logic, rationality and knowledge in ramsey's thought: reassessing ‘human logic’
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Logic, rationality and knowledge inRamsey's thought: reassessing ‘humanlogic’Marion Gasparda
a Department of Economics, Université Lumière Lyon 2, TriangleResearch Center (UMR5206), Lyon, FrancePublished online: 16 Apr 2014.
To cite this article: Marion Gaspard (2014) Logic, rationality and knowledge in Ramsey'sthought: reassessing ‘human logic’, Journal of Economic Methodology, 21:2, 139-157, DOI:10.1080/1350178X.2014.907441
To link to this article: http://dx.doi.org/10.1080/1350178X.2014.907441
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Logic, rationality and knowledge in Ramsey’s thought: reassessing‘human logic’
Marion Gaspard*
Department of Economics, Universite Lumiere Lyon 2, Triangle Research Center (UMR5206),Lyon, France
(Received 15 April 2012; accepted 6 May 2013)
This paper reconsiders Frank Ramsey’s essay on subjective probability (1926) as aconsistent way to articulate logic, rationality and knowledge. The first part of the essaybuilds an axiomatic theory of subjective probability based on ‘formal logic’, definingrationality 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 theformal logic underlying the neoclassical theory of individual behaviour. The analysis ofRamsey’s method in the entire paper, the relation between logic and rationality itconstructs and the conception of uncertainty it reveals, lead me to note on the contrarythat Ramsey’s human logic was a complementary logic rather than an alternative toformal logic. Defining a standard to evaluate beliefs formation according to afrequentist criterion, it completes a normative representation of rationality whichsupports an original theory of knowledge that appears more in line with furtherdevelopments of neoclassical methodology than with Keynesian economics.
Keywords: Frank P. Ramsey; subjective probabilities; human logic; rationalbehaviour; theory of knowledge
1. Introduction
The new edition by D.H. Mellor of Frank P. Ramsey’s Philosophical Papers (1990) and the
book N.E. Sahlin (1990) devoted to Ramsey’s works have profoundly renewed the interest
philosophers have brought to Ramsey’s original theory of knowledge: a procedure to
evaluate the truth of mental representations through the success of the actions they imply
(Dokic & Engel, 2002; Whyte, 1990). Among Ramsey’s articles, ‘Truth and Probability’
(1926), the essay he devoted to subjective probability, represents a turning point: themoment
whereRamsey emancipated from the logical atomismofhis education years and turned to the
construction of his own philosophical system (Sahlin, 1990). Oddly enough, historians of
economic methodology have largely neglected the essay, except in a roundabout way in the
literature studying the philosophical foundations of Keynes’ economics. The fact that an
original theory of knowledge emerged on the occasion of a reflection on rational behaviour
under uncertainty could have, however, deserved more direct attention.
Delivered at theMoral Science Club in 1926, ‘Truth and Probability’ was a response to
Maynard Keynes’ Treatise on Probability (1921)1 and to his project – to build a logical
theory of probabilities. Taking Keynes’ project seriously but rejecting his methodological
premises, Ramsey had to put forward his own theory and did so in two steps. The first part
of the essay is an attempt to exhibit what could be a theory of subjective probabilities using
q 2014 Taylor & Francis
*Email: [email protected]
Journal of Economic Methodology, 2014
Vol. 21, No. 2, 139–157, http://dx.doi.org/10.1080/1350178X.2014.907441
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formal logic as foundations. From a historical point of view, it deserves attention from
economists because it proposes an axiomatic theory of subjective probability, anticipating
axiomatic theories of individual preferences.2 Ramsey uses an expected utility criterion,
builds cardinal utility scales and defines rationality as choice-consistency through the
Dutch book argument. As such, Ramsey’s theory initiates a modern vision of rationality
and could be added as a step in recent histories of rationality representations in economics
(Giocoli, 2003; Lagueux, 2010). The second part of this essay involves trying to bypass the
intra-logical criterion of choice-consistency by raising the question of the relevancy of
isolated choices which seems to open up different horizons: the evaluation of reasoning
through a pragmatist criterion summarised under the term of human logic. Human logic,
also described as a ‘logic of truth’ (Ramsey, 1926, p. 82) or as a ‘logic of discovery’
(Ramsey, 1926, p. 86) represents the main conceptual innovation of this second part.
Since human logic had been recognised by Keynes (1931) as a promising way to
enlighten individual decision-making processes in an uncertain environment3, Ramsey’s
concept has been associated in economics with Keynes’ own notion of ‘enlarged’ or
‘ordinary’ logic (Carabelli, 1988; Coates, 1996; Gerrard, 1992a; Winslow, 1986).4 It has
been thought of as a third way between formal logic and descriptive psychology (Keynes,
1931), between Cartesianism and scepticism (Gerrard, 1992a) or between formalism and
nihilism (Coates, 1996; Fitzgibbons, 1991). As such, it has been considered as a possible
alternative to the formal logic which founds the neoclassical theory of individual
behaviour; an alternative logic that could clarify ‘every day reasoning and beliefs’ and
therefore found alternative ‘scientific Knowledge and resulting policy recommendations’
(Chick & Dow, 2001, p. 711).
On the contrary, what I would like to defend here is the idea that Ramsey’s ‘human
logic’ was initially thought of as a complementary logic rather than an alternative logic to
formal logic. Formal logic is in charge of the definition of consistent sets of subjective
probabilities (degrees of belief) and desires, whereas human logic defines the condition of
consistency of such degrees with facts. Both are necessary to establish knowledge. Far
from being a tool used to describe any actual individual behaviour, human logic appears as
normative as formal logic: it prescribes the selection of mental habits and degrees of belief
that could allow us to successfully adapt our actions to the world. The standard of rational
degrees of belief it delivers is the adequacy of these degrees with the proportion of cases
where the reasoning behind these degrees leads to the truth. Far from being consistent with
‘every day reasoning’, human logic should therefore establish truth conditions of beliefs –
conditions that are defined here in reference with objective frequencies. As such, human
logic completes the definition of a normative and abstract conception of rational behaviour
which is the base of Ramsey’s theory of knowledge.
My argument basically rests on the investigation of three types of questions that can be
addressed to Ramsey’s analysis of subjective probabilities and to his discussion of ‘human
logic’. First, is there a unified methodology for dealing with formal and human logic in
Ramsey’s (1926) paper? Second, what is the conception of uncertainty underlying
Ramsey’s global theory? As far as I know, these issues have been neglected by both
philosophers and economists. Third, what are the respective parts of formal and human
logic in the theory of knowledge that Ramsey elaborates from ‘Truth and Probability’
onwards? This implies not only considering human logic as a way of reasoning but also
questioning its epistemological status.
