, but I do tend to find your reference to Wittenstein's dictum a lot more compelling, and very apposite as a final word on the subject.

On the other hand, I'm a logician and not a physicist (though married to one, so I'm at least superficially familiar with various physicists' views), and I have a fundamental problem with predications that, albeit perhaps less obviously, violate the type-theoretical prohibition on arguments that are themselves predicates of a same or higher order. An argument always implicitly present in *any* predication about the world that's nevertheless almost invariably omitted from the explicit expression is that of time, and so temporality gets absorbed into the predicate itself, and thus, when you make a statement about time, you're using an argument that's part of the predicate (exists at the same level), and so a foul has to be called on the resultant meaningless predication.

In short, as sentient beings who cogitate (and predicate) *in* time, we can't logically make statements *about* time, because the statements would have the circular attribute of affecting the meaning of the statements themselves.

Hence, the appropriateness of your final word ("speak not..."). :)

Paul P. Mealing said...

Hi Peter,

It's been a while since you've put your head above the parapet. Nothing wrong with that, mind.

Trust you to raise such an interesting and well-honed point, assuming I understand it correctly.

A sentence, by its very structure, is temporal, no matter how you look at it.

I love it.

Regards, Paul.

Timmo said...

Peter,

I think your argument needs to be fleshed out more, even if you accept some form of the theory of types. You say that statements cannot refer to time because they "would have the circular attribute of affecting the meaning of the statements themselves." But, what makes that problematic? Consider:

(1) This statement is six words long.

The number words in that sentence is part of its syntax, and therefore part of what determines its meaning. Nevertheless, it is a robust example of a sentence that references something which contributes to its meaning. So, it needs to be explained how statements about the nature of time exhibit any kind of "vicious" circularity. In fact, every use of the indexical "now" is like this:

(2) We should go to the movies now.

The indexical 'now' references the time when that very statement was made -- that rule is part of what 'now' means. It's self-referential about its own temporal properties.

Not only is it unclear how this self-referentiality is problematic, it is unclear whether statements about the nature of time exhibit it:

(3) Time forms, together with space, a space-time which is described by a four-dimensional pseudo-euclidean geometry.

That's no more self-referential or philosophically problematic than someone uttering:

(4) Sentences in natural language are composed of sequences of phonemes.

Should we say that we can't speak about phonemes because "would have the circular attribute of affecting the meaning of the statements themselves"?

Peter Kent said...

Hi Timmo,

I appreciate your thoughtful reflection on my probably insufficiently formal argument, but I'd wanted to eschew logical formalisms and elaborate discussions of the difference between predicates themselves as semantic objects and their lexical or other codifications (e.g., the one involved in Goedel's Theorem, wherein the problem is circumvented by using prime numbers to encode a particular statement)... as syntactic objects. And also the difference between time as an entity, and temporal indices used, as you say (quite properly), "indexically," to reference points in the dimension that aren't the same thing as "Time," itself (whatever that is).

It's not self-referentiality, per se, that's a problem, but only certain kinds of self-referentiality (such as that exhibited in Epimenides' paradox).

Mainly, the problem arises where you have a statement of the form:

P(o1,o2,...oi...,on)

where oi (or perhaps, more properly, "oy!" :) ) is actually not an object, real, imaginary or syntactic, but a predicate in its own right and either P, itself, or some other predicate of the same (or of a higher) type-ordinality.

Anyway, briefly to address your four examples:

#1 isn't a problem because the object referenced by the statement isn't the statement, itself (as a predicate, or "meaning-object"), but only the syntactic representaion of the statement. Again, this is the same reason the proof of Goedel's Theorem is perfectly ok. The semantic self-referentiality is eliminated by referencing not the meaning, but the encoding of the meaning.

#2 doesn't make a statement about itself (and isn't a predication about the nature of time in any case, i.e., it's not of the form Time(Time)), but only uses a temporal index as an object. It's really more of the form Go(we,movies,t1), where t1 is an index of the current instant. Actually, more properly, it's "Should(Go(we,movies,t1))" in the parlance of linguists, who would point out that it's an example of modal logic, but that's kind of irrelevant to the point, so I'm not sure why I bring it up, except that I'm in non-terse mode, and it occurs to me. :)

In #3, we've objectified time (referenced it strictly as a geometric entity, or one dimension to be combined with three others), and made a statement that is actually about nomenclature, or a classificatory statement about something that is a member of the set of pseudo-euclidean geometries. The predication doesn't actually itself incorporate any notion of Time, perceptual or otherwise, and it is in this sense that I spoke too imprecisely (or too universally) in expressing my objections to inherently self-reflective temporal predications, because the strictly formal and objectifying ones aren't necessarily. So mea culpa for off-handedness, though I could see myself arguing for or against the legitimacy of this usage at a deeper level, mainly if it were somehow subconsciously bouncing back to affect the intended meaning of the utterer of the statement.

