[hist-analytic] Russell's Early View on Meaning

Roger Bishop Jones rbj at rbjones.com
Fri Sep 25 17:23:34 EDT 2009

On Friday 25 September 2009 12:43:09 Baynesr at comcast.net wrote:
>In my book I devote a few pages to the use of the private language argument.
> Along the way, I became curioius about the origin of the idea that meaning
> is what an expression has in common with its translation. One finds this
> idea throughout the literature in semantics. Few state the thesis
> explicitly but do accept it at least implicitly. Quine is explicit on this
> in Word and Object (p. 32).
>However I notice it is, also, explicit in Russell's very early work, circa
> 1904. I'm wondering if this originates with Russell. I think it does. I
> don't think it is anywhere in Frege but it has been a long time since I
> looked at Frege seriously.

There is an analogy with the notion of cardinal number here,
which is a model for a general technique of abstraction used
in set theory (though awkward in well-founded set theories).

Frege's definition of cardinal number, also adopted by Russell,
is an equivalence class under equipollence.
i.e. a class of sets all of which are related by one-one
correspondences. Following this pattern it is possible to define
a meaning as an equivalence class of synonymous expressions.
I suppose this does go one step further, representing
a common notion by an equivalence class.
(I think the first bit came from Cantor,
but I don't know whether he identified the cardinal number
with the equivalence class, he might have realised that
it would be an inconsistent totality.)

Generally, if you don't know what kind of thing some characteristic
is, but you do know the identity conditions for the characteristic,
then you can identify the characteristic with an equivalence class.
In mathematics this is fine, because you generally don't care
exactly what something is, you just care how it behaves, and you
just chose a kind of set over which you can define the operations
you need to get the desired mathematical structure.

This also points out a weakness in the simple formulation
     "meaning is what an expression has in common with its translation".
If you just take a single translation then the sentence and its
translation may have things in common which are not part of the
meaning of the sentence.
For example, it is possible that some sentence may have a translation
which has the same number of words, so we might then imagine 
incorrectly that the number of words in the sentence is part
of its meaning.
For something to be part of the meaning it would have to be
common to all translations, and that would probably have to
include into possible languages as well as actual languages.

However, this seems to me to be less profound (or useful)
than you might imagine.
Its really just an odd way of saying that translation is
a mapping between languages which preserves meaning.
Neither of these ways of talking about the relationship
between meaing and translation really helps a great deal
in understanding semantics.

> Does anyone know of an earlier statement of this
> position? By the way, this position leads Russell to regard meaning as an
> abstract entity, a position he later abandons; but when he abandoned it
> later what became of his view of the idea of a meta-language as a result if
> anything?

I'm interested to know when and how he abandoned the idea
that meanings are abstract.
(or indeed exactly what that means)

In "The Philosophy of Logical Atomism" he talks of propositions,
which I'm guessing he takes to be the meanings of sentences,
as complex entities which will include concrete elements,
(e.g. the objects named in the proposition).
So they are neither purely abstract nor concrete.
I would guess in his metaphysics they are logical fictions
(logical constructions).

I'm not acquainted with "the idea of meta-language" you speak of above.

Roger Jones

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