Potential vs actual infinity

[Peter Percival]

From time to time in these ngs there is mention of potential infinity
vs. actual infinity. I found this paper of Peter Fletcher interesting:
http://eprints.keele.ac.uk/62/1/Infinity%20%28PFletcher%29.pdf.

[Eram semper recta]

Post by Peter Percival
From time to time in these ngs there is mention of potential infinity
http://eprints.keele.ac.uk/62/1/Infinity%20%28PFletcher%29.pdf.

I stopped after the first sentence:

"Infinity occurs in many shapes and forms in mathematics".

The sound of empty drums being beaten is music to the ears of idiots.

No one cares what interests a retard like you.

[Watt Mcgregor]

Post by Eram semper recta

Post by Peter Percival
From time to time in these ngs there is mention of potential infinity
http://eprints.keele.ac.uk/62/1/Infinity%20%28PFletcher%29.pdf.

"Infinity occurs in many shapes and forms in mathematics".
The sound of empty drums being beaten is music to the ears of idiots.
No one cares what interests a retard like you.

mind blowing they can state in the very first line, having no idea what
on earth they are talking about.

[David Petry]

Post by Peter Percival
From time to time in these ngs there is mention of potential infinity
http://eprints.keele.ac.uk/62/1/Infinity%20%28PFletcher%29.pdf.

The question is, do you feel you understand the subject better after reading that article?

I only started the article, but I thought it was rather bland, and would do little to clear up the debates in this newsgroup.

[Ross A. Finlayson]

Post by Peter Percival
From time to time in these ngs there is mention of potential infinity
http://eprints.keele.ac.uk/62/1/Infinity%20%28PFletcher%29.pdf.

It's a neat survey.

It doesn't go much into the "continuum" of numbers
and the infinitude of elements of a continuous domain,
vis-a-vis, the infinitude of elements of a discrete
(if everywhere dense) domain.

"The paradoxes must be resolved...", can be agreed.

It's fair to constructivism but doesn't much
address intuitionism (and its overall constructivism).

"... all bottom-up theories have difficulties
conforming to the intended meaning of proof."

"Top-down theories, which are more appropriate to intuitionism,
rely on our supposed ability to grasp and quantify over an
ill-defined universe of proofs. They appeal to ad hoc assumptions
of stratification and reducibility to make constructive implication
manageable. They make heavy use of mentalistic notions such as
‘understanding of meaning’and‘humanly computable rule’,
which seem to entangle them with intractable problems
in the philosophy of mind."

"[Volpenka and Schokor's] AST provides a useful new view
of the relation between the continuum and discrete structures,
in terms of infinitesimals and indiscernibility relations ...".

Then, closing section 3 there is some mention of Brouwer
and intuitionism, so it seems at least an inclusive survey,
which is relevant for foundations.

Then are detailed a bunch of paradoxes,
all of which to be resolved.

[Ross Finlayson]

Post by Ross A. Finlayson

Post by Peter Percival
From time to time in these ngs there is mention of potential infinity
http://eprints.keele.ac.uk/62/1/Infinity%20%28PFletcher%29.pdf.

It's a neat survey.
It doesn't go much into the "continuum" of numbers
and the infinitude of elements of a continuous domain,
vis-a-vis, the infinitude of elements of a discrete
(if everywhere dense) domain.
"The paradoxes must be resolved...", can be agreed.
It's fair to constructivism but doesn't much
address intuitionism (and its overall constructivism).
"... all bottom-up theories have difficulties
conforming to the intended meaning of proof."
"Top-down theories, which are more appropriate to intuitionism,
rely on our supposed ability to grasp and quantify over an
ill-defined universe of proofs. They appeal to ad hoc assumptions
of stratification and reducibility to make constructive implication
manageable. They make heavy use of mentalistic notions such as
‘understanding of meaning’and‘humanly computable rule’,
which seem to entangle them with intractable problems
in the philosophy of mind."
"[Volpenka and Schokor's] AST provides a useful new view
of the relation between the continuum and discrete structures,
in terms of infinitesimals and indiscernibility relations ...".
Then, closing section 3 there is some mention of Brouwer
and intuitionism, so it seems at least an inclusive survey,
which is relevant for foundations.
Then are detailed a bunch of paradoxes,
all of which to be resolved.

[Ross Finlayson]

Post by Ross A. Finlayson

Post by Peter Percival
From time to time in these ngs there is mention of potential infinity
http://eprints.keele.ac.uk/62/1/Infinity%20%28PFletcher%29.pdf.

It's a neat survey.
It doesn't go much into the "continuum" of numbers
and the infinitude of elements of a continuous domain,
vis-a-vis, the infinitude of elements of a discrete
(if everywhere dense) domain.
"The paradoxes must be resolved...", can be agreed.
It's fair to constructivism but doesn't much
address intuitionism (and its overall constructivism).
"... all bottom-up theories have difficulties
conforming to the intended meaning of proof."
"Top-down theories, which are more appropriate to intuitionism,
rely on our supposed ability to grasp and quantify over an
ill-defined universe of proofs. They appeal to ad hoc assumptions
of stratification and reducibility to make constructive implication
manageable. They make heavy use of mentalistic notions such as
‘understanding of meaning’and‘humanly computable rule’,
which seem to entangle them with intractable problems
in the philosophy of mind."
"[Volpenka and Schokor's] AST provides a useful new view
of the relation between the continuum and discrete structures,
in terms of infinitesimals and indiscernibility relations ...".
Then, closing section 3 there is some mention of Brouwer
and intuitionism, so it seems at least an inclusive survey,
which is relevant for foundations.
Then are detailed a bunch of paradoxes,
all of which to be resolved.