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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.
And without delay Peter went quickly out of the synagogue (assembly) and went unto the house of Marcellus, where Simon lodged: and much people followed him...And Peter turned unto the people that followed him and said: Ye shall now see a great and marvellous wonder. And Peter seeing a great dog bound with a strong chain, went to him and loosed him, and when he was loosed the dog received a man's voice and said unto Peter: What dost thou bid me to do, thou servant of the unspeakable and living God? Peter said unto him: Go in and say unto Simon in the midst of his company: Peter saith unto thee, Come forth abroad, for thy sake am I come to Rome, thou wicked one and deceiver of simple souls. And immediately the dog ran and entered in, and rushed into the midst of them that were with Simon, and lifted up his forefeet and in a loud voice said: Thou Simon, Peter the servant of Christ who standeth at the door saith unto thee: Come forth abroad, for thy sake am I come to Rome, thou most wicked one and deceiver of simple souls. And when Simon heard it, and beheld the incredible sight, he lost the words wherewith he was deceiving them that stood by, and all of them were amazed. (The Acts of Peter, 9)
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#2
RE: Mathematicians who are finitists.
Those guys have caused endless arguments...
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#3
RE: Mathematicians who are finitists.
I had hoped that Polymath would have responded here, but it appears that he is gone?
And without delay Peter went quickly out of the synagogue (assembly) and went unto the house of Marcellus, where Simon lodged: and much people followed him...And Peter turned unto the people that followed him and said: Ye shall now see a great and marvellous wonder. And Peter seeing a great dog bound with a strong chain, went to him and loosed him, and when he was loosed the dog received a man's voice and said unto Peter: What dost thou bid me to do, thou servant of the unspeakable and living God? Peter said unto him: Go in and say unto Simon in the midst of his company: Peter saith unto thee, Come forth abroad, for thy sake am I come to Rome, thou wicked one and deceiver of simple souls. And immediately the dog ran and entered in, and rushed into the midst of them that were with Simon, and lifted up his forefeet and in a loud voice said: Thou Simon, Peter the servant of Christ who standeth at the door saith unto thee: Come forth abroad, for thy sake am I come to Rome, thou most wicked one and deceiver of simple souls. And when Simon heard it, and beheld the incredible sight, he lost the words wherewith he was deceiving them that stood by, and all of them were amazed. (The Acts of Peter, 9)
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#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.
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#5
RE: Mathematicians who are finitists.
These are the people that add letters together, right?
One thing you never see: A guy in Boston, Mass. with a Union flag yelling "The Nawth's gonna rise again!"






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#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.
And without delay Peter went quickly out of the synagogue (assembly) and went unto the house of Marcellus, where Simon lodged: and much people followed him...And Peter turned unto the people that followed him and said: Ye shall now see a great and marvellous wonder. And Peter seeing a great dog bound with a strong chain, went to him and loosed him, and when he was loosed the dog received a man's voice and said unto Peter: What dost thou bid me to do, thou servant of the unspeakable and living God? Peter said unto him: Go in and say unto Simon in the midst of his company: Peter saith unto thee, Come forth abroad, for thy sake am I come to Rome, thou wicked one and deceiver of simple souls. And immediately the dog ran and entered in, and rushed into the midst of them that were with Simon, and lifted up his forefeet and in a loud voice said: Thou Simon, Peter the servant of Christ who standeth at the door saith unto thee: Come forth abroad, for thy sake am I come to Rome, thou most wicked one and deceiver of simple souls. And when Simon heard it, and beheld the incredible sight, he lost the words wherewith he was deceiving them that stood by, and all of them were amazed. (The Acts of Peter, 9)
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#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
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#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.
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#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
And without delay Peter went quickly out of the synagogue (assembly) and went unto the house of Marcellus, where Simon lodged: and much people followed him...And Peter turned unto the people that followed him and said: Ye shall now see a great and marvellous wonder. And Peter seeing a great dog bound with a strong chain, went to him and loosed him, and when he was loosed the dog received a man's voice and said unto Peter: What dost thou bid me to do, thou servant of the unspeakable and living God? Peter said unto him: Go in and say unto Simon in the midst of his company: Peter saith unto thee, Come forth abroad, for thy sake am I come to Rome, thou wicked one and deceiver of simple souls. And immediately the dog ran and entered in, and rushed into the midst of them that were with Simon, and lifted up his forefeet and in a loud voice said: Thou Simon, Peter the servant of Christ who standeth at the door saith unto thee: Come forth abroad, for thy sake am I come to Rome, thou most wicked one and deceiver of simple souls. And when Simon heard it, and beheld the incredible sight, he lost the words wherewith he was deceiving them that stood by, and all of them were amazed. (The Acts of Peter, 9)
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#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.
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