Alexander of Aphrodisias picks up Aristotle’s insufficient treatment of simultaneous perception and develops an adequate solution for the problem, thereby offering an account of the unity of perceptual consciousness—the single mental activity of a single subject with complex content. I show the adequacy of the solution by using as criteria the requirements that have been identified by Aristotle and approved (and explained) by Alexander. I analyze Alexander’s solution in two turns. First, with respect to heterogeneous perceptibles, (...) Alexander adopts and reformulates Aristotle’s metaphorical account invoking the analogy with a point. Second, with respect to homogeneous opposites, accordingly, perception is judgement, but it involves physical changes in diverse parts of the primary sense-organ. By this account Alexander resolves the issue of the unity of the subject on the level of the capacity of the soul, and coordinates the complexity of content with the complexity on the physical level. In addition to being adequate, the solution is faithful to Aristotle. I suggest that the interpretative decisions Alexander makes (the clarification of the analogy; the reference he finds to the analogy; the two components of the solution, judgement and parts of the organ) form an ingenious extension of Aristotle’s treatment. Interestingly, even though many elements in Alexander’s interpretation are taken up by modern commentators, no one has followed it in its entirety, nor even treated it in its own right. (shrink)

ABSTRACT: Alexander of Aphrodisias’ commentaries on Aristotle’s Organon are valuable sources for both Stoic and early Peripatetic logic, and have often been used as such – in particular for early Peripatetic hypothetical syllogistic and Stoic propositional logic. By contrast, this paper explores the role Alexander himself played in the development and transmission of those theories. There are three areas in particular where he seems to have made a difference: First, he drew a connection between certain passages from (...) Aristotle’s Topics and Prior Analytics and the Stoic indemonstrable arguments, and, based on this connection, appropriated at least four kinds of Stoic indemonstrables as Aristotelian. Second, he developed and made use of a specifically Peripatetic terminology in which to describe and discuss those arguments – which facilitated the integration of the indemonstrables into Peripatetic logic. Third, he made some progress towards a solution to the problem of what place and interpretation the Stoic third indemonstrables should be given in a Peripatetic and Platonist setting. Overall, the picture emerges that Alexander persistently (if not always consistently) presented passages from Aristotle’s logical œuvre in a light that makes it appear as if Aristotle was in the possession of a Peripatetic correlate to the Stoic theory of indemonstrables. (shrink)

The first English translation of the commentary of Alexander of Aphrodisias on Aristotle's De Sensu.With notes.

To study the influence of divinity on cosmos, Alexander uses the notions of ‘fate’ and ‘providence,’ which were common in the philosophy of his time. In this way, he provides an Aristotelian interpretation of the problems related to such concepts. In the context of this discussion, he offers a description of ‘nature’ different from the one that he usually regards as the standard Aristotelian notion of nature, i.e. the intrinsic principle of motion and rest. The new coined concept is (...) a ‘cosmic’ nature that can be identified with both ‘fate’ and ‘divine power,’ which are the immediate effect of providence upon the world. In the paper it is exposed how the conception of providence defended by Alexander means a rejection of the divine care of the particulars, since the divinities are only provident for species. Several texts belonging to the Middle Platonic philosophers will convince us that such thinkers (and not directly Aristotle) are the origin of the thesis that will be understood as the conventional Aristotelian position, namely that divinity only orders species but not individuals. (shrink)

The philosophical problem of universals is traditionally framed as the problem about the ontological status of universals. It is often said that the ontological status of universals is a post-Aristotelian problem that was bequeathed to the Middle Ages by a famous sentence in Porphyry's Isagoge. 1 Porphyry raises but then refuses to answer three questions about the ontological status of genera and species, saying that they are too "deep" for the present investigation. 2 Although Porphyry is the first to announce (...) the problem, it was Boethius's commentary on Porphyry, rather than the Isagoge itself, that made this sentence famous and that is therefore responsible for the problem of universals in .. (shrink)

SUMMARY. The works of Alexander of Aphrodisias were written a few decades after the publication of the most successful -astrology hand- book in antiquity, Ptolemy's Tetrabiblos Syntaxis, which attempts to naturalize astrology, i.e. to make it agree with Aristotelian theory of science. A comparison of the doctrines between the Tetrabiblos and some passages of Alexander'p works on fate demostrates a noteworthy con¬vergere of the two scholars, and probably a dependence of the lasi great greek Aristotle's exegete on (...) the theories of Ptolemaic astrology, at least in reference to three points: theory of fate; justification of de- vining as a technical and naturai conjecture about man's fate; ana¬lysis of the stars' influence on the sublunary world in physical and phi¬losophical terms. (shrink)

One of the main philosophical works by Alexander of Aphrodisias, De principiis, is lost in its original Greek text, but it is preserved in three extant Medieval Semitic versions, one in Syriac and two in Arabic, which were written in the Near East between 500 and 950 AD. These versions are not totally identical and, as we have shown in 2012, they are in a rather complex textual relationship. As we will show in this article, a tentative reconstruction (...) of the lost text should be based upon an attentive and point‑to‑point comparative analysis of some aspect of all three versions. We have tentatively called the abore way “critical translation”. (shrink)

