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Showing posts from February, 2011

Teddy bears, guns and modal logic

It's the time of the year when a new semester starts in Poland and I'm in Gdansk for a while (it's annoyingly and unusually cold, it feels like Calgary for some reason -  seems I haven't escaped after all. Damn you, global warming!). Anyway, one of the courses I'm teaching is non-classical logic and I'm using Graham Priest's awesome book. If you've ever taught modal logics, you probably observed that it's sometimes difficult to get the students to remember which normal modal logic is related to which properties of the accessibility relation. Here's a trick I invented last year, feel free to use it (just give credit where it's due).
First off, Priest uses Greek letters to denote the main properties of the accessibility relation: 
 \rho stands for reflexivity \sigma stands for symmetricity \tau stands ofr transitivity \eta stands for extendability
The main logics worth remembering in a basic course are T, D, B, S4 and S5:

- T is determined by th…

Reichenbach on the philosophical insignificance of G's second incompleteness theorem

Nowadays, one standard answer to various exaggerated claims about Gödel's second incompleteness theorem (the unprovability of consistency) is that even if an interesting mathematical theory could prove its own consistency, this wouldn't help us much because inconsistent theories also prove their own consistency, (so we would still have no idea whether the theory is consistent). (For instance, I think this sort of remarks, without further references, can be found in Franzen's and Smith's books, but I don't have them handy now). In a somewhat uninspired moment of mine, I wondered why this rather straightforward observation didn't get through to the wider philosophical audience earlier and when it was formulated. The earliest mention I run into so far (although, it's not like I spent days browsing stuff systematically) is in Reichenbach's 1948 unpublished lecture notes (which, by now, have been published in 1978). The fragment comes from the first volume:   …