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Logical Expressivism and Carroll's Regress

Published online by Cambridge University Press:  18 September 2019

Corine Besson*
Affiliation:
University of Sussex

Abstract

In this paper, I address a key argument in favour of logical expressivism, the view that knowing a logical principle such as Modus Ponens is not a cognitive state but a pro-attitude towards drawing certain types of conclusions from certain types of premises. The argument is that logical expressivism is the only view that can take us out of Lewis Carroll's Regress – which suggests that elementary deductive reasoning is impossible. I show that the argument does not hold scrutiny and that logical cognitivism can be vindicated. In the course of the discussion, I draw substantially on a comparison with a similar argument in meta-ethics, for moral expressivism.

Type
Papers
Copyright
Copyright © The Royal Institute of Philosophy and the contributors 2019 

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References

1 Carroll, Lewis, ‘What the Tortoise Said to Achilles’, Mind 4 (1895), 278280CrossRefGoogle Scholar.

2 The distinction was made popular by Anscombe, Elizabeth G. M., Intention (Oxford: Basil Blackwell, 1957)Google Scholar. See Smith, Michael A., The Moral Problem (Oxford: Basil Blackwell, 1994)Google Scholar for its connection to the Humean theory of motivation. See Humberstone, Lloyd, ‘Directions of Fit’, Mind 101(401) (1992), 5983CrossRefGoogle Scholar, for a discussion of its role in various philosophical contexts.

3 See Davidson, Donald, ‘Actions, Reasons and Causes’, The Journal of Philosophy 60 (1963), 685700CrossRefGoogle Scholar.

4 Smith, op. cit. note 2, 60ff. I set aside the view according to which it is a desire-like state necessarily connected to the judgment that motivates but not strictly speaking the judgment itself. I also set aside the issue of whether it is really moral judgments rather than the moral facts those judgments are about that ultimately motivate. These won't matter for our discussion.

5 Gunnar Björnsson et al., ‘Motivational Internalism’, Gunnar Björnsson, Caj Strandberg, Ragnar Francén Olinder, Eriksson, John, and Björklund, Fredrik (eds), Motivational Internalism, (Oxford: Oxford University Press, 2015), 1Google Scholar.

6 There is a plethora of formulations of Internalism, many of which are weaker or conditional, so as to allow for proper qualifications as to the kinds of agents (rational, psychologically normal, morally perceptive, etc. that are at issue). These need not concern us here but see op. cit. note 5.

7 Smith, op. cit. note 2, 71–77.

8 For this argument see inter alia Smith op. cit. note 2, 75–76. For discussion, see Copp, David, ‘Belief, Reason, and Motivation: Michael Smith's The Moral Problem’, Ethics 108 (1997), 3354CrossRefGoogle Scholar.

9 Brink, David, Moral Realism and the Foundation of Ethics. (Cambridge: Cambridge University Press, 1989)CrossRefGoogle Scholar, argues for the possibility of amoralism. On the internalist side, for instance, Smith, op. cit. note 2, 68–71, argues for the incompetence claim. See also Lenman, James, ‘The Externalist and the Amoralist’, Philosophia 27 (1999), 441457CrossRefGoogle Scholar.

10 For classical defenses of pure non-cognitivism, see Blackburn, Simon, Ruling Passions: A Theory of Practical Reasoning, (Oxford: Oxford University Press, 1998)Google Scholar and Gibbard, Allan, Thinking How to Live. (Cambridge, Mass.: Harvard University Press, 2003)Google Scholar

11 Notice that there are global expressivists, such as Price, Hugh, Expressivism, Pragmatism and Representationalism, (Cambridge: Cambridge University Press, 2013)CrossRefGoogle Scholar, who hold that language is never descriptive and do not tie expressivism to normative language in particular, but to a general commitment to naturalism.

12 There are of course other ways of being a non-cognitivist than expressivism – e.g. emotivism (Ayer, Alfred, Language, Truth and Logic (New York: Dover, 1936)Google Scholar) and prescriptivism  (Hare, Richard M., The Language of Morals (Oxford: Oxford University Press, 1952)Google Scholar). However it is typically thought that non-cognitive expressivism ties in nicely with motivational internalism: motivation seems to require pro-attitudes such as desires.

