Posts

May 21, 2013

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3:11 PM | What do you think of Enderton’s Mathematical Introduction to Logic?

Now I’m back from my Bahamian break, I’m intermittently doing some reading, preparing for another version of the Teach Yourself Logic Guide to be put online at the end of the month. I’ve just been taking another look at Enderton’s … Continue reading →

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11:32 AM | Gödel Without Tears, again?

Last year, a couple of thousand people downloaded Gödel Without (too many) Tears, and the notes continue to be downloaded at the same rate. Which makes me think I could usefully update/expand the notes so that, for a start, they integrate … Continue reading →

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1:14 AM | Cognizing a Language

I see metasemantics has having two major components (cf, David Lewis 1970, "General Semantics"). One component studies languages, what their properties are, how they're individuated, etc. The other component studies how languages are "cognized".On the first issue, for the metasemantics I prefer, languages are finely-individuated mixed mathematicalia, whose intrinsic syntactic, phonological, semantic, pragmatic, orthographic properties are essential. The corresponding individuation [â€¦]

May 20, 2013

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3:29 AM | Mayo: Meanderings on the Onto-Methodology Conference

Writing a blog like this, a strange and often puzzling exercise[1], does offer a forum for sharing half-baked chicken-scratchings from the back of frayed pages on themes from our Onto-Meth[2] conference from two weeks ago[3]. (The previous post had notes from blogger and attendee, Gandenberger.) Several of the talks reflect a push-back against the idea that […]

May 19, 2013

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4:32 PM | Joyce's argument for Probabilism

In January, the Department of Philosophy at the University of Bristol launched an ERC-funded four-year research project on Epistemic Utility Theory: Foundations and Applications. The main researchers will be: Richard Pettigrew, Jason Konek, Ben Levinstein, Pavel Janda (PhD student), and Chris Burr (PhD student). The website is here.I thought it would be good to write a few blog posts explaining what I take epistemic utility theory to be, and describing the work that has been done in [â€¦]

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2:27 PM | Der logische Aufbau der Welt

The title of Rudolf Carnap's 1928 book, Der logische Aufbau der Welt, is normally translated as "The Logical Structure of the World", although apparently a more accurate rendition would be "The Logical Construction of the World".In working on how to make sense of the claim/significance of Leibniz Equivalence from spacetime theories (roughly: isomorphic spacetime models represent the same possible worlds), I've been trying to work out a version of a propositional view of possible worlds. This [â€¦]

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3:00 AM | ⚠ It’s A Trap ⚠

Re: Kenneth W. Regan The most common mathematical trap I run across has to do with Triadic Relation Irreducibility, as noted and treated by the polymath C.S. Peirce. This trap lies in the mistaken belief that every 3-place (triadic or ternary) … Continue reading →

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1:57 AM | Gandenberger on Ontology and Methodology (May 4) Conference: virginia Tech

Gregory Gandenberger Ph.D graduate student: Dept. of History and Philosophy of Science & Dept. of Statistics University of Pittsburgh http://gsganden.tumblr.com/ Some Thoughts on the O&M 2013 Conference I was struck by how little speakers at the Ontology and Methodology conference engaged with the realism/antirealism debate. Laura Ruetsche defended a version of Arthur Fine’s Natural Ontological […]

May 17, 2013

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3:00 AM | Triadic Relation Irreducibility : 3

References Relation Theory • MyWikiBiz • PlanetMath Sign Relations • MyWikiBiz • PlanetMath Triadic Relations • MyWikiBiz • PlanetMath Relation Composition • MyWikiBiz • PlanetMath Relation Construction • MyWikiBiz • PlanetMath Relation Reduction • MyWikiBiz • PlanetMath

May 16, 2013

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3:31 PM | http://mathrising.com/?p=1005

My post appeared on the Scientific American Guest Blog this morning. Here’s the link: Quantum Mechanical Words and Mathematical Organisms

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3:30 PM | grabitational singularity

the trouble with a bubble on a pyramid top is the point when it pop ⚠ ⚠⚠ ⚠⚠⚠ ⚠⚠⚠⚠ ⚠⚠⚠⚠⚠ ⚠⚠⚠⚠⚠⚠

May 14, 2013

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7:45 PM | What part do arguments from authority play in mathematical reasoning?

In forming your answer you may choose to address any or all of the following aspects of the question: Descriptive What part do arguments from authority actually play in mathematical reasoning? Normative What part do arguments from authority ideally play … Continue reading →

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6:01 PM | “A sense of security regarding the future of statistical science…” Anon review of Error and Inference

Aris Spanos, my colleague and co-author (Economics),recently came across this seemingly anonymous review of our Error and Inference (2010) [E & I]. It’s interesting that the reviewer remarks that ” The book gives a sense of security regarding the future of statistical science and its importance in many walks of life.” I wish I knew just […]

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1:51 PM | What's wrong with Mochizuki's 'proof' of the ABC conjecture?

(Cross-posted at NewAPPS)A few days ago Eric had a post about an insightful text that has been making the rounds on the internet, which narrates the story of a mathematical ‘proof’ that is for now sitting somewhere in a limbo between the world of proofs and the world of non-proofs. The ‘proof’ in question purports to establish the famous ABC conjecture, one of the (thus far) main open questions in number theory. (Luckily, a while back Dennis posted an extremely helpful and precise [â€¦]

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5:42 AM | Juggling, interviews and grant opportunities

My time this week is again taken up with work on a few writing projects I’m trying to wrap up (and end of the term grading). But I should be back on track with my regular blogs next week. In the meantime, an article on scientificamerican.com caught my attention, being about the mathematics of juggling! [...]

