Abstract
The paradox of analysis has been a problem for analytic philosophers at least since Moore’s time, and it is especially significant for those who seek an account of analysis along classical lines. The present paper offers a new solution to the paradox, where a theory of analysis is given where (1) analysandum and analysans are distinct concepts, due to their failing to share the same conceptual form, yet (2) they are related in virtue of satisfying various semantic constraints on the analysis relation. Rather than distinguish between analysandum and analysans by appeal to epistemic considerations, the paper appeals to semantic considerations in giving a candidate account of the identity conditions for concepts. The distinctness of analysandum and analysans then serves to block the paradox in a straightforward way.
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Notes
In what follows, unless otherwise indicated I am speaking only of conceptual analyses. Russell wrote extensively on the problem of how to analyze propositions, for instance, but that sort of analysis is not my focus here. As for concepts themselves, I take them to be semantic values of various sorts of verbal expressions, not the verbal expressions themselves. For instance, in the sentence ‘Grass is green’, the concept of being green is expressed by the predicate ‘is green’. I also take concepts not to be ideas, mental representations, or any sort of mental particular whatsoever: In some of the literature on concepts, such mental particulars are often called “concepts”, but my discussion will not use the term in that sense.
Sometimes it is ambiguous in the literature whether ‘analysis’ refers to a kind of sentence or to a kind of proposition. Nothing here turns on this distinction, but for purposes of presentation I consider an analysis to be a sort of proposition. Similarly, I take analysanda and analysantia to be concepts, rather than the verbal expressions used to express them.
A complex concept is a concept with an analysis in terms of some other concepts. Those other concepts themselves have analyses in terms of still other concepts, and so on. It would seem then that there has to be some collection of primitive concepts that themselves have no analyses, and in terms of which all complex concepts are ultimately analyzed. It is beyond the scope of this paper to delve into the nature of primitive concepts further, but suffice it to say that views of concepts friendly to classical analysis would seem committed to the thesis that there are such primitive concepts, whatever their nature happens to be. For otherwise such views would have to allow for there to be circular analyses, or allow for the process of analyzing concepts in terms of simpler concepts to go on ad infinitum, or allow for there to be analyses in terms of concepts that are more complex.
This example is used by Sosa in his (1983).
See Ackerman (1990, 535–536).
Aside from such intuitive considerations, there are other reasons for denying that the proposition that a cube is a cube is an analysis. These will be noted below.
Sosa’s (1983) discussion is in terms of properties, and here I have modified his argument to reflect a parallel worry about analyses of concepts.
In what follows, I use square brackets to mention intensional entities such as propositions and concepts. For instance, the proposition expressed by ‘A cube is a cube’ is [A cube is a cube]. The predicate ‘is a cube’ expresses the concept of being a cube, or [cube].
For a response to Sosa, see Bealer (1983). For my own part, it seems that one of Sosa’s premises is false. Sosa suggests that for those who grasp [cube]’s aspect of being identical to [CS w/ SAS], they will then take [A cube is a CS w/ SAS] to be trivial. Yet when (for sake of argument) I suppose that [cube]=[CS w/ SAS], [A cube is a CS w/ SAS] still seems informative. Prima facie, expressions of that proposition tell me something that expressions of [A cube is a cube] does not.
There are other questions to raise as well, which seem to have easy answers on strategy (I). For instance, on strategy (II) the analysandum differs from the analysans, but in virtue of what is a correct classical analysis a necessary truth? Second, whether or not analyses are analytic or synthetic propositions, how is this further property to be accounted for if analysandum and analysans are distinct concepts? Strategy (I) provides fairly easy answers here. First, if analysandum and analysans are identical concepts then one can be sure that analyses are necessary truths: Since identical concepts necessarily have the same possible-worlds extension, analyses would have to be necessary truths. On strategy (I), analyses look to be analytic propositions as well, since if expressions of analyses are expressions of conceptual identities, and both analysandum and analysans are the same concept, then it appears that an analysis comes out analytic on all of the normal conceptions of analyticity. As far as strategy (II) is concerned, analyses are necessary truths on account of the analysandum and analysans sharing the same possible-worlds extension, just as for strategy (I). For the question of whether analyses are analytic or synthetic, however, the issue is not so clear. Ackerman addresses the question in her (1992, 174), where she subscribes to the view that analyses are synthetic. Yet this seems counter to the received view that analyses are paradigmatic cases of analytic propositions. As resolving the issue would require a comprehensive discussion of analyticity and syntheticity, I will not pursue the matter further here.
