If (2) is true then we can stop without stopping on some finite number. — Michael
Not in those words. "Does not allow for a minute to pass", like somehow the way a thing is described has any effect at all on the actual thing. — noAxioms
Anyway, I see nothing in any of the supertask descriptions that in any way inhibits the passage of time (all assuming that time is something that passes of course). — noAxioms
Ah, it slows, but never to zero. That's the difference between my wording and yours. Equally bunk of course. It isn't even meaningful to talk about the rate of time flow since there are no units for it. The OP makes zero mention of any alteration of the rate of flow of time. — noAxioms
Socrates (as presented by Plato) considered himself wiser than anyone else because he knew he didn't know anything, which doesn't seem to leave much room for anyone else (at least in Athens) to be a philosopher. However, his dialogues with sophists do not show Socrates treating them disrespectfully and this is something of a puzzle. The orthodox interpretation regards Socrates' respect as ironic. Maybe it is. But maybe Plato's practice was a bit less dismissive than all this implies. — Ludwig V
Says the proponent that time stops. — noAxioms
I suspect Zeno believed his premise to be false... — noAxioms
No evidence of your interpretation here. — Ludwig V
Fair enough, but to go on, as Plato does, to accuse the sophists of deliberate deception or wilful blindness is completely unjustified (except when, as in the Protagoras,(?) Gorgias (?) someone boasts about doing so – though it doesn’t follow that everyone that Plato accuses of rhetoric and sophistry did so boast.). — Ludwig V
But accepting that connection is a long way from accepting that he had any doubts about the validity of his conclusions. — Ludwig V
That there is no first number to recite is the very reason that it is logically impossible to begin reciting them in reverse and it astonishes me that not only can't you accept this but you twist it around and claim that it not having a first number is the reason that it can begin without a first number. — Michael
They're clearly being confused by maths. They think that because a geometric series of time intervals can have a finite sum and because this geometric series has the same cardinality as the natural numbers then it is possible to recite the natural numbers in finite time. Their conclusion is a non sequitur, and this is obvious when we consider the case of reciting the natural numbers (or any infinite sequence) in reverse. — Michael
There is a far more fundamental problem, and they're just ignoring it. — Michael
I'm not sure it is possible to articulate what people who have not thought about the question think the answer to it is. — Ludwig V
I don't think we have anything near the evidence required to divine Zeno's motives. We don't even have his articulation of the argument. — Ludwig V
But you don't know that he recognised what is so very clear to you, that the argument was ridiculous, or that he had "apprehended the faults in that ontology", though I admit that if he had understood what you understand, he might well have been poking fun at it. Still, other people since then have poked plenty of fun at it. But that's not a substitute for understanding the argument. — Ludwig V
I think that's perfect. It's the conjunction of mathematics and - what can I say? - the everyday world.
What's difficult is the decision which is to give way - mathematics or the everyday world. Zeno was perfectly clear, but some people seem to disagree with him. — Ludwig V
That suggests that we do know roughly how things move. I don't think that's what at stake in Zeno's thinking. His conclusion was that all motion is illusory. The only alternative for him was stasis. But I guess we can do better now. — Ludwig V
That's apparently what somebody else reported about what Aristotle reported. I've seen it conveyed about 20 different ways. — noAxioms
This particular wording says 'never' and 'always', temporal terms implying that even when more than a minute has passed, (we're assuming a minute here), Achilles will still lag the tortoise. — noAxioms
The logic as worded here is invalid for that reason since the argument doesn't demonstrate any such thing. — noAxioms
. I've seen more valid ways of wording it (from Aristotle himself), in which case it simply becomes unsound. — noAxioms
I just didn't like the fact that the quote didn't match the site linked. — noAxioms
You mean because they allow the convergent infinite series?
Mathematically? Physically? (I'm inclined to think you mean physically, because of your reference to fundamental particles.) — Ludwig V
Is the direct spatial route not available because it contains a convergent regress?
What path does Achilles take? (I assume he is not a fundamental particle.) — Ludwig V
I know the story. You seem to have reworded it for your purposes, since the quote you give does not come from that site, but the site also seems to be conveying the story in its own words, not as reported by Aristotle. — noAxioms
The second is the so-called 'Achilles', and it amounts to this, that 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. — Aristotle Physics 239b 14-17
Yes, and without justification, or at least without explicitly stating the additional premise that makes the conclusion valid. — noAxioms
So are you going to conclude, with Zeno, that motion is impossible? or that Zeno is analyzing the situation in a misleading way? — Ludwig V
Anyway, I deny that Zeno in any way suggests that the overtaking will never take place. He just says that another step always follows any given step. — noAxioms
https://iep.utm.edu/zenos-paradoxes/According to this reasoning, Achilles will never catch the tortoise, says Zeno. — Internet Encyclopedia of Philosophy
Zeno Paradox 1: Achilles and the Tortoise
Achilles is a lightening fast runner, while the tortoise is very slow. And yet, when the tortoise gets a head start, it seems Achilles can never overtake the tortoise in a race. For Achilles will first have to run to the tortoise's starting point; meanwhile, the tortoise will have moved ahead. So Achilles must run to the tortoise's new location; meanwhile the tortoise will have moved ahead again. And it seems that Achilles will always be stuck in this situation.
Case closed, then. — Ludwig V
Great. Then show the logic that concludes this, without resort to another premise. — noAxioms
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
There is no first natural number to start with. It is logically impossible to have started reciting the natural numbers in descending order. — Michael
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
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
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
That second premise might well be that supertasks cannot be completed. — noAxioms
That premise is indeed in contradiction with the first premise and empirical observation. At least one of the three is wrong. — noAxioms
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
Declaring something to be impossible is a strong claim and requires strong evidence. — noAxioms
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
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
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
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
And if constrained, then not God — tim wood
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
Reality is the realm of nature, and recall we put that to the question. — tim wood
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
However, I think I can distinguish between purpose and function. — tim wood
Ontology is choosing between languages. It consist in no more than stipulating the domain, the nouns of the language. — Banno
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
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
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
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
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
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
Applied mathematics is actually not mathematics. — Tarskian
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
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
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
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
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
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
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
And as God is supposed to be unconstrained, he cannot be in reality nor rationally supposed to be there. — tim wood
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
Aren't there things with a constant meaningful duration? — javi2541997
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
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
How do we demonstrate such a statement? Which god, by the way? — Tom Storm
And may I ask what God, and how you know? — tim wood
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
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
Yes, I’ve heard of voting. Isn’t that what educated people do? — NOS4A2
I see NOS has put everyone to sleep on this thread. Nice. — Mikie
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