This paper is organised as follows. First, I shall recall that the first and second parts of
Ramsey’s essay are linked by a rejection of the methodological premises of Keynes’
Treatise on Probability (Section 2). Although Ramsey tries, like Keynes, to build a logical
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theory of probabilities, he offers to completely reconstruct the project resorting to
pragmatism on one hand (Section 3) and delimiting the possible contribution of formal
logic on the other hand (Section 4). I then recall that human logic which tries to evaluate
the relevance of reasoning and mental habits governing beliefs formation, consists in fine
of the application of a frequentist criterion applied to actions resulting from beliefs
(Section 5). Human logic defines a standard for ‘reasonable’ degrees of belief which
suggests a desirable adaptation of beliefs systems to an unchanging world. At the limit of
inquiry, the association of formal and human logic should allow to approach a
representation of the world close to that of an omniscient agent (Section 6). Concluding
considerations (Section 7) suggest that if we consider Ramsey’s articulation of formal and
human logic per se (and not through the lenses of Keynes’ interpretation), some new
perspectives appear concerning both Ramsey’s method in economics and the history of
neoclassical economics’ methods.
2. Re-working Keynes’s project5
Dissatisfied with the frequency and mathematical theories of probabilities, Keynes
suggests that in a world characterised by complexity and uncertainty the problem of
probabilities starts where calculation stops. He intends to apprehend such a world thanks to
a logical theory of probabilities. His theory consists in assigning a degree of probability to
a proposition affirming the occurrence of an event, according to a set of given and
contingent informational premises relative to the individual who assesses the probability.
The degree of probability is therefore the expression of an individual judgement derived
from introspection and analogy according to past experiences and a more or less complete
set of direct knowledge.
This judgement which must ‘justify’ a degree of belief in the occurrence of an event
is formulated on the basis of a partial implication relationship between the (certain)
premises and the (uncertain) conclusions. Keynes presents this partial implication as an
extension of Cambridge formal logic, that of Russell in particular, to ‘inconclusive’
arguments. He thus tries to pass ‘from the logic of implication and the categories of
truth and falsehood to the logic of probability and the categories of knowledge,
ignorance, and rational belief’ (Keynes, 1921, p. 8). Probabilities are not conceived here
as revealing the relation between an individual and an external event but as logical and
objective relations between propositions, relations that could take various degrees. They
are not concerned with an intrusion of the individuals’ psychology but with a new logic;
a logic of probable inferences within which traditional logic appears as a limit case
(Keynes, 1921, p. 137).
Because these judgements of probability are derived from ‘the laws of valid thought’
(logic), they are likely to deliver degrees of rational belief. Beyond the complexity and
changeability of the world, and the idiosyncrasy of the premises of individual judgements
of probability accordingly, one will indeed find an objectifying principle in human skill or
power of logical inference.
Human power of logic intuition belongs to a set of ‘direct acquaintances’ or knowledge
available to individuals. Moreover, it is a pledge for the rationality of judgements and
actions – ‘If our grounds are reasonable, are they not logical in an important sense?’
(Keynes, 1921, p. 107). It is also a reliable source for the objectivity of moral sciences,
distinct from that prevailing in natural sciences. The shared power of making correct
logical inferences (Davis, 1991) allows to define the outlines of human rationality –
a contextualised and practical rationality, anchored both in the common logical power
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(the shared intuition of the laws of valid thought) and in the individual evaluation of the
historically given context of any action.
Ramsey’s text is both a criticism of the Treatise and an attempt to pursue the
Keynesian plan to set up a logical theory of probabilities. A logical theory that could be
more general than the frequentist and mathematical theories and could therefore establish
individual judgements in uncertainty and be used as a practical guide ‘to conduct’
(Ramsey, 1926, p. 79). However, Ramsey rejects two crucial assumptions of Keynes’
theoretical system: the ability of the individuals to derive their degrees of partial belief by
introspection or intuition on one hand, and the feasibility of expressing a degree of partial
belief as the result of a logical relation of partial inference on the other. The first criticism,
of a methodological nature, led Ramsey to rebuild a logical theory of subjective
probabilities according to a pragmatist criterion of beliefs revelation. The second
criticism, of an epistemological nature, brings the distinction between two kinds of logic to
the forefront: a formal logic and a human logic whose functions in a theory of knowledge
remain to be defined.
3. Against intuitionism: a pragmatist theory of subjective probabilities
Ramsey’s first criticism relates to the intuitionist foundations of Keynes’s analysis through
the assumed individual power to establish degrees of probability by direct intuition.
According to Ramsey, we cannot expect individuals to intuitively perceive partial logical
relations between two propositions (Ramsey, 1926, p. 57). Ramsey’s reservations about
such use of a logical intuition is made explicit in one of his lectures to the Apostles Society
dated 1923 – ‘Induction: Keynes and Wittgenstein’ (Ramsey, 1923). In this short talk, the
above-mentioned reservations took the form of an analogy:
There seems to me to be some analogy between this question and that of objective or intrinsicgood; in the latter we consider the justification of our actions, and are at once presented withthe simple solution that this lies in their tendency to promote intrinsic value, a mysteriousentity not easy to identify; if now we turn to the justification of our thoughts we have theequally simple solution that this lies in their following certain logical probability relations,equally mysterious and difficult to identify [ . . . ]. I think that both these simple solutions arewrong, and the true answers are in terms not of ethics or logic, but of psychology [ . . . ].(Ramsey, 1923, p. 300)
Here, Ramsey questions both the intuitionist grounds of Moore’s ([1903] 1993) moral
philosophy dominating Cambridge at that time, and the logical inference faculty Keynes
intends to use.6 He puts forward the classic subjectivist criticism against intuitionism that
Hume contradicted Butler or Stuart Mill had opposed Whewell’s moral intuitionism – an
action is deemed to be good according to its consequences compared with private
preferences and not because it stems from any ethical intuition. The same argument
applies here – an action will not be interpreted with regard to a logical intuition but with
regard to its suitability to private subjective preferences and beliefs. Thus, just like
intuitionist ethics cannot explain the specific ability of moral judgements to guide moral
action, Keynes’s logical intuition cannot ‘justify’ a degree of rational belief. It cannot
consequently be used as a general ground for a theory of human behaviour. Such a theory
should be reconsidered along subjectivist lines. In the 1920s, however, Ramsey’s
subjectivist argument is renewed by his interest for what he elsewhere (Ramsey, 1925,
p. 332) presents as the queen of social sciences: psychology.
