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?

when we say "life" we know exactly what each other mean. — Lionino

So if I were to ask you (in some language other than English), if you believe that there is "life" in some places of the universe other than on earth, would you be able to tell me exactly what I mean by "life" in this context?

Maybe in English you don't. In other languages we have no trouble using the word that comes out of Google translate when you write "life". — Lionino

Then why did you say there is no agreement between you and some biologists on the question of whether or not viruses are alive? Isn't this an instance of "trouble"?

Step 1 occurs after 30 seconds, step 2 occurs after a further 15 seconds, step 3 occurs after a further 7.5 seconds, and so on. — Michael

I see that 30 and 15 and 7.5 sums up to 52.5 seconds. I also see that as it progresses the sum approaches 60. But I do not see how it could ever get to 60. Show me how you believe that "and so on" could indicate a sum of 60 is achieved please.

Then your argument should be that supertasks are impossible, not that 60 seconds cannot elapse. — keystone

No, clearly I made the appropriate choice in deciding what to argue. The described "supertask" is incompatible with 60 seconds elapsing. We seem to agree on that now. The supertask is derived from the premises of your example, therefore the supertask is the valid conclusion to your premises. You have provided no propositions or premises whatsoever, to conclude that 60 seconds may actually elapse. This is derived from your prejudice about the the nature of time, and the conventions of measuring the passage of time. To base my argument on unstated premises, and prejudices, is to produce an invalid argument. Therefore I have no principles to validly argue that 60 seconds can pass, and no principles to argue logically that the described supertask is impossible. Your assertion that 60 seconds may pass is inconsistent with your stated premises, and is not supported by any premises.
It is derived merely from your prejudice.

The example is simply: after 30 seconds a single-digit counter increments to 1, after a further 15 seconds it increments to 2, after a further 7.5 seconds it increments to 3, and so on for 60 seconds, resetting to 0 at every tenth increment. — Michael

Clearly, what is implied by "and so on", contradicts "for 60 seconds". The two are inconsistent, incompatible. Therefore your example is self-contradicting and incoherent. To me, it is analogous to saying "the big blue computer is designed to produce the complete numerical expression of pi, and when it is finished we'll throw a big party. Do you see how "when it is finished" (analogous with "after 60 seconds") contradicts the described supertask "produce the complete numerical expression of pi" ( analogous with what is meant by "and son on")?

I don't agree with them, but that is just a personal preference of mine. — Lionino

All this, I take as evidence that we do not know what "life" is. We seem to believe that there is something called "life", (and it's sort of odd that we name it as a thing, harkening back to "the soul"), but we really do not understand what it means to be alive.

Kant agreed that all our knowledge begins with experience, but he disagreed with Hume's conclusion that it therefore arises solely from experience. Kant introduced a critical distinction between the forms of intuition (space and time) and the categories of understanding (including but not limited to causation), which are necessary for us to interpret sensory information.

According to Kant, these categories are not derived from experience but rather are the preconditions that make experience intelligible in the first place. They are the innate structures of the mind that organize sensory data into coherent perceptions ('percepts'). For example, when we perceive one event following another, our understanding interprets this as causation, allowing us to see one event as causing the other, rather than just as two events occurring sequentially. Thus, Kant argued that Hume's reduction of knowledge to mere sensations and perceptions overlooks the active role of the mind's inherent structures, which underpin experience. — Wayfarer

I would think that since having these categories is actually having a form of knowledge, then we cannot truthfully say "Kant agreed that all our knowledge begins with experience". There is a bit of inconsistency here, whereby it is necessary to either break knowledge into two types, a priori and a posteriori (such as innate and learned), or else we need to provide different principles for understanding the a priori as something other than knowledge.

The latter, which appears to be the direction you've taken, is a very strenuous task. This course of explanation drives toward the resolution of Plato's "knowledge is recollection" problem. Without a proper separation between the potential for a specific form of knowledge, and actually holding that knowledge, the two become one and the same, with something separating them. So as Plato demonstrates, learning is nothing other than recollection. That produces the problem of infinite regress, and the conclusion that all knowledge has eternal existence.

