September 01, 2014

5:00 PM | Frederik Stjernfelt • Natural Propositions : 1
Re: Frederik Stjernfelt • Natural Propositions Frederik, One small point that I find myself making on a periodic basis:  I think it is better to describe Peirce’s take on logic as “non-psychologism” rather than “anti-psychologism”, the main thing being that … Continue reading →
11:00 AM | Robin Williams Redux...
Now for something completely different (for MathTango)… I've written before how much I admire Cathy O'Neil's keen ability to touch on varying topics over at her blog. Despite coming from a mathematics academic background and titling her blog "Mathbabe," Cathy writes on a wide range of topics that rattle around in her head. So I'll sorta take that cue today to veer off and relate an odd,

August 29, 2014

5:34 PM | What we see when….
I recently listened to Krys Boyd’s interview with Peter Mendelsund, author of the new book What We See When We Read,  on North Texas’ public radio. Mendelsund is an award-winning book jacket designer. The interview had the effect of connecting his thoughts about reading to thoughts that I have had about mathematics. It wasn’t immediately [...]
3:04 PM | Breaking the Law (of likelihood): only way to keep their fit measures in line (A)
An Assumed Law of Statistical Evidence (law of likelihood) Nearly all critical discussions of frequentist error statistical inference (significance tests, confidence intervals, p- values, power, etc.) start with the following general assumption about the nature of inductive evidence or support: Data x is better evidence for hypothesis H1 than for H0 if x are more probable under H1 than […]
11:15 AM | Friday Wrap-up
Another week from the world of math: 1)  Article touting the role of rote memorization in early math education: http://tinyurl.com/lj759wd 2)  Fawn Nguyen describes the beginning of her classroom school year, as perhaps only she can: http://fawnnguyen.com/first-two-days-school/ 3)  LA Times op-ed on the gender-gap in mathematics: http://www.latimes.com/opinion/op-ed/

August 27, 2014

6:27 AM | CFP: SoTFoM II 'Competing Foundations?', 12-13 January 2015, London.
The focus of this conference is on different approaches to the foundationsof mathematics. The interaction between set-theoretic and category-theoreticfoundations has had significant philosophical impact, and represents a shiftin attitudes towards the philosophy of mathematics. This conference willbring together leading scholars in these areas to showcase contemporaryphilosophical research on different approaches to the foundations ofmathematics. To accomplish this, the conference has the […]

August 25, 2014

12:19 PM | What’s the big deal with consistency?
(Cross-posted at NewAPPS)It is no news to anyone that the concept of consistency is a hotly debated topic in philosophy of logic and epistemology (as well as elsewhere). Indeed, a number of philosophers throughout history have defended the view that consistency, in particular in the form of the principle of non-contradiction (PNC), is the most fundamental principle governing human rationality – so much so that rational debate about PNC itself wouldn’t even be possible, as famously stated by […]
9:20 AM | Servus, New York! Invitation to the MCMP Workshop "Bridges" (2 and 3 Sept, 2014)
MCMP Workshop "Bridges 2014"New York City, 2 and 3 Sept, 2014www.lmu.de/bridges2014The Munich Center for Mathematical Philosophy (MCMP) cordially invites you to "Bridges 2014" in the German House, New York City, on 2 and 3 September, 2014. The 2-day trans-continental meeting in mathematical philosophy will focus on inter-theoretical relations thereby connecting form and content of this philosophical exchange. The workshop will be accompanied by an open-to-public evening event with Stephan […]
3:00 AM | C.S. Peirce • Syllabus • Selection 1
Selection from C.S. Peirce, “A Syllabus of Certain Topics of Logic” (1903) An Outline Classification of the Sciences 180.   This classification, which aims to base itself on the principal affinities of the objects classified, is concerned not with all … Continue reading →

August 24, 2014

11:20 AM | Extending a theory with the theory of mereological fusions
"Arithmetic with fusions" (draft) is a joint paper with my graduate student Thomas Schindler (MCMP).  The abstract is:In this article, the relationship between second-order comprehension and unrestricted mereological fusion (over atoms) is clarified. An extension $\mathsf{PAF}$ of Peano arithmetic with a new binary mereological notion of ``fusion'', and a scheme of unrestricted fusion, is introduced. It is shown that $\mathsf{PAF}$ interprets full second-order arithmetic, $Z_2$.Roughly […]

