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actual infinity vs. potentially infinity - Math philosophy

highmath

Member
Sep 24, 2018
36
what the differences between actual infinity to potentially infinity?
 

Janssens

Well-known member
Sep 16, 2017
204
Have you searched for this? I get a wiki-article, some articles (scholarly and otherwise) and a few videos that claim to provide explanations.
(For example, to my relief, I just learned from this that I apparently side with the majority of mathematicians that "accept actual infinities".)

If you have a more specific question, I am quite sure there are more capable people here to answer it.

Note: I think one of the confusions that often appears in such discussions, is that people oppose the actually infinite on the grounds of limitations imposed by physical reality. This is not correct: Rather, the discussion does not depend on physical, but philosophical and foundational constraints.
 

highmath

Member
Sep 24, 2018
36
Have you searched for this? I get a wiki-article, some articles (scholarly and otherwise) and a few videos that claim to provide explanations.
(For example, to my relief, I just learned from this that I apparently side with the majority of mathematicians that "accept actual infinities".)

If you have a more specific question, I am quite sure there are more capable people here to answer it.

Note: I think one of the confusions that often appears in such discussions, is that people oppose the actually infinite on the grounds of limitations imposed by physical reality. This is not correct: Rather, the discussion does not depend on physical, but philosophical and foundational constraints.
I don't understand the bold and underline texts.
Can you explain it?
 

Janssens

Well-known member
Sep 16, 2017
204
I don't understand the bold and underline texts.
Can you explain it?
Physical quantities such as mass and velocity have a finite magnitude. (In the case of velocity, there is even a particular upper bound.) However, this is not relevant in the context of "actual vs. potential infinity", because in that context we are concerned with sets as abstract mathematical structures, not as representations of the values of physical quantities.
 

DavidCampen

Member
Apr 4, 2014
66
I find a quote from Dedekind somewhat apropos: "If space has at all a real existence it is not necessary for it to be continuous; ... And if we knew for certain that space was discontinuous there would be nothing to prevent us, in case we so desired, from filling up its gaps, in thought, and thus making it continuous;"

Dedekind, "Continuity and Irrational Numbers" in "Essays On the Theory of Numbers"; translation by Wooster Woodruff Beman.