In mathematics, one has to distinguish intensional definitions from extensional interpretations. The former refers to analytic tautologies of an assumed convention, such as Pi being declared as the "exact" ratio of circumference to diameter. Such propositions say nothing of the actual world, because they are norms of linguistic representation.

On the other hand, extensional interpretations of a convention refer to worldly observations to which a mathematics convention is applied, such declaring a visible circle to represent or "approximate" Pi. Here the word "approximate" is misleading, for the visible circle isn't part of the convention but an imprecise application of it. (Any application of a convention is invariably imprecisely applied)

Ok then mister, please give me the exact value of Pi :rofl: — invicta

You persist with this crap, that’s a formula of Pi.

Please paste below the infinite non-repeating sequence of Pi

As I said, it cannot be express with a finite number of digits in decimal notation.

But that does not make it infinite.

It is expressed exactly by

But that does not make it infinite — Banno

Surely you’re winding me up, but I’m not laughing … Pi is serious business

Me? Never.

The supposed issues that trouble you arise from your own lack of clarity.

Pi is clear as day to me, let the below image remind you again. Read @sime’s post

, Pi and infinity are two quite different numbers. Pi is not infinity.

They’re one and the same, or at least our closest understanding and interpretation of infinity. Neatly summed up and expressed by

@Banno anyway we seem to be going in circles. Or perhaps we’re walking in Pies

If you think Pi and infinity are the same number, then you're view is pretty much fucked.

So I'll leave you to it.

Well thank you for that :rofl: pi is not infinite apparently according to Banno, geez!

They’re one and the same, or at least our closest understanding and interpretation of infinity. Neatly summed up and expressed by — invicta

They're not, the sign expressed for infinity is simply ∞

Further, you have different levels of infinity labeled א (aleph)
Expressed as an infinite step, aleph-null, aleph-one, aleph-two, and so on.

Pi is not infinity, it is an irrational number that has its most common use in the measurement of circles, but it's much broader than that, featuring areas like trigonometry, probability, gaussian function, equation for the wave function etc.

First of all that infinite sign that you’ve put there the sideways 8 is a distorted circle, but a circle nonetheless.

Secondly do you deny that Pi goes on forever ? If you deny such a fact and don’t believe that Pi goes on forever then you’re as badly mistaken as Banno I’m afraid.

@Christoffer

Doesn't matter how you twist it, these symbols are established mathematical symbols and terms that have a specific use. ∞ and א are used for infinity in mathematics, while π is not.

This is what Banno is saying. The fact that the decimals goes on in infinity does not make π infinity. A property of a function or thing is not the thing itself. Your hand is not you, it's a part of you. If you say that Pi's decimals goes on in infinity, then you are basically saying π goes on for ∞ in level ℵ₀.

Basically: π ≠ ∞

There's nothing to really dispute in this, you're talking about mathematics, and in mathematics there are no real grey areas, it is what it is.

whatever Pi is not infinite believe what you want. — invicta

It's not belief, mathematics is mathematics, so you either learn it and understand it or you don't.

But before I leave to your own devices just a quick reminder of a couple of things. Pi is an irrational number, the circular circumference divided by diameter means that it will take roughly 3.14 diameters to recreate the circle. — invicta

What does this have to do with confusing infinity with pi?

Also, cutting the circle with metaphorical scissors creates a finite line, with finite length. Those scissors however don’t exist and neither does the circle as it’s just a close approximation or manifestation of such an infinity (and there are other ones too) — invicta

So?

As for the infinity symbol being a twisted circle, just consider this. There are more ways than one of seeing the same thing. — invicta

Does not change the terms and numbers used in mathematics.

keep believing that Pi is not infinite. I’m not here to change opinions but establish truth. — invicta

Pi's decimals are infinite, it is not a term for infinity. I don't know why you persist in talking about beliefs like that, you just sound deeply confused.

Where's your argument? What's your argument and what's the conclusion you're trying to convey? I've read a lot of posts by you since you joined but there's very little philosophical scrutiny and practice in your arguments, you simply tell others to believe what they believe and that you are correct anyway. It mostly seems like you're just bombarding the forum with posts everywhere but have little interest in actual philosophical discussion or accepting established facts. In here you're actually trying to establish your own interpretation of something that has no interpretative angle, the terms and mathematics are as objective as anything comes. Their use is established and there's no post-modern deconstruct of any of it because it's based on pure mathematical logic.

So Pi goes on infinitely buts it’s not infinite, whatever dude.

So Pi goes on infinitely buts it’s not infinite, whatever dude. — invicta

π is not the term for infinity.
∞ and א is the terms used for infinity.

If you profess some knowledge of Mathematics then you’re clearly unaware of this.

https://en.m.wikipedia.org/wiki/Uncountable_set

Still, π ≠ ∞

In mathematics, an uncountable set (or uncountably infinite set) is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal number is larger than that of the set of all natural numbers.

An infinite set is not infinity itself. You are confusing ∞ with π having an infinite set.

I don't know how to describe the simplest of logic here. I'm far from being a mathematician or anywhere good at it, but you don't have to be in order to understand basic logic. As an analogy, this is basically as logical as 2 + 2 = 4, but you are claiming that 4 is 2 because there are two 2s creating a sum of 4. All of this is basic mathematical logic and proper use of the terms. To say that π is ∞, is simply just wrong. That π possesses ℵ₀ of its decimals, is correct, which is just what you linked to as a description. ℵ₀ is an infinite set, the decimals of π is an infinite set... but π itself is not infinity.

