Although revolutionary, Teilhard de Chardin's true thought was not contradictory with the Christian dogma. This is what Henri de Lubac, authoritative interpreter of Teilhard, claims. In this article we report its essential theses.

En este artículo, tengo dos objetivos distintos. En primer lugar, mostrar que no es una buena idea tener una teoría de la verdad que, aunque consistente, sea omega-inconsistente. Para discutir este punto, considero un caso particular: la teoría de Friedman-Sheard FS. Argumento que en los lenguajes de primer orden omega inconsistencia implica que la teoría de la verdad no tiene modelo estándar. Esto es, no hay un modelo cuyo dominio sea el conjunto de los números naturales en (...) el cual esta teoría de la verdad pueda tener una interpretación consistente. En ese sentido, la introducción del predicado veritativo no mantiene la ontología estándar. Además, cuando se considera un lenguaje de orden superior, la situación es aun peor. En teorías de segundo orden con semántica estándar, la misma introducción produce una teoría que no tiene modelo. Por eso, si la omega-inconsistencia es un mal síntoma, la insatisfacibilidad de una teoría es aun peor. En segundo lugar, propongo abandonar el principio de unión de teorías FSn y aceptar una extensibilidad indefinida de teorías FS0, FS1, FS2, FS3,.... De acuerdo a mi punto de vista, la secuencia de teorías tiene las mismas virtudes que FS sin sus desagradables consecuencias. In this paper, I have two different purposes. Firstly, I want to show that it's not a good idea to have a theory of truth that is consistent but omega-inconsistent. In order to bring out this point, it is useful to consider a particular case: FS. I argue that in First-order languages omega-inconsistency implies that a theory of truth has not standard model. Then, there is no model whose domain is the set of natural numbers in which this theory of truth could acquire a consistent interpretation. So, in theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. I add that in Higher-order languages the situation is even worst. In second order theories with standard semantic the same introduction produces a theory that doesn't have a model. So, if an omega-inconsistent theory of truth is bad, an unsatisfiable theory is really bad. Secondly, I propose to give up the union principle of theories FSn and accept an indefinite extensibility of theories FS0, FS1, FS2, FS3,... According to my view, the sequence of theories has the same virtues of FS without its disgusting consequences. (shrink)

In this note, the problem of tracking random references and rejecting random perturbations in a quadrotor, both generated by an auxiliary system named exosystem, is solved by extending the deterministic tracking problem to the area of stochastic processes. Besides, it is considered that only a part of the state vector of the quadrotor is available through measurements. As a consequence, the state vector of the plant must be estimated in order to close the control loop. On this basis, a controller (...) to track random references and to reject random perturbations is developed by combining a Kalman filter to estimate the references and perturbations of an exosystem and an observer to estimate the states of a quadrotor. Besides, to obtain a more practical controller, the analysis is carried out in discrete time. Numerical simulations are used in a quadrotor to confirm the validity and effectiveness of the proposed control. (shrink)

You omega know something when you know it, and know that you know it, and know that you know that you know it, and so on. This paper first argues that omega knowledge matters, in the sense that it is required for rational assertion, action, inquiry, and belief. The paper argues that existing accounts of omega knowledge face major challenges. One account is skeptical, claiming that we have no omega knowledge of any ordinary claims about the (...) world. Another account embraces the KK thesis, and identifies knowledge with omega knowledge. This position faces counterexamples, and struggles to make sense of inexact knowledge. The paper then develops a new account of knowledge, by proposing the principle of Reflective Luminosity: if you know that you know something, then you omega know it. I argue that Reflective Luminosity allows for omega knowledge while avoiding the problems for KK. (shrink)

We explore the interplay between $\omega $ -categoricity and pseudofiniteness for groups, and we conjecture that $\omega $ -categorical pseudofinite groups are finite-by-abelian-by-finite. We show that the conjecture reduces to nilpotent p-groups of class 2, and give a proof that several of the known examples of $\omega $ -categorical p-groups satisfy the conjecture. In particular, we show by a direct counting argument that for any odd prime p the ( $\omega $ -categorical) model companion of the (...) theory of nilpotent class 2 exponent p groups, constructed by Saracino and Wood, is not pseudofinite, and that an $\omega $ -categorical group constructed by Baudisch with supersimple rank 1 theory is not pseudofinite. We also survey some scattered literature on $\omega $ -categorical groups over 50 years. (shrink)

In this paper, we discuss semantical properties of the logic \(\textbf{GL}\) of provability. The logic \(\textbf{GL}\) is a normal modal logic which is axiomatized by the the Löb formula \( \Box (\Box p\supset p)\supset \Box p \), but it is known that \(\textbf{GL}\) can also be axiomatized by an axiom \(\Box p\supset \Box \Box p\) and an \(\omega \) -rule \((\Diamond ^{*})\) which takes countably many premises \(\phi \supset \Diamond ^{n}\top \) \((n\in \omega )\) and returns a conclusion (...) \(\phi \supset \bot \). We show that the class of transitive Kripke frames which validates \((\Diamond ^{*})\) and the class of transitive Kripke frames which strongly validates \((\Diamond ^{*})\) are equal, and that the following three classes of transitive Kripke frames, the class which validates \((\Diamond ^{*})\), the class which weakly validates \((\Diamond ^{*})\), and the class which is defined by the Löb formula, are mutually different, while all of them characterize \(\textbf{GL}\). This gives an example of a proof system _P_ and a class _C_ of Kripke frames such that _P_ is sound and complete with respect to _C_ but the soundness cannot be proved by simple induction on the height of the derivations in _P_. We also show Kripke completeness of the proof system with \((\Diamond ^{*})\) in an algebraic manner. As a corollary, we show that the class of modal algebras which is defined by equations \(\Box x\le \Box \Box x\) and \(\bigwedge _{n\in \omega }\Diamond ^{n}1=0\) is not a variety. (shrink)

A recent article of Chernikov, Hrushovski, Kruckman, Krupinski, Moconja, Pillay, and Ramsey finds the first examples of simple structures with formulas which do not fork over the empty set but are universally measure zero. In this article we give the first known simple $\omega $ -categorical counterexamples. These happen to be various $\omega $ -categorical Hrushovski constructions. Using a probabilistic independence theorem from Jahel and Tsankov, we show how simple $\omega $ -categorical structures where a formula forks (...) over $\emptyset $ if and only if it is universally measure zero must satisfy a stronger version of the independence theorem. (shrink)

This paper concerns the relationship between transitivity of entailment, omega-inconsistency and nonstandard models of arithmetic. First, it provides a cut-free sequent calculus for non-transitive logic of truth STT based on Robinson Arithmetic and shows that this logic is omega-inconsistent. It then identifies the conditions in McGee for an omega-inconsistent logic as quantified standard deontic logic, presents a cut-free labelled sequent calculus for quantified standard deontic logic based on Robinson Arithmetic where the deontic modality is treated as a (...) predicate, proves omega-inconsistency and shows thus, pace Cobreros et al., that the result in McGee does not rely on transitivity. Finally, it also explains why the omega-inconsistent logics of truth in question do not require nonstandard models of arithmetic. (shrink)

Der Beitrag untersucht die Formation, also gleichermaßen die Genese und die Gestalt der Londoner Werkstatt ‚Omega‘ im frühen 20. Jahrhundert, die aus dem Bloomsbury Kreis hervorgegangen ist. Es handelt sich um einen dichten Zusammenhang von Lebens-, Arbeits- und Gestaltungsformen und das Zusammenspiel von affektiven und instrumentellen Beziehungsweisen auch in der Organisationsform, die durch weitgehende Strukturlosigkeit gekennzeichnet ist. Wie sich vor diesem Hintergrund Prozesse der Konstituierung, der Entscheidungsfindung und der oft verdeckten Hierarchiebildung in künstlerischen Gemeinschaften nachvollziehen lassen, wird vor der (...) Folie der gegenwärtigen Diskussion um Kollektive entfaltet. (shrink)

I present an outline of the Omega Point theory, which is a model for an omnipresent, omniscient, omnipotent, evolving, personal God who is both transcendent to spacetime and immanent in it, and who exists necessarily. The model is a falsifiable physical theory, deriving its key concepts not from any religious tradition but from modern physical cosmology and computer science; from scientific materialism rather than revelation. Four testable predictions of the model are given. The theory assumes that thinking is a (...) purely physical process of the brain, and that personality dies with the brain. Nevertheless, I show that the Omega Point theory suggests a future universal resurrection of the dead very similar to the one predicted in the Judeo‐Christian‐Islamic tradition. The notions of “grace” and the “beatific vision” appear naturally in the model. (shrink)

