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This article was downloaded by: [Ludwig van den Hauwe]On: 13 January 2013, At: 09:38Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Journal of Economic MethodologyPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/rjec20
Hayek, Gödel, and the case formethodological dualismLudwig M.P. van den Hauwe aa Avenue Van Volxem, 326 Bus 3, 1190, Brussels, BelgiumVersion of record first published: 28 Nov 2011.
To cite this article: Ludwig M.P. van den Hauwe (2011): Hayek, Gödel, and the case formethodological dualism, Journal of Economic Methodology, 18:4, 387-407
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Hayek, Gödel, and the case for methodological dualism
Ludwig M.P. van den Hauwe*
Avenue Van Volxem, 326 Bus 3, 1190 Brussels, Belgium
On a few occasions F.A. Hayek made reference to the famous Gödel theorems inmathematical logic in the context of expounding his cognitive and social theory. Theexact meaning of the supposed relationship between Gödel’s theorems and the essentialproposition of Hayek’s theory of mind remains subject to interpretation, however. Theauthor of this article argues that the relationship between Hayek’s thesis that the humanbrain can never fully explain itself and the essential insight provided by Gödel’stheorems in mathematical logic has the character of an analogy, or a metaphor.Furthermore the anti-mechanistic interpretation of Hayek’s theory of mind is revealedas highly questionable. Implications for the Socialist Calculation Debate arehighlighted. It is in particular concluded that Hayek’s arguments for methodologicaldualism, when compared with those of Ludwig von Mises, actually amount to astrengthening of the case for methodological dualism.
Keywords: Hayek; theory of mind; Austrian methodology; Gödel; incompletenesstheorems; methodological dualism; Socialist Calculation Debate
JEL Codes: B0; B4; B53
F.A. Hayek was not only a Nobel-prize-winning economist who made important
contributions to monetary, capital, and business cycle theory. Pursuing an interest he had
cultivated since his student days, he also made important contributions to neural science
and to the theory of mind. These can be found in his book The Sensory Order which was
published in 1952, and the essentials of which were already contained in a manuscript
entitled ‘Beiträge zur Theorie der Entwicklung des Bewusstseins’ which Hayek wrote as a
young man at the age of 21. It has been acknowledged, however, that The Sensory Order
should not be considered as a mere aside, isolated from Hayek’s main preoccupations
(Aimar 2008, p. 25). His work in the Austrian tradition in economics, his defense of
political liberalism, and his work in theoretical psychology constitute a unified and
integrated theoretical perspective (Horwitz 2000).1
The work of the mathematical logician Kurt Gödel, in particular his famous
incompleteness theorems, will appear to some as far removed from Hayek’s main concerns
in social and political theory and in the theory of mind. According to one author, however,
‘Hayek may have anticipated by a decade Gödel’s own proof’ (Tuerck 1995, p. 287). Since
claims like these are somewhat remarkable, the relationship between Hayek’s theory of
mind, and to some extent also his social theory and his methodology, on the one hand, and
Gödel’s theorems, on the other, will be examined more closely in this article.
ISSN 1350-178X print/ISSN 1469-9427 online
q 2011 Taylor & Francis
http://dx.doi.org/10.1080/1350178X.2011.628045
http://www.tandfonline.com
*Email: [email protected]; [email protected]; [email protected]
Journal of Economic Methodology,
Vol. 18, No. 4, December 2011, 387–407
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http://dx.doi.org/10.1080/1350178X.2011.628045http://www.tandfonline.com
1 Introduction: Tacit knowledge and mechanism
A recurring theme in writings within the Austrian School of economics relates to the role
and function of tacit knowledge. Practical knowledge of the kind that is relevant to the
exercise of entrepreneurship is mainly tacit, inarticulable knowledge, so this argument
goes. This means that the actor knows how to perform certain actions (know how), but
cannot identify the elements or parts of what is being done, nor whether they are true or
false (know that) (Huerta de Soto 2008, p. 20).
Much of what Hayek has to say about the role and function of tacit knowledge was
already implicitly contained in his The Sensory Order (Hayek [1952] 1976). The main
conclusion of The Sensory Order was that ‘in discussing mental processes we will never be
able to dispense with the use of mental terms, and that we shall have permanently to be
content with a practical dualism’ since ‘(i)n the study of human action ( . . . ) our starting
point will always have to be our direct knowledge of the different kinds of mental events,
which to us must remain irreducible entities’ (Hayek [1952] 1976, p. 191). This conclusion
was based on ‘the fact that we shall never be able to achieve more than an “explanation of
the principle” by which the order of mental events is determined,’ or, stated differently, on
the demonstrable limitations of the powers of our own mind fully to comprehend itself.
Hayek’s conclusion thus was that ‘to us mind must remain forever a realm of its own
which we can know only through directly experiencing it, but which we shall never be able
fully to explain or to “reduce” to something else’ (ibid., p. 194). Despite a certain
parallelism of language, Hayek’s conclusions were thus markedly different from those of
Ludwig von Mises, who seems to have believed that at least the conceptual possibility of
such an ultimate reduction of the mental to the physical could not be excluded. In his
subsequent papers Hayek also referred on a few occasions to the contribution of Michael
Polanyi, in particular his Personal Knowledge2 (Polanyi 1958). Polanyi goes so far as to
assert that tacit knowledge is in fact the dominant principle of all knowledge (Polanyi
1959, pp. 24–25). Even the most highly formalized and scientific knowledge invariably
follows from an intuition or an act of creation, which are simply manifestations of tacit
knowledge.
Both Polanyi and Hayek refer to particular limitative meta-mathematical results, in
particular Gödel’s theorems, in developing the tacit knowledge thesis.3 As will be argued
in this article, however, their positions are subtly although not insignificantly different.
Polanyi generally concluded that ‘(t)he proliferation of axioms discovered by Gödel ( . . . )
proves that the powers of the mind exceed those of a logical inference machine ( . . . )’
(1958, p. 261) and seems to have rejected Turing’s thesis in concluding that ‘neither a
machine, nor a neurological model, nor an equivalent robot, can be said to think, feel,
imagine, desire, mean, believe or judge something ( . . . )’ (ibid., p. 263). As will be
illustrated further in this article, Hayek’s position actually departs from this view and is
consistent with the thesis that it is possible to build a machine that passes the Turing test.4
In recent times the debate over the wider philosophical implications of Gödel’s
theorems has sometimes been framed in terms of ‘mechanism’ versus ‘anti-mechanism.’5
While Polanyi clearly seems to belong to the anti-mechanist camp, we should certainly
guard ourselves against characterizing Hayek’s position simply as ‘mechanist’ or
‘mechanistic,’ however. The term ‘mechanism’ seems to have no uniform or fixed meaning,
although it has often been regarded as a term of abuse. The role of mechanism in human
cognition was much discussed in the seventeenth century, in particular by Descartes,
Hobbes, and La Mettrie (Davis 2004, p. 208).6
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In the terms that are familiar from these classical mechanist/vitalist debates, however,
Hayek’s position cannot be characterized as either mechanist or vitalist. Hayek’s approach
is actually more akin to that of an author like Ludwig von Bertalanffy whose contributions
are cited approvingly in The Sensory Order.7 Von Bertalanffy contends that neither
classical mechanism nor vitalism provides an adequate model for understanding organic
phenomena, and his work in the interdisciplinary field called ‘General System Theory’ can
actually be seen as an attempt to transcend the classical dichotomy between mechanism
and vitalism (von Bertalanffy [1969] 2009).8 The question has been the subject of renewed
interest in the context of the possibility of machine intelligence. There is every reason to
believe that one of the things our brains do is to execute algorithms although it is unknown
and actually subject to controversy whether that is all that they do (Davis 2004, p. 208).
