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The Mystery of Deduction and Diagrammatic Aspects of Representation

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Abstract

Deduction is decisive but nonetheless mysterious, as I argue in the introduction. I identify the mystery of deduction as surprise-effect and demonstration-difficulty. The first section delves into how the mystery of deduction is connected with the representation of information and lays the groundwork for our further discussions of various kinds of representation. The second and third sections, respectively, present a case study for the comparison between symbolic and diagrammatic representation systems in terms of how two aspects of the mystery of deduction – surprise-effect and demonstration-difficulty – are handled. The fourth section illustrates several well-known examples to show how diagrammatic representation suggests more clues to the mystery of deduction than symbolic representation and suggests some conjectures and further work.

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Notes

  1. I thank an anonymous reviewer for the recommendation to emphasize the role of users.

  2. Shin (2002), Section 4.1–4.3.

  3. Here is C4 [Convention 4]: The scroll is the sign of a conditional proposition de inesse (that is, of material implication). (Peirce, Ms 450, p. 14, cited by (Roberts 1973), pp. 33–35.)

  4. A construction history of a given sentence is unique, and in the case of (1) the first negation comes at the end of the construction process. For more technical discussions about unique readability see (Enderton 2001 [1972]), Section 1.4.

  5. For the algorithm of multiple readings, see Section 4.3, (Shin 2012).

  6. For a formal proof, see Section 4.2.2, Shin (2012).

  7. Roberts (1973), p. 39.

  8. (Polya 1973 [1971]), pp. 107–8.

  9. (Berkeley 1920 [1776]), Introduction Section 13

  10. For further discussions of this topic, refer to Shin (2012).

  11. (Anderson 2000), (Barwise 1993), (Barwise and Allwein 1996), (Barwise and Etchemendy 1989, 1991, 1995), (Barwise and Hammer 1994), (Chandrasekaran 1995), (Hammer 1995), (Harel 1988), http://www.cmis.brighton.ac.uk/research/vmg/, (Miller 2008), (Mumma 2006), (Shin 1994, 2002), and (Sowa 1984)

  12. (Boolos et al. 2002), p. 26. Symbol S 0 stands for a blank and S 1 for 1.

  13. Non-enumerability of functions can be proven using a diagonalization, and this is another well-known place where diagrammatic representation is more intuitive.

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  1. Department of Philosophy, Yale University, 344 College St, New Haven, CT, 06511-6629, USA

    Sun-Joo Shin

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Shin, SJ. The Mystery of Deduction and Diagrammatic Aspects of Representation. Rev.Phil.Psych. 6, 49–67 (2015). https://doi.org/10.1007/s13164-014-0212-5

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