August 23, 2014

9:46 PM | Has Philosophical Superficiality Harmed Science?
I have been asked what I thought of some criticisms of the scientific relevance of philosophy of science, as discussed in the following snippet from a recent Scientific American blog. My title elicits the appropriate degree of ambiguity, I think.  Quantum Gravity Expert Says “Philosophical Superficiality” Has Harmed Physics By John Horgan | August 21, 2014 |  14 “I interviewed […]
2:30 PM | ¿Shifting Paradigms? • 4
Re: Harvey Friedman • Foundational Crisis? 2014 Aug 22 Shock and surprise are relative to a prior state of belief.  The belief that mathematics reduces to logic, and that of a purely deductive sort from given axioms, seems to be … Continue reading →

August 22, 2014

4:00 PM | ¿Shifting Paradigms? • 3
Re: Harvey Friedman • Good Math 2014 Aug 17 Speaking of mathematics in the context of “general intellectual activity” brings to mind Raymond Wilder’s take on “mathematics as a cultural system”. I would like to keep that in mind, if … Continue reading →
11:00 AM | Another Friday Collection
From this week's wonderful world of math: 1)  Shortly, after last week's potpourri came out the 113th Carnival of Mathematics went up; if by any chance you missed it, a lot more mathy links there: http://www.walkingrandomly.com/?p=5537 2)  I've referenced this research before, but just last week NPR covered findings that indicate winners of the Fields Medal (and other prizes) actually lowers
7:26 AM | L. A. Paul on transformative experience and decision theory II
In the first part of this post, I considered the challenge to decision theory from what L. A. Paul calls epistemically transformative experiences.  In this post, I'd like to turn to another challenge to standard decision theory that Paul considers.  This is the challenge from what she calls personally transformative experiences.  Unlike an epistemically transformative experience, a personally transformative experience need not teach you anything new, but it does change you in […]

August 19, 2014

8:12 AM | Is the human referee becoming expandable in mathematics?
(Cross-posted at NewAPPS)Mathematics has been much in the news recently, especially with the announcement of the latest four Fields medalists (I am particularly pleased to see the first woman, and the first Latin-American, receiving the highest recognition in mathematics). But there was another remarkable recent event in the world of mathematics: Thomas Hales has announced the completion of the formalization of his proof of the Kepler conjecture. The conjecture: “what is the best way to stack […]

August 18, 2014

1:43 PM | Model theory without tears?
Ah well, you win some and you lose some. I was writing for months about recursive ordinals and proof theory with a view to a short-ish book. And now, quite a way in, I realise that I have to go … Continue reading →
3:21 AM | Are P Values Error Probabilities? (installment 1)
Despite the fact that Fisherians and Neyman-Pearsonians alike regard observed significance levels, or P values, as error probabilities, we occasionally hear allegations (typically from those who are neither Fisherian nor N-P theorists) that P values are actually not error probabilities. The denials tend to go hand in hand with allegations that P values exaggerate evidence against […]

August 17, 2014

5:06 PM | Bohemian gravity
Tim Blais, a McGill University physics student made this really great a capella version of "Bohemian Rhapsody", called "Bohemian Gravity", with physics lyrics explaining superstring theory, like "Manifolds must be Kahler!" (lyrics here).Another article on this.
12:00 PM | Forest Primeval → Riffs & Rotes
Re: Shifting Paradigms? • (1) • (2) • (3) • (4) • (5) Prompted by the discussion of Catalan numbers on the Foundations Of Math List, I dug up a few pieces of early correspondence and later discussions that bear … Continue reading →

August 16, 2014

10:32 AM | Reinstatement
M-Phi readers may or may not have paid attention to the bizarre events during the last twelve months, over which I was initially dismissed by the University of Oxford, and smeared with lies in the national press. I described some of this in a statement Prof. Leiter put up on 26 March 2014:From late 2013, Oxford proceeded with a prosecution, involving failures of due process and proportionality, despite the support I received from my College and several members of the Faculty. The prosecution […]

