ABSTRACT In recent debates about conceptual engineering, it appears that the internalist has an explanatory advantage when it comes to accounting for meaning change and conceptual change. In this paper, I argue against this impression. I show how two different varieties of externalism, originalism and anti-individualism, can coherently explain various cases of meaning change, irrespective of whether they involve proper names or kind terms; and also irrespective of whether they occur in everyday, legal, or scientific contexts. I point out which (...) mechanisms and interpretational strategies the originalist and anti-individualist can invoke, relative to their respective background assumptions about the nature of concepts. Furthermore, I offer an argument in favour of the claim that externalism as such has no implications concerning whether concepts can undergo change. I establish this by showing that originalism allows for conceptual change while anti-individualism insists on conceptual stability. (shrink)

Vector spaces over fields are pseudofinite, and this remains true for vector spaces over division rings that are finite-dimensional over their center. We also construct a division ring such that the nontrivial vector spaces over it are not pseudofinite, using Richard Thompson's group F. The idea behind the construction comes from a first-order axiomatization of the class of division rings all whose nontrivial vector spaces are pseudofinite.

For any group satisfying a suitable chain condition, we construct a finitely additive measure on it that is invariant under certain actions.

In lieu of an abstract, here is a brief excerpt of the content:PLATO'S PARMENIDES AND ST. THOMAS'S ANALYSIS OF GOD AS ONE AND TRINITY SHERWIN KLEIN Fairleigh Dickinson University Hackensack, New Jersey IN HIS CRITICISM of the Neopfatonic interpretation of the Parmenides, Cornford says, "The fanguage throughout is as dry and prosaic as a textbook on algebra; there is little here to suggest that the One has any religious significance as there is in the other case to suggest that x, (...) y, and z are a trinity of unknown gods." 1 I agree with Cornfo11d that the Neopl1 atoniJc interpreta.tion is very speculative and seriously flawed. Nonethe1ess, the "negative theology" these interpreters attribute to Plato is instruic1tive. More than this, it can be shown that opinions like Cornford's are, to say the least, unimaginative. I intend to est1 ablish, in the first and main part of this artide, the logical agreement between the PJatonic and Thomistic analyses of an absoJuteiy simple unity. The argument at Parmenides 137b-142a, Blato's analysis of the absoluteJy one, prov ]des a basis for determining what God, as an absolutdy simple unity, is not. By applying this 'argument in the Parmenides to St. Thomas's discussion of God as one, I shaill show that what appears to be " as dry and prosai:c as a textbook on algebra " has, contrary to Cornfo11d, " religious significance." In the second part of this article, I shall use the arguments at Parmenides 157b-159b and 159b-160b to determine what can 1 Plato and Parmenides: Parmenides' Way of Truth and Plato's Parmenides, trans. with introduction and commentary by Francis MacDonald Cornford (London: Routledge and Kegan Paul, 1939), p. 131. 229 230 SHERWIN KLEIN be predicated of God, if St. Thomas's analysis of the Trinity is to aoco:rd with the articles of faith (God as an abso1utely simple unity as weU as a Trinity). Once again, we shall see the ":religious significance" of Plato's analysis and the irony of Cornfo11d's suggestion about the meaninglessness of applying Plato's analysis to " a trinity of unknown gods." I We should first he clear about how St. Thomas uses the term "one" as applied to God. In Q. n, A. 1 of the Prima Pars (The Unity of God),2 he distinguishes between one as "the negation of division" and one as "the principle of number." The first sense, which he calls the transcendental sense, applies to God; in this sense the one is opposed to the many as the undivided is :to the divided. Human beings cannot know what God is, but we can determine what God is not, e.g., not-many, the transcendental sense of being absolutely simple. (The human intdlect can only know the composite or tha,t which pertains to the composite; it cannot know that which is abso1ut ~ly sample or undivided.) St. Thomas says, "He is supremely undivided inasmuch as He is divided neither actually nor potentially by any mode of division; since He is altogether simple." 3 If we :compare the analysis of God as absolutely one or simple with the first hypothesis of the one in the Parmen~des, i.e., if the one is one, what can be predicated of it, then we shall notice an important similarity. If the one is simply one, none of the categories which can determine the nature of the one are predicable of it. Similarly, God as absolutely one or simple cannot be understood in,a positive manner (His nature is incomprehensible). However, He can be understood negatively. And what we can say negatively about God parallels 2 References are to the Summa Theologica in Basic Writings of Saint Thomas Aqu-Ynas, ed. Anton C. Pegis, vol. I (New York: Random House, 1945). a ST, I, q. 11, a. 4, c.; Pegis, p. 90. PLATO AND AQUINAS 231 Plato's determination of what is not predicable of the one as simple. To show what God is not, we must negate what does not apply to Him; this reveals the simplicity of God. If the one is one (in St. Thomas's transcendenta.l sense of "one " as simple ), says Plato, it cannot be many and, therefor:e, cannot have... (shrink)