Mechanism in the philosophy of nature was originally associated with determinism but
eventually parted company with it upon the introduction of probability laws. Its essential
feature was then seen to be, in general, a finitistic approach to the description of nature
(Webb 1980, p. 30).
The foundation for modern mechanism is Turing’s thesis: a procedure (function) is
‘effective’ just in case it can be simulated (computed) by a Turing machine. This is a very
strong thesis, for it says that any effective procedure whatever, using whatever ‘higher
cognitive processes’ one can imagine, is after all finitely mechanizable (Webb 1980, pp. 9,
30). In this context it will be worth reminding that Gödel’s theorems have been cited in
support of mechanism, contrarily to what is sometimes supposed. Actually this seems to
have been the viewpoint of professional logicians generally (Webb ibid., passim).
While Hayek does not refer explicitly to the work of Turing, it remains a remarkable
and somewhat paradoxical fact that although Hayek’s theoretical psychology culminates
in an argument for the indispensability of verstehende psychology – thus strengthening
previous arguments for methodological dualism, in particular those of Ludwig von
Mises – this conclusion is arrived at without requiring or without any appeal to any anti-
mechanistic or nonmechanistic line of argumentation.
2 Hayek’s biologically based trans-mechanistic conception of mind
2.1 The sensory order
Clearly the few explicit references to Gödel’s theorems which can be found in Hayek’s
writings (see further Section 3.2.2) lead us back to the significant contribution provided in
his The Sensory Order (Hayek [1952] 1976). This important work in theoretical
psychology has evoked some illuminating comments and elaborations but also some
misinterpretations.9
Credit for the resuscitation of The Sensory Order should probably be given to Weimer
(1982). Hayek’s contribution to cognitive theory has also received explicit recognition
from professional neuroscientists such as Gerald Edelman and Joaquin Fuster (Edelman
1982, 1987, 1989; Fuster 2005). An illuminating and recent review of Hayek’s theory of
mind from an economic perspective is contained in Butos and Koppl (2006). According to
these authors, ‘The Sensory Order provides an account of a particular adaptive classifier
system – the central nervous system – that produces a classification over a field of sensory
inputs. The specific form and character of this classification depends in Hayek’s theory on
the configuration of the pathways and sorting mechanisms by which the brain organizes
itself. But this classificatory structure enjoys a certain plasticity or mutability that reflects
the capacity for adaptive responses by the individual in the face of the perceived external
environment. Positive and negative feedback helps to maintain a rough consistency
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between behavior and the actual environment. The way an individual responds to external
conditions is fully dependent upon the particular classifications he generates, which is to
say that for Hayek individual knowledge is the adaptive response of an individual based on
the classification the brain has generated’ (ibid., p. 31).10
From a more strictly neuroscientific perspective, The Sensory Order has been cited as
an important scholarly contribution to the understanding of the cerebral foundation of
perception and memory (Edelman 1982, p. 24ff., 1987, passim; 1989, p. 281; Fuster 2005,
p. 8).
The essence of Hayek’s theory from this perspective is the proposition that all of an
organism’s experience is stored in network-like systems (maps) of connections between
the neurons of its cerebral cortex. Those connections have been formed by the temporal
coincidence of inputs from various sources (including the organism itself). In their
strength, those connections record the frequency and probability with which those inputs
have occurred together in the history of the organism or of the species. A key point, in
terms of the representational properties of Hayek’s model, is that there is no basic core of
elementary sensation. Each sensation derives from experience and from other sensations
with which it has been temporally associated in the past, including the past of the species.
To postulate in the human cortex representation, networks as broad as those envisioned by
Hayek presuppose extensive and intricate systems of connections between distant cortical
neurons. It was an insightful supposition that he made long before such systems were
anatomically demonstrated in the brain of the primate (Fuster ibid., p. 8). Hayek’s
contribution has sometimes been cited in conjunction with that of Hebb (1949), of which it
was independent, however.11
2.2 The mind as machine
Since the publication of the important papers of Gödel and Turing,12 various positions in
the philosophy of mind have been categorized according to whether it is believed that
machines can (at least potentially) think, that is, whether artificial intelligence is possible,
or conversely, whether the human mind can plausibly be conceived of as some sort of
machine.13
It is beyond dispute that Hayek’s conception of mind has mechanistic traits. Hayek
repeatedly uses machine examples in order to illustrate his theory of the human mind. Thus
similar to the classification mechanism of the mind are ‘certain statistical machines for
sorting cards on which punched holes represent statistical data’ (Hayek [1952] 1976,
p. 49). When Hayek discusses the differences and analogies between mechanical and
purposeful behavior (Hayek [1952] 1976, p. 122ff.) we can still read that similar to the
models by which the mind ‘reproduces, and experimentally tries out, the possibilities
offered by a given situation’ are machines like antiaircraft guns and the automatic pilots in
airplanes, which show all the characteristics of purposive behavior. Although ‘such
machines cannot yet be described as brains, with regard to purposiveness they differ from
a brain merely in degree and not in kind’ (ibid., p. 126). The provisional conclusion that
thus suggests itself is that in the grand debate ‘for’ and ‘against’ the possibility of AI, it
seems more likely that Hayek is to be put in the ‘for’ camp.
Hayek’s theory of mind has been characterized as connectionist (Smith 1997). The
older and more orthodox ‘symbol-processing’ paradigm sees intelligence as a matter of the
sequential manipulation of meaningful units (terms, concepts, ideas) of roughly the sort
with which we are familiar in reasoned introspection. In contrast to this, the common
feature of many species of information processing systems all covered by the general term
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‘connectionism’ is that they are conceptualized as massively parallel processing devices,
made up of many simple units. A unit’s activity is regulated by the activity of neighboring
units, connected to it by inhibitory or excitatory links whose strength can vary according to
design and/or learning (Boden 1990b, p. 14).14
A strongly oppositional history of the two branches of AI was provided by Dreyfus and
Dreyfus (1988) explaining how, in particular, traditional AI failed to capture holistic
perception, context sensitivity, and the recognition of family resemblances and relevance –
each better handled by connectionism. In defending their position, Dreyfus and Dreyfus
(1988) related AI work to a wide range of philosophical literature, contrasting the Western
rationalist tradition with Continental phenomenology and the later Wittgenstein. According
to this skeptical view about AI, people do not use a theory about the everyday world, because
there is no set of context-free primitives of understanding. Our knowledge is skilled know-
how, as contrasted with procedural rules, representations, and so forth, or knowledge that.
This issue is also related to the so-called ‘frame problem’ of AI (Dennett [1984] 1990)
which, philosophically speaking, is reminiscent of the eminently Hayekian themes of the
tacit domain and the contextual nature of knowledge (Boettke and Subrick 2002, p. 56). The
‘frame problem’ relates to the question of unconscious information appreciation that we all
engage in when making choices. For instance, everyday thinking about the material world
does not employ theoretical physics, but rather ‘naı̈ve physics’ (Hayes 1979), our untutored
and largely unconscious knowledge of the environment, which is involved in sensorimotor
skills and linguistic understanding. Likewise, our practical and linguistic grasp of social life
depends on ‘naı̈ve psychology,’ consisting not of empirical generalizations about how
people behave but of the fundamental concepts and inference-patterns defining everyday
psychological competence.15
Also mentioned in Dreyfus’ paper was D.O. Hebb’s inspiring (1949) contribution
which suggested ‘that a mass of neurones could learn if when neurone A and neurone B
were simultaneously excited, that excitation increased the strength of the connection
between them’ (ibid., pp. 311–312).
Adepts of the physical symbol system hypothesis have remained unconvinced,
however, while the debate has gone on. As Simon explains, ‘[u]ntil connectionism has
demonstrated, which it has not yet done, that complex thinking and problem-solving
processes can be modeled as well with parallel connectionist architectures as they have
been with serial architectures, and that the experimentally observed limits on concurrent
cognitive activity can be represented in the connectionist models, the case for massive
parallelism outside the sensory functions remains dubious’ (Simon 1996, p. 82).
One might also object that connectionism, too, studies computational systems, whose
units compute by rigorously specified processes or rules (Boden ibid., p. 17).
Thus Edelman considers with respect to connectionist systems that ‘[u]nlike classical
work in artificial intelligence ( . . . ) these models use distributed processes in networks, and
changes in connections occur in part without strict programming. Nonetheless,
connectionist systems need a programmer or operator to specify their inputs and their
outputs, and they use algorithms to achieve such specification. While the systems allow for
alterations as a result of “experience,” the mechanism of this “learning” is instructional not
selectional ( . . . ). The architectures of neural networks are removed from biological
reality, and the networks “function” in a manner quite unlike the nervous system.’
(Edelman 1992, p. 227) This author intends to develop a biologically based epistemology
and to dispel ‘the notion that the mind can be understood in the absence of biology’ (ibid.,
p. 211).
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However, Hayek’s theory also has a solid grounding in evolutionary theory. Hayek
summarizes the central thesis by saying that ‘we do not first have sensations which are then
preserved by memory, but it is as a result of physiological memory that the physiological
impulses are converted into sensations. The connexions between the physiological
elements are thus the primary phenomenon which creates the mental phenomena ( . . . )’
(Hayek [1952] 1976, p. 53), a phrase already contained in the early German draft of what
would later become The Sensory Order.
Evolution establishes certain connections. Many properties of the set of connections
(and perhaps many specific connections) are determined by the history of the organism’s
species. The history of the individual then operates on these connections at, as it were, a
higher level to form higher order classes of connections among nerve fibers. Evolution
may also establish a set of possible patterns of connection, implementing one rather than
the others on the basis of the organism’s personal history (Butos and Koppl ibid., p. 13).
The theory is thus also consistent with the hypothesis of a certain variability and plasticity
of the classificatory apparatus at the individual level.
Hayek sees a distinction between the phenomenal order of the mind and the physical
order of the external world. Hayek is no vitalist, however, and he clearly sees both
phenomenal and physical orders in quasi-mechanistic terms. Nevertheless, as Butos and
Koppl explain, ‘[f]or human cognitive functioning, ( . . . ) this process ( . . . ) has the
capacity for self-conscious and reflective activity, thus providing substantial scope for
critical, argumentative, and self-reordering properties.’ Thus individuals are not mere
processors of information, passively responding to stimuli. Human cognitive activity,
despite being constrained by rules and its own physiology, should be understood as an
active, input-transforming, knowledge-generating adaptive system (ibid., p. 31).
3 The computational legacy: Hayek and Gödel’s incompleteness theorems
3.1 Hayek as a precursor of modern complex systems theory
The recent literature on the role and functioning of markets as complex adaptive
systems (CAS) has acknowledged the significance of certain developments in the
foundations of mathematics permitting definitive formulations of CAS in terms of what
cannot be formally and practically computed (NP-hard problems)16 and hence needs to
emerge or self-organize. In particular the Gödel–Turing results on incompleteness and
algorithmically unsolvable problems are perceived as having established, for the first
time, the logical impossibility limits to formalistic calculation or deductive methods.
In the absence of these limits on computation there is in principle no reason why all
observed patterns and new forms cannot be achieved by central command (Markose
2005, p. F160). Hayek’s early contributions are invariably cited in this context. Thus
according to Markose (2005, p. F165) ‘Hayek ( . . . ) was one of the first economists
who explicitly espoused the Gödelian formalist incompleteness and impossibility limits
on calculation which he referred to as the limits of constructivist reason. This led
Hayek to the necessity of experientially driven adaptive solutions with the abiding
premise of his large oeuvre of work being that market institutions which co-evolved
with human reason enable us to solve problems which are impossible to do so by direct
rational calculation.’ The precursory role of the classical eighteenth-century political
economy of the Scottish Enlightenment is also frequently cited in this context. As
Markose (ibid., pp. F159–F160) explains ‘[i]t has been held that order in market
systems is spontaneous or emergent: it is the result of “human action and not the
execution of human design.” This early observation, well known also from the
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Adam Smith metaphor of the invisible hand, premises a disjunction between system
wide outcomes and the design capabilities of individuals at a micro level and the
distinct absence of an external organizing force.’17
Another towering figure of the twentieth century to be mentioned here is John von
Neumann. According to Markose (ibid., p. F162), it is the work of John von Neumann in
the 1940s on self-reproducing machines as models for biological systems and self-
organized complexity which provides a landmark transformation of dynamic systems
theory based on motion, force, and energy to the capabilities and constraints of
information processors modeled as computing machines. Indeed the von Neumann models
based on cellular automata have laid the ground rules of modern complex systems theory
regarding:
(a) The use of large ensembles of micro-level computational entities or automata
following simple rules of local interaction and connectivity,
(b) The capacity of these computational entities to self-reproduce and also to produce
automata of greater complexity than themselves, and
(c) Use of the principles of computing machines to explain diverse system-wide or
global dynamics.
Although at least one author has attempted to make the case that ‘[s]ociety is for Hayek a
complex automaton in the sense of Von Neumann ( . . . )’ (Dupuy 1992, p. 39) and that
‘Hayek’s critique of “constructivist rationalism” in social science can therefore be seen as
having anticipated von Neumann’s critique of McCulloch’s artificialist philosophy’
(Dupuy 2009, p. 140) the relationship between Hayek’s contribution and that of von
Neumann is perhaps somewhat less clear.18
3.2 Hayek on the significance of Gödel’s theorems
3.2.1 The meaning of Gödel’s theorems
Hayek indeed refers to Gödel’s theorems on a few occasions – see the next section – but
let us first remind of the meaning and content of Gödel’s theorems.19 Considered the
greatest mathematical logician of the twentieth century, Gödel is renowned for his proofs
of several fundamental results, one of which established the syntactic incompleteness of
formal number theory.
Gödel’s idea was to construct a statement S that, in effect, asserts ‘There is no proof of
me,’ or, ‘I am not provable,’ of the constructed statement ‘S.’ Gödel’s remarkable
achievement was to manage to encode such a statement in the language of number theory.
The first theorem states the following:
Any consistent formal system S within which a certain amount of elementary arithmetic canbe carried out is incomplete with regard to statements of elementary arithmetic: there are suchstatements which can neither be proved, nor disproved in S (Franzén 2005, p. 16).