August 14, 2014

6:34 PM | Friday Bonanza
ICYMthem: 1)  Fun li'l anecdote about topologist Egbert Rudolf van Kampen from MathOverflow.net last week: http://mathoverflow.net/questions/178104/a-topologist-is-not-a-mathematician-a-small-question 2)  New popular statistics (…I know, that sounds like an oxymoron! ;-)) book out from Gary Smith, "Standard Deviations": http://tinyurl.com/poefeew (haven't read it, but it's from a professor at
12:47 PM | L. A. Paul on transformative experience and decision theory I
I have never eaten Vegemite---should I try it?  I currently have no children---should I apply to adopt a child?  In each case, one might imagine, whichever choice I make, I can make it rationally by appealing to the principles of decision theory.  Not according to L. A. Paul.  In her rich and fascinating new book, Transformative Experience, Paul issues two challenges to orthodox decision theory---they are based upon examples such as these.(In this post and the next, I'd like […]
10:44 AM | Worlds Without Domain
An article "Worlds Without Domain" arguing against the idea that possible worlds have domains. The abstract is: "A modal analogue to the "hole argument" in the foundations of spacetime is given against the conception of possible worlds having their own special domains".

August 11, 2014

10:10 PM | Egon Pearson’s Heresy
Today is Egon Pearson’s birthday: 11 August 1895-12 June, 1980. E. Pearson rejected some of the familiar tenets that have come to be associated with Neyman and Pearson (N-P) statistical tests, notably the idea that the essential justification for tests resides in a long-run control of rates of erroneous interpretations–what he termed the “behavioral” rationale of tests. In an […]

August 10, 2014

1:31 AM | Blog Contents: June and July 2014
Blog Contents: June and July 2014* (6/5) Stephen Senn: Blood Simple? The complicated and controversial world of bioequivalence (guest post) (6/9) “The medical press must become irrelevant to publication of clinical trials.” (6/11) A. Spanos: “Recurring controversies about P values and confidence intervals revisited” (6/14) “Statistical Science and Philosophy of Science: where should they meet?” (6/21) […]

August 09, 2014

4:01 AM | Winner of July Palindrome: Manan Shah
Winner of July 2014 Contest: Manan Shah Palindrome:  Trap May Elba, Dr. of Fanatic. I fed naan, deli-oiled naan, deficit an affordable yam part. The requirements:  In addition to using Elba, a candidate for a winning palindrome must have used fanatic. An optional second word was: part. An acceptable palindrome with both words would best an acceptable palindrome with just […]
2:55 AM | What mathematics can make of our intuition
The CogSci 2014 Proceedings have been posted and there are a number of links to interesting papers. Here are some math-related investigations: A neural network model of learning mathematical equivalence The Psychophysics of Algebra Expertise:  Mathematics Perceptual Learning Interventions Produce Durable Encoding Changes Two Plus Three is Five:  Discovering Efficient Addition Strategies without Metacognition Modeling [...]

August 08, 2014

11:15 AM | Friday Potpourri
Another week's-worth of schtuff: 1)  Sue VanHattum has started a new "Math Mama's Gazette" for students and teachers. First issue here: http://mathmamawrites.blogspot.com/2014/08/math-mamas-gazette-issue-number-one.html 2)  Stephen Stigler's 7 pillars of statistics: http://blogs.sas.com/content/iml/2014/08/05/stiglers-seven-pillars-of-statistical-wisdom/ 3)  The fifth run of Keith Devlin's "

August 07, 2014

12:35 AM | What did Nate Silver just say? Blogging the JSM 2013
Memory Lane: August 6, 2013. My initial post on JSM13 (8/5/13) was here. Nate Silver gave his ASA Presidential talk to a packed audience (with questions tweeted[i]). Here are some quick thoughts—based on scribbled notes (from last night). Silver gave a list of 10 points that went something like this (turns out there were 11): […]
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