| 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.

Last 100 entries

Headphone Test Recordings; Causal Consistency; The Quest for Randomness; Chat Wars; Real-life Financial Co Without ACID Database...; Flexible Muscle-Based Locomotion for Bipedal Creatures; SQL Performance Explained; The Little Manual of API Design; Multiple Word Sizes; CRC - Next Steps; FizzBuzz; Update on CRCs; Decent Links / Discussion Community; Automated Reasoning About LLVM Optimizations and Undefined Behavior; A Painless Guide To CRC Error Detection Algorithms; Tests in Julia; Dave Eggers: what's so funny about peace, love and Starship?; Cello - High Level C Programming; autoreconf needs tar; Will Self Goes To Heathrow; Top 5 BioInformatics Papers; Vasovagal Response; Good Food in Vina; Chilean Drug Criminals Use Subsitution Cipher; Adrenaline; Stiglitz on the Impact of Technology; Why Not; How I Am 5; Lenovo X240 OpenSuse 13.1; NSA and GCHQ - Psychological Trolls; Finite Fields in Julia (Defining Your Own Number Type); Julian Assange; Starting Qemu on OpenSuse; Noisy GAs/TMs; Venezuela; Reinstalling GRUB with EFI; Instructions For Disabling KDE Indexing; Evolving Speakers; Changing Salt Size in Simple Crypt 3.0.0; Logarithmic Map (Moved); More Info; Words Found in Voynich Manuscript; An Inventory Of 3D Space-Filling Curves; Foxes Using Magnetic Fields To Hunt; 5 Rounds RC5 No Rotation; JP Morgan and Madoff; Ori - Secure, Distributed File System; Physical Unclonable Functions (PUFs); Prejudice on Reddit; Recursion OK; Optimizing Julia Code; Cash Handouts in Brazil; Couple Nice Music Videos; It Also Works!; Adaptive Plaintext; It Works!; RC5 Without Rotation (2); 8 Years...; Attack Against Encrypted Linux Disks; Pushing Back On NSA At IETF; Summary of Experimental Ethics; Very Good Talk On Security, Snowden; Locusts are Grasshoppers!; Vagrant (OpenSuse and IDEs); Interesting Take On Mandela's Context; Haskell Cabal O(n^2) / O(n) Fix; How I Am 4; Chilean Charity Supporting Women; Doing SSH right; Festival of Urban Intervention; Neat Idea - Wormholes Provide Entanglement; And a Link....; Simple Encryption for Python 2.7; OpenSuse 13.1 Is Better!; Little Gain...; More Details on Technofull Damage; Palmrest Cracked Too....; Tecnofull (Lenovo Support) Is Fucking Useless; The Neuroscientist Who Discovered He Was a Psychopath; Interpolating Polynomials; Bottlehead Crack as Pre-amp; Ooops K702!; Bottlehead Crack, AKG K701; Breaking RC5 Without Rotation; Great post thank you; Big Balls of Mud; Phabricator - Tools for working together; Amazing Julia RC5 Code Parameterized By Word Size; Chi-Square Can Be Two-Sided; Why Do Brits Accept Surveillance?; Statistics Done Wrong; Mesas Trape from Bravo; European Report on Crypto Primitives and Protocols; Interesting Omissions; Oryx And Crake (Margaret Atwood); Music and Theory; My Arduino Programs; Elliptic Curve Crypto; Re: Licensing Interpreted Code; Licensing Interpreted Code; ASUS 1015E-DS03 OpenSuse 12.3 SSD

© 2006-2013 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