Most models of generational succession in sexually reproducing populations necessarily move back and forth between genic and genotypic spaces. We show that transitions between and within these spaces are usually hidden by unstated assumptions about processes in these spaces. We also examine a widely endorsed claim regarding the mathematical equivalence of kin-, group-, individual-, and allelic-selection models made by Lee Dugatkin and Kern Reeve. We show that the claimed mathematical equivalence of the models does not hold. *Received January 2007; revised (...) April 2008. †To contact the authors, please write to: Elisabeth Lloyd, Department of History and Philosophy of Science, 130 Goodbody Hall, Indiana University, Bloomington, IN 47405; e-mail: [email protected]; Richard Lewontin, Department of Organismic and Evolutionary Biology, Harvard University, 26 Oxford Street, Cambridge, MA 02138; Marcus Feldman, Department of Biological Sciences, Stanford University, Stanford, CA 94305; e-mail: [email protected]. (shrink)

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability of being (...) true, what probability should be ascribed to other (query) sentences? A natural wish-list, among others, is that the probability distribution (i) is consistent with the knowledge base, (ii) allows for a consistent inference procedure and in particular (iii) reduces to deductive logic in the limit of probabilities being 0 and 1, (iv) allows (Bayesian) inductive reasoning and (v) learning in the limit and in particular (vi) allows confirmation of universally quantified hypotheses/sentences. We translate this wish-list into technical requirements for a prior probability and show that probabilities satisfying all our criteria exist. We also give explicit constructions and several general characterizations of probabilities that satisfy some or all of the criteria and various (counter) examples. We also derive necessary and sufficient conditions for extending beliefs about finitely many sentences to suitable probabilities over all sentences, and in particular least dogmatic or least biased ones. We conclude with a brief outlook on how the developed theory might be used and approximated in autonomous reasoning agents. Our theory is a step towards a globally consistent and empirically satisfactory unification of probability and logic. (shrink)

This book presents new research into key areas of the work of German philosopher and mathematician Gottfried Wilhelm Leibniz (1646-1716). Reflecting various aspects of Leibniz's thought, this book offers a collection of original research arranged into four separate themes: Science, Metaphysics, Epistemology, and Religion and Theology. With in-depth articles by experts such as Maria Rosa Antognazza, Nicholas Jolley, Agustín Echavarría, Richard Arthur and Paul Lodge, this book is an invaluable resource not only for readers just beginning to discover Leibniz, but (...) also for scholars long familiar with his philosophy and eager to gain new perspectives on his work. (shrink)

On 1 November 1755, the city of Lisbon in Portugal was virtually destroyed by the largest documented seismic event ever to hit Europe. It is often claimed that the catastrophe severely damaged the plausibility of Leibniz’s optimism, and even the wider project of theodicy. Leibniz died several decades before the Lisbon earthquake struck, and so was unable to address it and the challenges thrown up by it, which would have included an account of how the event was consistent with God’s (...) providence. Contemporary scholars are of the view that Leibniz explained natural disasters like earthquakes as nothing more than the unfortunate consequences of the normal workings of simple laws of nature, and that God permits such disasters to happen because it would be unworthy of him to overrule the laws he has established. There certainly is this line of thinking in Leibniz’s writings, but it is far from being the whole story, as we shall see. The aim of this paper is to determine what Leibniz’s response to the Lisbon earthquake would have been, had he lived to know about the event. (shrink)

This Article explores the interpretation and construction of executive orders using as examples President Trump’s two executive orders captioned “Protecting the Nation From Foreign Terrorist Entry Into the United States” (the “Two Executive Orders”). President Trump issued the Two Executive Orders in the context of (among other things) Candidate Trump’s statements such as: “Islam hates us,” and “[W]e can’t allow people coming into this country who have this hatred.” President Trump subsequently provided further context including his tweet about the second (...) of his Two Executive Orders: “People, the lawyers and the courts can call [the second of the Two Executive Orders] whatever they want, but I am calling it what we need and what it is, a TRAVEL BAN!” Although President Trump replaced the first of the Two Executive Orders with the second one and although the Supreme Court by orders dated October 10, 2017 and October 24, 2017, vacated and remanded litigation involving the second order on grounds of mootness, the Two Executive Orders remain highly instructive for those who would understand the interpretation and construction of executive orders. This article therefore examines in detail the original speaker's (i.e., President Trump's) intended meaning and effect of the Two Executive Orders. It performs such examination using insights from the semiotic subfield of pragmatics, a semiotic subfield which explores how real-world people actually use, interpret, and construe language in various real-world contexts (including contexts where the issuer of the Two Executive Orders himself has claimed that “Islam hates us” and has tweeted “TRAVEL BAN!”). Using such insights of pragmatics, this Article also explores why reasonable judges thoroughly versed in legal theory, legal practice, and pragmatics should conclude that President Trump unlawfully targeted Muslims in the Two Executive Orders. This Article, among other things, also questions the sensibility of such notions as “facial legitimacy” to the extent such notions suggest text has meaning apart from context. Keywords: executive orders, speaker meaning, interpretation, construction, semiotics, pragmatics, originalism, speech acts, context, facial legitimacy, Constitutionality, First Amendment,Trump v. Int’l Refugee Assistance Project, Scalia, immigration, semantics, original meaning, travel ban, Trump, textualism. (shrink)

La traduction latine du livre de Maïmonide Moreh Nevukhim | Guide des égarés, a été l'ouvrage juif le plus influent des derniers millénaires (Di Segni, 2019 ; Rubio, 2006 ; Wohlman, 1988, 1995 ; Kohler, 2017). Elle marqua le début de la scolastique, fille du judaïsme élevée par des penseurs juifs, selon l'historien Heinrich Graetz (Geschichte der Juden, L. 6, Leipzig 1861, p. xii). Imprimée par la première presse mécanique de Gutenberg, son influence en Occident s'étendit jusqu'au Vème concile du (...) Latran (1512-1517) « où les savants furent encouragés à lever les difficultés qui semblaient diviser l'ensemble de la théologie et de la philosophie — (Leibniz, Théodicée, 11 ) ». Pendant des siècles, le Guide a révolutionné le programme d'instruction scolaire en réintégrant dans le domaine de la foi les lois de la pensée (dont la quatrième est devenue le principe de la raison suffisante de Leibniz). Cette collection complète de notes qui expose les idées du Guide fournit tous les passages sélectionnés et réécrits par Leibniz. Cette première traduction complète bilingue annotée des manuscrits originaux en latin sert de porte d'entrée à la foi conforme à la Raison. -/- « L'excellent livre du Rabbin Moïse Maïmonide, le Guide des égarés, est plus philosophique que je ne l'avais imaginé et mérite une lecture attentive. L'auteur, distingué par son intelligence en philosophie, était versé dans les mathématiques, l'art médical, et aussi dans la connaissance de Saintes Écritures. » — G. W. LEIBNIZ, 1685, Anthologie de Leibniz du Guide de Maïmonide, Chapitre III. (shrink)

