FOM: Frege and singular propositions

[Dean Buckner]

A correspondent has suggested that Frege never held any theory of "direct"
reference.  However:


(1) In the closing parts of the his review of Schroder's Logic (Geach/Black
pp86-106) Frege spells out pretty clearly how the semantic relation between
a common name and the objects that "fall under" it is indirect, whereas that
between a proper name (which for Frege also means a definite description)
and its bearer is by contrast direct.

(2) There follows the "African chief" argument which Gareth Evans echoes in
Varieties: "all men are mortal" does not say anything about "some Chief
Akpanya".  By inference, singular propositions are essentially *about* their
subjects (cf Evans p. 64).

(3) Frege says here, and in many other places, that empty singular
propositions aren't really propositions at all.  He is following an old
tradition according to which  "logical meaning" belongs only to what is
capable of being true or false.  "Pegasus flies" therefore cannot express a
thought.  See for example Locke (Essay) Bk II. xxxii. 1, or indeed any old
(pre-Frege) textbook on logic

(4) Suggest reading the first chapter of Evans, where he argues that
"Frege held, both before the distinction between sense and Meaning [i.e.
reference] and, despite appearances, after it, a highly Russellian view of
singular terms" (p. 38)

(5)  See also an early pre-sense & reference version of the Akpanya argument
in Grundlagen.  Frege may have been addressing Mill's argument, which was
well known in its time, that "all men are mortal" actually asserts the
proposition that Socrates is mortal.  (thus making it unnecessary to
postulate that Socrates is man, in order to prove he is mortal - this was
known as the petitio principii problem).  (See S.O.L. II. iii. 1. & passim)

(6)  In "Sense and Reference" itself Frege says that in singular
propositions we presuppose, rather than assert the existence of the subject.
i.e. in "Venus is a planet" we assert the existence of something falling
under "planet", but we presuppose the existence of something corresponding
to "Venus".  This also is connected with a 19C dispute see e.g. Ueberweg,
who Frege may have studied.  Bosanquet (Logic) also discusses it.

Strawson famously resurrected this idea in a paper ("On Referring") that for
many years was taken as an argument against Frege (rather than as a
re-statement of the Fregean position).  The idea of "sense" was for many
years confused with Russellian descriptions, which of course embed general
terms.

(7) If "Pegasus flies" has a logical meaning, then we could of course talk
about "Pegasus" being satisfied (namely by Pegasus existing).  But Frege
says
we can't.  On Kripke's idea of a causal connection between Names and their
bearer, well, this connection has to be more than just accidental, otherwise
we could speak of the set of things satisfying "Pegasus" being a subset of
the things that satisify "flies".  This is precisely what Frege has to
avoid, and precisely why he (and perhaps Peano) needs a symbol for "is a
member of".  The object has to "get through" to the surface of the
proposition, I don't see how a merely causal connection can achieve this.
Searle's arguments are still pertinent i think.

(8)  We should not confuse the distinction between sense and reference with
that
between connotation and denotation.  "Denotation" is what Frege calls the
satisfaction (Erfuellung) of a concept.  Connotation is what he calls the
Bedeutung of a concept-word.  The idea that proper names also have a
Bedeutung (a significance, a connotation) may also be an argument against
Mill, who as is well known thought proper names had no meaning.  Mill got
this idea from Reid (Essay), who in turn got it from Aristotle (Metaphysics
1040a 27 - b2 & elsewhere).  Traditional logicians thought we had no
"singular concepts" at all.  They believed in singular propositions, but
that's because "proposition" originally meant a sentence of a certain kind
rather than, as now, a thought or meaning.

On the idea of "sense", it's an incoherent idea that Frege incorporated in
order to address the problems about "direct" reference, namely that
emptynames seem to be perfectly meaningful, and that we seemingly cannot
substitute names for the same thing in "that" clauses.

Frege's biggest single contribution to logic was his incorporation of the
singular proposition into logic.  This, as I say, is inseparable from the
ideas that "is a member of" is distinct from "is a subset of", that sets are
different from their members, that there can be empty sets, singleton sets,
infinite sets indeed, and that their is a fundamental difference between
common and proper names, general and singular propositions.  No other
philosopher before Frege (as far as I know) had ever proposed this.

(9) The problem of direct reference is to explain singular existential
propositions, and this is a defect of Frege's theory as much as of any
contemporary one.  "unicorns do not exist" says (for Fregeans) that the
concept "unicorn" is unsatisfied.  We can't do the same for "Pegasus does
not exist", and Frege says this in many places.  In one place, (the dialogue
with Punjer) he thinks we could say "there is no x such that x = Pegasus".
But his own theory should condemn this for then we could speak of the class
of x's such that x = Socrates, and then singular propositions could be
re-analsysed as general ones.  "Socrates is wise" would subordinate the
class satisfying "x is Socrates", to the class "y is wise".  This we cannot
do.  This is exactly why we need Peano's symbol!


"With a concept the question is always whether anything, and if so what,
falls under it.  With a proper name such questions make no sense"
Grundlagen ( ~51 )


Dean


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