13 Op. cit. note 10.

14 For discussion, see Schroeder, Mark, Being For: Evaluating the Semantic Programme of Expressivism (Oxford: Oxford University Press, 2008), ch. 3CrossRefGoogle Scholar.

15 For a critical survey of hybrid expressivism, see for instance Ridge, Michael, ‘Ecumenical Expressivism: Finessing Frege’, Ethics 116 (2006), 302–36CrossRefGoogle Scholar; and Schroeder, Mark, ‘Hybrid Expressivism: Virtues and Vices’, Ethics 119 (2009), 257309CrossRefGoogle Scholar.

16 See William W. Bartley III, (ed.), Lewis Carroll's Symbolic Logic: Part I, Elementary, 1896, Fifth Edition; Part II, Advanced, Never Previously Published: Together with Letters from Lewis Carroll to Eminent Nineteenth-Century Logicians and to his “Logical Sister,” and Eight Versions of the Barber-shop Paradox (New York: Clarkson N. Potter/Hassocks, Sussex: Harvester Press, 1977. [2nd ed., 1986]).

17 There are as many interpretations of Carroll's Regress as there are interpreters. For detailed discussion of key interpretations, see my Norms, Reasons and Reasoning: a Guide Through Lewis Carroll's Regress Argument’, in Star, Daniel (ed.), The Oxford Handbook of Reasons and Normativity, (Oxford: Oxford University Press, 2018), 504528Google Scholar; and Logic, Reasoning and the Tortoise, (Oxford: Oxford University Press, forthcoming).

18 It is clear that Carroll takes conditionals to be propositions, but there are of course dissenting views. See for instance Edgington, Dorothy, ‘On Conditionals’, Mind 104 (1995), 235329CrossRefGoogle Scholar.

19 This point has been made by pretty much every commentator on the Regress in one form or the other. To my knowledge Moore, George E., ‘Experience and Empiricism’, Proceedings of the Aristotelian Society 3 (1902–1903), 8095CrossRefGoogle Scholar, is the first to make it in print. For extended discussion, see also Ryle, Gilbert, ‘Knowing How and Knowing That’, Proceedings of the Aristotelian Society, 46 (1945–1946)Google Scholar, reprinted in Collected Papers, vol. 2, (London: Hutchinson, 1971), 212–225; and Gilbert Ryle, ‘If, So, Because’ (1950), reprinted in his Collected Papers, vol. 2. (London: Hutchinson 1971), 244–260.

20 Sometimes commentators suggest that Carroll is mistaken in taking his rules of inference to be premises. But of course (Cond) is not what philosophers mean by a rule, as it is not about how to reason.

21 There is a tradition of thinking of logical principles of reasoning as imperatives, rather than using ‘ought’, with the intention of capturing obligation. See Ryle (op. cit. note 19). For the idea that rules are commands, see Ludwig Wittgenstein, Remarks on the Foundations of Mathematics, G. E. M. Anscombe et al. (eds), trans. G. E. M Anscombe. (Oxford, 1956 [1978]: Blackwell). For a recent defence of the claim that logical norms are imperatives see Field, Hartry, ‘Epistemology from an Evaluativist Perspective’, Philosophers’ Imprint 18(12), (2018)Google Scholar, 12ff. The difference between these two ways of thinking about logical principles of reasoning will not matter here.

22 Many philosophers think that we can know logical principles such as Modus Ponens, or, at any rate, they take themselves to be specifying conditions for knowing a logical principle, or the form that such knowledge would take. I will thus follow the orthodoxy in focusing on knowledge.

23 I can only really sketch these views here and cannot do justice to their sophistication and differences. Slogans are convenient, but simplifying, and I hope that this one is not so simplifying as to misrepresent any of these views. See op. cit. note 17 for a fuller discussion of some of them.

