Notes for Philosophy of Language – University of Oslo
A. Compositionality Requirement
1. “I propose what seems to me clearly to be a necessary feature of a learnable language:
it must be possible to give a constructive account of the meaning of the sentences in the
language. Such an account I call a theory of meaning for the language, and I suggest that
a theory of meaning that conflicts with this condition, whether put forward by philosopher,
linguist, or psychologist, cannot be a theory of a natural language; and if it ignores this
condition, it fails to deal with something central to the concept of a language” (Davidson,
Inquiries, p. 3, emphasis mine)
2. A constructive account of the meanings of sentences in a natural language requires that
we be able to define a predicate that applies to all and only grammatical sentences of the
language, and, as Davidson puts it: ‘that we...be able to specify, in a way that depends
solely on formal considerations, what every sentence means’ (Inquires, p. 8).
3. A compositional meaning theory for a language L specifies what every sentence in L
means by exhibiting its meaning as a function of the meanings of its significant parts and
their arrangement in the sentence.
`Snow
is white' means that snow is white.
`Grass is green' means that grass is green.
`Water is wet' means that water is wet
………
B. Argument for Compositionality
1. Natural languages contain an infinite number of non-synonymous expressions, and in
particular, an infinite number of non-synonymous sentences.
2. We can (keeping fixed our cognitive capacities and life spans) learn natural languages.
3. "...we do not at some point suddenly acquire an ability to intuit the meanings of
sentences on no rule at all".
4. "...each new [i.e., semantically primitive] item of vocabulary, or new [primitive]
grammatical rule, takes some finite time to be learned";
5. "...man is mortal" (Inquires, pp.8-9).
6. Therefore, natural languages have "a finite number of semantical primitives" (Inquires,
p.9) (follows from premises1-5)
7. Therefore, it must be possible to give an account of how the meanings of an infinite
number of non-primitive expressions in natural languages are determined in terms of a
finite vocabulary of semantic primitives.
Semantic Primitive: An expression is a semantic primitive provided that the rules which
give the meaning for the sentences in which it does not appear do not suffice to determine
the meaning of the sentence in which it does appear (Inquires, p. 9).
C. Understanding Language
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1. A theory of meaning "explicitly states something knowledge of which would suffice for
interpreting utterances of speakers of the language to which it applies" ("Reply to Foster,"
my emphasis, Inquires, p. 171);
2. "What could we know that would enable us [to interpret another's words]...[This] is not
the same as the question what do we know that enables us to interpret the words of
others. For there may easily be something we could know and don't, knowledge of which
would suffice for interpreting, while on the other hand it is not altogether obvious that there
is anything we actually know which plays an essential role in interpretation" ("Radical
Interpretation," Inquires, my emphasis, p. 125)
3. "All that we should require of a theory of truth for a speaker is that it be such that IF an
interpreter had explicit propositional knowledge of the theory, he would know the truth
conditions of utterances of the speaker"
4. "A theory of truth for a speaker is a theory of meaning in...that explicit knowledge of the
theory would suffice for understanding the utterances of that speaker" ("The Structure and
Content of Truth," my emphasis, Journal of Philosophy, 87, 1990, p. 312)
D. Ordinary Sense of Meaning
5. "...that task of a theory of meaning as I conceive it is not to change, improve, or reform
a language, but to describe and understand it" ("Truth and Meaning," p.29).
6. Like Quine, I am interested in how English and languages like it (i.e., all languages)
work, but unlike Quine, I am not concerned to improve on it or change it. (I am
conservative and he’s the Marxist here (Davidson, "Reply to Qine on Events", in Actions
and Events, 1985, eds., E. Lepore and B. McLaughlin, p. 172).
E. Compositional Meaning Theory
7. A compositional theory of meaning in the sense in which Davidson seeks one is (i) a
formal theory with (ii) a finite number of rules and (iii) a finite number of semantical
primitives which (iv) enables us to specify the meaning of every sentence of the language.
8. We would have the sort of theory we want if we had a theory meeting the constraints (i)(iii) and which entailed for each sentence of the object language L a sentence in the metalanguage of the form
(M) s in L means p
where 's' is replaced by a structural description in the meta-language of a sentence of the
object language; and 'p' is replaced by a sentence of the meta-language which means the
same as the object language sentence denoted by the structural description that replaces
's'.
F. Reifying Meanings
9. What is the meaning of 'rouge' in French?
10. What is you favorite book?
G. The Third Man Argument
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13. If we assign Virginia Woolf as the meaning of 'Virginia Woolf' and the property of being
the author of A Room of One's Own to 'is the author of A Room of One's Own', this tells us
nothing about what the meaning of 'Virginia Woolf is the author of A Room of One's Own'
is.