We extend the field of Laurent series over the reals in a canonical way to an ordered differential field of “logarithmic-exponential series” , which is equipped with a well behaved exponentiation. We show that the LE-series with derivative 0 are exactly the real constants, and we invert operators to show that each LE-series has a formal integral. We give evidence for the conjecture that the field of LE-series is a universal domain for ordered differential algebra in Hardy fields. We define (...) composition of LE-series and establish its basic properties, including the existence of compositional inverses. Various interesting subfields of the field of LE-series are also considered. (shrink)

Peter Singer’s defense of the duty to aid the world’s poor by the pond analogy is self-defeating. It cannot be both true that you ought to save the drowning child from a pond at the expense of ruining your shoes and that you ought to aid the world’s poor if you thereby do not sacrifice anything of comparable moral importance. Taking the latter principle seriously would lead you to let the child in front of you drown whenever you could thereby (...) save more children in the developing world. Though Singer can defend the duty to aid the world’s poor starting from consequentialist principles requiring you to make things go best in the impartial sense, he cannot have it invoking the commonsense judgment about what you ought to do in the pond case. There is no sound path from commonsense morality to Singer’s principles of beneficence. (shrink)

We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.

I solve here some problems left open in “T-convexity and Tame Extensions” [9]. Familiarity with [9] is assumed, and I will freely use its notations. In particular,Twill denote a completeo-minimal theory extending RCF, the theory of real closed fields. Let (,V) ⊨Tconvex, let=V/m(V)be the residue field, with residue class mapx↦:V↦, and let υ:→ Γ be the associated valuation. “Definable” will mean “definable with parameters”.The main goal of this article is to determine the structure induced by(,V)on its residue fieldand on its (...) value group Γ. In [9] we expanded the ordered fieldto a model ofTas follows. Take a tame elementary substructure′ ofsuch thatR′ ⊆VandR′maps bijectively ontounder the residue class map, and make this bijection into an isomorphism′ ≌ofT-models. (We showed such′ exists, and that this gives an expansion ofto aT-model that is independent of the choice of′.). (shrink)

In this volume, Baumstark deals with the transmission of Aristotelian philosophy into Syriac and Arabic. Syriac texts with German translations are included, alongside a detailed study of their textual interrelationships.

The differential field of transseries extends the field of real Laurent series and occurs in various contexts: asymptotic expansions, analytic vector fields, and o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field and report on our efforts to understand its elementary theory.

We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.

