Logica Universalis

, Volume 4, Issue 2, pp 241–254 | Cite as

Is Logic Necessary?

  • Gregory McColmEmail author


“Logic” entails both a toolkit for dealing with situations requiring precision, and a prescription for a type of public reasoning. A sufficiently extended society facing a stream of genuinely novel opportunities and challenges will benefit from an ability to generate and encourage the use of such reasoning systems to deal with these opportunities and challenges. The study of “logic” is the result of using the toolkit on itself, which would appear to be a necessary and not unnatural step for a society developing sufficient familiarity with the toolkit. Many societies have developed something like logic, and past and present use of logic-like toolkits in learning situations and transmission of skills suggests that many societies will develop something like logic.

Mathematics Subject Classification (2000)

Primary 00A30 Secondary: 01A80 03A10 


Anthropology of logic cultural frames folk logic linguistic frames objective reasoning origins of logic sequential learning task hierarchies 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bunt L.N.H., Jones P.S., Bedient J.D.: The Historical Roots of Elementary Mathematics. Dover, New York (1988)zbMATHGoogle Scholar
  2. 2.
    Burke J., Ornstein R.: The Axemaker’s Gift: A Double-Edged History of Human Culture. G. P. Putnam, New York (1995)Google Scholar
  3. 3.
    Butterworth B.: What Counts: How Every Brain is Hardwired for Math. Simon & Schuster, New York (1999)zbMATHGoogle Scholar
  4. 4.
    Chalmers S.: What is this thing called Science? 2nd edn. University of Queensland Press, Queensland (1976)Google Scholar
  5. 5.
    Davison P.: Catches of Breath, Breathing Room. Knopf, New York (2000)Google Scholar
  6. 6.
    Debaene S.: The Number Sense: How The Mind Creates Mathematics. Oxford University Press, Oxford (1997)Google Scholar
  7. 7.
    Devlin K.: The Math Gene: How Mathematical Thinking Evolved And Why Numbers Are Like Gossip. Basic, London (2001)Google Scholar
  8. 8.
    Fagan B.M.: People of the Earth. Little Brown, Boston (1986)Google Scholar
  9. 9.
    Filmore, C.: Frame semantics. In: Linguistics Society of Korea. Linguistics in the Morning Calm, pp. 111–138. Hanshin, Seoul (1982)Google Scholar
  10. 10.
    Fitts P.M.: Perceptual-motor skill learning. In: Melton, A.W. (eds) Categories of Human Learning, pp. 243–285. Academic Press, New York (1964)Google Scholar
  11. 11.
    Gallese V., Lakoff G.: The brain’s concepts: the role of the sensory-motor system in conceptual structure. Cogn. Neuropsychol. 22, 455–479 (2005)CrossRefGoogle Scholar
  12. 12.
    Goffman E.: Frame Analysis: An Essay on the Organization of Experience. Harper & Row, New York (1974)Google Scholar
  13. 13.
    Herodotus, The Persian Wars (Project Gutenberg)Google Scholar
  14. 14.
    Hilbert D.: On the Infinite, repr. In: Benacerraf, P., Putnam, H. (eds) Philosophy of Mathematics, pp. 183–201. Cambridge University Press, Cambridge (1983)Google Scholar
  15. 15.
    Hobbes, T.: Leviathan (Project Gutenberg)Google Scholar
  16. 16.
    Hume, D.: An Enquiry Concerning Human Understanding (Project Gutenberg)Google Scholar
  17. 17.
    Joseph G.G.: The Crest of the Peacock: Non-European Roots of Mathematics, new ed. Princeton University Press, Princeton (2000)Google Scholar
  18. 18.
    Katz V.J.: A History of Mathematics: An Introduction. HarperCollins, New York (1993)zbMATHGoogle Scholar
  19. 19.
    Lakoff G.: The Political Mind: A Cognitive Scientist’s Guide to Your Brain and its Politics. Penguin, London (2009)Google Scholar
  20. 20.
    Lakoff G., Nunez R.E.: Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being. Basic, London (2000)zbMATHGoogle Scholar
  21. 21.
    Leibniz G.: Of the Art of Combination, selection. In: Parkinson, G.H.R. (eds) Leibniz: Logical Papers, pp. 1–11. Clarendon Press, Oxford (1966)Google Scholar
  22. 22.
    McColm G.: A metaphor for mathematics education. Notices AMS 54(4), 499–502 (2007)zbMATHMathSciNetGoogle Scholar
  23. 23.
    Beam Piper, H.: Omnilingual (Project Gutenberg)Google Scholar
  24. 24.
    Plutarch: Life of Marcellus, Lives (Project Gutenberg)Google Scholar
  25. 25.
    Rosenbaum D.A., Carlson R.A., Gilmore R.O.: Acquisition of intellectual and perceptual-motor skills. Ann. Rev. Psychol. 52, 453–470 (2001)CrossRefGoogle Scholar
  26. 26.
    Sweller J.: Cognitive load during problem solving: effects on learning. Cogn. Sci. 12, 257–285 (1988)CrossRefGoogle Scholar
  27. 27.
    Waterhouse W.C.: The discovery of the regular solids. Arch. Hist. Exact Sci. 9(3), 212–221 (1972)zbMATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Wheeler W.M.: The ant colony as a superorganism. J. Morphol. 22(2), 307–325 (1911)CrossRefGoogle Scholar
  29. 29.
    Wilson E.O.: The Insect Societies. Belknap Press of Harvard University Press, Cambridge (1971)Google Scholar
  30. 30.
    Wittgenstein L.: Philosophical Investigations. Blackwell, New York (1953)Google Scholar

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of South FloridaTampaUSA

Personalised recommendations