Transcript Powerpoint template for scientific posters (Swarthmore College)

Introduction
Must I exist? Common sense seems
to indicate not. My parents might
not have met and therefore I might
never have been born. But it is well
known that we can prove that any
and every object must necessarily
exist in S5 (Prior 1956). Here is a
standard proof (from Menzel 2005)
1 x=x
2 (y) (y≠x) → (x≠x)
3 (x=x) → ~(y) (y≠x)
4 (x=x) → Ey (y=x)
5 Ey (y=x)
6 □Ey (y=x)
7 (x)□Ey (y=x)
Language, Thought, Logic, and Existence
Richard Brown
NDT
So for instance on this view the
sentence ‘Saul Kripke likes tea,’
would be rendered as (3),
(3) The English sentence ‘Saul Kripke likes tea’ is
true if and only if (Ex) (is called “Saul Kripke”(x) &
Likes tea(x))
Its truth condition is that there is an
object which is called ‘Saul Kripke’
and which likes tea.
Rigid Designation?
Open Minded?
Necessary existence is usually
reserved for such lofty beings as
numbers and God; who would’ve
thought that my computer and I
kept such company?! So what are
we to do? Luckily for those who feel
like I do there is Kripke’s well known
solution to this problem (Kripke
1963) which has two parts
But how do we reconcile this with
the thesis of rigid designation?
Indeed, isn’t adopting NDT really
admitting that there is no such
semantic property? Who the
description in (3) picks out can vary
from counter-factual situation to
counter-factual situation. The
reference of the name depends on
pragmatic facts.
On the other hand
One might take the semantic task to
be that of giving the meaning of
sentences independently of their
being used to express any thought.
This way of thinking about
semantics has it as simply a part of
grammar. According to Bach the job
of semantics is to provide an
account of how information is
linguistically encoded.
I Choose Both
We have two legitimate
conceptions of what the semantic
task is. I will use ‘P-semantics’ for
theories that want to give a theory
of the meaning of thoughts and ‘Lsemantics’ for theories that want to
give a theory of the meaning of
sentences considered apart from
their being used to express any
given thought.
Frigidity
Semantical Considerations
Following Quine, he invokes the
‘generality interpretation’ of
variables and requires that no free
variables be allowed in our
instances of axioms in a proof
(Quine 1940). Kripke’s next move is
to require that there be no singular
terms in our formal language. His
quantified modal logic includes only
variables.
I have coined the term ‘frigidity’
and ‘frigid designator’ as a way to
contrast a view like Bach’s with the
semantic conception of rigidity. But
this begs the question about the
‘right’ way to draw the
semantic/pragmatic distinction. If
there is a real issue here then it
should be possible to formulate it in
a way that is neutral
Neutrality
Frigidity is the claim that there is no
such L-semantic property of rigidity.
So what I think the problem of
necessary existence shows is that
our L-semantic theory cannot
contain rigid designators. When we
treat names as singular terms our
best logic goes off the rails.
The Semantic Task
◊ ~Ex (x=SK)
How do we say that Kripke might
not have existed in a language with
no singular terms? One option is
Kent Bach’s Nominal Description
Theory (NDT). NDT says that a name
N is semantically equivalent to the
description that mentions N,
something like ‘is called “N”’ or, as
Bach prefers, ‘is the bearer of “N”’.
One might take the semantic task to
be that of giving the meaning
of and truth-conditions
for thoughts, as Michael Devitt
does (Devitt 1997). For Devitt
meaning is primarily a property of
thoughts and the semantic task is to
explain what property they have
which allows them to play the role
in behavior that they do
Conclusion
The causal theory of reference is a
P-semantic theory. It says that
we can have singular thoughts,
given that the right kinds of
causal/historical connections hold
between certain thought contents
and the world. But we express
those thoughts using a language
that itself does not have singular
terms as per NDT.