In lieu of an abstract, here is a brief excerpt of the content:BreathingLuk Van den Dries (bio)This text, "Breathing," was conceived for the book From Act to Acting: Fabre's Guidelines for the Performer of the 21st Century (2021). The book was conceived and designed by Jan Fabre, author, theatre artist, and visual artist, active since the 1970s. The book was written by Luk Van den Dries, dramaturg and theatre researcher of the University of Antwerp, in tight collaboration with (...) Jan Fabre and the three most important performers/teachers of the Belgian theatre company, Troubleyn (Annabelle Chambon, Cédric Charron, and Ivana Jozic). The book sheds new light on the physical, mental, and vocal training of the performer and furthermore gives insight into Fabre's revolutionary thoughts on contemporary theatre.1Breathing is the first of the ten performative principles that together create the basic grammar in which the language of the performers is grounded.Three-phased breathing (one part in, one part out, one part nothing) is a basic condition in the series of exercises Jan Fabre developed throughout his career. This respiration technique returns in all exercises. Also, it is the first principle that the performers are taught: by dividing breathing into three equal parts, energy is built up and stress or fatigue is canalized. It is a way to rebalance, to find a place of rest after a strenuous effort, or it can also be used as a springboard to a heightened performance. Very regularly during individual exercises, Fabre will refer to this respiration technique, especially in specific situations of high adrenaline, but of course the performers should learn to use this respiration technique autonomously. They should become so familiar with the rhythm of this breathing that they automatically fall back on it when necessary. Because this respiration technique is so crucial to Fabre's acting pedagogy, it is described in detail as the very first exercise in his book. Its basic principles are explained below as well, as the first performative principle.Breathing is a sign of life, and on this primal and essential level it needs to be understood that, through breathing, the performer gives life. He breathes life into the performance. Fabre himself has described this basic condition for the birth of theatre through breathing very precisely: [End Page 30]The most important weapon of the warrior of beauty is his respiration. When the performance starts, life stops. Life itself dies. The warrior of beauty is alive, but life itself is dead. The warrior of beauty remains with just his own breath. When he enters the stage, he needs to breathe life into deceased life. Like a god gives his breath to create life. In the same way he will create life with his breath. How will he achieve this? By breathing correctly: one-third inhaling through the nostrils, one-third exhaling through pursed lips, one-third without breathing. And then the miracle happens. The breath becomes imagination and the imagination breathes. The warrior of beauty is the master of breath and life.2Fabre's abdominal breathing differs from regular forms of breathing, such as techniques derived from Asian yoga techniques, Chi-kung or Tai-chi, as it stresses different parts. At the same time, it is closely related to it, because these practices also adopt the notion that breathing in the first place rouses vitality and spirit and that the right kind of breathing thus aims at controlling life currents and bringing about a clear mind. In yoga it is called pranayama: prana meaning spirit or force of life, ayama meaning 'control' or 'grasp.' Yoga knows many variants in directing the breath, depending on the asanas (yoga postures) in which they are bedded. Sometimes focusing mainly on the diaphragm and the flanks, sometimes on abdominal breathing. Also, suspending your breath (kumbhaka) is a yoga technique, applied at the end of inhalation as well as after exhalation and during taking breath.In Fabre's case, abdominal breathing is stressed: first, air is inhaled through the nose, subsequently sent in the direction of the peritoneal cavity and the flanks, and then again exhaled via a very precise blowing technique (a dosed flow of air through an imaginary straw). During the cycle the diaphragm remains... (shrink)

The Euclidean algorithm on the natural numbers ℕ = {0,1,…} can be specified succinctly by the recursive programwhere rem is the remainder in the division of a by b, the unique natural number r such that for some natural number q,It is an algorithm from the remainder function rem, meaning that in computing its time complexity function cε, we assume that the values rem are provided on demand by some “oracle” in one “time unit”. It is easy to prove thatMuch (...) more is known about cε, but this simple-to-prove upper bound suggests the proper formulation of the Euclidean's optimality among its peers—algorithms from rem:Conjecture. If an algorithm α computes gcd from rem with time complexity cα, then there is a rational number r > 0 such that for infinitely many pairs a > b > 1, cα > r log2a. (shrink)

