Online research in philosophy

I show that the standard approach to modeling phenomena involving microscopic classical electrodynamics is mathematically inconsistent. I argue that there is no conceptually unproblematic and consistent theory covering the same phenomena to which this inconsistent theory can be thought of as an approximation; and I propose a set of conditions for the acceptability of inconsistent theories.

We put forward the hypothesis that there exist three basic attitudes towards inconsistencies within world views: (1) The inconsistency is tolerated temporarily and is viewed as an expression of a temporary lack of knowledge due to an incomplete or wrong theory. The resolution of the inconsistency is believed to be inherent to the improvement of the theory. This improvement ultimately resolves the contradiction and therefore we call this attitude the ‘regularising’ attitude; (2) The inconsistency is tolerated and both contradicting elements in the theory are retained. This attitude integrates the inconsistency and leads to a paraconsistent calculus; therefore we will call it the paraconsistent attitude. (3) In the third attitude, both elements of inconsistency are considered to be false and the ‘real situation’ is considered something different that can not be described by the theory constructively. This indicates the incompleteness of the theory, and leads us to a paracomplete calculus; therefore we call it the paracomplete attitude. We illustrate these three attitudes by means of two ‘paradoxical’ situations in quantum mechanics, the wave-particle duality and the situation of non locality.

I elaborate and defend the inconsistency view on vagueness I have earlier argued for in my (2002) and (forthcoming). In rough outline, the view is that the sorites paradox arises because tolerance principles, despite their inconsistency, are meaning-constitutive for vague expressions. Toward the end of the paper I discuss other inconsistency views on vagueness that have been proposed, and compare them to the view I favor.

Stephen Read has presented an argument for the inconsistency of the concept of validity. We extend Read’s results and show that this inconsistency is but one half of a larger problem. Like the concept of truth, validity is infected with what we call semantic pathology, a condition that actually gives rise to two symptoms: inconsistency and indeterminacy. After sketching the basic ideas behind semantic pathology and explaining how it manifests both symptoms in the concept of truth, we present cases that establish the indeterminacy of validity and that link this indeterminacy with the concept’s inconsistency. Our conclusion is that an adequate treatment of the semantic pathology thus revealed must deal with both of its symptoms. Further, it must extend to the occurrences of this condition elsewhere: in the concept of truth, in the other central semantic notions, and even in certain philosophical concepts outside semantics.

Summary It is here shown that the relativistic doctrine of the relativity of simultaneity is untenable and that both the special and general theories of relativity are inconsistent. It is also shown that the theories can perhaps be made consistent, but excessively weak, through the reintroduction of absolute space and a weakening of the Lorentz transformations. Non-relativistic hypotheses for some events thought to require relativity are suggested. Finally, some conjectures are made on how so wrong a theory could have been accepted by so many for so long.

The aim of this paper is to show that it’s not a good idea to have a theory of truth that is consistent but ω -inconsistent. In order to bring out this point, it is useful to consider a particular case: Yablo’s Paradox. In theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. Firstly, I exhibit some conceptual problems that follow from so introducing it. Secondly, I show that in second order theories with standard semantics the same procedure yields a theory that doesn’t have models. So, while having an ω - inconsistent theory is a bad thing, having an unsatisfiable theory of truth is actually worse. This casts doubts on whether the predicate in question is, after all, a truthpredicate for that language. Finally, I present some alternatives to prove an inconsistency adding plausible principles to certain theories of truth.

We provide an overview of consistent fragments of the theory of Frege’s Grundgesetze der Arithmetik that arise by restricting the second-order comprehension schema. We discuss how such theories avoid inconsistency and show how the reasoning underlying Russell’s paradox can be put to use in an investigation of these fragments.

It is argued that Yablo’s Paradox is not strictly paradoxical, but rather ‘ω-paradoxical’. Under a natural formalization, the list of Yablo sentences may be constructed using a diagonalization argument and can be shown to be ω-inconsistent, but nonetheless consistent. The derivation of an inconsistency requires a uniform fixed-point construction. Moreover, the truth-theoretic disquotational principle required is also uniform, rather than the local disquotational T-scheme. The theory with the local disquotation T-scheme applied to individual sentences from the Yablo list is also consistent.

Frank Jackson endorses epiphenomenalism because he thinks that his knowledge argument undermines physicalism. One of the most interesting criticisms of Jackson's position is what I call the 'inconsistency objection'. The inconsistency objection says that Jackson's position is untenable because epiphenomenalism undermines the knowledge argument. The inconsistency objection has been defended by various philosophers independently, including Michael Watkins, Fredrik Stjernberg, and Neil Campbell. Surprisingly enough, while Jackson himself admits explicitly that the inconsistency objection is 'the most powerful reply to the knowledge argument' he knows of, it has never been discussed critically. The aim of this paper is to evaluate the objection and to identify and consider its implications. The objection is alleged to be based on a causal theory of knowledte. I argue that the objection fails by showing that any causal theory of knowledge is such that it is either false or does not support the inconsistency objection. In order to defend my argument, I offer a hypothesis concerning phenomenal knowledge.

• How to construct a ‘canonical’ Gödel sentence • If PA is sound, it is negation imcomplete • Generalizing that result to sound p.r. axiomatized theories whose language extends LA • ω-incompleteness, ω-inconsistency • If PA is ω-consistent, it is negation imcomplete • Generalizing that result to ω-consistent p.r. axiomatized theories which extend Q..