Gödel’s proof is based on two simple ideas. The first is Gödel numbering, which is a
means of encoding each formula or sequence of formulas as a natural number in a
systematic and mechanical way. The second idea of the proof is self-reference: the proof is
based on the construction of a formula which is carefully devised so that it asserts its own
unprovability.
Gödel’s second theorem can be stated as follows:
For any consistent formal system S within which a certain amount of elementary arithmeticcan be carried out, the consistency of S cannot be proved in S itself.
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The proofs of these theorems apply to any (consistent) system of mechanically recognizable
axioms that is powerful enough to describe the natural numbers. Thus, completeness cannot
be restored simply by adding a true but unprovable statement as a new axiom, for the
resulting system is still strong enough for Gödel’s theorem to apply to it.
It was generally believed that these two remarkable incompleteness theorems proved
by Gödel destroyed the hope that it would possible, at least in principle, to fulfill the
program set out by Hilbert.
Hilbert’s program had two main goals concerning the foundations of mathematics. The
first was descriptive, the second justificatory. The descriptive goal was to be achieved by
means of the complete formalization of mathematics. The justificatory goal was to be
achieved by means of a finitary (and hence epistemologically acceptable) proof of the
reliability of those essential but nonfinitary (and hence epistemologically more suspect)
parts of mathematics. Work by both formalists and logicists during the first two decades of
the last century had effectively accomplished the former of these two goals. Ideally a
finitary consistency proof would accomplish the latter (Irvine 1996, p. 27).
It is precisely the satisfaction of this requirement – of finitarily demonstrable
consistency – that is thought to have been called into question in particular by Gödel’s
second incompleteness theorem. One of the philosophically significant corollaries of
the second incompleteness theorem is that any consistency proof for a theory of which the
second incompleteness theorem holds will have to rely upon methods logically more
powerful than those of that theory itself.
3.2.2 Hayek on Gödel
On at least two occasions Hayek explicitly mentions and comments upon Gödel’s
incompleteness theorem. In his Rules, Perception and Intelligibility (Hayek 1967a),
Hayek considers the possibility of ‘an inherent limitation of our possible explicit
knowledge and, in particular, the impossibility of ever fully explaining a mind of the
complexity of our own’ (ibid., p. 60). He states that ‘there will always be some rules
governing a mind which that mind in its then prevailing state cannot communicate, and
that, if it ever were to acquire the capacity of communicating these rules, this would
presuppose that it had acquired further higher rules which make the communication of the
former possible but which themselves will still be incommunicable’ (ibid., p. 62).
He then pursues:
To those familiar with the celebrated theorem due to Kurt Gödel it will probably be obviousthat these conclusions are closely related to those Gödel has shown to prevail in formalizedarithmetical systems. It would thus appear that Gödel’s theorem is but a special case of amore general principle applying to all conscious and particularly all rational processes,namely the principle that among their determinants there must always be some rules whichcannot be stated or even be conscious. At least all we can talk about and probably all we canconsciously think about presupposes the existence of a framework which determines itsmeaning, i.e., a system of rules which operate us but which we can neither state nor form animage of and which we can merely evoke in others in so far as they already possess them(ibid., p. 62).
The second occasion occurred during the Symposium that was held in 1968 in Alpbach in
the Austrian Tyrol, and was a major event in the history of systems theory. Participating
were, besides Hayek, among others, Paul Weiss, Ludwig von Bertalanffy, and C.H.
Waddington.
The notion of self-organization was the real theme of the conference, even if it was not
called by this name (Dupuy 2009, p. 76).
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The conference proceedings (containing the papers presented during this symposium
as well as most of the content of the discussions) were edited and published by Arthur
Koestler and J.R. Smythies under the title Beyond Reductionism – New Perspectives in the
Life Sciences (Koestler and Smythies 1969). It was during this symposium that Hayek
presented a paper entitled ‘The primacy of the abstract’ (ibid., pp. 309–333) in which he
expounded and defended a thesis already implicitly contained in his earlier book The
Sensory Order, namely that ‘all the conscious experience that we regard as relatively
concrete and primary, in particular all sensations, perceptions and images, are the product
of a super-imposition of many “classifications” of the events perceived according to their
significance in many respects,’ and that ‘[t]hese classifications are to us difficult or
impossible to disentangle because they happen simultaneously, but are nevertheless the
constituents of the richer experiences which are built up from these abstract elements’
(ibid., p. 310).
During the lively discussion that followed, this theme – of the mind eluding full self-
awareness or self-consciousness – was further elaborated upon, and Hayek further
explained:
The example is the thesis that on no adding machine with an upper limit to the sum it can showis it possible to compute the number of different operations this machine can perform (if anycombination of different figures to be added is regarded as a different operation). ( . . . ) Itseems to me that this can be extended to show that any apparatus for mechanical classificationof objects will be able to sort out such objects only with regard to a number of propertieswhich must be smaller than the relevant properties which it must itself possess; or, expresseddifferently, that such an apparatus for classifying according to mechanical complexity mustalways be of greater complexity than the object it classifies. If, as I believe it to be the case, themind can be interpreted as a classifying machine, this would imply that the mind can neverclassify (and therefore never explain) another mind of the same degree of complexity. It seemsto me that if one follows up this idea it turns out to be a special case of the famous Goedeltheorem about the impossibility of stating, within a formalized mathematical system, all therules which determine that system (ibid., p. 332).20
It is nevertheless important not to be mistaken about the strength of the relationship
between Hayek’s thesis that ‘any explanation – which always rests on classification – is
limited by the fact that any apparatus of classification must be of a higher degree of
complexity than what it classifies, and that therefore the human brain can never fully
explain itself’ (Weimer and Palermo ibid., p. 292), on the one hand, and Gödel’s theorem
in mathematical logic, on the other. This relationship is of the nature of an analogy, or even
merely metaphorical; it is not inferential, nor of a strictly logical character.21
4 Hayek’s theory of mind and the philosophy of AI
As highlighted already, Hayek saw Gödel’s proof as a special case of the more general
argument offered in The Sensory Order about the inability of the brain to explain itself.
Just as there are statements about the brain that are true but that cannot be explained in
terms of the logic of the brain, there are statements about a formal system that are true but
that cannot be explained in terms of the logic of that system. In reflections such as these, it
is commonly also the second incompleteness theorem that is implicitly or explicitly
referred to. The inability of a formal system, say S, to prove its own consistency is
interpreted as an inability of S to sufficiently analyze and justify itself, or as a kind of blind
spot. The system does not ‘understand itself’ (also Franzén 2005, p. 125).
As mentioned previously, one author concludes that, ‘[w]ith this insight, Hayek may
have anticipated by a decade Gödel’s own proof’ (Tuerck 287). However, as also pointed
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out already, one should not be mistaken about the strength of the relationship between
Gödel’s proof and Hayek’s insight. While Gödel’s proof may be thought of as providing a
metaphor for or an analogy with a true statement about the brain, the proposition that
‘according to Gödel’s Incompleteness Theorem, understanding our own minds is
impossible,’ is, when taken literally, clearly mistaken if ‘according to’ means ‘as stated or
implied by,’ since of course Gödel’s Incompleteness Theorem neither states nor implies
that understanding our own minds is impossible.
