According to the standard view of definition, all defined terms are mere stipulations, based on a small set of primitive terms. After a brief review of the Hilbert-Frege debate, this paper goes on to challenge the standard view in a number of ways. Examples from graph theory, for example, suggest that some key definitions stem from the way graphs are presented diagramatically and do not fit the standard view. Lakatos's account is also discussed, since he provides further examples that suggest (...) many definitions are much more than mere convenient abbreviations. (shrink)

I aim to show how and why some definitions can be benignly circular. According to Lloyd Humberstone, a definition that is analytically circular need not be inferentially circular and so might serve to illuminate the application-conditions for a concept. I begin by tidying up some problems with Humberstone's account. I then show that circular definitions of a kind commonly thought to be benign have inferentially circular truth-conditions and so are malign by Humberstone's test. But his test is too demanding. The (...) inferences we actually use to establish the applicability of, e.g., colour concepts are designed to establish warranted assertability and not truth. Understood thus, dispositional analyses are not inferentially circular. (shrink)

Those who have a brief against the analytic-synthetic distinction raise problems for what seem to supporters of the distinction to be some of the clearest cases. That bachelors are unmarried seems to many to be analytically true. But to hold this seems to imply that there is a definition of "bachelor" that includes being unmarried. But critics of the analytic-synthetic distinction, such as Jerry Fodor, deny that there are true definitions (reportive, not stipulative). So there can be no definition of (...) "bachelor". And many have noted that defining "bachelor" is not as easy as appears at first blush. (shrink)

Paul Boghossian advocates a version of the analytic theory of a priori knowledge. His defense of an "epistemic" notion of analyticity is based on an implicit definition account ofthe meaning of the logical constants. Boghossian underestimates the power of the classical Quinean criticisms, however; the challenge to substantiate the distinction between empirical and non-empirical sentences, as forcefully presented in Two Dogmas, still stands, and the regress from Truth by Convention still needs to be avoided. Here, Quine also showed that there (...) are no implicit definers for the logical constants. Moreover, even if they existed, their epistemic analyticity would, on Boghossian's own account, be doubtful. (shrink)

Operational definitions were once considered the backbone of semantics of natural science. Still in 1955 A. W. Burks published an explication of the general scheme of these definitions. In the fifties of the last century however they became outmoded, while high school teachers for presumably good reasons were still in favour of them. I consider the banishment of this kind of definitions premature, and try to improve the explication of Burks in a way which qualifies them for a rehabilitation. In (...) the improved explication the concept of intrinsic property becomes important, for which I give a new definition on the basis of a structuralist account of physical processes. German Die operationalen Definitionen galten einst als der Kern der Semantik der Naturwissenschaft. Eine letzte Explikation des allgemeinen Schemas der operationalen Definitionen hat A. W. Burks noch 1955 vorgelegt. In den fünf ziger Jahren kamen sie indessen aus der Mode, während sie noch weiterhin von Gymnasiallehrern - wohl aus berechtigten Gründen - geschätzt wurden. Ich halte die Verbannung dieser Art von Definitionen für voreilig und versuche die Explikation von Burks in einer Weise zu verbessern, dass man sie wieder in der Wissenschaftstheorie rehabilitieren kann. In der verbesserten Explikation wird der Begriff der inneren Eigenschaft eines Dinges oder Vorgangs wichtig, den ich auf der Basis einer strukturalistischen Darstellung physikalischer Vorgänge neu definieren möchte. (shrink)

Saul Kripke famously argued that some truths are both contingent and knowable a priori. For instance, one who stipulatively introduces the term ‘one meter’ as a rigid designator for the length of a certain stick s at time t is said to be in a position to know a priori that if s exists at t then the length of s at t is one meter.1 Call this the meter proposition. Many are unmoved by this or by Kripke’s other examples. (...) There are two main sources of dissent. The first has to do with the stipulator’s lack of acquaintance with the length in question which, in one way or another, is meant to prevent the stipulator from knowing the meter proposition at all (let alone a priori).2 The second has to do with the epistemic status of associated semantic knowledge. The stipulator’s knowledge of the meter proposition would arguably have to be based on her knowledge that the term ‘one meter’ refers in her language to the length of an object iff the length of that object is one meter. Call this further proposition the ‘meter’ proposition. The question of whether the meter proposition is known a priori therefore turns on the question of whether the ‘meter’ proposition is known a priori—but the latter, according to many, is substantive semantic information which can be known only a posteriori. (shrink)

Much of The Reason’s Proper Study is devoted to defending the claim that simply by stipulating an abstraction principle for the “number-of” functor, we can simultaneously fix a meaning for this functor and acquire epistemic entitlement to the stipulated principle. In this paper, I argue that the semantic and epistemological principles Hale and Wright offer in defense of this claim may be too strong for their purposes. For if these principles are correct, it is hard to see why they do (...) not justify platonist strategies that are not in any way “neo-Fregean,” e.g. strategies that treat “the number of Fs” as a Russellian definite description rather than a singular term, or employ axioms that do not have the form of abstraction principles. (shrink)

Gupta"s and Belnap"s Revision Theory of Truth defends the legitimacy of circular definitions. Circularity, however, forces us to reconsider our conception of meaning. A readjustment of some standard theses about meaning is here proposed, by relying on a novel version of the sense–reference distinction.

