The Train Paradox

When two omnipotent beings are randomly and sequentially selecting positive integers, the being who selects second is almost certain to select a larger number. I then use the relativity of simultaneity to create a paradox by having omnipotent beings select positive integers in different orders for different observers.

The No-No Paradox Is a Paradox

The No-No Paradox consists of a pair of statements, each of which ‘says’ the other is false. Roy Sorensen claims that the No-No Paradox provides an example of a true statement that has no truthmaker: Given the relevant instances of the T-schema, one of the two statements comprising the ‘paradox’ must be true (and the other false), but symmetry constraints prevent us from determining which, and thus prevent there being a truthmaker grounding the relevant assignment of truth values. Sorensen's view is mistaken: situated within an appropriate background theory of truth, the statements comprising the No-No Paradox are genuinely paradoxical in the same sense as is the Liar (and thus, on Sorensen's view, must fail to have truth values). This result has consequences beyond Sorensen's semantic framework. In particular, the No-No Paradox, properly understood, is not only a new paradox, but also provides us with a new type of paradox, one which depends upon a general background theory of the truth predicate in a way that the Liar Paradox and similar constructions do not.     

Truthlikeness and the Lottery Paradox via the Preface Paradox

In a 2017 AJP paper, Cevolani and Schurz (C&S) propose a novel solution to the Preface Paradox that appeals to the notion of expected truthlikeness. This discussion note extends and analyses their approach by applying it to the related Lottery Paradox.     

The Cookie Paradox

We’ve all been at parties where there's one cookie left on what was once a plate full of cookies, a cookie no one will eat simply because everyone is following a rule of etiquette, according to which you’re not supposed to eat the last cookie. Or at least we think everyone is following this rule, but maybe not. In this paper I present a new paradox, the Cookie Paradox, which is an argument that seems to prove that in any situation in which everyone is truly following the rule, no one eats any cookies at all, no matter how many there are to be eaten. The ‘Cookie Argument’ resembles the more familiar argument that surprise exams are impossible, but it's not exactly the same. I argue that the biggest difference is that, unlike the surprise exam argument, the Cookie Argument is actually sound! I conclude the paper by explaining how it could be possible for a group of people to engage in behavior (eating cookies) that guarantees that at least one of the members of the group will violate a rule, even when it's common knowledge in the group that everyone is committed to following that very rule.

Sometimes me think, “What is friend?” and then me say, “Friend is someone to share the last cookie with.” ‐ Cookie Monster, http://youtu.be/LHh0A_bH5ig 1 1 I’m grateful to Eric Carter for this quote.

     

Platitudes against Paradox

We present a strategy to dissolve semantic paradoxes which proceeds from an explanation of why paradoxical sentences or their definitions are semantically defective. This explanation is compatible with the acceptability of impredicative definitions, self-referential sentences and semantically closed languages and leaves the status of the so-called truth-teller sentence unaffected. It is based on platitudes which encode innocuous constraints on successful definition and successful expression of propositional content. We show that the construction of liar paradoxes and of certain versions of Curry’s paradox rests on presuppositions that violate these innocuous constraints. Other versions of Curry’s paradox are shown not to be paradoxical at all once their presuppositions are made explicit. Part of what we say rehearses a proposal originally made by Laurence Goldstein in 1985. Like Goldstein we dispose of certain paradoxes by rejecting some of the premises from which they must be taken to proceed. However, we disagree with his more recent view that the premises to be rejected are neither true nor false.     

The Abridgement Paradox

When axiomatizing a body of truths, one first concentrates on obtaining a set of axioms that entail all and only those truths. The theorist expects that this complete system will have some needlessly strong axioms that can later be weakened or even deleted. What happens if the theorist includes in his system recognition of this superfluity? Contradiction! Even admitting the possibility of superfluity dashes all hope of consistency. Any suspicion of superfluous information must be voiced from outside the system.     

Endurantism and Paradox

Mereological challenges have recently been raised against the endurantist. For instance, Barker and Dowe (2003) have argued that eternalist endurantism entails (1) persisting objects are both 3D and 4D, and that (2) the lives of persisting objects last longer than they actually do. They also argue that presentist endurantism also entails, albeit in a tensed way, that (3) the lives of persisting objects last longer than they actually do. While they’ve further argued (2005) that the objections raised by McDaniel (2003) and Beebee and Rush (2003) fail, here I show that such objections are tenable without requiring further significant metaphysical commitments; I argue that such endurantist defences are tenable, contra to prior analyses.     

The Apology Paradox

Some leaders and citizens think it appropriate to apologize for historical injustices like slavery or the dispossession of indigenous people. But can we sincerely say 'Sorry' for the deeds of our forebears? By making an apology we are expressing regrets for what they did: we are saying that we prefer that these deeds had not been done. However, if these deeds had not been done, history would have been different, and probably we would not exist. Since most of us are glad to be alive, it seems that our apologies must be insincere. I discuss a number of proposed solutions to this paradox.