Online research in philosophy

Extending Gödel's Dialectica interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite recursion on well-founded trees.

Students of politics cleave to a welter of conflicting conceptions of their subject. We all know that these conceptions shape the questions researchers put to politics, as well as the assumptions on which they make their inquiries. But we lack any attempt to list and classify these conceptions. This research note does just that, listing and classifying 29 1/2 definitions of politics I have found in the scholarly literature. I present the definitions and divide them into seven classes: power-seeking definitions, power-distributing definitions, struggle-and-competition definitions, collective decision and -action definitions, group- and social order-production definitions, authority-asserting definitions, and shaping -values and -arrangements definitions. Among those listed are the Weberian, Marxist, feminist, collective-choice, and conservative definitions of politics.

Many different modes of definition have been proposed over time, but none of them allows for circular definitions, since, according to the prevalent view, the term defined would then be lacking a precise signification. I argue that although circular definitions may at times fail uniquely to pick out a concept or an object, sense still can be made of them by using a rule of revision in the style adopted by Anil Gupta and Nuel Belnap in the theory of truth.

In this paper, we prove the wellfoundedness of recursive notation systems for reflecting ordinals up to Π₃-reflection by relevant inductive definitions.

Overall, Max Black's defense of the inductive support of inductive rules succeeds. Circularity is best explained in terms of epistemic conditions of inference. When an inference is circular, another inference token of the same type may, because of a difference of surrounding circumstances, not be circular. Black's inductive arguments in support of inductive rules fit this pattern: a token circular in some circumstances may be noncircular in other circumstances.

On a rather popular conception, the paradox of analysis suggests that the intersubstitutivity of analysans and analysandum should be restricted to non-psychological contexts. This is typically taken to be compatible with the idea that two sentences differing only in that one has the analysandum where the other has the analysans express exactly the same proposition. In this note we argue that this should be pondered upon in light of the view that many important ordinary concepts are circular. In particular, we submit that if there are correct analyses grounding circular definitions, then we are bound to further restrict the substitutivity principle, for we must admit that it might fail even in non- psychological contexts.

We consider various concepts associated with the revision theory of truth of Gupta and Belnap. We categorize the notions definable using their theory of circular definitions as those notions universally definable over the next stable set. We give a simplified (in terms of definitional complexity) account of varied revision sequences-as a generalised algorithmic theory of truth. This enables something of a unification with the Kripkean theory of truth using supervaluation schemes.

This original and enticing book provides a fresh, unifying perspective on many old and new logico-philosophical conundrums. Its basic thesis is that many concepts central in ordinary and philosophical discourse are inherently circular and thus cannot be fully understood as long as one remains within the confines of a standard theory of definitions. As an alternative, the authors develop a revision theory of definitions, which allows definitions to be circular without this giving rise to contradiction (but, at worst, to “vacuous” uses of definienda). The theory is applied with varying levels of detail to a circular analysis of concepts as diverse as truth, predication, necessity, physical object, etc. The focus is on truth, and hope is expressed that a deeper understanding of the Liar and related paradoxes has been provided: “We have tried to show that once the circularity of truth is recognized, a great deal of its behavior begins to make sense. In particular, from this viewpoint, the existence of the paradoxes seems as natural as the existence of the eclipses” (p. 142). We think that this hope is fully justified, although some problems remain that future research in this field should take into account.

I aim to show how and why some definitions can be benignly circular. According to Lloyd Humberstone, a definition that is analytically circular need not be inferentially circular and so might serve to illuminate the application-conditions for a concept. I begin by tidying up some problems with Humberstone's account. I then show that circular definitions of a kind commonly thought to be benign have inferentially circular truth-conditions and so are malign by Humberstone's test. But his test is too demanding. The inferences we actually use to establish the applicability of, e.g., colour concepts are designed to establish warranted assertability and not truth. Understood thus, dispositional analyses are not inferentially circular.

Gupta"s and Belnap"s Revision Theory of Truth defends the legitimacy of circular definitions. Circularity, however, forces us to reconsider our conception of meaning. A readjustment of some standard theses about meaning is here proposed, by relying on a novel version of the sense–reference distinction.