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We've seen that sloppy or misleading use of ordinary language can seriously limit our ability to create and communicate correct reasoning. As philosopher John Locke pointed out three centuries ago, the achievement of human knowledge is often hampered by the use of words without fixed signification. Needless controversy is sometimes produced and perpetuated by an unacknowledged ambiguity in the application of key terms. We can distinguish disputes of three sorts:
The most common way of preventing or eliminating differences in the use of languages is by agreeing on the definition of our terms. Since these explicit accounts of the meaning of a word or phrase can be offered in distinct contexts and employed in the service of different goals, it's useful to distinguish definitions of several kinds:
A lexical definition simply reports the way in which a term is already used within a language community. The goal here is to inform someone else of the accepted meaning of the term, so the definition is more or less correct depending upon the accuracy with which it captures that usage. In these pages, my definitions of technical terms of logic are lexical because they are intended to inform you about the way in which these terms are actually employed within the discipline of logic.
At the other extreme, a stipulative definition freely assigns meaning to a completely new term, creating a usage that had never previously existed. Since the goal in this case is to propose the adoption of shared use of a novel term, there are no existing standards against which to compare it, and the definition is always correct (though it might fail to win acceptance if it turns out to be inapt or useless). If I now decree that we will henceforth refer to Presidential speeches delivered in French as "glorsherfs," I have made a (probably pointless) stipulative definition.
Combining these two techniques is often an effective way to reduce the vagueness of a word or phrase. These precising definitions begin with the lexical definition of a term but then propose to sharpen it by stipulating more narrow limits on its use. Here, the lexical part must be correct and the stipulative portion should appropriately reduce the troublesome vagueness. If the USPS announces that "proper notification of a change of address" means that an official form containing the relevant information must be received by the local post office no later than four days prior to the effective date of the change, it has offered a (possibly useful) precising definition.
Theoretical definitions are special cases of stipulative or precising definition, distinguished by their attempt to establish the use of this term within the context of a broader intellectual framework. Since the adoption of any theoretical definition commits us to the acceptance of the theory of which it is an integral part, we are rightly cautious in agreeing to it. Newton's definition of the terms "mass" and "inertia" carried with them a commitment to (at least part of) his theories about the conditions in which physical objects move.
Finally, what some logicians call a persuasive definition is an attempt to attach
emotive meaning to the use of a term. Since this can only serve to confuse the literal meaning of the term, persuasive definitions have no legitimate use.
A rather large and especially useful portion of our active vocabularies is taken up by general terms, words or phrases that stand for whole groups of individual things sharing a common attribute. But there are two distinct ways of thinking about the meaning of any such term.
The extension of a general term is just the collection of individual things to which it is correctly applied. Thus, the extension of the word "chair" includes every chair that is (or ever has been or ever will be) in the world. The intension of a general term, on the other hand, is the set of features which are shared by everything to which it applies. Thus, the intension of the word "chair" is (something like) "a piece of furniture designed to be sat upon by one person at a time."
Clearly, these two kinds of meaning are closely interrelated. We usually suppose that the intension of a concept or term determines its extension, that we decide whether or not each newly-encountered piece of furniture belongs among the chairs by seeing whether or not it has the relevant features. Thus, as the intension of a general term increases, by specifying with greater detail those features that a thing must have in order for it to apply, the term's extension tends to decrease, since fewer items now qualify for its application.
With the distinction between extension and intension in mind, it is possible to approach the definition of a general term (on any of the five kinds of definition we discussed last time) in either of two ways:
A denotative definition tries to identify the extension of the term in question. Thus, we could provide a denotative definition of the phrase "this logic class" simply by listing all of our names. Since a complete enumeration of the things to which a general term applies would be cumbersome or inconvenient in many cases, though, we commonly pursue the same goal by listing smaller groups of individuals or by offering a few examples instead. In fact, some philosophers have held that the most primitive denotative definitions in any language involve no more than pointing at a single example to which the term properly applies.
But there seem to be some important terms for which denotative definition is entirely impossible. The phrase "my grandchildren" makes perfect sense, for example, but since it presently has no extension, there is no way to indicate its membership by enumeration, example, or ostension. In order to define terms of this sort at all, and in order more conveniently to define general terms of every variety, we naturally rely upon the second mode of definition.
A connotative definition tries to identify the intension of a term by providing a synonymous linguistic expression or an operational procedure for determining the applicability of the term. Of course, it isn't always easy to come up with an alternative word or phrase that has exactly the same meaning or to specify a concrete test for applicability. But when it does work, connotative definition provides an adequate means for securing the meaning of a term.
Classical logicians developed an especially effective method of constructing connotative definitions for general terms, by stating their genus and differentia. The basic notion is simple: we begin by identifying a familiar, broad category or kind (the genus) to which everything our term signifies (along with things of other sorts) belongs; then we specify the distinctive features (the differentiae) that set them apart from all the other things of this kind. My definition of the word "chair" in the second paragraph of this lesson, for example, identifies "piece of furniture" as the genus to which all chairs belong and then specifies "designed to be sat upon by one person at a time" as the differentia that distinguishes them from couches, desks, etc.
Copi and Cohen list five rules by means of which to evaluate the success of connotative definitions by genus and differentia: