A common argument in support of a beginning of the universe used by advocates of the kalām cosmological argument (KCA) is the argument against the possibility of an actual infinite, or the “Infinity Argument”. However, it turns out that the Infinity Argument loses some of its force when compared with the achievements of set theory and it brings into question the view that God predetermined an endless future. We therefore defend a new formal argument, based on the nature of time (...) (just as geometrical reasoning is based on the nature of space), which addresses more directly the question of beginningless time. (shrink)

The strong law of large numbers and considerations concerning additional information strongly suggest that Beauty upon awakening has probability 1/3 to be in a heads-awakening but should still believe the probability that the coin landed heads in the Sunday toss to be 1/2. The problem is that she is in a heads-awakening if and only if the coin landed heads. So, how can she rationally assign different probabilities or credences to propositions she knows imply each other? This is the problem (...) I address in this article. I suggest that ‘p whenever q and vice versa’ may be consistent with p and q having different probabilities if one of them refers to a sample space containing ordinary possible worlds and the other to a sample space containing centred possible worlds, because such spaces may fail to combine into one composite probability space and, as a consequence, ‘whenever’ may not be well defined; such is the main contribution of this article. 1The Sleeping Beauty Game2Groisman’s and Peter Lewis’s Approaches3Discussing Beauty’s Credences4The Principle of Equivalence's Failure5Making Sense of the Principle of Equivalence's Failure6Elga’s and Lewis’s Approaches7ConclusionAppendix. (shrink)

Cantor’s proof that the powerset of the set of all natural numbers is uncountable yields a version of Richard’s paradox when restricted to the full definable universe, that is, to the universe containing all objects that can be defined not just in one formal language but by means of the full expressive power of natural language: this universe seems to be countable on one account and uncountable on another. We argue that the claim that definitional contexts impose restrictions on the (...) scope of quantifiers reveals a natural way out. (shrink)

We use two logical resources, namely, the notion of recursively defined function and the Benardete-Yablo paradox, together with some inherent features of causality and time, as usually conceived, to derive two results: that no ungrounded causal chain exists and that time has a beginning.

The structure of Yablo’s paradox is analysed and generalised in order to show that beginningless step-by-step determination processes can be used to provoke antinomies, more concretely, to make our logical and our on-tological intuitions clash. The flow of time and the flow of causality are usually conceived of as intimately intertwined, so that temporal causation is the very paradigm of a step-by-step determination process. As a conse-quence, the paradoxical nature of beginningless step-by-step determina-tion processes concerns time and causality as usually (...) conceived. (shrink)

We model infinite regress structures — not arguments — by means of ungrounded recursively defined functions in order to show that no such structure can perform the task of providing determination to the items composing it, that is, that no determination process containing an infinite regress structure is successful.

Following an idea from Gödel and Carnap we show how we can speak with absolute generality even if we cannot quantify with absolute generality.

In response to Bhupinder Singh Anand''s article CAN WE REALLY FALSIFY TRUTH BY DICTAT? in THE REASONER II, 1, January 2008,that denies the existence of nonstandard models of Peano Arithmetic, we prove from Compactness the existence of such models.

Poincaré in a 1909 lecture in Göttingen proposed a solution to the apparent incompatibility of two results as viewed from a definitionist perspective: on the one hand, Richard’s proof that the definitions of real numbers form a countable set and, on the other, Cantor’s proof that the real numbers make up an uncountable class. Poincaré argues that, Richard’s result notwithstanding, there is no enumeration of all definable real numbers. We apply previous research by Luna and Taylor on Richard’s paradox, (...) indefinite extensibility and unrestricted quantification to evaluate Poincaré’s proposal. We emphasize that Poincaré’s solution involves an early recourse to indefinite extensibility and argue that his proposal, if it is to completely avoid Richard’s paradox, requires rejecting absolutely unrestricted quantification: Richard’s paradox provides a context in which paradox seems inescapable if unrestricted quantification is possible. In proposing his solution to the apparent conflict between Richard’s and Cantor’s results, Poincaré employs temporal expressions whose exact meaning he does not clarify. We suggest an interpretation of these expressions in terms of order of availability and briefly discuss its explanatory power in topics like paradoxes, limitation theorems and indefinite extensibility. (shrink)

The Monist’s call for papers for this issue ended: “if formalism is true, then it must be possible in principle to mechanize meaning in a conscious thinking and language-using machine; if intentionalism is true, no such project is intelligible”. We use the Grelling-Nelson paradox to show that natural language is indefinitely extensible, which has two important consequences: it cannot be formalized and model theoretic semantics, standard for formal languages, is not suitable for it. We also point out that object-object mapping (...) theories of semantics, the usual account for the possibility of non intentional semantics, doesn’t seem able to account for the indefinitely extensible productivity of natural language. (shrink)

Computationalism is the claim that all possible thoughts are computations, i.e. executions of algorithms. The aim of the paper is to show that if intentionality is semantically clear, in a way defined in the paper, then computationalism must be false. Using a convenient version of the phenomenological relation of intentionality and a diagonalization device inspired by Thomson's theorem of 1962, we show there exists a thought that canno be a computation.

We develop an argument sketched by Luna (2011) based on the Pinocchio paradox, which was proposed by Eldridge-Smith and Eldridge- Smith (2010). We show that, upon plausible assumptions, the claim that mental states supervene on bodily states leads to the conclusion that some proposition is both paradoxical and not paradoxical. In order to show how the presence of paradoxes can be harnessed for philosophical argumentation, we present as well a couple of related arguments.

We model infinite regress structures -not arguments- by means of ungrounded recursively defined functions in order to show that no such structure can perform the task of providing determination to the items composing it, that is, that no determination process containing an infinite regress structure is successful.

¿Podría estar amenazado el futuro de nuestra civilización por un abuso secular de la razón? Cabe argumentar que la Modernidad se construyó sobre la ambición cartesiana de conocer y regular el mundo mediante el discurso racional, postergando el conocimiento sensible y descartando cualquier posibilidad de un conocimiento intelectual diferente de la razón científico-matemática. Según el autor, esta ambición ha moldeado el quehacer científico, filosófico y matemático de la Modernidad y persiste todavía en el discurso ético-político del capitalismo global. Laureano (...) Luna explora las limitaciones del proyecto racionalista moderno rastreando sus límites desde la lógica matemática hasta la racionalidad social, política y económica de la sociedad contemporánea, argumentando la tesis de que los límites del discurso racional que las paradojas o en el teorema de Gödel revelan en la lógica se reproducen en los ámbitos de la ciencia, la ética y la política, porque esos límites dependen todos de un rasgo esencial de la fenomenología del pensamiento. En la elaboración de esta síntesis la obra emprende un análisis de la racionalidad vigente que desemboca en la consideración de sus limitaciones para encarar el futuro. (shrink)

We propose certain clases that seem unable to form a completed totality though they are very small, finite, in fact. We suggest that the existence of such clases lends support to an interpretation of the existence of proper clases in terms of availability, not size.

Hume’s famous character Cleanthes claims that there is no difficulty in explaining the existence of causal chains with no first cause since in them each item is causally explained by its predecessor. Relying on logico-mathematical resources, we argue for two theses: (1) if the existence of Cleanthes’ chain can be explained at all, it must be explained by the fact that the causal law ruling it is in force, and (2) the fact that such a causal law is in force (...) cannot explain the occurrence of the events in the chain. In order to perform (1), we manage to express in mathematical terms the intuitive idea that indefinitely delayed explanation is ultimately no explanation. In order to achieve (2), we identify a logical relation we can prove to be as strong as the causal relation at issue in the Cleanthes passage, according to a precise notion of strength of relations. (shrink)

The Russellian argument against the possibility of absolutely unrestricted quantification can be answered by the partisan of that quantification in an apparently easy way, namely, arguing that the objects used in the argument do not exist because they are defined in a viciously circular fashion. We show that taking this contention along as a premise and relying on an extremely intuitive Principle of Determinacy, it is possible to devise a reductio of the possibility of absolutely unrestricted quantification. Therefore, there are (...) intuitive reasons to believe that the counter-argument fails to support the possibility of absolutely unrestricted quantification. (shrink)