The Euclidean algorithm on the natural numbers ℕ = {0,1,…} can be specified succinctly by the recursive programwhere rem is the remainder in the division of a by b, the unique natural number r such that for some natural number q,It is an algorithm from the remainder function rem, meaning that in computing its time complexity function cε, we assume that the values rem are provided on demand by some “oracle” in one “time unit”. It is easy to prove thatMuch (...) more is known about cε, but this simple-to-prove upper bound suggests the proper formulation of the Euclidean's optimality among its peers—algorithms from rem:Conjecture. If an algorithm α computes gcd from rem with time complexity cα, then there is a rational number r > 0 such that for infinitely many pairs a > b > 1, cα > r log2a. (shrink)

The aim of our study is to single out a possible path towards the recognition culture in a world strained by deep social cleavages and by a strong conflict among values. In this context, we consider that a recognition culture is possible only by activating the comprehensive being that each of us, humans, is. The study attempts to answer the desideratum of the recognition culture by developing a model of the political founded on the correlation of certain aspects of the (...) human and of the political. The identification of the hypostases of the political and the human and the correlations between them help us understand one of the specific anthropo-political mechanisms that may allow us to reach the recognition culture that is based on accepting the other and assuming one’s own fallibility. This is what we define as the anthropological model of the comprehensive political. (shrink)

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

An influential objection to the view that intentions are non-derivatively relevant to the moral permissibility of actions states that if intentions were relevant to permissibility in such a way, one would have to take them into account in decision making, which would be odd (in some morally relevant sense of ‘oddness’). The paper outlines and assesses three candidates for the oddness: that considering intentions in decision making is an unordinary practice, that it is impossible or conceptually confused, and that it (...) assigns intentions the weight as moral considerations that they intuitively do not have. The paper rejects the first two and shows that the third is probably what motivates most critics of the relevance of intentions who raise this objection. If this is correct, the objection is a non-starter as it assumes what it has to prove. Towards the end, it is argued that the objection does not serve as a plausible error theory either. (shrink)

The aim of this paper is to single out the path towards a model of fallibility assumed by the establishment and implementation of the culture of recognition and comprehensive truth. Starting from the hypostases of the human, this anthropological model defines the fallible human being, the author of the comprehensive truth oriented towards the culture of recognition. The main idea of this demarche is, in fact, that between recognition and comprehension there is a deep, organic connection and the comprehensive truth (...) lies at the basis of the culture of recognition. (shrink)