Aristotle offered a resolution by portraying this as two distinct layers of potentiality. Kant's a priori can be understood as the capacity, or potential for learning. This potentiality underlies all a posteriori, or empirical knowledge, which is describe by Aristotle as the capacity, or potential to act. Notice the two distinct levels of potentialities. Knowledge proper, is the potential to act in a specific way. But in order to act in a specific way, we must first learn how to act in that way. Below this though, supporting it as a foundation, is the capacity, or potential to learn, which is a necessary requirement to learning. This, the lower level capacity to learn, appears to have all the characteristics of being a form of knowledge itself. Learning is a type of acting, so the capacity to learn is itself a capacity to act.

What separates these two forms of potential (two types of knowledge) is a form of activity. That type of activity is described by Aquinas as the creation of habits. This is how the one type of potential, the capacity to learn, becomes the other type of potential, as the capacity to act in a specific learned way. The former "capacity to learn" is the more general, and the latter is to focus the general potential in a more specific way. The importance of habits in the shaping and forming of living beings through evolution is what Lamarck focused on in his evolutionary speculations.

The first point is that what is significant to you, what is important to you, conditions your desires. We all have first order desires for pleasure, satisfaction, gratification, stimulation and so on. But in case those desires lead to habits that are unhealthy, they may be countermanded by stronger concerns like personal health, social harmony, or even simply by introjected moral prescriptions and proscriptions. — Janus

This seems to support my claim rather than yours. Since you name a multitude of types of desires, and the human being must prioritize one over the other in many situations, this seems to support what I said, that we can choose what we want. Please note, that having a general inclination in some way, is not the same as having a want. The want is for something specific an "object". So for example, I may have an emptiness in my stomach producing a general uneasy anxious feeling called "hunger", but this is completely different from the "want" of "I want a hamburger".

The second point is that what you desire in the first order sense; food, warmth, shelter, sex, and so on simply is what it is. — Janus

Notice, that all these so-called "desires" manifest simply as general uncomfortable, or even painful feelings. You only call them "desires" because you assume that there is an object involved. A desire is for something specific, this is the end, or object. The objects of all your mentioned desires, "food, warmth, shelter, sex," are very general. These generalities do not serve as objects at all, in reality. You just mention them as if they do, because it makes your argument. In reality, the desire is for a specific object, and since the person has the choice between many different objects, you can use the general terms, ""food, warmth, shelter, sex,".

Suppose for example, that you have the general feeling which we know as "hunger". This you seem to describe as "the desire for food". Hunger is clearly not the desire for food. It is a feeling within your body having an effect on your mind. The effect is not the general "desire for food", it is the desire to eat something. Then that desire to eat something is turned more specific by the conscious mind, toward the desire to eat a specific thing. The saying, "the desire for food" is simply a feature of the mode of description. Since we observe that the desire to eat something may be satisfied by many different food substances, we can simply call it "the desire for food". However, when hunger, the desire to eat something, actually manifests in the particular circumstances that it does, there is the opportunity for the hungry person to choose from many different food items, so that the feeling of hunger transforms to the want for a specific item, without ever actually being "the desire for food". That generalization is just the way that we describe the reality that the hungry person, the person with that feeling, has the freedom of choice to choose whatever object that one wants, to eat.

The third point is that each person's capacities just are that person's capacities—some are more capable than others at overcoming their compulsions or addictions. Some people simply don't and cannot, feel empathy, for example—they cannot force themselves to care for others, although is they are smart, they may at least be able to bring themselves to act as though they do. — Janus

This is simply a copout, the position of a determinist, fatalist, defeatist. As described in my reply to wayfarer above, a person's capacities are multilayered. And, through habit forming we are very able to shape and direct our capacities. This is because they are based in the most general, yet are actualized in the most particular, as in my description of hunger above. Because there are layers, and the opportunity of choice at each layer, and what is formed at the higher level is a further capacity, we very clearly have the ability to shape and form our own capacities. This for example is what we do when we grow up from childhood to being an adult, we shape our capacities in the directions that we choose, and eventually take on a career. And this ability to shape our capacities continues through our lives.

