Case closed, then. — Ludwig V

I think so, but we'll have to see what noAxioms is talking about with the reference to a requirement for further premises. I think noAxioms looks at Zeno in a different way.

Great. Then show the logic that concludes this, without resort to another premise. — noAxioms

I don't see the need for any other premise. Achilles is moving, and described as doing this in a way in which he will always have to move further before he can overtake the tortoise. Since he will always have to move further before he will overtake the tortoise, we can conclude logically that he will never overtake the tortoise in that described activity. Why do you see the need for another premise?

I'm afraid that if you condescend to use ordinary arithmetic, one can predict exactly when Achilles will overtake the tortoise, given data about how fast each contestant moves and the size of the handicap. — Ludwig V

Sure, but those mathematical principles are not the premises described by Zeno.

There is no first natural number to start with. It is logically impossible to have started reciting the natural numbers in descending order. — Michael

Obviously, the described process has no start, that is implied by the description. So your conclusion that it is logically impossible to have started such a process is irrelevant, as what is already known. You need to show that such a process, one without a start, is logically impossible.

That's what "first cause" arguments attempt to do. They describe the temporal aspect of "a process", "a thing", or similar term, in such a way that it necessarily has a beginning and an end in time, then they produce a logical argument from that description. It's an attempt to bring the realm of material (physical, or temporal) reality to bear on the realm of logical possibility, by stating premises which are supposed to represent the essence of material (physical) reality, and restricting logic with them. Another example of a similar restriction is the law of identity, and the other two fundamental principles.

How does it start? That's easy. When the appropriate time comes, the number to be recited at that time is recited. That wasn't so hard, was it? It works for both scenarios, counting up or down. — noAxioms

This is not the issue. It clearly does not have a start. The question is whether it is logically necessary for such a task to have a start. This is argued in "first cause" arguments.

@Michael @fdrakeThe problem is that what is described is an activity, and the way that we understand activities is that they have a beginning. Activities are all physical. But if you remove that requirement of "physical", then the activity might be proceeding without a beginning, just like it could proceed without an end. It's the way that we look at the difference between past and future, which makes it difficult. If there is no such difference, then the past supertask must be logically possible, just like the future one.

Nah. That's an appeal to metaphysical or physical impossibility. Not logical impossibility! — fdrake

It is logically impossible to have recited every natural number in descending order because it is logically impossible to even start such a task. — Michael

I think that's actually a very difficult issue to resolve. It's basically the same question as whether an infinite regress is logically possible. I believe the infinite regress actually is logically possible, and it requires a contradictory premise to make it impossible.

Correct, but a second unstated premise must be assumed in order to draw this conclusion, since without it, one can only say that the tortoise cannot be overtaken at any particular step. — noAxioms

If no particular step can overtake the tortoise, then the tortoise, by the described motion cannot be overtaken. Where's the need for another premise?

That second premise might well be that supertasks cannot be completed. — noAxioms

Following from the described premises, the supertask cannot be completed. It is logically implied that there is always further distance for Achilles to cover before overtaking the tortoise. Therefore the described task can never be completed. There is no further premise required, it is a logical conclusion, the described "supertask" cannot be completed.

That premise is indeed in contradiction with the first premise and empirical observation. At least one of the three is wrong. — noAxioms

The conclusion that Achilles cannot overtake the tortoise does contradict empirical evidence, that's the reason it's called a paradox. But I do not see how it contradicts "the first premise". Which premise would that be? The argument is valid, so how could it contradict a premise?

I beg to differ. That simply does not follow from the description. Zeno describes a physical completable supertask, which is only as possible as the soundness of his first premise. — noAxioms

I think you misunderstand Zeno's paradoxes. Zeno concluded that Achilles cannot overtake the tortoise. That is explicit. And therefore, it indicates that he is arguing that the supertask is not completed. The "supertask" of passing an infinite number of spatial divisions is never finished, therefore the faster runner never surpasses the slower.

The paradox is that physical evidence indicates that the faster runner always does overtake the slower, in reality, even though the logic proceeding from fundamental axioms proves that the faster overtaking the slower is a supertask which cannot be completed.

