In this paper, we recover the idea cast by Graham Priest to our ears in 2000: That it was possible to experience Ontological Paraconsistency in life. He had, back then, as a translation of his thinking, a painting by Escher: The stairs could be going up or down, and one could not tell where they were going by simply examining the painting. The most obvious argument as to why that was not an instance of Ontological Paraconsistency found in reality was (...) that the perspective from which you would have to stare at the painting to see something different would be different too, so that it was impossible that we were getting up and down at the same time, that is, from the same perspective. That would happen with anything we picked in this world. We recently found something that does not entirely belong to this world, however, something that could finally satisfy the requirements of Priest, and therefore prove to us that there is a place for Ontological Paraconsistency. We observe that the paraconsistent robot, Emmy (Abe et al., 2006), is an application of the Non-ontological Paraconsistency, which we always believed to be passive of existence, but we here talk about another type of paraconsistency, which would be intrinsic to the being. The purpose of this paper is then providing a definite answer to the questions: Is there any real life instance of Ontological Paraconsistency? Is Ontological Paraconsistency a useful concept in terms of logical theories? (shrink)

Recently, there have been several attempts to generalize the counterfactual theory of causal explanations to mathematical explanations. The central idea of these attempts is to use conditionals whose antecedents express a mathematical impossibility. Such countermathematical conditionals are plugged into the explanatory scheme of the counterfactual theory and—so is the hope—capture mathematical explanations. Here, I dash the hope that countermathematical explanations simply parallel counterfactual explanations. In particular, I show that explanations based on countermathematicals are susceptible to three problems counterfactual explanations do (...) not face. These problems seriously challenge the prospects for a counterfactual theory of explanation that is meant to cover mathematical explanations. (shrink)

One of our purposes here is to expose something of the elementary logical structure of abductive reasoning, and to do so in a way that helps orient theorists to the various tasks that a logic of abduction should concern itself with. We are mindful of criticisms that have been levelled against the very idea of a logic of abduction; so we think it prudent to proceed with a certain diffidence. That our own account of abduction is itself abductive is methodological (...) expression of this diffidence. A second objective is to test our conception of abduction's logical structure against some of the more promising going accounts of abductive reasoning. We offer our various suggestions in a benignly advisory way. The primary targets of our advice is ourselves, meant as guides to work we have yet to complete or, in some instances, start. It is possible that our colleagues in the abduction research communities will find our counsel to be of some interest. But we repeat that our first concern is to try to get ourselves straight about what a logic of abduction should encompass. (shrink)