The example is simply: after 30 seconds a single-digit counter increments to 1, after a further 15 seconds it increments to 2, after a further 7.5 seconds it increments to 3, and so on for 60 seconds, resetting to 0 at every tenth increment. — Michael

I guess I misunderstood your example. It is obviously not consistent with the OP. That little part where you say "and so on for 60 seconds" is unclear. The OP lays out the conditions in steps, but your "and so on" tells me very little.

The obvious point is that we can describe a scenario which is logically possible, but physically impossible. When working with this scenario, we need to bare in mind, the fact that it is physically impossible, and adhere rigidly to the logic of the scenario, only. If one's mind gets influenced by other principles, such as what is physically possible in the universe, and what is going on in the physical universe, this will surely create confusion.

60 seconds will pass in the universe. The counter is just one thing that exists in the universe and it changes according to the prescribed rules.

So given the prescribed rules, when the universe is 60 seconds older, what digit will the counter show? — Michael

Yes, that is the point. Your expressed conceptualization "60 seconds will pass in the universe" is not consistent with the conceptualization prescribed by the OP. But this conceptualization "60 seconds will pass in the universe" is not part of the example. So your introduction of it is not valid. We could call it an equivocation fallacy. We have "time passing" as prescribed in the example, and "time passing" in the universe. The two are not consistent. To introduce the latter into the example, is to equivocate.

Sorry Lionino, I am not a biologist, and spoke hastily without understanding what I was saying. Google has told me that viruses are not alive, so I apologize for the misleading comment.

Let's recast Zeno's ideas using contemporary terminology. In his era, the dominant philosophical view was presentism, which posits that only the present moment is real, and it unfolds sequentially, moment by moment. — keystone

I wouldn't say that. If you read Aristotle's Physics, you'll see that he describes the principal definition for "time" being used at his time, as a sort of number, used for measurement. That, he distinguished from a secondary sense, as something measured. So the secondary sense might be consistent with what you say, but it's not the primary definition for "time" at that time.

No end to the staircase but the end is reached - Yes, this is the very issue I'm trying to highlight. And this has nothing to do with continuous acceleration or motion. — keystone

But the end is not reached. According to what is stipulated Icarus always has more steps before a minutes passes. Here's what I wrote in the other thread:

"For Icarus a minute cannot pass because he always has steps to cover first, just like Achilles cannot pass the tortoise for the same reason. Maybe if we call the staircase a line, and the steps are "points" it would make more sense to you. No matter where Icarus stands on the prescribed line, he has to cover an infinite number of points before a minute can pass. And to traverse each point requires a non-zero amount of time. Therefore no matter where Icarus is on the line (stairs), there will always be time left before a minute passes. A minute cannot pass, and Icarus' journey cannot end."

You only claim that the end is reached, because you assume that a minute passes. But that assumption is not provided for, as explained. Therefore, the valid conclusion is that Icarus never reaches the bottom, just like Zeno concluded that Achilles never surpasses the tortoise. The required premises about space and time, to conclude otherwise, are not provided.

I suggested that movement was discrete, not that space was discrete. — Michael

This is a very good point, to keep in mind when we get a good understanding of, and move beyond, the appearance of paradoxes like Zeno's. What is indicated is that motion is discrete. To account for the reality of this, we need to model either space or time as discrete, but not necessarily both. So when we employ the concept of "space-time" we deny ourselves the capacity of separating time from space, and considering the possibility that one is continuous, and the other is discrete.

To me, what works best for understanding the nature of reality is to allow for a continuous time, with a discrete space. This means that the so-called "quantum jump" is a feature of space. As time passes, the things which we know as having spatial (material) existence change in discrete jumps. Those discrete jumps limit our empirical capacity to understand the true nature of time, because no change can be observed to occur during the time which passes in between such jumps. However, since time would be conceived as continuous, while spatial motion is discrete, we can still conceive of time as passing in between such jumps.

Those premises allow us to understand the "immaterial realm of Forms", as the activity which is occurring between the spatial jumps. The immaterial realm of Forms is what determines how the spatial world will be, at each moment of ("observable") time. The human being as a free willing agent, has causal power within the immaterial realm of Forms, to influence what will be spatially present at any moment as time passes. Notice the requirement of real points in time. These are the points when the observable (spatial) world is materialized as discrete "jumps" during the passage of time.