Due to the strength of the empirical evidence, we are led toward the conclusion that the fundamental axioms concerning the continuity of space and time, and the infinite divisibility of those continuums, must be faulty. Those axioms are the "unsound premises".

Declaring something to be impossible is a strong claim and requires strong evidence. — noAxioms

This is why we cannot simply accept the empirical evidence, and conclude that the supertask is a descriptive impossibility derived from faulty axioms. Empirical evidence is known to be unreliable. So, we need stronger principles to demonstrate the actual faults in the axioms.

Exactly so. I have correct my post. I meant valid and wrote 'sound' in haste. A simple application of modus ponens shows the lack of soundness of Zeno's conclusion iff empirical knowledge is given any weight.

The conflicting premise which would be used to disprove this, the limitations of divisibility
The conflicting premise seemed to be a denial of the completability of a supertask. He never suggests a limit to divisibility. — noAxioms

In Zeno's Achilles and the tortoise, empirical knowledge shows that Achilles will pass the tortoise. But empirical knowledge has problems like what Hume showed with the problem of induction. Because of this, empirical knowledge does not prove the supertask to be impossible.

That the supertask is not completable is not denied, that it is not completable is what actually leads to the problem. In Zeno' paradox Achilles never catches the tortoise because the supertask is never completed. By the premises of the op, Icarus cannot reach the bottom of the staircase, just like Achilles cannot reach the tortoise. So "the supertask" by the nature of what it means to be a supertask, cannot be completed.

The problem is that empirical evidence shows us that tasks will be completed, Achilles will pass the tortoise, and in the op 60 seconds will pass. This shows that the supertask as a fiction. However, due to the problem of induction, empirical evidence does not provide a proper proof. That is why I suggested we look at the divisibility of time as the means for providing a better proof.

To demonstrate the impossibility of Zeno's physical supertask, one must attack the premise, not the logic. The logic is sound, at least until he additionally posits the impossibility of the first premise, but that only gives rise to a direct contradiction, not a paradox.

X is a true fact of motion. X is is a false fact of motion. Therefore either motion is impossible, or at least one of the premises is wrong. — noAxioms

That's almost right, the logic is valid, but not necessarily sound. Soundness requires true premises. Generally though, judgement of the premises is dependent on empirical knowledge, which all good philosophers know is unreliable. Therefore we have valid logic and if the premises are disproven they would be disproven by competing premises, and the judgement ought not be based on empirical knowledge..

The premise of infinite divisibility is provided from mathematical axioms. The conflicting premise which would be used to disprove this, the limitations of divisibility, cannot be derived from the unreliable empirical knowledge, and it has not yet been provided. So we need to defer judgement, until we can disprove the mathematical axioms in a more reliable way.

My posts are invaluable... so good luck trying to get money for them.

In wide open flatland production, American grain fields are very large and spraying them before harvest would probably not be cost effective. That's probably true in Ukraine and Russia, too. — BC

The practise may be more common in northern countries (Canada for example), where the drying conditions are not as reliable:
https://mbcropalliance.ca/directory/production-resources/staging-for-pre-harvest-glyphosate-application/

Perhaps I was wrong to call it "common practise", but that was the information I was reading at the time. The degree of such usage has been debated, and there doesn't seem to be any hard statistics on it. I suppose any statistics would rely on the honesty of the farmers engaged in the activity, and negative press would influence their admissions. But, it is an approved practise. Check this:
https://extension.umn.edu/small-grains-harvest-and-storage/managing-wheat-harvest


In the following article, the representatives of wheat producers claim that use is not common, but do not deny that it is done:

https://kswheat.com/news/the-truth-about-roundup-in-wheat

"Glyphosate is typically applied with a ground rig, and a ground rig will only run the wheat down," said Brett Carver, Wheat Genetics Chair in Agriculture at Oklahoma State University. "In most U.S. wheat regions, it takes a situation of no-other-choice desperation to consider glyphosate as a harvest aid….certainly not the usual scenario."

And here's Anita Dille, Ph.D., a professor of weed ecology at Kansas State University.

