Click here to download

FORMALIZING DARWINISM, NATURALIZING MATHEMATICS
Journal Title: PARADIGMI 
Author/s: Fabio Sterpetti 
Year:  2015 Issue: Language: Italian 
Pages:  28 Pg. 133-160 FullText PDF:  125 KB
DOI:  10.3280/PARA2015-002009
(DOI is like a bar code for intellectual property: to have more infomation:  clicca qui   and here 


In the last decades two different and apparently unrelated lines of research have increasingly connected mathematics and evolutionism. Indeed, on the one hand different attempts to formalize darwinism have been made, while, on the other hand, different attempts to naturalize logic and mathematics have been put forward. Those researches may appear either to be completely distinct or at least in some way convergent. They may in fact both be seen as supporting a naturalistic stance. Evolutionism is indeed crucial for a naturalistic perspective, and formalizing it seems to be a way to strengthen its scientificity. The paper shows that, on the contrary, those directions of research may be seen as conflicting, since the conception of knowledge on which they rest may be undermined by the consequences of accepting an evolutionary perspective.
Keywords: knowledge, mathematics, naturalism, scientific realism, truth

  1. Ao P. (2005). Laws in Darwinian Evolutionary Theory. Physics of Life Reviews, 2, 2: 117-156.
  2. Balaguer M. (2009). Realism and Anti-Realism in Mathematics. In: Gabbay D., Thagard P. and Woods J., eds., Philosophy of Mathematics. Amsterdam: Elsevier: 117-151.
  3. Barberousse A. and Samadi S. (2015). Formalising Evolutionary Theory. In: Heams T., Huneman P., Lecointre G. and Silberstein M., eds., Handbook of Evolutionary Thinking in the Sciences. Dordrecht: Springer: 229-246. Batty C.J.K., Crewe P., Grafen A. and Gratwick R. (2014). Foundations of a Mathematical Theory of Darwinism. Journal of Mathematical Biology, 69, 2: 295-334.
  4. Brown J.R. (2012). Platonism, Naturalism, and Mathematical Knowledge. New York: Routledge.
  5. Bunge M. (2012). The Correspondence Theory of Truth. Semiotica, 188: 65-75.
  6. Burgess A.G. and Burgess J.P. (2011). Truth. Princeton: Princeton University Press.
  7. Cellucci C. (2013a). Rethinking Logic. Logic in Relation to Mathematics, Evolution, and Method. Dordrecht: Springer.
  8. Cellucci C. (2013b). Top-Down and Bottom-Up Philosophy of Mathematics. Foundations of Science, 18, 1: 93-106.
  9. Cellucci C. (2014). Knowledge, Truth and Plausibility. Axiomathes, 24, 4: 517-532. Cellucci C. (forthcoming). Rethinking Knowledge. Metaphilosophy.
  10. Chaitin G. (2012). Proving Darwin. New York: Pantheon Books.
  11. De Cruz H. (2004). Why Humans Can Count Large Quantities Accurately. Philosophica, 74: 63-83.
  12. De Cruz H. (2006). Towards a Darwinian Approach to Mathematics. Foundations of Science, 11, 1-2: 157-196.
  13. De Cruz H. (2007). Innate Ideas as a Naturalistic Source of Mathematical Knowledge. PhD thesis. Brussel: Vrije Universiteit.
  14. De Cruz H. (2011). Through a Mind Darkly. PhD thesis. Groningen: University of Groningen.
  15. De Cruz H., Boudry M., De Smedt J. and Blancke S. (2011). Evolutionary Approaches to Epistemic Justification. Dialectica, 65, 4: 517-535.
