We elaborate Weiermann-style phase transitions for well-partial-orderings (wpo) determined by iterated finite sequences under Higman-Friedman style embedding with Gordeev’s symmetric gap condition. For every d-times iterated wpo ${\left({\rm S}\text{\textsc{eq}}^{d}, \trianglelefteq _{d}\right)}$ in question, d > 1, we fix a natural extension of Peano Arithmetic, ${T \supseteq \sf{PA}}$ , that proves the corresponding second-order sentence ${\sf{WPO}\left({\rm S}{\textsc{eq}}^{d}, \trianglelefteq _{d}\right) }$ . Having this we consider the following parametrized first-order slow well-partial-ordering sentence ${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{d}, \trianglelefteq _{d}, r\right):}$ $$\left( \forall K > 0 (...) \right) \left( \exists M > 0\right) \left( \forall x_{0},\ldots ,x_{M}\in {\rm S}\text{\textsc{eq}}^{d}\right)$$ $$\left( \left( \forall i\leq M\right) \left( \left| x_{i}\right| < K + r \left\lceil \log _{d} \left( i+1\right) \right\rceil \right)\rightarrow \left( \exists i < j \leq M \right) \left(x_{i} \trianglelefteq _{d} x_{j}\right) \right)$$ for a natural additive Seq d -norm |·| and r ranging over EFA-provably computable positive reals, where EFA is an abbreviation for IΔ 0 + exp. We show that the following basic phase transition clauses hold with respect to ${T = \Pi_{1}^{0}\sf{CA}_{ < \varphi ^{_{\left( d-1\right) }} \left(0\right) }}$ and the threshold point1. If r < 1 then ${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{d}, \trianglelefteq _{d},r \right) }$ is provable in T. If ${r > 1}$ then ${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{d}, \trianglelefteq _{d},r \right) }$ is not provable in T.Moreover, by the well-known proof theoretic equivalences we can just as well replace T by PA or ACA 0 and ${\Delta _{1}^{1}\sf{CA}}$ , if d = 2 and d = 3, respectively.In the limit case d → ∞ we replaceEFA-provably computable reals r by EFA-provably computable functions ${f: \mathbb{N} \rightarrow \mathbb{R}_{+}}$ and prove analogous theorems. (In the sequel we denote by ${\mathbb{R}_{+}}$ the set of EFA-provably computable positive reals). In the basic case T = PA we strengthen the basic phase transition result by adding the following static threshold clause ${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{2}, \trianglelefteq _{2}, 1\right)}$ is still provable in T = PA (actually in EFA). Furthermore we prove the following dynamic threshold clauses which, loosely speaking are obtained by replacing the static threshold t by slowly growing functions 1 α given by ${1_{\alpha }\left( i\right)\,{:=}\,1+\frac{1}{H_{\alpha }^{-1}\left(i\right) }, H_{\alpha}}$ being the familiar fast growing Hardy function and ${H_{\alpha }^{-1}\left( i\right)\,{:=}\,\rm min \left\{ j \mid H_{\alpha } \left ( j\right) \geq i \right\}}$ the corresponding slowly growing inversion. If ${\alpha < \varepsilon _{0}}$ , then ${\sf{SWP}\left({\rm S}\text{\textsc{eq}}^{2}, \trianglelefteq _{2}, 1_{\alpha}\right)}$ is provable in T = PA. ${\sf{SWP}\left( {\rm S}\text{\textsc{eq}}^{2}, \trianglelefteq _{2},1_{\varepsilon _{0}}\right)}$ is not provable in T = PA. We conjecture that this pattern is characteristic for all ${T\supseteq \sf{PA}}$ under consideration and their proof-theoretical ordinals o (T ), instead of ${\varepsilon _{0}}$. (shrink)

Self-driving cars currently face a lot of technological problems that need to be solved before the cars can be widely used. However, they also face ethical problems, among which the question of crash-optimization algorithms is most prominently discussed. Reviewing current debates about whether we should use the ethics of the Trolley Dilemma as a guide towards designing self-driving cars will provide us with insights about what exactly ethical research does. It will result in the view that although we need the (...) ethics of the Trolley Dilemma as important input for self-driving cars, the route towards simply implementing it into automated cars is blocked. (shrink)

:Brain–computer interfaces are driven essentially by algorithms; however, the ethical role of such algorithms has so far been neglected in the ethical assessment of BCIs. The goal of this article is therefore twofold: First, it aims to offer insights into whether the problems related to the ethics of BCIs can be better grasped with the help of already existing work on the ethics of algorithms. As a second goal, the article explores what kinds of solutions are available in that body (...) of scholarship, and how these solutions relate to some of the ethical questions around BCIs. In short, the article asks what lessons can be learned about the ethics of BCIs from looking at the ethics of algorithms. To achieve these goals, the article proceeds as follows. First, a brief introduction into the algorithmic background of BCIs is given. Second, the debate about epistemic concerns and the ethics of algorithms is sketched. Finally, this debate is transferred to the ethics of BCIs. (shrink)