See also Chisholm (1992), which appeals to much the same claim with respect to the individuation of properties.
The phrase “contained in the thoughts” is Ackerman’s. This seems to suggest that thoughts are propositions, and concepts are “contained in” them, in some sense of ‘contained’. Perhaps Ackerman is a sort of conceptualist or physicalist with respect to the metaphysics of propositions and concepts. But the phrasing here should be read in a general sense to mean just this: At least some thoughts are of propositions, and propositions are analyzed (at least partly) in terms of concepts.
See Sosa (1983, 696–697). Again, Sosa’s version of the argument given here is in terms of analyses of properties, while mine is in terms of analyses of concepts, but the point would again appear to be the same.
If Sosa’s view is that the identity conditions for concepts differs from those for properties, then apologies are necessary here. But it is still the case that one might object to taking expressions of analyses to be expressions of the logical constitution of the analysandum in the same way as given in the text above.
She adds the further conditions that the analysandum be simpler than the (whole) analysans, and that the analysans does not contain the analysandum as a constituent (1992, 171–172).
Chisholm and Potter (1981; 1, 6) draw this distinction as well, though they do not use the term “the ‘is’ of analysis”. They take a sentence like ‘A cube is a CS w/ SAS’, when taken as an analysis, to be short for ‘being a cube is analyzed by being a CS w/ SAS’.
One can now see that the more or less standard way of expressing analyses in terms of necessary biconditionals is somewhat misleading (as by ‘x is a cube iff x is a CS w/ SAS’, for instance). If the ‘is’ of analysis does not signify the ‘is’ of identity, then expressing analyses in terms of open sentences joined by a biconditional looks to be inadequate. I have chosen to use the expression ‘isA’ to distinguish analyses from mere predications and identifications, but one could also use the standard schema with the biconditional expressed by ‘iffA’ or ‘iffdef’ to serve the same purpose.
I thus allude to Wittgenstein’s (1922) distinction between showing and saying here. Yet contra Wittgenstein’s claim that “What can be shown cannot be said [italics in original] (4.1212),” I mean to suggest quite a bit about what is shown by an expression of an analysis.
Why is the A -relation a three-place relation instead of a two-place relation, as in the other uses of ‘is’? In other words, why take a sentence like “F isA a G” to express a three-place relation, when the surface grammar seems to suggest that a two-place relation is being expressed? My suggestion is that the predicate ‘isA G’ does double-duty: It not only expresses [G], but it shows a logical constitution of [F] in virtue of expressing [G]. Thus not only do analysandum and analysans have places in the A -relation, but so must the logical constitution shown by that expression of that analysans.
The condition here is to avoid circular analyses. See also Chisholm and Potter (1981, 1).
See Sosa (1995). According to Sosa, Q is a metaphysically necessary condition for P iff necessarily, if P, then Q. Similarly, Q is a metaphysically sufficient condition for P iff necessarily, if Q, then P.
See also Ackerman (1986, 307–308; 1992,171–172; 1995). She leaves this condition on an intuitive level (1992, 172), and for my purposes here I will do the same: It seems that an analysis of a concept cannot be given solely in terms of a less complex concept. See also Moore (1966, 159; 1968, 666, 667), Greig (1970, 260), Langford (1968; 325–326,337–338), and Chisholm and Potter (1981,1). This suggestion seems to fit with a common intuition concerning analysis: Ackerman (1995) expresses that intuition with the claim that “[S]omething is analyzed by breaking it down into its parts” (citing Moore 1903/1994, §§8, 10).
Note further that a pair of concepts [F] and [G] can fail corollary (c2) in two ways: One of [F 1],...,[F n] could be either identical to [F] or one of [F 1],...,[F n] could be merely necessarily coextensive with [F].
Such an extension might be imprecise, in the sense that an extension may not be specified in such a way that necessarily, any particular thing is either definitely in or definitely not in that extension. In addition, if there are necessarily uninstantiated concepts, their analyses would seem to specify the null extension (or the null set) as its extension across possible worlds.