"There's all sorts of research that goes on before information gets put onto a label as a legal recommendation," said Dr. Dille. "It starts with the companies. They've done the research. Then, it always goes to a contract research or university level, unbiased and independent kind of sources. Then, all that information goes together in a petition to the EPA (Environmental Protection Agency), before it can be put onto a label as a legal recommendation. All that is regulated. The label is a legal document that the growers have to go by."

Further:

"U.S. wheat producers do NOT routinely use Roundup®, or other formulations of glyphosate, for pre harvest applications," said Steve Joehl, Monsanto’s Industry Affairs Director for wheat. "Quite the contrary, it is the exception rather than the rule. You should be aware that Roundup has an approved label with the EPA for pre harvest use, in the event farmers desire to control perennial weeds, like Canadian thistle, prior to harvest; or for farmers in areas of short growing seasons where crop maturity can be delayed. When used according to labeled recommendations, it is a very safe application. But because Roundup is used in Roundup Ready crops of corn and soybeans, these perennial weeds infestations have been reduced and the practice has been reduced even more."

he usual claim is omnipotence - God can do anything and everything, which if the author and creator of the universe we live in, he would pretty much have to be. — tim wood

Why do you conclude this? Do you have absolute control over anything you created? Why do you think that God would have absolute control over the universe He created? It seems to me, that "creations", whether they are by human beings, some other creatures, or even God, are just not like that.

And if constrained, then not God — tim wood

Why? What makes you think that God must be absolutely unconstrained? I think that if you took the time to read some theology, you would see that even if it is often said that God is "all mighty", and sometimes said that He is "omnipotent" these conceptions are qualified, and it is not very often meant that he is absolutely unconstrained. Consider for example that it is often said that God only does what is good, and he exercises complete self-control to only do good. Clearly this indicates a special sort of constraint, which we as human beings also share with God. However, since we do not really understand self-constraint, and therefore have not been able to perfect it, we tend to imagine it in a very strange paradoxical way. The complete and perfect self-constraint which God is often said to have, is portrayed as an absolute freedom to do anything. And this is paradoxical because even though there are many things God could do, He also cannot do them, because of His self-constraint.

As to any necessity for his reality - yours sounding like Anselm's - that is only a "proof" for those who already take that real existence as axiomatic. — tim wood

I was not handing you that argument as a "proof". I was only trying to make it clear to you that if you want to talk about "God", then you need to talk about "God" as He is understood. I find this to be a common problem with the atheist approaches to God. The atheist commonly approaches God with the presupposition, that God is an imaginary, fictitious thing, not real. But this is not how God is understood in theology. This prejudice which the atheist holds is completely contrary and contradictory to how God is actually understood, so it prevents the atheist from having any understanding of God. Aquinas, for example, asserted that God's essence is His existence. This implies that the very first principle one must accept before being able to understand anything about God, in any way, is that He has real existence. So if the atheist has any bit of intent whatsoever, to understand God, this prejudice must first be dismissed. Otherwise it's a waist of time.

Reality is the realm of nature, and recall we put that to the question. — tim wood

Your claim, "reality is the realm of nature" is fundamentally false. By saying "the realm of nature" you imply the possibility of other realms not contained within the realm of nature. And as a "realms" these must be real. So even the statement itself, as written, implies its own falsity. It's like saying "there is only one multiplicity". The statement is self-defeating.

Consider, that "the artificial" is often contrasted with "the natural". We cannot say that the artificial is not real. So many will class artificial as part of the natural. But by doing this we lose the meaning of "natural", which is defined as "not artificial". The intent of the person who redefines "natural" in this way, may be to include the artificial into the realm of the natural, to argue that only the natural is real, but what's the point? That statement is self-defeating as shown, and to class the artificial as natural, is to ignore the substantial difference between the two.

