Having read the thread, I think I get some of the point, but not
entirely, (01)
1) If I have a three valued logic, things are true because they are true
in the world, false because they are false in the world, and * because
they cannot be determined. That is, the semantics of this logic enable the
logic to
talks about sentences such as "zero divide by zero is greater than one",
which is otherwise undefined. (02)
2) A formal system - a game played to a particular set of rules - uses a
limited concept of semantics, since The World is limited to statements that
can be expressed in the system
and "truth" to the ones which the rules allow. A system with rules such as
1*1 = 1, 1*0 = 0 and 1+0 = 1
can be interpreted as (1 = true, 0 = false, * = and, + = or) or
(0 = true, 1 = false, * = or, + = and)
I suspect that "two stage semantics" referred to is the combining of the
(limited) semantics of the formal system with the subsequent mapping of
the formal symbols onto "real world" semantics. However, (I think this
might be Pat Hayes' objection), immediately you do this, you have not
done anything new or interesting in semantics, you have only rewritten
the language in which you present your semantics. (03)
3) The termptation to two stage semantics may arise from the desire to make
statements
about the truth (validity, correctness) of the formal system independently
of its use
to make statements about the world. In mathematics there is some sense in
this, since 1+1=2 for
teabags and apples, but not for pools of water. (04)
4) The options seem to be
a) The semantics of logic is just the semantics of logic, and the fact that
it happens to be representable
by a formal system is neither here nor there;
b) Logicians are claiming a privileged status for logic (that it is a formal
system that does not need two stage semantics);
c) Something else. (05)
Pat Hayes - if this is total wrong, just send the word "Flame" - I'll put my
asbestos suit on. (06)
Sean Barker
Bristol, UK (07)
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