As usual, we have here a vocabulary conflict between people with opposing points of view. Such disagreements are not resolved by disparagement. The word "infinity" has several definitions, depending on context*1.Gnomon
A circle is a very close approximation of Pi which is infinity itself. — invicta
This is gobbledygook. But I would not be surprised were you unable to see that. — Banno
And the clear answer is no, it doesn't. There is a difference between an infinite progression and a loop....if infinite causes are the chain of sequences ad infinitum does such a chain not imply a closed loop... — invicta
Of course, we do know pi. A formula for it was given above, and the definition is the subject of primary school mathematics. The discussion continued with Invicta playing on the two meanings of "irrational", only to arrive atIf you only knew Pi, which you obviously can’t as it’s irrational and infinite …could you draw a circle? — invicta
...which as i said, is gobbledegook. A circle is no more an approximation to pi than a fish is an approximation to a democracy; And Pi is not infinity itself.A circle is a very close approximation of Pi which is infinity itself. — invicta
Philosophy is about getting the words right — Banno
That is not the sum total of the subject although it's an important part. — Wayfarer
Sorry, I forgot to provide a link. That quote came from a math website. I didn't make it up. :smile:In Mathematics, “infinity” is the concept describing something which is larger than the natural number. — Gnomon
Huh? — jgill
No. As I pointed out above, the meaning of "infinite" varies depending on context and intent. So, I'm merely allowing to use the word in a way that suits his context. I don't necessarily agree with his conclusions, but I want to hear his argument -- in his own words -- not necessarily in my personal vocabulary. :smile:A circle is a very close approximation of Pi which is infinity itself. — invicta
You would deny Invicta the privilege of meaning what he says? — Banno
Note: The above theorem is an artifact of the construction of the reals as equivalence classes. The theorem only says that the CARDINALITY of pi is infinite; it does NOT say that pi has infinite MAGNITUDE. Cardinality and magnitude are DIFFERENT. pi does not have infinite magnitude. — TonesInDeepFreeze
Math definitions will not resolve the terminology disputes in this thread because is not making a mathematical proposition. "Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics : the abstract science of number, quantity, and space. That may be why such open-ended (infinite???) concepts are annoying to some posters, since it can't be ruled True or False by numerical authority. Satisfactory (not true or false) answers will depend as much on intuition as on logic.Disagreements about terminology are unnecessary. Discussants can instead acknowledge the clear definitions in mathematics: — TonesInDeepFreeze
Pi is not a circle
— Banno
Of course it’s a circle — invicta
As previously noted, I interpret his use of "infinity" as a philosophical postulation, not a mathematical proposition. Apparently, your more restrictive*1 vocabulary (your account) does not allow that distinction. :smile:↪Gnomon
"Pi is infinity" is not a mathematical proposition?
Or will you claim anything in order to defend your account? — Banno
, I interpret his use of "infinity" as a philosophical postulation, not a mathematical proposition. — Gnomon
Math definitions will not resolve the terminology disputes in this thread because ↪invicta is not making a mathematical proposition. "Infinite Regress" and "First Cause" are philosophical concepts that are not addressed by Mathematics — Gnomon
In Mathematics, “infinity” is the concept describing something which is larger than the natural number. — Gnomon
Huh? — jgill
Sorry, I forgot to provide a link. That quote came from a math website. I didn't make it up. — Gnomon
Tarski came up with another concise definition that can be shown identical to Dedekind's. — jorndoe
All I had to say is in the title. :smile:If you would like to make some point about what is written in a paper, then you can say what that point is, rather than just have me scurry and sidetrack to read something that you haven't said what about it you think is important to consider relative to what I've said. — TonesInDeepFreeze
Irrelevant ! I didn't intend to defend 's conclusions, but just to defend his right to use a colloquial meaning of "infinite" in a philosophical proposition, without being challenged to present a mathematical or scientific justification. The OP presents metaphors of snake-circles, not mathematical proofs. Is "self-caused" a mathematical concept?Wrong. I and others have studied infinite regress in detail, as infinite compositions or iterations. — jgill
I'm not a mathematician, so I don't discriminate between Natural and Super-natural numbers. Is Infinity literally supernatural? :smile:What is "the natural number" ? — jgill
ght to to use a colloquial meaning of "infinite" in a philosophical proposition, without being challenged to present a mathematical justification. — Gnomon
incensed — Gnomon
That is not my intention for using links. Instead, I try to say what I have to say in the post, and then add the links "for further reading"--- if someone is interested in more detail. In contentious threads like this though, where my limited knowledge will be challenged & dismissed, another function of links is to let the experts speak on the same topic, with the kind of authority I lack. :smile:Usually when someone posts a link, it is taken as a suggestion to visit that link. So, without you saying what specifically you wanted me to take from the article, I would have detoured to read and study an article of which all you mean to say is what you posted anyway. — TonesInDeepFreeze
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