I always get a little uppity when people try to dismiss Zeno's paradoxes with the fact that an infinite series can have a sum. It misses the point entirely. — Voyeur

While I welcome your approach and think that it is among the more promising ways of looking at the problem, I must object to the remark about "missing the point." The problem is that most statements of Zeno's so-called paradoxes not only fail to make your points, but fail to make any cogent points, as has been largely the case in this thread.

The point about the convergence of infinite series, to which you take an exception, is an effective response to those statements that boil down to the thesis that an infinite sequence of events necessarily, as a matter of logical reasoning, takes an infinite amount of time. But I agree that the response is often given reflexively to statements that either rely on different assumptions or are so vague that one cannot confidently make out their core assumptions.

So I would set aside the two questions that you formulated - is motion a supertask? and are supertasks (metaphysically?) possible? - as open questions that, prima facie at least, are not incoherent or trivial. Other things that you mention, such as Thompson's lamp, might actually be less problematic than you think, being ultimately language problems rather than problems of metaphysics.

But anyway, if you want to talk about the point, a good way to start would be to give a crisp statement of the alleged paradox.

Are your comments directed at any particular person or post? — aletheist

My comments were directed at your OP and some following posts. It seemed to me that your dissatisfaction with Cantorian mathematical theories of continuity stemmed from the idea that according to these theories the continua are composed of discrete points - a seeming contradiction. But it's not about composition - it rarely is.

When wondering about what a thing really is, asking "what is it made of?" is a good way to proceed in many common-place situations. For instance, if you find that something is made of wood and not wax, that is going to tell you quite a bit about that thing's properties. But this intuition often trips up people when more subtle questions are asked. In mathematics, and to a large extent, in science, the question "what is it made of" is often unproductive and misleading, as it is in this case.

Anyway, I see that this discussion has long since turned to Peircian exegetics, which interests me not at all, so I'll bow out.

It seems to me that you are laboring under a simplistic mereological and atomistic understanding of topology. In topology a line is not just a bunch of points that are put side by side, which indeed sounds wrong - how can you get a one-dimensional object from any number of zero-dimensional objects thrown together? Of course you can't, and that's not how it works.

In order to get what we intuitively understand as a continuous line (for example), you need to build up some mathematical structure, such as ordering and neighborhoods. You won't get that just from a point, the structure is global and independent of the properties of individual points or their aggregates. (By the way, we keep saying "points", but topology is agnostic about what those elementary entities are: in fact, they can be anything, such as functions, for example.) So it is really the structure of the continuum that makes it what it is, and this focus on "points" is misguided. Or I should say a structure, because our intuitive requirements for a continuum can be realized with multiple mathematical structures, some of them isomorphic, some not.

If motion is discrete, it's not motion as we understand it to be. As object A "moves" from discrete point 1 to point 10, what is the time lapse between 1 and 2? Does A go out of existence during the lapse, and how do we claim A maintains identity during teleport and reappearance?

You can't just offer discrete movement as a solution to the paradoxes associated with analog movement without also explaining how discrete movement really works. It might be there's no coherent explanation to something as basic as movement, just like there's not with causation.

Anyway, discrete movement is an obvious adoption of the computer graphics model imposed on reality. Identity of a computer graphic over time is preserved by the underlying programming, which is a quite literal deus ex machina. If we're going to insert Deus, I suppose anything is possible, including analog movement. — Hanover

I think that you are making some unconscious metaphysical assumptions here. Why does continuous motion preserve identity and discrete motion does not? You can construe your idea of identity this way, but this construal doesn't have the force of logical necessity - it is just one possibility among many.

You ask how discrete motion "really works." What do you mean by this question? Do you understand how continuous motion "really works?"

This is the assumption that I'm showing to be false. Each movement from one point to the next is a tick. — Michael

I am afraid that you just can't get past the concept of counting, or rather to see it in its context. There's no point in me trying to explain it to you now, because I would just be repeating myself. But later, when you are no longer engaged in defending your position, I suggest that you acquaint yourself with the basics of set theory and calculous.