The arguments of Fodor, Garret, Walker and Parkes [(1980) Against definitions, Cognition, 8, 263-367] are the source of widespread skepticism in cognitive science about lexical semantic structure. Whereas the thesis that lexical items, and the concepts they express, have decompositional structure (i.e. have significant constituents) was at one time "one of those ideas that hardly anybody [in the cognitive sciences] ever considers giving up" (p. 264), most researchers now believe that "[a]ll the evidence suggests that the classical [(decompositional)] view is (...) wrong as a general theory of concepts" [Smith, Medin & Rips (1984) A psychological approach to concepts: comments on Rey, Cognition, 17, 272], and cite Fodor et al. (1980) as "sounding the death knell for decompositional theories" [MacNamara & Miller (1989) Attributes of theories of meaning, Psychological Bulletin, 106, 360]. I argue that the prevailing skepticism is unmotivated by the arguments in Fodor et al. Fodor et al. misrepresent the form, function and scope of the decompositional hypothesis, and the procedures they employ to test for the psychological reality of definitions are flawed. I argue, further, that decompositional explanations of the phenomena they consider are preferable to their primitivist alternatives, and, hence, that there is prima facie reason to accept them as evidence for the existence of decompositional structure. Cognitive scientists would, therefore, do well to revert to their former commitment to the decompositional hypothesis. (shrink)

This article treats three aspects of Frege's discussions of definitions. First, I survey Frege's main criticisms of definitions in mathematics. Second, I consider Frege's apparent change of mind on the legitimacy of contextual definitions and its significance for recent neo-Fregean logicism. In the remainder of the article I discuss a critical question about the definitions on which Frege's proofs of the laws of arithmetic depend: do the logical structures of the definientia reflect the understanding of arithmetical terms prevailing prior to (...) Frege's analyses? Unless they do, it is unclear how Frege's proofs demonstrate the analyticity of the arithmetic in use before logicism. Yet, especially in late writings, Frege characterizes definitions as arbitrary stipulations of the senses or references of expressions unrelated to pre-definitional understanding. I conclude by examining some options for conceiving of the status of Frege's logicism in light of this apparent tension, and outline a suggestion for a philosophically fruitful way of resolving this tension. (shrink)

7.3.1 Ostension 7.3.2 Extensional Definition by Naming 7.3.3 Extensional Definition by Unique Description 7.4 Two Case Studies in the Application of the Intension/Extension Distinction 7.4.1 "God exists, by definition" 7.4.2 The 'Width' of an Intensional Definition..

These are some of the rules of classification and definition. But although nothing is more important in science than classifying and defining well, we need say no more about it here, because it depends much more on our knowledge of the subject matter being discussed than on the rules of logic. (Arnauld and Nicole (1683/1996) p.128).

On a rather popular conception, the paradox of analysis suggests that the intersubstitutivity of analysans and analysandum should be restricted to non-psychological contexts. This is typically taken to be compatible with the idea that two sentences differing only in that one has the analysandum where the other has the analysans express exactly the same proposition. In this note we argue that this should be pondered upon in light of the view that many important ordinary concepts are circular. In particular, we (...) submit that if there are correct analyses grounding circular definitions, then we are bound to further restrict the substitutivity principle, for we must admit that it might fail even in non- psychological contexts. (shrink)

This original and enticing book provides a fresh, unifying perspective on many old and new logico-philosophical conundrums. Its basic thesis is that many concepts central in ordinary and philosophical discourse are inherently circular and thus cannot be fully understood as long as one remains within the confines of a standard theory of definitions. As an alternative, the authors develop a revision theory of definitions, which allows definitions to be circular without this giving rise to contradiction (but, at worst, to “vacuous” (...) uses of definienda). The theory is applied with varying levels of detail to a circular analysis of concepts as diverse as truth, predication, necessity, physical object, etc. The focus is on truth, and hope is expressed that a deeper understanding of the Liar and related paradoxes has been provided: “We have tried to show that once the circularity of truth is recognized, a great deal of its behavior begins to make sense. In particular, from this viewpoint, the existence of the paradoxes seems as natural as the existence of the eclipses” (p. 142). We think that this hope is fully justified, although some problems remain that future research in this field should take into account. (shrink)