In 1923, Ramsey had suggested substituting psychology for logic and ethics. In 1926,
he recommends developing ‘a purely psychological method of measuring belief’
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(Ramsey, 1926, p. 62). Calling upon psychology as a basis for his theory seems like a
provocation since Ramsey chooses precisely here what aroused sharp criticism in
Moore’s Principia Ethica.7 Above all, by suggesting the possibility of using a
‘psychogalvanometer or some such instrument’ (Ramsey, 1926, p. 57), Ramsey seems to
revive Jevons or Edgeworth’s wish to devise a measuring instrument for psychics data; a
wish that Keynes strongly opposed in Chapter II of his Treatise. However, the
provocation should not be taken literally. Indeed, Ramsey calls upon a new kind of
psychology strongly renewed by psychoanalysis. According to Ramsey (1924),8 Freud’s
discoveries have shown that any conscious reflection on our own subjectivity, desires or
beliefs would be revealed as suspicious: the discovery of the unconscious makes it
impossible to get any reliable understanding of the reasons behind our actions from
introspective inquiry. It also condemns any plan of direct measurement of beliefs by
introspection.9 The originality of Ramsey’s subjectivism then emanates from the use of a
new philosophy in the English tradition: pragmatism. If we cannot simply ask
individuals about their degrees of belief – or evaluate our own degrees of belief by
introspection – they can be revealed by the actions they imply. It is the first lesson that
Ramsey learns from Charles S. Peirce’s pragmatism, quoting on occasions ‘How to
Make our Ideas Clear’ (1878), and ‘The Fixation of Belief’ (1877) (Ramsey, 1926, pp.
82, 90).10 Actions, actual or potential, may often reveal vague or unclear private
conceptions. A certain kind of action is favoured in ‘Truth and Probability’: betting, as a
generic action expressed by odds and as such, considered as a suitable support for
measurement or quantification.11 The betting method could more precisely reveal
degrees of dispositional belief that individuals assign to a proposition related to the
occurrence of an event.12
Ramsey then imagines a fictitious procedure in which an omnipotent bookmaker
subjects an individual to a sequence of betting options.13 The interpretation of the
subject’s choices (i.e. the odds) rests on two crucial assumptions. The first is that
individuals follow ‘a simple psychological law’ – they maximise a mathematical
expectation which combines degrees of belief with ‘ultimate values’ that are subjectively
assigned to each possible course of the world. The second assumption is the existence of
‘ethically neutral propositions’14 and more generally the definition of a series of axioms
which eventually allow distinguishing subjective degrees of belief (probabilities) from
subjective ‘ultimate values’.15 A first sequence of bets allows him to use the
axiomatisation in order to build a ranked scale of ‘ultimate values’, to define these sets of
values as isomorphous to the set of the real numbers and eventually to establish what
economists would call utility scales. On the basis of the above-mentioned established sets
of values, a second sequence of bets makes it possible to deduce the degrees of belief
individuals assign to the occurrence of possible states of the world.16 Finally, Ramsey
proposes to check that the thus revealed and measured degrees of belief satisfy the
mathematical laws of probabilities.
The last step is decisive: it makes the procedure of measurement swing into a
veritable theory of subjective probability since it allows an interpretation of the degrees
of belief in terms of probabilities. It also validates a posteriori the axioms used to build
these degrees of beliefs. As such, it validates the entire conceptual procedure. We should
therefore infer the entire theory itself from what Ramsey meant by ‘psychogalvan-
ometer’: the fictitious revelation procedure of subjective data (preferences and beliefs) by
actions (pragmatist principle) as well as the definition of a theoretical reading framework
(the axioms and the mathematical laws of probability) for the revealed data, thus allowing
their quantification.
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4. Logic and rationality: what formal logic can do
The theoretical framework – axiomatic plus mathematical laws of probability – shapes
the system of partial beliefs by the tools of formal logic; a formal logic that Ramsey
defines in 1926 as ‘the logic of consistency’:
We find, therefore, that a precise account of the nature of partial belief reveals that the laws ofprobability are laws of consistency, an extension to partial beliefs of formal logic, the logic ofconsistency. They do not depend for their meaning on any degree of belief in a propositionbeing uniquely determined as the rational one; they merely distinguish those sets of beliefs,which obey them as consistent ones. (Ramsey, 1926, p. 78)
When formal logic is in charge of full beliefs (it is then identified with deductive logic), it
assures a consistent and valid thought process in which the truth of the premises guarantees
the truth of the conclusions. According to Ramsey, the strength of formal logic precisely
lies in the objectivity of its tautologies. The very idea of a partial logic appears to be a
contradiction in terms: ‘it is absurd to say that the sense of the conclusion is partially
contained in that of the premises. We could accept the premises and utterly reject the
conclusion without any sort of inconsistency or contradiction’ (Ramsey, 1926, p. 82).
Keynes’s enlarged logic would thus not only be inaccessible to human understanding but
also impossible to consider as an extension of deductive logic.17 What would be lost here is
that which specifically creates an interest in formal logic: its tautological character which
precisely confers to it its status as a norm for consistent speech.18 Traditional logic, that of
Frege, Russell and Wittgenstein – Ramsey (1926, p. 83) also includes mathematics –
cannot be directly used to justify degrees of partial beliefs as partial inferences. It could get
our thoughts in order but does not succeed in increasing knowledge or in compensating
uncertainty as does inductive reasoning. Within the space of subjective probabilities,
Ramsey therefore had to find a way to transfer what in deductive logic guarantees the
consistency of judgements. The extension of formal logic to the problem of partial beliefs
requires the definition of additional axioms governing the objects of such logic; axioms that
lay down the conditions for a theoretical representation of consistent sets of beliefs and
subjective utilities. In Ramsey’s analysis, this is therefore the carefully constructed system
organising subjective beliefs and preferences (‘ultimate values’) that may be regarded as a
generalisation of formal logic, usually concerned with valid implications between certain
propositions (deductive logic), to the articulation of uncertain propositions. It is clear
because the definition of partial beliefs as a ratio of value differences satisfies the
mathematical laws of probabilities that we are sure to have obtained a consistent
construction. Thus, ‘formal logic can be interpreted objectively as a body of tautology and
subjectively as the laws of consistent thought’ (Ramsey, 1926, p. 84). Consistency is not
directly founded on an export of deductive logic but indirectly, via a mental construction
permitting the use of these laws.
One of the consequences of such considerations is the rejection of the immediate
assimilation between the adoption of a logically founded reasoning and the rationality of
the decision resulting from this reasoning.19 In Ramsey’s thought, the insertion of a
decision in the category of ‘rational’ decisions is not derived only from the conformity of
the reasoning to the laws of logic. To say that p implies q is to draw the necessary
conclusion that p and : q cannot be true simultaneously, but does not mean to be rational.
