Results for 'Hilbert's programme'

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  1.  45
    Hilbert's programme.Georg Kreisel - 1958 - Dialectica 12 (3‐4):346-372.
    Hilbert's plan for understanding the concept of infinity required the elimination of non‐finitist machinery from proofs of finitist assertions. The failure of the original plan leads to a hierarchy of progressively less elementary, but still constructive methods instead of finitist ones . A mathematical proof of this failure requires a definition of « finitist ».—The paper sketches the three principal methods for the syntactic analysis of non‐constructive mathematics, the resulting consistency proofs and constructive interpretations, modelled on Herbrand's theorem, and (...)
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  2.  12
    Hilbert's Programme.Georg Kreisel - 1962 - Journal of Symbolic Logic 27 (2):228-229.
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  3.  22
    Hilbert's Programme and Gödel's Theorems.Matthias Schirn Karl‐Georg Niebergall - 2002 - Dialectica 56 (4):347-370.
    In this paper, we attempt to show that a weak version of Hilbert's metamathematics is compatible with Gödel's Incompleteness Theorems by employing only what are clearly natural prov‐ ability predicates. Defining first “T proves the consistency of a theory S indirectly in one step”, we subsequently prove “PA proves its own consistency indirectly in one step” and sketch the proof for “If S is a recursively enumerable extension of , S proves its own consistency indirectly in one step”. The (...)
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  4. Hilbert's programme and gödel's theorems.Karl-Georg Niebergall & Matthias Schirn - 2002 - Dialectica 56 (4):347–370.
  5.  16
    Hilbert’s Programme and Ordinal Analysis.Wolfram Pohlers - 2016 - In Peter Schuster & Dieter Probst (eds.), Concepts of Proof in Mathematics, Philosophy, and Computer Science. Boston: De Gruyter. pp. 291-322.
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  6.  93
    The pragmatism of Hilbert's programme.Volker Peckhaus - 2003 - Synthese 137 (1-2):141 - 156.
    It is shown that David Hilbert's formalistic approach to axiomaticis accompanied by a certain pragmatism that is compatible with aphilosophical, or, so to say, external foundation of mathematics.Hilbert's foundational programme can thus be seen as areconciliation of Pragmatism and Apriorism. This interpretation iselaborated by discussing two recent positions in the philosophy ofmathematics which are or can be related to Hilbert's axiomaticalprogramme and his formalism. In a first step it is argued that thepragmatism of Hilbert's axiomatic (...)
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  7.  14
    Kreisel Georg. Hilbert's programme. Englisch, mit englischem und deutschem Résumé. Ebd., S. 142–168; auch ebd., S. 346–372. [REVIEW]G. Hasenjaeger - 1962 - Journal of Symbolic Logic 27 (2):228-229.
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  8.  7
    Review: Georg Kreisel, Hilbert's Programme[REVIEW]G. Hasenjaeger - 1962 - Journal of Symbolic Logic 27 (2):228-229.
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  9. Leibniz's and Kant's Philosophical Ideas and the Development of Hilbert's Programme.Roman Murawski - 2002 - Logique Et Analyse 45.
  10.  44
    Hilbert's 'Verunglückter Beweis', the first epsilon theorem, and consistency proofs.Richard Zach - 2004 - History and Philosophy of Logic 25 (2):79-94.
    In the 1920s, Ackermann and von Neumann, in pursuit of Hilbert's programme, were working on consistency proofs for arithmetical systems. One proposed method of giving such proofs is Hilbert's epsilon-substitution method. There was, however, a second approach which was not reflected in the publications of the Hilbert school in the 1920s, and which is a direct precursor of Hilbert's first epsilon theorem and a certain "general consistency result" due to Bernays. An analysis of the form of (...)
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  11.  25
    Quine, VV. vo, 34, 43.K. Hawley, H. Hertz, D. Hilbert, R. Holton, F. Jackson, Y. Kirsch, W. Kneale, M. Lange & S. McCall - 2012 - Oxford Studies in Metaphysics 7:315.
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  12. Hilbert’s Invariant Theory Papers Vol. Viii.David Hilbert, Michael Ackermann & Robert Hermann - 1978 - Math Science Press.
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  13. Color and Color Perception: A Study in Anthropocentric Realism.David R. Hilbert - 1987 - Csli Press.