#4 is no problem for the same reason that #1 is no problem. The object of the sentence is particulate elements of a syntactic codification of the sentence, and not the meaning of the sentence, which puts it in an entirely different kettle of ichthyoids from "This statement is a lie." :) (eth-Is steytm-schwa-nt Iz a lay)

Anyway, thanks for the careful reading and reflective comments. To clarify, my original intent was just to give Paul (whom I know from days long gone on this site, when velociraptors roamed the epistemological forest), a heads up on his apposite reference to Wittgenstein -- not to ban from logical discourse the whole science of physics, for which latter intent my spouse would undoubtedly kill me, even if ever I harboured so demented an idea!

Regards,

Peter

Peter Kent said...

Hi Paul,

Sorry to have been so long in absentia (and perhaps, prospectively, so to be soon again), but you know how it is: quotidian matters of health and the general intractability of life, the universe and everything tend to obtrude. Odd world, this one, even outside the realm of philosophy.

Anyway, great to talk to you again, and especially nice to see your website deservedly thriving.

Regards,

Peter

Paul P. Mealing said...

Hi Peter,

Not surprisingly, you and Timmo have taken this discussion into realms where I struggle to follow.

Nevertheless, happy to be a forum for such esoterica.

Regards, Paul.

Timmo said...

Hi Peter,

I think you’re right that it is important to distinguish different kinds of “self-referentiality.” One potentially problematic possibility you suggest is permitting ourselves to define properties such that the range of things which might have that property include the property itself. For example, if there is a property of being a property, then the property of being a property is an example of a property which has itself as a property. But, then we have to worry about the property of non-self-exemplification: the property had by all properties which do not have themselves as properties. Type-theoretic restrictions are designed to avoid these contradictions, but it’s not clear to me how this family of logical paradoxes is related to issues about time.

To press the point a little, it’s at least arguable that all indexicals have a “self-referential” quality. Let’s use a toy language L: it is the propositional calculus supplemented with the operator ‘Now()’. Then, letting A range over wff of L,

(NOW) If S utters “Now(A)” at a time t, then “Now(A)” is true if and only if A is true at time t.

Such an utterance is inherently self-referential in the sense that its truth-conditions are partly determined by the moment the sentence token itself is produced. I am vaguely remembering a paper by David Kaplan laying out a formal semantics for a formal language with indexicals, and the truth-conditions he gives have this self-referential character. Searle, in Intentionality, emphasizes the self-referential character of speech acts that include indexicals (although I have to admit I’m a little rusty on this stuff). To it another way, the semi-formal translation you gave of “we should go to the movies now” introduces a constant denoting some time, but in order to specify the semantic value that constant takes one needs to appeal to the sentence token itself.

Peter Kent said...

Hi Timmo,

OK, we can't talk about the set of all sets that aren't members of themselves, nor send to know whether "heterologous" is heterologous (nor ask, probably, for whom Bell's Theorem tolls -- just kidding). Clearly, we're on the same page relative to the meaning and purpose of type-theoretic restrictions, so we can put that aside. I apologize for my apparently supererogatory attempts to elucidate: hadn't realized you were deeply conversant with logic, but perhaps, by way of consolation, our respective divagations on the subject will have been illuminating (or, at least, zanily diverting) to some other readers.

On deeper reflection, I think the root problem inheres in use of the word, "now." There'd be nothing logically thorny about the sentence, "We went (or will go) to the movies at 7:32 p.m. on April 14, 2010," since we don't have to know when it was uttered to understand what it means or whether or not it's true. "We are going to the movies now," however, comports a veritable plague of logical problems of self-referentiality, unless "now" is a constant and not dependent on the moment of utterance of the sentence, since the predicate, "go," incorporates a hidden temporal semantic component.

