Fishfry doesn't quite grasp the reality of the fact that the judgement of true or false, which we subject premises to, is really just a judgement of repugnant or not repugnant. OED, repugnant: 2 "contradictory", 3 "incompatible".

I didn't say infinite capacity. I denied that your free will has any capacity at all, since even the most trivial capacity would get you back to your ship 2 meters away, even if not quickly. — noAxioms

I told you how the person gets back to the ship using free will. That's one point for free will, zero for you.

A robot has the same capacity to make such a call, and robots by definition lack it. — noAxioms

A robot cannot decide whether or not to make the call, a person can. The person could decide not to, if perhaps the release of the tether was intentional. Two for free will, zero for you.

This is also utterly off topic to this discussion, but I took the easy bait anyway. — noAxioms

It's not off topic, because there is an issue of what is "physically possible", and whether physical possibility" is limited by the laws of physics. My argument is that there is a number of physical activities such as the effects of dark matter and dark energy, which violate the laws of physics. Furthermore, free will violates Newton's first law, and it causes physical movements. Therefore physical possibility is not limited by the laws of physics.

And the passage of time that we would measure as being 60 seconds occurs even when we don't measure it. — Michael

Yes, I agree with that. But, there is no "seconds" inherent in that passage of time, nor does it appear like there are any natural points for division within that passage of time, which appears to us to be absolutely continuous. This is why we assume principles which allow for infinite divisibility of time, because we see no reason for any real restrictions to its division. Therefore we tend to believe that we can simply insert a point (T1) at any random place, and another point (T2) at another random place, and determine the amount of time that has passed between those two arbitrarily assigned points.

Now, in your opening post in the thread, you concluded a "metaphysically necessary smallest period of time", and you used reference to the empirically based principle "60 seconds will pass" to support this conclusion. Therefore you've exposed inconsistency between two empirically based principles. The one principle being the assumption that the passing of time is continuous, as it appears, and the consequent principle that we can arbitrarily insert points, and divide it in absolutely any way that we please. The other principle being that "60 seconds will pass". There is inconsistency because the former leads to the example of the stairway to hell in the op, in which there is always more steps, and more time to pass, before 60 seconds can pass.

Given the logical paradoxes that continuous space and time entail, I think that discrete spacetime is not just a physical fact but a necessity. — Michael

Since you dismiss general relativity as probably false, then there is no need to maintain "spacetime". When we analyze space and time separately, then one might be discrete, and the other continuous. Logically, motion, which is a change of spatial location (place) requires the passing of time. We cannot conceive of a change in place without time passing because that implies the thing is in two different places at the same time. However, when time is separated from the constraints of spatial change we can conceive of time passing without spatial change. This allows that spatial change occurs as discrete 'quantum leaps', position at T1, to position at T2, without any spatial continuity between them. Between T1 and T2 there would be time passing, but no spatial change until that time has passed. That passage of time during which spatial change does not occur, is justified by activity at a deeper level, non-spatial, or immaterial activity, which determines the relationship between the spatial positions at T1 and the spatial positions at T2.

The question makes no sense. You're asking for some second "level" of time to define the time between T1 and T2. There's no such thing. The only time is T1, T2, T3, etc. — Michael

You continue to refuse to acknowledge the difference between the measurement and the thing measured. T1 and T2 are points designated by the measurer, therefore a feature of the measurement. The measurement is the difference between T1 and T2. However, the thing measured is the passage of time which occurs. Your confusion is due to your refusal to acknowledge a distinction between the measurement (the specified number of seconds) and the thing measured (the passage of time). You've been insisting that the thing measured is a number of seconds, rather than recognizing that seconds is the measurement, not the thing which is measured. And so I gave up trying to explain to you the difference.

LOL. Tell that to the guy stranded 2 meters from his space ship without a tether. No amount of free will is going to get you back to it. You're going to need a little help from Newton. — noAxioms

No one said free will has infinite capacity? Obviously we are limited by the circumstances we are in. But limitations are not absolutely either. So free will has it's own niche, to act according to a judgement of the circumstances.

In the circumstances you describe, an appeal to Newton would not help the poor soul, but a radio call to someone inside the spaceship, to please shoot me a line, might help. That demonstrates the benefit of free will, allowing one to act according to a judgement of the circumstances. And. it demonstrates how free will could actually get the person back to the space ship, in contrast to your suggestion of asking Newton to help, which of course, would be useless.

I think the person to whom I was replying was suggesting that somebody had asserted a proof that a physical supertask was possible. But I did not recall anybody posting such an assertion. — noAxioms

The use of "physical" in this thread has gotten so ambiguous, that equivocation abounds everywhere.

How can a human body move by free will? — fishfry

I think, and then I do. The "force" which moves me comes from within me, and therefore cannot be described by Newton's conceptions of force.

The rotational rate of galaxies is physical, even if our current theory of gravity doesn't explain it.

...

The speed of the rotating galaxies is physical — fishfry

"Speed", and "rate" are measurements derived from comparing things. This is explained in the theory of relativity, and by that theory such things are dependent on the frame of reference. A measurement does not exist without the act which measures. I see that this is indicative of your way of thinking, when you say that by referring to the axiom of infinity you can count all the natural numbers. This is a new fangled sort of doing by proxy, where the assertion (here called an "axiom") "I have done X" means that X has been done. That is the same sort of mistake which Michael was making in insisting that measurements like seconds and days exist without being measured. I referred Michael to Wittgenstein's "standard metre" example.

I hope you don't mind my saying that your choice of free will as an example was perhaps ill-advised. It's far too contentious to work. Quantum mechanics is a much better choice. But there is the problem that there are many interpretations of it, so it is not clear that it proves what you think it proves. — Ludwig V

I do not pretend to be providing a proof when I provide an example. However, I'll take your advise and refer to quantum mechanics if I'm asked to provide examples of how it is that a measurement cannot exist without an act which measures.

If I understood the OP, the walker spends arbitrarily small amounts of time on each step, 1/2 second, 1/4 second, etc. That violates the known laws of physics. So it's not a physical situation. It's a cognitive error to think we're contrasting math to physics. There is no physics in this problem. — fishfry

I dealt with this already. If you restrict the meaning of "physical" to that which abides by the law of physics, then every aspect of what we would call "the physical world" which violates the laws of physics, dark energy, dark matter, for example, and freely willed acts of human beings, would not be a part of the "physical" world.

But a physical thing must obey the known laws of physics. — fishfry

That's not true at all. It does not correctly represent how we use the word "physical". "Physical" has the wider application than "physics". We use "physical" to refer to all bodily things, and "physics" is the term used to refer to the field of study which takes these bodily things as its subject. Therefore the extent to which physical things "obey the known laws of physics" is dependent on the extent of human knowledge. If the knowledge of physics is incomplete, imperfect, or fallible in anyway, then there will be things which do not obey the laws of physics. Your claim "a physical thing must obey the known laws of physics" implies that the known laws of physics represents all possible movements of things. Even if you are determinist and do not agree with free will causation, quantum mechanics clearly demonstrates that your statement is false.

Sorry, what? Given me an example of something that violates Newton's laws, unless it's an object large enough, small enough, or going fast enough to be subject to quantum or relativistic effects. — fishfry

I gave you an example. A human body moving by freely willed acts violates Newton's first law.

"Newton’s first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This tendency to resist changes in a state of motion is inertia."

There is no such "external force" which causes the freely willed movements of the human body. We might create the illusion that the violation can be avoided by saying that the immaterial soul acts as the "force" which moves that body, but then we have an even bigger problem to account for the reality of that assumed force, which is an "internal force". Therefore Newton's first law has no provision for internal forces, and anytime such forces act on bodies, there is a violation of Newton's laws.

That's why I included the word "known." I allow that the laws of physics are historically contingent approximations to the laws of nature. — fishfry

If you understand this, then you ought to understand that being physical in no way means that the thing which is physical must obey the laws of physics. It is not the case that we only call a thing "physical" if it obeys the laws of physics, the inverse is the case. We label things as "physical" then we apply physics, and attempt to produce the laws which describe the motions of those things. Physical things only obey the laws of physics to the extent that the laws of physics have been perfected.

Ok. Scary that you and I are thinking along the same lines. What is your point here with respect to the subject of the thread? — fishfry

Ok, now we're getting somewhere. The point, in relation to the "paradox" of the thread is as follows. There are two incompatible scenarios referenced in the op. Icarus descending the stairs must pass an infinite number of steps at an ever increasing velocity because each step represents an increment of time which we allow the continuum to be divided into. In the described scenario, 60 seconds of time will not pass, because Icarus will always have more steps to cover first, due to the fact that our basic axioms of time allow for this infinite divisibility. The contrary, and incompatible scenario is that 60 seconds passes. This claim is supported by our empirical evidence, experience, observation, and our general knowledge of the way that time passes in the world.