  16. De Cruz H. and De Smedt J. (2012). Evolved Cognitive Biases and the Epistemic Status of Scientific Beliefs. Philosophical Studies, 157, 3: 411-429.
  17. Dehaene S., Duhamel J.-R., Hauser M.D. and Rizzolatti G., eds. (2005). From Monkey Brain to Human Brain. Cambridge (MA): MIT Press.
  18. Dipert R.R. (1977). Peirce’s Theory of the Geometrical Structure of Physical Space. Isis, 68, 3: 404-413.
  19. Dorato M. (2012). Mathematical Biology and the Existence of Biological Laws. In:
  20. Dieks D., González W.J., Hartmann S., Stöltzner M. and Weber M., eds., Probabilities, Laws, and Structures. Dordrecht: Springer: 109-121.
  21. Downes S.M. (2000). Truth, Selection and Scientific Inquiry. Biology and Philosophy, 15, 3: 425-442.
  22. Dutilh Novaes C. (2012). Formal Languages in Logic. A Philosophical and Cognitive Analysis. Cambridge: Cambridge University Press.
  23. Enoch D. and Schechter J. (2008). How Are Basic Belief-Forming Methods Justified? Philosophy and Phenomenological Research, 76, 3: 547-579.
  24. Gardner A. (2013). Ultimate Explanations Concern the Adaptive Rationale for Organism Design. Biology and Philosophy, 28, 5: 787-791.
  25. Giere R.N. (2006). Modest Evolutionary Naturalism. Biological Theory, 1, 1: 52-60.
  26. Grafen A. (2002). A First Formal Link between the Price Equation and an Optimization Program. Journal of Theoretical Biology, 217, 1: 75-91.
  27. Grafen A. (2007). The Formal Darwinism Project: a Mid-Term Report. Journal of Evolutionary Biology, 20, 4: 1243-1254. Grafen A. (2014). The Formal Darwinism Project in Outline. Biology and Philosophy, 29, 2: 155-174.
  28. Griesemer J. (2013). Formalization and the Meaning of “Theory” in the Inexact Biological Sciences. Biological Theory, 7, 4: 298-310.
  29. Halvorson H. (2012). What Scientific Theories Could Not Be. Philosophy of Science, 79, 2: 183-206.
  30. Jacquette D. (2012). Applied Mathematics in the Sciences. In: Trobok M., Miščević N. and Žarnić B., eds., Between Logic and Reality. Dordrecht: Springer: 29-57.
  31. Kitcher P. (1978). The Naturalists Return. The Philosophical Review, 101, 1: 53-114.
  32. Kornblith H. (2002). Knowledge and its Place in Nature. Oxford: Oxford University Press.
  33. Kragh H. (2012). Is Space Flat? Nineteenth Century Astronomy and Non-Euclidean Geometry. Journal of Astronomical History and Heritage, 15, 3: 149-158.
  34. Krebs N. (2011). Our Best Shot at Truth: Why Humans Evolved Mathematical Abilities. In: Frey U.J., Störmer C. and Willführ K.P., eds., Essential Building Blocks of Human Nature. Dordrecht: Springer: 123-141.
  35. Kyburg H. (1965). Comments on Salmon’s “Inductive Evidence”. American Philosophical Quarterly, 2, 4: 274-276.
  36. Lycan W.G. (2006). On the Gettier Problem Problem. In: Hetherington S., ed., Epistemology Futures. Oxford: Oxford University Press: 148-168.
  37. Millikan R. (1984). Naturalist Reflections on Knowledge. Pacific Philosophical Quarterly, 65, 4: 315-334.
  38. Nisbett R. and Ross L. (1980). Human Inference: Strategies and Shortcomings. Englewood Cliffs (NJ): Prentice-Hall.
  39. Nozick R. (1993). The Nature of Rationality. Princeton: Princeton University Press.
  40. Nozick R. (1995). Socratic Puzzles. Phronesis, 40, 2: 143-155.
  41. Nozick R. (2001). Invariances. Cambridge (MA): Harvard University Press.