Anyway, I like your ingenious and provocative "toy language," which I think goes right to the point in invoking a "Now" modal predicate, but it almost tends to impel me to argue that any language that includes statements whose "truth-conditions are partly determined by the moment the sentences [themselves are] produced," while excluding express usage of indexicals as temporal arguments to specify the nominal "moment of truth," is not, in actuality, a single language, but an infinitude of them (whether countably or uncountably infinite would depend, I suppose, on whether you posit a smallest, indivisible time quantum -- more your bailiwick than mine -- but it's not, in any case, critical to the argument), one for each such quantum in the past 14 billion years or so and going forward, if we want to talk about the real universe. :) So, again, absent the ability to assign truth values to sentences for want of an explicit mention within those sentences of when they're supposed to be true, but allowing time nevertheless to enter the equation non-explicitly by having a language in which truth values can be time-dependent, I guess one would have either to introduce an infinitude of predicates, on the order of "Now(S)" but time-indexed, and none of them utterance-time-dependent (which would banish "Now" and substitute "At-time-i" for whichever "now" we meant to reference)... or abstract the problem out (or up) to the next level by considering "L-sub-i" to be one of the aforementioned infinitude of languages in the set L, each identical except in respect of the indexed time at which its statements are meant to be evaluated. Take all this, if you will, cum grano salis as just a slightly whimsical but also semi-serious Gedankenexperiment-ish attempt at resolving the issue, inspired by your invention of "L" and its focus on "Now" -- but in any case, I still do see time as a problem, both in its potential for generating type-theoretically inadmissible utterances, and (incidentally) in regard to the consistency of logics that don't somehow handle it formally. (Not that any logic has to be consistent, and of course it's provable, as you obviously know, that none of them is both consistent and complete, but consistency is still a nice thing to aim for, and truth-indeterminacy sort of undercuts the mission. :))

I have, BTW, enough bones to pick with Searle to populate the skeleton of an apatosaurus, but they're mostly not germane to this topic, so I'll forbear to elaborate intentionally, and leave that for another day. :)

Peter Kent said...

Hi Paul,

Profoundly sorry about the duplicative posts. I made 2 (apparently unsuccessful, based on a "length-exceeded" message from blogger) to post the entirety of my message, then resorted to division into two parts. Howsoever, as you can see, blogger's claim to have rejected my first two attempts seems, in the event, not to have been true (in any indexed moment of time :)), hence the three redundant posts.

Never seen that problem before, so I was taken unawares.

Again, sincerest apologies,

Peter

Paul P. Mealing said...

Hi Peter,

Not a problem: redundant comments deleted.

Regards, Paul.

Timmo said...

Hi Peter,
I am happy to meet someone who makes logic smile as much as it makes me. You’re certainly part of a venerable philosophical tradition when you suspect that there are logical paradoxes about time. Zeno attempted to demonstrate that change was impossible; Hegel saw motion as internally contradictory or dialectical; McTaggert argued (persuasively to Bertrand Russell at one moment in his life) that time was illusory. If you think that the self-referentiality of ‘now’ is problematic, then there is going to be an even wider range of contradictions. Indexicals typically bring the properties of the utterances they are part of to the truth-conditions of those utterances.

Let’s make another toy language L1. We have n-place relations signs R; ordinary constants c; and some special indexicals ‘i’; and the usual barrage of logical connectives. (It’s not quite a first-order predicate calculus, because L1 doesn’t have variables or quantifiers which bind them.) An interpretation I is an ordered pair , where D is a set of objects including the speakers of L1 and V is a function which maps ordinary constants to elements of D and relation signs to sets of n-tuples of D-elements. Wff comprised of formulae where there are no occurrences of the indexical symbol ‘i’ have standard truth-conditions. What about the special indexical symbol i?

(SELF) If S utters “R(c1, … , i, …, cn)”, then “R(c1, … , i, …, cn)” is true in an interpretation if and only if [V(c1), …, S, …, V(cn)] ∈ V(R).

Such an utterance is inherently self-referential in the sense that its truth-conditions are partly determined by who produced the sentence token itself. And, it looks like we can generalize this by having ‘here’ include the location where the sentence token itself is produced; ‘you’ to include the intended listener of the sentence token; and so on. So, following your suggestion, the alternative would be to have an infinity of languages each indexed to a possible time, speaker, listener, location, etc. What I’d like to say is that if you smell type-theoretical problems for words like ‘now’ then there are even more type-theoretical dangers lurking just a little further up the trail!

Timmo said...
This comment has been removed by the author.
Timmo said...
This comment has been removed by the author.
Timmo said...

Hi Paul, I had the same redundant comment trouble! Mia Culpa.

Timmo said...

Typo! "I am happy to meet someone who makes logic smile as much as it makes me." I didn't mean to say Peter makes logic smile; I meant the other way around. I'm happy to know another logophile! (If the postmodernists can make words up, so can I.)