Thanks to Ramos for comments and confession: >Actually, I've always thought that it was impossible to imagine a logical impossibility (e.g., >2+2=5). The statement is one of those facts in philosophy that has gone unexamined. Everyone >thought it was true. Let's revise the source of the mistake: McEvoy. He writes: >I did two philosophy options at Oxford - >philosophy of mind being one. ... I had >not known what I had let myself in for. >The questions in finals things like:- Can I imagine '2+2=5'? Can I imagine '2+2=4'? >This is about a number of things - but the >questions are so framed that it is nigh-on >impossible to say anything about them from >non-linguistic turn point of view >They are 'clever-clever' or smart-arse ways - >but an answer to this effect would be punished >_as not answering the >question_, if not seen as just insulting polemic. O, I pity you. And how did _you_ answer, if you recall. Because apparently you passed 'with flying colours', as they say in UC/Berkeley. I suppose by "I" the questions means _you_ McEvoy. Or does it mean, she, the professor? Or is it the neutral "Man" of German, Can _one_ imagine that 2 + 2 = 5 I would pose the query more as a statement. Criticise the following statement: 2 + 2 = 5, I imagine? 2 + 2 = 4, I imagine. Note that "?" indicates doubt on the part of the stater. On the other hand, the dot, '.', indicates a falling tone, and it's a statement-statement. But you knew that. Andreas is right that people can imagine lots of things. The Greeks imagined centaurs, tritons, nymphs, and flying horses. -- and 'irrational numbers' (more to the point). E. Dodds wrote this beautiful book, "The Greeks and the Irrational" which is all about irrational numbers, if you've seen one. But this arithmetic summations are not _that_ animal. One problem with imagining 2 + 2 = 5, or 2 + 2 = 4 has to do with Hilbert's Heritage. As A. Palma writes: Hilbert was adopting a specific view of the notion of containment (the basis of analyticity.) Indeed, for Kant, it's the subject-predicate notion. If it can be shown that the concept of "4" is included in the concept of "2", the concept of "+" and, again, the concept of "2", _then_ the statement "2 + 2 = 4" would be analytic (and tautological). Contrariwise, no Kant's example was, as we know: "5 + 7 = 12" which was for him _synthetic_ (never mind a priori). So, against Hilbert, he is saying that you do not _deduce_ the concept "12" (if it's deduced that you do with a concept) out of the concepts 5, 7 and +. Philosophers alla Hume and Ayer, are usually not concerned with analytic mathematical statements, since all they want to know is more oriented towards what McEvoy calls the causal theory of perception, i.e. whether the pillar box _is_ red or just _seems_ so (synthetic a posteriori -- the dogma of Empiricism). Now the transcendental Ego, for Kant, was indeed _rational_ (pure reason), so for a purely reasonable (or rational) creature -- poorly reasonable creature, as I'd spell it -- she cannot _imagine_ 2 + 2 = 5. As she cannot imagine the quadratura circuli. The phrasing of the question is slightly irritating, "Can one ...". When I rephrased that into 'know', it sounded awkward and clumsy. "Can you know" -- Can you kennst du John Peele?" sort of thing. "Can" is an ability, but it doesn't _force_ anything. It's also disrespectful to ask 'can' questions ("Can you write?"). If taken in theory, of course one can always _learn_, so even if I were not able to write shorthand, I would answer, "Yes, I can", meaning, "Yes, I do have the ability -- want to teach me?" (This reminds me of the job interview of Sweet Charity in the eponymous comedy -- brilliant). A further problem is with 'imagine' --With G. E. Moore I have many problems imagining apples in a basket. But still, I can imagine an apple in a basket, and 2 + 2 apples making 4 apples. But 2 + 2 = 4 _in the abstract_ it's *harder* to imagine. This is the reason why when Wittgenstein taught mathematics in Switzerland -- "The Lost Years" -- he always used apples and pears. Goedel was a smart guy, and he would have answered your professor's silly question in ways which would have blown his socks off, if that's the expression. Of course if he was really into linguistic turn, the expected reply would be, "Depends on how you define "2", "+" and "4". It's all conventional and artificial -- and it's a formal language, and the assignment of value to artificial symbols is arbitrary. So I can imagine a parallel universe (or next door, actually) where 2 + 2 making 5 is _the_ perfectly sensible thing for 2 + 2 to make. Cheers, J. L. Author of "From Zero to the Infinite" -- and Back. ************************************** See what's new at http://www.aol.com