On 12/3/2018 7:31 AM, Bruno Marchal wrote:
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}.
Right. T and F are just formal markers in logic and the rules of
inference are supposed to preserve T.
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's satisfaction relative to some particular axioms and rules of
inference.
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.
That's the correspondence theory of truth, which is what ordinary
discourse and physics assume. So there are at least three kinds of
"true". To which we might add the Trump theory of truth, "If it makes me
look good it's true."
I recommend the book by Torkel Franzen “Inexhaustibility” for a more detailed
explanation of the concept of truth.
I have the book but I haven't read it (so many books, so little time).
Brent
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.