Journal of Mathematical Logic, Volume 23, Issue 02, August 2023. In mathematical logic there are two seemingly distinct kinds of principles called “reflection principles.” Semantic reflection principles assert that if a formula holds in the whole universe, then it holds in a set-sized model. Syntactic reflection principles assert that every provable sentence from some complexity class is true. In this paper, we study connections between these two kinds of reflection principles in the setting of second-order arithmetic. We prove that, for (...) a large swathe of theories, [math]-model reflection is equivalent to the claim that arbitrary iterations of uniform [math] reflection along countable well-orderings are [math]-sound. This result yields uniform ordinal analyzes of theories with strength between [math] and [math]. The main technical novelty of our analysis is the introduction of the notion of the proof-theoretic dilator of a theory [math], which is the operator on countable ordinals that maps the order-type of [math] to the proof-theoretic ordinal of [math]. We obtain precise results about the growth of proof-theoretic dilators as a function of provable [math]-model reflection. This approach enables us to simultaneously obtain not only [math], [math] and [math] ordinals but also reverse-mathematical theorems for well-ordering principles. (shrink)

We present the axioms of Alternative Set Theory in the language of second-order arithmetic and study its ω- and β-models. These are expansions of the form , M ⊆ P, of nonstandard models M of Peano arithmetic such that ⊩ AST and ω ϵ M. Our main results are: A countable M ⊩ PA is β-expandable iff there is a regular well-ordering for M. Every countable β-model can be elementarily extended to an ω-model which is not a β-model. The Ω-orderings (...) of an ω-model are absolute well-orderings iff the standard system SS of M is a β-model of A−2. There are ω-expandable models M such that no ω-expansion of M contains absolute Ω-orderings. There are s-expandable models which are not β-expandable. For every countable β-expansion M of M, there is a generic extension M[G] which is also a β-expansion of M. If M is countable and β-expandable, then there are regular orderings <1, <2 such that neither <1 belongs to the ramified analytical hierarchy of the structure , nor <2 to that of . The result can be improved as follows: A countable M ⊩ PA is β-expandable iff there is a semi-regular well-ordering for M. (shrink)

RESUMEN El siguiente artículo tiene como objetivo destacar el carácter polifónico del pensamiento platónico y poner en cuestión el sentido de la autoría de Platón. Suponer, a partir de obstinados prejuicios modernos, que Platón, tal como cualquier escritor moderno, habría expuesto su propia doctrina, es ignorar la importancia de la forma dramática de su pensamiento. El testimonio de la variedad de interlocutores y de puntos de vista que se suceden en los diferentes diálogos, nos invita a prestar atención a la (...) compleja trama del pensamiento platónico, cuya variedad de funciones corresponde a los límites y al alcance del discurso de quienes en un determinado momento y situación cooperan en el diálogo. ABSTRACT The following paper aims to highlight the polyphonic character of Platonic thought and to question the meaning of Plato's authorship. To assume, from obstinate modern prejudices, that Plato, like any modern writer, would have exposed his own doctrine, is to ignore the importance of the dramatic form of his thought. The testimony of the variety of interlocutors and points of view that take place in the different dialogues, invites us to pay attention to the complex plot of Platonic thought, whose variety of functions corresponds to the limits and scope of the discourse of those who, in a given moment and situation, cooperate in the dialogue. (shrink)

Reseña de "Punto de inflexión: Crisis climática y ecológica” de Pamela Poo.

I gratefully acknowledge and respond here to four reviews of my recent book, Cosmology from Alpha to Omega. Nancey Murphy stresses the importance of showing consistency between Christian theology and natural science through a detailed examination of my recent model of their creative interaction. She suggests how this model can be enhanced by adopting Alasdair MacIntyre's understanding of tradition in order to adjudicate between competing ways of incorporating science into a wider worldview. She urges the inclusion of ethics in (...) my model and predicts that this would successfully challenge the competing naturalist tradition in contemporary society. John F. Haught weighs the alternatives of viewing divine action as objective versus subjective and of divine action at one level in nature or at all levels. He asks whether physics is fundamental to nature, arguing instead that metaphysics should be considered as fundamental. Michael Ruse assesses occasional versus universal divine action, the problems raised to divine action when it is related to quantum mechanics, and the way these relations exacerbate the challenge of natural theodicy. As an alternative he suggests viewing God as outside time and acting through unbroken natural law. Willem B. Drees discusses my use of the bridge metaphor for the relation between theology and science, the implications when science is inspired by theology, the role of contingency and necessity in the anthropic principle/many-worlds debate, and the challenge of cosmology to eschatology with the ensuing problem of theodicy. (shrink)

