Abstract
The relation between indicative conditionals in natural language and material implication wasn’t a major topic in the Lvov-Warsaw school. However, a major defense of the claim that the truth conditions of these two are the same has been developed by Ajdukiewicz (Studia Logica IV:117–134, 1956). The first major goal of this paper is to present, assess, and improve his strategy. It turns out that it is quite similar to the approach developed by Grice (Studies in the Way of Words, Harvard University Press, Cambridge, MA, 1991), so our second goal is to compare these two and to argue that the accuracy of Ajdukiewicz’s explanation is less dependent on controversial properties of a systematic but convoluted general theory of cooperative communicative behavior. In Lvov-Warsaw school the relation between material implication and indicative conditionals was also discussed by Goł ąb (Matematyka 3(5):27–29, 1949) and Słupecki (Matematyka 4(6):32–35, 1949), so the third part of our paper is devoted to their discussion and relating it to Ajdukiewicz’s views.
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Notes
- 1.
- 2.
For the purposes of this paper we follow Ajdukiewicz in taking acts of acceptance to be public, and so we ignore the distinction between accepting and asserting.
- 3.
In fact, he died on April 12, 1963, and so the first disjunct is true.
- 4.
Among others, such as: calculability, non-conventionality, non-detachability, indeterminacy or re-inforcerability. An interested Reader can consult e.g. Levinson [5].
References
Ajdukiewicz, K.: Okres warunkowy a implikacja materialna [Conditional sentence and material implication]. Studia Log. IV, 117–134 (1956)
Goł ąb, S.: O kilku trudnościach zwi ązanych z prostymi kwestiami logicznymi [On a few difficulties connected to simple logical issues]. Matematyka 3(5), 27–29 (1949)
Grice, P.: Studies in the Way of Words. Harvard University Press, Cambridge (1991)
Jackson, F.: Conditionals. Blackwell, Oxford (1987)
Levinson, S.C.: Pragmatics. Cambridge University Press, Cambridge (1983)
Quine, W.V.: Methods of Logic, 2nd edn. Holt, Rinehart and Winston, Austin (1966)
Quine, W.V.: Mathematical Logic, Revised edn. Harvard University Press, Cambridge (1981)
Słupecki, J.: O własnościach okresu warunkowego [On the properties of a conditional]. Matematyka 4(6), 32–35 (1949)
Acknowledgment
This work was completed with the support of the Research Foundation Flanders and Polish National Science Centre (grant DEC-2016/22/E/HS1/00304)
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Urbaniak, R., Godziszewski, M.T. (2018). Material Implication and Conversational Implicature in Lvov-Warsaw School. In: Garrido, Á., Wybraniec-Skardowska, U. (eds) The Lvov-Warsaw School. Past and Present. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-65430-0_7
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