Approaching Infinity addresses seventeen paradoxes of the infinite, most of which have no generally accepted solutions. The book addresses these paradoxes using a new theory of infinity, which entails that an infinite series is uncompletable when it requires something to possess an infinite intensive magnitude. Along the way, the author addresses the nature of numbers, sets, geometric points, and related matters. The book addresses the need for a theory of infinity, and reviews both old and new theories of infinity. It (...) discussing the purposes of studying infinity and the troubles with traditional approaches to the problem, and concludes by offering a solution to some existing paradoxes. (shrink)

In a recent article, ‘Tensed Time and Our Differential Experience of the Past and Future,’ William Lane Craig attempts to resuscitate A. N. Prior's ‘Thank Goodness’ argument against the B-theory by combining it with Plantinga's views about basic beliefs. In essence Craig's view is that since there is a universal experience and belief in the objectivity of tense and the reality of becoming, ‘this belief constitutes an intrinsic defeater-defeater which overwhelms the objections brought against it.’ An intrinsic defeater-defeater is a (...) belief that enjoys such warrant for us that it simply overwhelms the defeaters brought against it without specifically rebutting or undercutting them. Thus, Craig claims that an effete philosophical argument like McTaggart's paradox is nothing more than ‘an engaging and recalcitrant brain teaser whose conclusion nobody really takes seriously.’ It is difficult to reconcile this statement with Craig's own writings elsewhere. For Craig has vigorously argued in at least two other articles that 'hybrid A-B theorists like McCall, Schlesinger, and Smith [who give ontological status to both A-properties and B-relations] are in deep trouble’ since they are all effectively refuted by McTaggart's Paradox. It is not Craig's inconsistency regarding the significance of McTaggart conundrum that I want to draw attention to, however. Rather I wish to raise a different issue. (shrink)

Mc Taggart's celebrated proof of the unreality of time is a chain of implications whose final step asserts that the A-series (i.e. the classification of events as past, present or future) is intrinsically contradictory. This is widely believed to be the heart of the argument, and it is where most attempted refutations have been addressed; yet, it is also the only part of the proof which may be generalised to other contexts, since none of the notions involved in it is (...) specifically temporal. In fact, as I show in the first part of the paper, McTaggart's refutation of the A-series can be easily interpreted in mathematical terms; subsequently, in order to strengthen my claim, I apply the same framework by analogy to the cases of space, modality, and personal identity. Therefore, either McTaggart's proof as a whole may be extended to each of these notions, or it must embed some distinctly temporal element in one of the steps leading up to the contradiction of the A-series. I conclude by suggesting where this element might lay, and by hinting at what I believe to be the true logical fallacy of the proof. (shrink)

McTaggart's argument for the unreality of time is generally believed to be a self-contained argument independent of McTaggart's idealist ontology. I argue that this is mistaken. It is really a demonstration of a contradiction in the appearance of time, on the basis of certain a priori ontological axioms, in particular the thesis that all times exist in parity. When understood in this way, the argument is neither obscure or unfounded, but arguably does not address those versions of the A-theory that (...) deny that all times exist in parity. (shrink)

I describe the general structure of most infinite regress arguments; introduce some basic vocabulary; present a working hypothesis of the nature and derivation of an infinite regress; apply this working hypothesis to various infinite regress arguments to explain why they fail to entail an infinite regress; describe a common mistake in attempting to derive certain infinite regresses; and examine how infinite regresses function as a premise.

Infinite regress arguments are part of a philosopher's tool kit of argumentation. But how sharp or strong is this tool? How effectively is it used? The typical presentation of infinite regress arguments throughout history is so succinct and has so many gaps that it is often unclear how an infinite regress is derived, and why an infinite regress is logically problematic, and as a result, it is often difficult to evaluate infinite regress arguments. These consequences of our customary way of (...) using this tool indicate that there is a need for a theory to re-orient our practice. My general approach to contribute to such a theory, consists of collecting and evaluating as many infinite regress arguments as possible, comparing and contrasting many of the formal and non-formal properties, looking for recurring patterns, and identifying the properties that appeared essential to those patterns. Two very general questions guided this work: How are infinite regresses generated in infinite regress arguments? How do infinite regresses logically function as premises in an argument? In answering these questions I clarify the notion of an infinite regress; identify different logical forms of infinite regresses; describe different kinds of infinite regress arguments; distinguish the rhetoric from the logic in infinite regress arguments; and suggest ways of improving our discussion and our practice of constructing and evaluating these arguments. (shrink)

The work is the presentation of a logical theory - Logic in Reality (LIR) - and of applications of that theory in natural science and philosophy, including ...

This dissertation is on infinite regress arguments in philosophy. Its main goals are to explain what such arguments from many distinct philosophical debates have in common, and to provide guidelines for using and evaluating them. Two theories are reviewed: the Paradox Theory and the Failure Theory. According to the Paradox Theory, infinite regress arguments can be used to refute an existentially or universally quantified statement (e.g. to refute the statement that at least one discussion is settled, or the statement that (...) discussions are settled only if there is an agreed-upon criterion to settle them). According to the Failure Theory, infinite regress arguments can be used to demonstrate that a certain solution fails to solve an existentially or universally quantified problem (e.g. to demonstrate that a certain solution fails to settle all discussions, or that it fails to settle even one discussion). In the literature, the Paradox Theory is fairly well-developed, and this dissertation provides the Failure Theory with the same tools. (shrink)