[hist-analytic] Carnap on Philosophy

Roger Bishop Jones rbj at rbjones.com
Sat Aug 8 12:09:25 EDT 2009

Steve's recent message raised a number of points in relation to
Carnap and Russell, particularly in relation to their
conception of philosophy as logic.

I'm going to mount a defence of this conception of philosophy
(though my own conception is very much wider than that).

First a few words about the phrase "the propositions of

This should be thought of along the same lines as the
phrase "the propositions of mathematics" when thinking
of the logicist thesis in relations to mathematics.
The phrase is not intended to refer every proposition
asserted by a mathematician, not even those which he
asserts "qua mathematician".  Nor is it to be presumed
that the enunciation of "the propositions of mathematics"
is the only or even the most important contribution
which mathematicians make to our knowledge.
Mathematicians propose definitions, describe methods,
talk about the work of previous mathematicians, about
the value of different parts of mathematics, sometimes
address philosophical matters, and engage in politics
and polemics. Some or all of these may be considered
genuinely mathematical and important, but they do not
consist in the discovery or enunciation of
"the propositions of mathematics".
The propositions of mathematics are those whose
subject matter is properly mathematical and which have
been proven by accepted methods.  This is a crude
characterisation, but probably good enough for
present purposes.  A more concise and precise modern
approximation is: those mathematical propositions
which can be rendered and proven in first order set theory.

The phrase "the propositions of philosophy", when used
by Russell, Carnap and Ayer should be understood in
an analogous way.
It may be, and in fact it probably is, that in Carnap's
conception of philosophy the principle task of the
philosopher is to make proposals about languages,
about analytic methods, about conceptual schemes, or
even about ostensibly metaphysical matters such
as "what exists", but none of this consists in the
enunciation of "propositions of philosophy" in the
sense in which this phrase is used when these are
asserted to be analytic.
Most importantly one must be aware of the distinction
between making a proposal, and making a claim, for
so much of Carnap's philosophy must be understood
as the former rather than the latter, even though
in his youthful enthusiasm, like Ayer, he often uses
language which sounds much more assertive and dogmatic
than one would expect from someone merely
making a proposal.
This is particularly relevant to ontology and metaphysics.
Carnap was happy to propose languages in which abstract
entities can be proven to exist, but not happy to
assert, except as propositions internal to such a
language (and in that case analytic) that abstract
entities exist.  This extends arbitrarily to any
apparently metaphysical claims which Carnap might
consider of practical utility, e.g. talk about

It might be useful to state my own position, which
I intend to articulate in my volume on Metaphysical
Positivism, since that is what I advocate, and my
defence of Russell and Carnap is based on my belief
that their position was similar in the most important

Metaphysical Positivism is a variety of analytic
philosophy based around a method of logical analysis,
the intention of which is to make deductive arguments
in philosophy as reliable as they are in mathematics.
The method is illustrated by my document on Aristotle
in which I have used formal modelling with ProofPower
in an attempt to analyse the logic and metaphysics
of Aristotle.
This document contains two parts, an informal part
and a formal part, of which the latter consists in
large part of definitions of various kinds, and of
theorems proven in the context of those definitions.

There is a clear distinction in this paper between
propositions which have been formally proven and
everything else.
The former are marked by the turnstile symbol "|-",
and are also listed separately in the appendices.
In the appendices are theory listings which contain
all the formal definitions and the theorems proven
from them.  These theorems are known to be necessary
with a very high level of confidence, it is improbable
that they will ever be refuted.
Everything else in the document, including the
question of whether the formal models have any relevance
to the work of Aristotle, is highly speculative. 

The idea of the method is to ensure the rigour 
of deductive reasoning in philosophy, in a way which
does not constrain the scope of philosophy.

Now, I believe that Russell and Carnap sought by similar
means (though lacking the technology) to establish
philosophical reasoning on a similarly solid footing.
They diverge from the neutrality of my method
(which says nothing about scope of philosophy),
in the addition of either or both of:

1. Claims about what philosophy is.
2. Claims about what philosophy should be.

I don't in fact believe that either philosopher
could credible be said to believe, despite their
explicit statements appearing to assert it, that
philosophy IS logic, and we can see when we read
them that they are rather advocating that it should
In this they are also to be understood in the manner
suggested above, as talking only of a rather select
number of the things which philosophers assert,
and with that caveat I think we can say that there
is very little between their position and my
advocacy of formal methods.

Let me now pass to some detailed responses on how
I believe these philosophers should be understood.

On Saturday 01 August 2009 12:45:42 Baynesr at comcast.net wrote:
>"Among the valid sentences some are analytic, namely
>those which are valid on the basis of the L-rules alone"
>Now if philosophy is the search for analytical sentences then it is the
> search for L-rules, 

I don't believe that Carnap would agree here,
and nor do I.
The L-rules constitute the definition of a language,
and they are thus proposals rather than results.

