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 2012-03-08 Is it impossible to suppose the Liar? Kris RhodesMartin University Here's an argument that you can't suppose the Liar, where the Liar is, basically, "this very sentence is false."If you can't suppose the liar, then one common way of setting forth the argument leading to paradox won't work--since it requires you to suppose the liar.(It's more common, probably, for it to require you to suppose the liar is true. Whether the below argument successfully extends to that supposition isn't something I've thought through yet.)What do you think of the argument?I worry about line 4. What do we know (or what do different people think they know) about how to individuate thoughts?Should I be worrying about any of the other three premises?Thanks for any comments. It's outside my field (as you can probably tell!) and doesn't really engage directly, as far as I can see, with any of the technical material people usually (need to) discuss when dealing with the liar paradox--which is probably a bad thing I'm afraid. 1.   A =­def  A is false. (definition)   2.   For all X, in order to suppose X, I must entertain the thought that whatever X says is the case. (Premise)   3.   For all X, in order to suppose X is false, I must entertain the thought that whatever X says is not the case. (Premise)   4.   For all X, to suppose X is to entertain a single thought. (Premise)   5.   To suppose A is not to entertain a conjunction. (Premise)   6.   In order to suppose A, I must entertain the thought that whatever A says is the case. (From 2)   7.   In order to suppose A, I must suppose A is false. (From 1)   8.   In order to suppose A is false, I must entertain the thought that whatever A says is not the case. (From 3 and 7)   9.   In order to suppose A, I must both entertain the thought that whatever A says is the case, and the thought that whatever A says is not the case. (From 7 and 8)   10.  Therefore: It is impossible to suppose A. (From 4, 5 and 9) Permanent link: https://philpapers.org/post/6649 Reply

 2012-03-12 Is it impossible to suppose the Liar? Reply to Kris Rhodes Stamatios GerogiorgakisLudwig Maximilians Universität, MünchenUniversity of Erfurt You can suppose any sentence you want in order to draw conclusions. To suppose a sentence does not mean that you are persuaded that it is true. And, of course, you can suppose conjunctions. After all, this is how reductio-proofs work. If, however, you insist to introduce a notion of supposition of "single thoughts" (suggested by your premise (4)), then you probably have to add one more premise to your argument with the strength of: A single thought is one which can be supposed (in the sense of the other premises) and of which every implication can be supposed. I.e. you would need to introduce a notion of supposition which is closed under implication. But then you would not need to suppose anything, because by supposing you would have to pre-suppose that you know all implications which your supposition has. So why bother to prove anything? Permanent link: https://philpapers.org/post/6658 Reply

 2012-03-12 Is it impossible to suppose the Liar? Reply to Kris Rhodes See All Liar, No Paradox for another analysis. Permanent link: https://philpapers.org/post/6659 Reply

 2012-03-12 Is it impossible to suppose the Liar? Reply to Kris Rhodes Samuel AlexanderOhio State University It's also worth noting that Kurt Goedel gave us, with his diagonal lemma, a way of constructing Liars which are purely statements of arithmetic.  There is a sentence phi involving nothing more than elementary arithmetical operations and quantifiers, such that Peano Arithmetic proves that phi is equivalent to "phi is not provable in Peano Arithmetic", the latter being an abbreviation for another purely arithmetical formula which merely encodes the intended statement.  (Peano Arithmetic can be replaced by even weaker theories, if you like.)  If the language is extended by a new unary predicate T (intended to be thought of as a truth predicate), the diagonal lemma even gives us a pure-arithmetic sentence phi such that PA proves phi is equivalent to ~T(_phi_) where _phi_ is a canonical code of phi.  Harvey Friedman and Michael Sheard wrote an excellent paper on this, http://philpapers.org/rec/FRIAAA, it's really a tragedy that it's barricaded behind an Elsevier paywall. Permanent link: https://philpapers.org/post/6665 Reply