Our server costs ~$56 per month to run. Please consider donating or becoming a Patron to help keep the site running. Help us gain new members by following us on Twitter and liking our page on Facebook!
Current time: September 18, 2019, 5:48 pm

Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Mathematicians who are finitists.
#1
Mathematicians who are finitists.
Not too many are left:

Wikipedia -- Finitism

Just updated the above Wiki article to change "is" to "was" with respect to Professor Reuben Goodstein.
Reply
#2
RE: Mathematicians who are finitists.
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!
Reply
#3
RE: Mathematicians who are finitists.
I had hoped that Polymath would have responded here, but it appears that he is gone?
Reply
#4
RE: Mathematicians who are finitists.
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 pre-defined rules. Mathematical objects can be purely abstract.
Reply
#5
RE: Mathematicians who are finitists.
These are the people that add letters together, right?
Brevity, soul, wit!









Reply
#6
RE: Mathematicians who are finitists.
(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 pre-defined 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.
Reply
#7
RE: Mathematicians who are finitists.
"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
Reply
#8
RE: Mathematicians who are finitists.
(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 pre-defined 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.
Reply
#9
RE: Mathematicians who are finitists.
(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
Reply
#10
RE: Mathematicians who are finitists.
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.
Reply





Users browsing this thread: 1 Guest(s)