Online research in philosophy

Some argue that theories of universals should incorporate structural universals, in order to allow for the metaphysical possibility of worlds of 'infinite descending complexity' ('onion worlds'). I argue that the possibility of such worlds does not establish the need for structural universals. So long as we admit the metaphysical possibility of emergent universals, there is an attractive alternative description of such cases.

Which objects (order types of total orderings) are the infinite numbers? Cantor answers: the infinite ordinals (that is, the order types of the infinite, well-ordered sets). In this paper, I argue that these objects are not the infinite numbers, but rather that objects of a different form are. Similar considerations will be seen to apply to infinite distance.

Galileo's Paradox Contradictory or Counter-Intuitive? Imagination v. Conception Infinity as a Positive Idea Do We Experience Anything Infinite? The Sublimity of the Infinite Conclusion Bibliography Notes Appendix: A Crash Course in the Mathematics of Infinite Sets..

We show that every infinite computable partial ordering has either an infinite Δ 0 2 chain or an infinite Π 0 2 antichain. Our main result is that this cannot be improved: We construct an infinite computable partial ordering that has neither an infinite Δ 0 2 chain nor an infinite Δ 0 2 antichain.

Part of the kalam cosmological argument draws upon the claim that an actual infinite cannot exist. Classical theists also maintain both that some individuals will earn eternal life and that God infallibly foreknows the future. The claim that these latter two theses do not require that an actual infinite exists because God possesses an intuitive, rather than propositional intellect, is examined and rejected. Although the future is potential, rather than actual, classical theism requires that the future be, in a sense, actually infinite.

The following syllogism is considered: a string is not an expression unless it is tokenable; no one can utter, write, or in anyway token an infinite string; so no infinite string is an expression. The second premise is rejected. But the tokenability of an infinite sentence is not sufficient for it being an infinite expression. A further condition is that no finite sentence expresses that sentence’s truth-conditions. So it is an open question whether English contains infinite expressions.

Open peer commentary on the target article “From Objects to Processes: A Proposal to Rewrite Radical Constructivism” by Siegfried J. Schmidt. Upshot: This commentary asks if Schmidt’s latest process-orientated philosophy is based on a vicious infinite regress argument. The commentator uses recent literature on the distinction of vicious and benign infinite regresses (from Claude Gratton and Nicholas Rescher) and tries to show that – taken verbatim – there is a serious logical problem in Schmidt’s argumentation.

Wes Morriston argues that even if we take an endless series of events to be merely potentially, rather than actually, infinite, still no distinction between a beginningless and an endless series of events has been established which is relevant to arguments against the metaphysical possibility of an actually infinite number of things: if a beginningless series is impossible, so is an endless series. The success of Morriston’s argument, however, comes to depend on rejecting the characterization of an endless series of events as a potential infinite. It turns out that according to his own analysis it is vitally relevant whether the series of events is potentially, as opposed to actually, infinite. If it is reasonable to maintain that an endless series of events is potentially infinite while a beginningless series is actually infinite, then a relevant distinction has been established for any person who thinks that an actual infinite cannot exist.

In a series of much discussed articles and books, William Lane Craig defends the view that the past could not consist in a beginningless series of events. In the present paper, I cast a critical eye on just one part of Craig's case for the finitude of the past – viz. his philosophical argument against the possibility of actually infinite sets of objects in the ‘real world’. I shall try to show that this argument is unsuccessful. I shall also take a close look at several considerations that are often thought to favour the possibility of an actual infinite, arguing in each case that Craig's response is inadequate.

One of the principal lines of argument deployed by the friends of the kalām cosmological argument against the possibility of a beginningless series of events is a quite general argument against the possibility of an actual infinite. The principal thesis of the present paper is that if this argument worked as advertised, parallel considerations would force us to conclude, not merely that a series of discrete, successive events must have a first member, but also that such a series must have a final member. Anyone who thinks that an endless series of events is possible must therefore reject this popular line of argument against the possibility of an actual infinite.