    Colour has often been supposed to be a subjective property, a property to be analysed orretly in terms of the phenomenological aspects of human expereince. In contrast with subjectivism, an objectivist analysis of color takes color to be a property objects possess in themselves, independently of the character of human perceptual expereince. David Hilbert defends a form of objectivism that identifies color with a physical property of surfaces - their spectral reflectance. This analysis of color is shown to provide a (...)
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  14.  21
    The Foundations of Geometry.David Hilbert - 1899 - Open Court Company (This Edition Published 1921).
    §30. Significance of Desargues's theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 CHAPTER VI. PASCAL'S THEOREM. §31. ...
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  15. Hardin, Tye, and Color Physicalism.David R. Hilbert - 2004 - Journal of Philosophy 101 (1):37-43.
    Larry Hardin has been the most steadfast and influential critic of physicalist theories of color over the last 20 years. In their modern form these theories originated with the work of Smart and Armstrong in the 1960s and 1970s1 and Hardin appropriately concentrated on their views in his initial critique of physicalism.2 In his most recent contribution to this project3 he attacks Michael Tye’s recent attempts to defend and extend color physicalism.4 Like Byrne and Hilbert5, Tye identifies color with the (...)
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  16.  14
    A simplification of takeuti's ordinal diagrams of finite order.Hilbert Levitz - 1969 - Mathematical Logic Quarterly 15 (7‐12):141-154.
  17.  27
    A simplification of takeuti's ordinal diagrams of finite order.Hilbert Levitz - 1969 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 15 (7-12):141-154.
  18.  10
    A Natural Variant of Ackermann's Function.Hilbert Levitz & Warren Nichols - 1988 - Mathematical Logic Quarterly 34 (5):399-401.
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  19.  32
    A Natural Variant of Ackermann's Function.Hilbert Levitz & Warren Nichols - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (5):399-401.
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  20.  13
    Harvey Gerber. An extension of Schütte´s Klammer-symbols. Mathematische Annalen, vol. 174 (1967), pp. 203–216.Hilbert Levitz - 1970 - Journal of Symbolic Logic 34 (4):655-655.
  21. How do things look to the color-blind?David R. Hilbert & Alex Byrne - 2010 - In Jonathan Cohen & Mohan Matthen (eds.), Color Ontology and Color Science. MIT Press. pp. 259.
    Color-vision defects constitute a spectrum of disorders with varying degrees and types of departure from normal human color vision. One form of color-vision defect is dichromacy; by mixing together only two lights, the dichromat can match any light, unlike normal trichromatic humans, who need to mix three. In a philosophical context, our titular question may be taken in two ways. First, it can be taken at face value as a question about visible properties of external objects, and second, it may (...)
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  22.  26
    Garfinkel's recovery of themes in classical sociology.Richard A. Hilbert - 1995 - Human Studies 18 (2-3):157 - 175.
    In order to derive functionalism from Durkheim and Weber, Parsons had to openly break with some twenty of their theoretical assertions. Express rejections of classical themes lie at the foundation of functionalist sociology. This very foundation is what came unglued by Garfinkel's empirical studies of Parsonian social dynamics. In correcting the inadequacies of functionalism, many of the themes rejected by Parsons have been inadvertently resurrected and developed by ethnomethodologists, albeit in altered form. This is not to say that Garfinkel and (...)
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  23.  33
    “Other minds than ours”: a controversial discussion on the limits and possibilities of comparative psychology in the light of C. Lloyd Morgan’s work.Martin Böhnert & Christopher Hilbert - 2018 - History and Philosophy of the Life Sciences 40 (3):44.
    C. Lloyd Morgan is mostly known for Morgan’s canon, still a popular and frequently quoted principle in comparative psychology and ethology. There has been a fair amount of debate on the canon’s interpretation, function, and value regarding the research on animal minds, usually referring to it as an isolated principle. In this paper we rather shed light on Morgan’s overall scientific program and his vision for comparative psychology. We argue that within his program Morgan identified crucial conceptual, ontological, and methodical (...)
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  24.  20
    Herschel's Investigation of the Nature of Radiant Heat: The Limitations of Experiment.Martin Hilbert - 1999 - Annals of Science 56 (4):357-378.
    Herschel's experiments on radiant heat are analysed to see how he understood the role of experiment and how he handled potential difficulties in measurement. He believed that experiments could answer essential questions about nature and was willing to change his mind in light of evidence. Potential problems with data did not shake his confidence in the results of his experiments. Herschel's critic, Leslie, had even less patience with experimental results that did not fit his theory. His harsh condemnations of Herschel's (...)
