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In this paper I will explain how the notions of necessity, a priority, and analyticity have traditionally been related in light of the classical notion of a concept. This notion has its roots in Gottlob Frege’s notion of a sense, and his division of reality into three realms. I will show that the Fregean view of how language relates to reality is difficult to maintain in light of an example put forward by Keith Donnellan. Both Donnellan and Hilary Putnam retain the Fregean view, leading to unsatisfying conclusions regarding the nature of necessity.
Frege divides reality into three distinct “realms.” The first two are relatively familiar: the outer world (public objects perceiveable by the five senses that exist independently of anyone’s thinking or perceiving) and the inner world (private ideas that are imperceptible to the five senses and depend for their existence on the subjective life of a thinker). Frege’s third realm consists of senses, which are not perceivable with the five senses, yet are public and exist independently.
A sense is a unique way that an object is presented to a thinker. On Frege’s account of language, the meaning of a term includes both its sense and its referent. A referent is what the term picks out in the world, and the sense is the unique way a referent is presented. For example, the terms ‘the morning star’ and ‘the evening star’ refer to the same object in the world (Venus), but have different senses—i.e., they pick out the referent in unique ways. Properly understood, a term expresses a sense and refers to an object. The sense determines the object.
A thought is the sense of a sentence, constituted by the senses of its terms. A thought, in virtue of its representational character, is “something for which the question of truth can arise at all” (Frege 36). That is, thoughts are about something other than themselves—namely, the stuff and structure of the world. Thus, philosophers who take a Fregean view of language attempt to analyze the properties of thoughts in order to learn about the structure of the world.
Fregean senses “embody” or “contain” what C.I. Lewis calls criteria of application. For Lewis, the criteria of application for a term, t, is the set of sensible features that determine the appropriate application of t. These features are the necessary and sufficient conditions for something to be appropriately called t. The classical notion of a concept is a mental representation of these conditions. Thus, while technically different, for this paper it will be sufficient to think of senses and concepts as uniquely characterizing sets of conditions.
For Lewis, we can reflect on the senses of terms and discover inclusion relations. For example, if we reflect on the sense of ‘square’ and the sense of ‘rectangle’, we find that the criteria of application for ‘square’ already include the criteria of application for ‘rectangle’. Thus, we come to know the necessary truth expressed by (1) “All squares are rectangles”. Necessity is a metaphysical property, characterizing features of the world and its structure. Necessary features must be the case, as opposed to contingent features, which could vary. One can know the necessity of (1) a priori as opposed to a posteriori. This is an epistemological distinction. A posteriori knowledge depends on sense experience, whereas (1) can be known simply by understanding the meanings of ‘square’ and ‘rectangle’, requiring no sense experience. Furthermore, (1) is analytic, and not synthetic. This is a semantic distinction, characterizing language and its relation to the world. Sentences that are true in virtue of the rules of language are analytic. Sentences that require something nonlinguistic to make them true are synthetic.
The concurrence of necessity, a priority, and analyticity is a feature of the Fregean view of language in which senses determine objects. If we consider Donnellan’s example, (2) “All whales are mammals”, we see that the Fregean view encounters difficulties. On this view we should see that (2) is analytic by reflecting on ‘whale’ and ‘mammal’, grasp the inclusion relations therein, and know a priori that (2) expresses a necessary truth. However, a sailor who clearly understands what ‘whale’ means, and can accurately identify whales without fail, may very well never know that all whales are mammals. The sailor’s sense of ‘whale’ is something like ‘large, oblong sea creature with a blowhole’. Clearly the sense of ‘whale’ does not include the criteria of application for ‘mammal’ if we consider the sailor a competent speaker. Now suppose that some of the creatures we have been calling whales turn out not to have mammary glands, precluding them from being called mammals. Are these creatures still whales? Does (2) still express a necessary truth?
Donnellan and Putnam both say this example confronts us with a choice about how we use language. On their Fregean view, what determines what a whale is is not distinct from what ‘whale’ means. If what we speak about is mediated by senses, then what a whale is is determined by the sense of ‘whale’. If we base our answer to the question of whether to call these new creatures whales on the sense of ‘whale’, there are metaphysical consequences; for (2) would no longer be necessary, and necessity is a metaphysical property. Thus, we are faced with the paradoxical conclusion that necessary truths can somehow change. Alternatively, we might base our answer on the nature of the creatures themselves, in which case these creatures without mammary glands are not whales.

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