The issue we have is that if there is no smallest unit of time then the counter is metaphysically possible, but this entails a paradox as the answer to what the counter shows after 60 seconds is undefined yet the counter will show something after 60 seconds. Assuming that paradoxes are metaphysically impossible then the counter is metaphysically impossible, and that suggests that it's metaphysically impossible for time to be infinitely divisible. — Michael

I don't think this is correct, I think Andrewk is correct. The counter is not programed to reach 60 seconds, that is outside its described capacity. Here's what you said:

What digit does the counter show after 60 seconds?

If there is no answer then perhaps it suggests a metaphysically necessary smallest period of time. — Michael

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See, the counter is not programmed to show anything after 60 seconds. "There is no answer", because if the counter were to do as prescribed, it would never get to 60 seconds. There is no such things as 60 seconds for the counter, it can never get there if it does what its supposed to do. The assumption that 60 seconds will pass, is the mistaken conclusion of the OP, because this requires a premise about time which is not provided in the example. That premise being that time will pass at some rate which will surpass the actor in the example. That's what creates the appearance of paradox, if you allow yourself to be influenced by the contradictory idea, that time will surpass the actor.

The paradox is that given the premise(s) what happens at the limit is undefined, and yet something must happen at the limit. — Michael

This is the mistaken assumption. There is no limit prescribed. The premises set up an infinite process, which means "no limit". The issue exposed now, is that training in mathematics (calculus specifically) inclines one to see the scenario as a limit at 60 seconds, when the example simply does not state it that way. Someone who knew no complicated mathematics, only simple arithmetic, would work through the prescribed process, adding up the periods of time, and then realize that the sum gets closer and closer to 60 seconds, without at all thinking that 60 seconds is "a limit" here.

This imaginary "limit" is added by the mathematical way of looking at the scenario. It is "the intent" in producing the example. Start with the limit, and set something up which approaches the limit but does not reach it. The limit though, is not part of the example, it was only employed by the mind which produced the example, as a guiding principle which does not enter into, or become part of the example. In other words, we need to read the premises exactly as they are written, and there is no mention of 60 seconds as a limit. It's only when you take the short cut, don't read, but jump to the end, the intent, that you think of 60 seconds as a limit.

You're suggesting that the issue lies in the impossibility of a minute passing? — keystone

I wasn't saying that this is "the issue", only that it is the logical outcome. For Icarus a minute cannot pass because he always has steps to cover first, just like Achilles cannot pass the tortoise for the same reason. Maybe if we call the staircase a line, and the steps are "points" it would make more sense to you. No matter where Icarus stands on the prescribed line, he has to cover an infinite number of points before a minute can pass. And to traverse each point requires a non-zero amount of time. Therefore no matter where Icarus is on the line (stairs), there will always be time left before a minute passes. A minute cannot pass, and Icarus' journey cannot end.

No end to the staircase but the end is reached - Yes, this is the very issue I'm trying to highlight. — keystone

No, the end is not reached, as explained above. This is what Andrewk neatly explained in the other thread. That a minute will pass, and the end will be reached, is a presumption outside the prescribed scenario. You are assuming that from some other principles.

What thread are we on? Did you combine this one with the other one? Maybe you could ask a mod to do that for you.

Hi andrewk. It's good to see you, been a while. Doing well? I hope.

This is not true. Perhaps you are reading a different account of the story than I did, which is the one on wiki, which says simply:
"In a race, the quickest runner can never over­take the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead". The 2nd bolded part is the non-sequitur, and the first bolded part follows from the 2nd. None of it makes the assertion you claim. The non-sequitur makes the argument invalid. There are ways (such as with the light switch) that make it seem more paradoxical. — noAxioms

Sorry no Axioms, I can't follow what you are saying, perhaps you could spell out your supposed "non-sequitur" in a clear explanation, instead of simply asserting it. In Zeno's paradox, the tortoise is given a head start.

