No, no, no. I wasn't looking for "the right way to reason things out." My question was not about life, the universe, and everything. I asked a specific, contextual question about the topic of discussion. But those who started and took part in the discussion have drifted off, so...

You were doing well until the last paragraph. Not only does it not follow from the reasoning that preceded it, it goes directly against it! If you concluded that the coin was biased towards heads, then you should bet on heads, not on tails.

If I recall correctly, Carl Sagan contributed to some research on meteoritic dust accretion. He is mostly remembered for being a great science popularizer and a sort of generalist visionary, but he actually did some good down-to-earth (as it were) science as well.

Although it seems to me that if the probability of getting heads or tails is really 50%, then if we have a bunch of one side in a row, that should increase the odds of getting the other side on a subsequent throw. Why am I thinking this? Well, for the 50% to have any real significance, it needs to be referring to what happens over a series of throws, where the more throws there are, the closer the data set gets to 50% for either side. Otherwise, how in the world would we be arriving at the 50% figure in th first place? — Terrapin Station

Probabilities are single-case, or nothing

But even if you do not agree with that view, you are still committing a fallacy in attributing a causal significance to that 50% probability. How did we arrive at the 50% figure in the first place? From the following assumptions:

• There are two possible outcomes,
• Trials are independent,
• On each trial there is no more reason to expect one outcome than the other.

Assuming a causal influence of preceding trials on subsequent trials would go directly against those assumptions.

Solving equations has nothing to do with positing real ontological entities. — Terrapin Station

That is a thoughtless and irrelevant retort. The question that started this line of discussion was whether black holes were "invented" in order to accommodate some observations that, as you said, did not fit existing gravitational models. That is exactly backwards. The observations that we now attribute to black holes fit our gravitational models like a glove.

That they're consistent with GR doesn't make them a prediction of GR. We invented them so that they'd be consistent with GR, otherwise we'd need to retool our gravitational theory. — Terrapin Station

We "invented" them only in the same sense that we "invent" solutions to equations. Black holes are what we can expect to see, given GR. And what we do see is in close agreement with what we expect to see. So whatever semantic point you are trying to score, it is irrelevant. Black hole physics is not an ad hoc addition to our gravitational models, as you implied.

What you didn't get is — quine

...pretty much everything. The thing is that your argument is so simple structurally that it is either trivial or the real meat of the argument needs some unpacking.

The structure and apparent motion of stars doesn't match what we're expecting given our gravitational model. Hence the need to invent black holes. — Terrapin Station

No. Black holes are a generic prediction of General Relativity. If GR is our gravitational model, then black holes are part of the package.

lexical concepts — quine

You'll need to explain what you mean by that.

I don't get it. Don't "composed" concepts have structure? If not, then I don't understand what you mean by having structure.

I was at first confused by your talk about the brain, until I realized that you meant something like rational deliberation, as opposed to intuition/subconscious. OK, so rationality vs. intuition, I get it. But, except for the rather cryptic conclusion, I don't see how this connects with objective vs. subjective morality. More importantly, I don't see how this connects to the OP question.

I should make it clear, I wasn't asking for someone to just make up something based on any associations evoked by the words "objective"/"subjective". The notions of objective vs. subjective morality are commonly invoked in discussions of morality everywhere from academic works to public speeches to forum discussions. People who use these terms seem to mean something specific by them - or at least they think they do. So I want to understand what it is that the OP and those here who argued for or against "objective morality" meant by that.

The only thing that's definitely there is numbers from our instruments that don't match what we're expecting given our current gravitational models. — Terrapin Station

They match what we're expecting given our current gravitational models to a high degree of accuracy.

Would anyone actually take a crack at explaining what "objective meaning" or "objective morals" are? It's not a trivial question.

For meaning and morals to just pop out of subjectivity seems a bit queer. — intrapersona

Interestingly, one of the classic arguments for the so-called error theory of morality (which perforce denies that moral truths can be objective, since it rejects any moral truths), advanced by Mackie, is known as "the argument from queerness." It basically says that mind-independent immanent moral properties would be metaphysically queer and epistemically inaccessible without some equally queer faculties for perceiving those properties.

Murder is unethical for a civilian, but is ethical for a soldier. Cutting some one open is unethical for most of us, but not for a surgeon. Similarly, in a given situation, lying to a dying person or a child can be merciful, while telling the truth may be cruel. How can morality not be subjective to the person, and to the situation? Compassion should be better parameter of morality than any other. — Ashwin Poonawala

Of course moral prescriptions often come with some qualifications. That's not what is usually meant by moral subjectivity (although what exactly is meant is rather hard to tease out, as I mentioned above).

Whether GR is accurate or not doesn't change the astronomical data. There is something there. Our understanding of it might be inaccurate, but that doesn't change the data. — Marchesk

It does change whether what we are seeing is a black hole, because a "black hole" is not a theory-free observation, it is a theoretical entity that happens to fit observations in the context of modern physics and astronomy. That is not to say that there is something particularly suspect about black holes: we could say the same about just about anything: atoms, eclipses, electrical currents, etc.

The only really suspect thing about black holes is the theoretically-predicted singularity at their center - many consider this to be problematic as such, and especially so if we assume that quantum mechanics is valid at the same time.