24 Op. cit. note 19.

25 Boghossian, Paul A., ‘How are Objective Epistemic Reasons Possible?’, Philosophical Studies 106 (2001), 2627CrossRefGoogle Scholar.

26 Ibid, 2.

27 Wittgenstein, Ludwig, Philosophical Investigations, Anscombe, G. E. M. et al. (eds), trans. Anscombe, G. E. M, (Oxford: Blackwell, 1953), §219.Google Scholar

28 See Boghossian, Paul A., ‘Blind Reasoning’, Aristotelian Society Supplementary Volume 77 (2003), 236ffGoogle Scholar.

29 Phillie, Patrice, ‘Carroll's Regress and the Epistemology of Logic’, Philosophical Studies 134 (2006), 183210CrossRefGoogle Scholar, 186.

30 Ibid, 206–7.

31 Engel, Pascal, ‘The Philosophical Significance of Carroll's Regress’, in Abeles, Francine and Moktefi, Amirouche (eds) ‘What the Tortoise Said to Achilles’. Lewis Carroll's Paradox of Inference, The Carrollian 28 (2016), 92Google Scholar.

32 Ibid, 96.

33 Ibid, 104.

34 Blackburn, Simon, ‘Practical Tortoise Raising’, Mind 104 (1995), 695CrossRefGoogle Scholar.

35 For an extended and helpful discussion of Blackburn's Practical Tortoise, see Broome, John, ‘Normative Requirements’, Ratio 12 (1999), 398419CrossRefGoogle Scholar.

36 There are intricate issues here concerning what is exactly involved in applying a general logical principle of reasoning to one's reasoning, which I do not have space to address. For discussion, see my ‘Knowledge of Logical Generality and the Possibility of Deductive Reasoning’, in Timothy Chang and Anders Nes (eds), Inference and Consciousness, (Cambridge: Routledge, forthcoming).

37 Boghossian, Paul A., ‘Knowledge of Logic’, in Boghossian, Paul and Peacocke, Christopher (eds), New Essays on the A Priori (Oxford: Oxford University Press, 2000), 230CrossRefGoogle Scholar.

38 It is widely presupposed that if logical principles are explicitly represented they cannot be, as such, action-guiding. However, for original and compelling arguments against the presupposition that explicit or metalinguistic representation is sealed from action – i.e. not action-guiding – see Simchen, Ori, ‘Rules and Mention’, The Philosophical Quarterly 51 (2001), 455473CrossRefGoogle Scholar. According to him, the Regress asks what it is for a rule to be ‘action-guiding’ (456) and wrongly suggests that explicit representation cannot be action-guiding.

39 Harman, Gilbert, Change in View (Cambridge, Mass.: MIT Press, 1986)Google Scholar.

40 For instance, Boghossian (op. cit note 37, 229; note 24, 2) explicitly adopts such a wide-scope principle. The difficult question of how to tie facts of validity to facts of obligation, or normative facts more generally – how to formulate so-called ‘bridge principles’ – is currently receiving a lot of attention. I cannot do it justice here. See e.g. John MacFarlane, ‘In What Sense (If Any) is Logic Normative for Thought?’, Unpublished (2004) for discussion.

41 Op. cit. note 35, 405.

42 There is more to be said about this characterization of logical cognitivism to which I come back in section 6.

43 Wittgenstein, Ludwig, Tractatus Logico-Philosophicus, trans. Ogden, C. K. (London: Routledge and Kegan Paul, 1922)Google Scholar; Brandom, Robert, Making It Explicit (Cambridge, Mass.: Harvard University Press, 1994)Google Scholar.

44 Field, Hartry, ‘Epistemology without Metaphysics’, Philosophical Studies 143 (2009), 249290CrossRefGoogle Scholar; op. cit. note 21.

45 Wright, Crispin, ‘Logical Non-Cognitivism’, Juhl, Cory and Schechter, Joshua (eds), Philosophy of Logic and Inferential Reasoning, Philosophical Issues (2018), 425450.Google Scholar.