Same non-sequitur. It is not true that Icarus always has more steps to take, only that he does while still on a step, but the time to complete all the remaining steps always fits in the time remaining in his minute. — noAxioms

That Icarus always has more steps to take is the valid conclusion from the premises. Yes, "the time to complete all the remaining steps always fits in the time remaining in his minute", as you say. However, the remaining steps are indefinite. Likewise the amount of divisions which can be made to the remaining time are indefinite. Therefore Icarus' minute is never completed, and he never completes his steps. That is the conclusion we must make.

However, the OP concludes that the minute passes, and the bottom reached. The OP therefore relies on a sense of physical reality, that a minute must pass, which is outside of the premises. That's why it's not a valid conclusion. There is nothing within the premises to indicate that a minute must pass, and everything indicates that a minute will never pass.

OK, which premise then is false in the Zeno case? The statement is really short. One premise that I see: "the pursuer must first reach the point whence the pursued started", which seems pretty true to me. — noAxioms

The false premise for Zeno is that each distance, and each time period will always be divisible. That's the problem points out. Think of the way a runner actually runs. One foot hits the ground, then the next foot hits the ground some distance further ahead. The runner does not cover every inch of ground in between, the motion of the feet in contact with the ground, takes place in increments.

I believe other animals are capable of reasoning and presymbolic language. The only difference I see is the advent of symbolic language with humans. I also think this is pretty much the standard view, so I'm not sure why you seem to think it isn't the standard view. — Janus

What does "presymbolic language" mean? Isn't all language by the meaning of "language", symbolic in some way? Adding "symbolic" to language, to say that human language is "symbolic language" is just redundancey.

"A man can do what he wants, but not want what he wants", which I take to mean that, apart from external constraints, you are free to do whatever you want but you are not free to choose what it is that you want. — Janus

Why not? I see no problem with a man choosing ones wants. That's what we learn how to do in moral training, mastering our habits.

Well, you could make an essentialist argument that understanding is exactly the discontinuity between humans and other animals, even if understanding itself is a power among others like movement etc. One can find many features that is shared by all (not deficient) humans and absent in other animals and claim that as the discontinuity, no matter whether the feature chosen is important. — Lionino

I do not agree. I think its' very clear that other animals "understand". We had a dog which clearly understood that it ought not get on the table, and so it did not ... as long as someone was around. But as soon as we went to bed it would be on the table. To me, that's obviously a form of "understanding". Of course, you can tailor a definition of "understand" to suit your purpose, but what's the point in that?

I'm just pointing out that there are many lines that can drawn between us and animals. — Lionino

And I'm just pointing out that the vast majority of those lines are arbitrary. In a similar way, we could draw a line between child and adult, and say that only an adult is responsible for one's actions, because an adult understands. But such boundaries are arbitrary.

Is there? What do you make of viruses? Specially something like a mimivirus. — Lionino

I think viruses are quire clearly living. You should ask about something like cancer, or prions, and things like that.

That's beautiful, simple and eloquent.

Sure, I already acknowledged that in the post above about Schumacher's ontology. — Wayfarer

"Mineral" = m
"Plant" = m + x
"Animal" = m + x + y
"Human" = m + x + y + z

In his theory, these three factors (x, y and z) represent ontological discontinuities — Wikipedia

This is what I think is not at all objective and obvious, and I also disagree with it. I see an ontological discontinuity between inanimate and alive. That discontinuity (signified as x above) is what Aristotle explained with his concept of "soul", and which forms the basis of vitalism. And, it is this ontological discontinuity which renders the common notion of abiogenesis as inadequate.

The other differences mentioned above as y and z display no such discontinuity. In fact, there is very much evidence for a continuity between them, as demonstrated by Darwin in support of his evolutionary theory. Furthermore, the continuity between them is described by Aristotle in "On the Soul". He describes all the powers of living beings as potentials, capacities, the powers of self-nutrition, self-movement, sensation, and intellection. Notice that intellection is classed with the others.

