Truth values are, properly understood, merely proxies for the various relations that can hold between language and the world. Once truth values are understood in this way, consideration of the Liar paradox and the revenge problem shows that our language is indefinitely extensible, as is the class of truth values that statements of our language can take – in short, there is a proper class of such truth values. As a result, important and unexpected connections emerge between the semantic paradoxes (...) and the set-theoretic paradoxes. (shrink)

In this paper, we present a formal recipe that Frege followed in his magnum opus “Grundgesetze der Arithmetik” when formulating his definitions. This recipe is not explicitly mentioned as such by Frege, but we will offer strong reasons to believe that Frege applied it in developing the formal material of Grundgesetze. We then show that a version of Basic Law V plays a fundamental role in Frege’s recipe and, in what follows, we will explicate what exactly this role is and (...) explain how it differs from the role played by extensions in his earlier book “Die Grundlagen der Arithmetik”. Lastly, we will demonstrate that this hitherto neglected yet foundational aspect of Frege’s use of Basic Law V helps to resolve a number of important interpretative challenges in recent Frege scholarship, while also shedding light on some important differences between Frege’s logicism and recent neo-logicist approaches to the foundations of mathematics. (shrink)

_Der Mythos der religiösen Neutralität_ bietet eine radikale Neuinterpretation der allgemeinen Beziehungen zwischen Religion, Wissenschaft und Philosophie.

Saul Kripke’s theory of truth suffers from expressive limitations – in particular, there are no extensional operators within that framework that allow one to characterize those sentences that fail to receive a truth value within the framework. Especially worrisome is the fact that there is no operator that outputs true on exactly the paradoxical sentences. In this paper I extend Kripke’s approach via the addition of extensional operators, which allows us to characterize many (but not all) such sentences, including the (...) paradoxical ones. (shrink)

Abstractionism is a philosophical account of the ontology of mathematics according to which abstract objects are grounded in a process of abstraction. Abstraction involves arranging a domain of underlying objects into classes and then identifying … Continue reading Abstractionism →.

En opposant comme deux substances irréductibles l’âme et le corps, Descartes n’explique pas l’unité qui est en l’homme. En décrivant l’effort comme une réalité intermédiaire entre le corps et l’âme, Maine de Biran ressaisit l’individualité même. Devant le mystère humain, il faut donc invoquer l’expérience biranienne et non la métaphysique cartésienne : il convient d’appréhender, avant toute analyse, l’unité d’un élan, qui se disperse peut-être, mais garde sa souplesse.

the lack of unity among Christians represents the grave obstacle for the proclamation of the gospel, we should take every suitable opportunity to increase the unity of all Christians. The present essay is meant as a contribution toward this goal.” . The increased unity he has in mind is a reconciliation of the traditional scholastic interpretation of Christian doctrine , and the Calvinist tradition . More specifically, he seeks a unity between them concerning the relation of faith and reason, that (...) is, the role of reason in belief in God. To this end he compares what he understands of the CT, as represented by Calvin and Dooyeweerd, with the TSC as represented by St Thomas and the encyclical, Fides et Ratio by Pope John Paul II. In all that follows I will be agreeing with Echeverria that this is, indeed, an important concern and a laudable goal, and I hope that what I offer here in reply to his essay will be taken in that same charitable spirit. So even though I find that Echeverria’s account of the differences between the TSC and the CT is seriously mistaken, I do agree that it would go a long way toward greater cooperation between our two traditions if we could at least agree on what our differences are and work toward resolving them. For that reason I will be more concerned here with clarifying those differences than with arguing for the CT. That does not mean that I will not at times offer brief accounts of why I think the CT is right to differ from the TSC on certain points; it only means that I do not regard the case I will make for these points as anywhere near complete. This brevity is made necessary because I find the misunderstandings of Calvin, and especially of Dooyeweerd, to be so many and so knotted in “Fides et Ratio” as to form a tangled skein that would require more than just one article to unravel. I have also decided that there are so many strands to this skein that for the sake of clarity I will restrict myself to only a few of them. My assumption is that it would be better to make real progress with getting a few key differences in focus, than to end up producing a tangle of my own in an attempt to cover every point raised in Echeverria’s long article. My hope is that the treatment of the points I do cover will be sufficient to indicate how a more thorough untangling would proceed. (shrink)

We extend the Embracing Revenge account of the semantic paradoxes by constructing two distinct consequence relations that reflect, in different ways, the transfinitely-many-valued semantics developed in earlier work. In particular, we adapt the underlying ideas of “gappy” approaches based on K3, and “glutty” approaches based on LP, to the Embracing Revenge framework, by treating the infinitely many non-classical truth values as infinitely many ways that a sentence might fail to receive a classical truth value in the former case, and as (...) infinitely many ways that a sentence might receive both classical truth values in the latter. In order to obtain deductive systems that are very nearly classical, we need to utilize different conditionals (and different negations) in each logic. (shrink)

Bumped from a flight? Relax with this defense of the big business practice of deliberately promising more services than one will provide. On a small scale, over‐promising yields a toxic moral dilemma and a lie. At a large scale, the dilemma becomes dilute, and the lie completely disappears. Overbooking is honest because there is a sufficiently high probability of fulfilling each promise. Overbooking is socially beneficial because the promised resources are used more efficiently. There are fewer wasted seats on jumbo (...) jets and hence cheaper tickets with less pollution. Widespread disapproval of overbooking is a fallacious scaling error. Instead of there being too much overbooking, there is too little. (shrink)

In "arguments for the existence of god" and "faith and knowledge", john hick argues for the rationality of religious belief on the basis of an analogy between religious and perceptual belief. i reply that the analogy does not obtain because there is no alternative solipsistic interpretation of perceptual belief possible. this is because (a) hick's phenomenology of dreaming is unsatisfactory and (b) wittgenstein's "private language" argument shows solipsism to be an unintelligible option.

It is proved that for every positive integer n, the number of non-Tukey-equivalent directed sets of cardinality $\leq \aleph _n$ is at least $c_{n+2}$, the $(n+2)$ -Catalan number. Moreover, the class $\mathcal D_{\aleph _n}$ of directed sets of cardinality $\leq \aleph _n$ contains an isomorphic copy of the poset of Dyck $(n+2)$ -paths. Furthermore, we give a complete description whether two successive elements in the copy contain another directed set in between or not.