Insofar as philosophy is "the search for analytic truths"
(I would not put it that way myself), these analytic
truths are not the L-rules, which are implicit definitions
rather than propositions, but in those sentences whose
truth can be established by the use of the L-rules.

> and if Carnap can be said to follow Russell remarks:
>"Philosophy, if what has been said is correct, becomes indistinguishable
> from logic as that word has now come to be used,"
>the actual record of his work should show it. It does not.

Yes, "indistinguishable from logic" is a bit strong, especially
as that phrase might today be understood
(given that logic is now largely meta-theoretic, and "logical
truth" tends to be narrowly construed).
However, I will try to defend Carnap's claim about the propositions
of philosophy being analytic (in the context of his demarcation
of philosophy).

>I won't repeat what I've already said about Carnap's methodology. That
> methodolgy consists in the construction of formal metalanguages that
> translate from an object language into the "syntax language." The
> "analyticity" of the analytical propositions is not in the sentences
> translated into. The "analyticity" resides in translatability from one
> language to another, that is capturing the meaning in the syntax language
> that remains once the "dross" is removed from object language. But there is
> a problem for Carnap's methodology.

I'm afraid I don't accept this account of Carnap's philosophy.
Semantic ascent does, unfortunately and unnecessarily, play a
role in his method of logical syntax, but to say that his method
consists in the construction of formal metalanguages to effect
the translation seems to me incorrect.
As far as his statement of method in "Philosophy and Logical Syntax"
is concerned, he does not to my recollection even mention
such formal languages, and it might be reasonable to criticise
the method he describes in that book because it lacks
any account of how this translation is to be effected.

The languages which he talks about defining there are, I think,
intended to be various languages for use in science.

The analyticity of the analytic propositions does not reside
in their translatability.  This is simply the method proposed
for demonstrating their analyticity.
We take a sentence in some formally defined language which
mentions "pseudo-object" and we demonstrate the analyticity
of that sentence via translation into some sentence about

However, if we look at the more precise statements in
LSL about the translation we find, to my relief, that its
role is largely one of explication.
Carnap does not tell us, even in LSL, how the translation
is to be accomplished, but he is quite precise about what
it must deliver.  It must deliver something which is
"equipollent" with the original.
So the method says, to prove a pseudo-object sentence,
take the sentence and translate it into some equipollent
sentence which is L-true, and then prove the translation
using the L-rules.
But "equipollence" is L-equivalence I believe, and in any
reasonable logical system, all L-true sentences will be
equipollent, and any sentence equipollent with an L-true
sentence will be provable using the L-rules whether or
not one proves it via an equivalence with some sentence
which is about syntax.

Carnap's stuff about translation is therefore inessential.
You have to supply a complete set of L-rules in the definition
of the language to fully capture the intended semantics,
and if you do that then all the analytic sentences will
be L-true, whether or not they mention objects.
Carnap's talk about analytic sentences being "about syntax"
(which I deprecate) can be seen to be a very minor defect,
since the methods proposed work just as well if you
delete all talk of semantic ascent.
It is only Carnap's explanations which are damaged by the

>It is not always clear what kind of translation you want and what and why
> you omit certain concepts is, also, subject to debate. Logic cannot resolve
> these questions, even for Carnap.

I hope I have now covered this.

> The Schilpp is fine for an idea of
> Carnap's final position on issues, but it is no substitute for approaching
> the original sources if your interest is understanding where is coming
> from.

Yes, but if his final position is more tenable than the earlier ones,
then a critique based too closely on the earlier work may not
be a sound critique of the overall conception.

> The problem for Carnap's methodology is that there are always
> sentences that logic simply cannot resolve. If I am right these are the
> philosophical questions. Let me give you an example. Carnap in Meaning and
> Necessity says,
>"Some remarks may help toclarify the sensein which we intend to us theterm
> 'proposition'. Like the term 'property', it is used neither for a
> linguistic expression nor for a subjective mental occurrence, but rather
> for something objective that may or may not be explemfied in nature." (MN.
> p. 27)
>Lest there be any doubt that Carnap is talking about the world and not
> logic, consider what he says just a bit later (after expressing
> disagreement with Russell),
>"Any proposition must be regarded as a complex entity, consisting of
> component entities, which, in their turn may be simple or again complex."
> (MN. p. 30)
>These are not analytic statement!

They probably are.
Even for Russell, who understood a proposition as a logical fiction
with real constituents, it is analytic that a proposition is complex.
Carnap might well have taken the position that propositions are
completely abstract, in which case any truth about them is going
to be analytic.

> They do not follow from logic alone; they
> are not empirical claims.  They are metaphysical CONCLUSIONS!