You might think that mathematics is this very specialized discipline that is only relevant to solving certain technical problems, but it's not. Mathematics is relevant to any abstract thought, metaphysics included. It expands your conceptual apparatus and gives you the tools for dealing with complex concepts in a systematic, disciplined way.

When you become familiar with the foundations of mathematics and see how concepts such as sets and numbers are built upon each other, perhaps then you will see what we have been trying to tell you. You might still resist the concept of a continuum on physical or metaphysical grounds, but at least you will be doing it with the clear understanding of its logical structure.

You seem to just be misunderstanding. What I'm trying to say there is that you can't answer the question "if we want to count every rational number between 1 and 2, what number do we count first?" with "pick any at random, and then pick the next one at random, and so on" (as Banno suggested). Each number must be greater than the previous, and we can't count a number if we haven't counted a smaller number.

And so by the same token, each coordinate an object passes through must be closer to the target than the previous, and it can't pass through a coordinate if it hasn't passed through one that's further away. — Michael

Yes, this nicely illustrates the very confusion that I've been talking about.

each coordinate an object passes through must be closer to the target than the previous, and it can't pass through a coordinate if it hasn't passed through one that's further away.

True enough, but this has nothing to do with counting.

I'm saying that the act of moving from one location to another can be considered an act of counting, like a clock counting the hours as the hand performs a rotation. — Michael

You are saying this, but you are not proving this.

Counting is just a physical act like any other. I don't know what you think it is. — Michael

True, but that doesn't imply that all physical acts involve counting.

I don't know why you're comparing counting to ordering. — Michael

Because I was responding to your own line of argument, e.g. here.

The comparison is between counting and moving. And as explained here, there's no reason to suggest that they're fundamentally different. — Michael

You haven't argued that moving is somehow related to counting, you just imagined some impossible contraption and asserted without any argument that continuous motion necessarily involves something of the sort.

I have, with my example of a machine that counts each coordinate as it passes through them in order. — Michael

Such a machine would not be possible. But we are not talking about this machine specifically, we are talking about any thing that moves, so this is a red herring.

As I said, as long as you persist in conflating ordering with counting, your argument won't get off the ground. It's simply not logical, because there is no logical requirement for counting here. If ever you allow yourself to realize this (and I realize how hard it would be, given the effort you've put into defending your position), there is still an option left for you: you could try to stake out a metaphysical claim instead of a logical one. At least it wouldn't be obviously incoherent.

Continuous motion is impossible for the same reason that continuous counting is impossible. The reason counting is possible is because it is discrete. And so the reason motion is possible is because it is discrete. — Michael

You are begging the question. You are essentially saying that motion is just like this impossible thing, therefore motion is impossible. You must show the necessary connection between motion and counting all rational numbers in an interval in order.

What's the difference between moving from one coordinate to the next and counting from one coordinate to the next? — Michael

When you are saying "the next" you are already implying a sequence.

Saying that passing all rational coordinates in order is not a problem is akin to saying that counting all rational coordinates in order is not a problem. — Michael

Nope. Order is not the same as sequence. Ordering is not the same as counting. Until you understand this you will keep running in circles.

Like I said, passing all rational coordinates in order is not a problem. After all, there is a (total) order relation for rational coordinates, so that for every pair of coordinates a and b, either a = b or a < b or a > b. But counting is not part of that.

That's what I said. But you are asking more than that. You must recognize the difference between there being an order and there being a sequence.

I did clarify that I was talking about the Achilles racing turtle paradox, which is not the one from the OP. Are you still claiming that it makes no sense? — Svizec

Yes. That "1 must be part of the sequence" came out of nowhere.

What I'm saying is that continuous motion between one place and another is possible if and only if it is possible to sequentially pass through each coordinate between them (and for the number or coordinates to be infinite). It seems to be that this is what it means for motion to be continuous (rather than discrete). — Michael

The superfluous assumption here is sequentially. It would be reasonable to say that for motion to be continuous the position of the body must pass every rational (or real for that matter) coordinate in order. But you demand something on top of that: that all of these coordinates form an ordered sequence. That demand is not motivated by any reasoning (indeed, you will necessarily run into a contradiction if you try).

f I try to use a bit more mathematical language... The sequence 1/2 + 1/4 + 1/8 + ... is a sequence with infinite number of terms. Each term corresponds to one step. The reason why Achilles will never reach point 1 is because 1 is not a term of this geometric sequence. 1 is the sum, yes, but in order for Achilles to reach the 1, point 1 would actually have to one of the terms of the sequence. — Svizec

That makes no sense.