Patrick Grim has put forward a set theoretical argument purporting to prove that omniscience is an inconsistent concept and a model theoretical argument for the claim that we cannot even consistently define omniscience. The former relies on the fact that the class of all truths seems to be an inconsistent multiplicity (or a proper class, a class that is not a set); the latter is based on the difficulty of quantifying over classes that are not sets. We first address the (...) set theoretical argument and make explicit some ways in which it depends on mathematical Platonism. Then we sketch a non Platonistic account of inconsistent multiplicities, based on the notion of indefinite extensibility, and show how Grim’s set theoretical argument could fail to be conclusive in such a context. Finally, we confront Grim’s model theoretical argument suggesting a way to define a being as omniscient without quantifying over any inconsistent multiplicity. (shrink)

We show how second order logic incompleteness follows from incompleteness of arithmetic, as proved by Gödel.

I address the claim by Valor and Martínez that Goldstein's cassationist approach to Liar-like paradoxes generates paradoxes it cannot solve. I argue that these authors miss an essential point in Goldstein's cassationist approach, namely the thesis that paradoxical sentences are not able to make the statement they seem to make.

Assuming the indefinite extensibility of any domain of quantification leads to reasoning with extensible domain semantics. It is showed that some theorems (e.g. Thomson's) in conventional semantics logic are not theorems in a logic provided with this new semantics.

We rely on a recent puzzle by Alex Blum to offer a new argument for the old Fitch’s thesis that what we learn a posteriori in Kripkean identity statements like ‘Tully is Cicero’ is contingent and what is not contingent in such statements is analytical, hence hardly a posteriori.

We offer a number of arguments for or against particular metaphysical theses. All of them are based in phenomena or results in mathematical logic, broadly conceived, and are offered as exemplification of the possibility of arguing in metaphysics from such results.

Under the name of ‘Basic Blindspot Theorem’, Paul Saka has proposed in the special issue on mind and paradox of this journal a Gödelian argument to the effect that no cognitive system can be complete and correct. We show that while the argument is successful as regards mechanical and formal systems, it may fail with respect to minds, so contributing to draw a boundary between the former and the latter. The existence of such a boundary may lend support to Saka’s (...) general thesis that paradoxes are mind-dependent. (shrink)

Godel's and Tarski's theorems were inspired by paradoxes: the Richard paradox, the Liar. Godel, in the 1951 Gibbs lecture argued from his metatheoretical results for a metaphysical claim: the impossibility of reducing, both, mathematics to the knowable by the human mind and the human mind to a finite machine (e.g. the brain). So Godel reasoned indirectly from paradoxes for metaphysical theses. I present four metaphysical theses concerning mechanism, reductive physicalism and time for the only purpose of suggesting how it could (...) be argued for them directly from paradoxical sentences. (shrink)

In ‘The Unsatisfied Paradox’ (The Reasoner 6(12), p.184-5), Peter Eldridge-Smith has argued that no unique solution for the logical paradoxes is likely to exist in the presence of the following two kinds of paradox: 1. The Unsatisfied kind. 2. The Satisfiable kind. We argue that both kinds of paradoxes typically contain some kind of self-reference used for an attempt of self-diagonalization, and that consequently they may solvable in the same way, namely, by the acknowledgement that no intensional object is available (...) to itself for reference or quantification. (shrink)

Computationalism is the claim that all possible thoughts are computations, i.e. executions of algorithms. The aim of the paper is to show that if intentionality is semantically clear, in a way defined in the paper, then computationalism must be false. Using a convenient version of the phenomenological relation of intentionality and a diagonalization device inspired by Thomson's theorem of 1962, we show there exists a thought that cannot be a computation.