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  25. Hallucination, sense-data and direct realism.David Hilbert - 2004 - Philosophical Studies 120 (1-3):185-191.
    Although it has been something of a fetish for philosophers to distinguish between hallucination and illusion, the enduring problems for philosophy of perception that both phenomena present are not essentially different. Hallucination, in its pure philosophical form, is just another example of the philosopher’s penchant for considering extreme and extremely idealized cases in order to understand the ordinary. The problem that has driven much philosophical thinking about perception is the problem of how to reconcile our evident direct perceptual contact with (...)
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  26. Are colors secondary qualities?Alex Byrne & David Hilbert - 2011 - In Lawrence Nolan (ed.), Primary and secondary qualities: the historical and ongoing debate. Oxford, United Kingdom: Oxford University Press.
    The Dangerous Book for Boys Abstract: Seventeenth and eighteenth century discussions of the senses are often thought to contain a profound truth: some perceptible properties are secondary qualities, dispositions to produce certain sorts of experiences in perceivers. In particular, colors are secondary qualities: for example, an object is green iff it is disposed to look green to standard perceivers in standard conditions. After rebutting Boghossian and Velleman’s argument that a certain kind of secondary quality theory is viciously circular, we discuss (...)
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  27.  30
    Norman and Sigmund: Comment on Denzin's "Harold and Agnes".Richard A. Hilbert - 1991 - Sociological Theory 9 (2):264-268.
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  28. Bureaucracy as belief, rationalization as repair: Max Weber in a post-functionalist age.Richard A. Hilbert - 1987 - Sociological Theory 5 (1):70-86.
    Weber's discussion of bureaucracy is generally taken as descriptive of organized social structure within a rational-legal society. This is understandable; yet elsewhere in Weber's sociology he cautions against precisely this kind of analysis. His counsel against reification, his emphasis upon subjective ideas standing behind social action, his characterization of "society" as subjective orientation to legitimacy, his discussion of organization and social relationships as probabilities of behavior in accordance with subjective belief in their existence, and his tendency to describe the wide (...)
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  29. Color relationalism and relativism.Alex Byrne & David R. Hilbert - 2017 - Topics in Cognitive Science 9 (1):172-192.
    This paper critically examines color relationalism and color relativism, two theories of color that are allegedly supported by variation in normal human color vision. We mostly discuss color relationalism, defended at length in Jonathan Cohen's The Red and the Real, and argue that the theory has insuperable problems.
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  30. Three Dialogues Between Hylas and Philonous.David Hilbert & John Perry (eds.) - 2013 - Center for the Study of Language and Inf.
    Deeply original, inspiring to some, abhorrent to others, George Berkeley’s philosophy of immaterialism is still influential three hundred years after the publication of his most widely read book, _Three Dialogues Between Hylas and Philonous. _Berkeley published the _Dialogues _because of the unenthusiastic reception of his _Principles of Human Knowledge _in 1710._ _He hoped the use of the_ _dialogue format would win a more favorable hearing, but unfortunately for Berkeley, the response was every bit as scathing as the reception of his (...)
     
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  31. Drink on, the jolly prelate cries.David R. Hilbert - 2007 - In Steven Hales (ed.), Philosophy and Beer. Routledge.
    The 18th century philosopher and Anglican bishop, George Berkeley, is chiefly known to posterity for advocating the radical thesis that there is no unthinking stuff in the world. According to Berkeley, bar stools, kegs, mugs and the all paraphernalia of ordinary life (plus everything else) are merely ideas and have no existence outside the mind of those seated on the stools, tapping the kegs, and drinking from the mugs. What is less well-known is that Berkeley devoted much of his energy (...)
     
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  32. Spraying color.David R. Hilbert - 2009 - In Katharina Grosse: Atoms Inside Balloons. Chicago, USA: The Renaissance Society at the University of Chicago. pp. 240-251.
    What is color? Of course, examples of colorful objects are not hard to come by (Fig. 1 provides numerous examples), so the question itself is slightly puzzling, suggesting that some confusion needs to be cleared up or ignorance enlightened. But how could anyone (who isn’t blind or Fig. 1 Atoms Inside Balloons totally lacking in color vision) possibly be confused about what color is? After all, if we learn anything about the world merely by looking at it, it’s the colors (...)
