Logic, rationality and knowledge in Ramsey's thought: reassessing ‘human logic’

Abstract

This paper reconsiders Frank Ramsey's essay on subjective probability (1926) as a consistent way to articulate logic, rationality and knowledge. The first part of the essay builds an axiomatic theory of subjective probability based on ‘formal logic’, defining rationality as choice-consistency. The second part seems to open up different horizons: the evaluation of degrees of belief by ‘human logic’. Because of the interest Keynes (1931) had taken in ‘human logic’, it was considered to be a possible alternative to the formal logic underlying the neoclassical theory of individual behaviour. The analysis of Ramsey's method in the entire paper, the relation between logic and rationality it constructs and the conception of uncertainty it reveals, lead me to note on the contrary that Ramsey's human logic was a complementary logic rather than an alternative to formal logic. Defining a standard to evaluate beliefs formation according to a frequentist criterion, it completes a normative representation of rationality which supports an original theory of knowledge that appears more in line with further developments of neoclassical methodology than with Keynesian economics.

Keywords::

• Frank P. Ramsey
• subjective probabilities
• human logic
• rational behaviour
• theory of knowledge

Acknowledgements

I thank Pascal Bridel, Gilles Dostaler and Emmanuel Picavet for helpful comments on previous drafts of the paper. The paper has also benefited from insightful critics and suggestions made by the two anonymous referees. The usual caveats apply.

Notes

^1. Ramsey had already commented on the Treatise in a book review for the Cambridge Magazine (Ramsey, 1922) and in talks at the Apostles Society or at the Moral Science Club (Ramsey, 1923). ‘Truth and Probability’ was published posthumously by R. Braithwaite (Ramsey, 1931).

^2. Newman (1987) remarks that the first reference to Ramsey's theory appears in Little (1950) who compares Ramsey's analysis to those of von Neumann and Morgenstern (1947); then in Arrow (1951) who notes that Von Neumann and Morgenstern were anticipated by Ramsey ‘in the axiomatic treatment of choice among probability distributions (…) leading to a new understanding of the rule of maximizing the expected utility’ (Arrow, 1951, p. 405). Savage (1954) also refers explicitly to Ramsey. The first discussions of Ramsey's theory can be found in Davidson and Suppes (1956), than in Anscombe and Aumann (1963).

^3. In his short review of Ramsey's works, Keynes indeed underlined that ‘In attempting to distinguish a ‘human’ logic from formal logic on the one hand and descriptive psychology on the other, Ramsey may have been pointing the way to the next field of study when formal logic has been put into good order and its highly limited scope properly defined’ (1931, p. 339).

^4. Keynes' (1931) review of Ramsey's works includes his partial but one-off reply to the criticism of the Treatise on Probability Ramsey had assessed in the 1926 paper. As such, the 1931 review feeds the discussion on the continuity and global consistency of Keynes' works (Carabelli, 1988; Gerrard, 1992b; O'Donnell, 1982; Winslow, 1986) and on the possibility to find in the Treatise methodological foundations for the GeneralTheory (Keynes, 1936). See also Runde, Winslow or Gerrard in Runde and Mizuhara (2003), or Davis (1994). I do not try here to address this issue. However, I take for granted that Keynes' (1931) point of view shows that while he may have partly abandoned his logical interpretation of probability, Keynes was still searching, at the beginning of the 1930s, for an enlarged logic able to lay the foundations of an alternative representation of human behaviour.

^5. Our aim in that section is not to discuss Keynes's theory but to recall its main principles and foundations in order to enlighten the nature of Ramsey's critique.

^6. The logical skill of human mind and the indefinable property of probability in the Treatise (‘probability begins and ends with probability’; Keynes, 1921, p. 356) are compared with Moore's moral faculty and the indefinable property of goodness in Principia Ethica ([1903] 1993). The parallel Ramsey identifies in 1923 has been since then frequently underlined. See for instance Harrod (1951, p. 652), Skidelsky (1983, p. 119). O'Donnell (1982, pp. 90–92, 97), Carabelli (1988, chap. 3), Davis (1994, chap.1 and 2).

^7. In Moore's philosophy and in the lineage of Sidgwick's thought, ethics must hold all by itself and psychology cannot be the basis of ethics.

^8. Allusions to Freud's discoveries are recurrent in Ramsey's lectures at the Apostles Society, between 1921 and 1925.

^9. Ramsey dissociates himself from the traditional English empiricism, where ‘it is natural to associate belief with a certain “vivid idea” in our mind or with a certain introspectible feeling towards some representations’ (Dokic & Engel, 2002, p. 7). Keynes had already distanced himself from this tradition. He accepted introspection as a basis for evaluating a degree of probability but unlinked the degree of belief and the intensity of such a degree with the notion of ‘weight of argument’ (Keynes, 1921, p. 77).

^10. Ramsey quotes the 1923 edition of Peirce's founding texts by M. Cohen, under the title ‘Chance, Love and Logic’. The reference also appears in Ramsey (1991, pp. 91–94).

^11. The propensity to bet had already been mentioned by Kant (1781) as a discriminating criterion to distinguish opinions, persuasion or ‘firm belief’, see Picavet (1996, pp. 176–179). De Finetti's project to ‘establish the logical laws of probabilities on subjective grounds’ (1937, p. 4) will later also be grounded on the betting method.

^12. The issue is the study of propositional attitudes of the form ‘x believes that p’. To believe that p means to be ready to act as though p is the case. On the part of beliefs as disposition to act in classical pragmatism, see Engel (2005).