What I believe, is that the first step to understanding this sort of paradox is to see that these two are truly incompatible, instead of attempting to establish some sort of bridge between them. The bridging of the incompatibility only obscures the problem and doesn't allow us to analyze it properly. Michael takes this first step with a similar example of the counter , but I think he also jumps too far ahead with his conclusion that there must be restrictions to the divisibility of time. I say he "jumps to a conclusion", because he automatically assumes that the empirical representation, the conventional way of measuring time with clocks and imposed units is correct, and so he dismisses, based on what I call a prejudice, the infinite divisibility of time in Icarus' steps, and the counter example.

I insist that we cannot make that "jump to a conclusion". We need to analyze both of the two incompatible representations separately and determine the faults which would allow us to prove one, or both, to be incorrect. So, as I've argued above, we cannot simply assume that the way of empirical science is the correct way because empirical science is known to be fallible. And, if we look at the conventional way of measuring time, we see that all the units are fundamentally arbitrary. They are based in repetitive motions without distinct points of separation, and the points of division are arbitrarily assigned. That we can proceed to any level, long or short, with these arbitrary divisions actually supports the idea of infinite divisibility. Nevertheless, we also observe that time keeps rolling along, despite our arbitrary divisions of it into arbitrary units. This aspect, "that time keeps rolling along", is what forces us to reject the infinite divisibility signified by Icarus' stairway to hell, and conclude as Michael did, that there must be limitations to the divisibility of time.

Now the issue is difficult because we do not find naturally existing points of divisibility within the passage of time, and all empirical evidence points to a continuum, and the continuum is understood to be infinitely divisible. So the other option, that of empirical science is also incorrect. Both of the incompatible ways of representing time are incorrect. What is evident therefore, is that time is not a true continuum, in the sense of infinitely divisible, and it must have true, or real limitations to its divisibility. This implies real points within the passage of time, which restrict the way that it ought to be divided. The conventional way of representing time does not provide any real points of divisibility.

"Real divisibility" is not well treated by mathematicians. The general overarching principle in math, is that any number may be divided in any way, infinite divisibility. However, in the reality of the physical universe we see that any time we attempt to divide something there is real limitations which restrict the way that the thing may be divided. Furthermore, different types of things are limited in different ways. This implies that different rules of division must be applied to different types of things, which further implies that mathematics requires a multitude of different rules of division to properly correspond with the divisibility of the physical world. Without the appropriate rules of divisibility, perfection in the laws of physics is impossible, and things such as "internal forces" will always be violating the laws of physics.

quote="fishfry;900943"]The walker spends ever smaller amounts of time on each step, and that eventually violates the Planck scale.[/quote]

The Planck limitations are just as arbitrary as the rest, being based in other arbitrary divisions and limitations such as the speed of light. The Planck units are not derived from any real points of divisibility in time.

The whole point of the puzzle is to sum 1/2 + 1/4 + ... = 1 — fishfry

No, the point of the puzzle is to demonstrate that the sum is always less than one, and that the mathematician's practise of making the sum equivalent to one is just an attempt to bridge the gap between two incompatible ways of looking at the theoretical continuum. The assumption that the sum is equivalent to one is what creates the paradox.

the completeness axiom of the real numbers is one of the crowning intellectual achievements of humanity. — fishfry

I hope you're joking, but based on our previous discussions, I think you truly believe this. What a strangely sheltered world you must live in, under your idealistic umbrella.

The premises violate the known laws of physics... — fishfry

Exactly, and since we know that many physical things commonly violate the laws of physics, the fact that the premises are logically consistent and that they violate the laws of physics, indicates that we need to take a closer look at the laws of physics.

Modern math is incoherent. Is it possible that you simply haven't learned to appreciate its coherence? — fishfry

No, I've read thoroughly many fundamental axioms, and found clear incoherencies, which I've shared in this forum. Many people accept premises and axioms because they are "the convention", so they do not proceed with the due diligence to determine whether there is inconsistency between them. Then, they proceed to utilize them because they are extremely useful. Problem would only arise under specific conditions which would be avoided, or a workaround developed for. So it's not a matter of learning to "appreciate its coherence", I've already learned to appreciate its usefulness, facility, and convenience. But I think that you are mistaken to think that facility necessarily implies coherency.

Totally agree, but I'm not aware of anybody claiming a proof that supertasks are possible. Maybe I missed it — noAxioms

You've got this backward. Some supertasks are coherent and consistent, therefore logically logically possible. In this case, that is the proof that they are "possible". If someone wants to insist that they are impossible then a poof is required.

Bohr felt that his discovery of the 'principle of complementarity' resolved many of the apparent paradoxes implied in quantum physics. — Wayfarer

I think that this principle says something about our capacity to observe. It might resolve paradoxes, but it does so by recognizing the limitations of the human being. These limitations are analogous to the fact that we cannot be watching with our eyes, in two different directions at the same time. Such limitations have significant impact on our capacity to understand.

He said 'everything we call real is made of things that cannot be regarded as real' and 'Physics is not about how the world is, it is about what we can say about the world.' I think he accepted the limitations of knowledge, in a rather Kantian way. — Wayfarer

I think that this supports very well, what I argued. "Physics" refers to our knowledge about the world, "what we can say about the world", it is not about how the world is. This indicates the huge gap, what I called a chasm, between our knowledge, and the way the world is. The world is not to be blamed for this, the chasm is evidence of deficiencies in our knowledge. We ought not blame the world for our own inabilities.

Isn't it possible that the world considered as a physical system is unintelligible (Plato's 'shadows on the cave wall')? — Wayfarer

To begin with, a "system" is by definition intelligible. If it were unintelligible (random) it could not be called a system. Next, do you believe that the shadows on Plato's cave wall are unintelligible? I thought the shadows were like representations which the cave dwellers took to be reality. The shadows are very real, and intelligible, as representations, however the cave dwellers mistake them for reality. This is not a case of unintelligibility of the shadows, but a mistake of the cave dwellers.

But the significant point here, as I've been discussing with fishfry, is that I still believe we ought to allow for the possibility that the world, or even some aspects of it, are in fact, unintelligible. This is because we do not know, and what we do not know, we cannot claim to have certainty about. So this is believed as a possibility, and that is a very distinct belief from the assumption that the world, or some aspect of it, actually is unintelligible.

Now, because we do not know whether or not the world is intelligible, we can only take it as a possibility that the world is intelligible. But we can cultivate faith in the idea that it is intelligible. And this faith supports, inspires, and propagates the will to speculate, hypothesize, observe, inquire, experiment, and the will to know in general. That is the philosophical desire to know. On the other hand it is utterly pointless to take it on faith that the world or any aspect of it, is unintelligible, because this kills the will to speculate, hypothesize, observe, inquire, experiment. and the will to know that aspect, in general. Simply put, to have faith in the idea that the world or part of it is random or unintelligible, annihilates the philosophical desire to know that part of the world.

So much the worse for it, many will say, but then Robert Jastrow did say, in God and the Astronomers,"For the scientist who has lived by his faith in the power of reason, the story ends like a bad dream. He has scaled the mountains of ignorance; he is about to conquer the highest peak; as he pulls himself over the final rock, he is greeted by a band of theologians who have been sitting there for centuries." — Wayfarer

I don't quite see the image here. In the example, the scientist has faith in the power of reason. The theologians have been saying that the current state of human reason is deficient, and is incapable of a complete understanding of the universe. The scientist comes to the end of his own capacity for understanding, but this ought not make him give up faith in reason, because there will be many more who come after him, and the human capacity to reason will always be growing. So is the example supposed to show a unity between science and theology, or a disjoint?

We're just arguing about a word. If you want to claim that "I prefer chocolate to vanilla, and my preference is logical," what is the point of my arguing with you about a thing like that? — fishfry

The word is "logic", and I think it's pretty important to a discussion like this, to have good agreement as to what this word means.

If I simply assert, as if a true proposition, "chocolate is better than vanilla", there is not logic here. But if I state my premises, I am allergic to vanilla, and to have an allergic reaction is bad, then my stated preference "i prefer chocolate to vanilla" is supported by logic and is logical. Do you agree? .