That the relationship is a matter of inspiration rather than implication is also brought
out by Hofstadter who writes (Hofstadter 1980, p. 697):
The other metaphorical analogue to Gödel’s theorem which I find provocative suggests thatultimately, we cannot understand our own minds/brains. This is such a loaded, many-leveledidea that one must be extremely cautious in proposing it. ( . . . ) All the limitative Theorems ofmeta-mathematics and the theory of computation suggest that once the ability to representyour own structure has reached a certain critical point, that is the kiss of death: it guaranteesthat you can never represent yourself totally.
Gödel’s theorems have stimulated many philosophical speculations outside the philosophy
of mathematics. In particular, Gödel’s theorem has been a battleground for philosophers
arguing about whether the human brain is a machine. One has repeatedly attempted to
apply Gödel’s theorems and demonstrate that the powers of the human mind outrun any
mechanism or formal system. Such a Gödelian argument against mechanism was
considered, if only in order to refute it, already by Turing ([1950] 1990, p. 52) who,
proposing the imitation game, concluded that ‘[w]e too often give wrong answers to
questions ourselves to be justified in being very pleased at such evidence of fallibility on
the part of the machines.’22
J.R. Lucas (1961, p. 43) famously proclaimed that Gödel’s incompleteness theorem
proves ‘that Mechanism is false, that is, that minds cannot be explained as machines.’ He
stated that ‘a machine cannot be a complete and adequate model of the mind. It cannot do
everything that a mind can do, since however much it can do, there is always something
which it cannot do, and a mind can’ (ibid., p. 47). More recently, very similar claims have
been put forward by Roger Penrose (1995, 1999).23
All these arguments insist that Gödel’s theorems imply, without qualifications, that the
human mind infinitely surpasses the power of any finite machine. It is now mostly
accepted, however, that these Gödelian anti-mechanist arguments are generally flawed
(Raatikainen 2005, p. 522ff.). They cannot be used to support the erroneous claim that
Gödel’s theorem can be used to show that mathematical insight cannot be algorithmic
(Davis 1993).
The basic error of such an argument can actually be pointed out rather simply, based on
an objection going back to Putnam (1960). The argument assumes that for any formalized
system, or a finite machine, there exists the Gödel sentence (saying that it is not provable in
that system) which is unprovable in that system, but which the human mind can see to be
true. Yet Gödel’s theorem has in reality the conditional form, and the alleged truth of the
Gödel sentence of a system depends on the assumption of the consistency of the system.
Putnam’s argument is still quite illuminating and worth being quoted in full:
It has sometimes been contended ( . . . ) that “the theorem (i.e., Gödel’s theorem) does indicatethat the structure and power of the human mind are far more complex and subtle than anynonliving machine yet envisaged” ( . . . ), and hence that a Turing machine cannot serve as amodel for the human mind, but this is simply a mistake.
Putnam further explains why this is a mistake:
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Let T be a Turing machine which “represents” me in the sense that T can prove themathematical statements I can prove. Then the argument ( . . . ) is that by using Gödel’stechnique I can discover a proposition that T cannot prove, and moreover I can prove thisproposition. This refutes the assumption that T “represents” me, hence I am not a Turingmachine. The fallacy is a misapplication of Gödel’s theorem, pure and simple. Given anarbitrary machine T, all I can do is find a proposition U such that I can prove:
(a) If T is consistent, U is true,
where U is undecidable by T if T is in fact consistent. However, T can perfectly well prove (a)too! And the statement U, which T cannot prove (assuming consistency), I cannot prove either(unless I can prove that T is consistent, which is unlikely if T is very complicated)! (Putnam1960, p. 77).
The anti-mechanist argument thus requires that the human mind can always see
whether the formalized theory in question is consistent, which is highly implausible.
In his Shadows of the Mind (Penrose 1995, Chapter 3), Penrose in particular also
considers the logical possibilities ‘that mathematical belief might be the result of an
unknown unconscious algorithm, or possibly of a knowable algorithm that cannot be
known to be – or firmly believed to be – one that underlies mathematical belief, and rejects
these as “not at all plausible ones”’ (ibid., p. 127 ff.). As Putnam points out, however,
Penrose, who limits his discussion to rules which are ‘simple enough ( . . . ) to appreciate in
a perfectly conscious way’ (ibid., p. 132), completely misses ‘the possibility ( . . . ) that each
of the rules that a human mathematician explicitly relies on, or can be rationally persuaded
to rely on, can be known to be sound and that the program generates all and only these rules
but that the program itself cannot be rendered sufficiently “perspicuous” for us to know that
that is what it does’ (Putnam 1995, p. 371).
While Lucas, Penrose, and others have thus certainly attempted to reply to such
criticism, and have made some further moves, the fact remains that they have never really
managed to get over the fundamental problem stated above. According to the view that
now prevails among professional logicians, they have at best changed the subject
(Raatikainen ibid., p. 523).
5 Hayek’s position: From mechanistic to trans-mechanistic thinking
Lucas’ critique was only one of several lines of attack on Turing’s position, arguing that,
contrary to his assumption, it is not actually possible – in principle or in practice – to get
computers to perform in a way that matches the depth, range, and flexibility of human
minds. According to this view, technological AI is not outlawed – useful AI systems have
already been produced – but the Holy Grail of AI and computational psychology – a
detailed computer model of human mental processes – are impossible and/or infeasible
(Boden 1990b, p. 6).
We were unable to locate any evidence, however, that Hayek actually embraces the
anti-mechanistic thesis. Surely this fact has not been acknowledged invariably (e.g.
Boettke and Subrick 2002, p. 54; see further).
Whereas arguments against the possibility of AI in the style of Lucas and Penrose tend
to suggest that our self-knowledge proves that we are better than machines, one could, as
the Hayekian recognizes, equally well use the fact that formal systems cannot ‘know’
themselves to claim that human self-knowledge is not possible (also Tuerck ibid., p. 288).
Recently one author has taken the fact of individual self-ignorance as the starting point for
a proposed extension of the Austrian paradigm, explaining that ‘[t]he existence of a zone
of tacit knowledge within the mind of actors gives rise to a phenomenon of internal
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ignorance which is itself at the origin of a problem of infra-individual dis-coordination.
It is in reaction to this situation that a process of awareness is implemented via an
“intropreneurial” activity, ( . . . ) but this very endeavor is faced with boundaries beyond
which the mind cannot go’ (Aimar 2008, p. 41).
Still any dichotomy between ‘mechanist(ic)’ and ‘anti-mechanist(ic)’ needs to be
treated with great delicacy and it would be misleading to characterize Hayek’s position
simply as ‘mechanistic’ or ‘mechanist.’ As pointed out already, Hayek’s approach is
actually more akin to that of Ludwig von Bertalanffy. Von Bertalanffy proposed an
organismic model on which a well-grounded explanatory theory of life can be built. His
model represents organisms as a whole or systems that have unique system properties and
conform to irreducible system laws. From this viewpoint which is better characterized as
‘trans-mechanistic’ the traditional dichotomy of mechanistic versus anti-mechanistic must
be rejected as hopelessly simplistic.
6 From the mind to the market
Some authors within the Austrian School go beyond the mere recognition of the existence
of certain functional similarities between the brain and markets – in particular the fact that
both exhibit a spontaneous, polycentric order – by arguing that there also exist certain
analogies and similarities between certain arguments against the possibility or viability of
strong versions of AI, in particular Searle’s and Hayek’s critique of socialist planning.