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2:28 AM | No-Shame Psychics Keep Their Predictions Vague: New Rejected post

See new rejected post.(You may comment here or on the Rejected Posts blog) Filed under: msc kvetch, rejected post

May 12, 2013

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4:13 AM | Science Versus Nominalism

The Indispensability Argument, developed by W.V. Quine and Hilary Putnam, and famously rebutted by Hartry Field, is fairly simple: (1) Nominalism states that there aren't strings, formulas, numbers, sets, sequences, functions, groups, etc.(2) Science (e.g., physics, linguistics) states that there are strings, formulas, numbers, sets, sequences, functions, groups, etc.Therefore, nominalism is inconsistent with science.This is not some containable inconsistency, say to do with idealization, or [â€¦]

May 10, 2013

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5:09 AM | Leibniz Equivalence (slides)

Here are some slides for a talk on "Leibniz Equivalence" which includes some topics I've written some previous M-Phi posts about (Leibniz abstraction; the notion of abstract structure; possible worlds; the abstract/concrete distinction as modal).

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3:08 AM | If it’s called the “The High Quality Research Act,” then ….

Among the (less technical) items sent my way over the past few days are discussions of the so-called High Quality Research Act. I’d not heard of it, but it’s apparently an outgrowth of the recent hand-wringing over junk science, flawed statistics, non-replicable studies, and fraud (discussed at times on this blog). And it’s clearly a […]

May 08, 2013

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8:51 PM | Postcard from the Bahamas

Another year, another trip to the Bahamas. Familial duty trip. But these things have to be done, you understand. Just have to put up with the crowded beaches and leaden skies as you can see … Holiday reading so far: … Continue reading →

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4:48 PM | Information = Comprehension × Extension : 1

Re: A Most Perplexing Mystery The inverse relationship between symmetry and diversity — that we see for example in the lattice-inverting map of a Galois correspondence — is a variation on an old theme of logic called the “inverse proportionality … Continue reading →

May 07, 2013

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5:28 PM | How relevant is relevant logic?

Review essays in the genre “Recent work in X” are often extremely useful, if only to confirm your suspicion that you can probably live pretty happily without getting too exercised about the latest lucubrations of X-ists. I’ve just read a … Continue reading →

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5:55 AM | A brief note and a little from Deutsch

I’m short on time today and working on a guest blog which I hope to be able to provide a link to shortly. But I did begin exploring a website that has short video interviews with some of my favorite thinkers. I found among a list of participants on the website Closer To Truth, Gregory [...]

May 06, 2013

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10:23 PM | Professorships in Scandal?

On page 1 of the New York Times yesterday was an article, “The Last Refuge From Scandal? Professorships”: The traditional path to an academic job is long and laborious: the solitude and penury of graduate study, the scramble for one of the few open positions in each field, the blood sport of competitive publishing. But while colleges [...]

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5:20 PM | Rock On

Elsewhere I have brought out the fact that human will had no other purpose than to maintain awareness. But that could not do without discipline. Of all the schools of patience and lucidity, creation is the most effective. It is … Continue reading →

May 04, 2013

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3:00 AM | Schedule for Ontology & Methodology, 2013

May 4 (Saturday): 8:30-9:00: Pastries & Coffee (Continental Breakfast) outside of Pamplin 2030 MORNING SESSIONS: 9:00-9:15—Welcome talk 9:15-10:00 Ruetsche: “Method, Metaphysics, and Quantum Theory” 10:00-10:25: Discussion 10:25-10:40 coffee break 10:40-11:05 Shech, “Phase Transitions, Ontology and Earman’s Sound Principle” 11:05-11:20: Discussion 11:20-12:05 Godfrey-Smith, “Evolution and Agency: A Case Study in Ontology and Methodology” 12:05-12:30: Discussion [â€¦]

May 01, 2013

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3:46 PM | An open problem about Rosser sentences?

Fix on a provability predicate Prov for a suitable theory T (there’s a lot of choices to make here, starting of course with a choice of Gödel coding). Then any Gödel sentence in the sense of a fixed point for … Continue reading →

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10:00 AM | Vickie Kearn... She Reads 'em Before You Ever Hear of 'em

Math-Frolic Interview #14 "Appreciating the power of math and what it has and can do for us is really important. It isn’t just a lot of numbers, it is about people and applications and improving everything we care about." -- Vickie Kearn You're likely not as familiar with the name 'Vickie Kearn' as most of the other names I've interviewed here... but it's a joy for me to bring her

April 30, 2013

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7:06 PM | Is Maths Fictional? Part II

From the last episode: there’s a philosopher out there who thinks that it’s possible to do science without mathematics and he isn’t afraid to put his money where his mouth is. His name is Harty Field, and he realised that the silver bullet in the Platonists’ arsenal is the apparent indispensibility of mathematical objects to [...]

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2:48 PM | Finding a Needle in a Cactus Patch

Re: Sex, Lies, And Quantum Computers Don’t know much about quantum computation, but my ventures in graphical syntaxes for propositional calculus did turn up a logical operator whose evaluation process reminded me a little of the themes involved in the … Continue reading →