All Questions
Tagged with philosophy infinity
28
questions
2
votes
4
answers
412
views
How to interpret what a set is to see how it could be infinite?
Currently, 'infinite set' sounds oxymoronic to me, so my question is how to interpret what a set is such that it is consonant with it being infinite. I understand that we take it as axiomatic that ...
- 3,019
1
vote
1
answer
433
views
Is an infinite distance traversable? [closed]
According to Wikipedia,
The electric potential energy of a system of point charges is defined
as the work required to assemble this system of charges by bringing
them close together, as in the system ...
- 3,186
0
votes
0
answers
78
views
Are there any statements that are n-undecidable for all n?
I understand that in a sufficiently complicated, consistent formal system, not all statements are true, not all statements are decidable, not all statements' decidability is decidable, 3-decidable, ......
- 1,486
6
votes
2
answers
258
views
Positive logical definition of finiteness
In his debate with Cassirer and in some other writing, Heidegger tries to define positively the concept of finiteness for the beings. It is a novel and difficult approach as traditionally, in theology ...
- 203
2
votes
1
answer
163
views
Is there a finitist semantics for transfinite mathematics? [closed]
I'm sympathetic to the Aristotelian view that potential infinity makes sense while actual (completed) infinity doesn't. However, I also find transfinite set theory to be fascinating, and I'm under the ...
- 415
3
votes
1
answer
582
views
A programmer’s doubts about countable vs uncountable infinity
(A short disclaimer: I'm not a mathematician, and I'm not trying to say anything is "wrong" about these famous proofs. I'm trying to get my bearings and maybe find where I can read more ...
- 389
23
votes
4
answers
5k
views
Why did mathematician construct extended real number systems, $\mathbb R \cup\{+\infty,-\infty\}$?
I know some properties cannot be defined with the real number system such as supremum of an unbounded set. but I want to know the philosophy behind this construction (extended real number system ($\...
- 657
0
votes
1
answer
216
views
Does Planck length contradict math? [closed]
I have a general question about math and infinity which really bothers me as a math student - can we actually divide every length by two?
I would like to believe the answer is yes, because it ...
- 493
8
votes
3
answers
778
views
What does Betrand Russell mean when he says the mathematicians refuted the philosophers on the existence of infinity?
In the second-to-last chapter of his book "The Problems of Philosophy", Bertrand Russell writes that philosophers used to think that there can't be such a thing as infinity, but they were disproved by ...
- 211
8
votes
4
answers
318
views
Balls and vase $-$ A paradox?
Question
I have infinity number of balls and a large enough vase. I define an action to be "put ten balls into the vase, and take one out". Now, I start from 11:59 and do one action, and after 30 ...
- 2,565
1
vote
5
answers
2k
views
How does one understand and resolve Zeno's paradox?
Zeno, a follower of Parmenides, reasoned that any unit of space or time is infinitely divisible or not. If they be infinitely divisible, then how does an infinite plurality of parts combine into a ...
- 870
33
votes
6
answers
8k
views
Why isn't finitism nonsense?
This is a by product of this recent question, where the concept of ultrafinitism came up. I was under the impression that finitism was just "some ancient philosophical movement" in mathematics, only ...
user378947
1
vote
2
answers
98
views
Infinity is Many-One
Bertrand Russell in Introduction to mathematical philosophy states, "It will be observed that zero and infinity, alone among ratios, are not one-one. Zero is one-many, and infinity is many-one." (P.40)...
- 353
3
votes
3
answers
1k
views
Division of segments into infinitely many parts.
Let AB and CD be two segments, so that the length of AB is 1, and the length of CD is 2.
If we divide AB and CD in infinitely many parts, how "long" would those parts be? I'm particularly interested ...
- 31
0
votes
1
answer
115
views
A box comprised of infinite number of small similar boxes.
On Wikipedia, I read, "A box can be thought of 'small boxes' infinitely repeating in all three dimensional directions"
I don't understand what does Wikipedia wants to say with a box containing ...
- 649