If we add that concatenating 'Virginia Woolf' with 'is the author of A Room of One's Own' is
itself a bit of syntax with meaning, and which is what combines the meanings of 'Virginia
Woolf' and 'is the author of A Room of One's Own', to be consistent we must treat it as
an entity as well, and then again we must ask how our three meanings go together to
generate the meaning of the whole, and we are no further than when we started.
14. “One may well ask what it adds to our understanding of an expression (or ability to
"grasp its meaning") to be told it corresponds to an entity when all we are told of the entity,
in effect, is that it is the meaning of the expression. When this is the only function served
by an entity within the theory then those who wish to be parsimonious may simply reject
the entity in question without serious consequences for Carnap's theory. In such a course
they may find encouragement in Carnap's remark that sameness of meaning can be
explained without reference to "problematic entities," provided we understand the concept
of truth and L-truth. Once superfluous entities are weaned on (suppose there are such),
the serious question will remain what entities MUST be presupposed in order to interpret
the sentences of Carnap's languages” (Davidson, ‘The Method of Extension and Intension
in Carnap’, Library of Living Philosophers vol. on Carnap, pp. 319-20).
Consider a language L consisting of a fragment of English containing the expression 'the
father of' and some proper names (say, those of Virginia Woolf and the members of the
Bloomsbury group) as the only referring terms. We might assign as a meaning to 'the
father of' a function which maps persons to their fathers. This does NOT help to explain
how the concatenation of 'the father of' and 'Virginia Woolf' denotes the father of Virginia
Woolf.
15. For any referring term r, the concatenation of 'the father of' with r refers to the father of
what r refers to.
16. __ refers to ..., where we replace '...' by the term that __ refers to, as in, e.g., 'Virginia
Woolf' refers to Virginia Woolf.
Use/Mention
14. Clemens is the name given to a famous American author by his parents.
15. Clemens is Twain.
16. Therefore, Twain is the name give to a famous American author by his parents.
17. `Clemens' is the name given to a famous American author by his parents.
Exercise 1: We will use single quotes in order to mention (name, or refer to) an
expression. So, for example, ``Italo Svevo'' mentions the name `Italo Svevo', which in turn
mentions the person Italo Svevo. Using single quotes according to this convention,
punctuate (1)-(5) in a way that renders them true.
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1. Saul is a name of Paul.
2. 2 + 2 = 4 is a mathematical truth.
3. Italo Svevo is a pseudonym of Ettore Schmitz.
4. 2 + 2 = 4 is named by 2 + 2 = 4, which in turn is named by 2 + 2 = 4.
5. Even if x is the 24th letter of the alphabet, some writers have said that x is the unknown.
Exercise 2: Assuming that single quotes are used in accordance with our convention,
which of (1)-(6) are true?
1. `The Iliad' is written in English.
2. `The Iliad' is an epic poem.
3. `The morning star' and `the evening star' mention (denote) the same planet.
4. `7 + 5' = `12'.
5. The expression ``the tower'' begins with a quote.
6. The expression ``der Haifisch'' is acceptable as the subject of an English sentence.
7. `Frank Frisch' names the Fordham Flash.
8. `The Fordham Flash' was the `the best second baseman ever to play for the Cardinals'.
H. The Slingshot Argument
17. (i) that "logically equivalent singular terms have the same reference" and (ii) that "a
singular term does not change its reference if a contained singular term is replaced by
another with the same reference" (Inquiries, p. 19).
18. Here’s the argument:
Let "S" and "R" be two sentences alike in truth value.
"R" is logically equivalent to "{x:x=x.R}={x:x=x}".
From "{x:x=x.R}={x:x=x}" we can obtain "{x:x=x.S}={x:x=x}" by the substitution of the
singular term "S" for "R".
However, "{x:x=x.S}={x:x=x}" is logically equivalent to "S".
Thus, since each of the steps are licensed by premises (i) and (ii), sentence "R" and "S"
have the same referent.
Since we chose arbitrary sentences, it follows that all sentences alike in truth value have
the same referents.
19. Given the meaning of 'Virginia Woolf' as argument to the meaning of 'is the author of A
Room of One's Own' yields the meaning of 'Virginia Woolf is the author of A Room of
One's Own'.
