[FOM] Another easy solution does not work

Dean Buckner Dean.Buckner at btopenworld.com
Fri Sep 13 13:10:43 EDT 2002

An enormous number of contributors to this FOM topic assume that it is
sentences, rather than anything else, that are the bearers of truth or
falsity.  However:

1.  Richard thinks, believes fears &c that what Dean says is true.  Richard
doesn't  think or fear *sentences*.

2.  Some philosophers (probably, at the time of writing, the majority who
write on this subject) argue that there are abstract entities called
"propositions".  These are what is stated or expressed by sentences, rather
than the sentences themselves.  People should at least be aware there is a
large body of literature on this.  (I have a list for anyone interested).
Compulsory reading in my view, if you can get a copy, is A.N.Prior's
"Objects of Thought", esp chapter "What we Think".  My old teacher CJF
Williams wrote a book called "What is Truth" (much influenced by Prior)
which is also good (but hard).  Frege's "The Thought" is also fun, and much
anthologised.  Christopher also wrote a book called "Being Identity and
Truth" which was his idea of a popular presentation of the subject and is
slighly cringeable as a result (he has a chapter called "Kooky Objects") but
is worth looking at and can be found at herb at philosophy-books.co.uk

3.  If we want to avoid abstract entities like thoughts or propositions,
consider how we report other people's thoughts beliefs, or the content of
the sentences they utter.  We use a verb likes "thinks", "believes" &c, plus
a construction that wraps the sentence that would otherwise express the
thought, in a so-called "that" clause.  So "Richard fears / that grass is
not green".  This is a neat trick that language has, of allowing us to
characterise what someone says or thinks, without expressing the thought or
opinion ourselves.  The report of what Richard fears actually contains the
words "grass is not green", without expressing the thought or fear
attributed to Richard himself.  If we didn't have this trick, we couldn't
entertain what other people think, or entertain thoughts that we know are
not true.

4.  Contemporary philosophy of language is v. much focused on the semantics
of "that" clauses, one of the best web sites on the whole topic is by Kent
Bach, with whom I occasionally correspond/argue/lunch with.:


I especially recommend his two pieces on "Belief Reports".  There's a good
survey of the literature, which will save anyone e-mailing me!  Anything by
Kent is worth reading, check out his other papers, especially "Searle
Against the World".  He also has a book called "Meaning and Reference"
(Clarendon Press) which is all about the contemporary problem of "singular

5.  On "The Liar": as I suggested in a sadly ignored posting last month, the
function of the word "true" is simply to signify assertion or affirmation.

That grass is not green

(a) is feared by Richard
(b) is thought by Richard
(c) is stated by Richard
(d) is not true

The sentences completed by (a) to (c) all report what Richard thinks,
believes &c, without offering any view on whether what he thinks or believes
is a fact or not.  I.e. the truth of the report does not depend on whether
grass is green or not.  However in (d) we take the content and deny it.  Now
I express an opinion, not on what Richard says or thinks, but on the
greenness of grass.

6.  Now consider

What this sentence says is true.

But what does the sentence say?  It's referring to the content of some
sentence, which happens to be the sentence itself.  Thus, if I'm right, and
every sentence consists of a content-part, analogous to a noun clause, and
an assertion part, analogous to a verb, then the content-part is what is
signified by "What this sentence says".  But we can't tell what it
signifies.  It's exactly the same as the expression "what this expression
signifies" - which signifies nothing.

If we suppose that there is an implicit assertion, in sentences like "what
Richard said is / is not true", that Richard said anything in the first
place, then the Liar sentence comes out false.  Thus there is no paradox.

7.  Now there is a more serious puzzle here worth mentioning.  Frege had
the idea that the meaning of a sentence is built out of components

"The possibility of our understanding propositions which we
have never heard before evidently rests on this, that we construct the sense
of a proposition out of parts that correspond to the words."

[ Frege, letter to Jourdain, see also Wittgenstein,
Tractatus 4.03]

So the component contributed by the verb of the sentence, the bit that
actually asserts the content, must also be a component of the meaning, since
"that grass is green" clearly means something different from "grass is
green".  But what is this component?  As soon as we try to say what it is,
we have to use a noun phrase.  So let the meaning of the sentence - a thing
- be M, and the assertoric component - another thing - be A.  And let's
denote the content as before, by a "that" clause.

M = that grass is green + A

But this is a noun phrase, not a sentence, and cannot therefore denote the
meaning  of "grass is green" at all.  This is "Arnauld's paradox".  Arnauld
thought that the function of a verb is to signify affirmation.  But the word
"affirmation" also signifies affirmation!

The science of Chemistry uses words or symbols for things like hydrogen,
oxygen, etc, and combines them in certain ways to get signs for chemical
compounds such as water.  The science of semantics (if there can be such)
cannot do this.  We cannot combine signs for the component meanings of a
sentence, to give a sign for the meaning of the sentence.  Otherwise we
would be asserting things like "grass is green", which is not an issue for a
theory of meaning.  Crispin Wright has a brilliant paper on this sort of
problem called "Why Frege does not deserve his grain of salt", but I don't
have journal reference (I think Nous).  Crispin argues that if "is a horse"
signified the Concept Horse, then "Shergar is a horse" would mean the same
as "Shergar the concept horse", which doesn't really mean anything at all.

I have a draft paper about the endless tangles and confusion that Frege and
others got caught up in (e.g. Frege's idea of the "judgment stroke") , with
this issue.  Email me if interested.

dean.buckner at btinternet.com

8.  On the connection, hinted at by Harvey Friedman (Fri, 30 Aug 2002)
between the Liar and Russell's Paradox.  I think there is a connection, but
maybe not the sort Harvey would like.

Mathematicians love functions.  For a grammarian, these are merely a way to
construct one noun phrase out of another.  They are just one small part of
the machinery of as sentence (analagous to expressions like "the father of
..."). The expression "f(a)" names an object, so does the expression "a".
Frege got into a horrid mess by imagining that the relation between logical
subject and logical predicate could be represented by a function.  Thus
"is_green()"  is the function, "grass" the argument, thus "is-green(grass)"
names an Object.  What?  No end of trouble, you can trace the anguish from
Frege's very earliest papers to stuff he wrote almost to his dying day.
We're still living the consequences of the mess, e.g. the ideas of
"propositional function" and "truth-function".

The mess is the result of ignoring how sentences are built up, ignoring
their grammar. Sentences express their meaning using components that aren't
noun-phrases at all, and we run into trouble when we try and access these
using such phrases (i.e. functions).

Is it impossible that Russell's paradox is the result of ignoring the strict
grammatical prohibition on representing the content of a predicate by a noun
phrase?  There seems a strong resemblance between the problems of
"getting to" Absolute Infinity, and those of talking about the semantic
contribution of the parts of sentences which are not noun phrases.

That is of course just an idea.  Though I would claim reasonable academic
competence (and have published work on) the problems mentioned above, I
claim *no* expertise in the subject of transfinite mathematics.

In summary: any theory of meaning has to be expressed in language somehow.
Any theory of meaning has to talk about meaning at some point.  To talk
about things is difficult without using noun phrases.  But there are, as it
were, some aspects of meaning that can't be named, and thus can't be talked
about.  Difficult eh?

Dean Buckner

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