"This thing is just like that thing" is not an argument. The best that I can make of your attempt is basically the same as before: you are saying that moving from place to place is possible if and only if it is possible to put all rational numbers between 1 and 2 into an ordered sequence (which, of course, is an impossibility). But you are not offering any argument for this assertion.

It was explicitly mentioned several times, and implied any time it wasn't, that the counting is sequential, given that it's an analogy to the movement between two points, which would involve an object passing sequentially through each rationally-numbered coordinate between them. — Michael

An analogy can only be useful for illustrating an argument, and you have yet to offer an argument. You assert that moving from place to place is possible if and only if one can utter all rational numbers between 1 and 2 in sequence and in finite time, but you haven't offered an argument for this assertion.

I suppose that etymology can be of use if you are interested in the history of ideas, and in particular in exegesis of old philosophers, which is what much of academic philosophy seems to be about.

You are making two mistakes:

1. Suppressed premises. You are assuming that your scenario is a stochastic process with a non-zero probability of failure on each trial. It doesn't have to be. There is no law of logic or nature that says that it has to be this way. It's just an assumption. It could be, for example, that your footballer cannot ever miss more than twice in a row. It's a more complicated model, to be sure, but it's a possible model.

2. You are over-awed by your intuitions. Our intuitions are passable for everyday, familiar occurrences, but when faced with something as incomprehensible to the imagination as infinity, your intuitions are of little help. Trust your reason, not your gut feelings.

I wouldn't put it that way, because the inaccuracy predicted by the HUP is much smaller than our ability to perceive. So HUP does not impinge on our reality. — andrewk

Well, the HUP has been experimentally confirmed, so that means we can perceive its predictions, albeit indirectly - but isn't that the case with any model prediction? You could further argue that, the HUP being an integral part of quantum physics, and quantum physics being a very accurate theory, then if the HUP was quite wrong, the world would probably have been very different. So different indeed that we wouldn't be around to make that observation.

Which brings me to the OP question. What do people mean when they say things like "the math is not the world," "the map is not the territory," etc.? In one trivial sense this is, of course, true and undisputed: a theory, a model, is just a concept that we hold in our minds, it is not that which the concept is supposed to describe.

Is the statement merely impugning the accuracy of the model or its justification? That would stake out a scientific position. Needless to say, whoever makes this statement had better know the subject really well and be prepared to marshal scientific arguments and data in support of their position - otherwise there is no reason to take them seriously.

Is the statement saying that the whole of world probably isn't perfectly accountable by any of the existing models? That would be a defensible philosophical and even scientific position, but it is a very general statement, while the original sounds like a much more specific indictment.

If not any of the above, then what?

I don't see what Schrodinger's cat has to do with a coin flip. Of course, probability is involved in both cases, one way or another, but that's not much to go on.

And I am simply suggesting that if it is conditionalized solely on someone's knowledge (or lack thereof), background or otherwise, then we should not call it "probability." Again, I recognize that this is a futile quest. — aletheist

It's not just futile to change a well-established vocabulary, it seems senseless. Is there any particular reason that the word "probability" should not mean what it means?

Which is to admit this is all an epistemological question and not an ontological one. That is, you're asking how accurate our knowledge is of an event. — Hanover

I am not sure what an ontological probability would even mean.

Guys, you are both swimming upstream, and for no good reason that I can see.

There are ways of talking about probability in both senses. Probability is always conditionalized on something, if only on the "tautological prior". Let E be an outcome (e.g. heads) of a single coin flip and H be the "fair coin" model, according to which

P(E|H) = 0.5

A different model may yield a different probability.

Now, when you talk about our confidence, we conditionalize on your background knowledge, K:

P(E|K) = ?

