The two competing cognitive practices of the Calculus: Leibniz and Robinson versus Newton andWeierstrass

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In their investigation about ‘the psychological foundations of culture’, Tooby and Cosmides (1992) advocate an “integrated causal model” for the social sciences. This model is first and foremost a naturalistic programme that promotes causal explanations in the realm of the social. Such a natural-istic programme, Tooby and Cosmides argue, requires building bridges between the social and the natural sciences. Of course, there is no ques-tion of eliminating the social sciences with the idea that natural sciences can do the explanatory job. But the goal is to understand what sort of causal events underlie social and cultural events and what natural phe-nomena make social phenomena possible. Tooby and Cosmides point out the importance of two bridges: between the social sciences and cognitive psychology, and between cognitive psychology and biology. The essen-tial import of this approach is that biology sets constraints on psychology, because mental processes are implemented in a biological organ, and psy-chology sets constraints on the social sciences, because social phenomena are realised by interacting thinking beings The authors contrast their pro-posal with current practice in the social sciences. They accuse the “Stan-dard Social Science Model” of considering the human realm and social or-der as outside of the natural causal world and to assume erroneously that the human mind is a like a blank slate. Tooby and Cosmides forcefully at-tack the theory that views the human mind as a blank slate and its modern counterpart, the mind as a general-purpose mechanism. Findings in de-velopmental psychology have shown that infants have some knowledge of the environment that is manifest so early as not to be possibly acquired in development. Against the blank slate metaphor of the mind, humans are endowed with innate knowledge. Among the reasons for the rejection of the existence of a general-purpose mechanism is evolutionary plausi-bility: there is no plausible evolutionary history for the advent of general-purpose cognitive abilities. Also, general-purpose mechanisms are unable to solve the current problems humans solve easily and rapidly (c.f. also the frame problem). More recently, Pinker (2002) has forcefully defended the scientific account of the innate organisation of the mind against the ‘dogma’ of the blank slate.
The theory asserting the existence of domain specific faculties presented in the previous section is a viable alternative account of the mind as a blank slate or as a general purpose information processing device. These evolved abilities allow dealing with the input in a quick, cost effective and reliable way. In order to achieve this, the cognitive devices have to as-sume things about the world — they have content; they embody innate knowledge.
One consequence of this view is that cognition does not consist in the mere extraction and organisation of information from the world; rather, it involves cognitive capabilities that shape our understanding of the world according to their internal organisational principle. Our na¨ıve and direct apprehension of the world involves cognitive construction. Tooby and Cosmides urge us not to stop here our investigations on cognition. Their Integrated Causal Model reveals the possibility and importance of linking these findings to evolutionary biology. The cognitive devices of the human mind are indeed themselves organs that have been selected during evolu-tionary history. A complete causal account of cognition and behaviour must therefore include an account of the evolutionary construction of the evolved information-processing device 1 The relevant aspect of this argu-ment, for our purpose, is that one cannot explain scientific cognition in terms of some special scientific competency if this competency does not have a plausible evolutionary history. Ironically, a similar argument is de-veloped by Latour (1986) who conclude that cognitive psychology is not relevant to science studies. By contrast, the conclusion I want to draw is that since scientific rationality as postulated by philosophers is not imple-mented in the mind, then scientific cognition needs be re-thought with the best theories in cognitive psychology. Moreover, one can expect that if the mind is not tailor made for science, then science must develop so as to ‘fit’ the nature of the human mind. In other words, scientific knowledge must be cognizable. Therefore the nature of the human mind can be expected to constrain the content of science.
1 It is worth noting that the programme of evolutionary psychology put forward by Cosmides and Tooby and others, and which I present as convincing, is NOT aiming at finding presumed biological causes for socio-cultural inequalities. On the contrary, the research programme is first and foremost aimed at understanding the universal psycho-logical traits of the human species.


