Score Card
1. Reference theory of propositions: Every meaningful proposition, whether true or false, refers to
something, and is true or false depending on the nature of its referent. (For Frege, all true propositions
refer to the True, and all false propositions refer to the False; for others [such as the very early Bertrand
Russell, whom we haven’t read], true propositions refer to really existing facts, and false propositions
refer to “facts” that “subsist” or have “being” but lack real existence.)
The problem with such a view is that it fails to explain how there can be meaningful propositions
that are false. After all, if false propositions referred to something (the False, non-existent “facts”,
etc.), then why wouldn’t they be true of it?
2. Idealistic theory of meaning: All meaningful words have as their primary meaning just subjective
ideas (such as mental images) literally contained within the speaker’s mind.
(This is incompatible with Frege’s view that two or more people can think and talk about literally the
same thought.)
3. Copulation (subject-predicate) theory of propositions/judgments/assertions: Every proposition
i.e., every thought that is either true or false, has just one predicate and – crucially – just one subject. A
proposition affirms (or denies) that all (or some) of the subject is contained in the predicate.
(This is incompatible with Frege’s inclusion of two-or-more-place relations in his formal logic.)
4. Implicit denial of Frege’s context principle: Words have meaning independently of their possible
uses in propositions. That is, individual words are semantically prior to propositions.
(This is incompatible with Frege’s treatment of predicates as functions, and Russell’s theory of
definite descriptions, both of which analyze the meaning of these terms not in isolation, but only in
the context of the propositions in which they occur.)
5. Generality theory of predicates: All predicates have not only an extension (i.e., the set of things that
the predicate applies to), but also an intension, or sense. According to the generality theory of
predicates, a predicate’s intension is a set of characteristic features that applies “generally” to the things
in its extension. A predicate’s extension is determined by its intension.
(This is incompatible with Frege’s view that predicates are just functions that map arguments –
either objects or truth-values – onto truth-values.)
6. Containment theory of analyticity (= logical truth): A proposition is analytic (= logically true) if
and only if the intension of the predicate is contained in the intension of the subject. (For example, the
proposition “All bachelors are unmarried” is true because “bachelor” just means “unmarried male”.
Therefore the intension of the predicate, “unmarried”, is contained in that of the subject, “bachelor”.
(This is incompatible with Frege’s inclusion of two-or-more-place relations in his formal logic.
After all, how could a relation possibly contain the things that it relates? For example, how does the
relation of is greater than “contain” the arguments 3 and 2? It is also incompatible with the fact that
there are some analytic propositions that can’t be forced into the subject-predicate form – such as “If
rain makes the streets wet and it rains, then the streets get wet”, which has the form
“([r  s] & r)  s”.)
1
2
3
4
5
6
Locke Y
Frege Y
Russell N
T.L.-P. N
Phil. I. N
Y
N
N
N
N
Y
N
N
N
N
Y (Leibniz) Y
N  N  N
N
N
N
N
N
N
N
N
N
28
7. Intension (“sense”) theory of proper names: Every meaningful proper name not only refers
to a particular thing, but also has an intension (i.e., a sense), which determines its reference.
Thus a proper name refers to a particular thing in exactly the same way as – according to the
generality theory of predicates – a predicate has an extension: by way of a set of characteristic
features contained in its intension. A proper name refers to just one thing because these
characteristic features apply just to that thing.
(This is incompatible with Russell’s theory of singular terms. Definite descriptions [i.e.,
singular terms containing “the”] lack a sense because, as their logical analysis shows, they
have no meaning in isolation, but only in the context of a whole proposition. And genuine
names lack a sense, because they get their meaning by referring directly to an object.)
8. Definition theory of logical analysis: All logical analysis proceeds by means of nominal
definitions, i.e., by replacing one term whose meaning is complex with a set of terms whose
meanings are simpler. Logical analysis is thus conceived on the model of breaking apart a
physical object into smaller bits.
(This is incompatible with Russell’s theory of definite descriptions, which can only proceed
by analyzing whole propositions that contain “the” – not just singular terms taken in
isolation.)
9. Reference theory of meaning: The primary meaning of any term is either its logical
definition or the object to which it refers. Thus every meaningful word ultimately gets its
meaning by referring to, signifying, or designating just one thing. This is equally true of proper
names, predicates, and logical constants (e.g., “all”, “some”, “not”, “and”, “or”).