If your background knowledge already includes the knowledge of which side the coin came up, the probability will, of course, be either 0 or 1. If you do not know the outcome, and nothing in your background knowledge otherwise informs you about what it might be, and you assume that the coin is fair, then the probability is the same as above:

P(E|H ^ K') = P(E|H) = 0.5

where K' is your background knowledge, not including the proposition "the coin is fair".

We can guess what it might be, and you may have a 50% chance of being right but that chance pertains to your guess — Jeremiah

That's just what we mean when we say that the probability of a coin toss outcome is 50%. So the answer to your question in the OP: it doesn't matter whether the coin toss has occurred or not - as long as you haven't looked.

Suppose I've never heard of physics and probability theory, and I (incorrectly) expect the outcome of a large number of coin tosses to be influenced by the force of wishful thinking in the vicinity of the coin.

It seems an ordinary probabilistic or statistical model is a model of something in addition to one's ignorance. — Cabbage Farmer

Well, if you haven't heard of probability theory (and have no sound intuitions to help you) then all bets are off. We usually assume a "rational agent" who makes the most of the information available to her - otherwise the possibilities are wide open and we cannot say anything at all. But the information available to you doesn't have to include the correct physics. You are right, probability can be a function of a model. But having a model (such as that your wishing can alter the result of a coin toss) influences your expectations - and thus your assignment of probabilities.

So the probabilities that you come up with are still a function of what you believe. If you have no expectations of the behavior of the observed system, then the best you can do is assign ignorance priors (although it should be noted that some don't believe in assigning probabilities in complete ignorance). If you have a model that yields a different result (cheating, power of thought or whatever) then your probabilities will be shaped by the superposition of that model with any remaining uncertainty.

Has anyone here read any existing literature on the subject? There's lots!

First it should be noted that nothing about evidence and confirmation is necessitated by classical logic, simply because these concepts do not belong in classical logic. That's not to say that a theory cannot be built on deductive foundations (that's what Hempel, who came up with the paradox, as well as a number of others, attempted to do). However, even with classical logic as a background there are various ways of going about it, and different models and starting assumptions will yield different results. And then there are various non-deductive theories of confirmation: Bayesian and even more exotic theories, such as two-parameter models. (A Popperian will just dismiss the challenge, since according to her there is no such thing as confirmation. And that's why few pay attention to Popperians :P)

Physicalism

As you can see, there isn't anything like a common agreement on what the term means, and the prospects of it amounting to a coherent stand-alone metaphysical doctrine without limiting it to an exclusive little niche look pretty dim. Your own definition is too narrowly reductionist, and even this definition is vulnerable to the criticisms referenced above.

I think that physicalism is most easily conceived as what it is not, i.e. in opposition to certain specific and wide-spread views, in particular to doctrines that single out the mental for a privileged role in the ontology of the world.

Personally, I care more about epistemology than I do about ontology, and for me physicalism is more about the method of inquiry than about specific ontologies. I associate physicalism with a broadly empiricist and skeptical epistemology.

Physicalism is an updated version of materialism, not the science of physics. It just says that everything is made up of whatever physics posits. Cars being made up of physical parts isn't an issue for materialists. But experience is problematic. — Marchesk

Physicalism isn't necessarily framed in mereological terms (I personally dislike this approach).

How experience is made up of physical stuff. Saying that meat experiences color, while cars don't because meat, isn't an answer. — Marchesk

Asking "how experience is made up of physical stuff" sounds as absurd as asking how the operation of a car is made up of physical stuff. Maybe you mean something by it, but if so, you need to explain.

You could say that brains are made up of physical stuff - an awkward statement, and not very informative. But it would be a better analogy here. But brains are not consciousness, brains are conscious [of stuff] - see the difference? It's not what the brains are made out of, it's what they do.

An answer that would make the puzzlement go away — Marchesk

I am afraid I still don't understand the reason behind the puzzlement. I mean, consciousness is a wondrous thing and it certainly has plenty to be puzzled about, but let me remind you again that physicalism isn't supposed to be an oracle that will answer all of your questions.

