FOM: certainty

[Arnon Avron]

On Wed, 23 Dec 1998 0:52:36 +0100 Xavier Noria wrote:

>    
>    We agree what is right about naturals and what not. All our N's have an
>    associative addition, and prime and composite numbers and questions to
>    know the answer, but I think that _truth_ have nothing to do with it.
>    
>    Our N's satisfy that 2 + 2 is equal to 4, but, to my mind, this is our
>    _agreement_ about our abstraction. Saying "2 + 2 = 4 is true" sounds
>    quite different to me.
>    

Fine. You have convinced me. From now on I shall never say that 
" `2 + 2 = 4' is true in N". I shall say instead  that " `2 + 2 = 4' is right
about  N". In fact, I shall be even more careful and say that it is
right about *my* N! 

  I am glad that you agree with me about what is right about my N. 
Unfortunately, I dont feel that I have the right to say what is right
about *your* N's. How can I know? The only thing I can say for sure is that 
since you (and Vladimir Sazonov) have several N's, you have at least one
which is different from my own poor, lonely N (this only follows, I admit,
from what is right about *my* logic. You may of course have several other
logics!). So how can we agree about your N's with which I will never
possibly have any acquaintance?

Happy New Year!

Arnon Avron
Computer Science Department
Tel-Aviv university