46 Wright is not an anti-realist about logic, unlike Field, and also, as he stresses, unlike Wittgenstein (op. cit. note 27).

47 Classic defenses in the specific case of moral cognitivism are e.g. Nagel, Thomas, The Possibility of Altruism (New York: Oxford University Press, 1970)Google Scholar; McDowell, John, ‘Are Moral Requirements Hypothetical Imperatives?’, Proceedings of the Aristotelian Society Supplementary Volume 52 (1978), 1329CrossRefGoogle Scholar; and Wiggins, David, ‘Moral Cognitivism, Moral Relativism and Motivating Moral Beliefs’, Proceedings of the Aristotelian Society 91 (1991), 6185CrossRefGoogle Scholar. Functionalists about mental states (e.g. Robert Stalnaker, Inquiry (Cambridge MA: MIT Press, 1984) can also develop resources to essentially relate belief to action. Furthermore, intellectualists about knowing how have argued that knowing how can be construed as a kind of propositional knowledge with a special relationship to action. See in particular Stanley, Jason and Williamson, Timothy, ‘Knowing How’, The Journal of Philosophy 98 (2001), 411444CrossRefGoogle Scholar; and Stanley, Jason, Knowing How (Oxford: Oxford University Press, 2011)CrossRefGoogle Scholar.

48 I will not settle here for one specific characterization of such goals as this would require a paper in itself.

49 Alvarez, Maria (‘Reasons for Action, Acting for Reasons, and Rationality’, Synthèse 195 (2018), 32933310)CrossRefGoogle Scholar persuasively argues that, contrary to orthodoxy, we should distinguish between motivating and explanatory reasons. As nothing turns on their differences here, I will however lump them together.

50 The matter is more delicate than I can do justice here, for four broad reasons. First, M/E reasons might not be transparent to agents. Second, agents might have different modes of presentation for the judgment that they ought not to eat meat – some normative (‘it's wrong’) some not so (‘I was raised a vegetarian’). Thus, the normative judgment might not always be the primary answer to the why question, even though it is the ultimate or one of the ultimate M/E reasons. Third, there might be other norms (perhaps conversational norms, norms of politeness, propriety, etc.) in place in a given context that do not permit asserting the normative judgment as an answer to the why question. Fourth, the interaction between normative reasons and M/E reasons is complex (For discussion, see Smith op. cit. note 2, ch. 4).

51 See for instance, Priest, Graham, ‘Logical Disputes and the A Priori’, Logique et Analyse 59 (2016), 347366Google Scholar; Field, op. cit. note 21. For discussion, see for instance MacFarlane, op. cit. note 40.

52 See e.g. Blackburn (op. cit. note 34), Engel (op. cit. note 31), Phillie (op. cit. note 29).

53 Davidson, Donald, ‘How Is Weakness of the Will Possible?’, in Davidson, Donald, Essays on Actions and Events (Oxford: Clarendon Press, 1980), 2142Google Scholar.

54 Again, this is presupposing the Humean theory of motivation.

55 For more details on how to articulate this cognitivist enabling view of knowledge of logical principles see my forthcoming (op. cit. note 17).

56 I first presented the ideas for this paper at the Normativity of Logic International Conference in Bergen in June 2017; I am grateful to its participants for their feedback. I am also grateful to the participants to the UCL Workshop on Expressivism, Knowledge and Truth organised by Maria-Jose Frápolli in October 2018, and for the follow-up discussions with Matthew Simpson, and Jose Zalabardo. Warmest thanks also to audiences at the Bristol Philosophy Seminar, and the Glasgow Senior Seminar. I am especially indebted to Ane Engelstad, Maria-Jose Frápolli, Anandi Hattiangadi, Gerald Lang and Adam Swift for comments on the penultimate draft of this paper. This research was partly funded by the Swedish Research Council (for the Research Project: Expressivism Generalised: the Scope of Non-Descriptive Thought and Talk (grant number: 421-2012-988) and the Bank of Sweden (for the Research Project: The Foundations of Epistemic Normativity (grant number P17-0487:1)). I am grateful to both funding bodies.