Abstract
This article uses tagmemic theory as a semiotic framework to analyze symbolic logic. It attends particularly to the issue of context for meaning and the role of personal observer/participants. It focuses on formal languages, which employ no ordinary words and from one point of view have “no meaning.” Attention to the context and the theorists who deploy these languages shows that formal languages have meanings at a higher level, colored by the purposes of the analysts. In fact, there is an indefinitely ascending hierarchy of theories of theories, each of which analyzes and evaluates the theories at a lower level. By analogy with Kurt Gödel’s incompleteness theory, no level of the hierarchy can capture within formalism everything in a sufficiently complex system. The personal analysts always have to make judgments about how a formalized system is analogous to the world outside the system. Arguments in analytic philosophy can be useful in clarification, but neither clarification of terms nor clarification of the structure of arguments can eliminate the need for personal judgment.
References
Aristotle. 1938. Categories; On interpretation; Prior analytics. Cambridge: Harvard University Press.Search in Google Scholar
Bochenski, Jósef M. 1961. A history of formal logic. Notre Dame, IN: Notre Dame University Press.Search in Google Scholar
Copi, Irving M. 1979. Symbolic logic, 5th edn. New York: Macmillan.Search in Google Scholar
Coquand, Thierry. 2018. Type theory. In Edward N. Zalta (ed.), The Stanford encyclopedia of philosophy. https://plato.stanford.edu/archives/fall2018/entries/type-theory (accessed 11 February 2020).Search in Google Scholar
Gabbay, Dov & John Woods (eds.). 2004. Handbook of the history of logic. Amsterdam: Elsevier.10.1007/978-94-017-0466-3Search in Google Scholar
Gödel, Kurt. 1931. Über formal unentscheidbare Sätze der Principia mathematica und verwandter Systeme, I [On formally undecidable propositions of Principia mathematica and related systems]. Monatshefte für Mathematik und Physik 38. 173–198. https://doi.org/10.1007/bf01700692.Search in Google Scholar
Gödel, Kurt. 1995 [1970]. Ontological proof. In Feferman Solomon, John W. DawsonJr., Warren Goldfarb, Charles Parsons & Robert M. Solovay (eds.), Collected works: Volume III: Unpublished essays and lectures, 403–404. New York & Oxford: Oxford University Press.Search in Google Scholar
Gödel, Kurt. 1992. On formally undecidable propositions of Principia mathematica and related systems, B. Meltzer (trans.). New York: Dover.Search in Google Scholar
Haaparanta, Leila (ed.). 2009. The development of modern logic. Oxford: Oxford University Press.10.1093/acprof:oso/9780195137316.001.0001Search in Google Scholar
Kamareddine, Fairouz D., Twan Laan & Rob P. Nederpelt. 2004. A modern perspective on type theory: From its origins until today. New York: Springer.Search in Google Scholar
Mancosu, Paolo. 1998. From Brouwer to Hilbert: The debate on the foundations of mathematics in the 1920s. Oxford: Oxford University Press.Search in Google Scholar
Nagel, Ernest & James R. Newman. 2008. Gödel’s proof. New York: New York University Press.Search in Google Scholar
Pike, Kenneth L. 1967. Language in relation to a unified theory of the structure of human behavior, 2nd edn. The Hague & Paris: Mouton.10.1515/9783111657158Search in Google Scholar
Pike, Kenneth L. 1972 [1959]. Language as particle, wave, and field. In Ruth M. Brend (ed.), Kenneth L. Pike: Selected writings to commemorate the 60th birthday of Kenneth L. Pike, 129–143. The Hague & Paris: Mouton.10.1515/9783110812213-010Search in Google Scholar
Pike, Kenneth L. 1982. Linguistic concepts: An introduction to tagmemics. Lincoln, NB & London: University of Nebraska Press.Search in Google Scholar
Polanyi, Michael. 1958. Personal knowledge: Towards a post-critical philosophy. Chicago: University of Chicago Press.Search in Google Scholar
Polanyi, Michael. 1964. Science, faith, and society. Chicago: University of Chicago Press.10.7208/chicago/9780226163444.001.0001Search in Google Scholar
Polanyi, Michael. 1967. The tacit dimension. Garden City, NY: Anchor.Search in Google Scholar
Polanyi, Michael. 1975. Meaning. Chicago: University of Chicago Press.Search in Google Scholar
Poythress, Vern S. 1976. Tagmemic analysis of elementary algebra. Semiotica 17(2). 131–151. https://doi.org/10.1515/semi.1976.17.2.131.Search in Google Scholar
Poythress, Vern S. 1982. A framework for discourse analysis: The components of a discourse, from a tagmemic viewpoint. Semiotica 38(3/4). 277–298. https://doi.org/10.1515/semi.1982.38.3-4.277.Search in Google Scholar
Poythress, Vern S. 2013a. An information-based semiotic analysis of theories concerning theories. Semiotica 193(1/4). 83–99. https://doi.org/10.1515/sem-2013-0005.Search in Google Scholar
Poythress, Vern S. 2013b. Logic: A God-centered approach to the foundation of western thought. Wheaton, IL: Crossway.Search in Google Scholar
Poythress, Vern S. 2015. Semiotic analysis of the observer in relativity, quantum mechanics, and a possible theory of everything. Semiotica 205(1/4). 149–167. https://doi.org/10.1515/sem-2015-0006.Search in Google Scholar
Poythress, Vern S. 2018. A simple traffic-light semiotic model for tagmemic theory. Semiotica 225(1/4). 253–267. https://doi.org/10.1515/sem-2017-0025.Search in Google Scholar
Reid, Constance. 1996. Hilbert. New York: Springer.10.1007/978-1-4612-0739-9Search in Google Scholar
Saussure, Ferdinand de. 1916. Cours de linguistique générale. Lausanne & Paris: Librairie Payot.Search in Google Scholar
Saussure, Ferdinand de. 1998. Course in general linguistics. Lasalle, IL: Open Court.Search in Google Scholar
Whitehead, Alfred N. & Bertrand Russell. 1910–1913. Principia mathematica, 3 vols. Cambridge: Cambridge University Press.Search in Google Scholar
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