As to hearts, I have to own up to my ideas about "purpose" being pretty clearly not as clear as I thought they were, or would have liked them to be. — tim wood

This is why it is a very good thread which you have started. If you learn something new then the thread is good, right? The issue here, I think, is the presuppositions which we commonly take for granted. These are what are commonly known as bedrock or hinge propositions. Since they are taken for granted they are not subjected to our doubt. Since we do not doubt them or subject them to any form of methodological skepticism, then we do not develop an adequate understanding of their meaning. So the use of many words, such as "purpose", just floats freely, being a facilitator of mundane communication, a word whose meaning is taken for granted allowing for fluid conversation. Because of this, the word's meaning gets shaped to the circumstances of conversation, and what comes out on top is the most common usage. If someone asks what is the meaning of "purpose", we have all sorts of examples in common usage to refer to. But since its such a commonly used word, we can restrict the meaning we express, to these common examples, and having not applied a methodic analysis like the skeptic does, the true deeper meaning escapes us.

However, I think I can distinguish between purpose and function. — tim wood

This is a good start. Let's look at the difference between "purpose" and "function". At first glance, we can say that the two might commonly be interchangeable, "a thing's purpose is the thing's function". But invert that and say "a thing's function is the thing's purpose", and that's not necessarily the case. This implies, right off the bat, that "function" has an even broader meaning than "purpose". Not all functions are purposes.

Further, we can see that "function" is most often an activity, whereas "purpose" is more often the goal of the activity, the end, or objective. This opens an even bigger rift between the two. What is exposed here is that "purpose" is something we attribute to an activity, the property of an activity, which puts it into a specific relation with an end, a goal. This makes the activity a means to an end. "Function" in its common usage does not necessarily imply such a relation of means to an end, because the function may be the activity itself, regardless of the purpose of the activity. So we might say, of a thing, that the thing has a function, and this function is the activity of the thing, without even indicating the purpose of that activity, or whether it even has a purpose.

So for example, if I am involved in a cooperative effort, I have a function, which is to bring the others coffee. That can be referred to as my function, what I am doing, bringing the coffee, and this can be said without any reference to the purpose, why I am bringing the coffee. In the heart example, the function of the heart can be stated as "to beat". The beating is the function of the heart, and this may be stated with a complete disassociation from the purpose of the heart. The thing has a function, an activity, and this is completely irrelevant to whether there is a purpose, goal, or end to that activity.

You can see how this has become a very convenient way to separate "function" from "purpose" thereby ignoring the question of "purpose". This is the way language evolves according to social circumstances to avoid areas of doubt, and facilitate mundane communication. We can talk about all sorts of things, and the function of each thing, with complete disregard as to whether that function has a purpose or not. That helps us to avoid having to think about whether or not natural activities have a purpose, thus keeping us away from the volatile "God" question.

Ontology is choosing between languages. It consist in no more than stipulating the domain, the nouns of the language. — Banno

Oh my God! Save this poor lost soul.

I'll try one more time: is God constrained in any way? Is He real? My point being that in belief in an idea, you can have what you want. But not in any reality. — tim wood

God has to be real, because that is stipulated in the conception of "God", as an essential aspect of "God". If God was not real, then the conception would be contradictory, and there would be no God to talk about, just self-contradictory nonsense. So, if we are talking about God here, we are by definition talking about something real. You can dismiss talk about God as self-contradictory nonsense if you like, but please don't ask me if God is real, because it just indicates that you are totally ignorant.

As for your other question, I have no knowledge as to whether God is constrained or not. Some say that God is not constrained in any way, but I think that's just conjecture.

Take a look at this problem tim. I said to you that the purpose of an animal's heart is to circulate blood, and you said that's not the sense of "purpose" I am talking about. Now you clarify the sense of "purpose you are talking about, with the following.

On a good day, if I do something, it is for a reason. If my effort is successful, it might be said I had achieved my purpose in doing it. In this sense purpose like a work order or chore or task, a thing to be done. — tim wood

How is this a different sense of "purpose" from when I said the purpose of the heart is to circulate blood? To circulate blood is "a thing to be done", by the heart, it is "the reason" for the heart. If the heart's effort is successful, it achieves its purpose. It's the very same sense of "purpose".

Classical Euclidean geometry is arguable not "real" mathematics. As Kant pointed out, it is incredibly married to sensory input, to the point that it is not pure reason. — Tarskian

That's the point, mathematics is always "married" to something, be it the world of sensory input, or the alternative, Platonic universe.