Yeah, one wonders how it is that people found out that they had brains in the first place. Or hearts. That's a real puzzler :-}

Physicalism can't explain why some physical systems have experience and others don't. — Marchesk

Physicalism also can't explain why some physical systems are cars and others are not. Take any summation of Physicalism as a philosophical doctrine, and more likely than not, you won't see "cars" mentioned at all. Isn't that just as bad?

You might ask so what, but physicalism is supposed to present a comprehensive ontology. It can't leave anything out and be true. — Marchesk

There's your problem. While there isn't anything like a received view of what "physicalism" stands for, I've never seen it claimed that physicalism is a theory of everything, capable of answering any question that you can think of. Physicalism posits answers to certain specific questions, and that's it.

Anyway, what question are you actually asking above? What sort of answer would you accept?

And so some physical systems have experiences, like my brain/body, and others don't, like my car (which could be smart and drive itself these days) or the rock I kicked.

That's why it remains problematic for physicalism. — Marchesk

Where is the problem? Some systems are cars and others are not. Is that a problem too?

This is genius.

I agree that such is the convention. But what do those who use and defend the convention mean when they say that something exists? — Perdidi Corpus

Well, you appear to be a competent speaker of English, don't you already know what people mean when they say that something exists? I didn't have any exotic or specialist meanings in mind.

A tempting answer is to say that the visual cortex of the brain generates color. But when the brain is examined, there is no color to be found there, of course. So where is that color experience taking place? — Marchesk

The brain doesn't generate color, it experiences color (or rather, your entire organism experiences color, since the brain does not function in isolation from the rest of the organism). It would be senseless to examine the brain looking for the experience of color - what would you expect to find? When you want to drive somewhere, do you just sit and stare at your car, expecting the driving to happen by and by?

But this is veering away from the OP and towards a well-worn debate about qualia. The OP was addressed to those who already accept that consciousness can be realized in a computer, and more broadly, in any system that possesses the same structure and undergoes the same processes as those that are supposedly responsible for producing consciousness in the brain. You didn't have many takers. Instead, some flatly stated that only "meat," so to speak, can be conscious. Or conversely, that "inanimate" things or "tools" cannot. But what are the reasons for such declarations? Or are they made by way of stipulating the very definition of consciousness? Something that Russell described (in a different context) as having "all the advantages of theft over honest toil?"

But let me ask in my turn: can any amount of "honest toil" yield objective criteria for having consciousness? I think the answer is "no". If you think that consciousness can only be realized in "meat," then that is so, by definition. But on the flip side, this doesn't resolve any interesting philosophical questions, this only resolves the meaning of the word "consciousness" in your preferred usage.

It may be fun to do some further thought experiments though. What if a few neurons in your brain were seamlessly replaced by a microcomputer (or a small Chinese city doing calculations with pencil and paper, if you like)? Would you still be conscious? Would you still be you? Well, you see where this is going...

My take is that there is no objectively right or wrong answer. And no way to justify any answer given.

"Where does truth exist?" looks like a question about truth. But is it? Try treating it as a question about how we use the words "truth" and "exist"; so that it morphs into something like "Does the word exist apply to truth?" — Banno

Or, more directly, does the word "exist" necessarily implies having a location? How could you argue for that? (You haven't even tried, as far as I can see.) If pretty much everyone, as appears to be the case, already uses the word "exist" so that it applies to things that do not have a clear location, then what's the point of this exercise?

It is except the focus is own conscious experience and not understanding. Arguably, a fair amount of progress has been made in computer understanding with machine translation, image recognition, search algorithms, etc. But no progress whatsoever, far as anyone can tell, has been made on experience. — Marchesk

But what motivated the Chinese Room and similar thought experiments is the very idea that without conscious experience there is not "true" understanding. All along, it wasn't technical competence of the AI that was at issue.

Of course, what constitutes "true" understanding, as well as "true" conscious experience, is anyone's guess. I don't think there is a metaphysical truth of the matter here, because we are ultimately just stipulating how we are going to use words such as "understanding" and "conscious experience". That is, unless one intends to posit some positive metaphysics specific to consciousness - you know, the soul or some such.

Well, a paper computer executes instructions just as a microprocessor computer does. So what is true of the one ought to be true of the other.