Says you. That is precisely the point at issue! — Wayfarer

I backed it up with logic. It was suggested that there was a fallacy involved in the logic, the fallacy of appeal to consequences. But referral to a description of that fallacy indicated that it is only a fallacy if the logic claims to deal with truth and not a fallacy if the logic deals with good and bad, "ought". So the logic shows why we ought not accept such an assumption. Here, I'll reprint it:

Ontological randomness may be logically possible but it's philosophically repugnant. The problem being that if something is deemed as random, it is in that sense unintelligible. So if something is deemed as ontologically random, and it is considered to be unintelligible, then there is no will to attempt at figuring it out.

Now the problem is that if something appears to be random there is no way of knowing whether it is epistemologically random, or ontologically random, because of the unintelligibility of it. So we won't know which until we figure it out, therefore we must assume it to be epistemologically random. And even if it is ontologically random, we will still never know that this is the case, so we will always have to assume that it is epistemologically random, and try to figure it out. The category of "ontological randomness" is absolutely useless. — Metaphysician Undercover

What do you think he means? I'm sure he doesn't mean that the indeterminate nature of quantum phenomena is simply due to gaps in our knowledge. — Wayfarer

On the contrary, I think that's exactly what he means, except he's not talking about simple "gaps" in our knowledge, he's talking about a huge chasm, hence the word "shocked". What the baffling nature of quantum phenomena reveals to us, is that the reality of the world is very far outside of our current ability to understand it. "Indeterminate" means beyond our capacities to determine, and why he thinks that we ought to be "shocked by quantum physics" is that these "indeterminate" aspects are so significant, and have been shown to be so far outside our capacity to understand, that it reveals how shockingly minimal our current capacity to understand the reality of spatial temporal existence actually is.

So what we currently know about physical reality is just like the proverbial tip of the iceberg, and the vast majority lies hidden from us. Meanwhile, the commonly held idea in the conceit of humanity, is that we're on the verge of knowing everything there is to know, and all of reality which is intelligible, is very close to being within our grasp. That's why he thinks that if we're not shocked, we don't understand, because what is revealed through an understanding of quantum reality annihilates that commonly held self-idolatry idea. It does this by revealing to us that we really only have a very slight grasp of a very small portion of the complete intelligible reality.

This is the reason for Aquinas positing God as fundamentally intelligible, and the most highly intelligible, despite the fact that the human intellect in its current condition of being united with matter, has not the capacity to understand God. We allow that the highest principles of reality are intelligible, yet the deficiencies of the human intellect are what make them appears as unintelligible to us. Aquinas' representation here, of God as a Form, makes God most highly intelligible, despite the fact that we cannot understand Him in our current condition. And this is how Christian theology put an end to the dead end direction which was Neo-Platonism, and Plotinus' representation of the highest principle, "One" as outside the realm of intelligibility.

Therefore, it is not simply "my opinion" which I am expressing. I have the support of some of the best metaphysicians and theologians who have lived, in my judgement as to which assumptions we ought to accept and ought to reject.

Call it anything you like, but not logic! Logic means something else. That term is already taken. You are using extra-logic. Morality, right or wrong, productive/nonproductive. All well and good, but not logic. If logic is to mean anything, it has to mean something. — fishfry

Slow down, you are not taking the time to understand what I said. In the application of logic, there is two aspects to soundness, the truth or falsity of the premises, and the validity of the logical process. The term "logic" refers to the validity of logical process, it does not apply to the premises. All applications of logic utilize premises as providing the content. The logical process is the form. A valid logical process may utilize faulty premises, and this will result in faulty conclusions even though the logic is valid, and in this case we say that the conclusions are valid, and logical, yet they are unsound.

Accordingly, what I've presented is logic! Moral philosophy uses logic, and it is rightfully called "logic", and it is valid. The issue is that it uses a different sort of premise. Instead of judging the premises as true or false, and the soundness of valid logic being decided according to such a judgement of the premises, the premise are judge according to principle of good and bad. If there was such a thing as what is "truly good", then the premises of moral logic could be judged as true and "sound" in the sense of true. But due to the is/ought incompatibility, there is really no such thing as the truth about "the good".

Therefore, we must respect the fact that moral arguments can proceed with valid logic, from premises which receive their "soundness" from moral judgements of good and bad. You might argue that all moral arguments are unsound, because soundness requires true premises, but to argue it's "not logic!" is an untenable principle. It is logic, using the very same formal systems for validity, only it employs different criteria for soundness, because it uses a different type of premise, as required by a different type of content.

If I'm choosing good versus bad I'm not using logic... — fishfry

The issue is that in most applications of logic, we do not use logic to judge the premises. And, in all applications premises are required. If it was always required that the premises are judged by logic, we'd have an infinite regress, these premises are justified by logic based in those premise, which are justified by premises based in a further set of premises, ad infinitum. So, we use principles with lesser degrees of certainty to support the premises, inductive reasoning (which is sometimes called logic), abductive reasoning, and most often principles which are just accepted by convention. These premises which are accepted because they are the convention are the social standard, or norm, so they are accepted as truth without doubt. The conventional principles, which account for very many premises in logical arguments are no different from a judgement of good and bad.

So, choosing good versus bad, is not a matter of using logic, just like you say. But neither is most instances of judging premises for truth or falsity. And even if premises are judged using logic, the premises of that logical process must be judged, so at some point the premises of all logic must be judged by something other than logic. Since much of this judgement is based in nothing other than what is the social norm for truth, it is fundamentally the very same type of judgement as choosing good versus bad. The difference is that "truth" deals with "what is" and this is justified by past experience, whereas "ought" deals with what should be, and this is justified by what we want for the future.

Yes but the contrary proposition of determinism is even more repugnant, as I've noted. Shouldn't we (logically!) choose the lesser of two repugnancies? — fishfry

As I explain, there is another option other than "determinism".

And you have not shown randomness philosophically repugnant. By the time I thought about it a little, I realized that randomness is our only hope for salvation. It's the only way we're not automatons. Clockwork oranges. So you haven't made your point here. I am a proud randomite. — fishfry

I suggest that the reason you are like this, is that you do not respect the fallibility of scientific knowledge. There are specific axioms, or fundamental laws of physics, such as Newton's first law, which create the illusion of determinism. The illusion is the assumption that all will continue to be as it has been in the past, unless "caused" by a force, to change. The force here is generally understood to be the energy of something else which has continued to be as it has been in the past. The result is causal determinism. However, when we allow that free will "causes" change in a way which is not determined by the past, we break this illusion. However, this requires accepting that there is a fundamental incompleteness of Newton's laws, which implies that physical reality is really not the way that it is represented by the laws of physics.

This is way past the lamp. The lamp is not a physical thing. These puzzles have no bearing on physical reality. That's a cognitive error everyone makes about them. — fishfry

The "bearing on physical reality" is always the way in which it is applied. This is no different from mathematics in general. Mathematics has no bearing on physical reality other than its application. This is why it is so important to distinguish between the logical process itself, and the axioms or premises, which determine the applicability. The relationship between the logic and physical reality, is a matter of the application, or practise, and this is the way that we take content from our beliefs about the way that the physical world is, and our beliefs about what is good and what ought to be, and apply the logical process to these beliefs. In philosophy it is assumed that the basic axioms ought (notice recognition of the overall supremacy of ought here) to be self-evident truths. But in mathematics, the basic axioms are simply whatever is desired for the purpose of the individual mathematician who is designing the applicability of the logical system. (So desire is veiled under the hidden intention of the mathematician rather than recognized as the overarching principle.

You say randomness and determinism are compatible, and your justification is to use an alternate and unrelated meaning of the word determined? — fishfry

I did not say that randomness and determinism are compatible. You offered the dichotomy, randomness or determinism, with no other option. I offered another option, free will, as a type of determining which is not consistent with determinism, nor is it consistent with randomness. Determinism is based in a highly restrictive sense of "determine" which limits any form of determining to a meaning of having itself been determined by prior causation. This sense of "determine" employed by determinism excludes the possibility of a free will act. It also excludes the possibility of a first act, which is demonstrably problematic. So the problem with your proposed dichotomy is that by restricting the definition of "determine" to that employed by determinism, which is a demonstrably faulty restriction, it does not give us realistic options.

But you talk about a "real physical boundary." Here you imagine that the staircase is physical. It's not. The conditions of the problem violate known laws of physics. — fishfry

I really don't see how there could be a staircase which is not physical. That really makes not sense. However, just like in the case of the word "determine", we need to allow for two senses of "physical". You seem to be saying that to be physical requires that the thing referred to must obey the laws of physics. But the classic definition of "physical" is "of the body". And when a body moves itself, as in the case of a freely willed action, that body violates Newton's first law. Therefore we have to allow for a sense of "physical" which refers to things which are known to violate the laws of physics, like human beings with freely willed actions.

