Starts with the greeks

By definition wrong

...=0.001

>in x amount of time Achilles runs 100 meter and the tortoise 10
>after x*2 amount of time after Achilles's start he has traveled 200 meter and the tortoise 120
I don’t get it

you don't get it, the whole point is to show that paradoxes are a flaw in logic rather than a flaw in reality. the simple fact that the guy would clearly pass up the tortoise is evidence enough that the paradox is limited to such an extent that it shouldn't even be taken seriously besides the example it sets.

>x=1
>By definition wrong
wat

Numbers are artificial constructs with rules.
Two different numbers cannot be the equal to eachother.
By definition.

this can't be a serious comment

why?

1.999... and 2 aren't two different numbers. They are the same number.

>1.999... and 2 aren't two different numbers. They are the same number.

>postmodernism

1.999... is infinitely lesser

.0 and 1 aren't two different numbers. They are the same number.
/2 and 0.5 aren't two different numbers. They are the same number.
and -0 aren't two different numbers. They are the same number.

>hur dur hes just talking about paradoxes, nothing to take seriously

There are a million ways to make paradoxes, why do you think every one of Zeno decided to study was based on the concept of division?

are you even trying?
try again without using the placeholder value 0

They are practically "the same" but they simply aren’t

anyone read this? is it good?

...

Sorry friendos but it's true. The last panel of contains a proof that 0.999... = 1
Therefore 1.999... = 1 + 0.999... = 1 + 1 = 2

>THE ARGUMENTS OF ZENO OF ELEA
>THE PRECEDING CONSIDERATIONS implicitly contain the solution to all problems of the sort raised by Zeno of Elea in his famous arguments against the possibility of motion, or at least in what appear to be such when one takes the arguments only as they are usually presented; in fact, one might well doubt whether this was really their true significance. Indeed, it is rather unlikely that Zeno really intended to deny motion; what is more probable is that he merely wished to prove the incompatibility of the latter with the supposition, accepted notably by the atomists, of a real, irreducible multiplicity existing in the nature of things. It was therefore origi- nally against this very multiplicity so conceived that these argu- ments origiz~ally must have been directed; we do not say against all multiplicity, tc:lf it goes without saying that multiplicity also exists within its order>~s does motion, which, moreover, like every kind of change, necessarily supposes multiplicity. But just as motion, by reason of its character of transitory and momentary modification, is not self-sufficient and would be purely illusory were it not linked to a higher principle transcendent with respect to it, such as the 'unmoved mover' of Aristotle, so multiplicity would truly be non- existent were it to be reduced to itself alone, and did it not proceed from unity, as is reflected mathematically in the formation of the sequence of numbers, as we have seen. What is more, the supposi- tion of an irreducible multiplicity inevitably excludes all real con- nections between the elements of things, and consequently all continuity as well, for the latter is only a particular case or special

but that's an even rating

i just meant that it was a tool to show a flaw in a certain type of logic. not so much as something to not concern yourself with. i don't think i disagree with you, i don't comprehend the mathematical concepts Zeno was trying to display here, but I do know the guy must have known that in reality the tortoise would be caught up with eventually.

>mathematical proof
Nice meme, kiddo

>form of such connections. As we have already said above, atomism necessarily implies the discontinuity of all things; ultimately, motion really is incompatible with this discontinuity, and we shall see that this is indeed what the arguments of Zeno show.
>Take, for example·, the following argument: an object in motion can never pass from one position to another, since between the two there is always an infinity of other positions, however close, that must be successively traversed in the course of the motion, and, however much time is employed to traverse them, this infinity can never be exhausted. Assuredly, this is not a question of an infinity, as is usually said, for such would have no real meaning; but it is no less the case that in every interval one may take into account an indefinite number of positions for the moving object, and these cannot be exhausted in analytic fashion, which would involve each position being occupied one by one, as the terms of a discontinuous sequence are taken one by one. But it is this very conception of motion that is in error, for it amounts in short to regarding the con- tinuous as if it were composed of points, or of final, indivisible ele- ments, like the notion according to which bodies are composed of atoms; and this would amount to saying that in reality there is no continuity, for whether it is a question of points or atoms, these final elements can only be discontinuous; furthermore, it is true that without continuity there would be no possible motion, and this is all that the argument actually proves. The same goes for the argu- ment of the arrow that flies and is nonetheless immobile, since at each instant one sees only a single position, which amounts to sup- posing that each position can in itself be regarded as fixed and determined, and that the successive positions thus form a sort of discontinuous series. It is further necessary to observe that it is not in fact true that a moving object is ever viewed as if it occupied a fixed position, and that quite to the contrary, when the motion is fast enough, one will no longer see the moving object distinctly, but only the path of its continuous displacement; thus for example, if a flaming ember is whirled about rapidly, one will no longer see the form of the ember, but only a circle of fire; moreover, whether one explains this by the persistence of retinal impressions, as physiolo- gists do, or in any other way, it matters little, for it is no less obvious