In this incisive study, John F. X. Knasas grounds the ideal of tolerance in Aquinas’s natural law ethics and connects the virtue of civic tolerance to the concept of being. If God is the source of being, argues Knasas, then we are the articulation of being, and it is in this capacity that we recognize our bond with other people and thus acknowledge our duty to be tolerant of one another. An important contribution to practical metaphysics and the philosophical foundations (...) of political theory, _Thomism and Tolerance_ will appeal to philosophy scholars and students at the undergraduate and graduate level. (shrink)

My article critically evaluates five key claims in Kerr’s interpretation of Aquinas’s De Ente et Essentia, ch. 4, proof for God. The claims are: the absolutely considered essence is a second intention, or cognitional being; à la John Wippel, the real distinction between essence and existence is known before the proof; contra David Twetten, Aristotelian form is not self-actuating and so requires actus essendi; the De Ente proof for God uses the Principle of Sufficient Reason; an infinite regress must be (...) eliminated before concluding to God. This author wonders if these questionable claims are traceable to the mindset of analytic philosophy which values precision and discreteness and so can fail to appreciate crucial paradoxes in Aquinas’s metaphysics. (shrink)

Inspired by a discussion about whether John Paul II grounded human dignity in a Kantian way, viz., emphasizing the person as an end unto itself, the author considers: the relations between Kant and Aquinas on the topic of the philosophical basis of human dignity, and John Paul II’s remarks on Kant’s ethics. He concludes that: both Kant and Aquinas ground human dignity upon human freedom, but both understand the human freedom differently; for Kant, human freedom is self-legislating and so exercised (...) without rational direction; the Thomistic notion of freedom is compatible with rational direction which consists, e.g., in the human understood as an intellector of being or as a willer of the good, though neither seem to be exploited by Wojtyla. (shrink)

By providing a phenomenological presentation of Aquinas’s duplex operatio intellectus, the author argues that a reader is better equipped to understand where and when Aquinas arrives at the real distinction between essence and existence in the much disputed De Ente et Essentia, chapter four. “Phenomenological presentation” means an honest description of one’s own mental life as it conducts the duplex operatio. From phenomenological observations in the Thomistic texts, the author argues that a penetrative and rebounding movement of attention upon some (...) initially presented multiplicity characterizes the duplex operatio. When this dynamic is conducted upon the multiplicity of a real thing juxtaposed to itself cognitionally existing in sensation, the rebound of the secunda operatio presents the real existence in a sui generis relation of priority to the individual thing understood as existence neutral. Unfortunately, the rebound of attention is too quick to discern accurately the nature of the borderline between the attribute of existence and its subject, the individual thing. The attribute of existence may actuate the thing by shading into it or by remaining distinct from it. Fortunately, the phenomenological situation is sufficient to leave phenomenology and to initiate the third intellectual operation of reasoning. Reasoning concludes to a first cause of phenomenologically observable attributive existence. In this first cause existence is the thing itself. In order for this first cause to have its proper effect corresponding to what it is, the author argues that the second of the above two alternatives for phenomenologically observable attributive existence must be the true one. After linking these reflections to stages of De Ente, chapter 4, the author critically relates them to other interpretations of the text. These interpretations include those of Cahalan, McDonald, Wippel, Dewan, Patt, Kenny, and Owens. (shrink)

M. Bonnefond-Coudry has performed a great service by compiling a list of senators who are known to have spoken in the senate in the first century b.c. Yet her list for the year 50 invites a thoroughgoing revision. Beside the rubric ‘supplicatio à Cicéron’ she gives the following list: Cato, Hirrus, Balbus, Lentulus, Domitius, Scipio, Favonius. She also notes that Pompey spoke at a session late in the year, and maintains that Scipio spoke on 1 December.

In this powerfully argued book, Knasas engages a debate at the heart of the revival of Thomistic thought in the twentieth century. Richly detailed and illuminating, his book calls on the tradition established by Gilson, Maritain, and Owen, to build a case for Existential Thomism as a valid metaphysics.Being and Some Twentieth-Century Thomists is a comprehensive discussion of the major issues and controversies in neo-Thomism, including issues of mind, knowledge, the human subject, free will, nature, grace, and the act of (...) being. Knasas also discusses the Transcendental Thomism of Maréchal, Rahner, Lonergan, and others as he builds a carefully articulated case for completing the Thomist revival. (shrink)

A complex world like ours demands for the teachers and professors to command intercultural competences in order to avoid the instrumentalization of the alterities. It is precisely the professionals of education who, given their social function, have the responsibility of forming the citizens of the future in attitudes and behaviours adjusted to plural communities. This article presents the first part of a research project carried out by researchers from Barcelona, Marseille, Rabat and Beirut on the complex world of the respect (...) necessary to face prejudices and stereotypes. (shrink)