What is implied here is that the laws of physics are in some way deficient in their capacity for understanding what is "physical" in the sense of "of the body". That's why people commonly accept that there is a distinction between the laws of physics and the laws of nature. The laws of physics are a human creation, intended to represent the laws of nature, that is the goal, as what is attempted. And, so far as the representation is true and accurate, physical things will be observed to obey the laws of physics, but wherever the laws are false or inaccurate, things will be observed as violating the laws of physics. Evidently there are a lot of violations occurring, with anomalies such as dark energy, dark matter, etc., so that we must conclude that the attempt, or goal at representation has not been successful.

It's only a conceptual thought experiment. And why shouldn't math apply to that? — fishfry

Sure, it's a conceptual thought experiment, but the interpretation must follow the description. A staircase is a staircase, which is a described physical thing, just like in Michaels example of the counter, such a counter is a physical object, and in the case of quantum experiments, a photon detector is a physical object. And of course we apply math to such things, but there are limits to what we can do with math when we apply it, depending on the axioms used. The staircase, as a conceptual thought experiment is designed to expose these limits.

But anyway, it's an upper bound. If it's a least upper bound, it's a limit. — fishfry

OK sure, but that's a limit created by the axioms of the mathematics. So it serves as a limit to the applicability of the mathematics. The least upper bound is just what I described as "the lowest total amount of time which the process can never surpass". Notice that the supposed sequence which would constitute the set with the bound, has already summed the total. This is not part of the described staircase, which only divides time into smaller increments. It is this further process, turning around, and summing it, which is used to produce the limit. The limit is in the summation, not the division.

It is very clear therefore, that the bound is part of the measurement system, a feature of the mathematical axioms employed, the completeness axiom, not a feature of the process described by the staircase descent. The described staircase has no such bound, because the total time passed during the process of descending the stairs is not a feature of that description. This allows that the process continues infinitely, consuming a larger and larger quantity of tiny bits of time, without any limit, regardless of how one may sum up the total amount of time. Therefore completeness axioms are not truly consistent with the described staircase.

However, since our empirical observations never produce a scenario like the staircase, that inconsistency appears to be irrelevant to the application of the mathematics, with those limitations inherent within the axioms. The limitations are there though, and they are inconsistent with what the staircase example demonstrates as logically possible, continuation without limitation. Therefore we can conclude that this type of axiom, completeness axioms, are illogical, incoherent. The real problem is that as much as we can say that the staircase scenario will never occur in our empirical observations, we cannot conclude from this that the incoherency is completely irrelevant. We have not at this point addressed other scenarios where the completeness axioms might mislead us. Therefore the incoherency may be causing problems already, in other places of application.

'I cannot believe that God plays dice', said Einstein, in response to the discovery of the so-called 'quantum leap'. (Bohr used to say 'stop trying to tell God how to manage the Universe'.) But it is a known fact, as is the stochastic nature of radioactive decay. That doesn't mean that maggots spring fully formed from damp cloth, of course, but that there is an inherent element of unpredictability at the most basic strata of nature. — Wayfarer

As already argued in this thread, above, the so-called "stochastic nature" of radioactive decay, is best understood as a feature of the means employed to understand it, rather than as a feature of the named activity itself. In other words, it is better to assume that the appearance of randomness is due to the deficiencies of the theories and methods used to understand the object, rather than to assume that the randomness inheres within the object.

I can agree with your reasoning that one "ought" not to accept it, but the reason is extra-logical. That is, if we are going by pure logic, you have not argued against it. It's like solipsism. Can't refute but pointless to believe it. — fishfry

There is no such thing as "going by pure logic", toward understanding the nature of reality. "Pure logic" would be form with no content, symbols which do not represent anything. All logic must proceed from premises, and the premises provide the content. And premises are often judged for truth or falsity. But as explained in the passage which referenced, in the case of an "appeal to consequences", there is no fallacy if the premises are judged as good or bad, instead of true or false. That's why I said that this type of logic is very commonly employed in moral philosophy, religion, and metaphysical judgements of means, methods, and pragmatics in general. So for example, one can make a logically valid argument, with an appeal to consequences, which concludes that the scientific method is good. No fallacy there, just valid logic and good premises.

Therefore it is not the case that the reasoning is "extra-logical", it employs logic just like any other reasoning. What is the case is that the premises are a different sort of premises, instead of looking for truth and falsity in the premises we look for good and bad. So this type of judgement, the judgement of good or bad, produces the content which the logic gets applied to.

But consider: If the world is not random, then it's determined. And is that not equally repugnant? Nothing matters because we have no choice. — fishfry

No, that is not the case, because there are two very distinct senses of "determined". One is the sense employed by determinism, to say that all the future is determined by the past. The other is the the sense in which a person determines something, through a free will choice. In this second sense, a choice may determine the future in a way which is not determined by the past. And, since it is a choice it cannot be said to be random. Therefore it is not true that if the world is not random then it's determined (in the sense of determinism), because we still have to account for freely willed acts which are neither determined in the sense of determinism, nor random.

God transcends logic, fair enough. But again, that's not a logical argument. — fishfry

As I said above, it is not a matter of transcending logic, the conclusions are logical, but the premises are judged as to good or bad rather than true or false. So from premises of what is judged as good (rejecting repugnant principles), God may follow as a logical conclusion.

Here you are arguing that just because an idea is repugnant is no logical reason to reject it! So you should apply the same reasoning to randomness. — fishfry

No I was not arguing that. In that case I was arguing that the idea ought not be accepted (ought to be rejected) unless it is justified. In the case of being repugnant, that in itself is, as I explained, justification for rejection. You appear unwilling to recognize what wonderer1's article said about the fallacy called "appeal to consequences". It is only a fallacy if we are looking for truth and falsity. If we are talking principles of "ought", it is valid logic. Therefore the argument that the assumption of randomness ought to be rejected because it is philosophically repugnant, cannot be said to be invalid by this fallacy, and so it may be considered as valid justification.

I agree with you there. I agree with most of what you wrote. Still I do want to understand why you see that Michael is wrong to say that supertasks are logically impossible, when they are merely repugnant; yet you seem to reject that same reasoning when applied to randomness. — fishfry

But Michael did not show that supertasks are philosophically repugnant. He showed that they are inconsistent with empirical science, and his prejudice for what is known as "physical reality" (reality as understood by the empirical study of physics) influenced him to assert that supertasks are impossible. As I explained in the other thread, in philosophy we learn that the senses are apt to mislead us, so all empirical science must be subjected to the skeptic's doubt. So it is actually repugnant to accept the representation of physical reality given to us by the empirical sciences, over the reasoned reality which demonstrates the supertask. And this is why that type of paradox is philosophically significant. It inspires us to seek the true reasons for the incompatibility between what reason shows us, and what empirical evidence shows us. We ought not simply take for granted that empirical science delivers truth.

Also, don't you think determinism is at least as repugnant as randomness? — fishfry

As explained above, I am not taking a standpoint of determinism. There are two very distinct senses of "determine", one consistent with determinism, one opposed to determinism (as the person who has a very strong will is said to be determined). I allow for the reality of both.

"The process carries on, unlimited, even though there's a limit." I haven't the keystrokes to untangle the myriad conceptual difficulties with that statement, and the beliefs and mindset behind it; even if I had the inclination. I hope you'll forgive me, and understand. — fishfry

I can explain it very easily. There is two different senses of "limit" being used here. One is a logical "limit" as employed in mathematics, to describe the point where the sequence "converges". And "unlimited" is being used to refer to a real physical boundary which would be place on the process, preventing it from proceeding any further. There is no such "limit" to a process such as that described by the op. The appearance of paradox is the result of equivocation.

So it seems that we are locked into two incompatible ways of thinking about infinity. One as if it were a sequence which stretches away for ever. The other as a succession of operations which can be continued for ever. (Two metaphors - one of space, one of time.) I'm not suggesting it needs to be resolved, just that we are subject to confusion and need to think carefully, but also recognize that our normal ways of thinking here will need to be adapted and changed. — Ludwig V

The problem, as displayed in my reply to fishfry above, is that each of the two incompatible ways will use the same terms. The same terms will then have incompatible meanings as you demonstrate with "ad infinitum", and the natural tendency for human beings not to take the time required to detect such differences, leads to equivocation and the appearance of paradox.