Black Feminist Sociology offers new writings by established and emerging scholars working in a Black feminist tradition. The book centers Black feminist sociology within the sociology canon and widens is to feature Black feminist sociologists both outside the U.S. and the academy. Inspired by a BFS lens, the essays are critical, personal, political and oriented toward social justice. Key themes include the origins of Black feminist sociology, expositions of BFS orientations to research that extend disciplinary norms, and contradictions of the (...) pleasures and costs of such an approach both academically and personally. Authors explore their own sociological legacy of intellectual development to raise critical questions of intellectual thought and self-reflexivity. The book highlights the dynamism of BFS so future generations of scholars can expand upon and beyond the book's key themes. (shrink)

This chapter contains sections titled: Yoga for Women? The Yoga Body as ‘Capital’ Yoga as a Beauty Practice Conclusion: Yoga for Everybody.

Unlimited growth — an uncontested economic “dogma” — is showing to be a vital threat for the Earth’s ecosystems, as well as for human civilization. A global collapse is a dreadful possibility within the century : we are relentlessly given warning signs of systemic degradation. Humans cannot live and prosper pretending to remain “outside” of nature’s realm and unfettered by nature’s laws. The human project is bound to the Earth’s vitality. Such is the global context that conditions any intellectual pursuit, (...) even more, the quest for meaning by Christian believers. This essay calls for a radical reassessment of the exegetical and the theological task. New creative ways of engaging the biblical heritage and a thorough questioning of our deadly lifestyle are some of the challenges we face, in view of an impending global collapse. (shrink)

I address the claim by Valor and Martínez that Goldstein's cassationist approach to Liar-like paradoxes generates paradoxes it cannot solve. I argue that these authors miss an essential point in Goldstein's cassationist approach, namely the thesis that paradoxical sentences are not able to make the statement they seem to make.

Resumo: Este artigo parte da análise da influência de Hegel na construção do conceito de capital e de ideologia, na obra de Marx. Para tal, buscou-se analisar a passagem dos primeiros escritos humanistas de Marx à sua teoria tardia. Da ruptura realizada por Marx em relação a suas obras de juventude, surge o problema de como determinar o sujeito, uma vez que a perspectiva humanista inicial é abandonada. A ideia é a de que, paradoxalmente, quando critica a dialética hegeliana, Marx (...) termina por encontrar problemas que poderiam ser resolvidos através de conceitos hegelianos, como a questão do sujeito de classe. É o que procuraremos argumentar por meio de uma análise sobre o papel da negatividade em Hegel.: This article starts with an analysis of the influence of Hegel on the construction of the concepts of capital and ideology in Marx's work. To this end, we analyze the transition from Marx's first humanist writings to his later theory. Due to the break achieved by Marx in relation to his early works, a problem arises: the determination of the revolutionary subject once the initial humanist perspective has been abandoned. Our thesis is that when Marx leaves Hegel, he paradoxically ends up encountering problems that can only be resolved by Hegelian dialectics,. We argue this by means of an analysis of the role of negativity in Hegel. (shrink)

This book investigates the concept of body shame and explores its significance when considering philosophical accounts of embodied subjectivity, providing phenomenological reflections on how the body is shaped by social forces.

En esta discusión abordo la hermenéutica analógica de Mauricio Beuchot comparándola con la hermenéutica filosófica de Hans-Georg Gadamer. Argumento que Beuchot vuelve a la idea clásica de la hermenéutica como método de interpretación y no la juzga, como Gadamer, como una fenomenología de la comprensión. Sin embargo, Beuchot no atiende las razones de Gadamer en contra de concebir la hermenéutica como una metodología. Si se considera como metodología centrada en la analogía, la hermenéutica analógica deja de lado otros recursos interpretativos (...) importantes. Finalmente, Beuchot adopta una teoría correspondentista de la verdad contra la que argumenta Gadamer y que es incompatible con una hermenéutica filosófica. In this paper I analyze Mauricio Beuchot's analogical hermeneutics by contrasting it with Hans-Georg Gadamer's philosophical hermeneutics. I argue that Beuchot goes back to the classical idea of hermeneutics as a method of interpretation, and does not see it, as Gadamer does, as a phenomenology of understanding. However, Beuchot does not address Gadamer's arguments against using hermeneutics as a methodology. Considered as a methodology centered on analogy, analogical hermeneutics overlooks other important interpretation resources. Finally, Beuchot adopts a correspondence theory of truth, which Gadamer objects and is incompatible with philosophical hermeneutics. (shrink)