The rationality of a decision is not deemed according to the validity of the argument but
via the coherence of this decision with the whole set of probability and value judgements
that are fitting to an individual. A whole consistent system of partial beliefs can reveal the
rationality of an individual, but each system remains peculiar to the individual whose
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beliefs are fictitiously tested.20 Moreover, where the consistency of personal data may be
tested logically by checking that mathematical laws of probabilities do apply, the
rationality of a behaviour or a decision is tested through the ‘Dutch book argument’,
i.e. the impossibility for ‘a cunning better’ to rank the bets options so as to win
systematically. The intrinsic impossibility of ‘making a book against the individual’
(Ramsey, 1926, p. 78) might reveal a definition of rationality as consistency of a system
articulating partial beliefs (subjective probabilities), preferences (subjective utilities or
‘ultimate values’) and actions (bets). An individual who would systematically loose her
bets (whose beliefs are inconsistent with each other) would be led to review her entire
beliefs system.
Ramsey’s axiomatic theory of subjective probability may be historically considered as
an important step towards the neo-Bernoullian decision theory21 apprehending the
decision through a maximisation of an expected utility function.22 More importantly,
perhaps for the first time it expresses the idea of rationality as consistency applied to
mental entities (Davidson, 2004).23 As for later Bayesian theories, the question of the
epistemological status of such an axiomatic representation of human behaviour arises.
As mentioned earlier, Ramsey intended to take part in the development of psychology.
In that sense, his theory has a descriptive ambition – not that it aims to be a stylised
representation of actual individual deliberations but because it nourishes the hope to
provide a basis for a predictive analysis resting on the adequacy of the theoretical
principles with the potential observation of betting behaviours. Ramsey’s descriptive
claim appears in a provocative assertion according to which it is not ridiculous to assert
that ‘All our lives we are in a sense of betting. Whenever we go to the station we are
betting that a train will really run, and if we had not a sufficient degree of belief in this we
should decline the bet and stay at home’ (Ramsey, 1926, p. 79). Our dispositional beliefs
would thus be actualised in every day actions, and life could be seen as a sequence of
bets.24
However, when it comes to establishing theoretical elements for measuring subjective
probabilities, it is necessary to complete the principle of beliefs revelation with
axiomatics, enabling the interpretation of the results and eventually the use of the laws of
probability. The ‘train scene’ does not mean anything if it is considered as an isolated
action; it does not say anything about the degree of belief. More generally, to observe the
actual behaviour of an individual who is not endowed with transitive preferences, or with a
consistent system of beliefs, even if she were able to choose or express indifference
between all the states of the world would not permit any measurement of her degrees of
belief. The theory can be nothing else but a theory of the behaviour of an ideal subject
whose preferences obey the axioms of the theory, i.e. a subject who would not be the
victim of a Dutch book. In Ramsey’s essay, the object (subject) of inquiry is therefore
abstractly shaped on the validity criterion of the theory, a criterion delivered by the logic
of consistency. In that sense, as in Keynes’ works, formal logic has something to say about
rational behaviour. It defines the norm that makes the theory possible (the measurement of
the degrees of belief) and the norm that gives meaning to it. It is not because the world (the
actual individual mind facing uncertainty) is ruled by formal logic that the theory finds its
justification but because it states the conditions of a measurement of partial beliefs, which
constitute the key for the interpretation of betting behaviours.
By definition, formal logic orders human discourses but does not order facts. Ramsey’s
parallel between the fictitious measurement procedure and the idea that we are somehow
always betting – suggesting that nature could be perceived like a bookmaker – seems an
improper use of what he has presented: the possibility of a theoretical measurement of
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degrees of subjective beliefs. A theory articulated by formal logic cannot claim to predict
effective betting behaviours; it can only enunciate what would be coherent to observe. The
theory above all is a tool to assist a scientist in measuring subjective probabilities, to give
the interpretative keys of individual behaviours and to guide these behaviours. We thus
arrive at the prescriptive status that will later be assumed by Savage,25 but not necessary
by neoclassical orthodoxy (Giocoli, 2003, 2005), and which will be more generally used to
justify the interest for the expected utility theory in spite of its multiple refutations
(d’Aspremont & Mongin, 1998). Therefore, if there is a practical lesson to be learnt from
this theory, it is to avoid the possibility of being prevented by a Dutch book. Because of the
unavoidable media of theorisation, we cannot escape a normative (or prescriptive) bias.
5. Logic and rationality: what human logic can do
At this stage of the argument, Ramsey still had to face the question (typical of post-
Rusellian philosophy) of how a discourse normalised by formal logic could have a hold
over facts. After the requirement of choices consistency, a second requirement turns up:
We put before ourselves the standard of consistency and construct these elaborate rules toensure its observance. But, obviously, this is not enough; we want our beliefs to be consistentnot merely with one another but also with the facts. (Ramsey, 1926, p. 87)
The requirement first concerns Ramsey’s own theory of subjective probabilities. But the
issue at stake is of course larger. If Ramsey wanted to challenge Keynes’s theory, he would
have had to scrutinise the matter of the validity of isolated degrees of belief and also
propose an analysis of the formation of such degrees of belief. With these questions, the
issue becomes the ability of individual beliefs to be a basis for knowledge. Formal logic
can assess an existing system of beliefs but cannot say anything about the origin of these
beliefs or about their empirical relevance. To deal with these questions, Ramsey
introduces the notion of human logic. Its part is anything but modest, since human logic
must be ‘a logic of truth’ (Ramsey, 1926, p. 86).
As a kind of logic, human logic is an investigation of the nature of thought and its
relevancy. Like formal logic, it is ‘concerned not with what men actually believe, but what
they ought to believe, or what it would be reasonable to believe’ (Ramsey, 1926, p. 90). It
is thus necessary to establish at least one criterion of what is reasonable to believe, i.e. to
define how human logic can function since it does not function with the same weapons as
formal logic. What exactly does it mean to argue that it is reasonable for a man to entertain
such a degree of belief? Several ways are possible:
First, it sometimes means something explicable in terms of formal logic: this possibility forreasons already explained we may dismiss. Secondly, it sometimes means simply that were Iin his place (and not e.g. drunk) I should have such a degree of belief. Thirdly, it sometimesmeans that if his mind worked according to certain rules, which we may roughly call‘scientific method’, he would have such a degree of belief. But fourthly it need mean none ofthese things for men have not always believed in scientific method, and just as we ask ‘But amI necessarily reasonable’, we can also ask ‘But is the scientist necessarily reasonable?’ In thisultimate meaning it seems to me that we can identify reasonable opinion with the opinion ofan ideal person in similar circumstances. What, however, would this ideal person’s opinionbe? As has previously been remarked, the highest ideal would be always to have a true opinionand be certain of it; but this ideal is more suited to God than to man. (Ramsey, 1926, p. 90)
However, human logic should not be founded on rules exceeding the cognitive capacities
of mortal men. We therefore have to consider the human mind and to wonder what we can
at best expect from it. Then there are two stages in Ramsey’s own proposal. The first stage
is to notice that the human mind works according to a set of habits as underlined by Hume
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and, more recently, by Peirce. The habits mentioned here might a priori be sophisticated
mental inferences as well as general ‘habits’ of ‘perception, memory or induction’
(Ramsey, 1926, p. 82) which formal logic cannot justify. The second stage is to evaluate
these habits, i.e. to establish which habits are best. The role of human logic in general is
therefore to establish the rules which make it possible to define the best mental habits.