^13. ‘If then we had the power of the Almighty, and could persuade our subject of our power, we could, by offering him options, discover how he placed in order of merit all possible courses of the world. In this way all possible worlds would be put in an order of value, but we should have no definite way of representing them by numbers’. (Ramsey, 1926, p. 72)

^14. ‘An atomic proposition p is called ethically neutral if two possible worlds differing only in regard to the truth of p are always of equal value’ (Ramsey, 1926, p. 73).

^15. For a detailed analysis of Ramsey's demonstrations, see for instance Sahlin (1990), Picavet (1996) or Dokic and Engel (2002).

^16. Probability expressed as a ratio of values differences.

^17. Contesting Keynes' idea according to which deduction and induction are distinguished by the degree of logical relation, Ramsey repeats that ‘deduction […] is merely a method of arranging our knowledge and eliminating inconsistencies or contradictions’ (Ramsey, 1926, p. 82).

^18. Ramsey's logicist past remains important here. The reduction of ordinary or scientific discourse to well-articulated logical propositions guarantees that they are meaningful.

^19. Ramsey never uses the words ‘rational’ or rationality' for referring to his own theory. Those words only appear when Ramsey comments on Keynes' theory and adopts critical viewpoint. Coates' appreciation (1996, p. 136) according to which Ramsey would associate ‘rational’ with ‘justified by formal logic’, and ‘reasonable’ as a vague expression of what is ‘in accord with reason’ (linked to human logic) is misleading. Ramsey always uses ‘reasonable’ to qualify his own results.

^20. In that sense, there is no logical foundation for the principle of indifference: ‘[The individual] original expectations may within the limits of consistency be any he likes’ (Ramsey, 1926, p. 85).

^21. Except the important fact that Ramsey does not use the Bayesian rule for updating the decision maker system of beliefs with experience. See Section 5.

^22. Ramsey does not establish the equivalence between the rule of expected utility maximisation and his axiomatics. He tries to deduce conditions for measuring degrees of belief and uses the maximisation of expected values as an assumption. He deduces that consistency is a necessary condition for measuring degrees of belief. According to Carnap (1962, p. 308), the fact that it is also a sufficient condition has been established by Kemeny (1955) and Leyman (1955).

^23. Savage highlights such a definition of rationality as consistency and describes his own theory of personal probability as ‘a code of consistency for the person applying it’ (1954, p. 59).

^24. The conditional inherent to the concept of dispositional belief does not prejudice any descriptive use of the theory. Beliefs are in substance dispositional and to imagine the betting method is precisely to imagine an actualisation process of dispositional beliefs.

^25. Savage presents his own theory as ‘a highly idealized theory of the behaviour of a “rational” person with respect to decisions’ (Savage, 1954, p. 7), which ‘enables the person using it to detect inconsistencies in his own real or envisaged behaviour’ (Savage, 1954, p. 57).

^26. Ramsey moves here from a pragmatist method of revealing beliefs to a pragmatist theory of truth like the second generation of American pragmatists, W. James or J. Dewey.

^27. Dokic and Engel evoke a ‘Ramsey's principle’, according to which ‘the truth conditions of a belief are the set of actions which are useful if and only if this belief is true’ (Dokic & Engel, 2002, p. 25).

^28. The reasonable degree of belief should, for instance, be equal to ‘the proportion of cases of lighting which are actually followed by thunder’ (Ramsey, 1926, p. 92) or to ‘the proportion of cases of 99 instances of a generalization being true, the 100th is true also’ (Ramsey, 1926, p. 92). As for memory is concerned, Ramsey proposes to apply the same principle: ‘If we ask what is the best degree of confidence to place in a certain specific memory feeling, the answer must depend on how often when that feeling occurs the event whose image it attaches to has actually taken place’ (Ramsey, 1926, p. 92).

^29. Such frequencies are objective in the sense that they are observed frequencies of expected or believed events. Of course, believed events are linked together under the same class of events by mental (subjective) representations and habits.

^30. Ramsey had noticed in the first part of the paper that a well-defined subjective degree of belief could be interpreted as a kind of ‘hypothetical or ideal frequency’ (Ramsey, 1926, p. 84). A subjective degree of belief can be formally conceived as a ratio m/n. In that case, ‘supposing goods to be additive, belief of degree m/n is the sort of belief which leads to the action which would be best if repeated n times in m of which the proposition is true’ (Ramsey, 1926, p. 84). This ideal frequency could then be seen as a frequency of potential actions leading to success (i.e. to the satisfaction of desires): if we act n times in the same manner (the action being determined by our system of subjective data), this action would be the most accurate in m cases, the m cases for which the believed proposition is true (the m cases where the event actually happens). The notion of ideal frequency should in that case be an answer to the problem raised by the fact that if mental representations support graduation (degrees of beliefs), the world only offers a binary structure: events are or are not.

^31. Ramsey sustains an epistemological monism at the antipodes of Keynes' vision. In ‘Truth and Probability’, he compares his measurement method with those used for measuring time or electric intensity in physics. He envisages that human logic should be able to test the validity of such methods in all sciences. In ‘Theories’ (1929b), he argues with examples borrowed from psychology, physics, or economics.

^32. On the implications of Keynes's method for his analysis in the General Theory, see, among others, O'Donnell (1982), Carabelli (1988), Gerrard (1992b) and Davis (1994).

^33. For instance, he explicitly mentions that the ‘ultimate values’ of the 1926 essay could be interpreted as utilities in economics (1929a, p. 95).

^34. Samuelson was one of the best knower of Ramsey's works (Duarte, 2009). The opening of Samuelson's archives could bring further elements for such a conjecture.