> On 2 Dec 2018, at 21:06, Brent Meeker <[email protected]> wrote:
>
>
>
> On 12/2/2018 4:52 AM, Bruno Marchal wrote:
>>
>> Language have no relation with truth a priori. Theories might have.
>> Semantics are truth “by definition”, by relativising it to the notion of
>> model/reality.
>>
>
> Then what is this "true" and "false" which you attribute to the propositions
> of modal logic?
In classical logic, truth is any object in a set of two objects, or it is the
supremum in a Boolean algebra. In propositional logic a “world” is defined by
any function from the set of atomic letters to {t, f}.
Then if the theory is “rich enough”, truth can be meta-defined by “satisfied by
the structure (N, 0, s, +, *).
Of course, this presuppose the intuitive understanding of 2+2=4, etc.
In our case, as all modal formula are arithmetical formula, it is the usual
informal mathematical notion just above (arithmetical truth, satisfaction by
the usual standard model).
That one can be define by V(‘p’) means the same as p. It is Tarski’s idea that
‘p’ is true when p, or when it is the case that p. Like wise, to say
Provable-and-true(p) we use []p & p.
I recommend the book by Torkel Franzen “Inexhaustibility” for a more detailed
explanation of the concept of truth.
We can come back, but I suggest to come back on this only when we need it, as
this is an very rich and complex subject by itself.
Bruno
>
> Brent
>
> --
> 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 https://groups.google.com/group/everything-list.
> For more options, visit https://groups.google.com/d/optout.
--
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 https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
