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Psychologism in the Logic of John Stuart Mill: Mill on the Subject Matter and Foundations of Ratiocinative Logic

2005; Taylor & Francis; Volume: 26; Issue: 2 Linguagem: Inglês

10.1080/01445340412331332809

1464-5149

David Godden,

Historical and Literary Studies

Abstract This paper considers the question of whether Mill's account of the nature and justificatory foundations of deductive logic is psychologistic. Logical psychologism asserts the dependency of logic on psychology. Frequently, this dependency arises as a result of a metaphysical thesis asserting the psychological nature of the subject matter of logic. A study of Mill's System of Logic and his Examination reveals that Mill held an equivocal view of the subject matter of logic, sometimes treating it as a set of psychological processes and at other times as the objects of those processes. The consequences of each of these views upon the justificatory foundations of logic are explored. The paper concludes that, despite his providing logic with a prescriptive function, and despite his avoidance of conceptualism, Mill's theory fails to provide deductive logic with a justificatory foundation that is independent of psychology. Acknowledgements First and foremost, I would like to thank David Hitchcock for his careful reading of earlier versions of this paper. His insightful comments and criticisms prompted considerable revisions and improvements to the paper, and contributed significantly to its final form. I would also like to gratefully acknowledge the contributions of Nick Griffin and Rockney Jacobsen with whom I had many enjoyable and instructive conversations concerning the topics discussed herein. The original version of this paper appears as chapter 3 of my doctoral thesis ‘Psychologism, Semantics and the Subject Matter of Logic’ (2004) written at McMaster University. Research for this paper was made possible by grants from the Social Science and Humanities Research Council of Canada, Ontario Graduate Scholarship, and McMaster University. Notes 1 That said, Frege does argue that Mill's account makes not only the truth but the very sense of arithmetical propositions contingent on psychological facts about our cognitive faculties (Frege Citation 1884 , §8; 1980, pp. 11–12). For a more complete treatment of Frege and Mill on the topic of arithmetic see Kessler Citation 1980 , and for a review of Frege's arguments against physicalist and abstractionist accounts of number see Cohen Citation 1998 . 2 As such, I set aside questions of whether Mill's account of such adjacent disciplines as arithmetic, geometry and even inductive logic are psychologistic. Instead, I am concerned only with Mill's account of the status and foundation of deductive logic, and with basic logical principles such as the law of non-contradiction. 3 Here, Mill seems to treat Ratiocination as coextensive with Syllogism. At other places, Mill makes (1843/1872, II.i.1; 1973, p. 158) the weaker claim that ‘syllogism is the general type [of ratiocination]’. 4 According to Mill ( Citation 1843 / Citation 1872 , II.i.3; 1973, p. 162), in addition to Induction and Ratiocination ‘there is a third species of reasoning, which falls under neither of these descriptions, and which, nevertheless, is not only valid, but is the foundation of both of the others’. While Induction is ‘reasoning from particulars to generals’ (1843/1872, II.i.3; 1973, p. 162), and Ratiocination is ‘reasoning from general to particulars’ (1843/1872, II.i.3; 1973, p. 162) this third species of reasoning appears to be reasoning from particulars to particulars—which encompasses all inference (1843/1872, II.iii.4; 1973, p. 193) and seems to have the form of reasoning by analogy (see 1843/1872, II.iii.3, 1973, pp. 186–92; 1843/1872, II.iii.7, 1973, p. 202). Mill describes this ‘universal type of the reasoning process’ as follows: ‘Certain individuals have a given attribute; an individual or individuals resemble the former in certain other attributes; therefore they resemble them also in the given attribute’ (1843/1872, II.iii.7; 1973, p. 202). 5 It should be noted that Jacquette himself does not hold this view (1997b, pp. 323–4). 6 See also Carnap's definition of ‘qualified psychologism’ (1950, §11; 1962, p. 39; as cited in Toulmin Citation 1958 , p. 86). 7 For an insightful account of Mill's views on the nature of belief see Mandit Citation 1984 . There, Mandit argues (1984, p. 86) that Mill held a fractured view on the nature of belief. In his writings on logic, Mill adopted a traditionally empiricist, psychological explanation of belief, while in his political writings Mill advanced an epistemic theory of belief ‘which in turn involves a philosophy of mind according to which mind is a social product forged in the intellectual and practical life of a community’. 8 Among these ‘more intricate states of mind’ Mill includes not only cognitive states and processes (e.g. inference) but also emotive states and processes (e.g. desire). 9 Since Mill considered inductive reasoning to be part of logic, Mill could be read as holding that the methodology of experimental psychology is part of logic. Yet, if one is concerned solely with the logic of necessary consequence, Mill's position obviously makes the psychologistic assertion that logic is dependent on psychology with respect to its methodology. 10 Here, Mill seems to relegate not only logic, but all of epistemology in general to psychology. 11 That is, on the naturalistic and psychologistic supposition that relations of evidence can and do hold between natural, psychological states. 12 But see Mandit Citation 1984 (cf. note 7 above). 13 Mill does offer five Canons of Induction which pertain to his four Methods of Experimental Inquiry (1843/1972, III.viii.1–7; 1973, pp. 388–406). Since I am concerned in this inquiry only with Mill's account of the foundations of the ratiocinative portion of logic, the foundations of induction are not a matter of immediate interest. That said, Mill holds that induction is involved in every real inference, including ratiocinative inference. Problematically, Mill draws no obvious or direct connection between these canons and the justification of ratiocinative inference. Instead, Mill provides a different set of principles, which he claims to provide the justificatory foundation of all ratiocinative inference, and it is these which I proceed to discuss below. 