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Mathematicians who are finitists.
April 2, 2019 at 8:49 am
Not too many are left:
Wikipedia  Finitism
Just updated the above Wiki article to change "is" to "was" with respect to Professor Reuben Goodstein.
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RE: Mathematicians who are finitists.
April 2, 2019 at 10:08 am
Those guys have caused endless arguments...
I never thought I'd live long enough to become a grumpy old bastard. Here I am, killing it!
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RE: Mathematicians who are finitists.
April 3, 2019 at 12:10 pm
I had hoped that Polymath would have responded here, but it appears that he is gone?
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RE: Mathematicians who are finitists.
April 4, 2019 at 4:49 pm
(This post was last modified: April 4, 2019 at 4:49 pm by Smaug.)
Interesting. Never heard of it before.
I'd say that rejecting infinite mathematical objects is pointless. In Math everything goes as long as it satisfies certain set of predefined rules. Mathematical objects can be purely abstract.
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RE: Mathematicians who are finitists.
April 4, 2019 at 5:43 pm
These are the people that add letters together, right?
Yeah, well, that's just, like, your opinion, man.  The Dude
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RE: Mathematicians who are finitists.
April 5, 2019 at 3:14 pm
(April 4, 2019 at 4:49 pm)Smaug Wrote: Interesting. Never heard of it before.
I'd say that rejecting infinite mathematical objects is pointless. In Math everything goes as long as it satisfies certain set of predefined rules. Mathematical objects can be purely abstract.
There are a small group of mathematicians and a somewhat larger group of philosophers (such as William Lane Craig) who reject the fact that the set of natural numbers is an actual infinite, that is, a set of objects (albeit, "abstract") that has an infinite cardinality, that is, an infinite number of members.
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RE: Mathematicians who are finitists.
April 5, 2019 at 3:55 pm
"Imagine a number, any number ... now add +1". There, infinity explained. Any unbounded recursive function will go on forever.
"The first principle is that you must not fool yourself — and you are the easiest person to fool."  Richard P. Feynman
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RE: Mathematicians who are finitists.
April 5, 2019 at 4:04 pm
(This post was last modified: April 5, 2019 at 4:05 pm by Smaug.)
(April 5, 2019 at 3:14 pm)Jehanne Wrote: (April 4, 2019 at 4:49 pm)Smaug Wrote: Interesting. Never heard of it before.
I'd say that rejecting infinite mathematical objects is pointless. In Math everything goes as long as it satisfies certain set of predefined rules. Mathematical objects can be purely abstract.
There are a small group of mathematicians and a somewhat larger group of philosophers (such as William Lane Craig) who reject the fact that the set of natural numbers is an actual infinite, that is, a set of objects (albeit, "abstract") that has an infinite cardinality, that is, an infinite number of members.
But how do they deal with the "recursive arguement" (i. e. "N+1"), I wonder? Also, what about Real numbers? Not only the set itself is infinite it's also any interval from it contains infinite number of objects.
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RE: Mathematicians who are finitists.
April 6, 2019 at 9:26 am
(April 5, 2019 at 3:55 pm)Sal Wrote: "Imagine a number, any number ... now add +1". There, infinity explained. Any unbounded recursive function will go on forever.
Craig would say that such is a "potential infinite" and not an actual infinite:
Wikipeida  Actual infinity
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RE: Mathematicians who are finitists.
April 6, 2019 at 4:33 pm
(This post was last modified: April 6, 2019 at 4:37 pm by Smaug.)
However, it's still unclear for me what is the principal difference between potential and actual infinity other than latter being, to put it simple, an 'end cap' of a set.