As far as the theory of subjective probability is concerned, a derived result of this
investigation is the definition of ‘reasonable’ degrees of belief – a reasonable degree of
belief will be the degree of belief that would be best for the habit to produce.
In order to define the best mental habits, Ramsey again uses Peirce’s idea according to
which intimate distinctions could be attained only through the actions they imply. By
considering the actions (effective or potential) resulting from individual beliefs, one will
be able to evaluate the relevance of the beliefs that led to these actions. While seeking to
evaluate the relevance of these beliefs, one would be able to judge the validity of the
mental habits (among them induction) which led to these beliefs. But more than a theory of
significance, the way Peirce considered pragmatism, Ramsey understands pragmatism as a
philosophy of truth26 and goes a step further. According to him, the best mental habits are
those that lead to true beliefs, i.e. beliefs that imply successful actions. Whyte (1990)
described Ramsey’s theory as a ‘semantic of success’: the conditions of truth of our beliefs
are derived from the conditions of success of our actions. A good mental habit will
therefore be that which always leads to true beliefs (and therefore to systematically
successful actions) or which leads to beliefs more often true than false or alternatively,
which leads to beliefs more often true than beliefs which would be obtained by any other
mental habit.27 According to human logic, one of the most efficient mental habits is,
precisely, induction. More generally, human logic received a specific mission in Ramsey’s
epistemology, that of considering ‘methods of thought and discovering what degree of
confidence should be placed in them, i.e. in what proportion of cases they lead to truth’
(Ramsey, 1926, p. 94).
On a human scale, our mental habits do not lead us to full beliefs (reserved for God)
but to degrees of belief. A good mental habit (the way of forming the opinion that p)
produces degrees of belief close to the actual proportion of cases in which p is true, i.e. the
cases in which the action is successful:
Thus given a single opinion, we can only praise or blame it on the ground of truth or falsity:given a habit of a certain form, we can praise or blame it accordingly as the degree of belief itproduces is near or far from the actual proportion in which the habit leads to truth. We canthen praise or blame opinions derivatively from our praise or blame of the habits that producethem. (Ramsey, 1926, p. 92)
The best mental habits will produce degrees of belief (subjective probabilities) equal to the
actual proportion of cases in which the habits lead to truth. In other words, a ‘reasonable
degree of belief’ would be equal to the actual proportion of cases in which the reasoning
leads to truth; i.e. the proportion of cases that supports successful actions. It is then that the
actual frequency of efficient actions stemming from mental habits reveals the relevance of
degrees of beliefs concerning the second requirement – consistency with facts:
Let us take a habit of forming opinion in a certain way; e.g. the habit of proceeding from theopinion that a toadstool is yellow to the opinion that it is unwholesome. Then we can accept thefact that the person has a habit of this sort, and ask merely what degree of opinion that thetoadstool is unwholesome it would be best for him to entertain when he sees it; i.e. granting thathe is going to think always in the sameway about all yellow toadstools, we can ask what degreeof confidence it would be best for him to have that they are unwholesome. And the answer isthat it will in general be best for his degree of belief that a yellow toadstool is unwholesome
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to be equal to the proportion of yellow toadstools, which are in fact unwholesome. (Ramsey,1926, p. 91)
The inference rule (mental habit) producing degrees of belief may be ‘narrow’ – like in the
above example or when ‘we expect thunder after lighting’ (Ramsey, 1926, p. 92) – or
‘wide’ (Ramsey, 1926, p. 91) – human logic in those cases will evaluate habits of habit
formations (inductive process, memory or scientific theories). In both cases, the
‘reasonable degree of beliefs’ should be equal to the proportion of cases in which the habit
actually leads to the truth, the proportion of cases in which the belief stemming from the
reasoning could be confirmed by reality.28
In the second part of ‘Truth and Probability’, degrees of beliefs are thus no longer
considered as simple weighting coefficients in a formula of expected utility. They turn into
a theoretical cogwheel within the mechanism, allowing to link subjective preferences with
the world. The subjective ultimate values (utilities) are independent of the realisation of
such or such a state of the world. What then guarantees the success of an action is the
suitable character of individual beliefs that lead to this action. When Ramsey connects the
question of the consistency of beliefs with facts, he once again does so in a roundabout
way through an intermediate question: what are the best mental habits (and resulting
reasonable degrees of belief)? The answer is supposed to defuse the normative connotation
of the question: the best degree of belief is that which gives the greatest chances of success
to the actions it entails. But the chances of success of an action are then supposed to be
largely determined by the proximity of the individual degrees of belief with objective
frequencies29, i.e. the answer the world offers to our beliefs or expectations.
If an individual (even unconsciously) uses his beliefs for the determination of the most
suitable actions (for the satisfaction of her desires), it would be reasonable to take
frequencies into account, just like it would be reasonable to modify an inconsistent system
of partial beliefs. The second consistency requirement (consistency with facts) could
therefore be understood as a second rationality criterion – a rational behaviour would rest
on an adaptation of the individual to the world via the adaptation of mental habits and
resulting degrees of belief. To follow the rules of human logic (also described as a logic of
discovery) is to thus adopt the best habits, i.e. habits leading to efficient degrees of belief
and actions. Eventually, that would also mean adopting subjective degrees of belief equal
to objective frequencies.
Just as with formal logic requirements, it does not mean that individuals actually obey the
standards of human logic. Like ordinarymen donot necessarily follow the standards of formal
logic, they do not follow the standards of human logic either. It is not because the world
(the actual individual mind facing uncertainty) is ruled by human logic that the criterion finds
its justification but because it states conditions for the evaluation of partial beliefs. Individuals
would, however, find the highest of advantages in adopting its precepts and searching to
adopt mental habits establishing subjective probabilities close to objective frequencies.