Predication is a lingual relation. We have this relation when a term is said (λέγεται) of another term. This simple definition, however, is not Aristotle’s own definition. In fact, he does not define predication but attaches his almost in a new field used word κατηγορεῖσθαι to λέγεται. In a predication, something is said of another thing, or, more simply, we have ‘something of something’ (ἓν καθ᾿ ἑνὸς). (PsA. , A, 22, 83b17-18) Therefore, a relation in which two terms are posited (...) to each other in a way that one is said (predicated) of the other is a predication. The term of which the other term is said is called a subject (ὑποκειμένον) and the other, which is said about the subject, is called the predicate. Thus, in a predication the predicate is predicated of the subject; given that being predicated is almost as the same as being said. The relation between being said and being predicated is so close that ‘if something is said of a subject both its name and its definition are necessarily predicated of the subject.’ (Cat., 5, 2a19-26) This, however, is true only about the second genera and not the accidents. a) Nature of relation in predication What is Aristotle’s theory about the nature of the relation in a predication? How does he fundamentally understand this relation? Phil Corkum distinguishes between predication logic and traditional term logic and argues that the relation between subject and predicate in Aristotle is of the latter kind. While in predicate logic, subjects and predicates have distinct roles, they have the same role in traditional term logic. In predication logic, subjects refer, but predicates characterize. Thereupon, a sentence expresses a truth if the object to which the subject refers is correctly characterized by the predicate. In traditional term logic, both subjects and predicates refer and a sentences expresses a truth if both name one and the same thing. He concludes that Aristotle ‘problematically conflates prediction and identity claims’ because while he thinks both subjects and predicates refer, he would deny that a sentence is true just in case the subject and the predicate name one and the same thing. Based on this, Corkum believes that Aristotle’s core semantic is not identity but the weaker relation of constitution, which is a mereological interpretation: ‘All men are mortal’ is true just in case the mereological sum of humans is part of the mereological sum of mortals. b) Aristotle’s theory of predication: one or two theories? Frank Lewis finds an inconsistent gap between the theory of predication in the Categories and that in the later books of the Metaphysics VII, 6. So too Joan Kung, Terry Irwin, Daniel Graham. c) Distinction of ‘being said of’ and ‘being in’ Owen enumerates the texts in which Aristotle’s distinction between ‘being said of’ and ‘being in’ is asserted: OI. 11b38-12a17; To., 127b1-4; Cat. 1a20-b9; 2a11-14; 2a27-b6; 2b15-17; 3a7-32; 9b22-24 d) Predication in Aristotle and the standard ‘S is P’ Marie De Rijk Lambertus thinks that the ‘S is P’ pattern is misleading when it comes to express predication in Aristotle. In his view, ‘The Aristotelian procedure should be described in terms of appositively assigning an attribute (κατηγορούμενον) to a substrate (ὑποκείμενον), rather than ascribing a predicate to a subject by means of a copula…. The comment should be considered an attribute which is said to fall to a substrate, without understanding this procedure in terms of sentence predication.’ e) Aristotle’s predication: bipartite or tripartite? It is a difficulty to make Aristotle’s theories of name-verb predication and tripartite predication consistent. The reason is that tripartite is not consistant with his name-verb structure based on which he says that the predicate term is the ‘verb.’ (20a31; 20b1-2; 16a13-5) The problem is that in a tripartite form like ‘Socrates is white’ we cannot take ‘is white’ as the verb because, based on Aristotle himself, no part of a verb can be significant itself. (16b6-7) However, his assertions about the equivalences between the two structures (OI. 12, 21b9-10; PrA. 51b13-16; Met., 1017b22-30) must mean that they are not inconsistent in his own view. Thus, as Allen Bāck points, ‘Aristotle seems to think that he has a single, consistent theory.’ The sense of saying or speaking as the root sense of rhema makes the relation between predication (saying something of something) and verb more interesting. The use of rhema in the sense of a long expression approves this. In Plato’s work (399ac) where Socrates claims that the name anthropos derives from anthron ha opopen (‘he who examines what he has seen’) we have an onoma from, or in place of, a rhema. 1) Subject The subject (ὑποκειμένον) is that of which another term is said or predicated. Aristotle’s own definition is of a much more philosophical value: ‘By subject I mean that which is expressed by an affirmative term (λέγω δὲ ὑποκείμενον τὸ κάταφάσει δηλούμενον).’ (Met., K, 1067b18) Throughout Aristotle’s work, three kinds of subjects can be found: possible, prime and absolute subject. a) Possible subject Those things that can take the position of a subject in a predication we call possible subjects, no matter they can or cannot take the position of predicate in any predication. All terms except the ultimate predicates are possible subjects because they can take the position of subject. b) Prime subject Those that in any predication can only take the position of a subject and not the position of a predicate are prime subjects. (Cat., 5, 3a36-b2; Met., Z, 1028b36-1029a1) This is the truest sense of subject and belongs only to substances. (Met., Z, 1029a1-2) In fact, ‘that which is not predicated of a subject, but of which all else is predicated’ is a substance. (Met., Z, 1029a7-9) In Categories, besides primary substances (Cat., 2, 1b3-6), individual qualities are also said not to be able to be said of anything else. (Cat., 2, 1a23-29) Aristotle’s examples are a certain ‘knowledge-of-grammar’ (τὶς γράμματικὴ) and ‘an individual white’ (τὸ τὶ λευκὸν). Thus, although substances are indeed in the truest sense individuals and, thereby, in the truest sense primary subjects, other individuals can take the position of subject as well. c) Absolute subject While substances are prime subjects of all other things, there is still something of which substances can be predicated and this predication is not an accidental predication: matter. (Met., Z, 1029a21-24) This predication is, indeed, the predication of a ‘form or this’ on matter and material substance. (Met., Θ, 1049a34-36) The only thing that is absolutely a subject, therefore, and can be a predicate is prime matter (πρώτη ὓλη). (Met., Θ, 1049a24-27) d) Subject and substance The most important thing in being a substance is being a subject: ‘It is because the primary substances are subjects for all the other things and all the other things are predicated of them or are in them, that they are called substances most of all.’ (Cat., 5, 2b15-17) And what is nearer to this position is more a substance as a species is more a substance than a genus.’ (Cat., 5, 2b7-8) e) Primary versus accidental subject A subject is a primary subject in a predication when the predicate is predicated of it as itself. In such a case, the subject is the subject of the predicate qua itself and not qua something else. A subject, on the one hand, is an accidental subject when it is not the primary subject of the predicate that is predicated on it. It means that a subject is an accidental subject when the predicate is predicated of it not qua itself but qua something else. An accidental subject is, therefore, anything other than a substance. 2) Predicate as universal It is evident from our discussion of kinds of subjects that except matter, primary substances (if we ignore both accidental predication and cases of absolute subjects) and other individuals, everything else can take the position of a predicate. Since primary substances are individuals, it results that everything except matter and individuals are capable to take the position of predicate. The immediate consequence of this is that the predicate must be a universal. When individuals cannot take the position of predicate, this position cannot be taken by any particular. Therefore, only universals can be predicated of others. Moreover, albeit universals can be a simple subject (for another universal), they are not prime subjects. The closeness of universal and predicate is to the extent that Aristotle differentiates universal from subject. (Met., Θ, 1049a27-30) 3) Categories or classes of predicates Aristotle distinguishes ten highest classes into one of which each predicate must necessarily fall: substance (or what a thing is), quality, quantity, relation, place, time, position, state, activity and passivity. (Cat., 4, 1b25-27; To., I, 9, 103b20- ; PsA., A, 22, 83b13-23) The substance counted among predicates must refer to secondary and not primary substances not only because Aristotle insists that primary substances cannot be predicated but also from his own examples of the category of substance: man and animal. (To., I, 9, 103b25) However, if a predicate be asserted of itself or its genus be asserted of it, the predicate signifies substance or what is; but if ‘one kind of predicate is asserted of another kind,’ it signifies one of the other nines. (To., I, 9, 103b30) These categories are so comprehensive that no predicate can remain outside them so that even non-being has as many senses as categories. (Met., M, 1089a26-30) a) That whether Aristotle’s categories are merely linguistic or fundamentally ontological is a so much controversial dispute. Some like G. E. R. Lloyd believe that ‘categories are primarily intended as a classification of reality … rather than of the signifying terms themselves.’ b) Although Aristotle’s categories have been historically regarded as a classification of predications, there are some recent commentators like Jonathan Barnes that think it is classifying predicates and not predications. 4) Kinds of predicates In his introduction of Categories, as J. W. Thorp truly points out , Aristotle distinguishes between the category of substance and the other categories using μὲν ... δὲ construction. This construction illustrates that beside tenfold classification of categories, there is an even more crucial differentiation between two kinds of predicates: substance or what is on the one hand and the other nine ones on the other hand: the distinction between what is predicated of the subject as what it is and what is predicated of it as an accident. Therefore, we have three kinds of classification - a twofold, a fourfold and a tenfold-complicatedly classifying the same thing, viz. the predicate. Predicates can be divided also to four kinds: property, definition, genus and accident. (To., I, 4, 101b11-20) A property is that predicate that is convertible with its subject and does not signify its essence. A definition is that predicate that is convertible with its subject and signifies its essence. It is a genus if it is not predicated convertibly and is contained in the definition of its subject. And it is an accident if it is neither convertible nor contained in the definition of its subject. (To., I, 8, ^103b3) All of these four kinds are among categories. (To., I, 9, 103b20) It seems that there might be some kind of relation between the twofold and the fourfold distinction: whereas genus and definition are predicated as what it is, accidents are not so predicated. There seems to be some rules that determine to each of these four kinds each predicate belongs. At To., IV, 123b30ff. Aristotle asserts: ‘If B has a contrary and A does not, then B does not belong to A as its genus.’ There is a dispute around per se accidents (τὰ καθ’ αὑτὰ συμβεβηκότα) (Topics., 102a18) whether they must be regarded as either of the four kinds or as a fifth kind. Barnes (1970) argued that they ‘do not fit at all neatly into the fourfold classification.’ He argues that based on the definition of accidents at A, 5, 102b4-5, they must be accidents but based on another definition, A, 5, 102b6-7, they cannot be accidents. He also defends the view that they are not properties. Barnes concludes: ‘This shows that the two definitions are not equivalent, and hence that the ‘predicables’ are not well-defined.’ Demetris J. Hadgopoulos defends the view that the two definitions of accidents are equivalent and per se accidents are properties. 5) Five types of predications We have five kinds of predications based on our division of subjects and our discussion of predicates: simple, primary (itself divided to substantial and accident), accidental (itself divided to primary and secondary), aoincidental and absolute predication. a) Simple predication. This is a predication in which a universal is predicated of either a particular or a universal subject. This sense of predication includes all other senses except the first kind of accidental predication. b) Primary predication. This is a predication in which a universal is predicated of a primary subject, namely a substance. A primary predication is of two kinds: i) Substantial predication. A primary predication in which the predicate is part of, or is included in, the definition of the subject. The universal that is the predicate here is the definition or the genus or the species or the diferentia of the subject. It is this predication that Aristotle calls a unity: ‘A statement may be called a unity … because it exhibits a single predicate as inhering not accidentally in a single subject.’ (PsA., B, 10, 93b35-37) It is only substantial predicates that can be predicated of each other: ‘Predicates which are not substantial are not predicated of one another.’ (PsA., A, 22, 83b18-19) Aristotle defines a substantial predication also in another way. A predication in which a higher genus is predicated on a lower genus, species, a substance or an individual, (or a species is predicated on an individual) is a substantial predication. Therefore, a substantial predication is a predication in a series that has individuals on one of its ends and a general category on its other end. In fact, only substantial predicates can be predicated of one another. (PsA., A, 22, 83b17-19) This series cannot be an infinite series because otherwise not only substances would not be definable but also a genus would be equal to one of its own species. (PsA., A, 22, 83b7-10) -/- ii) Accident predication. A primary predication in which the predicate is not part of, or is not included in, the definition of its subject. The universal that is the predicate here is the property or the accident of the subject. c) Accidental predication. This is a predication in which the subject is not a primary subject and its predicate is a substance. This predication is of two kinds: i) Primary accidental predication. This is a predication in which an accident is predicated of substance. Such a predication can go ad infinitum, which is inferable from Aristotle’s assertion that the secondary accidental predication cannot go ad infinitum. ii) Secondary accidental predication. It is a predication in which an accident is predicated of another accident. Such a predication, Aristotle asserts, cannot go ad infinitum because even more than two accidents cannot be combined. Now what is the meaning of Aristotle’s assertion that we cannot continue this ad infinitum? Does it mean that we cannot continue the predication ‘The musician is white’ and say ‘The white is Athenian?’ But why not? Or maybe he means that by adding any predication, we are still in a condition of predicating two accidents of a substance on each other. -/- As primary subjects, substances can also take the position of predicate though not essentially but accidentally. In propositions like ‘the white is a log’ or ‘That big thing is a log’ we observe substance taking the position of predicate but this is only accidentally: ‘When I affirm ‘the white is a log,’ I mean that something which happens to be white is a log- not that white is the subject in which log inheres (οὐχ ὡς τὸ ὑποκείμενον τῷ ξύλῳ τὸ λευκόν ἐστι), for it was not qua white or qua a species of white that the white (thing) came to be a log (οὔτε λευκὸν ὄν οὔθ᾿ ὃπερ λευκόν τι ἐγἐνετο ξύλον), and the white (thing) is consequently not a log except incidentally.’ (PsA., 22, 83a3-9) Aristotle compares this accidental use of substance in the position of predicate with the substantial use of it in the place of a subject: ‘On the other hand, when I affirm ‘the log is white,’ I do not mean that something else, which happens to be a log, is white (οὐχ ὃτι ἓτερόν τί ἐστι λευκόν, ἐκείνῳ δὲ συμβέβηκε ξύλῳ εἶναι), (as I should if I said ‘the musician is white,’ which would mean ‘The man who happens also to be a musician is white’); on the contrary, log is here the subject- the subject which actually came to be white, and did so qua wood or qua a species of wood and qua nothing else.’ (PsA., 22, 83a8-14) Aristotle asks us not to call propositions like ‘The white is a log’ a predication at all or at least call them accidental predication instead of simple (ἁπλως) predication. (PsA., A, 22, 83a14-17) An accidental predication, in which we have a substance in the place of predicate, is different from an essential predication in that while the subject of an accidental predication is said to be the predicate not by itself but as something different with which it coincides, the subject of an essential predicate is said to be the predicate by itself and not because it is something else: ‘Since there are attributes which are predicated of a subject essentially and not accidentally- not, that is, in the sense in which we say ‘That white (thing) is a man,’ which is not the same mode of predication as when we say ‘The man is white’: the man is white not because he is something else but because he is man, but the white is man because ‘being white’ coincides with ‘humanity’ within one subject. Therefore, there are terms such as are essentially subjects of predicates. (PsA., A, 19, 81a24-29) This capability of ‘non-essentially and only accidentally’ being a subject does belong, in fact, to all sensible things. (PsA., A, 27a32-36) d) Coincidental predication. this is a predication in which none of the subject and predicate are a substance or an individual. In this predication, one of the accidents of a substance or individual is predicated of one of the other accidentals of the same substance or individual. For example, when it is said that ‘The white is musical,’ there is an individual, say Socrates, for which both of white and musical are accidents. e) Absolute predication. This is a predication in which a form or a substance is predicated of a matter or a material substance. Some commentators like Loux and Lewis regarded this predication as close to accident predication, both based on inherence. As R.M. Dancy points out, these predications make Aristotle’s theory of predication immanentist: not only accident predications are explained by the immanence of accidents in substances, some of the substantial predications, which were not explained in Categories, are also explained by the immanence of form in matter. It is interesting that in this kind of predication, it is the predicate and not the subject, which is in the strictest sense substance. As the central books of Metaphysics claim, the form is the substance. Thus, in this predication, substance gets away from the sense of ὑποκείμενον. Corkum mentiones 68a19 as the only instance where Aristotle explicitly claims that a term may be predicated of itself, a passage that is, in Corkum’s view, problematic. 6) Demonstrable predicates Those predicates are demonstrable that are so related to their subjects that there are other predicates prior to them predicable of their subjects (ἔτι δ᾿ ἄλλος, εἰ ὧν πρότερα ἄττα κατηγορεῖται). (PsA., A, 22, 83b32-34) 7) Series of predications Since it is possible for a predicate to be itself the subject of another predication, we can have a series of predications in which the predicate of a predication is the subject of the next predication. This series has the following features: a) It has a limit (in number) (PsA., A, 22, 83b14-16) on the side of subjects: there are subjects that cannot themselves be predicated (PsA., A, 27, 43a39-41), which are, as we noted, prime subjects: particulars, i.e. prime substances and other individuals. (PsA., A, 19-22) Aristotle calls them ultimate (ὓστατον). (PsA., 21, 82a36-b1) b) It has a limit (in number of kinds) (PsA., A, 22, 83b14-16) also on the side of predicates: there must be predicates that cannot be subjects. (PsA., A, 19-22; PsA., A, 27, 43a36-39) Aristotle calls them primary (πρῶτον). (PsA., A, 21, 82b1-4) These are the highest categories or the highest genera of categories. (PsA., A, 22, 83b14-16) c) The series has an escalating shape from mere subjects at its downside to mere predicates at its upside. It is Aristotle himself whos uses the words up and down in this sense. (e.g. PsA., A, 22, 83b2-3) d) The predications that lie between lowest and highest ones must be finite in number. (PsA., A, 19-22 especially: 20, 82a21-35) These have subjects and predicates, each capable of both of the roles of being subject and being predicated. A result of this fitness is that neither demonstration can go to infinity nor everything is demonstrable, the two points Aristotle always insist on. e) The upward side includes the more universal ones and the downward the more particular ones. (PsA., 20, 82a21-23) f) It follows from the above features that ‘neither the ascending nor the descending series of predications … are infinite.’ (PsA., A, 22, 83b24-25) g) Reciprocation and convertibility. Except in case of terms (i.e. subjects and predicates) that are at each of the ends of series of predications, namely ultimates and primaries, it is possible to reciprocate (ἀντιστρέφειν) terms and convert the predication. (PsA., A, 19, 82a15-20) h) Antipredication. Antipredication means that in a predication (S is P), the subject becomes the predicate of its predicate (P is S) in the same category its predicate was predicated on it. For example, if P is in the category of quality, antipredication means that S be predicated of P in the category of quality. In other words, P is a quality of S and S is a quality of P. Aristotle rejects this. (PsA., A, 22, 83a36-b3) i) Self-predication versus other-predication. Aristotle distinguishes between a predication in which a term is said of itself and a predication in which a term is said of another. (Phy., Δ, 2, 209a31-33) j) Predicablity (Cat., 5, 3a36-b2): 1) Primary substances and individuals are not predicable. 2) Secondary substances are of two kinds: genus and species i) Genus is predicable able both of the species and of the individuals. ii) Species is predicable of the individual. 3) Differentiae are predicable both of the species and of the individuals. 8) Predication as classification a) Richard Patterson believes that Aristotle’s so repeated construction using hoper (estin A hoper B) in Topics (120a23 sq., 122b19, 26sq., 123a, 124a18, 125a29, 126a21, 128a35. Also in Posterior Analytics (83a24-30) (Brunschwig’s list. ‘expresses the fact that A is a kind of B (esti A B tis), that A is a species of the genus B.’ 9) Universal predication Aristotle defines universal predication (κατὰ παντὸς κατηγορεῖσθαι) as such: ‘wherever no instance of the subject (τῶν τοῦ ὑποκειμέμνου) can be found of which the other term cannot be asserted.’ (PrA., A, 24b27-29) In this predication, the subject is included in another as in a whole (ἐν ὃλῳ εἶναι) and the predicate is predicated of all of the subject (κατὰ παντὸς κατηγορεῖσθαι). (PrA., A, 24b26-27) Attach another discussion we had about ἐν ὃλῳ here. 10) Quantity of predication A predication, truly stated, has a quantity, which is the number of objects under the name of the subject of which the predicate is predicated. The quantity of subject can be stated in four ways: a. Indefinite: when the predicate belongs or does not belong to the subject without any mark to show to haw many of the particulars under the name of the subject it does or does not belong. E.g. ‘Man is white’; ‘Man is not white.’ (PrA., A, 24a20; OI., I, 7, 17b8-12) b. Universal quantity: When the predicate belongs to all or none of the subject. E.g. ‘Every man is animal’; ‘No man is animal.’ (PrA., A, 24a18-19; OI., I, 7, 17b5-6) The contrary of a predication of a universal quality is a predication of a universal quality. E.g. the contrary of ‘Every man is white’ is ‘No man is white.’ (OI., I, 7, 17b20-23) c. Particular quantity: When the predicate belongs (or does not belong) to some of the subject. E.g. ‘Some men are white’; ‘Some men are not white.’ (PrA., A, 24a19-20) d. Single quantity: when the subject is a proper name of only one object. E.g. ‘Socrates is white’; ‘Socrates is not white.’ The contrary of this predication is of a single quantity: ‘Socrates is not white.’ (OI., I, 7, 17b38-18a4) 11) Convertibility of predication. Some predications are convertible, that is, it is possible to change the place of subject and predicate in a true proposition so that the converted proposition remains true. This is supposed to mean that given the truth of a predication, the truth of the converted predication is inferable. The convert form of a predication depends on its quantity. a. Indefinite quantity: This predication has no strictly true convert because its quantity is not stated. b. Universal quantity: It can be converted in two ways: i) A negative universal can be converted to a negative universal in which the terms are changed. E.g. ‘No pleasure is good’ can be converted to ‘No good is pleasure.’ (PrA., A, 2, 25a5-8 and a14-19) ii) An affirmative universal can be converted to an affirmative particular in which the terms are changed. E.g. ‘Every pleasure is good’ can be converted to ‘Some good is pleasure.’ (PrA., A, 2, 25a7-9) c. Particular quantity: If it is negative, it cannot be converted but if it is affirmative, it can be converted to an affirmative predication with particular quantity. E.g. ‘Some pleasure is good’ can be converted to ‘Some good is pleasure.’ (PrA., A, 2, 25a10-13 and a20-24) d. Single quantity: It cannot be converted. 12) Characteristics of relations between subject and predicate 1. A predicate is of a wider range than its subject. It is based on this fact that Aristotle: a) Prevents individuals to be predicate because there is nothing of which an individual be of a wider range. In other words, it is due to the fact that since an individual is only ‘one particular’ thing and, thus, cannot be of a wider extent than anything that Aristotle prevents them of being a predicate. Matthews, however, thinks we cannot use Socrates, a substance and an individual, in the place of predicate and say it of Socrates because ‘Socrates does not classify Socrates: it names him.’ b) Prevents differentia, species and things under species to be predicated of genus. (To., Z, 6, 144a27-) c) Prevents the species and the things under it to be predicated of the differentia. (To., Z, 6, 144b1-4) d) Also about the effect because it is wider than its subject. (PsA., B, 17, 99a) e) Each attribute is wider than every individual it is predicated on, though several attributes, collectively considered, might not be wider but exactly the substance of a thing. (PsA., B, 13, 96a32-b1) 2. The predicate of a predicate of a subject will be predicated of the subject too: ‘whenever one thing is predicated of another as of a subject, all things said of what is predicated will be said of the subject too.’ (Cat., 3, 1b10-15) In fact, it is due to its predication of the subject that it is predicated of its predicate. (Cat., 5, 2a36-b1) Moreover, what is not predicated of the predicate of a subject cannot be predicated of it as well. (PrA., A, 27, 43b22-27) Thus, what, for example, is not predicated of animal, cannot be predicated of man. 3. The predicate of a subject can be predicated of its predicates as well. (Cat., 5, 3a1-6) For example, you call the individual man grammatical and, thence, you call both a man and an animal grammatical. Nonetheless, the predicate of a subject belongs to it more properly than to its higher predicates. (PrA., A, 27, 43a27-32) 4. It is only the subject that can be distributed and not the predicate. (PrA., A, 27, 43b16-22; OI, I, 7, 17b12-16) Therefore, we can say e.g. ‘Every man is animal’ but we cannot say ‘Every man is every animal.’ 5. It is the reason of the relation between subjects and predicates, that is the reason of predication, which is the subject of inquiry. (Met., Z, 1041a20-24) In other words, since it is a meaningless inquiry to ask why a thing is itself (Met., Z, 1041a14-15), the only remaining meaningful inquiry is to ask why something is something else, i.e. to ask about the reason of predication. 6. A subject cannot categorize its predicate in the same category in which it is categorized by it. If e.g. A is a quality of B, B cannot be a quality of A. Therefore, there is no reciprocation in the same category. (PsA., A, 22, 83a36-39) 13) Characteristics of series of predications 1. A series of secondary accidental predication cannot go ad infinitum for not even more than two terms can be comnbined. For an accident is not an accident of an accident, unless it be because both are accidents of the same subject. (Met., Γ, 1007b1-4) 2. Infinite series cannot be traversed in thought. (PsA., A, 22, 83b6-7) 3. The predications of genera on each other must be ended and cannot go to infinity because otherwise not only substances would not be definable but also a genus would be equal to one of its own species. (PsA., A, 22, 83b7-10) Therefore, a series of predication of genera on each other must be limited on both sides. There must be an upward limit in general categories as well as a downward limit in individual because they cannot be predicated of others. Whatever lies between these limits can both be predicated of others and others be predicated of them. (PrA., A, 27, 43a36-43) 4. The order of predicates matters: it makes a difference whether the series be ABC or BAC. (PsA., B, 13, 96b25-32) . (shrink)