Each of these various potentials, are dependent on the material body, matter as potential, but they are properly attributed to the soul which is the active principle that activates and operates them. So there is a continuity between all the powers of the soul (intellection included), as shown by Darwin, each being dependent on the material body which provides the specific potency/act relation, as described by Aristotle, and these are all understood through their similarity.

However, there is a distinct discontinuity between living and inanimate, and this is understood through a principle of actuality, the active principle responsible for the causation of the material body which provides the potential, and this is known as the soul.

Objective - and obvious, isn't it? Again, actual language, as distinct from linear communication through calls or displays, is unique to h. sapiens. As is tool-making, philosophy, technology, art, science, mathematics, music, drama. As is the capacity to reflect on the nature of being and question the meaning of existence. — Wayfarer

Well Vera Mont clearly doesn't think that it is objective and obvious, and I'm not convinced either way. Let me see if I can put this in another way.

Look at the difference between plants and animals. If there is such a thing as a "highly significant difference" which marks a threshold in evolving life forms, wouldn't this qualify as such a threshold? Plants are rooted in the ground, whereas animals are free to move around and sense things. Now, look at the difference between human beings and other mammals. Human beings communicate, socialize, cooperate, and build things. So we might also say that this is a highly significant difference which marks a threshold. But how many other things can we look at as highly significant differences which mark a threshold? do the development of a heart, lungs, brain, legs, wings, hands, not qualify as highly significant differences? It appears to me like we may call the difference between human beings and other mammals a "highly significant difference", but that's just one in a multitude highly significant differences we observe between life forms. Therefore, in reality life is rife with "highly significant differences" and "thresholds". But this makes that one specific difference or threshold, just another difference, and nothing special.

Agree that humans and other species are on a biological continuum, but I also believe that humans crossed a threshold with the advent of language, tool use, and so on, and that it is a highly signficant difference, that though we're related to other animals, we're more than 'just animals'. — Wayfarer

I've seen you state this before, and I find it interesting and would like to see it better supported. What type of "threshold" are you talking about here? would this be an objective, or a subjective threshold, and in what form does it exist?

By "subjective threshold", and "objective threshold" let me give you an example of what I mean. Suppose that within a given species there is a significant degree of variation, but not enough variation to warrant sub-classes, as sub-species within a species, the sub-classes are only variations. Now suppose one particular variation refuses to interbreed with the other variations, and only breeds amongst others of that particular variation. Then, suppose that this variation branches off and becomes a distinct species. When it was a variation within a species, the "threshold" was subjective, because it was by choice that they bred only amongst themselves avoiding the other variants. But when it became a distinct species, it can no longer breed with the other variety, by physical impossibility, so the threshold is an objective threshold, supported by that physical impossibility.

So what I am asking about your claim "that humans crossed a threshold with the advent of language, tool use, and so on", is to say whether this is objective or subjective. Is it the case that we, as human beings, have subjectively decided to say that we are different (perhaps referring to human intellect), and that our minds have produced some sort of mental, or psychological threshold, or barrier, or is it the case that there is real physical principles (opposing thumb?) which supports your claim of a threshold?

What do you mean stipulated? That Achilles cannot overtake is a non-sequitur. It simply doesn't follow from there being a way to divide the journey into infinite segments. — noAxioms

It's not a non-sequitur, the conclusion follows logically from the way that Achilles' movement is described. From the description there is always further distance for Achilles to move before he overtakes the tortoise. Therefore he cannot overtake the tortoise. The issue is not that the argument is invalid, it is that the argument is unsound. The description of motion employed provides false premises.

Time not being allowed to pass was never a specification in the OP. — noAxioms

In the OP, it is not the case that time is not allowed to pass, but the premises imply that a minute cannot pass for Icarus, who always has to take more steps before a minute can pass. Just like in Zeno's paradox, the premises which describe how Icarus moves down the stairs are faulty.

So, in the OP, the false premise is the description of acceleration. Acceleration from rest is described as continuous and open ended (infinite). But this is false, acceleration does not happen like this in reality. Imagine if the OP was expressed in the following way. Someone states that the universe is infinite in size. Then the person states that a rocket accelerates from being at rest on earth at a rate of acceleration which will take it to the edge of the universe before a minute passes. Then the person concludes that after a minute passes the rocket is at the edge of the universe. Do you see the incoherency? That's what's going on in the OP. The premises are arranged so that there cannot be an end to the staircase, just like there cannot be an end to pi. Then it concludes, that after a minute has passed, the end has been reached.