This condition leads to the standard ways of testing candidate analyses by means of seeking such counterexamples. See, e.g., Ackerman (1995), Jackson (1998, 31–37). The history of philosophy has of course seen various criticisms of this method, the most famous of course being Wittgenstein (1953, §§65–78), although Fodor et al. (1980/1999) is well-known. See also Ramsey (1992) and Stich (1998).
Conditions (a) and (c) are indeed redundant with conditions (i)-(iii). But I mention them again here since conditions (i)-(iii) are conditions on a proposition’s being a classical analysis, while conditions (a)-(c) are conditions on a concept’s being an analysans in a classical analysis.
One might take a concept to have itself as a logical constitution, and thus that in some very general sense ‘A cube isA a cube’ does show a logical constitution of [cube] (namely ([cube])). But even if this sort of consideration holds, there are other difficulties with taking ‘A cube is a cube’ to express a genuine analysis of [cube].
For instance, there is one sort of consideration (suggested in conversation by George Bealer) that allows for a distinction between what is expressed by and what is shown by an analysans expression, yet still allows for analysandum and analysans to be identical. For one might paraphrase ‘An F isA a G’ as ‘[F] is that concept [G] the expression of which shows a logical constitution of [F], namely ([G 1],..., [G n])’. So then ‘A cube isA a CS w/ SAS’ would be paraphrased as ‘[cube] is that concept [CS w/ SAS] the expression of which shows a logical constitution of [cube], namely ([CS], [SAS])’. On this view of analysis, [cube] and [CS w/ SAS] can be identical, yet ‘A cube is a cube’ expresses a proposition distinct from ‘A cube isA a CS w/ SAS’. For ‘is a cube’ shows a logical constitution of [cube] (namely just ([cube])) that is distinct from that logical constitution shown by ‘is a CS w/ SAS.’
This is a promising strategy for solving the paradox of analysis as well, but I note two considerations against it. First, I cannot help but worry that if [cube]=[CS w/ SAS], ‘A cube isA a CS w/ SAS’ expresses a circular analysis, and noncircularity is a condition on a proposition’s being a classical analysis. Second, if [cube]=[CS w/ SAS], then the following two analyses would seem to be equivalent:
[cube] is that concept [CS w/ SAS] the expression of which shows a logical constitution of [cube], namely ([CS], [SAS]).
[CS w/ SAS] is that concept [cube] the expression of which shows a logical constitution of [CS w/ SAS], namely ([cube]).
Yet they are not equivalent: The former is what is expressed by the paraphrase of ‘A cube isA a CS w/ SAS’ and the latter is what is expressed by the paraphrase of ‘A CS w/ SAS isA a cube’, and the latter seems not to express an analysis. There may be ways of strengthening this sort of strategy for solving the paradox of analysis, but I set it aside here and continue to focus on a strategy that takes analysandum and analysans to be distinct.
I will note one point here that has been raised by both George Bealer and Michael Tooley in conversation. Whatever the logic of immediate inference is, it would have to be somewhat different than ordinary first-order logic. For instance, the logic of immediate inference would have to allow for inferences such as that expressed by ‘(P&Q&R), therefore R’ to be immediately inferable, as well as for ‘(P&Q&R)’ to be well-formed. In standard forms of sentential logic this kind of inference is of course disallowed, for strictly speaking ‘(P&Q&R)’ is not well-formed, and nor is ‘(Fx&Gx&Hx)’ in predicate logic. I suppose there are at least two options here: On one hand, one might use a standard form of logic for the logic of immediate inference and include some specification of what chains of inferences still count as “immediate” inferences. Or on the other hand, one might give a different logic for immediate inference where such inferences that are to count as immediate are capable of being made with one step.
If this sort of suggestion is worthwhile, one might now have in hand a means of deciding whether one concept is more complex than another. For one might hold that a concept [F] is more complex than [G] iff the immediately inferable logical constitution of [F] has more members than the immediately inferable logical constitution of [G]. Similarly, a concept [F] is at least as complex as [G] iff the immediately inferable logical constitution of [F] has at least as many members as the immediately inferable logical constitution of [G].
References
Ackerman, D. F. (1981). The informativeness of philosophical analysis. In P. French, et al. (Eds.), Midwest studies in philosophy (vol. 6 pp. 313–320). Minneapolis, MN: University of Minnesota Press.