Yes, quite so. But it follows that applying the calculus to Achilles doesn't demonstrate that Achilles will overtake the tortoise. I think that only ordinary arithmetic can do that. — Ludwig V

That's right, and the issue with Achilles and the tortoise has extra complexities which are often overlooked. Achilles and the tortoise are both moving. At any point in time, t1, Achilles is at a location and the tortoise is at a location. At t2, Achilles reaches the location where the tortoise was at t1. But the tortoise has moved to a new location. At t3 Achilles reaches the location where the tortoise was at t2, the tortoise has moved to a new location. And so on. In this case, therefore, it is not only impossible for Achilles to overtake the tortoise, it is also impossible for Achilles to catch up to the tortoise, so it appears like the tortoise will necessarily beat Achilles to the finish line.

We cannot describe the tortoise's position as a simple limit to Achilles' position, because the tortoise is already moving at a constant velocity, and no matter how fast Achilles accelerates he cannot catch up to the tortoise. This is the problem of acceleration, which demonstrates the fundamental incompatibility between distinct rest frames. Einstein attempted to bridge this incompatibility by stipulating the speed of light as the limit, (therefore absolute rest frame) in his special theory of relativity.

Read carefully. I didn't say that. — noAxioms

That's why I was asking, "are you saying...". You seemed to be saying what I asked about, but I was not sure. Now you are making it clear that you were saying something else. So I now understand that you were attacking a straw man effigy of me, and that's why I couldn't understand you.

2), that you [cannot / choose not to] understand what others mean when they presume what Michael conveyed better than I could: — noAxioms

If I don't understand, then I don't understand. I believe that I said that I don't understand why someone would make an assumption which to me is so clearly false. So to explain why someone would make such an assumption, would require an explanation as to how this obviously false assumption makes some sense to the person. The quoted passage, in which you say Michael makes sense of his perspective, makes no sense to me, because it is a straw man representation of what I am arguing. I told Michael that I didn't understand how this was relevant, and he needed to explain its relevance. I now fully understand that it was a straw man, and that's why I couldn't apprehend the relevance. Michael did not understand what I was arguing, therefore produced a straw man representation of me, and I could not understand what Michael was accusing me of, because he did not understand me and tried to defend against a straw man of me.

You (M-U) seem to either not be able to separate "X" and Y, or you refuse to communicate with those that do. — noAxioms

I have no problem distinguishing between the sign and what is signified. The problem here is that Michael refused to recognize the distinction between when the thing signified is a real physical object, and when the thing signified is a mental fabrication, a fiction, or an ideal. So Michael was talking about ideals, principles of measurement, like a day, and a second, as if these mental fabrications have some sort of existence independent from human minds, in some Platonic realm or something like that.

My personal beliefs in this matter are irrelevant. I simply know what somebody means when they treat Y as something independent of "X". — noAxioms

I'll repeat, just so that you'll quit with this utterly ridiculous straw man accusation you are hitting me with. I have no problem whatsoever with the separation between the symbol and the thing represented by the symbol. That is not at all what is at issue here, so you are simply making a straw man representation of what I am arguing.

The problem here is with the nature of the thing represented. Do you understand that sometimes what is represented by a symbol is a real physical object, and sometimes what is represented by a symbol is an ideal, such as a mathematical object? And do you understand that these two types of objects are completely different, and need to be understood in completely different ways. My claim is that it is highly doubtful that an ideal such as "a second" has any existence independent from the human minds which I believe fabricate them, and propagate them through educational processes.

Michael has been arguing that "a second" has some sort of real independent existence, just like a physical object which we can point to, instead of being an ideal which is propagated by human minds, as I claim. So, I've asked him to show me such a thing as "a second". All he has provided is a definition referring to some ideal state (ground state) of a cesium atom. Since the definition refers to an ideal state (ground state), rather than any real existing physical object, it seems very clear that "a second" is an ideal, not an independent physical thing.

That this period of time is named "60 seconds" depends on us. That 60 seconds pass does not depend on us.

You don't seem to understand how reference works. — Michael

This is not a simple issue of reference, it is an issue of the type of thing which is referred to. In the example here "seconds" is an ideal, just like any other principle of measurement, metre, foot, degree Celsius, circle, triangle, and number in general. They are all ideal, and are therefore dependent on the human minds which employ them, unless you assume some sort of Platonic realm for the independent existence of such ideals.

So, we say "time is passing", just like we say "the earth is spinning around the sun", and we refer to real independent things with those phrases, "time", "the earth", "the sun". However, when we go to measure those things, we employ principles, which are ideals, and have no such independent existence. So, when we say "60 seconds has passed", "60 seconds" refers to an ideal which has been applied to measure the independent passing of time. The 60 units of seconds do not pass, time passes, and "60 seconds" refers to the ideal which is employed.

For example, we could say "the earth circles the sun". In this case, "circles" refers to the ideal which is employed in measuring the earth's motions. We know that a circle is an ideal figure, and that true circles do not have any real existence independently from human minds, because pi, which is the essential feature of a circle, is an indefinite, irrational number. So the motion of the earth isn't really a circle, that's just the ideal which is referred to in that statement. Likewise, in the statement "60 seconds" has passed, "seconds" is just the ideal which is referred to, as the principle employed in the act of measurement. And we find these ideals in all forms of measurements, metres, degrees of temperature, frequencies, etc..

Surely a lot of these problems go away if you concede that nature contains an element of spontaneity, as well as patterns which we characterise as "laws". — Wayfarer

It is not useful to assume spontaneity, just like it is not useful to assume randomness. Are you familiar with the theory of "spontaneous generation"? It used to be the accepted "scientific" theory for how tiny organisms like maggots come into existence. They just kind of pop out from inanimate matter. Of course the theory has been disproven, I think by Louis Pasteur. However, old habits die hard, and now we have the very similar "scientific" theory of abiogenesis and other things like spontaneous symmetry breaking. In general spontaneity does not serve as a good explanatory principle.

If I am understanding you: You say that if we have a sequence; that if that sequence happens to have a limit, then the limit is not inherent to the sequence, but is rather imposed by the observer. — fishfry

That's not quite what I'm saying. The process described by the op has no limit. That should be clear to you. It starts with a first step which takes a duration of time to complete. Then the process carries on with further steps, each step taking half as much time as the prior. The continuity of time is assumed to be infinitely divisible, so the stepping process can continue indefinitely without a limit. Clearly there is no limit to that described process

I think what's confusing you into thinking that there is a limit, is that if the first increment of time is known, then mathematicians can apply a formula to determine the lowest total amount of time which the process can never surpass. Notice that this so-called "limit" does not actually limit the process in any way. The process carries on, unlimited, despite the fact that the mathematician can determine that lowest total amount of time which it is impossible for the process to surpass.

Clearly, the supposed "limit" is something determined by, and imposed by, the mathematician. To understand this, imagine the very same process, with an unspecified duration of time for the first step. The first step takes an amount of time, and each following step takes half as much time as before. In this case, can you see that the mathematician cannot determine "the limit"? All we can say is that the total cannot be more than double the first duration. But that's not a limit to the process at all. It's just a descriptive statement about the process. It is a fact which is implied by an interpretation of the described process. As an implied fact, it is a logical conclusion made by the interpreter, it is "not inherent to the sequence", but implied by it.

That it is not inherent, but implied, can be understood from the fact that principles other than those stated in the description of the process, must be applied to determine the so-called "limit".

Exactly so.
Your disagreement with views that suggest this is a subject for a different topic. Your displayed lack of comprehension of what the person means when he says things like that is either in total ignorance of the alternatives or a deliberate choice. Being the cynic I am, I always suspect the latter. It's my job as a moderator elsewhere.

I do thank you for verifying my earlier assessment. — noAxioms

Are you saying that you believe that there would still be an April 29, even if there never was any human beings with their time measuring techniques, and dating practises? And do you believe that there would still be "seconds" of time without those human beings who individuate those temporal units in the act of measurement? I don't understand how you can believe that I should accept this as a reasonable alternative. Care to explain?

So they don't want a better government, better economic policies, or better anything. What they want, is to bring down the whole system, because they don't accept the principles on which it was founded. — Wayfarer

They don't know what they're voting for in terms of politics, they aren't educated enough or they are so within their own bubble that they don't have any access to anything but the notion of "us and them". — Christoffer

Anarchists, who are not well educated in politics, or moral and social philosophy in general, are the modern day libertarians.

Your whole argument for less ambiguity is based on an impractical desire for words to be absolutely concrete and defined. — Benj96

No, it's not based on such a desire at all. I recognize that to be impossible. My desire is that the writer of the material which I am reading, would have a good understanding of what they are saying, so that they can express themselves with clarity, instead of using ambiguous words to coverup the fact they know very little about the subject that they pretend to be knowledgeable of.