     
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  33.  54
    Comments on anthropomorphism.David Hilbert - 1993 - Philosophical Studies 69 (2-3):123-127.
  34.  11
    Review: Harvey Gerber, An Extension of Schutte's Klammer-Symbols. [REVIEW]Hilbert Levitz - 1969 - Journal of Symbolic Logic 34 (4):655-655.
  35. Hoffman’s “proof” of the possibility of spectrum inversion.Alex Byrne & David Hilbert - 2006 - Consciousness and Cognition 15 (1):48-50.
    Philosophers have devoted a great deal of discussion to the question of whether an inverted spectrum thought experiment refutes functionalism. (For a review of the inverted spectrum and its many philosophical applications, see Byrne, 2004.) If Ho?man is correct the matter can be swiftly and conclusively settled, without appeal to any empirical data about color vision (or anything else). Assuming only that color experiences and functional relations can be mathematically represented, a simple mathematical result.
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  36.  81
    Hilbert and the internal logic of mathematics.Yvon Gauthier - 1994 - Synthese 101 (1):1 - 14.
    Hilbert's programme is shown to have been inspired in part by what we can call Kronecker's programme in the foundations of an arithmetic theory of algebraic quantities.While finitism stays within the bounds of intuitive finite arithmetic, metamathematics goes beyond in the hope of recovering classical logic. The leap into the transfinite proved to be hazardous, not only from the perspective of Gödel's results, but also from a Kroneckerian point of view.
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  37.  17
    Structures algébriques dynamiques, espaces topologiques sans points et programme de Hilbert.Henri Lombardi - 2006 - Annals of Pure and Applied Logic 137 (1-3):256-290.
    A possible relevant meaning of Hilbert’s program is the following one: “give a constructive semantic for classical mathematics”. More precisely, give a systematic interpretation of classical abstract proofs about abstract objects, as constructive proofs about constructive versions of these objects.If this program is fulfilled we are able “at the end of the tale” to extract constructive proofs of concrete results from classical abstract proofs of these results.Dynamical algebraic structures or geometric theories seem to be a good tool for doing this (...)
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  38. Did Einstein's programme supersede lorentz's?S. J. Prokhovnik - 1974 - British Journal for the Philosophy of Science 25 (4):336-340.
  39.  7
    Extending and interpreting Post’s programme.S. Cooper - 2010 - Annals of Pure and Applied Logic 161 (6):775-788.
    Computability theory concerns information with a causal–typically algorithmic–structure. As such, it provides a schematic analysis of many naturally occurring situations. Emil Post was the first to focus on the close relationship between information, coded as real numbers, and its algorithmic infrastructure. Having characterised the close connection between the quantifier type of a real and the Turing jump operation, he looked for more subtle ways in which information entails a particular causal context. Specifically, he wanted to find simple relations on reals (...)
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  40.  15
    Extending and interpreting Post’s programme.S. Barry Cooper - 2010 - Annals of Pure and Applied Logic 161 (6):775-788.
    Computability theory concerns information with a causal–typically algorithmic–structure. As such, it provides a schematic analysis of many naturally occurring situations. Emil Post was the first to focus on the close relationship between information, coded as real numbers, and its algorithmic infrastructure. Having characterised the close connection between the quantifier type of a real and the Turing jump operation, he looked for more subtle ways in which information entails a particular causal context. Specifically, he wanted to find simple relations on reals (...)
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  41.  19
    Human speech: A tinkerer's delight.Harvey M. Sussman, David Fruchter, Jon Hilbert & Joseph Sirosh - 1998 - Behavioral and Brain Sciences 21 (2):287-295.
    The most frequent criticism of the target article is the lack of clear separability of human speech data relative to neuroethological data. A rationalization for this difference was sought in the tinkered nature of such new adaptations as human speech. Basic theoretical premises were defended, and new data were presented to support a claim that speakers maintain a low-noise relationship between F2 transition onset and offset frequencies for stops in pre-vocalic positions through articulatory choices. It remains a viable and testable (...)
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  42.  12
    Pro and Contra Hilbert: Zermelo’s Set Theories.Volker Peckhaus - 2005 - Philosophia Scientiae:199-215.