With the introduction of the second rationality requirement (consistency with facts)
arises the problem of the compatibility of the two standards of consistency defined in
‘Truth and Probability’. Ramsey then suggests the idea of a rational learning process that
will later characterise orthodox Bayesian decision theory:
Since an observation changes (in degree at least) my opinion about the fact observed, some ofmy degrees of belief after the observation are necessarily inconsistent with those I had before.We have therefore to explain how exactly the observation should modify my degrees of belief;obviously if p is the fact observed, my degree of belief in q after the observation should beequal to my degree of belief in q given p before, or by the multiplication law to the quotient ofmy degree of belief in pq by my degree of belief in p. When my degrees of belief change in
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this way we can say that they have been changed consistently by my observation. (Ramsey,1926, p. 88)
Ramsey eventually rejects this possibility, that which prevents him from the construction of a
complete theory of Bayesian rational learning (Levi, 2004): the problem with such a position
is that it assumes the individual would already belong to the category of ideal individuals
who are not victims of Dutch books and who have a priori consistent sets of beliefs. It would
lead to the acceptance of the idea that human logic is absorbed in formal logic.
Moreover, one may think that an adapted isolated belief (likely to meet success)
inconsistent with other degrees of belief may be a lesser evil than a consistent system of
beliefs that never leads to success. Intra-logical consistency may take a back seat here.
In that sense, human logic can appear ‘independent’ and ‘sometimes actually incompatible
with formal logic’ (Ramsey, 1926, p. 87). However, the concession does not hinder the
consideration that the ‘best solution’ would be to pursue this double requirement. If ‘only
God’ could bring the two requirements together, it would not hinder imagining what the
ideal behaviour would be like.
As such, this best solution has little descriptive virtue but can keep alive an explanatory
virtue. It remains the objective that the use of human logic allows to approach. Ramsey’s
definition of a ‘human scale’ is thus not the horizon of the ordinary man but that of the man
who is not God and can at best use and organise what he knows in order to approach the
unknown and so satisfy her desires. At best, that is thanks to the use of formal and human
logic. If these two kinds of logic are independent, it is because they do not deal with the
same object and therefore do not enunciate the same criterion and rules. But such
independence describes complementary kinds of logic more than alternative kinds of
logic. When they are sometimes incompatible, it is precisely when formal logic cannot say
anything (when, for instance, the issue is to evaluate an isolated belief) and not because of
its incapacity to apprehend the actual world. Moreover, it is because Ramsey has been able
to express degrees of belief as probabilities thanks to the use of formal logic that he can
associate in his study of human logic the degrees of belief with the proportion of cases in
which our reasoning leads to truth, i.e. with frequencies of successful actions.30
The combination of formal logic which defines the conditions for measuring degrees of
belief, and human logic which defines the conditions of truth of beliefs, forms an ideal
which also appears to be an objective – the objective that Ramsey the philosopher defines
as the horizon for scientists.
6. Formal logic and human logic: two pillars in Ramsey’s theory of knowledge
Like in a mise en abyme process, ‘Truth and Probability’ delivers the organising principles
of the epistemology Ramsey will develop in subsequent writings.
A condition for the measurement of the degrees of dispositional beliefs in ‘Truth and
Probability’, formal logic remains the basis of his later writings from ‘Facts and
Propositions’ (Ramsey, 1927a) until ‘Theories’ (Ramsey, 1929b) or ‘General propositions
and Causality’ (Ramsey, 1929c). It remains the condition for the identification of the
relevant distinctions of language and the assurance of the consistency of discourse,
whether philosophical or scientific. Formal logic outlines sets of general propositions that
are consistent with each other without necessarily having a truth-value. These general
propositions – and among them, scientific laws – stand nonetheless at the basis of our
expectations and degrees of belief and guide our actions. In Ramsey’s last texts, scientific
laws, as general propositions, are not called judgements likely to be true or false but ‘rules
for judging’ (Ramsey, 1929c, p. 149) in which confidence is more or less placed. More
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precisely, as ‘rules for judging’, the scientist’s general propositions are described as
mental habits of beliefs formation. Always considered as dispositions to act, the validity of
beliefs is evaluated by the success of the actions they imply. Accordingly, scientific work
consists of defining instructions (rules) to form beliefs (judgements or opinions). Scientific
theories become ‘plans’ in both the senses of the word. They are thought as some sort of
topological map organised by formal logic (Ramsey, 1929c, p. 146), and also as definitions
of future actions (planning) (Ramsey, 1929c, p. 149). They draw the cognitive plans that
guide future actions. Just like in ‘Truth and Probability’, these laws are subjective because
they result from rules invented by human beings in order to plan future actions. They are
nevertheless objectified by the meeting of their consequences (actions) with the world. If
the actions are successful, laws will be credited with some explanatory power (Sahlin,
1990, p. 112). Thus, the term human logic disappears in Ramsey’s later texts but the spirit
of the 1926 concept remains: we judge theories (mental habits) by their capacity to
establish beliefs that lead to successful actions.
A tight interrelation between the knowledge of facts, the trust we place in the ‘rules for
judging’ and the beliefs they imply, and the systematic adjustment of human behaviour to
these beliefs all stem from Ramsey’s original vision of scientific laws. The objectivity of
(scientific) laws then rests on a postulate according to which human behaviour is always an
optimising reply related to a beliefs system.
The reliability of scientific theories is appreciated through their capacity to deliver beliefs
leading to efficient actions. The temptation is then high to simply identify true beliefs and
useful beliefs as in James’ (1907) pragmatism. However, it should be noticed that Ramsey
does not separate the analysis of truth from an analysis of causality. The ‘instrumentalist’ side
of his epistemology remains the result of an intrinsic difficulty for human knowledge: the
lack of omniscience. This is because if we were endowed with omniscience,
causal laws (would be) the consequences of those propositions which we should take asaxioms if we knew everything and organized it as simply as possible in a deductive system.(Ramsey, 1929c, p. 150)
Once again, the difficulty is that we are not God and that we must contend with organising
acquired knowledge in formal systems in order to produce approximate scientific
propositions tested by the success of the actions they imply. Moreover, theoretical fiction
does not derive its utility from its simplicity – its legitimacy depends on the frequency of
successful actions it is able to imply. Theories are strengthened or invalidated via the success
or failure of our actions andmay be sharpened in a way leading tomore andmore fitting laws.