Thus Boettke and Subrick (2002, p. 54) argue that ‘the sort of criticisms that John
Searle ( . . . ) raises against hard AI concerning the distinction between syntax and
semantics is analogous to the criticism that one finds in Hayek ( . . . ) about the knowledge
problem that socialist modes of economic organization would have to confront. Moreover,
Hayek’s ( . . . ) own work on theoretical psychology raises the same Godelesque critique of
the study of the mind that Roger Penrose (1999) offers against overzealous claims of the
computational theory of the mind.’24
The implications of this interpretation seem to be: first, that Hayek belongs to the anti-
mechanist camp in the philosophy of AI, together with Penrose and other similarly minded
thinkers, and second, that in the grand debate for and against the possibility of AI, Hayek
belongs to the ‘against’ camp, or at least to the group of those who have skeptical doubts
about the possibility of AI.
On a closer reading, and as pointed out already, both these theses are highly
questionable. As David Tuerck concludes, ‘[m]arkets, like the brain (and potentially
computers), exhibit a spontaneous, polycentric order. Gödel’s proof, correctly understood,
reminds us that there are limits to knowledge, human and mechanical, while permitting us
to consider the possibility that knowledge can, indeed, be mechanized. The supposed
distinction between mechanistic and economic thinking stems from a failure to understand
that thinking can be both mechanistic and spontaneous’ (Tuerck 1995, p. 290).
There can be no doubt that in The Sensory Order Hayek explicitly envisions the
possibility of a simulation of the human brain by a machine or computer, a thesis which at
first sight may certainly seem paradoxical. Indeed, according to Hayek, the fact that the
human brain cannot provide an explanation of itself does not ‘exclude the logical
possibility that the knowledge of the principle on which the brain operates might enable us
to build a machine fully reproducing the action of the brain and capable of predicting how
the brain will act in different circumstances’ (Hayek [1952] 1976, p. 189).
Hayek pursues that ‘[s]uch a machine, designed by the human mind yet capable of
“explaining” what the human mind is incapable of explaining without its help, is not a
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self-contradictory conception in the sense in which the idea of the mind directly explaining
its own operations involves a contradiction. The achievement of constructing such a
machine would not differ in principle from that of constructing a calculating machine
which enables us to solve problems which have not been solved before, and the results of
whose operations we cannot, strictly speaking, predict beyond saying that they will be in
accord with the principles built into the machine. In both instances our knowledge merely
of the principle on which the machine operates will enable us to bring about results of
which, before the machine produces them, we know only that they will satisfy certain
conditions’ (ibid., p. 189).
It is thus fairly clear that Hayek’s account implies the possibility of building a machine
that passes the Turing test.
Apparently the explanation lies in the distinction between what the apparatus of
classification – mind or machine – produces in the form of results and the principles
according to which it generates those results. According to one author, a machine whose
principles of operation we understand but that nevertheless generates results that
‘reproduce’ the actions of the human brain would be somehow functionally equivalent to
such a brain (Tuerck ibid., p. 284). But actually a machine that could predict our thoughts
would not be equivalent to a human mind, but superior to it. The machine Hayek describes
in The Sensory Order has super-human capabilities.25
This conclusion will perhaps seem to be at odds with a widespread perception among
Austrian economists that there is in economics no room for any thinking of a mechanistic
kind. Ludwig von Mises ([1949] 1996, p. 25) distinguishes between ‘two principles
available for a mental grasp of reality, namely, those of teleology and causality.’ The study
of economics is aimed at those aspects of mind and of human action that are purposeful.
Mechanism is the bailiwick of other sciences such as physics. Buchanan carries the
dichotomy between thinking of a mechanistic kind and economic thinking even further,
rejecting as sterile the whole ‘means-end’ characterization of the economic problem, and
arguing that ‘[t]he market or market organization is not a means toward the
accomplishment of anything. It is, instead, the institutional embodiment of the voluntary
exchange processes that are entered into by individuals in their several capacities’
(Buchanan 1964, pp. 30–31).
Nevertheless the market organization to which Buchanan refers, when it is conceived
of as a spontaneous or polycentric social order – that is, as a decentralized price system –
rather than as planned or monocentric, presents a clear analogy with the human brain.26
An explanation is provided by Hayek in the following terms:
In both cases we have complex phenomena in which there is a need for a method of utilizingwidely dispersed knowledge. The essential point is that each member (neuron, or buyer, orseller) is induced to do what in the total circumstances benefits the system. Each member canbe used to serve needs of which it doesn’t know anything at all. Now that means that in thelarger (say, economic) order, knowledge is utilized that is not planned or centralized or evenconscious. The essential knowledge is possessed by literally millions of people, largelyutilizing their capacity of acquiring knowledge that, in their temporary position, seems to beuseful. Now the possibility of conveying to any kind of central authority all the knowledge anauthority must use, including what people know they can find out if it becomes useful to them,is beyond human capacity ( . . . ). In our whole system of actions, we are individually steeredby local information – information about more particular facts than any other person orauthority can possibly possess. And the price and market system is in that sense a system ofcommunication, which passes on (in the form of prices, determined only on the competitivemarket) the available information that each individual needs to act, and to act rationally(Weimer and Hayek 1982, pp. 325–326).
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Hayek acknowledges the fact that the similarity is only a partial one: whereas for the
individual brain, decisions are made by first modeling the question of what action to take
and then sending the results to a central authority for execution, for a decentralized price
system, decisions take place directly without the necessity of communicating them first to
any central authority, thus making ‘the use of more information possible than could be
transmitted to, and digested by, a centre’ (Hayek 1967b, pp. 73–74).27
A decentralized price system is superior over central planning, despite the fact that the
actions of every organism that makes up a spontaneous or polycentric social order are
themselves centrally directed by a brain. This superiority rests precisely on the brain’s
ability to model alternative courses of action before selecting the course of action to be
taken by the organism that it directs. Purposive behavior takes place when the organism
selects from these alternative courses of action the one that it identifies as having the most
desired consequences.
The inferiority of central planning, by contrast, rests on the fact that it wastes
information, not only because of the limited capacity of the planners to receive and digest
the information communicated to them, but also because of the inability of individual
economic agents to communicate all of the information that they have. This inability stems
from their more general inability to state or communicate all the various rules that govern
their actions and perceptions, which brings us back to the Gödelian metaphor.
7 The socialist calculation debate
The foregoing remarks, in particular concerning the absence of any anti-mechanistic line
of argumentation in Hayek’s reasoning, could thus never throw into doubt the ongoing
relevance of the Austrian critique of socialist economic planning. In particular it seems
that economists who thought that the model of market socialism effectively answered the
critique of socialism proposed by Ludwig von Mises and F.A. Hayek were misled by
the general equilibrium model. General equilibrium theory captures in abstract form the
interconnectedness of all markets in an economic system, but it does so at the cost of
assuming away the processes through which the division of knowledge in society is
coordinated so that the interconnectedness can be realized.
Interconnectedness of economic behavior was coordinated through conscious design
by hypothesis but the question of how in actuality agents would indeed acquire and utilize
the information needed to realize efficient solutions was left unexamined (Boettke and
Subrick ibid., pp. 55–56).
A particular dimension has been added to this ongoing debate since the more recent
development of the research program of computable economics.28
Computational economics can be seen as a discipline that encompasses three different
ways of looking at economic and social systems: (1) Can we computationally predict the
behavior of some (economic, social) phenomenon? (2) Can we formulate in a constructive
way the main results from mathematical economics? (3) Finally, can we look at economic
(and social) processes as computing devices? (Bartholo, Cosenza, Doria, and de Lesa
2009, pp. 72–73).