The fact that Euclidean geometry has too much meaning and does not fit the formalist narrative, points out a problem with Euclidean geometry and not with the formalist ontology. If it is not possible to interpret it as meaningless string manipulation, then it is not real mathematics. — Tarskian

You're jumping to a conclusion. How does the imaginary Platonic universe provide a less problematic grounding for meaning than the sensed universe?

You yourself described how the formalist approach does not get rid of correspondence, it only replaces the objects of the sensible universe, with the objects of the Platonic universe, as that which the mathematics corresponds with. But there is a huge problem here, the objects of the Platonic universe are simply whatever strikes the fancy of the mathematician. So for example, the mathematician might think, "I wish I could count to infinity". Then, one could create an axiom which states that the natural numbers are countable, and stipulate a 'set of the natural numbers', and voila, the mathematician has counted to infinity, within that imaginary universe of Platonic objects.

In its anti-realist take, mathematics is indeed "about nothing". In its realist take, mathematics is about an abstract, Platonic universe that is completely divorced from the physical universe. In both cases, any downstream application of mathematics is completely irrelevant to mathematics itself. That is a feature and not a bug. — Tarskian

What you describe is what formalism would be like if it could achieve its goal in an absolute sense. It would be "about nothing" but as I indicated, at the same time it would be "about everything", providing infinite applicability, and at the same time, as you say, no applicability. But of course, no mathematician would seek this, because it would be incomprehensible nonsense.

So formalist mathematics is always tainted, and rules of application always inhere within the axioms, whether the influences are the sensible universe, the Platonic universe, or both. Your claim, "any downstream application of mathematics is completely irrelevant to mathematics itself" is simply false, because that's what the axioms of mathematics do, lay the grounds for application.

Model theory makes anti-realist views unsustainable. Model theory makes mathematics decisively correspondentist. Because of model theory, mathematical realism and more specifically, Platonism, are unavoidable. Mathematics is about abstract Platonic worlds and is not just string manipulation. — Tarskian

How would you classify model-dependent realism? Clearly this is not "correspondentist". You can argue that it is a form of "realism" as the title suggests, but where does the correspondence lie. I suggest that you consider that correspondence inheres within the formal system itself. When the math is applied correctly there is correspondence between the symbols, and what you call the "Platonic universe".

But "correspondence" in the common sense, means to correspond with the empirical world of observable sense objects. Your thread does not seem to make a distinction between these two very different senses of "correspondence". The common sense is correspondence with an assumed observable, sensible world, and the sense you mention here is correspondence with an assumed Platonic universe.


In the op. you do not address the nature of axioms. In reality, the axioms dictate the applicability of mathematics, and it is how mathematics is applied which determines whether it is formalist or realist. In other words, the meaning of the symbols is dependent on the context of the application, and the applicability, therefore context, is dependent on the axioms. And, I would argue that in general, the axioms are intentionally extremely vague and ambiguous in this respect, for the very purpose of allowing the mathematics the widest possible context of applicability. You will see however, axioms like those of set theory, which are explicitly realist. Such restrictions limit the applicability of the mathematics, (which is evident from the recent paradox threads of @keystone), by doing things like limiting "infinite" to fit it into the confines of "an object".

Applied mathematics is actually not mathematics. — Tarskian

If you think clearly about this idea, you will see that the inverse is actually the case. To analyze, let's separate form from content, and assume that the formalist's goal is to remove all vestiges of content from the formal system. How can this be accomplished? If the axioms have no designated relationship with anything outside the logical system, then the system my be infinitely useful, but at the same time infinitely useless, because it is robbed of all meaning. So the formalist allows a little bit of meaning, content, to inhere within the form of the structure.

For example,

Mathematics proper seeks to establish the correspondence between an abstraction and a Platonic universe -- when interpreted according to realism -- or between an abstraction and another abstraction -- when interpreted according to anti-realism. Mathematics proper is never about the physical universe. — Tarskian

In this example, you have an assumed "Platonic universe". This assumed universe provides the content. So consider the following two possible sets of rules for the processes of counting. The first set of rules would be to produce a bijection between the symbols and the physical objects to be counted. You want to count chairs, you biject "1" and a chair, "2" and a chair, etc.. In that case, the formal structure, and the set of rules for application are completely distinct from the content, the content being the physical objects counted, which is dependent on the application The second possible set of rules for the process of counting would be to produce a bijection between the symbols and a "Platonic universe" of "numbers". In this case, the content, being the numbers as objects, is built right into the formal structure. The limits of applicability are built into the structure, instead of being defined by a further set of rules.