Ackerman, D. F. (1986). Essential properties and philosophical analysis. In P. French, et al. (Eds.), Midwest studies in philosophy (vol. 11 pp. 304–313). Minneapolis, MN: University of Minnesota Press.
Ackerman, D. F. (1990). Analysis, language, and concepts: The second paradox of analysis. Philosophical Perspectives, 4, 536–543.
Ackerman, D. F. (1992). Analysis and its paradoxes. In E. Ullman-Margalit (Ed.), The scientific enterprise: The Israel colloquium studies in history, philosophy, and sociology of science (vol. 4 pp. 169–178). Norwell, MA: Kluwer.
Ackerman, D. F. (1995). Analysis. In J. Kim, & E. Sosa (Eds.), A companion to metaphysics (pp. 9–11). Oxford: Blackwell.
Bealer, G. (1982). Quality and concept. New York: Clarendon Press.
Bealer, G. (1983). Remarks on classical analysis. Journal of Philosophy, 80(11), 711–712.
Chisholm, R. (1992). Identity criteria for properties. Harvard review of Philosophy, 2(1), 14–17.
Chisholm, R., & Potter, R. C. (1981). The paradox of analysis: A solution. Metaphilosophy, 12(1), 1–6.
Fodor, J. A., Garrett, M. F., Walker, E. C. T., & Parkes, C. H. (1980/1999). Against definitions. In E. Margolis, & S. Laurence (Eds.), Concepts: Core readings (pp. 421–512). Cambridge: M.I.T. Press.
Greig, G. (1970). Moore and analysis. In A. Ambrose, & M. Lazerowitz (Eds.), G. E. Moore: Essays in retrospect (pp. 242–268). London: Humanities Press.
Jackson, F. (1998). From metaphysics to ethics: A defence of conceptual analysis. Oxford: Clarendon Press.
Jubien, M. (1997). Contemporary metaphysics. Oxford: Blackwell Publishers.
King, J. (1998). What is a philosophical analysis? Philosophical Studies, 90, 155–179.
Langford, C. H. (1968). The notion of analysis in Moore’s philosophy. In P. Schlipp (Ed.), The philosophy of G. E. Moore (pp. 321–342). LaSalle, IL: Open Court.
Moore, G. E. (1903/1994). Principia ethica. Cambridge: Cambridge University Press.
Moore, G. E. (1966). Lectures on philosophy. In C. Lewy, (Ed.) London: Humanities Press.
Moore, G. E. (1968). A reply to my critics. In P. Schlipp (Ed.), The philosophy of G. E. Moore (pp. 660–677). LaSalle, IL: Open Court.
Ramsey, W. (1992). Prototypes and conceptual analysis. Topoi, 11, 59–70.
Rieber, S. D. (1994). The paradoxes of analysis and synonymy. Erkenntnis, 41, 103–116.
Sellars, W. (1964). The paradox of analysis: A neo-Fregean approach. Analysis, 24, 84–98.
Sosa, E. (1983). Classical analysis. Journal of Philosophy, 80(11), 695–710.
Sosa, E. (1995). Condition. In R. Audi, (Ed.), The Cambridge dictionary of philosophy (p. 149). Cambridge: Cambridge University Press.
Stich, S. (1998). Reflective equilibrium, analytic epistemology and the problem of cognitive diversity. In M. DePaul, & W. Ramsey (Eds.), Rethinking intuition: The psychology of intuition and its role in philosophical inquiry (pp. 95–112). Lanham, MD: Rowman and Littlefield.
Wittgenstein, L. (1922). Tractatus logico-philosophicus. London: Routledge., (Trans C. K. Ogden).
Wittgenstein, L. (1953). Philosophical investigations. 3rd Ed. New York: MacMillan.
Acknowledgments
I would like to thank George Bealer, Graham Oddie, Christopher Shields, Michael Tooley, and especially Robert Hanna for helpful comments and discussion with respect to the thoughts presented in this paper.
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Earl, D. A Semantic Resolution of the Paradox of Analysis. Acta Anal 22, 189–205 (2007). https://doi.org/10.1007/s12136-007-0010-0
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DOI: https://doi.org/10.1007/s12136-007-0010-0