Cosmides and Tooby’s attack, indeed, bears on Science Studies. The crit-icised view of the functioning of the mind is at the basis of the argument of both those who deny the role of cognition and those who deny the role of social interactions in scientific knowledge production. In each case the mind is but an empty bag that is either filled by the ‘social’ or through empirical observations only.
The latter view has been sustaining some form of ‘direct realism’ — the view that scientific truths are directly (without social bias) given to the mind observing the world. Maybe the most elaborate view of that sort has been proposed by Gopnik and Meltzoff (1997), who argues that the development of science is accounted for by the mere accumulation of data made available to the minds of scientists: data are processed by the mind’s general-purpose cognitive abilities, which compile scientific theo-ries. Not surprisingly, such a view has been criticised for not taking into account the social nature of scientific practice by even the most people opposed to the Strong Programme (e.g. Carruthers, 2002, section 3). Di-rect realism overlooks the determinative role of active experimenting (sci-entists are not just ‘listening’ to what the world says, they also choose which questions to ask), communication (scientists need convince others), and the inter-subjective control of scientific production that is supposed to guarantee objectivity. However, the fact that such views are attacked not only for their misconception of science but also for being wrong about cognitive processes opens new prospects for the analysis of the relation between cognitive and social phenomena in scientific knowledge produc-tion. Hutchins (1995) has noted that cognitive scientists have made the mistake to attribute to the individual mind processes that are in fact done by larger cognitive systems, sometimes including several people. Science is a case in point: it is thought that it could be the product of isolated sci-entists, as if one brain living long enough would have developed the same kind of knowledge as centuries of scientific disputes and confrontations of ideas The hypothesis that scientific thinking relies on evolved cogni-tive abilities provides a promising alternative, as it does not take science, a collective achievement, as the paradigmatic illustration of what minds can do. In the perspective of evolutionary psychology, mental abilities have a biological basis that has evolved as issuing adaptive behaviour; but doing science is not a behaviour that played a role in the evolutionary history of the genetic basis of mental abilities; science is much too recent and local. Scientific cognition not being already squeezed within scien-tists’ mind, one can wonder anew about what, in the mind, makes science possible: take what abilities have probably evolved, what abilities account for day to day behaviour, what abilities seem to exist before scientific train-ing is done; on this basis attempt to account for scientists’ behaviour out of which science emerge. This is, for instance, the explicit method used by Carruthers (2002), when he attempts to relate the cognitive skills of the hunter — which have presumably been selected for — with the skills put at work in doing science.
The opposite ‘social reductionist’ view, which denies any determining role to our cognitive apparatus in the formation of scientific beliefs (Latour and Woolgar 1986, p. 280; Latour 1987, p. 247) is also at odd with the thesis that the human mind is endowed with domain specific abilities that signif-icantly constrain cognition, and thus belief formation. Numerous works in social studies of science appear to be embedded in the Standard Social Sci-ence Model and its erroneous assumptions about how the mind works. In-sofar as one admits that the scientist’s mind is involved in scientific knowl-edge production, the a priori claim that the nature of the mind has no role in framing knowledge cannot be justified but by the assumption that the human mind is totally plastic, so that it does nothing but reflect the so-cial structure or the context. The social reductionist view, insofar as it is committed to the thesis that the mind is totally framed by enculturation, is erroneous. Against ‘social reductionism’, scientists use their biologically endowed and already content loaded cognitive apparatus when investi-gating the world. Rather than just taking on current scientific theories, they put their cognitive resources at work to understand, remember and apply them. Thus the cognitive structure and innate endowment of our mind is always empowering and constraining our thoughts — whether the thoughts are meant to be scientific or not. In particular, scientists are always forced to rely and assess the relevance and meaning of their intu-itions. Intuitions remain at the basis of scientific reasoning. One reason why scientific cognition cannot do without intuitive beliefs is that reason-ing and argumentation must always stop at a point (this is tantamount to the Wittgensteinnian remark about rule following: at some point the rule must be applied without having a meta-rule explaining how to apply it). This let scientists in front of claims that must be accepted at face value. Scientists accept claims without arguments proving its truth for different reasons. One reason can be that the claims are upheld by some other sci-entists whom they trust. Another pervasive reason is that the claims are obvious as they are. Why is that so? The intuitive appeal of the obvious claims is the result of some mental cognitive processes. How dependent from cultural knowledge are the processes that provide intuitive appeal? This is a question that cannot be answered a priori. Probably, the answer depends from case to case. One sure thing, however, is that these processes are not independent from pre-wired 2 mental mechanism; in particular, they are not independent from the pre-wired aspects of perception mod-ules (i.e. what we perceive is never fully determined by what we believe). I will further argue that they are not independent from conceptual abilities (i.e. mental mechanisms not directly dealing with perception) such as the domain specific abilities mentioned above.

