C I Lewis showed up Down Under in 2005, in e-mails initiated by Allen Hazen of Melbourne. Their topic was the system Hazen
called FL (a Funny Logic), axiomatized in passing in Lewis 1921. I show that FL is the system MEN of material equivalence with negation.
But negation plays no special role in MEN. Symbolizing equivalence with → and defining ∼A inferentially as A→f, the theorems of MEN are just those of the underlying theory ME of pure material equivalence. This accords with the treatment
of negation in the Abelian l-group logic A of Meyer and Slaney (Abelian logic. Abstract, Journal of Symbolic Logic 46, 425–426, 1981), which also defines ∼A inferentially with no special conditions on
f. The paper then concentrates on the pure implicational part AI of A, the simple logic of Abelian groups. The integers Z were known to be characteristic for AI, with every non-theorem B refutable mod some Zn for finite n. Noted here is that AI is pre-tabular, having the Scroggs property that every proper extension SI of AI, closed under substitution and detachment, has some finiteZn as its characteristic matrix. In particular FL is the extension for which n = 2 (Lewis, The structure of logic and its relation to other systems. The Journal of Philosophy 18, 505–516, 1921; Meyer and Slaney, Abelian logic. Abstract. Journal of Symbolic Logic 46, 425–426, 1981; This is an abstract of the much longer paper finally published in 1989 in G. G. Priest, R. Routley and J.
Norman, eds., Paraconsistent logic: essays on the inconsistent, Philosophica Verlag, Munich, pp. 245–288, 1989).
Meyer was supported in this work as a Visiting Fellow in the College of Engineering and Computer Science, ANU. 相似文献
Materialists argue that there is no place for God in the universe. Chance and contingency are all that structure our world. However, the materialists’ dismissal of subjectivity manifests a flawed metaphysics that invalidates their arguments against God. In this essay I explore the following: (1) How does personal metaphysics affect one's ability to do science? (2) Are the materialist arguments about contingency used to dismiss the importance of our place in the universe valid? (3) What are the implications of subjectivity on belief and science? To answer the first question, I examine the later years of Sir Alfred Russel Wallace, one of the cofounders of evolution through natural selection with Darwin. His belief in nineteenth–century spiritualism profoundly affected his standing in the scientific community. I describe the effect of spiritualism on Wallace's science. To answer the second question, I use my own work in mathematical modeling of evolutionary processes to show that randomness, and contingency at one level, can actually be nearly deterministic at another. I demonstrate how arguments about chance and contingency do not imply anything relevant about whether there is a designer behind the universe. To answer the third question I begin by exploring a paradox of consciousness and show how the existence of subjective truths may provide a paradigm for sustaining a rational belief in God. These questions form the framework of a structured belief in a creator while yet embracing what science has to offer about the development of life on our planet. 相似文献
We describe a KB Gödelian ontological system, and some other weak systems, in a fully formal way using theory of types and natural deduction, and present a completeness proof in its main and specific parts. We technically and philosophically analyze and comment on the systems (mainly with respect to the relativism of values) and include a sketch of some connected aspects of Gödel's relation to Kant. 相似文献
A semantics may be compositional and yet partial, in the sense that not all well-formed expressions are assigned meanings by it. Examples come from both natural and formal languages. When can such a semantics be extended to a total one, preserving compositionality? This sort of extension problem was formulated by Hodges, and solved there in a particular case, in which the total extension respects a precise version of the fregean dictum that the meaning of an expression is the contribution it makes to the meanings of complex phrases of which it is a part. Hodges' result presupposes the so-called Husserl property, which says roughly that synonymous expressions must have the same category. Here I solve a different version of the compositional extension problem, corresponding to another type of linguistic situation in which we only have a partial semantics, and without assuming the Husserl property. I also briefly compare Hodges' framework for grammars in terms of partial algebras with more familiar ones, going back to Montague, which use many-sorted algebras instead.