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1

MODAL LOGIC BEFORE KRIPKE

100%
Cresswell M.
Organon F. medzinárodný časopis pre analytickú filozofiu
|
2019
|
vol. 26
|
issue 3
323 – 339
EN
100 years ago C.I. Lewis published A Survey of Symbolic Logic, which included an axiom system for a notion of implication which was ‘stricter’ than that found in Whitehead and Russell’s Principia Mathematica. As far as I can tell little notice was taken of this until 1930 when Oskar Becker provided some additional axioms which led Lewis in Symbolic Logic (written with C.H. Langford, 1932) to revise the system he had produced in 1918, and list five systems which could be obtained using Becker’s suggested formulae. The present paper reviews the development of modal logic both before and after 1932, up to 1959 looking at, among other work, Becker’s 1930 article and Robert Feys’s articles in 1937 and 1950. I will then make some comments on the completeness results for S5 found in Bayart and Kripke in 1959; and I will finally look at how modal logic reached New Zealand in the early 1950s in the work of Arthur Prior.
2

EXPLODING A MYTH: C. I. LEWIS, PRAGMATISM, AND THE GIVEN

100%
Misak C.
Filozofia (Philosophy)
|
2014
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vol. 69
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issue 4
332 – 341
EN
Clarence Irving Lewis is one of the mostly unjustly neglected philosophers of the last century. This paper shows how he is the inheritor of Peirce’s view; and did not succumb to the myth of the given, but rather, put forward a view that was picked up, almost in whole, by his student Quine.
3

C.I. LEWIS, E.J. NELSON, AND THE MODERN ORIGINS OF CONNEXIVE LOGIC

88%
Mares E., Paoli F.
Organon F. medzinárodný časopis pre analytickú filozofiu
|
2019
|
vol. 26
|
issue 3
405 – 426
EN
Modern logic owes an important debt to C.I. Lewis and his students. In addition to Lewis’s five modal logics, they are responsible for the creation (or discovery) of the logic of analytic implication and connexive logic. In this paper, we examine E.J. Nelson’s connexive logic as an attempt to formalise the notion of entailment while avoiding the paradoxes of strict implication. We also look briefly at the reception of Nelson’s logic and at Lewis’s reply to it.
4

WIREDU CONTRA LEWIS ON THE RIGHT MODAL LOGIC

88%
Martens D. B.
Organon F. medzinárodný časopis pre analytickú filozofiu
|
2019
|
vol. 26
|
issue 3
474 – 490
EN
This paper is a critical study of an argument put forward by Kwasi Wiredu in his engagement with C. I. Lewis on choosing the right modal logic for logical necessity. Wiredu argues that Lewis “could have been more adventurous modally with perfect logicality” and could justifiably have accepted S4 rather than being “to the last cautious of any system stronger than S2” (Wiredu 1979). I address terse, incomplete, and provocatively incongruous notes on Wiredu’s paper by (Makinson 1980) and (Humberstone 2011), as well as a paper by (Cresswell 1965) that Humberstone cites, and I draw on recent work by (Lewitzka 2015; 2016). I conclude that Wiredu’s argument cannot be accepted as sound but a variant argument can be accepted as sound.
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