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The relation between the cognitive and the social in scientific knowledge production can fruitfully be re-thought along the following questions: What is the role of evolved cognitive mechanism in scientific practice? How can a species, which evolved as a hunter-gatherer species, do science? The in-tegrated Causal Model shows the relevance of these questions by putting forward the results of developmental and evolutionary psychology, which assert that the mind is so structured that it heavily constrains the content of our thoughts — including, of course, our scientific thoughts. Now, if scientific thoughts are produced by some highly specified mental abilities, then there is important reason to think that these abilities did let their im-print on our scientific knowledge. We have the opportunity to analyse the implications of the nature of the mind, as it is discovered by psychologists, on the content of science. We have the opportunity to understand scientific history and scientific practices more thoroughly.

Table of contents :

I Motives and means for integrating cognitive and social studies of science 
1 Introduction
1.1 The social and the cognitive
1.2 Means of integration
1.3 Theoretical claims about the principles of scientific evolution
1.4 Organisation of the thesis
2 Cognitive studies of science and the social
2.1 Why integrating social and cognitive studies of science
2.2 Impediments to integration
2.2.1 Philosophers’ qualms about social determination
2.2.2 Homo-economicus, homo-scientificus
2.2.3 When foundational concerns get in the way
2.2.4 Psychology and the myth of the isolated scientist
2.3 Integrative projects
2.3.1 Cognitive history of science
2.3.2 Environmental approaches
2.3.3 The psychology of social studies
2.4 Cognitive anthropology of science
3 Integrating the Strong Programme
3.1 The Strong Programme and its attitude towards psychology
3.1.1 The symmetry principle
3.1.2 methodological relativism
3.1.3 Social theory of the Strong Progamme
3.1.4 The Strong Programme’s attitude towards psychology
3.2 Alternatives to the Strong Programme
3.2.1 rational reconstruction
3.2.2 The Bath School
3.2.3 Latour and ANT
3.2.4 Ethnomethodology
3.2.5 The practice turn
3.2.6 Distinguishing the schools of social studies of science
3.3 Naturalising epistemology: via sociology, towards psychology
3.3.1 Candidate solutions to the under-determination problem
3.3.2 Methodological individualism as a naturalistic method for epistemology
II Psychology and the history of science 
4 Scientific thinking and rationality
4.1 Rationality: Mind and Culture
4.1.1 The psychologist, the epistemologist and the social scientist about rationality
4.1.2 From minds to epistemic norms
4.2 The rational foundations of relativism
4.2.1 Sperber’s rationalism and methodological relativism
4.2.2 Same world, same minds, but different beliefs
4.2.3 A naturalistic look at reasons
5 Nativism for science studies
5.1 Nativism and cognitive abilities
5.1.1 Some cognitive abilities with innate bases
5.1.2 How to characterise innateness
5.1.3 Evolutionary causal cycle: genes—neural device(s)—cognitive processes—behaviour—gene selection
5.2 Why the structure of the mind constrains the content of science
5.2.1 Against the Blank Slate
5.2.2 Science Studies without the Blank Slate
5.2.3 Science studies with theories of evolved cognitive abilities
5.3 The Odd Couple: Nativism and social constructivism
5.3.1 Compatibility between nativism and social constructivism
5.3.2 Evolutionary psychology and the Strong Programme
5.3.3 Latour against evolutionary psychology
5.4 The epistemic value of innate factors of cognition
5.4.1 Psychological reliabilism versus the evolution of credibility
5.4.2 Evolved cognitive abilities are not sufficiently reliable for science
5.4.3 Dissatisfaction with cognitive performances
5.4.4 Is there any scientific-friendly evolved cognitive ability?
