On 2/15/2011 12:28 PM, Quentin Anciaux wrote:
2011/2/15 Brent Meeker <[email protected] <mailto:[email protected]>>On 2/15/2011 11:28 AM, Quentin Anciaux wrote:2011/2/15 1Z <[email protected] <mailto:[email protected]>> On Feb 15, 6:13 pm, Bruno Marchal <[email protected] <mailto:[email protected]>> wrote: > On 15 Feb 2011, at 18:16, 1Z wrote: > > > > > > > On Feb 15, 4:51 pm, Bruno Marchal <[email protected] <mailto:[email protected]>> wrote: > >> On 15 Feb 2011, at 16:23, 1Z wrote: > > >>> On Feb 15, 1:27 pm, Bruno Marchal <[email protected] <mailto:[email protected]>> wrote: > >>>> On 14 Feb 2011, at 20:05, 1Z wrote: > > >>>>> On Feb 14, 2:52 pm, Bruno Marchal <[email protected] <mailto:[email protected]>> wrote: > >>>>>> On 14 Feb 2011, at 13:35, 1Z wrote: > > >>>>>>> On Feb 14, 8:47 am, Bruno Marchal <[email protected] <mailto:[email protected]>> wrote: > >>>>>>>> Do you believe that Goldbach conjecture is either true or > >>>>>>>> false? If > >>>>>>>> you agree with this, then you accept arithmetical realism, > >>>>>>>> which is > >>>>>>>> enough for the comp consequences., > > >>>>>>> Nope. Bivalence can be accepted as a formal rule and therefore > >>>>>>> not as a claim that some set of objects either exist or don't. > > >>>>>> That's my point. > > >>>>> Such a formal claim cannot support the conclusion that > >>>>> I am an immaterial dreaming machine. > > >>>> It entails it formally. Then you interpret it like you want, with > >>>> the > >>>> philosophy you want. > > >>> I want to say "number aren't real, so I'm not really a number" > > >> All your talk about numbers which are not real seems to me > >> nonsensical. Also you seems to know what is real and what is not > >> real, > > > Sure. Horses are real and unicorns aren't. Didn't you know that? > > I meant "in general". I don't need anything more than 1) I am real 2) Unreal things don't generate real things I think both of those are hard to dispute. You arbitrarily choose the unreal things... without any argument that prove that they are unreal (or real or whatever). The principle is sound, the choice is not without arguments. You say numbers don't exist... but as I said before, I can think about them in my mind...Actually I don't think you can. You can think of the symbol "7" and the word "seven" and you can probably think of seven things, xxxxxxx, but I doubt you can think of the number seven. I'm pretty sure you can't think of the set of all sets with seven members. And I'm quite sure you can't think of all the integers or all arithmetic.I exist, hence they transitively exist through my mind at the least. I do not chose if a number is prime or not hence I'm not inventing them as I'm not inventing the world around me.Can you think of Sherlock Holmes? a pink unicorn? Can you think of a number that is one bigger than the biggest number you can think of (which per Peano must exist)? BrentThe difference is I can choose what are/who are/the behavior of... Sherlock holmes/pink unicorn/whatever... not the numbers once an axiomatic system is chosen.
No, it's only a difference of degree. You can't choose Sherlock Holmes to be an American or a bus driver. He "exists" in a looser axiomatic system than integers, but he is still defined by being consistent with the character in the stories by Conan Doyle. Similarly, you can't imagine a pink unicorn that is blue and has two horns.
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