Notice, in your referred article, that when the argument's conclusion concerns good and bad, rather than true or false, it is not considered to be a fallacy.

I use the term "information" myself because I think it is useful and has its own flavour of characteristics outside of just energy transfer or material arrangements. — Benj96

That "flavour of characteristics" is what I call ambiguity. Your use of this word conflicts with the idea you expressed above, about using well defined words with less baggage.

Perhaps it's better to ask someone to clarify how they use a seemingly ambiguous term- because the ambiguity rarely comes from the user of the word. They usually know exactly how they're using it. Therefore ambiguity is more based on the interpreter which may not be sure what thr details of their definition are. — Benj96

I flatly disagree with this. In a place such as this, TPF, the use of ambiguous words is more often than not an indication that the person does not know what they are talking about. It's like a child, just learning to talk, who uses big words to sound proficient, but really doesn't say anything with those words.

Logic is: reasoning conducted or assessed according to strict principles of validity. — Barkon

Empirical does not mean absolute, it means more probably. — Barkon

Deductive logic proceeds from premises which are often produced from inductive reasoning and empirical evidence. As you noticed, empirical evidence does not provide absolute certainty, so inductive principles are based n probability. So when we judge empirical premises as true or false, these are judgements of probability. If I say "Premise A is true", I really mean it is probably true, and this is because I don't "understand everything there is to know", and something may be overlooked, as you mention in the op.

Logic is: reasoning conducted or assessed according to strict principles of validity. — Barkon

This statement is applicable to deductive logic, but inductive reasoning (logic) does not proceed according to strict principles. This is why induction cannot be relied on to provide certainty.

You are falling into the trap of thinking a limit "approaches" but does not "reach" its limit. It does reach its limit via the limiting process, in the same sense that 1/2, 3/4, 7/8, ... has the limit 1, and 1 is a perfectly good real number, and we all have had literally billions of experiences of one second of time passing. — fishfry

There is no limiting process in the premises of the op, nor in what is described by . The "limiting process" is a separate process which a person will utilize to determine the limit which the described activity approaches. Therefore it is the person calculating the limit who reaches the limit (determines it through the calculation), not the described activity which reaches the limited.

Striking that he used the same word you used, repugnant. But repugnance is not a logically argument, and what's repugnant in 1733 may turn out to be exactly what's needed to model general relativity in 1915. You never know. — fishfry

"Repugnant", is a commonly used word in philosophy. The argument I gave is logical, but what is concluded is that the assumption, "there is ontological randomness" is philosophically repugnant, because it would be counter-productive to the desire to know. Therefore it's more like a moral argument. The desire to know is good. The assumption of ontological randomness hinders the desire to know. Therefore that assumption is bad and one ought not accept it.

Since the argument concerns an attitude, the philosophical attitude, or desire to know, you're right to say that it is an argument concerning "feelings". But that's what morality consists of, and having the right attitude toward knowledge of the universe is a very important aspect of morality. This is where "God" enters the context, "God" is assumed to account for the intelligibility of things which appear to us to be unintelligible, thereby encouraging us to maintain faith in the universe's ability to be understood. Notice how faith is not certainty, and the assumption that the universe is intelligible is believed as probable, through faith

In this sense you are putting the idea of a random universe in the same category of solipsism. You can't prove it's false, but it's pointless to believe it because it leads nowhere. Therefore we should reject it on that basis. They're both essentially nihilistic ideas. — fishfry

Not only is it pointless to believe it, but I would say it is actually negative. Choosing the direction that leads nowhere is actually bad when there are good places to be going to.

In any event, I conclude that it's still logically possible that the true nature of the universe, if there even is such a thing, is random. And then we can still wonder ... how does all this apparent order arise from underlying randomness? So the philosophers would still have something useful to do, even in a fully random world. — fishfry

I agree that it is very important to leave as undecided, anything which is logically possible, until it is demonstrated as impossible. Notice what I argue against is the assumption of real randomness, that is completely different from the possibility of real randomness. That we ought to leave logical possibilities undecided was the point I argued Michael on the infinite staircase thread. Michael argued that sort of supertask is impossible, but I told him the impossibility needed to be demonstrated, and his assumption of impossibility was based in prejudice.

I believe that paradoxes such as Zeno's demonstrate an incompatibility between empirical knowledge, and what is logically possible. Most people will accept the conventions of empirical knowledge, and argue that the logically possible which is inconsistent with empirical knowledge is really impossible, based on that prejudice. But I've learned through philosophy to be skeptical of what the senses show us, therefore empirical knowledge in general, and to put more faith and trust in reason. So, to deal with the logical possibility presented in that thread, we must develop a greater intellectual understanding of the fundamental principles, space and time, rather than appeal to empirical knowledge. Likewise, here, to show that the logical possibility of ontological randomness is really impossible, requires a greater understanding of the universe in general.

60 seconds can pass without anyone measuring it. — Michael

That's like saying today would be April 29 even if there was never any human beings to determine this. If you can't understand how this is wrong, I don't know what else to say.

Yes there are. A second is "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the caesium-133 atom". This occurs even if we don't measure it. — Michael

Nice try Michael, but "ground state" is an ideal which does not occur in nature. It's like a "blackbody" and things like that, ideals used for theory, which do not ever truly exist. Like "60 seconds" in the OP it is approached as a limit, but never truly achieved.

Besides, what you've provided does nothing to resolve the problem I explained. It's just the same as your example of "a year". The activity is what occurs, time passes. What you gave is the definition of "a second", that means that a second is the duration of time which is equivalent to that activity. A second is not that activity itself. So the activity occurs, and there are no seconds unless someone determines the duration of time required for the specified number of oscillations. That's why beginning and end points are required which constitute a measurement, just like I explained to you in the case of "a year".

Yet again you can't seem to get beyond our use of labels to understand that our labels refer to things that exist and do things even when we're not around. — Michael

I have no problem accepting that things exist even when we're not around, and I gave you examples of such things, dogs and cats. However, what you are not getting, is that some labels refer to things created by human beings, these are called "ideals". So, we have two categories of labeled things, natural things which exist even when we're not around, and things created by minds, such as ideals, which are dependent on minds. And, you refuse to distinguish between the natural things, and the artificial ideals. So you insist that because it is a labeled thing, it must exist even when were not around. That's the folly of Platonism. Do you not understand that "the second" is a mathematic object of ideal time, just like "the circle" is a mathematical object of ideal space?

Your reading comprehension skills are also off. I never suggested converting you to some opinion other than the one which you hold. I simply suggests that you seem incapable of understanding alternatives, to the point where you don't understand people who presume one of these alternatives. — noAxioms

I think you misunderstand. I understand the alternatives very well, so well in fact that I can comprehend the contradictions which inhere within some of these alternatives. So I see the need to reject them. The people who assert, and insist on some of these alternatives do so without proper understanding themselves. They accept and assert by the force of convention, which is simple prejudice, and they refuse to acknowledge the contradictions within, assuming that convention cannot be faulty.

If we take the term “1 year” as an example, the Earth orbiting the Sun does not depend on us measuring it. It just orbits it, independently of us. — Michael

OK, the earth goes around the sun indefinitely, even if there were no humans on earth. But there is no "years", nor is there any individual "orbits" separated out without someone, or a device to make the judgement of beginning and end.

That is the problem with your example. Time passes, we agree on that, but there are no seconds unless measured out. Now, both the counter doing the supertask, and the ordinary stopwatch are designed to measure the passage of time. The counter, with it's supertask has one way of counting out time, by dividing seconds into shorter and shorter increments, while the stopwatch is designed to measure an endless procession of seconds. The two are incompatible.

A white box turns red when the Earth completes a half-orbit, turns blue when it completes another quarter-orbit, turns back to white when it completes another eighth-orbit, and so on.

What colour is the box when the Earth completes its orbit around the Sun? — Michael

Same problem, the device is not designed to reach the end of an orbit. It will keep on changing colours faster and faster without ever getting to the end of an orbit. I assume it would probably burn up though, from going too fast.

The previous attempts were at the urging of spouse, or because of the usual arguments about what's good for you. — Vera Mont

So these attempts were a matter of caring about something else (your spouse, your health), more than smoking. And this is what actually failed for you, the method which involved caring about something else more than smoking.