If you categorize the first as "formalist", then you have a separation between the formal structure and the content (physical things) which the structure is applied to. However, the structure is useless without rules of application, so we proceed toward axioms of geometry, and rules of categorizing, to provide rules of application. The rules of application are still a part of the formal system, and there is no proper "formalist" separation. If you categorize the second as "formalist", then the content inheres within the formal structure, and there is no proper separation, as required for a true formalism.

Either way, mathematics cannot escape the need for, or its dependence on, application. There is always some form of application built into the formal structure, as axioms. Either the rules for application are a distinct part of the structure, as in the first case, or the application itself is already built into the structure, as in the second case. In no way can mathematics completely escape application, without it becoming something other (a useless bunch of symbols) than mathematics. So the inverse of your statement is actually the truth. With absolutely no application, mathematics would be absolutely nothing. And in reality mathematics is nothing other than application, pure means without any defined end.

Oh I see, "I exist now", is an eternal truth. So the "eternal truth" is a truth which obtains the highest degree of certainty. The other less certain truths are not eternal because we allow that they may fall out of the status of being true at some time, just like what happened to "Pluto is a planet". The truths with a really low level of certainty, which we employ commonly in our mundane thinking, like "it will not rain today", are only true for as long as they are useful.

What if we could consider 'cogito ergo sum' as an eternal truth?

Alas, being aware that we exist or being aware of our consciousness could be an eternal truth.
I can't imagine a decrease in the level of meaningfulness in Cartesianism. — javi2541997

Wouldn't this mean that your existence is eternal?

If you'd read the OP, you could not have failed to observe that this, your sense of purpose here, is not the topic, and so without relevance. — tim wood

If you'd have read what you said to me, you would know that you asked me "in terms of purpose - of any kind -". I assume that the clearly stated "any kind", implies that any such restrictions are to be put aside.

Anyway, I just reread your op, and cannot understand your proposed restrictions at all. Can you explain clearly how you are proposing to restrict the meaning of "purpose" in this thread?

And in passing since you claimed earlier that there could be no propose before purpose, I assume you also would hold that there can be no hearts until there was a heart. — tim wood

What are you talking about? Of course there can be no hearts until there is a heart. That's a self-evident truth. But that's not at all relevant to what I said. I said purpose is prior to a display of purpose. A heart is a display of purpose, so purpose (or intent if you prefer) must be prior to the heart. How do you get from this to the self-evident truth of "there can be no hearts until there was a heart"?

But let's try these: is God constrained in any way? Is He real? My point being that in belief in an idea, you can have what you want. But not in any reality. — tim wood

How is this relevant? In reality, sometimes you get what you want, sometimes you do not. In what way do you believe that the constraints placed on human beings are related to the constraints placed on God, if there are any?

The point of my example with the ship was to counter your assertion of Newton forces not being necessary to move and free will being enough. I said you'd need help from Newton. Asking for a line to be thrown to you is you admitting the help from Newton was necessary. That's what the tether is: a way to do it by exerting an external force, since the free will couldn't do it itself. — noAxioms

It seems you misunderstood.

I understand reality as being the world we all live in, and also a set of constraints which things not of or in reality are not subject to. I don't object to beliefs, except when, as concerning things not of or in reality, the believer tries to place them into reality. — tim wood

I cannot quite apprehend what you mean by "a set of constraints which things not of or in reality are not subject to". I assume you are saying that there are things which are not part of reality, and those things are not subject to this particular set of constraints you are referring to. Are these non-real things subject to any kind of constraints, and what kind of existence do they have if they are non-real?