I. Davidson’s Project
20. "... we have found no more help in meanings of sentences than in meanings of words,
let us ask whether we can get rid of the troublesome singular terms that are supposed to
replace 'm' and to refer to meanings. In a way, nothing could be easier: just write 's means
that p', and imagine 'p' replaced by a sentence. Sentences, as we have seen, cannot
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name meanings, and sentences with 'that' prefixed are not names at all, unless we decide
so. It looks as though we are in trouble on another count, however, for it is reasonable to
expect that in wrestling with the logic of the apparently non-extensional 'means that' we
will encounter problems as hard as, or perhaps identical with, the problems our theory is
out to solve. The only way I know to deal with this difficulty is simple, and radical. Anxiety
that we are enmeshed in the intensional springs from using the words 'means that' as
filling between description of sentence and sentence, but it may be that the success of our
venture depends not on the filling but on what it fills. The theory will have done its work if it
provides, for every sentence s in the language under study, a matching sentence (to
replace 'p') that, in some way yet to be made clear, 'gives the meaning' of s. One obvious
candidate for matching sentence is just s itself, if the object language is contained in the
meta-language; otherwise a translation of s in the meta-language. As a final bold step, let
us try treating the position occupied by 'p' extensionally: to implement this, sweep away
the obscure 'means that', provide the sentence that replaces 'p' with a proper sentential
connective, and supply the description that replaces 's' with its own predicate. The
plausible result is
(T) s is T if and only if p.
What we require of a theory of meaning for a language L is that without appeal to any
(further) semantical notions it place enough restrictions on the predicate 'is T' to entail all
sentences got from schema T when 's' is replaced by a structural description of a
sentence of L and 'p' by that sentence (Davidson, ‘Truth and Meaning’, Inquiries, p. 23).
Intensionalty
1. The last president of the U.S. is from the south.
2. The last president of the U.S. = the husband of Hilary Clinton.
3. Therefore, the husband of Hilary Clinton is from the south.
4. Harry believes that the last President of the U.S. is from the south.
5. The last president of the U.S. = the husband of Hilary Clinton.
6. Harry believes that the husband of Hilary Clinton is from the south.
Grammar (syntax) of Language L:
1. `P' is a sentence of L.
2. `Q' is a sentence of L.
3. For any sentence S of L, `-'^S is a sentence of L.
4. For any sentences S and S’ of L, `('^S^`&'^S’^`)' is a sentence of L.
Samples Sentences (Well-Formed Fomulas WFFs):
i.
ii.
iii.
iv.
`(P & Q)' is a sentence of L
`-P' is a sentence of L.
`-(Q & Q)' is a sentence of L.
`(-(P & Q) & P)' is a sentence of L.
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Compositional Meaning Theory I for L
1. `P' means it's raining.
2. `Q' means it's snowing.
3. For any sentences S, and S’, (S^&^S) means whatever S means and whatever S’
means.
4. For any sentence S of L, `-'^S means it is not the case that whatever means.
Sample Derivations
i. `(P & Q)' means whatever `P' means and whatever `Q' means. (from 3 by instantiation)
ii. `(P & Q)' means it's raining and it's snowing. (from 1 and 2)
i. `-P' means it's not the case that whatever `P' means. (from 4)
ii. `-P' means it's not the case that it's raining. (from 1)
Extensional Theory of Meaning
Compositional Theory of Meaning II for L
1. `P' is true in L iff it's raning.
2. `Q' is true in L iff it's snowing.
3. For any sentences S and S’, ‘(S & S’)’ is true in L iff ‘S’ is true in L and ‘S’’ is true in L.
4. For any sentence ‘-S’ is true in L iff it is not the case that S is true in L
Rule of Inference
A. If S is a theorem, and if ‘a iff b’ is a is a theorem, then so is S’ a theorem (where ‘S’
differs from ‘S’’ at most in that is has one or more a’s where S’ has one or more b’s
Sample Derivations.
i. `(P & Q)' is true in L iff ‘P’ is true in L and ‘Q’ is true in L. (from 3)
ii. `(P & Q)' is true in L iff it's raining and it's snowing. (from 1, 3 by rule A)
i. `-P' is true in L iff it's not the case that `P' is true in L. (from 4)
ii. `-P' is true in L iff it's not the case that it's raining. (from 1, rule A)
1. (p)(‘p’ is T if L iff p)
(1') (S)( p)(if `p' translates s, then s is T in L iff p)
Problems for giving a Tarski-style theory of truth for natural languages.
(i) semantic paradoxes.
A simple example is sentence (L). Let's call this sentence `The Liar':
(L) The Liar is false.
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(TL) 'The Liar is false' is true in English iff The Liar is false.
The Liar = `The Liar is false',
(C) The Liar is true iff The Liar is false,
(ii) Syntax and change.
The Problem of Extensionality
A (finite) theory T is a truth theory for language L iff, for each sentence E of L, T entails a
T-sentence of the form:
(T) E is true-in-L iff P.
