Silhouette, the other way the paradox works is that by the tortuous taking the first step, the tortuous is the finish line!!! That means that Achilles can ever reach the tortuous.
Zeno’s argument is grounded on the premise that space is infinitely divisible. One can argue that the flaw in Zeno’s argument lies precisely in this premise (that this premise is false) and that the rest of his argument is fine. I think that’s John’s position.
My position, however, is that even if we accept that space is infinitely divisible, Zeno’s conclusion does not follow. In other words, his argument is logically invalid.
What Zeno has shown is that you cannot cross an infinitely divisible distance by following Zeno’s algorithm. Zeno’s algorithm consists of making sure that each one of our steps is equal to one half of the remaining distance. This is where I agree with him. You can’t cross a path if you’re trying to walk this way (in the same exact way you can’t cross a path if you’re simply standing in one place.) However, he goes further than this, as he takes this to mean that no other algorithm exists that can allow us to cross an infinitely divisible distance, which means that no motion is possible if space is infinitely divisible. That’s where I disagree.
I argue that one way one can cross an infinitely divisible distance is by making sure that all of our steps are equal in size. If each each one of our steps is (1cm) in size, and if we’re crossing a distance of (1m), it will take us exactly (100) steps to cross it. However, if space is infinitely divisible, this means that (1cm) consists of an infinite number of points, so in order to make a step that is (1cm) in size, one has to cross an infinite number of points.
The question is: is this possible?
The answer depends on one’s definition of the word “infinity”.
Depending on how one defines the word “infinity”, the answer can be either “Yes” or “No”.
If the meaning of the word “infinity” is captured by the contradictory statement “A number greater than every number (including itself)” (Sense A) then one cannot visit an infinite number of points because regardless of how many points one visits there is still more points to visit.
However, if the meaning of the word “infinity” is captured by the statement “A number larger than every integer” (Sense B) then it might be possible to visit an infinite number of points since there is more than one such number. A number greater than every number including itself is only one such number. If the number of points is equal to some other number greater than every integer (not the one greater than literally every number) then one can cross all of the points.
The word “infinite” in Sense A is not the polar opposite of the word “finite”. In other words, if something is not infinite in Sense A, it does not mean it is finite. It might actually be infinite in Sense B.
Gotta love that auto-correct: tortoise → tortuous 
Yeah, just change the metric that you’re dividing into fractions and the problem disappears - increase it from what Zeno stipulates by any amount and poof, gone, even though the scenario itself of Achilles racing a tortoise does not change.
It’s dubious to talk about which of the two takes the first step though. That’s not a part of Zeno’s paradoxes unless you make it one.
The paradox does actually have the tortoise as the finish line, by the way - the whole idea is that Achilles never overtakes it. But yeah, if you insert turn-based steps into the paradox and double the distance being divided into fractions, Achilles would never even move before he lost… but as I was saying - that’s not actually part of Zeno’s paradox, just a modification of it.
Btw, you didn’t answer my question about why you don’t “believe” in Experientialism.
Magnus,
You love that phrase “number greater than every integer”. Unfortunately for you, infinity is not a number, it’s an operator upon numbers.
And thus you are refuted.
You know, I have to say, I enjoy debating everyone in this thread. I think you guys are awesome.
Right. So “3 infinity 5” must be a perfectly sensible mathematical expression (: What’s the result of it?
You don’t enjoy debating, you enjoy talking.
Well…
3 infinity 5 (without parentheses) would mean an infinite number of 3’s with a five that’s separate from the infinite number of 3’s.
Not so hard is it.
Just as saying, of the two representations, the turtle or Mobius, which is the in-verse, that is all forms of turtles up in each other? It is Mobius, …
In verse is not merely lots of ex cathedral talk, for it is not a simulatied archetype ahead of it’s time, but a directly attributtal response to Wittgenstein’s idea of similitude.
In method, the infinitely reproducible artifact, is only limited by the inconceivable scintilla that only a god can conceive .
