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Concluding Remarks

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Meaning and Proscription in Formal Logic

Part of the book series: Trends in Logic ((TREN,volume 49))

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Abstract

This concluding chapter reflects on the import of the work as a whole. The concrete fruits of the work are surveyed alongside its limitations, leaving the reader with a list of important open problems remaining along with suggestions for how these problems might be addressed.

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Notes

  1. 1.

    This description of the prohibition does not necessarily presuppose cases in which, e.g., all elements of some domain are assigned names (or constants). Even if the name ‘Flash Gordon’ is not, e.g., expressible within the bounds of a Sherlock Holmes story, Daniels’ position equally suggests that the proposition that Flash Gordon was an accomplice is not part of the proposition expressed by the sentence ‘Everyone was an accomplice.’

References

  1. Ackermann, W.: Begründung einer strenger implikation. J. Symb. Log. 21(2), 113–128 (1956)

    Article  Google Scholar 

  2. Ackermann, W.: Über die Beziehung zwischen strikter und strenger implikation. Dialectica 12(3–4), 213–222 (1958)

    Article  Google Scholar 

  3. Anderson, A.R., Belnap Jr., N.D.: Enthymemes. J. Philos. 58(23), 713–723 (1961)

    Article  Google Scholar 

  4. Bloom, S.L., Suszko, R.: Semantics for the sentential calculus with identity. Stud. Log. 28, 77–81 (1971)

    Article  Google Scholar 

  5. Bloom, S.L., Suszko, R.: Investigations into the sentential calculus with identity. Notre Dame J. Form. Log. 13(3), 289–308 (1972)

    Article  Google Scholar 

  6. Ciuni, R.: Conjunction in paraconsistent weak Kleene logic. In: Arazim, P., Dank, M. (eds.) The Logica Yearbook 2014, pp. 61–76. College Publications, London (2015)

    Google Scholar 

  7. Ciuni, R., Carrara, M.: Characterizing logical consequence in paraconsistent weak Kleene logic. In: Felline, L., Paoli, F., Rossanese, E. (eds.) New Developments in Logic and the Philosophy of Science. College Publications, London (2016)

    Google Scholar 

  8. Cresswell, M.J.: S1 is not so simple. In: Modality, Morality, and Belief: Essays in Honor of Ruth Barcan Marcus, pp. 29–40. Cambridge University Press, New York (1995)

    Google Scholar 

  9. Daniels, C.: A story semantics for implication. Notre Dame J. Form. Log. 27(2), 221–246 (1986)

    Article  Google Scholar 

  10. Dos̆en, K.: A note on the law of identity and the converse Parry property. Notre Dame J. Form. Log. 19(1), 174–176 (1978)

    Google Scholar 

  11. Dunn, J.M.: A modification of Parry’s analytic implication. Notre Dame J. Form. Log. 13(2), 195–205 (1972)

    Article  Google Scholar 

  12. Epstein, R.L.: The algebra of dependence logic. Rep. Math. Log. 21, 19–34 (1987)

    Google Scholar 

  13. Epstein, R.L.: The Semantic Foundations of Logic: Propositional Logics, 2nd edn. Oxford University Press, New York (1995)

    Google Scholar 

  14. Fine, K.: Analytic implication. Notre Dame J. Form. Log. 27(2), 169–179 (1986)

    Article  Google Scholar 

  15. Fitting, M.: Bilattices are nice things. In: Bolander, T., Hendricks, V., Pedersen, S.A. (eds.) Self-reference, pp. 53–77. CSLI Publications, Stanford (2006)

    Google Scholar 

  16. Gödel, K.: Eine Interpretation des intuitionistischen Aussagenkalküls. In: Ergebnisse eines mathematischen Kolloquiums 4, 39–40 (1933)

    Google Scholar 

  17. Halldén, S.: A question concerning a logical calculus related to Lewis’ system of strict implication, which is of special interest for the study of entailment. Theoria 14(3), 265–269 (1948)

    Article  Google Scholar 

  18. Hume, D.: A Treatise on Human Nature. Oxford University Press, New York (1888)

    Google Scholar 

  19. Jaśkowski, S.: Rachunek zdań dla systemów dedukcyjnych sprzecznych. Stud. Soc. Sci. Torun. Sect. A, I (5), 57–77 (1948)

    Google Scholar 

  20. Loptson, P.: Logic and contingent existence. Hist. Philos. Log. 1(1–2), 171–185 (1980)

    Article  Google Scholar 

  21. Loptson, P.: \(\sf Q\), entailment, and the Parry property. Log. Anal. 23(90–91), 305–317 (1980)

    Google Scholar 

  22. McKinsey, J.C.C., Tarski, A.: Some theorems about the sentential calculi of Lewis and Heyting. J. Symb. Log. 13(1), 1–15 (1948)

    Article  Google Scholar 

  23. Nelson, D.: Constructible falsity. J. Symb. Log. 14(1), 16–26 (1949)

    Article  Google Scholar 

  24. Nowak, M.: Two logics of analytic classical implication. Log. Trianguli 6, 25–40 (2002)

    Google Scholar 

  25. Parry, W.T.: Ein Axiomensystem für eine neue Art von Implikation (analytische Implikation). Ergebnisse eines mathematischen Kolloquiums 4, 5–6 (1933)

    Google Scholar 

  26. Parry, W.T.: Comparison of entailment theories. J. Symb. Log. 37(2), 441–442 (1972)

    Google Scholar 

  27. Parry, W.T.: Comparison of entailment theories. Relevance Log. Newslett. 1(1), 16–26 (1976)

    Google Scholar 

  28. Parry, W.T.: Analytic implication: its history, justification, and varieties. In: Norman, J., Sylvan, R. (eds.) Directions in Relevant Logic, Reason and Argument, pp. 101–118. Kluwer Academic Publishers, Boston (1989)

    Chapter  Google Scholar 

  29. Routley, R., Meyer, R.K.: Every sentential logic has a two-valued worlds semantics. Log. Anal. 19(74–76), 345–365 (1976)

    Google Scholar 

  30. Szmuc, D.: Track-down operations on bilattices (2016). Manuscript

    Google Scholar 

  31. Urquhart, A.: A semantical theory of analytic implication. J. Philos. Log. 2(2), 212–219 (1973)

    Article  Google Scholar 

  32. Walton, D.N.: Conditionals in act-sequences. In: R.L. Epstein (ed.) Relatedness and Dependence in Propositional Logics. Iowa State University Logic Group, USA (1980)

    Google Scholar 

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Correspondence to Thomas Macaulay Ferguson .

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Ferguson, T.M. (2017). Concluding Remarks. In: Meaning and Proscription in Formal Logic. Trends in Logic, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-319-70821-8_8

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