Andrew Cooke | Contents | Latest | RSS | Twitter | Previous | Next

C[omp]ute

Welcome to my blog, which was once a mailing list of the same name and is still generated by mail. Please reply via the "comment" links.

Always interested in offers/projects/new ideas. Eclectic experience in fields like: numerical computing; Python web; Java enterprise; functional languages; GPGPU; SQL databases; etc. Based in Santiago, Chile; telecommute worldwide. CV; email.

Personal Projects

Lepl parser for Python.

Colorless Green.

Photography around Santiago.

SVG experiment.

Professional Portfolio

Calibration of seismometers.

Data access via web services.

Cache rewrite.

Extending OpenSSH.

C-ORM: docs, API.

Last 100 entries

Get Coffee Quotes for Cat Soft LLC; [Link, Politics, USA] The Future Of American Democracy; Mass Hysteria; [Review, Books, Links] Kazuo Ishiguro - Never Let Me Go; [Link, Books] David Mitchell's Favourite Japanese Fiction; [Link, Bike] Rear Suspension Geometry; [Link, Cycling, Art] Strava Artwork; [Link, Computing] Useful gcc flags; [Link] Voynich Manuscript Decoded; [Bike] Notes on Servicing Suspension Forks; [Links, Computing] Snap, Flatpack, Appimage; [Link, Computing] Oracle is leaving Java (to die); [Link, Politics] Cubans + Ultrasonics; [Book, Link] Laurent Binet; VirtualBox; [Book, Link] No One's Ways; [Link] The Biggest Problem For Cyclists Is Bad Driving; [Computing] Doxygen, Sphinx, Breathe; [Admin] Brokw Recent Permalinks; [Bike, Chile] Buying Bearings in Santiago; [Computing, Opensuse] Upgrading to 42.3; [Link, Physics] First Support for a Physics Theory of Life; [Link, Bike] Peruvian Frame Maker; [Link] Awesome Game Theory Tit-For-Tat Thing; [Food, Review] La Fabbrica - Good Italian Food In Santiago; [Link, Programming] MySQL UTF8 Broken; [Link, Books] Latin American Authors; [Link, Computing] Optimizatin Puzzle; [Link, Books, Politics] Orwell Prize; [Link] What the Hell Is Happening With Qatar?; [Link] Deep Learning + Virtual Tensor Machines; [Link] Scaled Composites: Largest Wingspan Ever; [Link] SCP Foundation; [Bike] Lessons From 2 Leading 2 Trailing; [Link] Veg Restaurants in Santiago; [Link] List of Contemporary Latin American Authors; [Bike] FTHR; [Link] Whoa - NSA Reduces Collection (of US Residents); [Link] Red Bull's Breitbart; [Link] Linux Threads; [Link] Punycode; [Link] Bull / Girl Statues on Wall Street; [Link] Beautiful Chair Video; Update: Lower Pressures; [Link] Neat Python Exceptions; [Link] Fix for Windows 10 to Avoid Ads; [Link] Attacks on ZRTP; [Link] UK Jazz Invasion; [Review] Cuba; [Link] Aricle on Gender Reversal of US Presidential Debate; {OpenSuse] Fix for Network Offline in Updater Applet; [Link] Parkinson's Related to Gut Flora; Farellones Bike Park; [Meta] Tags; Update: Second Ride; Schwalbe Thunder Burt 2.1 v Continental X-King 2.4; Mountain Biking in Santiago; Books on Ethics; Security Fail from Command Driven Interface; Everything Old is New Again; Interesting Take on Trump's Lies; Chutney v6; References on Entropy; Amusing "Alexa.." broadcast; The Shame of Chile's Education System; Playing mp4 gifs in Firefox on Opensuses Leap 42.2; Concurrency at Microsoft; Globalisation: Uk -> Chile; OpenSuse 42.2 and Synaptics Touch-Pads; Even; Cherry Jam; Lebanese Writer Amin Maalouf; C++ - it's the language of the future; Learning From Trump; Chinese Writer Hu Fayun; And; Apricot Jam; Also; Excellent Article on USA Politics; Oh Metafilter; Prejudice Against The Rurals; Also, Zizek; Trump; Why Trump Won; Doxygen + Latex on CentOS 6; SMASH - Solve 5 Biggest Problems in Physics; Good article on racism, brexit, and social divides; Grandaddy are back!; Consciousness From Max Entropy; Democrats; Harvard Will Fix Black Poverty; Modelling Bicycle Wheels; Amusing Polling Outlier; If Labour keeps telling working class people...; Populism and Choice; Books on Defeat; Enrique Ferrari - Argentine Author; Transcript of German Scientists on Learning of Hiroshima; Calvert Journal; Owen Jones on Twitter; Possible Japanese Authors

© 2006-2017 Andrew Cooke (site) / post authors (content).

ACA0, Russell's Paradox, ZF, Arithmetic

From: "andrew cooke" <andrew@...>

Date: Tue, 14 Feb 2006 10:33:40 -0300 (CLST)

I have joined the FOM mailing list -
http://www.cs.nyu.edu/mailman/listinfo/fom/

Someone there mentioned ACA0, RCA0.  ACA0 is, I think, the Axiom of
Comprehension - http://planetmath.org/encyclopedia/ComprehensionAxiom.html
- that every formula defines a set.

That article appears to imply that ZF is open to Russell's paradox.  That
is not correct.  However, my initial argument for it not being correct
(from the Regularity Axiom) is wrong.  There's a good comment here -
http://en.wikipedia.org/wiki/Axiom_of_regularity - which I'll quote:

  Russell's paradox is the paradox whereby consideration of "the set of
  all sets that do not contain themselves as members" leads to a
  contradiction in naive set theory. Since the axiom of regularity implies
  that no set contains itself as a member, it can be tempting for the
  non-expert to think that the presence of the axiom of regularity in
  Zermelo-Fraenkel set theory (ZF) has something to do with the way in
  which ZF resolves Russell's paradox. (For example, this misconception is
  perpetuated in David Foster Wallace's Everything and More.) In fact, the
  contradiction of Russell's paradox is avoided because the separation
  axioms in ZF are of limited power (as compared with naive set theory).
  Indeed, a contradiction can only be eliminated from a theory by
  weakening or removing axioms; adding the axiom of regularity (or any
  other axiom) to a theory only makes it more likely that a contradiction
  will be encountered. The axiom of regularity is irrelevant to the
  resolution of Russell's paradox.

And if you look at the Separation Axiom then the "architect approach" is
pretty clear - "If X is a set and P is a condition on sets, there exists a
set Y whose members are precisely the members of X satisfying P".  That is
weaker than the Axiom of Comprehension given above.


Vaguely related to the above, some articles on arithmetic:

Second order arithmetic -
http://en.wikipedia.org/wiki/Second-order_arithmetic

Peano arithmetic - http://en.wikipedia.org/wiki/Peano_arithmetic

An article on Frege that is beginning to make more sense, now that I
understand more of the notation and history -
http://plato.stanford.edu/entries/frege-logic/

Andrew

Comment on this post