One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley–Meyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions of conditionality. We close by briefly discussing (...) a general conception of conditionality that may unify the three given conceptions. (shrink)
The partitions of a given set stand in a well known one-to-onecorrespondence with the equivalence relations on that set. We askwhether anything analogous to partitions can be found which correspondin a like manner to the similarity relations (reflexive, symmetricrelations) on a set, and show that (what we call) decompositions – of acertain kind – play this role. A key ingredient in the discussion is akind of closure relation (analogous to the consequence relationsconsidered in formal logic) having nothing especially to do (...) with thesimilarity issue, and we devote a final section to highlighting some ofits properties. (shrink)
The representation of quantification over relations in monadic third-order logic is discussed; it is shown to be possible in numerous special cases of foundational interest, but not in general unless something akin to the Axiom of Choice is assumed.
This paper presents a defense of Epistemic Arithmetic as used for a formalization of intuitionistic arithmetic and of certain informal mathematical principles. First, objections by AllenHazen and Craig Smorynski against Epistemic Arithmetic are discussed and found wanting. Second, positive support is given for the research program by showing that Epistemic Arithmetic can give interesting formulations of Church's Thesis.
C I Lewis showed up Down Under in 2005, in e-mails initiated by AllenHazen 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 finite Zn 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). (shrink)
In a paper published in 1975, Robert Jeroslow introduced the concept of an experimental logic as a generalization of ordinary formal systems such that theoremhood is a (or in practice ) rather than . These systems can be viewed as (rather crude) representations of axiomatic theories evolving stepwise over time. Similar ideas can be found in papers by Putnam (1965) and McCarthy and Shapiro (1987). The topic of the present article is a discussion of a suggestion by Allen (...) class='Hi'>Hazen, that these experimental logics might provide an illuminating way of representing “the human mathematical mind”. This is done in the context of the well-known Lucas-Penrose thesis. Though we agree that Jeroslow's model has some merit in this context, and that the Lucas-Penrose arguments certainly are less than persuasive, some semi-technical doubts are raised concerning the alleged impact of experimental logics on the question of knowable self-consistency. (shrink)
Machine generated contents note: 1. Astrobiology in societal context Constance Bertka; Part I. Origin of Life: 2. Emergence and the experimental pursuit of the origin of life Robert Hazen; 3. From Aristotle to Darwin, to Freeman Dyson: changing definitions of life viewed in historical context James Strick; 4. Philosophical aspects of the origin-of-life problem: the emergence of life and the nature of science Iris Fry; 5. The origin of terrestrial life: a Christian perspective Ernan McMullin; 6. The alpha and (...) the omega: reflections on the origin and future of life from the perspective of Christian theology and ethics Celia Deane-Drummond; Part II. Extent of Life: 7. A biologist's guide to the Solar System Lynn Rothschild; 8. The quest for habitable worlds and life beyond the Solar System Carl Pilcher; 9. A historical perspective on the extent and search for life Steven J. Dick; 10. The search for extraterrestrial life: epistemology, ethics, and worldviews Mark Lupisella; 11. The implications of discovering extraterrestrial life: different searches, different issues Margaret S. Race; 12. God, evolution, and astrobiology Cynthia S. W. Crysdale; Part III. Future of Life: 13. Planetary ecosynthesis on Mars: restoration ecology and environmental ethics Christopher P. McKay; 14. The trouble with intrinsic value: an ethical primer for astrobiology Kelly C. Smith; 15. God's preferential option for life: a Christian perspective on astrobiology Richard O. Randolph; 16. Comparing stories about the origin, extent, and future of life: an Asian religious perspective Francisca Cho; Index. (shrink)