An analysis—in its simplest form—is an assertion aiming to capture a certain intimate link between a given concept (the analysandum) and another, typically more precise and fully explicit concept (the analysans). In some cases, even a whole theory may be regarded as a constituting an analysis. For example, Russell’s celebrated theory of definite descriptions may be viewed as an analysis of that formal concept which in natural language can be expressed by means of the definite article. Analyses are also called philosophical, real, or simply analyzing definitions

Varzi, Achille C.

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1A Note on Analysis and Circular DefinitionsFrancesco OriliaDepartment of Philosophy, University of Macerata (Italy)Achille C. VarziDepartment of Philosophy, Columbia University, New York (USA)(Published in Grazer philosophische Studien 54 (1998), 107–115.)IAn analysis—in its simplest form—is an assertion aiming to capture a cer-tain intimate link between a given concept (the analysandum) and another,typically more precise and fully explicit concept (the analysans). For in-stance, the following are classical examples of analyses proposed for thegeometric concept of a circle and the epistemic concept of knowledge, re-spectively:(1) A circle is a locus of points in the same plane equidistant fromsome common point.(2) Knowledge is justified true belief.In some cases, even a whole theory may be regarded as a constituting ananalysis. For example, Russell’s celebrated theory of definite descriptionsmay be viewed as an analysis of that formal concept which in natural lan-guage can be expressed by means of the definite article.1Analyses are also called philosophical, real, or simply analyzing defi-nitions. This is appropriate, since analyses are implicitly assumed to fulfillthe following Definition Constraint:(DC) An analysis must obey the laws governing definitions, wherethe expression standing for the analysans i  viewed as a defi-niens and the expression standing for the analysandum as acorresponding definiendum.22Given the ordinary account of definitions, (DC) in turn implies the follow-ing Substitutivity Principle: (SP) The expression standing for the analysandum and the onestanding for the analysans are mutually substitutable, salvaveritate.For instance, (1) should ground our acceptance of the following definition:(3) x is a circle =df x is a locus of points in the same plane equi-distant from some common point.By appealing to (SP), we should thus take any pair of sentences having thesame form, respectively, as the definiens and the definiendum of (3) to bemutually substitutable sa va veritate. For instance, if (in the appropriatecontext) the following is true:(4) John is drawing a circle,then so is the following:(5) John is drawing a locus of points in the same plane equidistantfrom some common point.Similarly, if we take Russell’s theory of descriptions as an analysis of theconcept expressed by the definite article, we should accept a definition alongthe following lines:(6) The F is G =df There is exactly one F, and it is G.Consequently, we should take any pair of sentences having the same form,respectively, as the definiens and the definiendum of (6) to be intersubsti-tutable salva veritate.Unfortunately, as is well known, once the Substitutivity Principle (SP)is accepted, the road to the so-called par dox of analysis i  open. Here is anexample. Suppose the following are both true:(7) John knows nothing about geometry.(8) John knows that a circle is a circle.3Then, given definition (3), the Substitutivity Principle would entitle one toexpect that the following be also true:(9) John knows that a circle is a locus of points in the same planeequidistant from some common point.Yet of course (9) contradicts (7). Similarly, in spite of def nition (6), itmight be true that(10) John is attending to the thought that the president of the USAis a bright man,without it being the the case that(11) John is attending to the tought that there is exactly one presi-dent of the USA.A popular reaction to the paradox of analysis is to restrict the Substitu-tivity Principle (SP) to non-intensional contexts. This, however, can only bepart of the story, for such a reaction must come to terms with a more fun-damental assumption underlying the acceptance of (SP) as well as of theDefinition Constraint (DC). Let us call this the Sameness View:(SV) Two sentences differing only because one contains a definiens(standing for an analysans) and the other the corresponding de-finiendum (standing for an analysandum) express the sameproposition as long as the analysis in question is correct, forthe analysans and the corresponding analysandum of a correctanalysis are one and the same entity.3For instance, the predicates of our first example—“ is a circle” and “x is alocus of points in the same plane equidistant from a common point”—wouldstand for the same geometric concept. Similarly, any sentences of the form“the F is G” and “there is exactly one F, and it is G” would stand for thesame proposition.Now, in light of the paradox of analysis, many a philosopher aveproposed to abandon the Sameness View (SV).4 Nevertheless one mightinsist that (SV) is compatible with the Substitutivity Principle (SP), pro-4vided only that the latter is suitably restricted to non-intensional contexts.Accordingly, one could insist that (SV) should find its place in a critical re-construction of the theory of meaning that underlies much contemporaryanalytic philosophy. We intend to question this point of view by showingthat (SV) is subject to a further difficulty, one which is quite independent ofthe paradox of analysis.IIThe difficulty we have in mind relates to the idea that various important ordi-nary concepts are circular, i.e., can be given a circular analysis. This view isbecoming increasingly popular, especially under the impact of Gupta andBelnap’s recent book The Revision Theory of Truth (1993). Gupta and Bel-nap suggest concepts uch as predication, set membership, necessity,knowledge, temporal stage of an object, and, above all, truth, as candidatesfor a circular analysis. For example, according to Gupta and Belnap, a cor-rect analysis of truth can