    Les recherches de Zermelo sur la théorie des ensembles et les fon­dements des mathématiques se divisent en deux périodes : de 1901 à 1910 et de 1927 à 1935. Elles s’effectuent en même temps que les deux projets de recherche sur les fondements des mathématiques de David Hilbert et de ses collaborateurs à Göttingen ; durant la première période, Hilbert élaborait son premier programme d’axiomatisation, auquel Zermelo souscrivait totalement. La seconde période correspond au développement du programme formaliste de (...)
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  43.  15
    Tversky and Kahneman’s Cognitive Illusions: Who Can Solve Them, and Why?Georg Bruckmaier, Stefan Krauss, Karin Binder, Sven Hilbert & Martin Brunner - 2021 - Frontiers in Psychology 12:584689.
    In the present paper we empirically investigate the psychometric properties of some of the most famous statistical and logical cognitive illusions from the “heuristics and biases” research program by Daniel Kahneman and Amos Tversky, who nearly 50 years ago introduced fascinating brain teasers such as the famous Linda problem, the Wason card selection task, and so-called Bayesian reasoning problems (e.g., the mammography task). In the meantime, a great number of articles has been published that empirically examine single cognitive illusions, theoretically (...)
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  44.  57
    Hilberts Logik. Von der Axiomatik zur Beweistheorie.Volker Peckhaus - 1995 - NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin 3 (1):65-86.
    This paper gives a survey of David Hilbert's (1862–1943) changing attitudes towards logic. The logical theory of the Göttingen mathematician is presented as intimately linked to his studies on the foundation of mathematics. Hilbert developed his logical theory in three stages: (1) in his early axiomatic programme until 1903 Hilbert proposed to use the traditional theory of logical inferences to prove the consistency of his set of axioms for arithmetic. (2) After the publication of the logical and set-theoretical (...)
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  45.  5
    Pro and Contra Hilbert: Zermelo’s Set Theories.Volker Peckhaus - 2005 - Philosophia Scientiae:199-215.
    Les recherches de Zermelo sur la théorie des ensembles et les fon­dements des mathématiques se divisent en deux périodes : de 1901 à 1910 et de 1927 à 1935. Elles s’effectuent en même temps que les deux projets de recherche sur les fondements des mathématiques de David Hilbert et de ses collaborateurs à Göttingen ; durant la première période, Hilbert élaborait son premier programme d’axiomatisation, auquel Zermelo souscrivait totalement. La seconde période correspond au développement du programme formaliste de (...)
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  46.  7
    Psychometric Properties of the German Version of the Self-Regulation of Eating Behavior Questionnaire.Ileana Schmalbach, Bjarne Schmalbach, Markus Zenger, Katja Petrowski, Manfred Beutel, Anja Hilbert & Elmar Brähler - 2021 - Frontiers in Psychology 12.
    Background: The Self-Regulation of Eating Behavior Questionnaire is an economical way of assessing an individual's self-regulatory abilities regarding eating behavior. Such scales are needed in the German population; therefore, the purpose of the present study was the translation and validation of a German version of the SREBQ.Method: First, we conducted a pilot study after the translation procedure. Second, we assessed the final scale in a representative sample of the German population and its underlying factor structure. Further, we tested for measurement (...)
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  47.  26
    Improving reading comprehension strategies through listening.C. Aarnoutse, S. Brand-Gruwel & R. Oduber - 1997 - Educational Studies 23 (2):209-227.
    The goal of this study was to determine whether it is possible to teach children with serious decoding problems four text comprehension strategies in listening contexts. The subjects were 9-11 year old students from special schools for children with learning disabilities. All the students were very poor at decoding; half of the group were also poor listeners, whereas the other half consisted of normal listeners. The experimental children were trained in strategies of clarifying, questioning, summarising and predicting through a combination (...)
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  48. The Spandrels of San Marco and the Panglossian Paradigm: A Critique of the Adaptationist Programme.S. J. Gould & R. C. Lewontin - 1979 - In E. Sober (ed.), Conceptual Issues in Evolutionary Biology. The Mit Press. Bradford Books. pp. 73-90.
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  49. The spandrels of San Marco and the Panglossian paradigm : a critique of the adaptationist programme.S. J. Gould & R. C. Lewontin - 2014 - In Francisco José Ayala & John C. Avise (eds.), Essential readings in evolutionary biology. Baltimore: The Johns Hopkins University Press.
     
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  50. Of Worms and programmes: Caenorhabditis elegans and the study of development.S. Chadarevian - 1998 - Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 29 (1):81-105.
     
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