On 25 January 2014 23:56, Bruno Marchal <[email protected]> wrote: > >> if p is true (in this world, say) then it's true in all worlds that p is >> true in at least one world. >> >> You need just use a conditional (if). The word asked was "if". >> >> OK? >> > > OK. I think I see. p becomes "if p is true" rather than "p is true" > > Yes. > > Rereading a previews post I ask myself if this is well understood. >
I have tended to work on the basis that 'p' means 'p is true' - to make it easier to get my head around what an expression like "[]p -> p" means. I realise it could also mean "if p is false in all worlds, that implies it is false in this one" > > You said that we cannot infer anything from Alicia song as we don't know > if his theory/song is true. > But the whole point of logic is in the art of deriving and reasoning > without ever knowing if a premise is true or not. Indeed, we even want to > reason independetly of any interpretation (of the atoical propositions). > Yes, I do appreciate that is the point. I was a bit thrown by the word usage with Alicia, "if A is singing...everybody loves my baby...can we deduce..." I mean, I often sing all sorts of things that I don't intend to be self-referential (e.g. "I am the Walrus") so I felt the need to add a little caveat. > > That error is done by those who believe that I defend the truth of comp, > which I never do. > In fact we never know if a theory is true (cf Popper). That is why we do > theories. We can prove A -> B, without having any clues if A is false (in > which case A -> B is trivial), or A is true. > I will come back on this. It is crucially important. > I agree. I think psychologically it's hard to derive the results from a theory mechanically, without at least having some idea that it could be true. But obviously one can, as with Alicia. > > A good example is Riemann Hypothesis (RH). We don't know if it is true, > but thousand of papers study its consequence. > If later we prove the RH, we will get a bunch of beautiful new theorem. > If we discover that RH leads to a contradiction, then we refute RH, and > lost all those theorems, but not necessarily the insight present in some of > the proofs. > Yes, I understand. (But I bet some of those people really, really wish that the RH will turn out to be true!) > > The negation of (p -> q) = ~(p -> q) = ~(~p V q) = ~~p & ~q = p & ~q. > That's all. It describes the only line where (p -> q) is false. p must be > false and q true. > Ah, so ~(~p V q) is ~~p & ~q. I would have naively assumed it was ~~p V ~q (though obviously using a truth table would show the error) > I will have to come back on this later! -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
