Is it X? P.
Mon Feb 24 8:47 PST 1997 The Meaning of Meaning?
Introduction
Consider the question "Is this a scientific theory?". How can we go about answering this question? It seems to me that before we try to answer this particular question, it will be worthwhile to abstract a few steps and consider the more general form of the question "Is this an X", or, perhaps "Is this X", in the general sense of "Is this an example of X" or "Does this have property X".
An exploration of these issues will inevitably lead us to the question of the meanings of words, and, if we are willing, to the meaning of meaning. We are also liable to encounter the shibboleth truth.
Some Preliminaries
Let us look briefly at some traditional notions of the meanings of words. Probably the two most standard notions are
The first notion, that the meaning of a word is its definition, is very appealing. When we encounter a new word, we look up its definition in a dictionary. We can also appeal to stipulative process, used most paradigmatically in formal Mathematics, by which new terms (or specialized uses of old terms) are introduced into language. In fact, some people seem to go so far as suggesting that ordinary natural language is essentially just a special case of a mathematician's formal language.
Unfortunately for this view of language, there are some fundamental difficulties. One primary difficulty is that this model of meaning either rests on circularity or appeals to undefined terms. The definition of a word in a dictionary is in terms of other words in the dictionary. Since the dictionary is finite, if we trace the definitions of the words used in a definition, etc., we must eventually either enter into a loop or, as happens in formal Mathematics, reach explicitly undefined terms such as point in classical geometry. This lack of groundedness makes the definition model of meaning problematic at best.
A second significant difficulty is that if we look at the ontogeny of a dictionary, we find that it is fundamentally a descriptive rather than a prescriptive work. A definition in the dictionary is essentially just a description of how the word was used at the time the dictionary was compiled, rather than a prescription from first principles of how the word must be used. The language and its use are prior to the dictionary. In particular, if contemporary usage of a word disagrees with the dictionary definition, then it is the dictionary which must be changed! Even the mathematician's stipulative definition is in effect just a method of abbreviation, under which any appeal to the meaning of the new term is actually just an appeal to the meanings of the terms for which it stands.
Thus, I find appeals to definitions to be a fruitless approach to understanding the meanings of words. This leads us then to a search for a method of grounding the notion of meaning, and thus to the second option above.
The second notion, that the meaning of a word is determined by its referent, I also find less than satisfying. In practice, this model of `meaning' typically appears in the form of ostensive `definitions' where we `point at' examples of referents. The prototypical model of this process is the use of proper names. We gesture towards someone and say ``His name is Joe.'' This prototypical model, however, seems lacking in some fundamental way - in particular, it would seem strange to be told that ``the meaning of the word `Joe' is that person over there.'' Rather we would expect to hear that ``his name is Joe.''
In a more general and abstract context, then, the referent of a word would be some appropriate set, or alternatively the characteristic property which determines the appropriate set. It is perhaps worth noting that if we were to find that this model of meaning held up under scrutiny, it might also provide a means to resurrect the definition version of meaning, where the definition of a word would simply be the characteristic property determining the appropriate set.
Unfortunately, this model of meaning also breaks down, except possibly in the most trivial case of proper names. Consider, as an example, the property of being yellow. How are we to determine whether an object X is yellow? The notion is that we simply check whether the object X is in the set of all yellow things. There are two potential difficulties in this enterprise: it may be that the set of all yellow things simply doesn't exist (as a set), or it may be that there is no method for determining whether any particular object is in the set.
There are two generic methods for specifying a set. The first is just to list all the elements of the set, as for example {this banana, that rubber ducky, and the fellow over there running away from a fight}. The second generic method is to specify the criteria an object must meet in order to be in the set, as for example {x: x reflects light of certain frequencies}.
In our example, the first method simply begs the question. How do we determine whether something is yellow? We see if it is in the set of yellow things. How does something get to be in the set? By being on the list. How does it get to be on the list? By being yellow! Clearly this method is useless for determining meaning.
We thus seem to be reduced to the last possibility for rescuing the concept of meaning: that meaning occurs through reference (to a set), and that the set is determined by a collection of criteria. At this point, we seem to have a great vested interest in assuring that this possibility works out. We have eliminated all the other possibilities suggested for the meaning of meaning and appear to be on the brink of meaninglessness if this one fails. This approach also has the benefit that it can resurrect the definition model: the definition of a word will be the criteria which determine the set. In fact, we are liable to cling to this possibility even in the face of powerful arguments against it, on the grounds that meaning must mean something, and this is all we have left ...
Properties
Let us consider the example ``that is yellow''. A traditional explanation is that a yellow object absorbs all colors of light except yellow, and reflects yellow light, thus appearing yellow to us. A yellow object, under this view, has a property (or collection of properties) which will make it appear yellow to us. The suggestion, then, is that there are criteria for determining whether an object is yellow: we can shine lights of various frequencies at the object and see which are absorbed and which are reflected. If all frequencies except yellow are absorbed, and yellow is reflected, then the object is yellow. Unfortunately, there are several difficulties obscured by this explanation.
What we have described so far would provide only positive conditions for claiming that something is yellow. We cannot say that things not satisfying the `criteria' are not yellow. In fact, examples of things which exactly satisfy the criteria we have described are so rare as to be almost irrelevant to the general question of what yellow means. However, we seem to want the model to work. We feel as though our difficulty is just that we haven't been careful or thorough enough - that if we worked a little harder, we could expand our criteria to capture the essence of yellow.
Suppose we try expanding the criteria. We soon come to some troubling examples. If we look carefully at a color television, we see only red, green and blue dots - no yellow dots. However, we certainly see a yellow lemon in the picture. Incorporating this into our analysis, we are led to the notion that there is no single common property which all yellow objects share, but rather that in certain circumstances involving people, light and objects, there is an experience of yellowness. This leads to the interesting suggestion that an object is yellow if someone sees it as yellow, or, perhaps, if someone says it is yellow ... Alternatively, as I would prefer to say it, ``The meaning of the word yellow is the use of the word yellow.'' There is no definition of the word yellow which allows us to determine whether some person's use of the word is appropriate. There is no common property which all yellow things share. There is not even a common experience which people have which would allow us to determine that they had ``seen something yellow.'' In a fundamental sense, the only ``criterion'' for yellow is people using the word yellow. In particular, there is no abstract property which an object may or may not have which is the property of being yellow. There is not any thing to which the word yellow refers.