El pensamiento de Unamuno es complejo y problemático. Realizar una lectura de los escritos de este autor, sin tomar previamente en consideración ciertos aspectos, puede resultar estéril y contradictoria. Examinando, a través de textos del propio autor, cómo concibe la “razón”, el “lenguaje”, la “filosofía” y la “realidad”, junto a la descripción de ciertos rasgos de su “personalidad”, queremos mostrar el talante verdaderamente filosófico de Unamuno, tantas veces puesto en cuestión. El presente artículo tiene como objeto exponer algunos puntos clave (...) que pueden servir como indicadores para descubrir la riqueza y profundidad que encierra la obra del filósofo vasco. Palabras clave: Unamuno; Razón; Lenguaje; Filosofía; Realidad. ABSTRACT The philosophical thinking of Unamuno is complex and problematic. Trying to interpret his writings previously taking into consideration certain aspects of his work could result fruitless and contradictory (paradoxical). The analysis of his conception of subjects like reason, language, philosophy and reality in his texts, together with the description of certain traits of his personality lead us to the real philosophical nature of his work, which has been repeatedly questioned by some authors. This paper is going to explain the main aspects of his work, which are the indicators to discover the true nature of the enriching and profound characteristics of the work of this Basque philosopher. Key words: Unamuno; Reason; Language; Filosofia; Reality. (shrink)

This paper reports on the integration of the higher-order theorem proving environment TPS [Andrews96] into the mathematical assistant OMEGA [Omega97]. TPS can be called from OMEGA either as a black box or as an interactive system. In black box mode, the user has control over the parameters which control proof search in TPS; in interactive mode, all features of the TPS-system are available to the user. If the subproblem which is passed to TPS contains concepts defined in (...) class='Hi'>OMEGA’s database of mathematical theories, these definitions are not instantiated but are also passed to TPS. Using a special theory which contains proof tactics that model the ND-calculus variant of TPS within OMEGA, any complete or partial proof generated in TPS can be translated one to one into an OMEGA proof plan. Proof transformation is realised by proof plan expansion in OMEGA’s 3-dimensional proof data structure, and remains transparent to the user. (shrink)

Sociologists studying gender have debated West and Zimmerman’s premise that “doing gender is unavoidable,” seeking to ascertain whether people can “undo” or only “redo” gender. While sociologists have been correct to focus on the interactional accomplishment of gender, they have neglected one of Garfinkel’s key insights about interaction: that people hold each other accountable to particular narratives. Neglecting the narrative aspect of doing—and undoing—gender impedes our ability to recognize processes of social change. Based on a qualitative study, we show how (...) the movement for LGBTQI acceptance within U.S. conservative Protestant churches works to make gender not “omnirelevant” by challenging conservative “complementarity” narratives that posit two complementary, opposite sexes as a commandment preceding the Ten Commandments in time and importance. We explore this movement’s ambivalent relationship with homonormativity, highlight three ways this movement resists projecting binary gender narratives into scripture, and examine how some in this movement see the pursuit of social justice as a Christian mandate. The efforts of LGBTQI conservative Christians exemplify how reshaping sex/gender/sexual narratives can create possibilities for undoing gender. (shrink)

An attempt to discover what can be learned from the recent work of Frank Tipler on the Omega Point theory requires an analysis of his framework of understanding from scientific, philosophical, and theological perspectives. A critique of his crucial ideas, and of the salient points raised by some of his critics, can then be undertaken within the compass of his strengths. A critique of the critiques of Tipler's work allows one to evaluate the extent and limitations of his contributions.

Depicts the history of the Omega Workshops, British decorative art studios, and examines the murals, furniture, pottery, textiles, and clothing produced by their members.

We examine the differences between three standard classes of forcing notions relative to the way they collapse the continuum. It turns out that proper and semi-proper posets behave differently in that respect from the class of posets that preserve stationary subsets of \.