6 The epidemiology of scientific representations
6.1 The epidemiology of representations—a brief account
6.1.1 A naturalistic characterisation of culture and its evolution
6.1.2 Psychology and the stabilisation of representations
6.2 The epidemiology of representations and the history of science
6.2.1 Questioning the distribution of scientific representations
6.2.2 Mechanisms distributing scientific representations
6.3 Some psychological principles of scientific evolution
6.3.1 Evaluating and routing intuitive representations
6.3.2 Factors of attraction in scientific evolution
7 A case study on mathematical cognition and history
7.1 Psychologism and the cognitive foundations of mathematics
7.1.1 Paths to psychologism
7.1.2 Where is then the norm? Strategies for avoiding psychologism
7.1.3 Considering the social aspects of mathematical production
7.1.4 Some conclusions on the historiography of mathematics
7.2 Attraction towards Newton’s fluxion
7.2.1 The number sense as a cognitive ability – brief review of the psychological literature
7.2.2 The two competing cognitive practices of the Calculus: Leibniz and Robinson versus Newton andWeierstrass
7.2.3 Why thinking with limits has been more appealing than thinking with infinitesimals
7.3 Mechanisms of distribution of mathematical representations
7.3.1 Trust-based mechanisms of distribution: Malebranche as a catalyst
7.3.2 Interests and strategic means of distribution: aiming at the institutional recognition of the calculus
7.3.3 An effect of psychological factors of attraction in the history of the calculus
7.4 Conclusion: historical analysis and cognitive hypotheses
III The cultural organisation of scientific cognition
8 Distributed cognitive systems in science
8.1 The idea of distributed cognition
8.2 Latour: Distributed cognitive systems without human minds
8.3 Giere: Distributed cognition is where the cognitive and the social merge
8.4 Nersessian: evolving distributed cognitive system
8.5 Prospects and limits of distributed cognition analyses
9 The social organisation of cognition
9.1 Emergent properties of distributed cognitive systems
9.2 Regulatory representations for distributed cognitive systems
9.3 Functional analysis of cognitive systems
9.4 Cognitive institutions
10 The evolution of cognitive systems of science
10.1 History of science and the transformation of distributed cognitive systems
10.2 How cognition culturally evolves
10.3 Minds and things in the making of distributed cognitive systems
10.4 How humans can distribute cognition
10.5 The role of trust in ascribing cognitive functions
10.6 Concluding on ANT
11 Distributing mathematical cognition
11.1 The significance of the 4-colour theorem
11.1.1 Brief history of the 4-colour theorem
11.1.2 The 4-colour theorem as food for thought for the students of mathematical knowledge production
11.1.3 Significance of the 4-colour theorem for the cognitive history of mathematics
11.2 Mathematical conjectures have cognitive appeal
11.3 Mathematical cognition as distributed cognition
11.3.1 Mathematical cognition involves non-mental representations and social interaction
11.3.2 The CSM: The cognitive system that produces mathematical knowledge
11.4 Rethinking the new 4-colour problem
11.4.1 Methodological consequences for the history of mathematics
11.4.2 How mathematicians came to trust computers
IV The exploitation of cognitive abilities and tools 
12 An integrated causal model for science studies
12.1 Evolutionary epistemology
12.1.1 Blind variation
12.1.2 Selective retention
12.1.3 The layered construction of knowledge
12.2 The scientists’ mind as being massively modular
12.2.1 Science and the modular mind: why it matters
12.2.2 How massive modular minds can be flexible: proposals from a cognitive science of science perspective 398
12.3 How scientific cognition evolves with culture


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