The following are the characteristics of a genus: 1. Those to which the same figure of predication applies are one in genus. (Met. , Δ, 1016b32-35) 2. Things that are one in genus are all one by analogy while things that are one by analogy are not all one in genus. (Met, Δ, 1016b35-1017a3) 3. A genus includes contraries. (Met., Δ, 1018a25-31) 4. All the intermediates are in the same genus as one another and as the things they stand between. (...) (Met., I, 1057a18-30; 1057b31-34) 5. Not every predicate is a genus of what it is predicated on; for this would equate a genus with one of its own species. (PsA., A, 22, 83b7-10) 6. The opposite of the genus should always be the genus of the opposite. (To., Δ, 4, ^125a27-29) 7. A genus divides the object from other things. (To., Z, 3, 140a^24) 8. None of unity and being is a genus. (Met., B, 998b22-27; Met., K, 1059b31-34; PsA., B, 7, 92b12-14) 9. There is no necessity or even no possibility that things that are the same specifically or generically should be numerically the same. (To., H, I, 152b30-) 10. To be called one due to having one genus is in a way similar to be one due to having the same matter. (Met., Δ, 1016a24-28) 11. The substance of a thing involves its genus, and thereby all the higher genera are predicated of the lower. (To., Z, 5, 143a^20- ) 12. Being falls immediately into genera. (Met., Γ, 1004a4-6) A. Characteristics of relations between genera The characteristics of relations between genera, the relations between genera and species excluded, are as follows: 1. Genus is not an element in the composition of things. (Met., I, 1057b20-22) 2. Things resulting from the same division of the same genus are simultaneous by nature. (Cat., 13, 15a3-4) 3. Processes of proof cannot pass from one genus to another. (PsA., A, 23, 84b14-18) 4. It is not necessary for subordinate genera to have different accounts. (To., I, 15, ^107a19-) E.g. when we say a raven is a bird, we also say it is a certain kind of animal. 5. It is necessary for genera that are not subordinate one to the other to have different accounts. (To., I, 15, ^107a27-30) E.g. whenever we call a thing an engine, we do not call it an animal, nor vice versa. 6. If one of the genera is predicated in what it is, all of them, both higher and lower than this one, if predicated at all of the species, will be predicated of it in what it is; so that what has been given as genus is also predicated in what it is. (To., Δ, 2, ^122a10) 7. The same object cannot occur in two genera of which neither contains the other. (To., Z, 139b32-140a2) 8. Those to which the same figure (σχῆμα) of predication applies, are the same in genus. (Met., Δ, 1016b32-35) 9. Attributes that inhere always in each several things can be divided to two groups: those that are wider in extent but not wider than its genus and those wider than its genus. (PsA., B, 13, 96a24-27) 10. The relation between A and B must be extendable in respect of all the genera of A. Thus, if A is double of B, it must also be in excess, the genus of double, to B. Aristotle accepts, however, that this may be objectable in some cases: while knowledge is called knowledge of an object of knowledge, it cannot be called a state and disposition (which is the genus of knowledge) of an object of knowledge. In fact, it is a state and disposition of the soul. (To., Δ, 4, 124b28-34) B. Characteristics of species The following are the characteristics of species: 1. Things are said to be other in species if they are of the same genus but are not subordinate the one to the other. (Met., Δ, 1018a38-b2; Met., I, 1057b35-37) 2. Contraries are other than one another in species. (Met., Δ, 1018b5-7; Met., I, 1058b26-) 3. It is not sufficient for a difference to be the basis of distinguishing species in a genus because it belongs to the genus in virtue of its nature as, e.g., the difference between men and women belongs to animal in virtue of its nature. It must also be a modification peculiar to the genus (οἰκεῖα πάθη τοῦ γένους) in the strongest sense. (Met., I, 1058a29-37) Thus, contraries which are in the formula (ἐν τῷ λόγῳ) make a difference in species, but those which are in the compound material thing do not make one as e.g. being male and female is a difference in matter. (Met., I, 1058a37-b23) 4. Some things are peculiar to the species as distinct from genus: there are attributes peculiar to each distinct species. (PrA., A, 27, 43b27-29) 5. There is no necessity or even no possibility that things that are the same specifically should be the same numerically. (To., H, I, 155b30-) C. Characteristics of relations between genera and species The following are the characteristics of relations between genera and their species: 1. Although species predicated of individuals seem to be principles rather than the genera, it is hard to say, Aristotle asserts, in what sense species are to be taken as principles. (Met., B, 999a14-21) 2. Things that are one in species are all one in genus, while things that are one in genus are not all one in species. (Met., Δ, 1016b35a1) 3. The relation of a species to its genus is like the relation of primary substance to all others: the species is a subject for the genus (ὑπόκειται γὰρ τὸ εἴδος τῷ γένει) and the genera are predicated of the species but the species are not predicated of them. (Cat., 5, 2b17-22) 4. Of the species themselves- those which are not genera- one is no more a substance than another: a certain horse is no more a substance than another horse. (Cat., 5, 2b22-26) 5. Genera are prior to species since they do not reciprocate as to implication of existence (κατὰ τὴν τοῦ εἶναι ἀκολούθησιν). For example, if there is a fish there is an animal, but if there is an animal there is not necessarily a fish. (Cat., 13, 15a4-7) 6. What belongs both to a species and to its genus, it belongs to the species more properly indeed than to the genus. (PrA., A, 27, 43b29-32) 7. A predicate drawn from the genus is never ascribed to the species in a derived form and as its genus. Thus, e.g. coloured cannot be a genus of ‘white’ when we say ‘white is coloured.’ (To., B, I, ^109b1-5) 8. Genera are predicated of their species synonymously because the species take on both the name and the account of their genera. (To., B, I, ^109b3-6) 9. All the attributes that belong to the species belong to the genus as well but there is no necessity that all the attributes that belong to the genus should belong also to the species. (To., B, 4, 111a20-32) 10. Those things of which the genus is predicated must also of necessity have one of its species predicated of them. (To., B, 4, 111a33-) 11. The higher genus should be predicated of the species in what it is. (To., Δ, 2, ^122a6) 12. The species, or any of the things which are under the species, is not predicated of the genus because the genus is the term with the widest range of all. (To., Z, 6, 144a27f.) 13. The same species cannot be in two genera neither of which contains the other. (To., Z, 6, 144b14f.) 14. None of the species of a genus is prior or posterior to other species but they are thought to be simultaneous by nature. (Cat., 13, 14b38-15a1) 15. Daniel W. Graham points that sometimes Aristotle speaks of species as classes (Cat., 5, 2a14-17) and sometimes as properties or a certain character (ποιόν τι) of substances, which is difficult to be distinguished from the category of quality. (Cat., 3b13-22) D. Characteristics of differentia 1. The last differentia will be the substance, the definition and the form of the thing. (Met., Z, 1038a18-28) 2. If we divide according to accidental qualities, there will be as many differentiae as there are processes of division. (Met., Z, 1038a25-28) 3. The differentia divides the object from any of the things contained in the same genus. (To., Z, 3, 140a24-) 4. A. C. Lloyd argues that Aristotle’s logic of classification contains a vicious circle because: ‘For a genus to be predicated unequivocally and essentially of a species the specific differentiae have to be ‘appropriate’; but in order to know whether a proposed differentia is appropriate we have to know whether the genus is predicable essentially of the species thus defined.’ The predication of differentia on primary substance seems to make difficulties in Aristotle’s system, as Terence Irwin points out. It seems to violate the distinction of strong predication and inherence, a distinction between predication of count-nouns and predication of characterizing adjectives. Irwin says that this violation is only apparent because although the differentia-term is an adjective, its gender agrees with the gender of the understood genus-term and not with that of the subject term. ‘Man is biped’ is indeed ‘Man is a biped animal.’ This shows, Irwin asserts, ‘why Aristotle can still mention that strong predication is nominal and inherence is adjectival.’ Differentiae are not, however, secondary substances, as Aristotle himself insists. A differentia does not say what the thing is, as secondary substances do, but only what it is like or what sort it is. (ποιον: To., 122b12-17; 128a20-29; 139a28-31; 142b25-29) Nonetheless, differentiae are not qualities because they are not inherent. Thus, they cannot be regarded in any of the ten categories. Irwin thinks that this anomaly is unnecessary because Aristotle could give good reasons for taking differentiae to be second substances. E. Characteristics of relations between differentia and genera or species 1. It is not possible for the genus to be predicated of the differentia taken apart from the species. (Met., B, 998b23-25; Met., K, 1059b31-33; To., VI, 6, 144a32-b1) 2. It is not possible for the species of the genus to be predicated of the proper differentiae of the genus. (Met., B, 998b24-26) 3. Where the differentia is present, the genus accompanies it, but where the genus is, the differentia is not always present. (Met., Δ, 1014b12-14) 4. The number of species are equal to the number of differentiae. (Met., Z, 1038a15-18) 5. The differentiae of genera which are different and not subordinate one to the other are themselves different in kind. (Cat., 3, 1b16-20; To., I, 15, ^107b19-) 6. There is nothing to prevent genera subordinate one to the other from having the same differentia. (Cat., 3, 1b20-22) 7. Since the higher genera are predicated of the genera below them, all differentiae of the predicated genus will be differentia of the subject also. (Cat., 3, 1b21-24) 8. The definition of the differentia is predicated of that of which the differentia is said. (Cat., 5, 3a25-28) 9. In giving what a thing is it is more fitting to state the genus than the differentia. For example, anyone who says that man is an animal shows what man is better than who describes him as terrestrial. (To., Δ, 6, ^128a24-27) 10. The differentia always signifies a quality of the genus, but the genus does not do this of the differentia. (To., Δ, 6, 128a27-29; To., Z, 6, 144a20-23) 11. A specific differentia, along with the genus, always makes a species. (To., Z, 6, 143b^1-) 12. A genus is always divided by the differentiae that are co-ordinate with it in a division and the differentiae that are co-ordinate in a division are all true of the genus. (To., Z, 6, 143b^1-) 13. Differentia cannot be predicated of the genus because genus is the term with the wider range. (To., Z, 6, 144a27-) In fact, genus is predicated, not of the differentia, but of the object of which the differentia is predicated. (To., Z, 6, 144a^31-b3) 14. Neither species nor the objects under it can be predicated of the differentia because the differentia is a term with a wider range than the species. (To., Z, 6, 144b4-) 15. The differentia is posterior to genus but prior to the species. (To., Z, 6, 144b^9-) 16. The same differentia cannot be used of two genera neither of which contains the other and if they do not both fall under the same genus. Otherwise, the same species will be in two genera neither of which contains the other, which is impossible. (To., Z, 6, 144b14-) 17. Genus and differentia are prior to and more familiar than the species: ‘For annul the genus and the differentia; and the species too is annulled, so that they are prior to the species. They are also more familiar; for if the species is known, the genus and differentia must of necessity be known as well (for anyone who knows what a man is knows also what animal and terrestrial are), whereas if the genus or the differentia is known it does not follow of necessity that the species is known as well; thus the species is less intelligible.’ (To., Z, 4, 141b15-) F. Characteristics of relations in series of classes 1. Mutually exclusive series. If no term in the series ACD… is predicable of any term in the series BEF…, and if G- a term in the former series- is the genus of A, clearly G will not be the genus of B; since, if it were, the series would not be mutually exclusive. (PsA., A, 15, 79b6-11) 2. Atomic disconnection of series. Of two mutually exclusive series ACD and BEF, if neither A nor B has a genus and A does not inhere in B, this disconnection must be atomic. (PsA., A, 15, 79b6-14) G. Characteristics of relations of individuals 1. No individual in a species is more substance than another individual in another species. (Cat., 5, 2b26-28) An individual man, for instance, is no more a substance than an individual ox. 2. Each attribute is wider than every individual it is predicated on, though several attributes, collectively considered, might not be wider but exactly the substance of a thing. (PsA., B, 13, 96a32-b1) 3. Not distinguishing between class membership and class inclusion? Some commentators like Vlastos and Ackrill (1963, 76) criticized Aristotle because he, they believe, did not distinguish between class membership (between species and particulars) and class inclusion (between genera and their species). Having accepted this point, Daniel W. Graham believes it is ‘question-begging in a curious way.’ Phil Corkum thinks that Aristotle employs mereological notions. (This criticism seems so strange because all the Aristotle’s point in distinguishing species 2 from genera is strictly the distinction of class membership and class inclusion as they call them so. (shrink)