? — WhiskeyWhiskers

Yeah, this is almost beautiful, isn't it? I've heard quite a few anti-AGW "arguments", but I suppose it takes a philosophy fan to take it to such a surreal level of idiocy.

I think some people are paralyzed by the awfulness of what the absence of cheap abundant oil, coal, electricity, transportation, etc. mean. It means an end to life as we know it. Some of those people are in positions of national power. If they aren't paralyzed, they may be too shocked to deal with it. — Bitter Crank

I think that the unwillingness to recognize and act upon the issues raised by climate change and natural resource exhaustion is more commonly caused by indifference than by shock and paralysis.

Contrary to common denialist conspiracies, governments hate to do anything that doesn't serve some immediate, tangible purpose, preferably with a turnaround within one or two election cycles. The only thing that would motivate them to expend limited resources and manpower on an issue that will be someone else's problem some time in an indefinite future is a strong public demand for action. (And that's democratic governments - undemocratic ones don't much care about anything other than staying in power, stuffing their pockets, and perhaps stroking their egos with grandiose projects; public welfare has little correlation with those goals.)

As for the common folk, especially of the conservative-libertarian temperament, their primary motivation tends to be self-interest. The fate of future generations is too abstract a concern. What have future generations ever done for me? Nothing, so fuck them. They want to take all they can for themselves, and they want it now. They will only sacrifice their wealth and comfort under compulsion, and future generations are not around to compel anyone.

Of course, put starkly like this, these are not very PC positions, and in any case, most people don't reason them out. Instead, these implicit positions motivate their reasoning about ostensibly scientific, factual matters. So we get a lot of hedging about how science is uncertain and evidence is insufficient.

I think one reason for the shift in terminology from "global warming" to "climate change" is that the latter is less controversial; of course the climate changes over time. The question then becomes the degree to which human activity is the cause of its detrimental aspects. — aletheist

Your last sentence is a non sequitur. The question of human contribution has no relation to whether the whole issue is nicknamed "global warming" or "climate change." Anyway, whatever the political expediency of one term or the other, "climate change" is a more accurate term, because the process is much more complex and diverse than just the rise of average global temperature (which does take place, of course).

I agree - my view is that the proposition that human activity has had and is having some negative effect on climate is "beyond a reasonable doubt," but so far there is not "a preponderance of evidence" that human activity is the sole or even dominant reason for allof the worrisome climate changes that we are observing. — aletheist

And you are basing this conclusion on your own extensive but unpublished research in climate science? Because published research paints quite a different picture.

Here is the first article title "The Universe as a Hologram": http://www.endlesssearch.co.uk/science_holographicuniverse.htm — Existensialissue

I read your quote as far as saying that "Aspect and his team discovered that under certain circumstances subatomic particles such as electrons are able to instantaneously communicate with each other regardless of the distance separating them." This is not true, and I didn't bother reading the rest.

The second article is titled "Journal of Theoretics, Empirical Evidence Supporting Macro-Scale, Quantum Holography in Non-Local Effects" and here is the link: http://www.journaloftheoretics.com/articles/2-5/benford.htm

Does the second article suggest or is saying that we live in a simulation or a hologram? — Existensialissue

This "Journal of Theoretics" is (was?) a crackpot publication. Anyway, I don't see what quantum holography, which apparently is a real thing, could possibly have to do with the idea that we live in a simulation.

Yes, this is exactly what I’m getting at, that the profundity of Zeno’s paradox (as well as Thomson’s) don’t lie in the realm of mathematics, but in logic/language. This is the point that I feel is often missed.

A form of the paradox that I like is this (from Wikipedia):

* Motion is a supertask, because the completion of motion over any set distance involves an infinite number of steps
* Supertasks are impossible
* Therefore, motion is impossible

From this, I think it's easy to see that the issues that can be taken with the paradox are issues of logic, not of mathematics and especially not of sums of series.

What does it mean for a motion to be "complete"? Is motion made up of "steps"? These are the core issues that the paradox is getting at. — Voyeur

These seem to be metaphysical questions, not questions of logic or language. There's nothing logically inconsistent or ambiguous about supertasks (and this is where mathematical treatment of convergence comes in). But one can still ask the questions that you ask as questions of metaphysics (informed by physics).

Thompson's Lamp, on the other hand, as well as a number of other such paradoxes, including the Bernardete paradox that you brought up later, are just logical puzzles. The key to their solution is that their premises are either inconsistent (Bernardete) or incomplete (Thompson). In the former case we can conclude that the premises cannot describe a possible state of affairs, which dissolves the paradox. In the latter case the problem (necessarily) does not have a unique solution, which again renders the seemingly surprising result as inevitable.

I am not sure Michael is even clear about what kind of argument he is trying to make. Syntactically, it is a purely logical argument, and it stems from his misunderstanding of mathematical concepts. He is, in effect, committed to the view that the only collections that are allowed to exist are those that are isomorphic to the natural numbers, and anything else is conceivable.

Why not? The electron's position is a value in its quantum state. — Michael

No, it isn't.

And I believe atomic electron transition is a known example of discrete motion in nature. — Michael

If you are thinking of discrete quantum states of electrons in an atom, that is not an obvious example of discrete motion (except in a generalized sense of "motion" as "change").

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.