But for Carnap any true claim which is not contingent is
analytic and logical.
L-true, Analytic, Logical, Necessary all mean the same thing.
And you can't argue this, it is a proposal for use of language,
and the entire philosophy has to be understood in relation
to this proposal.
You can reject then proposal if you like, but you can't
adopt some other usage and then criticise Carnap's claims
about analyticity of philosophy as if he meant by that term
something other than he actually did mean.

> The problem
> for Carnap is that he must at some point exorcise these ontogical
> commitments.

Carnap has a well articulated position in relation to such
things, both I think in relation to his syntactic and his
semantic phases, though I think the latter stronger.
This later one is of course that in
         "Empiricism, Semantics and Ontology".

>Take Russell. The guy quoted above identify logic with philosophy. NONE of
> Russell's philosophical work of significance is pure logic. Take The
> Analysis of Matter or even Our Knowledge of the External World or many of
> those essays in Mysticism and Logic. Very little logic in these works. In
> fact the best logic in the second cited is on continuity and I don't think
> continuity is a logical notion as such.

Russell, it seems to me, made less serious attempts to carry through
his logicist conception of philosophy, partly I think because
his appetite for formalism had been quenched by Principia.
Also I think he actually had a rather less formal conception
of the key features of Principia Mathematica (than Carnap).

Russell had a conception of analysis.  He begins with
a kind of analysis which he inherited from Leibniz,
in which complex predicates are analysable into
simple predicates (which I think is questionable).
His more original contribution is that of logical construction.
In the Principia mathematical objects were logical constructions
from individuals.
Russell following ideas of Whitehead, wanted to show that
mind and matter, and hence all else, could both be construed
as logical constructions from individuals (events? sense data?).

Now if talk about mind and matter is talk about logical
constructions of this kind, then claims to that effect
will be analytic elucidations of the meaning of the concepts
and of conclusions inferred from those meanings.

So I think there is a rationale here which might explain
how Russell could conceive of at least some of his
post Principia philosophy as logic (if not formal).

I would draw an analogy here with theoretical physics.
Theoretical physics might seem to be about material
objects and hence to be making contingent claims.
But a theoretical physicist is likely to be doing
just mathematics. He makes no empirical claims,
he simply takes some theory as given, e.g.
general relativity, and works out the logical
consequences of the theory (the mathematical
consequences, which for logicists are logical).

Russell's "analysis" of mind and matter is not intended
to make contingent claims about mind and matter,
it is intended to draw conclusions from the concepts.
Possibly to be drawing conclusions from proposals about
what the concepts should mean, but possibly not
for Russell seemed to have a natural metaphysical
dogmatism, which I agree is a bit at odds with
his logicist conception of philosophy.
Carnap seems to start out with that same conflict,
but as he matures he realises that he must present
himself as making proposals about languages and methods
if his philosophy is to be self-consistent.

>So my polint is: Carnap makes a lot of metaphysical claims; the metaphysical
> work is done before constructing canonical languages. As Bergmann said:
> there is a metaphysics to positivism! Carnap was such a metaphysician
> during his most productive years.

Carnap has to be construed as proposing or adopting a particular
usage of "metaphysical" as well as of concepts like "analytic".
In "Philosophy and Logical Syntax" he does explicitly exclude
certain kinds of metaphysics from the scope of his critique.
His account is on p15, he has a paragraph beginning:

    "I will call metaphysical..."

and says:

   "I do not include in metaphysics those theories -- sometimes
    called metaphysical --
    whose object is to arrange the most general propositions
    of the various regions of scientific knowledge in
    a well-ordered system."

These he regards as empirical.
To this one may add, certain non empirical claims about
abstract objects, e.g. those of mathematics, which he
regarded as analytic.

When we progress to the later philosophy, when he
adopts the principle of tolerance and writes about
ontology in "Empiricism, Semantics and Ontology",
we find an enormous range of what might have been
thought of as metaphysics, has now been slotted into
Carnap's scheme of legitimacy.

So to condemn Carnap of inconsistency it does not suffice
to establish some proposition of metaphysics which he
asserts.  Usually when he does this he should be
construed either as putting forward a proposal for
usage, or as elaborating the consequences of such
proposals.  (I don't think he engages in the synthetic
metaphysics which he finds acceptable, because that
would not be philosophy).

Too many words I'm afraid, but I have tried to explain
why I do not myself think, on the basis of my rather
limited reading of Carnap that his properly
philosophical assertions violated his conception of
philosophy as analytic.
I do accept however, that there probably were such
things, I think it would be a great achievement
if he had been consistent about this in the course
of trying to put together this conception of philosophy,
it is normal for philosophers not to comply with their
own conception of philosophy, but I think Carnap came
closer than most, and that a similar conception
of philosophy could be consistently adopted.
i.e. whatever other faults it has, I don't think
it is an incoherent conception of philosophy.


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