PARADOXES AND THEIR RESOLUTIONS, 2017

PARADOXES AND THEIR RESOLUTIONS: This 'thematic compilation' comprises expositions and resolutions of many (though not all) ancient and modern paradoxes, including: the Protagoras-Euathlus paradox, the Liar paradox and the Sorites paradox, Russell’s paradox and its derivatives the Barber paradox and the Master Catalogue paradox, Grelling’s paradox, Hempel's paradox of confirmation, and Goodman’s paradox of prediction. This volume also presents and comments on some of the antinomic discourse found in some Buddhist texts (namely, in Nagarjuna and in the Diamond Sutra).

2019

This paper includes nearly all my paradoxes and some bullshit, which is however difficult to prove wrong, because it happens in the Future...Hope you will enjoy reading it...

Philosophical Studies, 1986

A well-ordered set is not isomorphic to any of its proper initial segments.

Manuscrito, n. 35, pp. 233-67 (FREE ACCESS), 2012

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.

Journal of the American Philosophical Association

According to a standard view, paradoxes are arguments with plausible premises that entail an implausible conclusion. This is false. In many paradoxes the premises are not plausible precisely because they entail an implausible conclusion. Obvious responses to this problem—including that the premises are individually plausible and that they are plausible setting aside the fact that they entail an implausible conclusion—are shown to be inadequate. A very different view of paradox is then introduced. This is a functionalist view according to which paradoxes are the kinds of things that puzzle people in characteristic ways. It is claimed that this view, too, fails and for the very same reason. The result is a new puzzle about the nature of paradoxes.

Family Process, 1981

and senior faculty member, Galveston Family Institute.

Archimedes’ “fixed point theorem”: Give me a fixed point in space, and I shall upset the Earth”.

The goal of this paper is to experiment new math concepts and theories, especially if they run counter to the classical ones. To prove that contradiction is not a catastrophe, and to learn to handle it in an (un)usual way.

Philosophy, 2020

I will use paradox as a guide to metaphysical grounding, a kind of non-causal explanation that has recently shown itself to play a pivotal role in philosophical inquiry. Specifically, I will analyze the grounding structure of the Predestination paradox, the regresses of Carroll and Bradley, Russell's paradox and the Liar, Yablo's paradox, Zeno's paradoxes, and a novel omega plus one variant of Yablo's paradox, and thus find reason for the following: We should continue to characterize grounding as asymmetrical and irreflexive. We should change our understanding of the transitivity of grounding in a certain sense. We should require foundationality in a new, generalized sense, that has well-foundedness as its limit case. Meta-grounding is important. The polarity of grounding can be crucial. Thus we will learn a lot about structural properties of grounding from considering the various paradoxes. On the way, grounding will also turn out to be relevant to the diagnosis (if not the solution) of paradox. All the paradoxes under consideration will turn out to be breaches of some standard requirement on grounding, which makes uniform solutions of large groups of these paradoxes more desirable. In sum, bringing together paradox and grounding will be shown to be of considerable value to philosophy.