A god is firmed put of that scintilla, by necessity, to enable man to make ultimate sense of the meaning to the question-why was He created.
I think if you were to search the Tractatus , I am pretty sure more inference could be drawn of the basic hypothetical re: intuitive analytical-mathematical assumptions.
At least one definition in black letter is evident: ignorance of the Law is no excuse.
If he took it to mean no motion is possible to discretely measure if space is infinitely divided, then he’d have been right. Motion is measured in distance per unit time, but if the units of distance are infinitely small we run into infinite numbers to denote motion, which prevents us from discretely dealing with it. The solution is obviously that you need merely treat things in terms of finite discrete divisions of distance that aren’t divided into infinite divisions of distance.
Let’s try not to make this thread into that one.
I mean, John has already shown himself incapable of understanding logic in its technical application to his arguments - so there’s not much to spoil - maybe I shouldn’t have brought up Zeno in the first place, but it was the perfect example to mirror a couple of John’s arguments that try to prove that there has to be a beginning to the universe.
If you can solve Zeno, you know why those arguments of his are false, that’s as far as it needs to go.
Just to wrap up what is meant when infinity is said to be an operator - it is only validly used in mathematics as part of an operation, more like an operator on an operator. This doesn’t mean it’s interchangeable with operators like addition and multiplication etc. - it means it can be used to apply to the number of times you add or multiply etc.
This isn’t up for debate by the way, I’m just quickly saying what math does - nothing more nothing less, no should or shouldn’t, just what math does.
What is up for debate are the arguments that open this thread 
Let’s resume, shall we?
This is actually quite a nice analogy for a conception of the universe defying the need for a beginning or end - in this case with the universe being temporally contained and “flat” (which is how physicists describe the universe) yet simultaneously temporally infinite through a simple half twist along a second time dimension.
But this requires the ability to perform multi-dimensional toplogy in your head, which is probably quite a bit beyond the calibre suggested by the opening post.
Silhouette,
You kinda waved your hands around in your reply to magnus in the first paragraph. More to Zeno’s point, basic math intuitions are insolvent towards basic understanding of what this is for all of us.
Zeno is basically saying “choose math or choose this”
You didn’t really solve anything in that paragraph other than to say “thus it must be finite”
But if you say that, it means you agree with John over gib.
I don’t wave my hands - you know that. I am extremely specific and pedantic, which you repeatedly and correctly accuse me of being.
If you think my conclusion means I agree with John over gib, you’ve misunderstood Experientialism - and you’ve still not said why you don’t “believe” in it.
It’s quite simple: experience is the concrete version of what existence is in the abstract. Experience is observably Continuous Experience, and rationally it is also continuous because there are no gaps of nothingness to divide it up. Yet we routinely do divide it up into discrete experiences (rationalise it into ratios) for explanatory power - that’s what math does when it is used validly. Math gets very messy once you delve into continuous infinites - I know you appreciate that much. I side with math and physics sticking to discrete experiences for the purposes of discretely measuring phenomena in a meaningful way - that’s all I’m saying when I say “treat things in terms of finite discrete divisions of distance”. This is different from saying that math and physics treat the universe as it is, because the universe is continuous and not discrete. It’s saying that it treats the universe differently in order to extract discrete knowledge about it.
Note what I’m saying about how one shouldn’t treat the universe as a whole as a discrete experience with a beginning and an end - this makes no sense as it wouldn’t be everythingness if it was discretely bounded, “with nothing outside of it”. This is where the religious flounder and assert a greater existence outside of all existence in place of this nothingness that would otherwise be outside of a discrete universe’s “bounds”. The universe has no bounds - everythingness is continuous.
What I am saying is that to create knowledge out of continuity (about the universe with no beginning or end), one must conceptually break it down into discrete parts, which have beginnings and ends because you can conceptually work with that. What you don’t do is then apply that back to the universe as a whole because of the contradictions that I just mentioned. You have to convert it back to continuity to get back to the universe as a whole. Scaling our knowledge of discrete parts back up to some “discrete whole” is where John is fundamentally erring.