Josef Pieper (1904–1997) wrote his autobiography in three distinct volumes. Composing one volume of his complete works in his Gesammelte Werke (Felix Meiner Verlag, 1995) edited by Berthold Wald, he writes on his early (1904–1945), middle (1945–1964), and late years (1964–1985). Between Ignatius Press and St. Augustine’s Press, Pieper’s autobiographical writings have been translated into English over the last three decades. The first volume, Noch wusste es niemand: Autobiographische Aufzeichnungen 1904–1945 (Kosel-Verlag, 1979), was translated into English as No One Could (...) Have Known: An Autobiography: The Early Years 1904–1945 (Ignatius, 1987). Three decades later the second volume, Noch nicht aller Tage Abend: Autobiographische Aufzeichnungen 1945–1964 (Kosel-Verlag, 1979), was published in English as Not Yet the Twilight: An Autobiography 1945–1964 (St. Augustine’s Press, 2017). Finally, the third volume, Eine Geschichte wie ein Strahl: Autobiographische Aufzeichnungen seit 1964 (Kosel-Verlag, 1988), has been published under the title A Journey to Point Omega: Autobiography from 1964 (St. Augustine’s Press, 2020). (shrink)

La visión tradicional del pensamiento crítico (PC) fundada en un enfoque racionalista ha sido puesta en duda a partir de fines del siglo pasado por la ‘segunda ola’ del PC, la cual, a pesar de no ser un movimiento del todo definido, ha incluido aspectos como la imaginación, la creatividad y el trabajo cooperativo en su comprensión y en su aplicación a la enseñanza. Paralelamente, perspectivas actuales en psicología moral como el modelo ‘intuicionista social’ propuesto por Jonathan Haidt, representan un (...) desafío al modelo racionalista de la moral que suponen gran parte de las éticas normativas canónicas. Siendo que tanto el PC como el fundamento moral representan factores fundamentales en la enseñanza de ética, se hace explicito que esta última precisa también ser revisada. Es por ello que el presente trabajo analiza una perspectiva del PC alternativa a la tradicional basada en el potencial aporte de la metacognición y del modelo intuicionista social, con el fin de abrir nuevas vías de investigación para la actualización del fundamento moral que se supone en la enseñanza de ética. Para ahondar en ello, se ejemplificará la relevancia y aplicabilidad de la metacognición en la enseñanza de ética con situaciones vinculadas a la actual pandemia por Covid-19. (shrink)

Este artículo examina algunos puntos de acuerdo y desacuerdo entre Francisco Suárez y Santo Tomás de Aquino en las áreas de la metafísica y la teología dogmática. Muestra que los desacuerdos en metafísica se deben al deseo de Suárez de evitar la reifi cación de conceptos después del desafío del nominalismo. En el campo de la teología dogmática, las diferencias se muestran entre Suárez y Santo Tomás en cristología, mariología y la relación entre la gracia y la libertad.

This article focuses on the Omega Point, an essential concept in Teilhard de Chardin’s evolutionary metaphysics. In certain passages about the Omega Point, Teilhard mentions the primeval atom hypothesis, a theory about the beginning of the universe proposed by Georges Lemaître, another contemporary Jesuit priest who was also a scientist. Although Teilhard and Lemaître are essentially evolutionists, besides being Jesuit priests, their evolutionary metaphysics and their philosophies of science are radically divergent, and two important differences are presented here (...) – about the eventual cosmic determinism and about the relationship between scientific knowledge and religious beliefs. This article also shows how Teilhard’s original concept was projected into two cosmological theories in which it reveals an essential transfiguration by losing its initial anthropic and religious matrix – the cosmological anthropic principle, proposed by physicists John Barrow and Frank Tipler, and the Omega Point Theory proposed later by Frank Tipler. (shrink)

The simultaneous publication in 1992 of two texts dealing with a global decline in sperm potency, P. D. James’s The Children of Men and Elisabeth Carlsen’s “Evidence for Decreasing Quality of Semen during the Past 50 Years,” inaugurates the exploration of another kind of sterility: the failure of feminist literary criticism and feminist science studies to converge as a fertile zone of inquiry and analysis. This article considers the modern discipline of literary studies, as well as feminist literary criticism and (...) feminist science studies, and suggests how Latour’s seven rules of method might be adapted to produce cross-fertilization between these fields... (shrink)

The Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega $$\end{document}-rule was introduced by W. Buchholz to give an ordinal-free proof of cut-elimination for a subsystem of analysis with Π11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^{1}_{1}$$\end{document}-comprehension. W. Buchholz’s proof provides cut-free derivations by familiar rules only for arithmetical sequents. When second-order quantifiers are present, they are introduced by the Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega $$\end{document}-rule and some residual cuts (...) are not eliminated. In the present paper, we introduce an extension of the Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega $$\end{document}-rule and prove the complete cut-elimination by the same method as W. Buchholz: any derivation of arbitrary sequent is transformed into its cut-free derivation by the standard rules. In fact we treat the subsystem of Π11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^{1}_{1}$$\end{document}-CA that W. Buchholz used for his explanation of G. Takeuti’s finite reductions. Extension to full Π11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi ^{1}_{1}$$\end{document}-CA is planned for another paper. (shrink)

Given an ideal $I$ , let $\mathbb{P}_{I}$ denote the forcing with $I$ -positive sets. We consider models of forcing axioms $MA(\Gamma)$ which also have a normal ideal $I$ with completeness $\omega_{2}$ such that $\mathbb{P}_{I}\in \Gamma$ . Using a bit more than a superhuge cardinal, we produce a model of PFA (proper forcing axiom) which has many ideals on $\omega_{2}$ whose associated forcings are proper; a similar phenomenon is also observed in the standard model of $MA^{+\omega_{1}}(\sigma\mbox{-closed})$ obtained from a supercompact cardinal. (...) Our model of PFA also exhibits weaker versions of ideal properties, which were shown by Foreman and Magidor to be inconsistent with PFA. Along the way, we also show (1) the diagonal reflection principle for internally club sets ( $\mathit{DRP}(IC_{\omega_{1}})$ ) introduced by the author in earlier work is equivalent to a natural weakening of “there is an ideal $I$ such that $\mathbb{P}_{I}$ is proper”; and (2) for many natural classes $\Gamma$ of posets, $MA^{+\omega_{1}}(\Gamma)$ is equivalent to an apparently stronger version which we call $MA^{+\operatorname{Diag}}(\Gamma)$. (shrink)

This paper presents a distinctively multiplicative quantificational principle that arguably captures the problematic aspects of Zardini's infinitary rules for a multiplicative quantifier within the context of the semantic paradoxes and the theoretical goal to obtain a (omega)-consistent theory of transparent truth. After showing that the principle is derivable with Zardini's rules and that one obtains through vacuous quantification an inconsistent theory of truth if truth is transparent, the paper presents two results regarding the principle and omega-inconsistency. First, the (...) principle is used to obtain a non-classical variant of McGee's omega-inconsistency result for certain classical theories of truth. Second, it is demonstrated that the conditions for a truth-theoretic variant of Bacon's omega-inconsistency result for certain non-classical theories of transparent truth implies that the principle holds for the paradoxical formula. Finally, the paper argues that the paradoxical reasoning that the principle enables is structurally similar to the kind of infinitary reasoning popularised by Hilbert's Grand Hotel. (shrink)

The work of Risieri Frondizi is an important historical and philosophical connection between the Hispanic world and American philosophy. Frondizi shares with the classical American pragmatists, especially with John Dewey, the same criticism of the starting point of modern philosophy, and a defense of ‘experience’ as the proper basis for any philosophical inquiry. Moreover, Frondizi can be read as making significant and original contributions to the history of doctrines such as pragmatism, which take ‘experience’ as their starting point.

The concept of freedom is not just another concept in Kierkegaard’s thought. On the contrary, it is one of the most significant issues which the Danish philosopher deals with. Thus, the article examines the meaning of this concept within the philosophy of Kierkegaard by following the interpretation of Cornelio Fabro. In order to achieve such a purpose, firstly, the general features of the thought of the Italian philosopher are presented. Subsequently, the metaphysical foundation for Human freedom within the thought of (...) Kierkegaard is developed. Afterwards, the radical determination of the will in its choice of evil and sin are analyzed, as well as the existential reality of Self as the first principle of action. Lastly, the dispute that Kierkegaard has with Hegel, which motivates his writings, is briefly exposed; and some of the ideas that Fabro takes from the Danish philosopher are listed. (shrink)