Here, Ramsey borrows the idea fromPeirce that our theoretical representations will converge
on the set of beliefs leading to successful actions under increasingly general conditions, and
that we would be able to approach a ‘true scientific system’ at the limit of inquiry:
But their system, you say, fitted all the facts known to them; if two systems both fit the facts, isnot the choice capricious? We do, however, believe that the system is uniquely determinedand that long enough investigation will lead us all to it. This is Peirce’s notion of truth as whateveryone will believe in the end; it does not apply to the truthful statement of matters of fact,but to the ‘true scientific system’. (Ramsey, 1929c, p. 161)
7. Concluding considerations: formal logic, human logic and economic
methodology
When, in 1931, Keynes pays tribute to Ramsey’s human logic, he undoubtedly hopes that
the notion may echo his own search for an enlarged logic. However, Ramsey’s human
logic could not really live up to his expectations:
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Thus he was led to consider ‘human logic’ as distinguished from ‘formal logic’. Formal logicis concerned with nothing but the rules of consistent thought. But in addition to this we havecertain ‘useful mental habits’ for handling the material with which we are supplied by ourperceptions and by our memory and perhaps in other ways, and so arriving at or towards truth;and the analysis of such habits is also a sort of logic. [ . . . ] So far I yield to Ramsey – I thinkhe is right. But in attempting to distinguish ‘rational’ degrees of belief from belief in generalhe was not yet, I think, quite successful. It is not getting to the bottom of the principle ofinduction merely to say that it is a useful mental habit. (Keynes, 1931, pp. 338–339)
There is something contradictory in Keynes’ judgement since Ramsey’s justification of
induction precisely rests on the application of human logic. The doubt expressed here is a
sign of Keynes’s split position on Ramsey’s (1926) text. If Keynes may have been
interested in the evocation of mental habits as sources of beliefs and actions, he certainly
would not have accepted Ramsey’s definition of ‘the best mental habits’ via a frequentist
criterion. In fact, Ramsey makes little room for Keynes’s fundamental question of the
social origin of uncertainty – or ontological uncertainty – which constitutes the
foundations of Keynes’s great contributions to economics (Davidson, 1996). Ramsey
certainly does not try to identify uncertainty with risk since probabilities remain
subjectively perceived degrees of belief, and observed frequencies used to define the
reasonable degree of beliefs remain structured by subjective mental habits (inference rules
or laws). However, Ramsey basically restricts the problems raised by uncertainty to those
stemming from the lack of omniscience of the human mind. Lack of omniscience is the
source for individual dithering as well as for the trials and errors of the scientific
community.31 As such, it involves a study of beliefs and degrees of belief. It implies
incomplete knowledge, but a knowledge that may be partially implemented with
experience and experiments (discoveries), something that is impossible in Keynes’
perception of uncertainty. In ‘Truth and Probability’, individuals prove to be alone face to
face with the fictitious bookmaker (in the procedure of personal probabilities revelation),
then alone face to face with nature (actual proportions) when it is time to define the
‘reasonable’ degrees of belief. Nature appears in Ramsey’s philosophy governed by
permanent laws that are inaccessible to human understanding but which exhibits fixed
coordinates systems as a necessary condition for testing and validating mental habits
through successful actions – a necessary condition allowing for the consideration of
convergence towards ‘the true scientific system’.
In Keynes’s works, the analysis of individual behaviour is the first step towards a more
general understanding of the social world that dominates economic decisions (Carabelli,
1991; Winslow, 2003). On the contrary, in Ramsey’s papers, the analysis of individual
decision is a theoretical goal per se. In 1926, the goal was to contribute to psychology by
simultaneously delivering a method to access subjective data and a theoretical framework
that gives sense to them. Ramsey’s primary interest for decision theory will remain the
basis of his later contributions to economics and even to macroeconomics (Ramsey,
1927b, 1928). If those articles no longer considered uncertainty, Ramsey would continue
to place the consistency of choices at the forefront of the analysis. His contribution to the
theory of intertemporal choice (Ramsey, 1928) reveals the distance that separates him
from Keynes. Both faced the question of the biased representation of future events – what
Pigou (1932, p. 25) had described as a ‘telescopic defective faculty’. Their contributions to
economics rest on two opposed methods. In Keynes works, short-sighted individuals who
are aware of the interference of others’ behaviours would rationally base their decisions on
conventions, contracts, or inter-subjective social norms determining the state of
confidence. On the contrary, Ramsey chooses to consider the telescopic defective faculty
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as ‘poverty of imagination’ (Ramsey, 1928, p. 543), i.e. as lack of rationality. By rejecting
the introduction of a positive discount rate in the optimisation problem, he proposes to
define what an omniscient, ‘imaginative’ and time-consistent nation should save. He then
concentrates on an analysis of the (bad) consequences of collective welfare of the
individual temptation to discount future events. The focus on decision theory leads him to
pure prescriptive contributions in economics defining optimisation and consistent
behaviour as rules we should follow to improve global welfare (Gaspard, 2003). On the
contrary, he never specifies the aggregation conditions or the way he thinks about social
interaction.
This prescriptive bias in economics comes from a methodological choice which may
again be opposed to Keynes’s. As shown by Davis (1994), Keynes methodology implies
an empathic point of view. The theorist comes as close as possible to the reasons of
individual choices, his own introspection faculties allowing him to reach mental processes
similar to those of the subjects he studies. The scientist shares the intuition of the reasons
of decisions with ‘ordinary’ men and relates them to the observations commonly available
at the moment of decision-making (Carabelli, 1988, p. 162).32 Ramsey takes on the
opposite view. At the forefront, he sets the fundamental subjectivity of human subjects and
the impossibility of any direct access to psychological personal data. He imagines an
indirect way towards such data and uses theorisation as a ‘psychogalvanometer’. The
procedure of beliefs revelation is a fictitious protocol which rests on the introduction of
abstract conceptual entities (such as the notion of dispositional belief or the character of
the omnipotent bookmaker) and a framework allowing the translation of the revealed data
into the language of formal logic. Ramsey projects the inaccessible world of mental data
as well as the inaccessible true laws of the physical world into the universe of formal logic,
which is controlled and organised by known rules warranting the consistency of reasoning.
Human logic is another tool of projection of the unknown (habits and individual
beliefs) into the known world of facts which allows judging the suitability of beliefs. It
once again relies on the ‘observable’ (frequencies) to give meaning to the unknown
(individual degrees of belief). Contrary to Keynes, Ramsey looks at the subject from an
external point of view. As for social sciences, the complexity of the subject is thus diverted
by a radical choice: the shaping of that inaccessible reality into the laws of consistent
thought on one hand, and the definition of a frequentist criterion of suitable mental habits
on the other. The theory is used as a decision-making guide because it prescribes the
consistent behaviour and because it is better to face the world with a consistent system
rather than with an inconsistent one. Just like formal logic, human logic also being ‘what
we ought to believe’ delivers a second standard of rationality: the best system of partial
beliefs should approximate actual frequencies of expected events. It is yet another
condition for an individual to adapt herself best to the world.