So the OP makes a non-sequitur by concluding that the end is reached. Zeno on the other hand, concludes that Achilles cannot overtake the tortoise, which is the valid conclusion. And the absurd conclusion reveals the falsity of the premises.

The dichotomy thing was better illustrated by something that actually seems to be a paradox.
You are at location x < 0. The goal is to traverse the space between x=0 and x=1.
Thing is, a magic barrier appears at x=1/2 if you are at x <= 1/2, but x > 1/4.
A second barrier appears at x=1/4 if you are at x <= 1/4, but x > 1/8.
And so on. Each barrier appears only if you're past the prior one.
Furthermore, for fun, the last barrier is red. The prior one blue, then green, then red again. Three colors in rotation, all the way up the line.

Per the dichotomy thing (and Keystone's stairs), there can be no first barrier. So you walk up to x=0 and are stopped, despite there not being anything there to stop you. I mean, if there's a barrier, you'd see it and know its color, which is like suggesting a remainder if you divide infinity by three.

So paradoxically, you are prevented from advancing despite a total lack of a first barrier. You can see the goal. But you can't move. — noAxioms

I don't think that this is representative of the OP at all. You have changed the divisibility of time in the OP to a divisibility of space in your interpretation. Then, instead of dealing with the problem of acceleration, which the OP is concerned with, you have to employ "magic barriers" to make sense of the steps. There are no such magic barriers employed by the OP, only steps, and each step is made in half the time of the prior step. So clearly, the OP deals with the issue of infinite acceleration.

I don't think the intention was for physics to be a problem. — flannel jesus

If a person does not take into account what is physically possible in this type of thought experiment, then one can make up false premises however one wants, and create the illusion of a "mathematical problem" when no such problem actually exists. The real problem is that the premises are false (physically impossible), and by employing the false premises the illusion of a mathematical problem is created.

Do you truly believe that Achilles is unable to surpass the tortoise? — keystone

By what is stipulated, yes, Achilles cannot surpass the tortoise. But, the stipulations are not a true representation and that is why there is a problem. The issue is with the way that motion is described. We employ a conception of time and space as a continuity which is infinitely divisible. However, if motion actually consists of discrete changes like a "quantum jump" for example, then the representation of a continuous existence, is false.

Do you think that Icarus's deeds influence the passage of time? — keystone

No, I do not think that Icarus's deeds influence the real passing of time. However, the passing of time is a subject in your example, and it is determined by the premises of the example. So. according to the premises of the example, half as much time is covered each time Icarus makes a step, as compared to the previous step, and Icarus can keep on stepping forever. Therefore the passage of time is defined in relations to Icarus's deeds in the example. That is what is stipulated in the example, That the passage of time is relative to Icarus's steps. Whether it is a truthful representation of the passage of time is irrelevant at this point.

It looks like a simple question, but it isn't. I wouldn't want to reply without looking up his argument for a start. One reply might start from the argument here, that solitary thinking (which may or may not be what he is talking about) doesn't produce the best ideas on its own. The answer from that stand-point would be, no. But that might mean rejecting his argument about "contemplation". That is thinkable. I'm not a fan of his hierarchical argument for the Supreme Good. — Ludwig V

For what it's worth, I believe you'll find it in Bk 6 of Nichomachean Ethics. A lot of any such argument is a sort of stipulation of intuitive principles, so of course the premises are debatable. I think the general idea is that contemplation produces the most universal, principles of theory, and these are required to ground practical principles, and practical principles are required for moral actions. Therefore contemplation produces the highest principles because these are a requirement for all the other virtues. So contemplation is the highest virtue. Then, he moves to show how contemplation is consistent with "happiness" at the end of Bk 10.

After a minute, yes. Do you contend otherwise, that the sum of 60/2**n is not 60? — noAxioms

The specifications do not allow for a minute to pass, that's the problem. It's just like Zeno's Achilles and the tortoise paradox. What is specified by Zeno, disallows the possibility of Achilles passing the tortoise. Here, what is specified in the op by keystone, disallows the possibility of a minute passing.

