Philosophy of Language

Ayer, Language, Truth, and Logic, Chapter 3

1. Definitions in use.

Philosophy's task, according to Ayer, is to provide a certain kind of definition, namely definitions in use. explicit definitions: synonymous expressions.

'bachelor' =def unmarried male

is an acceptable definition only if 'unmarried male' can replace 'bachelor' in any sentence in which 'bachelor' occurs without changing the meaning of that sentence, e.g.

Two-year-olds cannot be bachelors


Two-year-olds cannot be unmarried males.

(In this case there does seem to have been a change of meaning, so ‘unmarried male’ isn’t an adequate definition of bachelor.) [But note that Ayer tries to make the point without appealing to the notion of meaning.]

definitions in use

showing how to translate sentences containing an expression into sentences which do not, without providing a synonym for that expression.

Ayer’s explanation of what philosophy does, then: "A complete philosophical elucidation of any language would consist, first, in enumerating the types of sentence that were significant in that language, and then in displaying the relations of equivalence that held between sentences of various types." That is, philosophy first explains which sentences are significant (because they are verifiable or because they are tautologies), and then provides definitions in use for those portions of the language which are liable to lead to philosophical confusion. "Thus we may regard any particular philosophical 'theory', such as Russell's 'theory of definite descriptions,' as a revelation of part of the structure of the given language."

Why do we need definitions in use, i.e. translations from ordinary English into a cleaner, more explicit language that will reveal the complexity hidden in the ordinary version? Because of problems such as these:


Syntactic ambiguity:

All that glisters is not gold. 

¬∀x (Glisters(x) → Gold(x))


∀x (Glisters(x) → ¬Gold(x))

Ernest wants to shoot a lion.

∃x (Lion(x) ∧ Ernest wants to shoot x)


Ernest wants it to be the case that: ∃x (Lion(x) ∧ Ernest shoots x)

Semantic ambiguity:

Ayer’s example here (p. 63) seems unsuccessful, actually. He distinguishes between two senses of ‘is’, namely that in

George is the author of that book

and that in

A cat is a mammal,

claiming that the first is the ‘is’ of predication while the other expresses the notion of subset. The idea seems to be that the first sentence should go into


while the second should go into

{x: x is a cat} {x: x is a mammal}.

But it seems we could equally well translate the first into

{x: x is george} {x: x authored that book},

or into

(x)(x is george É x is the author of that book)

and the second into

(x) x is a cat É x is a mammal.

A better example, perhaps, would be to distinguish the "is" of identity and the "is" of predication. "Hesperus is Phosphorus" means (hesperus = phosphorus), while "Hesperus is a planet" means Planet(hesperus).


Definite descriptions. (E.g. "The F is G.")

A definition in use will provide rules for translating sentences containing definite descriptions into sentences which do not contain definite descriptions, but without providing a synonym for the definite descriptions involved. The idea is this (I follow Ayer’s exposition, more or less):

"Nothing is F" might be symbolized like this:  ¬∃x F(x)

"There is an F and there is only one F and all F are G" might be symbolized like this: 

∃x (F(x) & ∀y (F(y) → x=y) ∧ G(x))

This is equivalent to, but more compact than:

∃x F(x) ∧ ¬∃x ∃y (F(x) ∧ F(y) ∧ x≠y) ∧ (∀x)(F(x) → G(x))

2. Reduction of material object language to language about sense-contents.

logical constructions (p. 63): if we can provide a definition in use showing how to get rid of a term 'a' in favor of other terms 'b','c', etc., then we may say that the thing supposedly referred to by 'a' is a logical construction out of the things referred to by 'b', 'c', etc. So, for example, tables are logical constructions out of sense-contents. (Here is the tendency for positivism to lead to idealism!)

sense-field: a whole sensory array at a particular moment (e.g. a visual sense-field will be something like a two-dimensional array of colored shapes -- though Ayer thinks that we also have visual sensations of depth, and that there may be Gestalt phenomena)

(sense-experience: the sum of one's sense-fields -- e.g. visual, olfactory, auditory -- at a moment)

sense-content: a portion of a sense-field. (How big a portion?)

x directly resembles y iff there is no discriminable qualitative difference between them (e.g. two patches of red in my visual field which appear to be of exactly the same shade, even though one may be infinitesimally different from the other)

x indirectly resembles y iff there are intermediate sense-contents x1, x2, . . . xn, such that x directly resembles x1, x1 directly resembles x2, . . . xn directly resembles y.

(Problem: you can get from red to green by such a series of indiscriminable differences, so red sense-contents indirectly resemble green ones. Similarly for round sense-contents and square ones, bright ones and dark ones, etc. etc. So, if we allow possible but nonactual sense-contents to provide the intermediaries x1, x2, . . . xn, then resemblance imposes no constraints at all on which sense-contents count as belonging to the same object. But if we don't allow possible sense-contents, then we'll have to say that every time I blink my eyes in class, I am looking at a different set of people, since each person will have changed position or expression slightly.)

Now, what about continuity? x is directly continuous with y iff x is part of a sense-field X, and y is part of a sense-field Y, and Y immediately follows X, and y's position in Y is at most infinitesimally different from x's position in X.

x is indirectly continuous with y if there are actual or possible intermediaries linking them, as in the definition of indirect resemblance.

(Problem: my experience of one person's left eye may be indirectly continuous with my later experience of someone else's right eye, since there is a set of possible intermediaries linking them.)

Now, x and y are elements of the same material thing iff "they are related to one another by a relation of direct, or indirect, resemblance in certain respects, and by a relation of direct, or indirect, continuity." But it the previously mentioned problems are correct, then any x is an element of the same material thing as every y, since there will be possible intermediaries linking any two sense-contents. (Even simultaneous sense contents will be linked: my experience of A's eye at t1 is linked to my experience of B's eye at t2, and my experience of B's eye at t1 is also linked to my experience of B's eye at t2, so by symmetry and transitivity, my experience of A's eye is linked to my simultaneous experience of B's eye.)

Still another problem: Ayer points out that on his view, no sense-content can be part of more than one object. But as we ordinarily discriminate things, lots of sense-contents are part of more than one object; a twig sense-content is an element of the branch and also of the tree; my A's-eye sense-content is an element of A's eye, A's head, and A's body; and so on. So one suspects that there must be something wrong here.

Last update: September 24, 2012
Curtis Brown  |  Philosophy of Language   |  Philosophy Department  |   Trinity University