With respect to the last question, several of the main contributions have been made by
A.A. Lewis and K.V. Velupillai. One of the most striking results in the meta-mathematics
of economic models was the proof by Lewis that the (formal) theory of Walrasian models
with a computable presentation is an undecidable theory. Lewis’ chief result on the
undecidability of game theory was that recursively presented games have a nonrecursive
arithmetic degree (Lewis 1992a, b).
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The central point emphasized by these authors is well summarized by Bartholo et al.
(2009, p. 73) who state that ‘once you build your argument within a framework that
includes enough arithmetic to develop recursive function theory in it, then you get Gödel
incompleteness everywhere, you get undecidable sentences of all sorts, including those
that deal with interesting or pressing theoretical questions.’ One of these questions relates
to the presumed possibility of planned economies.
Reference in this context can be made to the pioneering attempts of Newton de
Costa and Francisco Doria who obtained some quite general undecidability and
incompleteness results/theorems of consequence to the sciences that use mathematics as
their main language and predictive tool. These results show some of the limits that come
to the forefront when one tries to look at some of the central questions of every science
from the perspective of the mathematician, such as: What can we know about the
future? What can we know about the world through a formal language? Which are the
limitations imposed on our empirical, everyday knowledge when we try to describe the
world around us with the help of a formalized language? (da Costa and Doria 1994, p. 1,
2005, pp. 16–17).
One implication of their results is that the main argument by Lange in favor of a
planned economy clearly breaks down. As these authors conclude, ‘Lange thought that
given the (possibly many) equations defining an economy, a huge and immensely
powerful computer would always be able to figure out the equilibrium prices, therefore
allowing (at least theoretically) the existence of an efficient global policy maker’ (da Costa
and Doria 1994, p. 13).
Generally the results obtained within the field of computational economics disprove the
once believed conjecture that given the equations defining an economy, some gigantic
supercomputer would always be able to calculate the equilibrium prices, therefore allowing
(at least theoretically) the existence of an efficient global policy maker. For general
mathematical models, the matter is algorithmically unsolvable (Bartholo et al. 2009, p. 78).
Clearly undecidability and incompleteness not only do matter for mathematical economics,
but also have important practical consequences.29
This author’s book Computable Economics sketches the main research lines in the field.
A full chapter (chap. 3, pp. 28–43) is devoted to the approach that identifies the rational
behavior of an economic agent with the behavior of a Turing machine. A central result,
which is proved as a direct consequence of the unsolvability of the halting problem for
Turing machines, is that, if rational agents are identified with Turing machines, preference
orderings are undecidable. There is no effective procedure to generate preference orderings
(ibid., p. 38).
Later chapters in the same book introduce some intriguing new explorations in
computable economics. In this context the author also reconsiders the status of the
socialist calculation debate in the light of algorithmic and computational complexity
theories.
As this author aptly concludes, ‘[i]t is as if the ghosts of Lange and Taylor have never
been properly exorcised, in spite of the powerful empirical reasons put forward by von
Mises, Hayek, and Robbins. ( . . . ) I conjecture that the tools of algorithmic and
computational complexity theory can be used to indicate the computational infeasibility of
the institutions of so-called socialist market economies based on Lange-Taylor type
arguments’ (Velupillai 2000, p. 164).
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8 The case for methodological dualism and concluding remarks
Hayek’s theoretical psychology culminates in an argument for methodological dualism
and the inevitability of a verstehende psychology. He concluded that ‘[w]hile our theory
leads us to deny any ultimate dualism of the forces governing the realms of mind and that
of the physical world respectively, it forces us at the same time to recognize that for
practical purposes we shall always have to adopt a dualistic view’ (Hayek [1952] 1976,
p. 179).30
While from a practical methodological perspective, the methodological theses and
conclusions of Hayek and Mises may be considered largely congruent, Hayek’s arguments
in favor of methodological dualism are clearly distinct from those of Mises. In particular
Hayek’s argument is of a more principled nature than that of Mises.
Hayek rejects the possibility of a reduction in the sense of a complete and detailed
explanation of mental processes in physical terms as a matter of principle. The fact that
‘any apparatus of classification must possess a structure of a higher degree of complexity
than is possessed by the objects which it classifies’ puts ‘an absolute limit to what the
human brain can ever accomplish by way of explanation – a limit which is determined by
the nature of the instrument of explanation itself ( . . . ).’ The capacity of any explaining
agent must be limited to objects with a structure possessing a degree of complexity lower
than its own (Hayek [1952] 1976, p. 185).
Mises recognizes that the mind–body problem has not been solved satisfactorily in the
sense that ‘[w]e do not know why identical external events result sometimes in different
human responses, and different external events produce sometimes the same human
response’ but he consistently adds qualifications such as ‘as far as we can see today’ or ‘at
least under present conditions,’ and so forth, which means that he does not exclude a
reduction of the mental to the physical as a matter of absolute impossibility. In fact he
seems to adopt an agnostic stance with respect to this issue since he argues that ‘[w]e may
or may not believe that the natural sciences will succeed one day in explaining the
production of definite ideas, judgments of value, and actions in the same way in which they
explain the production of a chemical compound as the necessary and unavoidable outcome
of a certain combination of elements. In the meantime we are bound to acquiesce in a
methodological dualism’ (Mises [1949] 1996, p. 18).
Let us summarize and conclude. On a few occasions Hayek referred to the famous
Gödel theorems in mathematical logic while expounding his cognitive theory. The exact
meaning of the supposed relationship between Gödel’s theorems, on the one hand, and the
essential proposition of Hayek’s theory of mind, on the other, remains subject to
interpretation, however. In this article I have argued that the relationship between Hayek’s
thesis that the human brain can never fully explain itself, on the one hand, and the essential
insight provided by Gödel’s Incompleteness theorems in mathematical logic, on the other,
has the character of an apt analogy or an illuminating metaphor. Thus, the anti-mechanistic
interpretation of Hayek’s theory of mind has been revealed as highly questionable and in
fact incorrect. It has also been concluded that Hayek’s arguments for methodological
dualism, when compared with those of Ludwig von Mises, amount to a strengthening of
the case for methodological dualism.
Acknowledgements
The author would like to thank K. Vela Velupillai as well as an anonymous reviewer for usefuladvice and comments on a previous version of this paper.
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Notes
1. On the place of cognitive psychology in the work of F.A. Hayek, see also Birner (1995).2. See Hayek (1967a, p. 44; 1978, p. 38).3. For Hayek’s references to Gödel, see Hayek (1967a, p. 62; 1969, p. 332); for Polanyi’s
references to Gödel, see Polanyi (1958, passim).4. Alan Turing ([1950] 1990) considered the question ‘Can machines think?’ The strategy he
adopted is eminently practical. Turing introduced his now-famous ‘Imitation Game,’ in whic.machine is deemed to be intelligent if an observer is unable to distinguish its behavior from thatof an agent (in this case, a human being) who is assumed a priori to behave intelligently.Polanyi clearly rejects this type of Turing test since he writes: ‘I dissent therefore from thespeculations of A.M. Turing ( . . . ), who equates the problem: “Can machines think?” with theexperimental question, whether a computing machine could be constructed to deceive us as toits own nature as successfully as a human being could deceive us in the same respect’ (Polanyi1958, p. 263). For a collection of papers exploring Turing’s various contributions, see inparticular also Teuscher (2004).