And as God is supposed to be unconstrained, he cannot be in reality nor rationally supposed to be there. — tim wood

Your conditions for "reality" do not state that there cannot be an unconstrained real thing. You said that things not in reality are not constrained by a specific set of constraints, but you didn't say that things in reality are necessarily constrained. What exactly do you mean by "a set of constraints"? I understand "sets" to be things created by human beings. Are these constraints artificial as well, or is it just the classifying of them into a specific set which is artificial?

And in terms of purpose - of any kind - can you point to or articulate any that do not come into being through a man's or a woman's speech or writing? — tim wood

Are you serious? Is it not the case that the purpose of an animal's heart is to circulate blood, and the purpose of sense organs is to sense, etc..?

Aren't there things with a constant meaningful duration? — javi2541997

That would be eternal truth, if there is such a thing. Some would attribute this to God, others to mathematics, and some perhaps to physics. It seems like people generally have a desire to assume some kind of eternal meaning, as a sort of principle of balance, because life, while it seems to strive in that direction, fails in its capacity to give us this.

Fair enough? And may we say as well, boot-strapped? By which I mean valued because they are valued, any other value being derivative and incidental. — tim wood

Doesn't "valued because they are valued" imply infinite regress, or maybe a vicious circle, rather than bootstrapping?

In the op you say "Bottom line, purpose is boot-strapped", but how could this be possible? Isn't it true that boot-strapping is a purposeful process? This would imply that purpose is necessarily prior to, as the intentional cause of any boot-strapping activity. Then purpose itself cannot be boot-strapped.

I believe it was Paul who insisted on the individual identity of the resurrected soul.

After rereading this thread, I want to once again commend you on continuing to maintain a respectful 'tone' despite what clearly looks to me - now at least - like my own unwarranted bristling/taking unwarranted offense at different times throughout. — creativesoul

Ha ha, evidence that meaning has a temporal duration. The thread has different meaning now than it did back then.

How do we demonstrate such a statement? Which god, by the way? — Tom Storm

It is demonstrated this way. Purpose is prior to any display of purpose. Therefore there must be a purpose which is prior to all things which display purpose. That purpose cannot be attributed to anything which displays purpose, being prior to all such things. So it is attributed to God, as the source of purpose.

The other question doesn't make sense. If we're talking about God as the source of purpose, then obviously that's the God we're talking about.

And may I ask what God, and how you know? — tim wood

See above

Good point, well said! But if not boot-strapped, then from what? Religion? Faith? Belief? Knowledge? Hope? Reason? That is, I disagree, and "finding" one of the great deceptions, often from those selling something. Purpose, then, has to be made, but no easy way to figure out how, or exactly what. . Ex nihilo because there is no other possible source - or do you know of such a source? — tim wood

Quite simply, God is the source of purpose. Those who do not believe in God have a big hole in their capacity for understanding, because the purpose we know and observe, seems to have no purpose when we do not recognize God. When we come to apprehend the reality of God then all that purpose makes sense. And the atheists think the theists are being unreasonable, but it's really the other way around because the atheists are denying themselves the capacity to understand, and that is being unreasonable.

But really the only reason people vote is for astronomical reasons, because the earth has spun on its axis 1460 times. So at least they know how to count. — NOS4A2

Faulty conclusion. If someone tells you the earth has spun on its axis 1460 times, therefore it's time for you to go and vote, so you do, this does not mean that you know how to count.

Yes, I’ve heard of voting. Isn’t that what educated people do? — NOS4A2

Oddly enough, voting is not just limited to those who are educated. Now, it has been argued that a certain degree of education ought to be mandatory, but that would be discriminatory. So... we get the problem described by Plato, being a successful candidate is like offering candy to children.

"Rockabye baby on the tree top ... down will come baby cradle and all".

Moral of the story: sleep with one eye open.

I see NOS has put everyone to sleep on this thread. Nice. — Mikie

The Lounge is where I go to take the edge off the day with a good lullaby.

The only thing an educated person can do politically is glorify and aggrandize the state, or disguise their statism as social and political philosophy, which is the direct consequence of their state education.

In any case, I’d love to see an educated refutation of any one of the aforementioned political stances, morally and socially, if you care to try. — NOS4A2

Thanks NOS, I slept well for four days after that one. Have you ever heard of voting?

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? .