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\begin{document}
\head{April 22, 1992}

\part{I}

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One of the fundamental difficulties which any theory on language must
take into account is the {\bf Russell Problem}.  The basis of this
problem is that there should be no exceptions to the Principle of
Excluded middle.  This Principle states that for any proposition $A$,
$A \vee \neg A$ is true.  The difficulty can be seen by looking at how
Frege, Russell, and Strawson would interpret the sentence
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(1) `The present King of France is bald or the present King of France
is not bald.'
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Apparently, there is a problem.  Since `the present King of France'
(call this sign `(2)') does not refer to anything, it is not obvious
how to interpret this sentence.

Frege's solution to this problem is to refute the 'Fido'-Fido claim
that every singular term has a reference.  According to Frege's
theory, the logical form of language consists of arguments and
single-argument functions.  Since the innermost argument in (1) has no
reference, none of the functions can have references either, and the
entire sentence lacks any truth value at all.  The flaw in Frege's
argument is his insistence that signs with no reference cannot have
any cognitive significance.  As much as Frege apparently would like to
have language be as logical and unambiguous as first-order logic, he
can't have it.  Natural languages have inherent inconsitencies.
Frege's ``solution'' seems more like a way to ignore the Russell
problem rather than actually addressing it.

Russell's solution involves manipulating the logical form of the
sentence.  It is not clear if (1) should be interpreted with the
definite description (2) in primary occurrence as `the present King of
France is bald or the present King of France is not-bald.' or in
secondary occurrence as `The present King of France is bald or not
the-present-King-of-France-is-bald.'  If the logical form used is that
corresponding to the latter interpretation, then the sentence is true,
regardless of the existence of the reference of `the present King of
France'.  Russell's solution is attractive from a logical point of
view.  However, there is a feeling that something is lost in
translation to logical form.  Although Russell's solution solves the
problem at hand, it is not clear (to me at least) that there is any
other reason to choose one logical form over another.

Strawson's solution is similar to Frege's.  He also asserts that a
statement does not necessarily have a truth value.  But rather than
doing what Frege says, and constructing a system of logic where
functions with no arguments have no value, Strawson deals with the
grammatical form of the speech act.  Under this theory, a sentence
which is neither true or false is simply meaningless.  Strawson's
theory also deals with other than ``eternal sentences''.  Rather,
Strawson would consider (1) to be an ``occasion sentence''.  It's
reference changes with each utterance.  If I were to utter (1) 300
years ago, there would be little difficulty in interpreting it.

I think that Strawson's solution is the best.  Logical forms tend to
have the quality that it is difficult to express concepts which have
no reference.  By not trying to come up with an explanation in logical
form, the explanation has a much stronger intuitive feel to it; there
is no feeling that something was contrived.

Another significant problem in theories of language is that of the
{\bf Negative Existential}.  When interpreting a language, what is
existence?  Is it a predicate?  Or is it something else?

Frege simply fails to adequately explain this case.  In his theory,
everything is an argument or a function.  Functions whose arguments
have no reference themselves have no reference.  Since ``existence''
must be a function, it can never return false, since the argument
would have no reference, and the function would have no value.  This
theory is just too simple to handle existentials.

Strawson's theory explains negative existentials as a kind of
assertion.  We already know that a sentence can be meaningless.  If it
is widely known what the meaning of an utterance with no reference is,
then a sentence such as `Santa Claus does not exist.' is meaningful,
and true.  A sentence such as `Freddled gruntbugglies do not exist.'
is meaningless, so it has no truth value.  Since people can conceive
of fictional objects, they can name them, and refer to them, even
though they do not exist.

The Russell theory is the only one of the three which recognizes that
existence is special; saying that something does or does not exist is
fundamentally different from saying that something is or is not green.
This is expressed in the logical form, which is entirely different for
statements of the two types.

I prefer Russell's solution to the {\bf Negative Existential} problem.
Strawson solves the problem, but doesn't make any distinction about
existence, which seems like a special concept.  There is no real
fundamental difference between `Santa Claus does not exist' and `Santa
Claus does not like ARA food`.  Russell does make this distinction,
and it is in this distinction which I find the strong appeal of
Russell's solution.

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\newpage
\part{II}

\begin{itemize}

\prob A.  A {\bf type} is an abstract instance within a class.  For
instance, an example of a word type would be the word `class'.  The
word type `class' has four letter types in it.  A {\bf Token} is an
instance of a type.  This paragraph is comprised of word tokens.
Since types are abstract, there is only one word type `class', but
there can be many instances of it; there are five instances in this
paragraph.  {\bf Occurrences} are abstract, but can occur multiple
times.  Earlier, I noted that in the word type of `class', there are
four letter types.  However, one of them has two occurrences.  Since
occurrences are abstract, it makes no sense to talk about them when
referring to tokens.

\prob C.  An {\bf eternal sentence} is a sentence whose truth value is
time-independent.  The most common form of these are mathematical
proofs, such as $2+2=4$.  An {\bf occasion sentence} is one which can
have a new reference each time is is spoken.  For instance, `I am
hungry' may be true as I write this, but it does not have to remain
true.  It needs to be reevaluated each time.

\prob D.  A {\bf locutionary act} is a the physical act of enunciating
words.  An {\bf illocutionary act} is a statement made according to
social convention, such as an observation (`The sky is red.') or an
order (`Stand up.').  A {\bf perlocutionary act} is a side-effect of
an illocutionary act, such as causing a person to look at the sky, or
embarrassing the recipient of an order.

\end{itemize}

\newpage
\part{III}

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Although there is no Santa Claus, the sentence `Santa Claus is a
legendary old man with a white beard.' is true.  This sentence is true
because by calling Santa Claus a ``legendary old man'', one can be
said to be presupposing the existence of a legend describing Santa
Claus.  In this legend, there does exists a Santa Claus, and he is
indeed an old man with a white beard.  If the legend did not exist, or
if the legend had Santa Claus as a young, clean-shaven man, then the
sentence would be false.  But the non-existence of Santa Claus does
not prevent the sentence from having a truth value.

Consider another example, `The intersection of the parallel lines in
the hypothetical space is labelled $\cal X$.'  Although this is not
the case in reality, there exist topological spaces where parallel
lines do intersect.  This statement presupposes the existence of such
a space, in the same way that Santa Claus presupposes a particular
legend.

So, the lack of references in this universe of `Santa Claus' or of
intersecting parallel lines does not preclude making statements about
them, as long as an appropriate universe is presupposed, implicitly or
explicitly.

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\end{document}