To be clear, Marchesk is not talking about a set of instructions once committed to paper and just sitting there. He is talking about a person or lots of people performing those instructions with pencil and paper instead of silicone and electric potentials.

P.S. The OP question is, of course, a variant of the Chinese Room problem.

Yes imagining something would be the best example for this situation I feel. — Rawrren

Well, if you stipulate from the start that you are merely imagining a thing, you are, ipso facto, stipulating that the thought is not about, does not not refer to any concrete object in the world, as far as you are concerned. That is already given by your formulation, no matter what approach you then take - physicalist or otherwise. So I still don't understand, what difficulty do you see specifically for physicalism in this scenario?

Do you know of any reasoning as to why some reject intentionality? And if so, how do they then explain what we call 'intentional states & concepts'. — Rawrren

One way of viewing intentionality is linguistically, by giving interpretations of our intentional language while eschewing intentional idioms. But I confess that I am not prepared to discuss this issue in much detail. However, here are a couple of SEP articles that you may find as a good starting point for exploring different views of intentionality and surrounding issues: Intentionality, Consciousness and Intentionality.

So you think there is a problem specifically in the case where we are contemplating something imaginary?

I should note that physicalists do not all share the same concept of the mind, and not all of them, I imagine, will even accept intentional states as a valid or useful concept. So you would also have to argue that intentional states are absolutely indispensable in any theory of mind.

Can you explain in more detail what it is that you see as a problem for physicalism wrt intentional content?

That quote was fabricated by yours truly ;)

if the phenomenon of politically-driven fact-indifference is a perennial one

&

if a new term has been coined, to refer to this same perennial phenomenon as though it's unprecedented

&

if one is interested in what is new about this situation

then: the phenomenon in question is not 'post-truth' but 'a collection of groups claiming that there is an unprecedented event/era/atmosphere called post-truth' — csalisbury

It is not unprecedented, but it feels like it is becoming more common and accepted. As for "a collection of groups" - tu quoque again in lieu of addressing the issue. Instead of reflexively pointing a finger at the opposition you could argue that there's really nothing special here, no sea-change in the culture, no "new era" - and I might agree with you. I am not too certain about my characterization of the phenomenon, perhaps I am just picking out what irks me rather than identifying an objective trend.

But it does feel like a new development. In the past authoritarians sought to tightly control and restrict information. They were very much concerned with preventing the truth from getting out. Remember what event started Winston on his fateful path? He was charged with destroying a photograph that would have exposed a lie that was currently being promulgated by the Ministry of Truth. Orwell was uncannily prescient: such expurgation of incriminating records in newspapers and books was indeed practiced in Stalin's Soviet Union. But you see much less of that today, not because the propaganda lies less, but because it seems less concerned about hiding the truth.

When Russian troops invaded Crimea, the obvious fact was denied by Russian officials and the media. The soldiers, whose only cover was the lack of national insignia, were ironically nicknamed vezhliviye liudy (polite men) by the locals who were not deceived by the ruse. (The troops were mostly just strolling around in their spiffy new uniforms and top-of-the-line gear, and although armed to the teeth, their behavior was markedly reserved - hence the nickname. The task of brutalizing opponents of the occupation and closing down pro-Ukrainian media was mostly outsourced to civilian volunteers and off-duty security officers bused in from the mainland.) By and by, after the annexation Putin, followed by others, acknowledged the invasion. Putin even boasted of his role in directing the operation in a later interview. But as a rule, the earlier lie was never acknowledged or apologized for, although no attempt was made to erase it from the public record. What's more, the vezhliviye liudy - once a symbol of duplicity and underhanded hybrid warfare - quickly became a popular meme, emblazoned on tee-shirts and even memorialized in a goofy public sculpture. People who just months earlier dismissed them as an insidious fabrication of the west never seemed to take an issue with being lied to - they took the about-face in stride.

And this cynicism and indifference to the truth characterized not just poorly educated provincials who only ever watch government-controlled TV channels, but even well-educated, well-traveled, English-speaking Moscow professionals who had all the information at their fingertips (I knew some of them). No burning of pictures was necessary - the pictures were all over the Internet, and nobody minded.