14 McCloskey rightly points out (1971, p. 22) that ‘traditional attempts to reduce all deductive forms of argument to the one syllogistic form would be widely questioned today’, and proceeds to give (1971, pp. 22–3) a number of deductively valid argument forms which are not reducible to a syllogistic form. Similarly, Skorupski ( Citation 1989 , p. 103) observes that the conversion rules for premises which allow syllogisms to be represented in the first figure are not all merely verbal. Instead, the conversion of some premises requires the law of non-contradiction which, as we will see, Mill considers a real proposition. 15 I here follow Mill's rather idiosyncratic categorization of inferences as false (or true), as opposed to the more common categorization of inferences as (deductively) valid or invalid according to whether they are necessarily truth-preserving, where the invalid ones are usually classified as (inductively) strong or weak according to whether they are generally truth-preserving. It might be speculated that Mill intended to indicate those inferences that are capable of leading one justifiably to the truth with his otherwise incorrect categorization here. 16 These features can be actual or possible (or sometimes even impossible), accurate or mistaken, past, present, or future. The point is that they must reach beyond the mental world of ideas to the world itself. 17 An interesting question for Mill's theory of language is how we arrive at ‘general concepts’ such as numbers. Supposing that our number concepts are based on physical objects or observed matters of fact, only two options appear to be available to explain the meaning of arithmetical expressions: number concepts result from a re-arrangement of the actual physical objects themselves; number concepts result from an abstraction from the particulars of the physical objects. These could be called the ‘physicalist account’ and the ‘abstractionist account’ respectively. It is not entirely clear whether Mill unequivocally held one or other of these views; instead he seems to waver between them. For instance, in some places (e.g. 1843/1872, II.v.1; 1973, pp. 224–7) Mill seems to advocate the abstractionist account, while in others (e.g. 1843/1872, II.vi.2; 1973, pp. 256–7) he seems to advance the physicalist (or aggregationalist) account. At any rate, Frege's arguments against each of these accounts are well known. Frege argues 1884[1980] against a physicalist account of number (which he attributes to Mill), while in his 1894[1972] Frege argues against an abstractionist account attributed to Husserl. Because my argument here does not explicitly concern the foundations of arithmetic or our number concepts, I leave a discussion of these matters for another occasion. 18 The dictum de omni et nullo was thought to derive from Aristotle's Prior Analytics i.I(24b 26), and through the middle ages it was commonly accepted as the foundational justificatory principle of syllogistic inference (Kneale and Kneale Citation 1962 , pp. 79, 272). 19 When Mill describes apparent inferences, he uses examples of ‘immediate inferences’ where the conclusion follows directly from just one claim and is obtained by a mere repetition of all or part of the claim from which it is derived (1843/1872, II.i.2; 1973, p. 158). Yet, the characteristic feature of an apparent inference is that: In all the cases [mentioned above] there is not really any real inference; there is in the conclusion no new truth, nothing but what was already asserted in the premises, and obvious to whoever apprehends them. The fact asserted in the conclusion is either the very same fact, or part of the same fact, asserted in the original proposition. (1843/1872, II.i.2; 1973, p. 160) Clearly, another class of inferences would also have the property just described: inferences where any derived claim follows necessarily from some claim taken from an initial list of premises (which may be real propositions) and a set of merely verbal truths about the meanings of the terms used in the initial list. Such inferences might be called ‘complex apparent inferences’. 20 Indeed, Mill claims (1843/1872, I.vi.5; 1973, pp. 116–17) that real general propositions like these axioms may be interpreted in two ways. He writes that all real general propositions may be looked at either ‘as portions of speculative truth, or as memoranda for practical use’ (1843/1872, I.vi.5; 1973, pp. 116–17). When viewed as ‘a portion of our theoretical knowledge’ the proposition makes a statement about whether certain attributes are accompanied by other attributes in things which are signified by a given term (1843/1872, I.vi.5; 1973, p. 117). This interpretation ‘points the attention more directly to what a proposition means’ (1843/1872, I.vi.5; 1973, p. 117). By contrast, ‘[t]he practical use of a proposition is, to appraise us or remind us what we have to expect, in any individual case which comes within the assertion contained in the proposition. In reference to this purpose, the proposition, All men are mortal, means that the attributes of man are evidence of, or are a mark of, mortality; an indication by which the presence of that attribute is made manifest’ (1843/1872, I.vi.5; 1973, p. 117). For Mill ‘[t]hese two forms of expression are at bottom equivalent’ (1843/1872, I.vi.5; 1973, p. 117). In this respect, Mill claims (1843/1872, II.ii.4; 1973, p. 180) that ‘every syllogism comes within the following general formula: Attribute A is a mark of attribute B; The given object has the mark A, therefore The given object has the attribute B’. Accordingly, Mill claims that the two axioms previously mentioned may be rephrased as follows: ‘Whatever has any mark, has that which it is a mark of’ ‘Whatever is a mark of any mark, is a mark of that which this last is a mark of’ (1843/1872, II.ii.4; 1973, p. 181). Here syllogisms are not divided according to whether the major premise is affirmative or negative, but rather according to whether the minor premise is universal or not. 21 Mill did not consider Hempel's ‘paradox of confirmation’ that flying squirrels contribute to the confirmation of the claim that all fish swim (Hempel 1945[1965], pp. 14–20; Quine 1969, pp. 114–16). 22 Importantly, Mill claims that an unqualified statement of the excluded middle is false, writing that ‘[b]etween the true and the false there is a third possibility, the Unmeaning’ (1843/1872, II.vii.5; 1973, p. 278). 23 It is likely that Mill added this passage either to the 7th edition of A System of Logic (which appeared in 1868) or to the 8th and final edition (which appeared in 1872). 24 Indeed, if the objects of experience are regarded as phenomena, the objects that we experience might best be thought of as the objects that are the ultimate causes of our experiences.