At first sight, Ramsey’s approach could join the project of the first marginalists
strongly criticised by Keynes. It extends W.S. Jevons or F.Y. Edgeworth’ project to base
the analysis of individual decisions on psychology to an uncertain environment and
perpetuates the reduction of rationality to a process of mathematical maximisation. The
commentaries he proposes in 1929 (Ramsey 1929a, pp. 95–96) about the ‘practical’
interest of his theory of subjective probabilities suggest that economics should be founded
on psychology.33 However, by rejecting introspection, Ramsey rejects one of the
methodological principles the British economists traditionally accepted. It does not lead
him, like I. Fisher, W. Pareto or P. Samuelson, towards a rejection of psychology as a
foundation for economics, or towards a concept of ordinal utility. Nevertheless, it implies
an important shift in the representation of individual rationality. By constructing a
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fictitious protocol revealing individual subjective data through betting behaviours and
elaborating axiomatics making it possible to give sense to such betting behaviours,
Ramsey defines a rationality that is not a mathematical translation of an intuition any
longer but is defined and axiomatised within a precise conceptual and theoretical
framework. The method may have prepared later orientations of neoclassical methodology
such as Samuelson’s (1938, 1948) project to base demand theory on potential observations
of choices revealing unobservable and inaccessible preferences under the condition of
well-defined axioms.34 An explicit bridge between Ramsey’s method and later
mainstream representations of rationality evidently passes through De Finetti (1937)
and Savage’s (1954) use of subjectivism, axiomatics and mental experiments.
More globally, as a first step towards a more general theory of knowledge, Ramsey’s
essay on probabilities may have sowed the seeds for a new justification of theorisation
combining the primacy of formal logic as a guarantee for internal consistency of theory
and a test process of the theory by its consequences and the actions they imply. As such,
Ramsey’s articulation between formal and human logic may have pointed a way, among
others, to articulate axiomatics and refutationnism which will both soon penetrate
neoclassical economics.
Acknowledgements
I thank Pascal Bridel, Gilles Dostaler and Emmanuel Picavet for helpful comments on previousdrafts of the paper. The paper has also benefited from insightful critics and suggestions made by thetwo 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 inArrow (1951) who notes that Von Neumann and Morgenstern were anticipated by Ramsey ‘inthe axiomatic treatment of choice among probability distributions ( . . . ) leading to a newunderstanding 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 foundin 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 todistinguish a ‘human’ logic from formal logic on the one hand and descriptive psychology onthe other, Ramsey may have been pointing the way to the next field of study when formal logichas 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 criticismof the Treatise on Probability Ramsey had assessed in the 1926 paper. As such, the 1931review 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 tofind in the Treatise methodological foundations for the General Theory (Keynes, 1936). Seealso Runde, Winslow or Gerrard in Runde and Mizuhara (2003), or Davis (1994). I do not tryhere to address this issue. However, I take for granted that Keynes’ (1931) point of view showsthat while he may have partly abandoned his logical interpretation of probability, Keynes wasstill searching, at the beginning of the 1930s, for an enlarged logic able to lay the foundations ofan alternative representation of human behaviour.
5. Our aim in that section is not to discuss Keynes’s theory but to recall its main principles andfoundations 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 withMoore’s moral faculty and the indefinable property of goodness in Principia Ethica ([1903]
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1993). The parallel Ramsey identifies in 1923 has been since then frequently underlined. Seefor 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 itselfand 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 toassociate belief with a certain “vivid idea” in our mind or with a certain introspectible feelingtowards some representations’ (Dokic & Engel, 2002, p. 7). Keynes had already distancedhimself from this tradition. He accepted introspection as a basis for evaluating a degree ofprobability but unlinked the degree of belief and the intensity of such a degree with the notionof ‘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 criterionto distinguish opinions, persuasion or ‘firm belief’, see Picavet (1996, pp. 176–179). DeFinetti’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 pmeans to be ready to act as though p is the case. On the part of beliefs as disposition to act inclassical pragmatism, see Engel (2005).
13. ‘If then we had the power of the Almighty, and could persuade our subject of our power, wecould, by offering him options, discover how he placed in order of merit all possible courses ofthe world. In this way all possible worlds would be put in an order of value, but we should haveno 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 inregard 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 ofarranging our knowledge and eliminating inconsistencies or contradictions’ (Ramsey, 1926,p. 82).
18. Ramsey’s logicist past remains important here. The reduction of ordinary or scientificdiscourse 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. Thosewords 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 withreason’ (linked to human logic) is misleading. Ramsey always uses ‘reasonable’ to qualify hisown 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 decisionmaker system of beliefs with experience. See Section 5.
22. Ramsey does not establish the equivalence between the rule of expected utility maximisationand his axiomatics. He tries to deduce conditions for measuring degrees of belief and uses themaximisation of expected values as an assumption. He deduces that consistency is a necessarycondition for measuring degrees of belief. According to Carnap (1962, p. 308), the fact that it isalso 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 theoryof 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 anydescriptive use of the theory. Beliefs are in substance dispositional and to imagine the bettingmethod is precisely to imagine an actualisation process of dispositional beliefs.
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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 todetect 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 oftruth 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 abelief 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 oflighting which are actually followed by thunder’ (Ramsey, 1926, p. 92) or to ‘the proportion ofcases 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 askwhat is the best degree of confidence to place in a certain specific memory feeling, the answermust depend on how often when that feeling occurs the event whose image it attaches to hasactually taken place’ (Ramsey, 1926, p. 92).
29. Such frequencies are objective in the sense that they are observed frequencies of expected orbelieved events. Of course, believed events are linked together under the same class of eventsby mental (subjective) representations and habits.
30. Ramsey had noticed in the first part of the paper that a well-defined subjective degree of beliefcould be interpreted as a kind of ‘hypothetical or ideal frequency’ (Ramsey, 1926, p. 84). Asubjective degree of belief can be formally conceived as a ratio m/n. In that case, ‘supposinggoods to be additive, belief of degree m/n is the sort of belief which leads to the action whichwould 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 beingdetermined by our system of subjective data), this action would be the most accurate inm cases,the m cases for which the believed proposition is true (the m cases where the event actuallyhappens). The notion of ideal frequency should in that case be an answer to the problem raisedby the fact that if mental representations support graduation (degrees of beliefs), the world onlyoffers a binary structure: events are or are not.
31. Ramsey sustains an epistemological monism at the antipodes of Keynes’ vision. In ‘Truth andProbability’, he compares his measurement method with those used for measuring time orelectric intensity in physics. He envisages that human logic should be able to test the validity ofsuch methods in all sciences. In ‘Theories’ (1929b), he argues with examples borrowed frompsychology, physics, or economics.
32. On the implications of Keynes’s method for his analysis in the General Theory, see, amongothers, 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 beinterpreted as utilities in economics (1929a, p. 95).
34. Samuelson was one of the best knower of Ramsey’s works (Duarte, 2009). The opening ofSamuelson’s archives could bring further elements for such a conjecture.
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