This study endeavours to demonstrate the dynamic “tolerance-recognition” in view of a comprehensive paradigm. Tolerance is presumed to be a „modus vivendi” – that is, the recognition of multiple ways of finding the good and happiness by human communities. In this context, the author proposes, as a heuristic device, a model of humanity based upon correlations between nature, condition, and essence as hypostases of humanity. In this way the study attempts to contribute to the planning of a necessary politics and (...) culture of recognition. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Notes and Discussions ARISTOTLE'S ALLEGED "REVOLT" AGAINST PLATO Hermippus' most conspicuous contribution to Aristotle's biography probably was his determined effort to depict Aristotle as the founder of an original school of philosophy which was wholly independent of Plato and Platonic teachings. Among the several and, in all likelihood, fanciful stories about Aristotle he invented or propagated, the most startling was the account, subsequently widely accepted (and widely exploited by (...) the detractors of Aristotle), that after having been a disciple of Plato for a while, he seceded from the Academy and from Plato's philosophic teachings while Plato was still alive. 1 Accordingly, he owed little to Plato and to the Academy. This story, invented and propagated by an inveterate Peripatetic (Hermippus), was intended to demonstrate the original philosophic genius of Aristotle which developed in complete independence of Plato and necessitated a break with the master's teachings. In devising his argument, Hermippus might have made use of a report, found in some of Aristotle's ancient biographers, that a few brash young men (members of the Academy?) revolted against Plato and, in a spirit of independence, defiance and antagonism, attempted to start a school of their own which would rival the intellectual standing of the Academy. 2 Hermippus, it appears, subsequently identified these young "rebels" with Aristotle, a substitution convenient to Hermippus" aim to depict Aristotle as a wholly independent and totally original philosopher who owed nothing whatever to Plato and his teachings. In all likelihood, Diogenes Laertius' statement that Aristotle "seceded from the Academy while Plato was still alive," a is just an echo either of a statement made by Hermippus himself or is a conclusion drawn from the several unpleasant stories about Aristotle invented and reported by some of Aristotle's detractors. According to these derogatory stories, there existed many serious personal as well as doctrinal 4 disagreements or rifts between Plato and the Stagirite--disagreeDiogenes Laertius, V. 2. See also Eusebius, Praeparatio Evangelica, XV. 2. 3, and ibid., XV. 2. 13 (Aristoxenus); Aelian, Varia Historia, IV. 9; Theodoretus, Graecorum Affectionum Curatio, IV. 46; St. Augustine, De Civitate Dei, VIII. 12; Philoponus, Comment. in Aristotelis Analytica Posteriora, CIAG, vol. XIII, part 3, pp. 133, 30 ft. 2 See Aelius Aristides, Oratio XLVI, 249. 10. See also note 1, supra. s Diogenes Laertius, V. 2. See also Vita Aristotelis Marciana 9; Vita Aristotelis Latina 9. 9 See, for instance, Plutarch, Adversus Coloten 14 (Moralia, III5A); Cicero, Academica I. 9. 33; Eusebius, op. cir., XV. 2, passim; Diogenes Laertius III. 37; Justin Martyr, Cohortatio ad Graecos 5 (Migne, PG. vol. VI. p. 247); Cyrillus, Contra Julianum II. 47; Proclus, [91] 92 HISTORY OF PHILOSOPHY ments whichmarred the relations between these two men and which were indicative of Aristotle's ingratitude, bad taste and unwarranted conceit. The report of Diogenes Laertius, in an oblique manner, may also refer to the fact that already during his active association with the Platonic Academy (367-348 B.c.), that is, in his On (the) Ideas and On the Good, Aristotle had begun to disagree with, and criticize, some of Plato's fundamental teachings. It may also, in a distorted form, refer to the following specific incident which, however, cannot be verified: According to Aristoxenus, during the absence of Plato in Syracuse (and while Heracleides of Pontus was the "acting scholarch" of the Academy),5 some unnamed young members of the Academy, or "students" or, perhaps, some "outsiders " attempted to start a rival school (within the Academy?).6 As a matter of fact, Aelian, who apparently dramatizes this incident, reports that during Plato's last years, that is, some time after Plato's return from his third and last voyage to Syracuse, a serious conflict or confrontation arose within the Academy. Aristotle, together with some of his friends, or "conspirators," we are told, harrassed and molested the aging Plato by constantly putting questions to him, by arguing with him in an insolent manner, by contradicting him on every point, and by attempting to involve him in hair-splitting dialectics. At the time Xenocrates was in Chalcedon, and Speusippus was gravely ill. Hence, neither of them could come to the succor of Plato. In... (shrink)

In his De Iside et Osiride, Plutarch writes: "The Chaldaeans call two of the planets, which they consider benign gods, the authors or sources of everything that is good, two, on the other hand, the authors or sources of everything that is evil, and the three remaining planets they regard as being 'in between,' participating in the two opposite qualities.... It is worthwhile also to observe that the [Greek] philosophers are in accord with the Chaldaeans. For this reason Heraclitus [of (...) Ephesus] declared 'war the father, king and ruler of everything....' After him Empedocles designates the benign principle as 'love and friendship,' and at times as 'the harmony of the serene eye,' while at the same time he defines the evil principle as 'the cursed discord' and 'the bloody struggle....' Aristotle [by following this tradition] proclaims the [principle of] form and [the principle of] privation....". (shrink)