  42. Núñez R. (2006). Numbers and Arithmetic: Neither Hardwired Nor Out There. Biological Theory, 4, 1: 68-83.
  43. Orzack S.H. and Forber P. (2012). Adaptationism. In: Zalta E.N., ed., The Stanford Encyclopedia of Philosophy. Winter 2012 Edition.
  44. Pelletier F.J., Elio R. and Hanson P. (2008). Is Logic All in Our Heads? From Naturalism to Psychologism. Studia Logica, 88, 1: 3-66.
  45. Peirce C.S. (CP) (1931-1958). Collected Papers of Charles Sanders Peirce. Voll. 1-6. Ed. by C. Hartshorne and P. Weiss; Voll. 7-8, ed. by A.W. Burks. Cambridge (MA): Harvard University Press.
  46. Plantinga A. (2006). How Naturalism Implies Skepticism. In: Corradini A., Galvan S. and Lowe E.J., eds., Analytic Philosophy Without Naturalism. New York: Routledge: 29-44.
  47. Plotkin H. (1997). Darwin Machines and the Nature of Knowledge. Cambridge (MA): Harvard University Press. Sage J. (2004). Truth-Reliability and the Evolution of Human Cognitive Faculties. Philosophical Studies, 117, 1-2: 95-106.
  48. Sankey H. (2008). Scientific Realism and the Rationality of Science. Burlington: Ashgate.
  49. Schechter J. (2010). The Reliability Challenge and the Epistemology of Logic. Philosophical Perspectives, 24, 1: 437-464.
  50. Schwartz J. (2008). The Pernicious Influence of Mathematics on Science. In: Kac M., Rota G.C. and Schwartz J., eds., Discrete Thoughts. Boston: Birkhäuser: 19-25.
  51. Stanford P.K. (2006). Exceeding Our Grasp. Oxford: Oxford University Press.
  52. Steiner M. (1998). The Applicability of Mathematics as a Philosophical Problem.
  53. Cambridge (MA): Harvard University Press.
  54. Stich S. (2011). Collected Papers. Volume 1. Oxford: Oxford University Press.
  55. Tegmark M. (2008). The Mathematical Universe. Foundations of Physics, 38, 2: 101-150.
  56. Tennant N. (2014). The Logical Structure of Evolutionary Explanation and Prediction: Darwinism’s Fundamental Schema. Biology and Philosophy, 29, 5: 611-655.
  57. Thompson P. (2007). Formalisations of Evolutionary Biology. In: Matthen M. and Stephens C., eds., Philosophy of Biology. Amsterdam: Elsevier: 485-523.
  58. Unger P. (1971). A Defense of Skepticism. The Philosophical Review, 80, 2, 198-219.
  59. Van Kerkhove B. (2006). Mathematical Naturalism: Origins, Guises, and Prospects. Foundations of Science, 11, 1-2: 5-39.
  60. Weir A. (2005). Naturalism Reconsidered. In: Shapiro S., ed., The Oxford Handbook of Philosophy of Mathematics and Logic. Oxford: Oxford University Press: 460-482.
  61. Wilkins J.S. and Griffiths P.E. (2013). Evolutionary Debunking Arguments in Three Domains: Fact, Value, and Religion. In: Maclaurin J. and Dawes G., eds., A New Science of Religion. New York: Routledge: 133-146.
  62. Williams M.B. (1973). The Logical Status of the Theory of Natural Selection and Other Evolutionary Controversies. In: Bunge M., ed., The Methodological Unity of Science. Dordrecht: D. Reidel Publishing Company: 84-102.
  63. Wray K.B. (2013). Success and Truth in the Realism/Anti-Realism Debate. Synthese, 190, 9: 1719-1729.

Fabio Sterpetti, in "PARADIGMI" 2/2015, pp. 133-160, DOI:10.3280/PARA2015-002009

   

FrancoAngeli is a member of Publishers International Linking Association a not for profit orgasnization wich runs the CrossRef service, enabing links to and from online scholarly content