Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: some amateurish opinions on CH
Replies: 57   Last Post: Apr 16, 2013 8:12 PM

 Messages: [ Previous | Next ]
 dan.ms.chaos@gmail.com Posts: 409 Registered: 3/1/08
Re: some amateurish opinions on CH
Posted: Apr 9, 2013 3:32 PM

Unlike a natural, or even a real number, sets are built in a
transfinite hierarchical manner as our ability to conceptualize them.
Difficulties begin to appear around unambiguously conceiving
uncountable cardinalites. What I consider important to remember is
that sets are objects of thought,therefore we can say that a sentence
is true when we find sufficient reason for it to be true . That means,
what we know is true is what we can Prove is true, for some unfinished
yet ever-expanding notion of Proof. Now , the crucial point to
remember is how the 'Proof modality' works .

P(a^b) <-> P(a)^P(b)
P(avb) <-> P(a)vP(b)
....................

All laws hold except the excluded middle .It isn't necessary either to
Prove a or to Prove not a .
While the logic of ontology is aristotelian , the logic of
epistemiology (what we can prove) is intuitionistic .
In Peano arithmetic we have a 'rule of thumb' :
If you cannot prove (exists x , G x), for a simple enough sentence
G , then (for all x , not(G x)) may be considered provable .
An extension of this principle for set theory would be wonderful .
Although , while PA seems to obey a 'minimality principle' , set
theory seems more suited to a 'maximality principle' .
Given that epistemology is intuitionistic, I'm open to the
possibility that neither CH nor its negation could provide a 'final
argument' .

Date Subject Author
4/7/13 fom
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 Bergholt Stuttley Johnson
4/7/13 dan.ms.chaos@gmail.com
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 dan.ms.chaos@gmail.com
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 dan.ms.chaos@gmail.com
4/7/13 mueckenh@rz.fh-augsburg.de
4/7/13 Virgil
4/8/13 dan.ms.chaos@gmail.com
4/8/13 mueckenh@rz.fh-augsburg.de
4/8/13 dan.ms.chaos@gmail.com
4/8/13 mueckenh@rz.fh-augsburg.de
4/8/13 dan.ms.chaos@gmail.com
4/8/13 mueckenh@rz.fh-augsburg.de
4/8/13 Virgil
4/8/13 Virgil
4/9/13 apoorv
4/8/13 Virgil
4/7/13 Virgil
4/9/13 Guest
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/10/13 Guest
4/10/13 dan.ms.chaos@gmail.com
4/10/13 fom
4/10/13 JT
4/11/13 apoorv
4/11/13 dan.ms.chaos@gmail.com
4/11/13 apoorv
4/11/13 fom
4/15/13 apoorv
4/15/13 fom
4/16/13 Shmuel (Seymour J.) Metz
4/16/13 fom
4/7/13 Virgil
4/7/13 William Elliot
4/7/13 fom
4/7/13 fom
4/8/13 William Elliot
4/8/13 fom
4/9/13 William Elliot
4/9/13 fom
4/9/13 William Elliot
4/9/13 fom
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/9/13 dan.ms.chaos@gmail.com
4/9/13 fom
4/10/13 fom
4/11/13 dan.ms.chaos@gmail.com
4/11/13 fom
4/11/13 dan.ms.chaos@gmail.com
4/11/13 fom
4/9/13 fom