You will give up smoking if you care more about stopping than you do about smoking. — Janus

OK, so do you agree, that this is pure will power? Attempting to quit smoking because one cares more about not smoking than smoking, and having success this way, is a matter of the will deciding to change, for no other reason than to change, and this is successful. That is purely, and absolutely a matter of determining "sui generis what is significant for us, what we care about". And that contradicts what you said earlier: "The point is that we do not determine sui generis what is significant for us, what we care about".

My point has only been that we care about what we care about, and we can't just magically decide to care more about something we previously cared less about—we need incentives to shift our concerns. — Janus

Yes, people often do "magically decide to care more about something we previously cared less about", this is known as changing one's priorities. That is what deciding to quit smoking because one cares more about not smoking than smoking, is representative of. Its actually very common, and it is what gives the person incentive to shift one's concerns. You have the causal order reversed. You seem to think that some random event must happen in the universe, a change in the star signs or something which pulls at the superstitions, and this provides incentive for change to a person. In reality what is required is simply a decision by the person, change my concerns, along with the will power, and that is what creates the incentive, the decision itself, and the capacity to adhere to the judgement made.

Attempting to discuss anything with you is usually an endless battle against strawmen. — Janus

Such statements are an indication of denial. You reveal to me, through what you say, your own ideas, and when I interpret what you've said, you claim it to be a strawman. This is because what you say, and reveal about your own beliefs, is not consistent with the metaphysical principles which you hold. Instead of recognizing that your beliefs are inconsistent with your principles, and acknowledging that the principles you hold are not consist with your own experience, so that you ought to change those principles, you simply deny my interpretation of what you've already told me, as a strawman. In reality, as demonstrated above, when pressed, you contradict yourself because the metaphysical principles you profess are inconsistent with your beliefs.

Once again, M-U cannot comprehend a view outside his own idealistic assumptions. — noAxioms

If someone would explain to me, in a way which makes sense, a better perspective, then I'd happily switch. Simple assertions like "It must", and "no it's not" just do not suffice for helping a poor lost soul such as myself, comprehend another view.

but it is a fact that 60 seconds of time can pass without anyone looking at a clock or a stopwatch. — Michael

Simple assertions do not help me to understand what you are trying to say. "60 seconds" is the reading we get of the clock. It's just a generic symbol, like "dog" or "cat". But I can show you many things which would be called "a dog", and things called "a cat". Now, if you think that there are some things called "60 seconds", other than the reading taken from a measuring device, then show them to me.

Consider Wittgenstein's example of "the standard metre in Paris". "One metre" is a measurement, and there are many items which can be measured to be a metre. The standard metre is the paradigm, the official example of that convention. But there are no objects in the world which "one metre" refers to, not even the standard metre, as this is the paradigm, it is not "one metre" itself. Likewise, we can measured a multitude of different times as "60 seconds", and there is a paradigm, or standard which is the oscilation of the cesium atom, but there is nothing in the world which is referred to by "60 seconds"

the second, defined as about 9 billion oscillations of the caesium atom. — Wikipedia

https://en.wikipedia.org/wiki/Unit_of_time#:~:text=The%20base%20unit%20of%20time,oscillations%20of%20the%20caesium%20atom.

Billions of years passed before humanity evolved, and this isn't some retroactive fact that only obtained when humanity started studying the past. — Michael

A ''year" is nothing but a human convention, a standard of measurement, just like "a metre". Therefore there was no years prior to humanity. What you talk about here is a projective measurement backward in time. There was something occurring prior to humanity, which we commonly call "the passing of time", but what is referred to as the passing of time did not consist of years, as "years" is the product of the measurement, just like "metres" is the product of the measurement. To claim that standards of measurement existed prior to humanity, which actually invented them, is Pythagorean idealism, Platonism. Then these standards become eternal principles, such that God was measuring the passage of time prior to humanity, to determine the passage of "years". But this Platonism is demonstrably wrong, because it excludes the possibility of error.

That the passing of time is something completely different than a succession of years is very evident from the fact that it can be measured as a succession of a vast multitude of different increments, years, days, minutes, seconds, picoseconds, nanoseconds. Each of these increments serves as a measurement standard, (just like metre, centimetre, kilometre, foot, inch, mile), but not one of them is the thing which is measured. And, the little inconsistencies between them which show up in conversions, where we have to adjust the clock so that they keep up with each other, shows that none of them is actually real or true. Notice the wiki quote, a second is "about nine billion oscillations".

I don't know whether you're arguing for some kind of antirealism or if you're failing to understand a use-mention distinction. — Michael

Perhaps if you took the time to explain to me how you understand this use-mention distinction, and how it is applicable in this context, that might be helpful to me understanding your position, which at the time seems completely ridiculous. I really do not understand how you can believe that the product of a measurement "one second" can exist without the act which produces it. Again, the best course of action for you to help me understand, would be to show me these things, called "a second", or explain to me how I might find one without performing the act of measuring which is what, I believe, actually creates them.

Regardless, the arguments I am making here are directed towards the realist who believes that supertasks are possible. — Michael

As I explained yesterday, we must consider that any such task (supertasks) are possible until proven otherwise. This is because they are logically possible, and the only thing which makes them appear to be impossible is that they are inconsistent (in contradiction with) the conventional way of doing things. But the conventional way is not necessarily the best way, it is only the way which is supported by empirical evidence, which has been proven to be unreliable and misleading. Therefore we cannot dismiss the supertasks as impossible until we have sound logic which disproves them. Simply asserting that supertasks are impossible just displays an empiricist prejudice. Then you support your prejudice with Platonism.

It's an open question, but ontological randomness is at least logically possible, as far as we know. — fishfry

Ontological randomness may be logically possible but it's philosophically repugnant. The problem being that if something is deemed as random, it is in that sense unintelligible. So if something is deemed as ontologically random, and it is considered to be unintelligible, then there is no will to attempt at figuring it out.

Now the problem is that if something appears to be random there is no way of knowing whether it is epistemologically random, or ontologically random, because of the unintelligibility of it. So we won't know which until we figure it out, therefore we must assume it to be epistemologically random. And even if it is ontologically random, we will still never know that this is the case, so we will always have to assume that it is epistemologically random, and try to figure it out. The category of "ontological randomness" is absolutely useless.

Notice your reference to "previous occasions". That's what I described, the will to get past the failed attempts, until you find the strategy which is appropriate for yourself. The overarching desire was to quit smoking, and it took you a few attempts to find the method suited to you. Then you found success. But you need to remember that the method suited to you is not necessarily the method suited to everyone else. So we can say that what works is to have a method which will bring you to the end goal. The end goal is to quit, but the successful method varies depending on the person. Therefore we cannot say that this or that method is the best method, only that it is necessary to have that one specific end goal, to quit.

No they mustn’t. — Michael

That's fundamentally incorrect. If you truly believe that an increment of time exists without being measured, tell me how I can find a naturally existing, already individuated increment of time.

You simply come to care about something more than the addiction, and are thus able to let it go, or you do not come to care about something more than the addiction and are thus unable to let it go. — Janus

It's pretty obvious that the exact thing which you need to care about more than smoking, to stop smoking, is not-smoking. If you look into the scientific research on the subject, as my brother did when he quit smoking, you'll find that what has been proven as the best way to quit smoking is to have a strategy, a method, or procedure, and to adhere to it. Having the will to following the prescribed method is not a matter of having something else which you care about more than smoking, unless you name that something else as "not-smoking".

The issue here is the possibility of failure, which is very strong with addictions. If a person proceeds toward quitting by caring about something, or someone, more than smoking, then the smoker depends on this other thing, or other person, to support one's own will power, as a sort of crutch. And of course this can, and often does work. However, if the other thing which the smoker cares about more than smoking fails in its capacity to support the quitter, then the support will be lost and the person will resume smoking without the will to quit. On the other hand, if the smoker approaches quitting with the pure goal of not-smoking, quitting, then the person may move ahead from one failed attempt to another attempt, with the will and determination to keep trying. In this way the appropriate strategy which is suitable to the particular person will inevitably be found. Failed attempts are very common with addictions, and the only thing which bridges the gap from one attempt to quit to the next is the will to stop the addiction.

If you accept that smoking is detrimental to your health, and you care more about maintaining good health than you do about gratifying your desire to smoke then you will give it up. if you care more about gratifying the urge to smoke you won't. The point is that you cannot simply decide by fiat what will be more important to you. — Janus

This is wrong in multiple ways Janus. First, addictions do not work like that. To break an addiction is not a matter of deciding that there is something you care about more than the addiction. It's actually the opposite of this, one must make the addiction, and breaking it, the top priority itself. Second, deciding by fiat is exactly what is done. It is decided that the addiction must be broken.

An ordinary stopwatch is started.