(This is incompatible with Wittgenstein’s view that an expression’s meaning is just its
contribution to the sense – i.e., the truth-and-falsity-conditions – of the propositions in which
it occurs.)
10. Clarification theory of logical analysis: The logical analysis of a proposition always gives a
clearer expression of the sense of the proposition than is given at the surface level of language.
11. Final analysis thesis: The logical analysis of a proposition must come to an end after a finite
number of levels of analysis, and consists entirely of simple (= primitive, indefinable,
unanalyzable) terms.
12. Humpty-Dumpty theory of meaning: All linguistic meaning is determined by the speaker’s
intentions.
The score so far:
1
2
3
4
5
6
Locke Y
Frege Y
Russell N
T.L.-P. N
Phil. I. N
Y
N
N
N
N
Y
N
N
N
N
Y (Leibniz) Y
N  N  N
N
N
N
N
N
N
N
N
N
7
8
9
10
11
12
Y (Leibniz) Y (Leibniz)(Leibniz) Y
Y
?
Y
Y
?
?
N  N
Y
Y
Y
Y
N
N
N
Y
Y
?
N
N
N
N
N
N
29
13. Generality theory of analyticity (= logical truth):
A proposition is a priori (i.e., knowable independently of sense-experience) if and only if it
mentions no particular objects, or (for Frege) can be proved using only such propositions. Non-a
priori propositions are a posteriori (i.e., knowable only on the basis of sense-experience). Thus
propositions such as “blue plus yellow is green” are a priori, but propositions such as “my book
is green” are a posteriori.
A proposition is analytic (i.e., logically true) if and only if it is both a priori and mentions no
particular properties, or (for Frege) it can be proved using only such propositions. Non-analytic
propositions are synthetic.
(This is incompatible with Wittgenstein’s view that a proposition is analytic if and only if it
is true in virtue of its structure alone [and not how the world happens to be]. Thus for
Wittgenstein analyticity has nothing to do with generality. What analyticity does have
everything to do with is necessity. That is, every analytic proposition [what he calls a
“tautology”] is necessarily true, i.e., denying it would be a contradiction. [Sometimes
philosophers characterize necessity as “truth in all possible worlds”.] Neither Frege nor
Russell had a real grasp of logical necessity.)
14. Axiomatic theory of logical proof:
All analytic propositions are either logical axioms or logical theorems. Logical axioms (what
Russell calls “primitive propositions”) are analytic truths that are true “generally” of every
particular thing and every particular predicate. All analytic propositions can be proved using just
these axioms. Frege hoped to be able to demonstrate that the propositions of arithmetic are
analytic, by proving them using a small set of (six) logical axioms.
(This is incompatible with Wittgenstein’s view that all analytic propositions are tautologies
(i.e., true just in virtue of their structure), and that this can be demonstrated just by analyzing
them and displaying them in a truth-table. Thus it’s possible to prove that a proposition is
logically true without using any logical axioms. Thus logical axioms are unnecessary.)
15. Platonic (= Realist) theory of logical truth:
Analytic propositions contain only “logical constants”, i.e., words such as “all”, “some”, “and”,
“not”, “or”, etc. In keeping with (9), the reference theory of meaning, each of these words gets
its meaning ultimately by referring to “logical objects”. Much like Plato’s Forms, logical objects
are eternal, unchanging, non-physical, but also non-mental. Analytic propositions are true just
because they correspond to “logical facts”, i.e., relations holding among logical objects. We can
understand analytic propositions because our minds are acquainted with these logical objects.
And we can know that analytic propositions are true because our minds can “intuit” the relations
holding among them.
(This is incompatible with Wittgenstein’s view that the meaning of a “logical constant” is
just its contribution to the sense of the propositions in which it occurs. And this contribution
is just to make complex propositions out of elementary propositions. Thus since the logical
constants don’t get their meaning by referring to objects, there are no logical objects.)
The final score:
… 9 … 13
Leibniz…Y… Y
Frege …Y… Y
Russell …Y… Y
T.L.-P. …N… N
Phil. I. …N… N
14
Y
Y
Y
N
N
15
N
Y
Y
N
N
30