On the omniscience of Aristotle\u2019s unmoved mover: a note on Metaphysics \u39b 4, 1070 b 34-35

This paper focuses on the final passage of Metaphysics \u39b 4, which contains the first explicit mention of the unmoved mover in book \u39b. The sentence is crucial for the problem of what, if anything, the Aristotelian god knows about the world. The author starts with a general enumeration of the main interpretations of the problem of the omniscience of god, which either admit a divine activity upon the world (Alexander of Aphrodisias, Thomas Aquinas), or that, by thinking himself, god thinks everything (Thomas Aquinas) or that, in knowing himself, he knows beings (Averro\uebs), or, finally, state that god knows only himself (Schwegler, Bonitz, Zeller, Ross and many others). In this section the importance of Metaphysics \u39b 9 has been stressed, which constitutes the only complete text on the topic which has come down to us, and where Aristotle, as it is well known, denies that god has knowledge of the world. \u39b 9 is, therefore, an essential and necessary reference for any other passage which contains a mention of the matter in question. In the following section, the paper analyzes the context in which the final passage of \u39b 4 is inserted. The attempt is to show that the reference to the unmoved movers in \u39b 4 is not introduced abruptly, but rather that it fits perfectly in the discussion of the chapter. The third section contains the analysis of the passage. In particular, the suggestion proposed by R. George is considered, who, after having recalled F. Brentano\u2019s position, asserts that the sentence would imply that the first of all things contains within itself the formal principle of what it brings forth, and that, since the first mover moves all things, it actually is all things. This paper aims to show that the first cause of all things, whose mention follows the enumeration of the four causes \u2013 matter, form and privation as 2 immanent elements, and the moving cause of natural substance as external principle \u2013, is not within the coincidence of formal and moving cause. Therefore the case of the proximate moving cause (for example the builder), which knows its effect (for example the form of the house), appears as different from the case of the first remote moving cause which moves all things, which does not seem to have knowledge of the world. This paper suggests that the coincidence between the formal and the moving cause may only work for natural substances and, therefore, for the moving cause in the weaker sense, while it does not apply to the remote moving cause. In this perspective the fact that the Aristotelian god cannot be a formal cause plays a fundamental role, being an external and separated principle. Consequently, the role of the mention of the unmoved mover in the final passage of \u39b 4 does not appear as a reference which is completely detached from the rest of the text, but it seems to perfectly fit in it and indeed appears to play a central role in the entire chapter

Is Aristotle's place really a surface? On Aristotle's concept of place in Physics IV and Categories 6

The attribution to Aristotle of the concept of place as bi-dimensional is firstly based on the identification of place with a surface, supposedly carried out by Aristotle in Physics IV. The identity of place with surface would indeed imply that place were missing the third dimension of depth, for the notion of surface was historically related to the notion of plane. Hence, since natural beings are, by definition, moving beings, and they have a three-dimensional extension, the doctrine of the bi-dimensionality of place would imply the impossibility to explain movement. Depth of place also seems to be neglected in another passage, in which Aristotle rejects the third definition of place as an extension between the extremities of the contained body. Scholars who admit the bidimensionality of Aristotelian place emphasize the contrast between the Aristotelian theory of place expounded in Physics and the theory contained in Categories, where the three-dimensionality of place is explicitly admitted. The aim of this paper is to try to convey additional arguments in favour of the three-dimensionality of Aristotelian place, based on the criterion of a more literal reading of the Aristotelian text

The Unity of Aristotle\u2019s Metaphysics: Book \u395 according to the Interpretation of the Ancient Commentators

This paper discusses the three ancient commentaries on Book E of Aristotle\u2019s Metaphysics, that have been handed down to us. It aims to demonstrate the fundamental part played by their particular interpretation of Aristotle\u2019s doctrines in the birth of the traditional interpretation of his Metaphysics, according to which all the books comprising the work were written as a function of Book \u39b, containing the well-known doctrine of the unmoved mover. Among the main elements supporting this assumption there is Aristotle\u2019s distinction between three types of science - the theoretical, the practical and the productive - and his claiming the primacy of metaphysics as a theological science. According to the ancient commentators, the remainder of Book E would belong to the unitary project of the Metaphysics, since it would indicate what is not encompassed in the object of metaphysics. This would mean that Aristotle\u2019s treatment of accidental being, being as truth and not-being as falsity, and being potentially and actually would take on a negative function. The theological interpretation of Aristotle\u2019s Metaphysics thus retains its ultimate foundations in premises contained in the Aristotelian text itself

The Notion of Being as Act in Neoplatonism and Its Transmission in the Translatio Studiorum