1. A (finite) theory T is an (interpretive) truth theory for language L iff for each sentence `E'
of L, theory T entails a T-sentence of the form:
`E' is true-in-L iff P
Extensional Adequacy
2. Call a truth theory extensionally adequate iff all the T-sentences that it entails are true.
Problem
Bad -T-sentences
3. (W) `Snow is white' is true iff grass is green.
‘Snow is white’’ is true iff snow is white.
Second proposal
4. Call a T-theory materially adequate if it is extensionally adequate and, in each Tsentence, the condition that P translates `E' is satisfied.
5. Solutions to The Extensionality Problem
Suggestion 1: Exploit the fact that natural languages exhibit compositional semantic
structure; in particular, that the same expressions can recur with the same meanings in
(indefinitely) many formulas. This is the main strategy contemplated in 'truth and
meaning."
Suggestion 2: Require that the T-sentences in favored truth theories be laws. This is the
strategy contemplated in Davidson’s paper 'Reply to foster" and in n. 11, added to 'Truth
and Meaning" in 1982
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Suggestion 3: Require the favored truth theory for L to entail T-sentences according to
which most of the sentences that speakers of L hold true are true. This is one version of
Davidson's principle of charity and is the main strategy contemplated in "Radical
interpretation."
6. Meaning theory must arrive at the truth conditions of "Snow is white" and every other
sentence of the object language in this way that we can expect the right side of the Tsentence to interpret the left side.
7. `This is white' is true iff this is green.
8. In short, `Snow is white' has the truth conditions that it does because `this is white' and
`this is snow' have the truth conditions that they do, and because a successful truth theory
is required to honor the structural relations among the sentences it analyzes.
9. The present thought is rather to expect to find a minimum of information about the
correctness of the theory at each single point; it is the potential infinity of points that
makes the difference ["Reality without Reference," p.225].
10. "The fact that each axiom of a truth theory has its impact upon an infinite number of Tsentences does indeed have the consequence that it is difficult for counterfeit theories to
pass the test ..." (Evans and McDowell,Truth and Meaning, 1976, p.xv).
11. (a) The proposal that invokes the truth conditions on `that's snow' to rule out (W) as
the T-sentence for `snow is white' works only because `snow' and `grass' are not
coextensive.
Consider, however, any pair of coextensive but not synonymous atomic predicates F, G.
Then, a T-theory which, as it were, swaps the truth conditions on the expression ...F... for
the ones on the expression ...G... will be extensionally adequate even if some of the
expressions in which F and G occur contain demonstratives.
"That's trilateral" is true iff that trilateral -- or iff that's triangular.
(b) Of course, one could still appeal to certain compositionality considerations to
distinguish the semantics of F from the semantics of G, since they will not, in general,
substitute salve veritate in intensional (e.g. counterfactual or propositional attitude)
contexts
(c) If it is replied that, well, at least the test works for intensional languages, the answer is
that if translation is not a concept at the disposal of semantic meta-theory, then neither is
intensionality, and for the same reasons.
The Logical Truth Problem
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12. If one of the theorems of a theory has a logical consequence expressible in the
vocabulary of that theory, then that logical consequence is also a theorem of the theory. If
for example "LT" is a logical truth expressible in the vocabulary of the truth theory of
English, then since Q is a logical consequence of the paradigmatic T-sentence T:
(T) "Snow is white" is true in English iff snow is white
(Q) "Snow is white" is true in English iff snow is white and LT
Interlude: The status of Radical Interpretation
13. Enumerate the evidential constraints that a successful meaning theory must meet, and
---since different evidential constraints will endorse different T-theories, all else being
equal--- an RI theory must justify the imposition of one set of evidential constraints in
preference to other candidates.
14. `Evidence plausibly available to an interpreter' where an interpreter is `someone who
does not already know how to interpret utterances the theory is designed to cover'
(‘Radical Interpretation’, Inquiries, p. 128).
15. [The evidence] must ... be evidence we can imagine the virgin investigator having
without his already being in possession of the theory it is supposed to be evidence for
(‘Belief and the Basis of Meaning’, Inquiries, p. 143).
16. Imagine someone in the position of a child exposed to a first language, or of a field
linguist exposed to an entirely alien language. The evidence relevant for the selection of a
T-theory is whatever data about the behavior of the informants it might reasonably be
supposed that the child or the field linguist does, or could, have access to.
17. The behavioral evidence available to the linguist/child which constitutes the
CONTINGENT constraints on his selection of a T-theory; plus general principles of nondemonstrative inference (i.e. whatever methodological principles mediate the construction
of empirical theories when intentional states and processes are not at issue;) plus
whatever `constitutive' principles (of charity, for example) can be justified by
transcendental arguments that reflect upon the conditions of intentional ascription as such.
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