So it's like you're saying, "after Achilles passes the tortoise...", when Achilles cannot pass the tortoise, because of what is specified, he must pass an infinite number of spaces first. Here, you are saying "after a minute..." when a minute cannot pass because of what is specified, Icarus must pass an infinite number of steps fist.

So it's just like the Achilles and the tortoise paradox, with a different conclusion. Here, instead of concluding that a minute cannot pass, as Zeno concluded that Achilles cannot pass the tortoise, keystone changes things up to say that after a minute has passed the infinite number of steps has been reached. But @keystone has made a invalid conclusion, and should have stuck to Zeno's formulation, to say that a minute cannot pass for Icarus because he always has another step to make first, and that step will be made in a shorter time than the last.

So her argument is that traditional philosophy privileges one kind of human experience, typified by Descartes' solitary thinker (and, perhaps Rodin's statue, which also suggests the thinking is a solitary occupation) or Virginia Woolf’s desire for a room of her own. — Ludwig V

So, philosophy, as the ideas which are produced from the solitary thinker, is a representation of that kind of human being, the solitary thinker. Now, Aristotle shows how contemplation is the highest virtue. So can we conclude that philosophy provides us with the very best ideas?

Despite the staircase being endless, he reached the bottom of it in just a minute. — keystone

But also, there is a slight of hand that occurs when we are encouraged to imagine Icarus's position immediately after he's finished traversing the infinitely long staircase in the original direction. If he would have traversed the staircase in Zeno like fashion, as specified, although he would have stepped on all the steps in a finite amount of time, there would be no definite position along the staircase that he was at immediately before he had arrived at his destination. — Pierre-Normand

Yes, there is a "slight of hand" involved. The real solution is that the only "finite time" in the description is the starting time, and the formula for figuring the increments. And, according to the prescribed formula for figuring the increments, there can be no finish time. It's analogous to finding the end of pi, you just keep going. Despite the defined, and finite starting point, Icarus is currently covering an infinite number of steps in an infinitely short period of time, and by adhering strictly to the description we must conclude that the bottom will never be reached. Bye bye Icarus, enjoy the "black hole's core".

He reaches the bottom of something with no bottom. It taking a minute is fine, but there being a bottom is contradictory. Hence I think resolution. Just as there is no first step to take back up, there is no last step to reach, even if it is all reached in a minute. — noAxioms

How does that work? He's traveling by steps. Each step takes a discernible amount of time which is a different time from the prior step. You say he reaches the bottom, yet there is not "last step". Clearly he doesn't do a bunch of last steps at the same time, so ambiguity is not the problem. How do you think it is possible that he got finished with all the steps, in the described order, yet there was no last step?

Peter Wohleben, a career forester has a very well written, bestselling book called "The Hidden life of Trees: What they feel, How they communicate". In it he talks as if trees act with intention, and he describes how trees communicate with each other through electrical impulses that travel through mycelium which grow around their roots. The electrical impulses of trees have now been studied scientifically.

To communicate through the network, trees send chemical, hormonal and slow-pulsing electrical signals, which scientists are just beginning to decipher. Edward Farmer at the University of Lausanne in Switzerland has been studying the electrical pulses, and he has identified a voltage-based signaling system that appears strikingly similar to animal nervous systems (although he does not suggest that plants have neurons or brains). Alarm and distress appear to be the main topics of tree conversation, although Wohlleben wonders if that’s all they talk about. “What do trees say when there is no danger and they feel content? This I would love to know.” Monica Gagliano at the University of Western Australia has gathered evidence that some plants may also emit and detect sounds, and in particular, a crackling noise in the roots at a frequency of 220 hertz, inaudible to humans. — Smithonian

https://www.smithsonianmag.com/science-nature/the-whispering-trees-180968084/

Wohleben now has a book called "The Inner Life of Animals: Love, Grief, and Compassion: Surprising Observations of a Hidden World". If it's as good as the tree one, it's well worth the read.