The problem related to the origin of the concept of actus essendi constitutes one of the central themes in the history of ancient philosophy, and is one of the most important in the process known as Translatio studiorum. The idea according to which Thomas Aquinas was the first to consider this concept has been contrasted to the idea that actus essendi had already been present in Neoplatonism. In fact, the concept of \u201cbeing\u201d in Thomas Aquinas\u2019 philosophy has been interpreted in many different ways over the years, especially in relation to Aristotle\u2019s concept of being. In his book about being according to Thomas, G. Ventimiglia recognizes three generations within the historiography on Thomistic ontology. The first generation, begun by R. Garrigou-Lagrange, lasted until the end of the 1930s and maintained that the being of Thomas equalled Aristotle\u2019s. During the second generation, lasting from the beginning of the 1930s till the end of the \u201950s and whose main exponent was E. Gilson, the being of Thomas is seen as the actus essendi. These scholars therefore interpreted it as a completely new and original concept compared to both Aristotle\u2019s being and the Neoplatonic school of thought, by which Thomas may have been influenced. Lastly, the third generation, in which Thomas\u2019 concept of being is considered to be unoriginal, having been elaborated within the world of Neoplatonism, originated at the beginning of the 1970s and lasts yet today. W. Beierwaltes and K. Kremer, among others, have lead this final generation. However, together with Ventimiglia, it is necessary to recognize the importance that the publication of two other works had on the assertion made by the \u201cthird generation\u201d. These works are P. Hadot\u2019s volume on Porphyre et Victorinus, published in 1968 and Beierwaltes\u2019 book entitled Platonismus und Idealismus, published in 1972. In the latter\u2019s book, the author demonstrates that the identification of God with being had been made by Plutarch and Porphyry as well as by Philo of Alexandria, Gregory of Nazianzus, Gregory of Nyssa, Victorinus and Augustine. In Hadot\u2019s volume, together with the observation that this identification had been expressed in Neoplatonism, also the definition of being as act is traced back to the same period. In the paper it is discussed the section of Hadot\u2019s study which appears in the appendix of the second volume, containing the text and the translation of the fragments of the anony\uacmous commentary to Plato\u2019s Parmenides. It also considered the introductory essay added in the Italian translation of this section. It is thanks to Hadot and the exponents of Ventimiglia\u2019s \u201cthird generation\u201d that the communis opinio, according to which the concept of actus essendi can be found first in the philosophy of Thomas, was disproved. Hadot in particular demonstrated that the notion of \u201cact of being\u201d originated from both the anonymous commentary to the Parmenides by Plato, which he attributes to Porphyry, and the Enneads by Plotinus. This paper will first examine the fragments of the commentary in order to show that in it may be found both the identification of God with being and the concept of being as actus essendi. An analysis of Enneads VI 8, 7 will follow. This is one of the passages in the work by Plotinus which most deserves to be considered in order to verify the effective anticipation of Neoplatonism in a doctrine that has traditionally been considered of Thomistic origin. Finally, of particular interest is the comparison between being as interpreted by Neoplatonism, especially by Plotinus, and act as conceived by Aristotle, unanimously recognized as its discoverer

Childbearing preferences and family issues in Europe: evidence from the Eurobarometer 2006 survey

This article provides an overview of major findings described in the report on 'Childbearing Preferences and Family Issues in Europe' written at the request of the European Commission, Directorate-General Communication, Opinion Polls (Testa 2006). The report confirms the emergence of below-replacement family size ideals in Europe: Austrian women aged 25-39 show indeed a mean value of 1.7 children. As expected, ideals are higher than actual or intended fertility, and when we add up the number of children already born with those people still intend to have in the future, several other countries show an average ultimately intended family size of less than two children. The presence of a supportive partner is the most important circumstance in childbearing decisions, and consistently, the lack of the right partner for raising children is the most frequent reason given for not meeting the fertility desires formulated at the beginning of the reproductive career. The contribution of both partners is considered necessary for a good family life, but the role of mothers is judged to be the more crucial one. Countries more liberal in terms of gender roles in family life also show preferences for larger families.

Lower bounds for regular genus and gem-complexity of PL 4-manifolds

Within crystallization theory, two interesting PL invariants for $d$-manifolds have been introduced and studied, namely {\it gem-complexity} and {\it regular genus}. In the present paper we prove that, for any closed connected PL $4$-manifold $M$, its gem-complexity $\mathit{k}(M)$ and its regular genus $\mathcal G(M)$ satisfy: $$\mathit{k}(M) \ \geq \ 3 \chi (M) + 10m -6 \ \ \ \text{and} \ \ \ \mathcal G(M) \ \geq \ 2 \chi (M) + 5m -4,$$ where $rk(\pi_1(M))=m.$ These lower bounds enable to strictly improve previously known estimations for regular genus and gem-complexity of product 4-manifolds. Moreover, the class of {\it semi-simple crystallizations} is introduced, so that the represented PL 4-manifolds attain the above lower bounds. The additivity of both gem-complexity and regular genus with respect to connected sum is also proved for such a class of PL 4-manifolds, which comprehends all ones of "standard type", involved in existing crystallization catalogues, and their connected sums.Comment: 17 pages, 3 figures. To appear in Forum Mathematicu

A note about complexity of lens spaces

Within crystallization theory, (Matveev's) complexity of a 3-manifold can be estimated by means of the combinatorial notion of GM-complexity. In this paper, we prove that the GM-complexity of any lens space L(p,q), with p greater than 2, is bounded by S(p,q)-3, where S(p,q) denotes the sum of all partial quotients in the expansion of q/p as a regular continued fraction. The above upper bound had been already established with regard to complexity; its sharpness was conjectured by Matveev himself and has been recently proved for some infinite families of lens spaces by Jaco, Rubinstein and Tillmann. As a consequence, infinite classes of 3-manifolds turn out to exist, where complexity and GM-complexity coincide. Moreover, we present and briefly analyze results arising from crystallization catalogues up to order 32, which prompt us to conjecture, for any lens space L(p,q) with p greater than 2, the following relation: k(L(p,q)) = 5 + 2 c(L(p,q)), where c(M) denotes the complexity of a 3-manifold M and k(M)+1 is half the minimum order of a crystallization of M.Comment: 14 pages, 2 figures; v2: we improved the paper (changes in Proposition 10; Corollary 9 and Proposition 11 added) taking into account Theorem 2.6 of arxiv:1310.1991v1 which makes use of our Prop. 6(b) (arxiv:1309.5728v1). Minor changes have been done, too, in particular to make references more essentia