On 11 Jun 2013, at 19:04, Jason Resch wrote:

From the video: "What we do is we use the story of math, which is very good and very complete"

I think that summarizes the error of fictionalism. To believe math is a human created invention requires believing that everything we can ever know about math comes from the starting assumptions we choose. We now know this to be untrue, our picture (or anyone's picture) of math will always be incomplete, there is always more math out there to discover. We make progress in math the same way we do in all the other sciences, making observations, drawing conclusions, seeing if our theories are consistent, etc. Over time we develop our accepted axioms the same way we develop our fundamental physical theories.

We observe and explore other mathematical structures/universes through the tool of simulation (either using our brains or using computers), and that is how information about other universes enters our own.

I agree completely. I do take incompleteness, or the consequences of Church thesis as illustrating very well the "objectivity" of arithmetic.

Above arithmetic, I have no problem to classify some construct as being epistemological, but the exact frontier between ontology and epistemology is unimportant, as the inside views will have an objective arithmetical behavior, even when not arithmetical. And this is well justified by the fact that although we can do easily intuitive number theory without ever formalizing the theory (like number theorist), this is no more the case for set theory, whose intuitive part is just inconsistent, and when it is formalized, the communicable part belongs to arithmetic.

So I agree with your for arithmetic, and above arithmetic it is a question of convention.

Arithmetic is large, and I do not know of any theorem in math which is not a theorem in arithmetic, except in mathematical logic, and universal algebra, which are typically "meta-"mathematics.

Bruno




Jason


On Thu, Jun 6, 2013 at 5:31 PM, Stephen Paul King <stephe...@charter.net > wrote: For your entertainment: https://www.youtube.com/watch?feature=player_embedded&v=TbNymweHW4E #!

--
You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list?hl=en .
For more options, visit https://groups.google.com/groups/opt_out.




--
You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list?hl=en .
For more options, visit https://groups.google.com/groups/opt_out.



http://iridia.ulb.ac.be/~marchal/



--
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list?hl=en.
For more options, visit https://groups.google.com/groups/opt_out.


Reply via email to