This is just another way that Experientialism makes entirely consistent sense of everything.
Why wouldn’t you “believe” in that?
Silhouette,
You keep using the term “discrete” much to my point.
Existence has a beginning and end, just like John argues.
Gib argues that it never started. I agree with gib.
I think atheism is much more mysterious than the god John always invokes.
The definition of the word “infinity” is precisely what one of his (I mean John’s) arguments rests upon. It’s unavoidable.
The problem with this discussion is that noone bothers to properly understand what the author is saying. Noone is asking him questions. Instead, everyone is merely assuming (and as a consequence, strawman attacking him.)
Silhuette said,
“But this requires the ability to perform multi-dimensional toplogy in your head, which is probably quite a bit beyond the calibre suggested by the opening post.”
I agree. The mathematicization of philosophy has to break the nominal descriptive presumptions relating to any attempt to pre position- a proof for a re-positional attempt like this. Therefore, an inversion or counter proposal has become a fitting and likely necessary model.
The Theistic/atheistic breakage still
figures in the conflated , undifferentiated world of basic modeling. What John is attempting to do is to regain an epoch(epoche) of a regression, whereby he can draw attention to the fact, that if he were unable to demonstrate the “impossibility of an unlimited to totally absolute level of regression” he would be open to the charge of severe structural damage.
That is to say, he couldn’t want to admit a problem of accepting an identifiable damage in reference to ‘God in Himself’ since that would severe damage to a personal (Das Sein) severance, and he may suffer consequential problems that befell the great philosophers, who dared thread similar grounds; but in John’s case it is an honest attempt to try to describe and interpret the problem, rather than to actually retain the momentum to reassert the claim Saint Anselm made, which has become a seriously contended probability of late.
I don’t think anyone is trying to place anyone on a downward incline and push him off the slope, its merely a showing of how strongly emotional the issue of God’s existence has tried to overcome the great 19th and 20th century’s explosion of rapid industrial progress.
Discrete is the opposite of continuous, what’s wrong with using the word?
Okay, lovely.
My point is that the universe is continuous therefore beginnings and ends don’t apply.
If you want to make useful and meaningful sense of the universe, you have to change it into something it isn’t: a collection of (discrete) parts that interact, which in turn have their beginnings and ends however we decide to define them for maximum perceived utility. This doesn’t mean the universe actually is a collection of parts, only that it’s useful to think of it that way. It’s an error to take this dissection of the universe, scale it up to the scale of the universe itself, and then speculate about what’s “outside everything”. If you make this error, at best you’ll meaninglessly conclude “nothing” is outside everything, and at worst you’ll anti-meaningfully conclude that there’s even greater existence outside of all existence. Ideally, you won’t even make that mistake in the first place, and you’ll undo your conceptual dissections (of Continuous Experience into discrete experiences) and get back to the universe as continuous - no beginning or end.
There’s literally no holes in using Experientialism like this to get to correct answers and to get to the bottom of misguided threads like this.
You’ve STILL not said why you don’t “believe” in Experientialism.
“A number larger than than every integer” is what 14 Cosmological Arguments for the Existence of God rests upon?
Are you sure?
Not true. I began my contributions to this thread by thoroughly dissected his first argument line by line in ways that he’d agree with, and he hasn’t said he disagrees with the meticulous way that I did it. What he disagrees with (or rather “dislikes”) is the lack of logical consistency that I’ve pointed out results from dissecting his argument.
What I got in return was a complete ignoring of my points, or blanket claims that they don’t exist/are weak with zero further explanation, and accusations that I’m the one making blanket claims without any further explanation, which is the literal opposite of what I’ve been doing.
I went to great lengths to parse what the author is saying, and I received nothing but bad faith. This is why I’ve concluded that nothing constructive can come from this, and why I’m largely avoiding any contact with him and instead only engaging others.