If you're gonna use mathematical terms in your argument (whatever that is), then you need to use them correctly in order for the argument to make sense, otherwise you will get into back and forths like this because no one understands your argument when you are confusing everything together and don't seem to understand the basic terms you use.

I don’t really care much what denotes what in mathematics but I do know that pi’s expansion goes on infinitely, hence me declaring it infinite.

I still don’t see how or even why you’d object to that.

Nice example of motte-and-bailey fallacy.

Me or you now I’m unclear which one of us is doing this fallacy, it must be you as my claim is rather simple that Pi goes on forever therefore infinite.

@Banno

What’s your problem ?

I don’t really care much what denotes what in mathematics but I do know that pi’s expansion goes on infinitely, hence me declaring it infinite. — invicta

You declaring something does not make it true. That's a sign of pure delusion and in terms of discussing philosophy, you've reached a dead end since there are no axioms surrounding any argument you discuss, your own opinions, or your interpretation of other's arguments. It's a dead end.

I still don’t see how or even why you’d object to that. — invicta

Object to you declaring new meanings of established mathematical terms, or object to Pi having an infinite set of decimals? The former, yes, the latter no.

I’m unclear — invicta

Correct

The former, yes, the latter no. — Christoffer

I take this as an admission then that pi goes on forever. Finally

Now then many have tried and many have failed in declaring pi as non-infinite…any other takers?

I take this as an admission then that pi goes on forever. Finally — invicta

Pi decimals goes on forever, it is an infinite set. However, that is not what you said:

They’re one and the same — invicta

That you cannot see the difference between "decimals go on forever" and Pi is infinity, is what makes you confused and unable to understand what everyone is saying. You simply seem unable to understand the difference, either due to a language barrier or simply a lack of knowledge, but you simply can't seem to accept that you are wrong in what you conclude here.

Now then many have tried and many have failed in declaring pi as non-infinite…any other takers? — invicta

...but you just keep on going in some delusion that you still know more than the others even to the point where no one can take you seriously when you keep on trying to win an argument that is so globally and logically defined and accepted by everyone except yourself.

Why do you persist with this low-quality level of philosophical engagement? You need to up your quality.

No. A closed loop does not answer Aristotle's quest for an explanation of Causation itself — Gnomon
I don't think Aristotle would have described his work that way. He was surrounded by those who rejected the idea of an intelligible whole. He fought them tooth and nail. — Paine

I'm not an Aristotle scholar, so that comment was just my general impression. But here's a quote*1 that seems to have it both ways : Causal Monism (general causality) and Causal Pluralism (sequential causes). I suspect that Plato might be more inclined to view the First & Final Cause as a Holistic, Ultimate, Ideal entity or concept. In any case, only an Eternal (timeless) Cause would put an end to the infinite regress (space/time) of causation. Perhaps Einstein's Block Time*2 would qualify as Causal Monism, since there is no cyclic time for sequential causes to do their thing. :smile:


*1. Causality is at the heart of Aristotle’s scientific and philosophical enterprise.
. . . Aristotle is committed to a form of causal pluralism . . .
https://plato.stanford.edu/entries/aristotle-causality/

*2. Block Time? : "Everything everywhere all at once"
Those like Aristotle and Leibniz, who think that time is not independent of the events that occur in time, deny the existence of absolute time, ..
https://plato.stanford.edu/entries/time/

During a discussion of his predecessors, Aristotle said Plato included two of the four Aristote worked with and why it was not enough:

And that for the sake of which actions, changes, and movements take place they speak of as in a way a cause, but not in this way—that is, not in the way in which it is its nature to be a cause. For those who speak of understanding or love (philia) posit these causes as good, but they do not speak as if anything is or comes to be for the sake of these things, but as if movements arise from them. In the same way too those who say that the one or being is such a nature say that it is a cause of the substance, but not that anything is or comes to be for its sake, so that in a way they do and in a way they do not say that the good is a cause, since they do not say it is so unconditionally but coincidentally. — Aristotle. Metaphysics, 988b5, translated by CDC Reeve

The addition of the fourth cause (efficient) comes from not being able to treat the eternal beings and what comes to be and passes away the same way. A step toward that method was to get past the monism of Parmenides:

But then if there is to be some being-itself and one-itself, there is much puzzlement as to how anything else will exist beyond these—I mean, as to how beings will be more than one. For what is other than being is not, and so, according to Parmenides’ argument, it necessarily follows that all beings are one, and this one is being. Either way, it is difficult. For whether the one is not substance or whether there is some one-itself, number cannot be substance. We said earlier why this holds if the one is not substance, but if it is substance, the puzzle is the same as that concerning being, For from what, beyond the one-itself, will there be another one? Indeed, it must be not-one. |1001b5| But all beings are either one or a many of which each is one. — ibid. 1001a28

In this respect, the Prime Mover is the beginning of the series of causes but not the 'first' of that series because its principle is not the same species as the "moved." I would not call that a denial of the 'existence of absolute time' but a limit to what we can be thought about it.

So Pi goes on infinitely buts it’s not infinite, whatever dude. — invicta

Sorry, arguing with bear-trap is pointless. Each of you is looking at the question from a different perspective, so your views will never meet, unless at Infinity. :joke:

Pi is infinite :
"Pi is magic. It is a number that is infinite, universal, transcendental, and irrational. It appears everywhere, and my mathematician friends tell me that Pi is as close to religion as you can get in math."
https://press.princeton.edu/ideas/pi-is-magic