Logic and dialectic

Since the 1980s, European and American logicians have attempted to provide mathematical foundations for logic and dialectic through formalisation,[1]:201–372 although logic has been related to dialectic since ancient times.[1]:51–140

For the meaning in Hegelian and Marxist thought, see Dialectical logic.

History

There have been pre-formal and partially-formal treatises on argument and dialectic, from authors such as Stephen Toulmin (The Uses of Argument),[2][3][1]:203–256 Nicholas Rescher (Dialectics),[4][5][1]:330–336 and van Eemeren and Grootendorst (pragma-dialectics).[1]:517–614 One can include works of the communities of informal logic and paraconsistent logic.[1]:373–424

Defeasibility

However, building on theories of defeasible reasoning (see John L. Pollock), systems have been built that define well-formedness of arguments, rules governing the process of introducing arguments based on fixed assumptions, and rules for shifting burden. Many of these logics appear in the special area of artificial intelligence and law, though the computer scientists' interest in formalizing dialectic originates in a desire to build decision support and computer-supported collaborative work systems.[6]

Dialog games
Main article: Game semantics

Dialectic itself can be formalised as moves in a game, where an advocate for the truth of a proposition and an opponent argue. Such games can provide a semantics of logic, one that is very general in applicability.

gollark: It's a GTech™ infinite computer, see.
gollark: What? No.
gollark: ... great?
gollark: Anyway, you could try the manual's search function.
gollark: Reflection is self-inverting, isn't it?

See also

References
  1. Eemeren, Frans H. van; Garssen, Bart; Krabbe, Erik C. W.; Snoeck Henkemans, A. Francisca; Verheij, Bart; Wagemans, Jean H. M. (2014). Handbook of argumentation theory. New York: Springer-Verlag. doi:10.1007/978-90-481-9473-5. ISBN 9789048194728. OCLC 871004444.
  2. Toulmin, Stephen (2003) [1958]. The uses of argument (Updated ed.). Cambridge, UK; New York: Cambridge University Press. doi:10.1017/CBO9780511840005. ISBN 978-0521827485. OCLC 51607421.
  3. Hitchcock, David; Verheij, Bart, eds. (2006). Arguing on the Toulmin model: new essays in argument analysis and evaluation. Argumentation library. 10. Dordrecht: Springer-Verlag. doi:10.1007/978-1-4020-4938-5. ISBN 978-1402049378. OCLC 82229075.
  4. Hetherington, Stephen (2006). "Nicholas Rescher: Philosophical Dialectics". Notre Dame Philosophical Reviews (2006.07.16).
  5. Jacquette, Dale, ed. (2009). Reason, Method, and Value: A Reader on the Philosophy of Nicholas Rescher. Frankfurt: Ontos Verlag. doi:10.1515/9783110329056. ISBN 9783110329056.
  6. For surveys of work in this area see, for example: Chesñevar, Carlos Iván; Maguitman, Ana Gabriela; Loui, Ronald Prescott (December 2000). "Logical models of argument". ACM Computing Surveys. 32 (4): 337–383. CiteSeerX 10.1.1.702.8325. doi:10.1145/371578.371581. And: Prakken, Henry; Vreeswijk, Gerard (2005). "Logics for defeasible argumentation". In Gabbay, Dov M.; Guenthner, Franz (eds.). Handbook of philosophical logic. 4 (2nd ed.). Dordrecht; Boston: Kluwer Academic Publishers. pp. 219–318. CiteSeerX 10.1.1.295.2649. doi:10.1007/978-94-017-0456-4_3. ISBN 9789048158775.


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