same applicability

Hold on guys...

WTF even are decimals? Like what does "1.5" even mean? How could something be not 1 or 2 but something "in the middle"? What the hell does that mean?

>that in such cases one grasps the continuity of motion directly, as it were, and in a perceptible manner. What is more, when one uses the expression 'at each instant' in formulating such arguments, one is implying that time is formed from a sequence of indivisible instants, to each of which there corresponds a determined position of the object; but in reality, temporal continuity is no more com- posed of instants than spatial continuity is of points, and as we have already pointed out, the possibility of motion presupposes the union, or rather the combination, of both temporal and spatial continuity.

are you home-schooled or american?

But then what kind of proof do you want?

so basically it's I

>mathematical objects
>expect a non-mathematical proof
really makes you think

>he thinks he can use nonsensical concepts like infinity in a proof
the only thing you proved was that you are a complete pseud

Your comment sounded dismissive, I must defend Zeno from the brainlets on this board that talk shit because they took a semester of pre-calc in highschool and think they know jack shit.

>tfw when you is a fish and you is swimming through the water but you doesn't even know the water there that you swimming through

sorry, i don't watch movies

>math is just faulty logic
Who in the everloving world would have thought?

Math isn't real, you're using self-defined system to justify itself

I understand, I probably didn't express myself as well as I liked. I was obsessed with paradoxes for a while as a kid. It felt like wordplay paradoxes were little perpetual motion machines of logic that wouldn't stop until you squared the circle by force of a gun. Do you think you could summarize what Zeno was trying to express by devoting his paradoxes to division?

>you're using self-defined system to justify itself
yeah, that's basically what math is, your point?

it's actually pretty much contingent on all of that.

youtube.com/watch?v=fjqjWC3Ycr4
this is all you need to see, really.

>Like what does "1.5" even mean?
1 + 5/10.

>How could something be not 1 or 2 but something "in the middle"?
The real question here is how we can have something like 1/10 or 1/2. And the answer is, we just decide that every integer has a multiplicative inverse, that is a number you can multiply it by to get 1. The inverse of 1 is 1, the inverse of -1 is -1, and the rest we pretty much just pull out of our ass by writing 1/x for whatever x. It's pretty sneaky. And from there it's trivial to prove that 1 < 1.5 < 2.

>thinking the concept of a limit as n approaches infinity actually involves the concept of inifinity
It appears it is you who is the pseud.

I think he means in the real world.
There's never 1.5 something.

It’s circular reasoning and should not be taken seriously

never seen half an apple?

There's never even 2 something.

You mean 2 uneven parts of a fruit?

and why should we care about seriousness?

this thread would've been deleted a year ago

It's not circular reasoning, it's reasoning from axioms.

if you insist in talking like a retard, i guess

The mistake is that the interval of time between the steps of that diagramm (and thus his argument) are decreasing. Essentially, you are 'zooming in' to the moment where he will overtake the tortoise. Also this

>and why should we care about seriousness?
So I can this
Not an argument

there's no longer an apple

*scribbles some greek letters and other symbols on a blackboard*
*solves millenia-old problems*
*doesn't even have a degree*
Hehe.... kid...

>2 parts
>1 fruit

So what you're saying is the apple as a concept is indivisible, and the parts are not the apple, but something else.