One of the most original contributions to the optimism debate of the eighteenth century was put forward by the maverick French Enlightenment thinker, André-Pierre Le Guay de Prémontval, in an essay entitled “General misunderstanding on the question of optimism”. This essay, which seeks to develop a “middle point” between the polarized pro- and anti-optimist positions that characterized the optimism debate, prefigures the development of process or neoclassical theism in important ways. The essay is presented here in English for the first (...) time, along with an analysis of the essay itself and of the context in which it was written. (shrink)

A fresh translation and in-depth commentary of Leibniz's seminal text, the Monadology. -/- Written in 1714, the Monadology is widely considered to be the classic statement of Leibniz's mature philosophy. In the space of 90 numbered paragraphs, totalling little more than 6000 words, Leibniz outlines - and argues for - the core features of his philosophical system. Although rightly regarded as a masterpiece, it is also a very condensed work that generations of students have struggled to understand. -/- Lloyd (...) Strickland presents a new translation of the Monadology, alongside key parts of the Theodicy, and an in-depth, section-by-section commentary that explains in detail not just what Leibniz is saying in the text but also why he says it. The sharp focus on the various arguments and other justifications Leibniz puts forward makes possible a deeper and more sympathetic understanding of his doctrines. (shrink)

One of the disadvantages of redistributive taxation is that it reduces people’s financial incentives to increase national wealth and benefit others by engaging in productive activities. It is natural to suppose that the severity of this disadvantage will be proportional to the socially prevailing level of human selfishness. Thus, several advocates of redistribution (inter alia G. A. Cohen; Ha-Joon Chang) have argued that this disadvantage of redistribution need not be as severe as critics often suggest, because human beings need not (...) be so selfish. My aim in this paper is to argue that even in a society entirely composed of unselfish and impartially beneficent individuals, redistributive taxation would still discourage activities which contribute to national wealth, because differing individuals have different views about what counts as benefitting themselves and others. I also relate my discussion to G. A. Cohen’s influential ‘camping trip’ argument for socialism (from Why Not Socialism?). (shrink)

Commentary in reply to an article by Jeff McMahan and Julian Savulescu.

