Philosophizing With J. D. Hawkins

 IF you can find the time for it, a 2+ hour new interview (podcast) with mathematician/philosopher Joel David Hamkins:

https://www.youtube.com/watch?v=acjJ5-OSuZM

Continuum Hypothesis via Scott Aaronson

 

Bored with the headlines, folks?... Is election news getting you down?... Or the blitz of political ads scraping on your last nerve?... Is that what's buggin' you, kiddies??? 

Well, OK, this won’t be everyone’s cup-a-tea, or fun distraction, but in a longish post (first of multiple) Scott Aaronson tackles the independence of the Continuum Hypothesis:

https://www.scottaaronson.com/blog/?p=4974

I knew it would be a great read when he started off with this quote from Bertrand Russell:

 ;)

“in adolescence, I hated life and was continually on the verge of suicide, from which, however, I was restrained by the desire to know more mathematics.”

Harvey Friedman and More

Very interesting piece in Nautilus this morning on Harvey Friedman and foundational aspects of mathematics:

http://nautil.us/issue/45/power/this-man-is-about-to-blow-up-mathematics

Dr. Friedman has a YouTube website here:
https://www.youtube.com/channel/UCdRdeExwKiWndBl4YOxBTEQ

Set Theory, Type Theory, HoTT, Univalent Foundations...

Quanta Magazine consistently offers some of the best STEM writing around for lay readers.  Remarkably, over half of their contributing writers are individuals I'd never even heard of prior to reading them in Quanta. This recent piece from Kevin Hartnett is perhaps the best quick introduction to "type theory" I've ever seen for a general audience:
https://www.quantamagazine.org/20150519-will-computers-redefine-the-roots-of-math/

(The above covered, briefly, several of the foundational topics I was hoping Eugenia Cheng's "How To Bake Pi" book might cover, but didn't -- I reviewed it yesterday HERE).

Should anyone care to see a bit more advanced discussion of some of these topics, check out the comments/discussion on a recent Michael Harris posting pertaining to such:
https://mathematicswithoutapologies.wordpress.com/2015/05/13/univalent-foundations-no-comment/#comments

Anyway, the Quanta piece made me want to know more about Kevin Hartnett, so I checked up a bit. His only prior piece for Quanta is here (also mathematically-inclined):
https://www.quantamagazine.org/20150113-a-proof-that-some-spaces-cant-be-cut/

But he's been writing a diverse column for the Boston Globe (entitled "Brainiac") for awhile:
http://www.bostonglobe.com/ideas/brainiac

He also writes a far more personal blog about fatherhood here:
http://growingsideways.net/

Raymond Smullyan's Church Perhaps...

Colm Mulcahy recently tweeted this photo, appropriate for a Sunday morning post:
 

Where's Bertie Russell when we need him?  Set theory conundrum here #foundmath #foundlogic #foundillogic pic.twitter.com/DmrA16kPOS
— Card Colm Mulcahy (@CardColm) October 19, 2013

A Choice Posting

If set theory is definitely NOT your cup-o-tea then stop here and just move along to LOLCats or elsewhere.
But otherwise, read on....

According to RJ Lipton, Gregory Moore's "Zermelo's Axiom of Choice" (from Dover) is quite a page-turner and beach-read -- 450 scintillating pages-worth! -- in fact, Lipton calls it "hard to put down" ;-) His latest post at "Gödel's Last Letter" is a glance at the Axiom of Choice based on Moore's volume, and worth a gander... if, you so choose:

http://rjlipton.wordpress.com/2013/07/30/making-choices/

(image via Norvy/WikimediaCommons)

Axiom of Choice... and Pigeonholes

The "Axiom of Choice" is one of those simple-seeming notions that is difficult to fully-grasp... or at least grasp its profound implications (I don't claim to). It probably requires a fairly deep grounding in set theory in order to fully wrap your brain around its significance.
Anyway, here is an older post I recently ran across that just sort of struck my fancy on the topic, so maybe it will yours as well (even though the author, Adam Bohn, admits at one point that the axiom of choice falls into the category of “things it is best to not think about”!):

http://yabm.wordpress.com/2010/04/22/the-axiom-of-choice/#more-456

Meanwhile, the best overall treatment of the Axiom of Choice (for layfolks) that I've seen on the Web is here (with plenty of further links):

http://www.math.vanderbilt.edu/~schectex/ccc/choice.html

Intro To Set Theory

An introduction to set theory from plus.maths.org here:

http://plus.maths.org/content/searching-missing-truth&src=fpii