Thus, we can't say 0.5 of an apple, since there is no such thing.

>but in theory infinite pieces of nothing is "nothing"
google what infinitesimals are. they are the very basis of integral calculation and thus many concrete subjects like electric fields.

By Zeus, Socrates, you're right!

this

Correct, these 2 parts are entirely unique

what's a part?

The series 1+1∕2+1/4+1/8+...1/2^n is convergent and S = 2. Solved.

The determiner of "sameness" in that sentence

lol faggot

What is their most prominent feature? Being like an apple, but (you can substite into here a calculation of the number of seeds, the amount of pulp and skin, the mass etc.)
Thus it seems reasonable to posit they're like an apple, but not like a full apple. If only we could represent that mathematically or with language...

I definitely find Zeno's paradoxes have much more content than the common logic/word paradox ("This a lie".... etc ). I study physical chemistry and dividing matter and energy into pieces is something we only developed in the past 100 years.

We genuinely cannot fathom how divisible matter is, animals are made of molecules, made of elements/atoms, made of proton/neutrons/electrons, made of quarks and shit, made of xx, made of xx .... made of waves? spooky nigga

Now with zeno's paradox contain the concept of time, can we possible quantize time? What even is time? There would be no time if there was no energy, if there was no motion we couldn't perceive of time. The more times we divide time the slower it gets, if we had infinite brain loading speed, time wouldn't progress.
The Godmind

ur like a little baby to me, go play with you reimann sums

you literally have autism, I can tell
typical purist mathfag

QUANTIZE

idk about a year ago, this guy recommended a book I will look into so its not a complete waste. Sorry Zeno doesn't have much primary literature.

We could but the result would be too vague, so we should just stick to living in caves and hitting rocks with sticks

the ancient world didn't have a concept of infinity. They also had no concept of 0.

lol

If a bystander came upon half an apple, what would lead him to consider that it was, in fact, a half, and not already whole in itself? But one who had seen a full apple would consider him foolish, and perhaps rightly so, but do we know that an apple is in itself full, and not in fact, merely one half of something else? For, despite this consideration, we are inclined to believe that there is some meaning in the notion of "an apple", a unity, a wholeness of completeness, which is not a negative or a positive of something but in fact completed, perhaps even annihilated, and it is this annihilation of opposites which actually constitues the full apple, which is at rest and thereby able to "be" a thing in itself. But can we know that the apple does not in fact constitute one half of something else? If two halves of an apple arise out of one apple, and the first man mistook this for a whole, whence arose the apple if not by division of something else? If we are unable to provide an explanation, then the person in our example who criticized the other for thinking that a half of something was in fact a whole something is guilty of the same criticism, in thinking that the apple is whole in itself.

>you literally have autism, I can tell
>typical purist mathfag
rude

>the ancient world didn't have a concept of infinity

>an apple is a 30th of a tree

yeah i don't think we disagree at all. i've been pretty similarly inclined for quite some time. it's stonerthought regarding time for sure. seriously though, this is i

The man who has seen an apple tree would call the man who has only seen an apple foolish

>But this new world is perfectly realised just as little as the new-born child; and it is essential to bear this in mind. It comes on the stage to begin with in its immediacy, in its bare generality. A building is not finished when its foundation is laid; and just as little, is the attainment of a general notion of a whole the whole itself. When we want to see an oak with all its vigour of trunk, its spreading branches, and mass of foliage, we are not satisfied to be shown an acorn instead. In the same way science, the crowning glory of a spiritual world, is not found complete in its initial stages. The beginning of the new spirit is the outcome of a widespread revolution in manifold forms of spiritual culture; it is the reward which comes after a chequered and devious course of development, and after much struggle and effort. It is a whole which, after running its course and laying bare all its content, returns again to itself; it is the resultant abstract notion of the whole. But the actual realisation of this abstract whole is only found when those previous shapes and forms, which are now reduced to ideal moments of the whole, are developed anew again, but developed and shaped within this new medium, and with the meaning they have thereby acquired.

What's but a leaf?
Where's the atmospheres' end?
Who can say where one thing ends and another begin?