5. See further under Section 4.6. On the classical mechanist/vitalist debates, see in particular also Shanker (1996).7. See in particular Hayek ([1952] 1976, pp. 47, 83).8. In view of these considerations Hayek’s position can probably be better characterized as ‘trans-
mechanistic.’ Hayek shows that the dichotomy of mechanistic versus anti-mechanistic, astraditionally understood, is deceptively simplistic. I thank an anonymous referee for havingmade this suggestion to me.
9. For a survey of some of these misinterpretations, see Butos and Koppl (2006).10. Other critical summaries of Hayek’s theory of mind can be found in, among others, the already
mentioned papers of Weimer (1982), Birner (1995), Tuerck (1995), and Horwitz (2000).11. As Hayek clarified in the Preface of The Sensory Order: ‘It seems as if the problems discussed
here were coming back into favour and some recent contributions have come to my knowledgetoo late to make full use of them. This applies particularly to Professor D.O. Hebb’sOrganization of Behaviour which appeared when the final version of the present book waspractically finished’ (ibid., p. viii).
12. See now Petzold (2008); also Turing ([1950] 1990) and Gödel ([1931] 1992).13. Philosophers use the term weak AI for the hypothesis that machines could possibly behave
intelligently, and strong AI for the hypothesis that such machines would count as having actualminds (as opposed to simulated minds). See Russell and Norvig (2010, Chapter 26).
14. For some time the definitive formulation of the connectionist paradigm was contained inSmolensky (1988).
15. The ‘frame problem’ did not announce the end of AI, however, nor did it lead to a completeloss of faith in the formalizability and/or axiomatizability of our basic common senseknowledge. See also Hayes (1979) and McDermott (1987), reprinted in Boden (1990a).For a contemporary textbook treatment of the frame problem, see Russell and Norvig (2010,p. 266 ff.).
16. A NP-hard problem is a mathematical problem for which, even in theory, no shortcut or smartalgorithm is possible that would lead to a simple or rapid solution. Instead, the only way to findan optimal solution is a computationally intensive, exhaustive analysis in which all possibleoutcomes are tested.
17. See in particular also Hayek (1967c).18. As Hayek himself explains, he was not aware of Von Neumann’s work at the time he was
writing The Sensory Order: ‘No, I wasn’t aware of his work, which stemmed from hisinvolvement with the first computers. ( . . . ) At the time his research on automata came out, itwas too abstract for me to relate it to psychology, so I really couldn’t profit from it; but I did seethat we had been thinking on very similar lines.’ See Weimer and Hayek (1982, p. 322). On theorigins of cognitive science, see also Dupuy (2009).
19. The economic methodologist interested in more complete accounts and/or discussions of thesetheorems can take a look at the following literature. Gödel’s original contribution is containedin Gödel ([1931] 1992). Other excellent discussions of these fundamental results can be foundin, among others, Hintikka (2000), Smith (2007), and more formally Smullyan (1992). Thebook by Peter Smith builds up the proofs of the theorems in a gradual and systematic manner.
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A very short account of Gödel’s theorems is provided by Cameron (2008). Franzén (2005) is aparticularly illuminating and thoughtful guide to uses and abuses of Gödel’s theorems.
20. For a similar example, see also Hayek ([1952] 1976, p. 188).21. For a critique of the idea itself by a logician, see Franzén (2005, p. 126) where this author
concludes that ‘[i]nspired by this impressive ability of PA to understand itself, we conclude, inthe spirit of metaphorical “applications” of the incompleteness theorem, that if the human mindhas anything like the powers of profound self-analysis of PA or ZFC, we can expect to be ableto understand ourselves perfectly.’ Still this does of course not refute Hayek’s ‘conclusionabout the absolute limit to our powers of explanation’ which is ‘of considerable importance forsome of the basic problems of what used to be called the mind-body relationship and the tasksof the mental and moral sciences generally’ (Weimer and Palermo, ibid.). But rigorouslyspeaking, Gödel’s theorem relates only to formal systems. In particular the incompletenesstheorem pinpoints a specific incompleteness in any formal system that encompasses some basicarithmetic: it does not decide every arithmetical statement. Unfortunately for the applicabilityof the incompleteness theorem outside mathematics, this also means that we learn nothing fromthe incompleteness theorem about the completeness or incompleteness of formal systems withregard to nonarithmetical or nonmathematical statements (Franzén 2005, p. 27).
22. The theoretical groundwork of both traditional and connectionist approaches to AI wasprovided by Alan Turing’s (1936) paper on computable numbers, which defined computationas the formal manipulation of (uninterpretsymbols by the application of formal rules. Thegeneral notion of an ‘effective procedure’ – a strictly definable computational process – wasillustrated by examples of mathematical calculation. It implied, however, that if intelligence isin general explicable in terms of effective procedures implemented in the brain, then it could besimulated by a universal Turing Machine or by some actual machine approximating it. In hisComputing Machinery and Intelligence (Turing [1950] 1990) he specifically asked whethersuch machines can think and argued that this should be decided, not on the basis of a prior (andpossibly question-begging) definition of ‘thinking’ but by enquiring whether some conceivablecomputer could play the ‘imitation game.’ Could a computer reply to an interrogator in a wayindistinguishable from the way a human being might reply, whether adding numbers orscanning sonnets? (see also Boden 1990b, p. 4).
23. For a detailed criticism of Penrose’s thesis, see also Shapiro (1998, 2003).24. See Searle’s argument (see Searle 1980) involving the imaginary ‘Chinese room,’ which
assumes that AI programs and computer models are purely formal-syntactic (as is a Turingmachine) and claims, on this basis, that no system could understand purely in virtue of carryingout computations.
25. I thank an anonymous referee for having drawn my attention to this point.26. Di Iorio provides a schematic summary of the analogies which exist between mind and market;
see Di Iorio (2010, pp. 197–199).27. Hayek writes: ‘The unique attribute of the brain is that it can produce a representative model on
which the alternative actions and their consequences can be tried out beforehand. ( . . . ) In so faras the self-organizing forces of a structure as a whole lead at once to the right kind of action( . . . ), such a single-stage order need not be inferior to a hierarchic one in which the wholemerely carries out what has first been tried out in a part’ (Hayek 1967b, pp. 73–74).
28. Computable economics, according to one notable contributor, is about basing economicformalisms on recursion-theoretic fundamentals. This means that economic entities, economicactions, and economic institutions have to be viewed as computable objects or algorithms(Velupillai 2000, p. 2). This development is mentioned here because of its links both with theHayekian theme of the impossibility of socialist central economic planning (the requirementthat computation processes be decentralized) and with the implications of Gödelian and/orrelated meta-mathematical limitative results.
29. See, among others, Velupillai (2000, 2005a, 2007).30. As is pointed out in Koppl (2008) Hayek essentially showed that ‘scientific’ and ‘humanistic’
approaches to social science can and should be compatible and complementary. As Kopplsummarizes this thesis: ‘Hayek was a methodological dualist and a hermeneut, but not anti-science. He was a scientific hermeneut’ (ibid., p. 117). However, in Koppl (2010, p. 22) it isalso argued that Hayek’s diagonal argument is ‘a direct consequence’ of ‘the celebratedCantor’s “Diagonal” theorem,’ but a more moderate and correct interpretation seems to be thatthe relation is at most one of analogy rather than one of strict logical inference or consequence.
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