In 1753, the Berlin Academy announced that the focus of the prize essay contest of 1755 would be optimism, with entrants required (among other things) ‘to put forward arguments that will be thought most fitting to confirm or destroy this system’. In line with these instructions, entrants submitted essays that were either pro- or anti-optimism. This was to the dismay of one of the judges of the contest, André-Pierre Le Guay de Prémontval (1716–1764), who had, by his own admission, surreptitiously (...) attempted to influence the entrants by sketching out a ‘middle point’ between the polarized pro- and anti-optimist positions in a series of books published between 1754 and 1755, namely Thoughts on Freedom, The Diogenes of d’Alembert, and On Chance under the Rule of Providence. The aim of this essay is to elucidate and historically contextualize Prémontval’s highly original ‘middle point’, as outlined implicitly in the aforementioned books and much more explicitly in a series of essays published after the essay contest had concluded. (shrink)

This chapter examines the pioneering work of Gottfried Wilhelm Leibniz (1646-1716) on various number systems, in particular binary, which he independently invented in the mid-to-late 1670s, and hexadecimal, which he invented in 1679. The chapter begins with the oft-debated question of who may have influenced Leibniz’s invention of binary, though as none of the proposed candidates is plausible I suggest a different hypothesis, that Leibniz initially developed binary notation as a tool to assist his investigations in mathematical problems that were (...) exercising him at the time, namely those concerning the divisibility of composite numbers, primality, and perfect numbers. The chapter then explores Leibniz’s development of binary, his little-known work on binary fractions and expansions, his use of binary as a symbol for creation in his philosophical-theology, and his response to the suggestion that there was a correlation between binary numeration and the hexagrams of the ancient Chinese divinatory text, the Yijing. The chapter then focuses on Leibniz’s work on other number systems, in particular his invention and exploration of hexadecimal as well as his work on duodecimal. The chapter concludes by revealing a hitherto unknown practical application of binary that Leibniz devised in the last year of his life. (shrink)

Neil Gorsuch lauds judges who purport to “apply the law as it is, focusing backward, not forward, and looking to text, structure, and history to decide what a reasonable reader at the time of the events in question would have understood the law to be . . . .” It’s hard to see how such a form of Originalism withstands scrutiny. -/- First, using “reasonable reader” understandings rather than speaker meaning turns language and law on their heads. Audiences effectively become (...) the speakers in ordinary speech (since reader or audience meaning prevails), and audiences (and thus the ruled) effectively become the rulers when interpreting law (since audiences’ meaning prevails). -/- Second, since laws look forward to govern conduct, how can best legal practices keep such a backward focus? -/- Third, words (however understood by others at the time “originally” uttered) may or may not (depending on speaker and not reader meaning) signify concepts whose meanings embrace change over time. For example, the word “planet” used by a speaker before the discovery of Uranus and Neptune may or may not include further planets depending upon what the speaker meant by “planet.” (The same applies to the inclusion or exclusion of Pluto had the speaker used the word “planet” after the discovery of Pluto but before its exclusion by current science.) Unlike the “reasonable” reader of Gorsuch’s Originalism as phrased above, speakers run the gamut from reasonable to unreasonable, from informed to uninformed, and from thoughtful to thoughtless. -/- Fourth, to the extent a judge is principally “constrained” by a text or texts (as he may determine), by dictionaries that he chooses, and by “history” as the judge understands it, isn’t judicial activism encouraged rather than restrained? Talk of a “reasonable” reader masks the fact that there can be multiple “reasonable” conclusions of what a reasonable or unreasonable speaker meant. Is a judge not therefore left to pick definitions and applications of terms that accord with the judge’s understandings of history, understandings that may well be colored by the judge’s politics and judicial philosophy? This applies to principles as well as labels for things. Principles are also subject to multiple frames, and their terms are subject to multiple definitions therefore raising the very same questions just raised above. -/- Finally, such Originalism doesn’t merely fail with legal texts. It also fails when applied to other texts (including sacred texts such as the Ten Commandments) and when used to interpret art (such as “Landscape with the Fall of Icarus” often attributed to Bruegel and which inspired such great ekphrasis as Auden’s “Musée Des Beaux Arts”). These further failures underscore the dysfunction of Originalism in Gorsuch's form noted above. -/- Keywords: Originalism, Neil Gorsuch, Text, Textualism, Scalia, Interpretation, Pragmatics, Speaker Meaning, Art, Painting, Bruegel, Auden, Ekphrasis, Icarus, Bible, Ten Commandments, Herod, Declaration of Independence, Abraham Lincoln. (shrink)

The first collection of Leibniz's key writings on the binary system, newly translated, with many previously unpublished in any language. -/- The polymath Gottfried Wilhelm Leibniz (1646–1716) is known for his independent invention of the calculus in 1675. Another major—although less studied—mathematical contribution by Leibniz is his invention of binary arithmetic, the representational basis for today's digital computing. This book offers the first collection of Leibniz's most important writings on the binary system, all newly translated by the authors with many (...) previously unpublished in any language. Taken together, these thirty-two texts tell the story of binary as Leibniz conceived it, from his first youthful writings on the subject to the mature development and publication of the binary system. -/- As befits a scholarly edition, Strickland and Lewis have not only returned to Leibniz's original manuscripts in preparing their translations, but also provided full critical apparatus. In addition to extensive annotations, each text is accompanied by a detailed introductory “headnote” that explains the context and content. Additional mathematical commentaries offer readers deep dives into Leibniz's mathematical thinking. The texts are prefaced by a lengthy and detailed introductory essay, in which Strickland and Lewis trace Leibniz's development of binary, place it in its historical context, and chart its posthumous influence, most notably on shaping our own computer age. (shrink)

We sley Salmon, in his influential and detailed book, Four Decades of Scientific Explanation, argues that the pragmatic approach to scientific explanation, “construed as the claim that scientific explanation can be explicated entirely in pragmatic terms” (1989, 185) is inadequate. The specific inadequacy ascribed to a pragmatic account is that objective relevance relations cannot be incorporated into such an account. Salmon relies on the arguments given in Kitcher and Salmon (1987) to ground this objection. He also suggests that Peter Railton’s (...) concepts of the ideal explanatory text and explanatory information (Railton 1981) can provide what the pragmatic approach lacks. This suggestion is not a conclusion of course; we read it as the promotion of part of a research program aimed at forging a greater consensus on scientific explanation-an admirable goal. However, we do not see the pragmatic approach as inadequate. We will show that a synthetic account inspired by Salmon’s adaptation of Railton would be equivalent to van Fraassen’s pragmatic account in three respects: accepting or rejecting requests for explanation; the practice of giving scientific explanations; and the evaluation of the goodness of explanations. We include all three under the general rubric of explanatory “practice.” Admittedly these are not the only three features by which an account of explanation might be evaluated. Roughly, we mean to show that a synthetic account cannot do a better job of accounting for the scientific practices which are of importance to the constructive empiricist, and therefore no argument can be presented to the constructive empiricist to convince her that by her own standards the synthetic account is superior. (shrink)

The oft-told story of Leibniz’s doctrine of the best world, or optimism, is that it enjoyed a great deal of popularity in the eighteenth century until the massive earthquake that struck Lisbon on 1 November 1755 destroyed its support. Despite its long history, this story is nothing more than a commentators’ fiction that has become accepted wisdom not through sheer weight of evidence but through sheer frequency of repetition. In this paper we shall examine the reception of Leibniz’s doctrine of (...) the best world in the eighteenth century in order to get a clearer understanding of what its fate really was. As we shall see, while Leibniz’s doctrine did win a good number of adherents in the 1720s and 1730s, especially in Germany, support for it had largely dried up by the mid-1740s; moreover, while opponents of Leibniz’s doctrine were few and far between in the 1710s and 1720s, they became increasing vocal in the 1730s and afterwards, between them producing an array of objections that served to make Leibnizian optimism both philosophically and theologically toxic years before the Lisbon earthquake struck. (shrink)