This is where I am not sure, for it seems very clear, intuitive that a half of an apple is in fact a half of an apple, and not something in itself, whereas the "rest of the tree" does not seem a half of the tree, but as says, if we are even to consider the apple as a fraction of the tree, we must consider it not half but much less, but this is only in regards to size, or mass, or density, and each of these would likely constitute a different fraction of the whole tree.

Now then, are we to say that a thing, such as an apple, can be one fraction of one thing and one fraction of another thing? As in, it is 1/30th of a tree, but also 1/60th of two trees? It seems to me that here we are not speaking of the apple anymore but merely the size of one object in relation to the size of another object, whereas in the example of the "half of an apple", we are not merely considering it in terms of the "size of this piece of matter" in relation to the "size of this twice as large piece of matter", but as something else, as a half of one essence, and the essence, considered in the metaphysical sense being the important part.

Well everything we percieve is nonsensical if you have no concrete perspective to view it from.

That is why humans are so indebted to the only axiom.

Everyone then who hears these words of mine and does them will be like a wise man who built his house on the rock. And the rain fell, and the floods came, and the winds blew and beat on that house, but it did not fall, because it had been founded on the rock.

>brainlet posters are THIS mathematically illiterate

i do believe that philosophically we are of the same spirit. though i do find that the rocks are in too short supply for my reckoning.

When we consider the notion of a half of an apple, we are not merely discussing size, since a third of an apple would have something in common with a half of an apple, in that both are considered as parts of an apple, and not merely as objects. There is something "apple-ish" about them, but where does the apple-ishness end? This is where it seems to delve into absurdity, since it seems that at a certain point, a sliver of an apple would become so small as to constitute seemingly nothing at all. It seems pertinent to consider the different parts of the apple considered as things in themselves, such as the flesh, the seed, the skin, the top and the bottom, and so forth. For, the top half of an apple would not match the bottom half, nor, even, would two halves of a vertical slice match each other, since I have never seen a perfectly symmetrical apple, and cannot prove that such a one exist, although neither can I determine that one does not exist either.

So when we are talking of one half of an apple, we cannot be said to, as far as we know empirically, be considering anything which has any basis in reality, since there is no "half of an apple" that is in fact perfectly one half, since every apple has its own unique asymmetry which does not lend itself to such precise divisions. Is it even possible to actually "slice and apple in half"? Or when we say this do we merely mean it approximately?

The half of an apple comes from an apple, just like the apple comes from an apple tree, just like the apple tree comes from the proto-apple tree, just like the proto-apple tree comes from the proto-proto-apple tree, etc
We're applying ideas like wholeness and sameness to things we cannot fully grasp

But it seems that half of an apple is, in fact, a half of an apple, whereas an apple is not half of an apple tree.

You're doing it again, you’re applying concepts of sameness and wholeness to things you cannot fully understand

t. JP

>not coupling multiple conflicting axioms to contradict inferior logic systems
perspective is more contingent on the status of the wise man himself, not the rock. if one relies more on that vision rather than the structure of his flesh and the interpretation of the data, then they will lead themselves over a number of cliffs.

Then are all things merely appearances? Is it merely an appearance for me to eat a fruit which is poisonous instead of a fruit that is not poisonous? Is my resulting death merely an appearance, and there was in fact, no apple to begin with, no fruit, no me, no poison, no digestion, no life, and no death?

Thanks I have been looking for that picture.

Peterson is brainlet, his statement is out of necessity, he had his ideas and looked for a way to justify them. The man doesn't believe and is constantly chased by his demons because of it.
The idea that humans can know all is utter hubris. The jump from human knowledge to divine knowledge can only be achieved through faith in the unknowable.

There is and can only be one truth.

Man I love the retarded wojak meme

>I love the retarded wojak meme

by that standard we can't either talk about an apple, as the apple is slowly rotting and accreting or losing mass all the time

You're right. As for where to go from here I've given up as it is clear man cannot attain to the divine by his own strength but only by faith in God alone.

BTW you can't use limits because limits are an incoherent concept

Nope, just saying everything is unique and nothing's the same.