After 30 seconds a white box turns red, after a further 15 seconds it turns blue, after a further 7.5 seconds it turns back to white, and so on.

When the stopwatch reaches 60 seconds, what colour is the box? — Michael

You have not avoided the contradiction, only obscured it. Increments of time must be measured, the are the product of a measuring device. The measuring device in this example is an ordinary stopwatch. What is implied by "and so on" is increments of time which the stopwatch cannot measure. There lies your contradiction. The stop watch is the designated device which measures time, but you talk about increments of time which cannot be measured by it, therefore contradiction.

In your other example, the counter was the device that measured the passage of time, and it was designed to measure all those increments (do the supertask). But that measuring device denied the possibility of 60 seconds of time passing, making the measurement of a separate timepiece which would measure 60 seconds, contradictory.

Therefore we can conclude that the contradiction lies between the two very distinct descriptions of how time is measured. One way is the supertask of the counter. This is obviously a theoretical way of measuring time. The other way is a description of how time is actually measured in practise. There is contradiction between these two ways of describing the measurement of time. As you yourself indicate, the practical way gets the nod, as the real way, because it is supported by empirical evidence, and the supertask way, since it contradicts the practical way, is designated as impossible. As philosophers though, we are trained to be skeptical of sense evidence, having been educated in the ways that the senses commonly deceive us. So the philosopher knows that there is more to this problem than what meets the eye. It's not simply a matter of dismissing the supertask, and accepting the conventional way of measuring time, as the true way to measure time.

As I said before, the supertask way needs to be proven to be wrong, rather than simply dismissed because it contradicts the way of current practise. The empirical evidence of the stop watch is nothing other than current practise, convention, so it is in fact manufactured evidence. If we always accepted the current practise as the best, or true way, then we'd never improve ourselves. This is why I say simply accepting it and dismissing the supertask, is prejudice, and nothing else. The fact that we have not devised a supertask machine, and so we use other ways to measure time, does not mean that it is impossible that the supertask way is the real "true" way to measure time, and our current practise is actually giving us a false measurement. Therefore the supertask must be proven to be impossible.

Here's an example of an attempt at a similar type of proof. In ancient Greece, there was a principle accepted by many, that the orbits of the sun, planets, etc., were eternal circular motions, as a sort of divine activity. Being a prescribed activity which continues for an infinite duration of time, the eternal circular motion is a supertask. Now, Aristotle in his "On the Heavens" (De Caelo) showed how eternal circular motion is a logically valid and consistent principle, a real logical possibility, just like the supertask counter is. However, he then went on to explain how anything which moves in such a spatial pattern must be a material body. He then described "matter" as the principle of generation and corruption, and determined that a material body must have been generated in the past, and will be destroyed in the future. In this way he provided the principles required, to prove logically, that (the supertask) eternal circular motion is actually logically impossible. This proved that the heavenly bodies were not eternal, and not divine. Then the principle which he employed, "matter", became the keystone for understanding the nature of the physical reality because it provided the principle for associating change and becoming on the earth, with change and becoming in the heavens.

I believe that is the essence of freedom of choice. Possibility is general, it is then divided by the mind, individuated into a multitude of specific possibilities. Then what is chosen is a particular. What puts the final nail in the coffin of determinism is the reality of the decision not to choose. Out of all the possibilities, not one is chosen. This is the case in your example of the person fasting. The person is hungry, and has an abundance of possible foods to choose from, yet decides to choose none. Plato used a similar example, of a thirsty man who has an abundance of water in front of him, yet he does not drink because he knows the water is not suitable.

No it doesn't. — Michael

The contradiction is very obvious. I'm surprised you persist in denial. The supertask will necessarily carry on forever, as the sum of the time increments approaches 60 seconds, without 60 seconds ever passing. Clearly this contradicts "60 seconds will pass".

You seem to take issue with that first paragraph, but your reasoning against it doesn't make any sense. Unless the universe ceases to exist then 60 seconds is going to pass. The passage of time does not depend on the counter. — Michael

In logic we must follow the premises regardless of truth or falsity. Your example makes premises which describe a machine doing what has been called a "supertask". We have no premises to say that a supertask is impossible, only the premises which describe an instance of doing it, therefore demonstrating the logical possibility of a supertask.

Now, you introduce another premise, "Unless the universe ceases to exist then 60 seconds is going to pass". This premise contradicts what is implied by the others which describe the supertask.

So, what we have is a contradiction, without the information required to resolve the contradiction. In your reply to fishfry, you simply choose "60 seconds is going to pass", and conclude "supertasks are not possible". But this choice is made without the required argument, it simply reveals your prejudice.

You do not seem to

Oh, you are trying to make that kind of sophistical argument...if the desire is merely for "something" to eat how is that different from the general desire for food? — Janus

I was clarifying what is meant by "hunger". And, rather than being sophistical, I was exposing your sophistry. When we say that someone has "the desire to eat", we recognize the generality of the supposed "object" by showing that what is actually desired is a particular type of activity, "to eat". There is no actual object, until the person forms a specific desire to eat a particular food item. That particular item is "the object" of the person's desire. When you insist that the very general concept "food" is the object of the hungry person's desire, instead of identifying the activity, you are employing ambiguity to obscure the reality of the situation, in a sophistical way.

n any case the argument is not over whether our desires are general or specific, but over whether we are able to determine by fiat what we desire, and/or are able to determine by fiat whether we desire one thing more than another. — Janus

It appears like you paid no attention whatsoever to my argument. Allow me to rephrase in a very simple way. First, you need to distinguish between the very indefinite feeling of want, or need, from the very specific desire for a particular object. The feeling, which gives rise to the desire, allows for many possible sources to serve as the means for satisfaction. The specific desire for a particular object is the result of a choice from one of the apprehended possibilities. The feeling of hunger for example, allows for a vast multitude of possible food items to serve as the means for satisfaction. The hungry person will choose from the multitude of possibilities and form a desire for one, or a number (perhaps a hierarchy in order of preference) of particular food items. Very clearly, the person determines "by fiat", the particular objects which are desired, and any hierarchical order of preference.

Your last paragraph is merely hand-waving. We are what we are and want what we want, and think what we think, and we cannot change any of that simply by fiat. Of course, people do change, but they only do so insofar as they have the capacity for change, and they cannot simply conjure up such a capacity if they don't already possess it. — Janus

OK, so you believe that a person is what a person is, and what that person is, is "the capacity for change". Since you insist that the person has no capacity to choose, "by fiat", in relation to that capacity to change, I assume you are a hard determinist.

For example, if you are addicted to tobacco, you won't be able to give it up unless you care about something else that contra-indicates smoking more than you care about smoking. You will either be able to do that, or you will not—we do not create ourselves from scratch. — Janus

You clearly understand nothing about will power and determination. The way to quit smoking is to have the will power to quit smoking, and this allows the person to choose a method which is suited for that particular person. It may require numerous attempts of trial and error, as some methods may fail. It is not necessary that the person substitutes the desire for a smoke with the desire for another object, though this may work for some people. The only thing which "contra-indicates smoking" to the extent required to guarantee that the person gives it up, is the will for non-smoking. Therefore, if to give up smoking, it is required that one cares about something else more than the person cares about smoking, this "something else" must necessarily be "not-smoking".

Because 60 seconds will pass. I don't understand the problem you're having. The passage of time does not depend on what the counter is doing. — Michael

You just reaffirmed the same contradictory statements. It's impossible, by way of contradiction, that the counter can do the assigned task, and 60 seconds can pass. I see the contradiction as very clear and obvious, so I do not understand why you can't see it as contradictory.

The counter, by the prescribed specifications, is designed so that 60 seconds cannot pass until the counter counts every logically possible fraction of a second. Since logical possibility is defined by convention, and the convention allows for an infinite number of possible divisions, the counter, by the prescribed specifications, cannot finish the task. Therefore 60 seconds cannot pass. Your insistence that it can is blatant contradiction.

We can determine whether or not something entails a contradiction. If time is infinitely divisible then supertasks are possible. Supertasks entail a contradiction. Therefore, time being infinitely divisible entails a contradiction.

You can argue that reality allows for the possibility of contradictions if you want, but most of us would say that it is reasonable to assert that it doesn't. — Michael

Why the double standard? When speaking to fishfry you readily acknowledge the contradiction. When speaking to me, you insist that the counter can perform the supertask and 60 seconds of time can also pass, as if there is no contradiction involved.

ince you'd translating from it in your head, and you don't seem to know. — Lionino

Are you saying that people do not use "life" in that way, in languages other than English?