Much debate in contemporary metaphysics of time has centred on whether or not tense is essential to the understanding of a temporal reality. The rival positions in this debate are associated with two very different pictures of the relationship between time and existence. Those who argue for the dispensability of tense see the phenomenon of tense as an epistemological accretion which infects our perception of the world but is in no way essential to a complete description of reality. With respect (...) to existence, things past and future are supposed to be on an equal footing with things present. Thus the Quinean ‘time slice’ ontology, which sees the world as a four-dimensional entity in space-time, repudiates any ontological significance to the differences between past, present and future. For the Quinean, what differences we see between past, present and future existents pertain to our limited mode of access to reality. In a perception which grasped the world as it really is tense differences would have no place. In this respect the Quinean position resembles Spinoza's claim in the Ethics that in so far as the mind conceives a thing under the dictates of reason it is affected equally, whether the idea be of a thing future, past or present. (shrink)

The present discussion takes up an issue raised in Section 5 of Ross Brady and Penelope Rush’s paper ‘Four Basic Logical Issues’ concerning the (claimed) triviality – in the sense of automatic availability – of soundness and completeness results for a logic in a metalanguage employing at least as much logical vocabulary as the object logic, where the metalogical behaviour of the common logical vocabulary is as in the object logic. We shall see – in Propositions 4.5–4.7 – that this (...) triviality claim faces difficulties in the face of Halldén incompleteness, for essentially the same reasons that Halldén thought this phenomenon raised seman- tic difficulties for the modal logics of C. I. Lewis exhibiting it. To counter any inclination to dismiss the phenomenon as providing at best a marginal range of counterexamples to the triviality claim, a Postscript assembles some reminders of the extent of – and the varied considerations favouring – Halldén incompleteness. (shrink)

As a lifelong Lutheran who resisted numerous attempts by Catholic acquaintances to convert him, one might reasonably expect Leibniz to have followedthe orthodox Lutheran line on disputed doctrinal issues, and thus held amongst other things that the doctrine of purgatory was false. Yet there is strong evidencethat Leibniz personally accepted the doctrine of purgatory. After examining this evidence, I determine how Leibniz sought to justify his endorsement of purgatory and explain how his endorsement sits alongside his frequent rehearsal of familiar (...) Protestant arguments against the doctrine. I then examine some of Leibniz’s other theological and philosophical commitments, including those on the afterlife, in order to tentatively tease out further details of the form of purgatory that wonhis approval. In considering these issues, I aim to make clear the extent to which Leibniz’s philosophical thinking underpins and shapes his theological beliefs. (shrink)

The concept of the best of all possible worlds is widely considered to be incoherent on the grounds that, for any world that might be termed the best, there is always another that is better. I note that underlying this argument is a conviction that the goodness of a world is determined by a single kind of good, the most plausible candidates for which are not maximizable. Against this I suggest that several goods may have to combine to determine the (...) goodness of a world, and because of logical conflicts between them, the goods can be optimized to give a genuine best of all possible worlds. (shrink)

This paper examines the fortunes of non-European philosophies in histories of philosophy written by European and American philosophers from the 17th century to the present day. It charts the shift from inclusive histories of philosophy, which included non-European philosophies, to exclusive histories of philosophy, which excluded and/or marginalized non-European philosophies, at the end of the 18th century. This shift was motivated by racial Eurocentrism, which cast a long shadow over histories of philosophy written during the 19th and 20th centuries. The (...) paper also considers recent attempts to produce a more inclusive history of philosophy. By examining the history of the inclusion and exclusion of non-European philosophies in histories of philosophy, this paper seeks to challenge the assumption that philosophy began and has been practised exclusively by European or western thinkers. (shrink)

Many have argued that if God exists then he must necessarily create the best possible world , which entails that the bpw necessarily exists, and is therefore the only possible world. But without any scope for comparison, the superlative term ‘best’ is clearly inappropriate and so the bpw cannot be the bpw at all! As such, it must be impossible for God to create it. Hence if God exists then he must of necessity make something that is impossible to create! (...) Because of its conclusion, I call this the repugnant argument. I consider a number of possible responses to this argument. (shrink)

In early modern times it was not uncommon for thinkers to tease out from the nature of God various doctrines of substantial physical and metaphysical import. This approach was particularly fruitful in the so-called beast-machine controversy, which erupted following Descartes’ claim that animals are automata, that is, pure machines, without a spiritual, incorporeal soul. Over the course of this controversy, thinkers on both sides attempted to draw out important truths about the status of animals simply from the notion or attributes (...) of God. Automatists – led by Nicolas Malebranche and Antoine Dilly – developed six such arguments, appealing to divine justice, providence, economy, glory (twice) and wisdom, while opponents to animal automatism developed two arguments, appealing to divine wisdom and goodness. In this article I shall examine the substance of all eight of these arguments, along with their origins, patronage, and variations, and the objections they elicited from opponents, with the aim of determining their suitability for use in contemporary debates about animal sentience and consciousness, and hence their relevance for contemporary philosophers. (shrink)

** This piece was originally titled "Beyond Borders: Exploring Ubuntu as a Lived Philosophy" but was later retitled "African thought can rescue Western philosophy" by the publisher. ** -/- Western philosophy is often abstract and disconnected from the real ethical problems we face today. Emmanuel Chiwetalu Ossai and Lloyd Strickland argue that the African philosophy of ubuntu, with its emphasis on community, interconnectedness, and practical application of ethical principles, offers a compelling alternative.

Proofs of God in Early Modern Europe offers a fascinating window into early modern efforts to prove God’s existence. Assembled here are twenty-two key texts, many translated into English for the first time, which illustrate the variety of arguments that philosophers of the seventeenth and eighteenth centuries offered for God. These selections feature traditional proofs—such as various ontological, cosmological, and design arguments—but also introduce more exotic proofs, such as the argument from eternal truths, the argument from universal aseity, and the (...) argument ex consensu gentium. Drawn from the work of eighteen philosophers, this book includes both canonical figures (such as Descartes, Spinoza, Newton, Leibniz, Locke, and Berkeley) and noncanonical thinkers (such as Norris, Fontenelle, Voltaire, Wolff, Du Châtelet, and Maupertuis). -/- Lloyd Strickland provides fresh translations of all selections not originally written in English and updates the spelling and grammar of those that were. Each selection is prefaced by a lengthy headnote, giving a biographical account of its author, an analysis of the main argument(s), and important details about the historical context. Strickland’s introductory essay provides further context, focusing on the various reasons that led so many thinkers of early modernity to develop proofs of God’s existence. -/- Proofs of God is perfect for both students and scholars of early modern philosophy and philosophy of religion. (shrink)

I propose a distinct type of robustness, which I suggest can support a confirmatory role in scientific reasoning, contrary to the usual philosophical claims. In model robustness, repeated production of the empirically successful model prediction or retrodiction against a background of independentlysupported and varying model constructions, within a group of models containing a shared causal factor, may suggest how confident we can be in the causal factor and predictions/retrodictions, especially once supported by a variety of evidence framework. I present climate (...) models of greenhouse gas global warming of the 20th Century as an example, and emphasize climate scientists’ discussions of robust models and causal aspects. The account is intended as applicable to a broad array of sciences that use complex modeling techniques. (shrink)

Moral latitude is only ever a matter of coincidence on the most popular decision procedure in the literature on moral uncertainty. In all possible choice situations other than those in which two or more options happen to be tied for maximal expected choiceworthiness, Maximize Expected Choiceworthiness implies that only one possible option is uniquely appropriate. A better theory of appropriateness would be more sensitive to the decision maker’s credence in theories that endorse agent-centred prerogatives. In this paper, we will develop (...) and defend a modified version of this view that allows for agent-centred prerogatives and supererogation as part of its verdicts about appropriateness. (shrink)

A question that has been largely overlooked by philosophers of religion is how God would be able to effect a rational choice between two worlds of unsurpassable goodness. To answer this question, I draw a parallel with the paradigm cases of indifferent choice, including Buridan's ass, and argue that such cases can be satisfactorily resolved provided that the protagonists employ what Otto Neurath calls an ‘auxiliary motive’. I supply rational grounds for the employment of such a motive, and then argue (...) against the views of Leibniz and Nicholas Rescher to show that this solution would also work for God. (shrink)

Recent philosophical attention to climate models has highlighted their weaknesses and uncertainties. Here I address the ways that models gain support through observational data. I review examples of model fit, variety of evidence, and independent support for aspects of the models, contrasting my analysis with that of other philosophers. I also investigate model robustness, which often emerges when comparing climate models simulating the same time period or set of conditions. Starting from Michael Weisberg’s analysis of robustness, I conclude that his (...) approach involves a version of reasoning from variety of evidence, enabling this robustness to be a confirmatory virtue.. (shrink)

This article discusses various dangers that accompany the supposedly benign methods in behavioral evoltutionary biology and evolutionary psychology that fall under the framework of "methodological adaptationism." A "Logic of Research Questions" is proposed that aids in clarifying the reasoning problems that arise due to the framework under critique. The live, and widely practiced, " evolutionary factors" framework is offered as the key comparison and alternative. The article goes beyond the traditional critique of Stephen Jay Gould and Richard C. Lewontin, to (...) present problems such as the disappearance of evidence, the mishandling of the null hypothesis, and failures in scientific reasoning, exemplified by a case from human behavioral ecology. In conclusion the paper shows that "methodological adaptationism" does not deserve its benign reputation. (shrink)

This paper is concerned with Leibniz’s Egypt Plan, written in 1671 and 1672, when Leibniz was in the service of the Elector of Mainz. One of the aims of this paper is to offer a more balanced and plausible reading of the religious benefits of war that Leibniz outlines in his Egypt plan.