be given, but this analysis is circular. This meansthat the following definitional schema(TD) “A” is true =df A,is perfectly legitimate, but may have circular instances. (Each instance of(TD) may be viewed as a “partial definition” of the truth predicate, the com-plete definition amounting to the totality of such instances.5)In fact, it bears emphasis that (TD) can be taken to underlie a correctanalysis of truth only if the truth predicate is allowed to occur in the de-finiens. This can be immediately appreciated if we consider such instancesof (TD) as, say,(12) ““Snow is white” is true” is true =df “Snow is white” is true.One attractive feature of Gupta and Belnap’s proposal is precisely that it af-fords a uniform treatment of all definitions which reduces to the standardaccount in the absence of circularity, but which also accounts for the possi-bility of circular definitions by distinguishing “innocuous” circular defini-tions (such as (12)) from “non-innocuous” ones. At worst, according to thismethod, a circular definition may give rise to “vacuous” (in a sense, mean-5ingless) uses of a definiendum, but in many cases (as in (12)) it grants in-formative content to the definiendum in question in quite the same sense inwhich this can be done by means of a standard non-circular definition. Re-garding truth, in particular, the attribution of informative content o in-nocuous circular definitions such as (12) can be illustrated by noting that insuch cases the Gupta-Belnap theory grants the Tarskian biconditional(TB) “A” is true if and only if A.Clearly, in these cases (TB) permit us to move from sentences that containthe truth predicate to sentences that do not contain it.Admitting non-innocuous circular definitions, however, collides withthe Substitutivity Principle (SP). Consider for example a Simple Liar such as(13) (13) is not true,The corresponding instance of (TD) is:(14) “(13) is not true” is true =df (13) is not true,which in view of the identity(15) (13) = “(13) is not true” reduces to(16) (13) is true =df (13) is not true.If the Substitutivity Principle (SP) held, we could then move from the tau-tology(17) (13) is true if and only if (13) is trueto the contradiction(18) (13) is true if and only if (13) is not true.6Hence, to the extent that we accept “circular analyses” of this kind, weshould question the validity of (SP) in its full generality.Note incidentally that (TD) can be viewed as a compact version of theinfinitary definition6(TD') x is true =df (x = “S1” and S1) or (x = “S2” and S2) or (x =“S3” and S3) or ...where “S1”, “S2”, “S3”, ..., are all the sentences of the language in ques-tion.7 (TD') shows better than (TD) that both the truth predicate and its cor-responding definiens, according to the Gupta-Belnap roposal, can beviewed as a monadic predicate.Now, if (TD), and hence (TD'), block the Substitutivity Principle (SP),it is problematic to view the definiens and the definiendum of (TD') asstanding for the same concept. To the extent that (TD) and (TD') are theformal counterparts (required by the Definition Constraint (DC)) of a correctanalysis of truth, as Gupta and Belnap propose, we are thus led to questiononce more the Sameness View (SV). However, this time we arrive at thisresult through a route that has nothing to do with the paradox of analysisand intensional contexts (or at least, we might say, with contexts that aretraditionally regarded as intensional).We can thus question (SV) from two quite different perspectives: theparadox of analysis on the one side, and circular analyses on the other. Ourmoral is that this provides further, stronger evidence for the need of theoriesof meaning and conceptual structure 8 centered around an explicit rejection of(SV).9Notes1See Moore 1944)2As Anderson (1993: 209) puts it, “A formal, abbreviative or stipulative definitionis not in itself an analysis—but is the formal counterpart thereof”.3The Sameness View seems to have been endorsed by Moore inter alia (see e.g.1968: 664).4See Ackerman (1986), Anderson (1993) and references therein, Castañeda (1980:59), Orilia (forthcoming).5Cf.  Gupta and Belnap (1993: 197).6Tarski (1956: 158) considers a similar argument (in a way that takes into accountsubtle considerations on quotation marks that we are ignoring here for simplicity’s sake)and offers a diagnosis along these lines: the biconditional schema (TB) cannot be regardedas a partial definition of the truth predicate, because “true” inescaply appears in what7should be the d finiens. Otherwise, Tarski presents the acceptable (by his standards) in-stances of (TB) as “partial definitions” of the truth predicate.7Cf. Gupta and Belnap (1993: 133).8Such as those foreshadowed, e.g., in Ackerman (1986), Anderson (1993), andOrilia (forthcoming).9An early version of this paper was presented at the Second National Meeting of theItalian Society of Analytic Philosophy, Vercelli (Italy), September 1996. We are thankfulto the audience for stimulating comments and discussion.ReferencesAckerman, D. F. (1986), ‘Essential Properties and Philosophical Analysis’, MidwestStudies in Philosophy, 11, 305-313.Anderson, A. (1993), ‘Analyzing Analysis’, Philosophical Studies, 72, 199-222.Castañeda, H.-N., On Philosophical Method, Bloomington, IN: oûs Publication.Gupta, A., and Belnap, N. (1993), The Revision Theory of Truth, Cambridge, MA, andLondon: MIT Press.Moore, G. E. (1944), “Russell’s Theory of Descriptions’, in P. A. Schilpp (ed.), ThePhilosophy of Bertrand Russell, N w York: Tudor, pp. 175-225.Moore, G. E. (1968), ‘A Reply to My Critics’, in P. A. Schilpp (ed.), The Philosophy ofG. E. Moore, La Salle, IL: Open Court, pp. 535-677.Orilia, F. (forthcoming), ‘Guise Theory, Property Theory, and Castañeda’s PhilosophicalMethodology’, in F. Orilia and W. Rapaport (eds.), Thought, Language, and Ontol-ogy, Essays in Memory of Hector-Neri Castañeda, Dordrecht: Kluwer.Tarski, A. (1956), ‘The Concept of Truth in Formalized Languages’,  in his Logic, Se-mantics, Metamathematics, Oxford: Clarendon, pp. 152-278.

A Note on Analysis and Circular Definitions

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A Note on Analysis and Circular Definitions

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