So why is time discrete? Why could you not get from t1 to t2 if time were not discrete? And what does that have to do with the possibility of an infinite regress?
I’m not trying to establish proof, I’m trying to get the necessity out of your arguments about why time must have a beginning. I just don’t see a problem with a retro-eternal universe.
We don’t know that that was the beginning. Even most scientists, when they’re being honest, will admit that we don’t know that. In fact, there’s been recent evidence (or maybe it was just accepted theory) that the BB wasn’t the beginning of the universe, that the universe goes through cycles of expansion and contraction, or that our universe exploded into existence from a parent universe.
Oh, well, since you added that third point, I guess time must have a beginning. I mean, if you stuck with only 2 points, your arguments would hold no weight whatsoever. But this third point, especially since it asserts the clarity of your paradox arguments despite my counter-arguments, settles the matter.
I get the point of your argument. I did offer a rebuttal if you care to read it. It was this: the need to traverse an eternity of time, or an infinite number of causes, is only a problem if you imagine starting from somewhere (somewhere eternally distant in the past). But the point of talking about a retro-eternal universe is to do away with any starting point. All points in the time, all events that occur therein, are just there–already in the past (relative to where you are now).
Understanding this depends on how you imagine time in the abstract. You can imagine time in a static context–such as when we plot time on a diagram–all points along the time axis “coexisting”. If this is the true state if time (and I would expect you to agree with something like this since you believe God exists in a timeless context) and our experience of time flowing by is just an illusion of subjectivity, then the problem of an eternal universe becomes the problem of an infinite (spatially) universe, which isn’t a problem at all as far as I’m concerned.
You can also imagine time in the subjective context–or dynamic context–the one in which time exists just as we experience it. But in this context, the past and future don’t exist. There is only now. Now is dynamic, ever changing, becoming the future and relegating its old states to the past. But in a context in which past and future don’t exist, what sense does it make to talk about an eternity of time OR a beginning. We’re left just talking about what kind of conceptual framework best models the past in our minds. And there’s nothing wrong with talking about a model featuring retro-eternal time. Nothing has to “traverse” all of time to get to now in a model. It’s just a picture.
They always come in 3s, don’t they?
You got it completely wrong again!
Physical reality is not continuous, i.e. comprised of infinitesimals. Physical reality is comprised of discrete indivisible units of reality.
Is that what I said? I’m not really sure. Let’s see.
The manner in which he defines the word “infinity” (the manner in which he defines it need not be “A number larger than every integer”) is what ONE of his arguments (not ALL of his arguments) rests upon.
If you wonder which one of the arguments, this one:
Note the underlied colored part. Note how he’s using the word “infinity”.
One has to know what he means when he says “infinity” before one can evaluate the validity of his argument.
The best way to figure that out is to ask him to define the word in sufficient detail. If he’s not willing to do so, then you simply ignore his argument.
Time is not continuous because time dilation proves that time can be stretched or slowed down. You can’t stretch infinitesimals. You can only add to them. You can however stretch discrete units.
There’s a big problem with an infinite regression. No scientific proof that infinities are real. NONE!
There is scientific proof of a beginning to the universe. There is NO scientific proof of a cyclic universe.
Actually, imagining a starting point in the past is a beginning point from which only a finite amount of time or causes need be traversed. I don’t see how this helps you at all.
Time is a REAL dimension of spacetime. Time is not an illusion. The block universe does not mean time is not a real dimension of spacetime.
Time is real and time dilation proves it. The past was once real and affects the present which affects the future.
I think that Silhouette is using these words (“continuous” and “discrete”) in a different way than you do (and perhaps even everyone else.) I for one have absolutely no idea what he means by those words.
Continuous means comprised of infinitesimals. Continuous means you can continuously subdivide without end. Discrete means comprised of a finite number of discrete units. Discreteness means you cannot continuously subdivide without end.
Mathematics is continuous. A number line is continuous.
Physical reality is discrete.