We discuss potential biorisks from large language models (LLMs). AI assistants based on LLMs such as ChatGPT have been shown to significantly reduce barriers to entry for actors wishing to synthesize dangerous, potentially novel pathogens and chemical weapons. The harms from deploying such bioagents could be further magnified by AI-assisted misinformation. We endorse several policy responses to these dangers, including prerelease evaluations of biomedical AIs by subject-matter experts, enhanced surveillance and lab screening procedures, restrictions on AI training data, and access (...) controls on biomedical AI. We conclude with a suggestion about future research directions in bioethics. (shrink)

Leibniz wished that his Theodicy (1710) would have as great and as wide an impact as possible, and to further this end we find him in his correspondence with Caroline often expressing his desire that the book be translated into English. Despite his wishes, and Caroline’s efforts, this was not to happen in his lifetime (indeed, it did not happen until 1951, almost 250 years after Leibniz’s death). But even though the Theodicy did not make quite the impact in England (...) that Leibniz had hoped it would, it did draw some attention from the English intelligentsia. In this paper I shall focus on two responses to the Theodicy that were made in England in the years immediately following its publication. First, I shall consider the response of Michel de la Roche and his efforts to promote the book to an English audience in 1711 (efforts which only came to Leibniz’s attention much later, in 1713). De la Roche’s response was broadly positive, though his admiration for the Theodicy was tempered by his belief that Leibniz had struggled – unsuccessfully – to reconcile free will with divine foreknowledge. Second, I shall consider the largely negative response of George Smalridge, the Bishop of Bristol, who delivered his verdict on the book in a letter to Sophie written in 1714. Leibniz subsequently wrote a point-by-point rebuttal of (most of) Smalridge’s criticisms in a letter to Caroline, conceding only one very minor point to the Bishop. As we shall see, some of the points of substance raised by de la Roche and Smalridge have loomed over the Theodicy ever since. (shrink)

The focus of this paper is a suite of Latin papers from 1685, some of which are still unpublished, in which Leibniz writes in the guise of a Catholic in order to defend Catholicism and counter Protestant objections, and this despite him being a lifelong Lutheran. After providing an overview of these writings (which I refer to as Leibniz’s “Catholic” writings) and the grounds for dating them to May–June 1685, I consider their purpose, arguing against the claim that they were (...) intended to support Church reunion and suggesting instead that they were apologetic in nature, intended as a reactivation or reimagining of Leibniz’s earlier “Catholic Demonstrations” project. I identify the patron Leibniz had in mind for these writings as Landgrave Ernst von Hessen-Rheinfels and support this by a detailed comparison of the “Catholic” writings with the Leibniz-Landgrave correspondence and the Landgrave’s still-unpublished essays. This reveals that the Protestant arguments Leibniz uses in the “Catholic” writings are the very ones that he himself used when writing to the Landgrave, and that the responses Leibniz gives to these arguments are the very ones that the Landgrave used. I also consider the context of the writings, suggesting they were crafted during a period of personal uncertainty for Leibniz and possibly aimed at securing a position under the Landgrave. (shrink)

In 1682, Leibniz published an essay containing his solution to the classic problem of squaring the circle: the alternating converg-ing series that now bears his name. Yet his attempts to disseminate his quadrature results began seven years earlier and included four distinct approaches: the conventional (journal article), the grand (treatise), the impostrous (pseudepigraphia), and the extravagant (medals). This paper examines Leibniz’s various attempts to disseminate his series formula. By examining oft-ignored writings, as well as unpublished manuscripts, this paper answers the (...) question of how one of the greatest mathematicians sought to introduce his first great geometrical discovery to the world. (shrink)

One of the more exotic and mysterious features of Leibniz’s later philosophical writings is the harmony between the kingdom of nature and the kingdom of grace. In this paper I show that this harmony is not a single doctrine, but rather a compilation of two doctrines, namely (1) that the order of nature makes possible the rewards and punishments of rational souls, and (2) that the rewards and punishments of rational souls are administered naturally. I argue that the harmony is (...) best considered as Leibniz’s distinctive collation, development, and rebranding of these doctrines, which were not themselves unique to Leibniz, nor uncommon in the seventeenth century. There follows a detailed examination of various concrete examples of the harmony in operation, from which I show that it is essentially the culmination of Leibniz’s lifelong thinking about divine justice. (shrink)

I discuss two types of evidential problems with the most widely touted experiments in evolutionary psychology, those performed by Leda Cosmides and interpreted by Cosmides and John Tooby. First, and despite Cosmides and Tooby's claims to the contrary, these experiments don't fulfil the standards of evidence of evolutionary biology. Second Cosmides and Tooby claim to have performed a crucial experiment, and to have eliminated rival approaches. Though they claim that their results are consistent with their theory but contradictory to the (...) leading non-evolutionary alternative, Pragmatic Reasoning Schemas theory, I argue that this claim is unsupported. In addition, some of Cosmides and Tooby's interpretations arise from misguided and simplistic understandings of evolutionary biology. While I endorse the incorporation of evolutionary approaches into psychology, I reject the claims of Cosmides and Tooby that a modular approach is the only one supported by evolutionary biology. Lewontin's critical examinations of the applications of adaptationist thinking provide a background of evidentiary standards against which to view the currently fashionable claims of evolutionary psychology. (shrink)

In philosophical circles, Electress Sophie of Hanover (1630-1714) is known mainly as the friend, patron, and correspondent of Leibniz. While many scholars acknowledge Sophie's interest in philosophy, some also claim that Sophie dabbled in philosophy herself, but did not do so either seriously or competently. In this paper I show that such a view is incorrect, and that Sophie did make interesting philosophical contributions of her own, principally concerning the nature of mind and thought.

The emphasis on the limitations of objectivity, in specific guises and networks, has been a continuing theme of contemporary analytic philosophy for the past few decades. The popular sport of baiting feminist philosophers — into pointing to what's left out of objective knowledge, or into describing what methods, exactly, they would offer to replace the powerful objective methods grounding scientific knowledge — embodies a blatant double standard which has the effect of constantly putting feminist epistemologists on the defensive, on the (...) fringes, on the run.This strategy can only work if objectivity is transparent, simple, stable, and clear in its meaning. It most certainly is not. In fact, taking objectivity as a sort of beautiful primitive, self-evident in its value, and all-powerful in its revelatory power, requires careless philosophy, and the best workers in metaphysics, epistemology, and philosophy of science have made reworked definitions of objectivity absolutely central to their own projects. In fact, classic feminist concerns with exploring the impact of sex and gender on knowledge, understanding, and other relations between human beings and the rest of the world fall squarely within the sort of human and social settings thatare already considered central in most current analytic metaphysics, epistemology, and philosophy of science. I argue that the burden of proof is clearly on those who wish toreject the centrality and relevance of sex and gender to our most fundamental philosophical work on knowledge and reality. (shrink)

In recent decades, philosophers and theologians have become increasingly aware of the extent of animal pain and suffering, both past and present, and of the challenge this poses to God’s goodness and justice. As a result, a great deal of effort has been devoted to the discussion and development of animal theodicies, that is, theodicies that aim to offer morally sufficient reasons for animal pain and suffering that are in fact God’s reasons. In this paper, I ask whether there is (...) a need to go even further than this, by considering whether effort should be made to extend theodicy to include plants as well. Drawing upon ideas found in some recent animal theodicies as well as in the work of some environmental ethicists, I offer three arguments for supposing that plants should indeed fall within the purview of theodicy: the argument from non-flourishing as evil, the argument from moral considerability, and the argument from intrinsic value. I also consider a possible objection to each of these arguments. Having outlined and defended the aforementioned arguments for broadening theodicy to include plants as well as humans and animals, I conclude by considering what a plant theodicy might look like. (shrink)

Leibniz Reinterpreted tackles head on the central idea in Leibniz's philosophy, namely that we live in the best of all possible worlds. Strickland argues that Leibniz's theory has been consistently misunderstood by previous commentators. In the process Strickland provides both an elucidation and reinterpretation of a number of concepts central to Leibniz's work, such as 'richness', 'simplicity', 'harmony' and 'incompossibility', and shows where previous attempts to explain these concepts have failed. This clear and concise study is tightly focussed and assumes (...) no prior acquaintance with Leibniz or optimism. It thus serves as an ideal entry point into Leibniz's philosophy. (shrink)

In this paper, I analyze a previously unpublished Leibniz text from the early 1700s. I give it the title “On Unities and Transmigration” since it contains an outline of his doctrine of unities and an examination of the doctrine of transmigration. The text is valuable because in it Leibniz considers three very specific versions of transmigration that he does not address elsewhere in his writings; these are (1) where a soul is released by the destruction of its body and is (...) then free to pass into another body, (2) where souls are exchanged without any destruction of bodies, and (3) where human souls (minds) are exchanged, again without any destruction of bodies. I show that when tackling these three versions of transmigration in “On Unities and Transmigration,” Leibniz develops a series of objections that are not found anywhere else in his published writings, despite his lifelong opposition to the doctrine of transmigration. This paper is completed by two appendices, the first of which presents the previously unpublished “On Unities and Transmigration” text in full, in the original French (with all deletions indicated), while the second presents its English translation. (shrink)