In this article I argue for the thesis that Alexander's main argument, in Ethical Problems I, is an attempt to block the implication drawn by the Stoics and other ancient philosophers from the double potential of use exhibited by human life, a life that can be either well or badly lived. Alexander wants to resist the thought that this double potential of use allows the Stoics to infer that human life, in itself, or by its own nature, is (...) neither good nor bad. Furthermore, I shall argue that Alexander's main argument establishes that human life, despite exhibiting a double potential of use, is by its own nature or intrinsically good. Finally, given that this is not a conclusion that the Stoics are likely to accept, I shall also contend that the argument should be regarded as conducted for the most part in foro interno, as a way of persuading the Peripatetics themselves of the falsity of the Indifference Implication, precisely because of the risk that such an implication be derived from their own theoretical framework. (shrink)

The differences between the theories of hearing held by Aristotle and by Alexander of Aphrodisias are explored. Alexander appears to have a more systematic approach which avoids the dilemma faced by Aristotle in deciding whether the hearing process constitutes a time-taking kinesis or an instantaneous energeia.

Alexander of Aphrodisias' treatise On Providence presents an argument that global warming is impossible based on the existence of divine providence: this raises the question of the compatibility of theism and environmentalism.

Aristotle sometimes claims that the perception of special perceptibles by their proper sense is unerring. This claim is striking, since it might seem that we quite often misperceive things like colours, sounds and smells. Aristotle also claims that the perception of common perceptibles is more prone to error than the perception of special perceptibles. This is puzzling in its own right, and also places constraints on the interpretation of. I argue that reading Alexander of Aphrodisias on perceptual error (...) can help to make good sense of both of Aristotle’s claims. (shrink)

The revised and polished version of Inwood’s 2011 Carl Newell Jackson at Harvard University, Ethics after Aristotle surveys the ethical teachings of the original “neo-Aristotelians,” namely those self-identified (although not always named) members of the Peripatetic school from the time of Theophrastus (fl. 300 BCE) until that of Alexander of Aphrodisias (fl. 200 CE). An initial chapter surveys the sorts of problems in Aristotle’s ethical corpus which would generate subsequent debate amongst members of the Peripatetic school. Chapter Two (...) examines the views of “Magnus,” the name which Inwood gives to the anonymous 3rd century author of the Magna Moralia (which Inwood takes to be pseudo-Aristotle), and those of Strato of Lampsacus, Lycon, and Hieronymus, 3rd century heads of the Peripatetic school, all of whom show the influences of Epicureanism in their re-articulations of Aristotelian positions. Chapter Three, entitled “The Turning Point,” finds in the work of Critolaus—head of the Peripatetic school in the middle of the 2nd century BCE—a move away from the centrality of activity within Aristotelian ethical thought, which Critolaus instead replaces with the notion of possessing specific goods, namely those of the body, the soul, and what is external. The same chapter argues that at approximately the same historical point Cicero, in the character of Piso in De finibus, articulated an account of Peripatetic ethics that was far more faithful to 4th century Aristotelianism. The final two chapters focus on neo-Aristotelian ethical philosophizing within a new and explicitly Roman cultural setting. (shrink)

Alexander of Aphrodisias understood the Aristotle´s Unmoved Mover as efficient cause only to the extent that it is the final cause of heaven, which by moving strives to imitate the divine rest. Aquinas seems to agree with him. However his interpretation is original and philosophically more satisfactory: God is the efficient cause of the world, not only as creator, but also as it´s ruler. In this way God is also the final cause.

In his commentary on Aristotle's Metaphysics, Alexander of Aphrodisias quotes from Aristotle's now-lost work On the Ideas -- his account of the arguments offered by Plato for the theory of Forms and his criticisms of those arguments. This paper considers one of these arguments, the Argument from Relatives (ta pros ti). It considers how Plato argued for Forms or Ideas such as the Large Itself, the Just Itself and so on and whether Plato supposed that there were Forms (...) corresponding to sortal terms like Man. (shrink)

This volume focuses on philosophical problems concerning sense perception in the history of philosophy. It consists of thirteen essays that analyse the philosophical tradition originating in Aristotle’s writings. Each essay tackles a particular problem that tests the limits of Aristotle’s theory of perception and develops it in new directions. The problems discussed range from simultaneous perception to causality in perception, from the representational nature of sense-objects to the role of conscious attention, and from the physical/mental divide to perception as quasi-rational (...) judgement. -/- The volume gives an equal footing to Greek, Arabic, and Latin philosophical traditions. It makes a substantial contribution not just to the study of the Aristotelian analysis of sense perception, but to its reception in the commentary tradition and beyond. Thus, the papers address developments in Alexander of Aphrodisias, Themistius, Avicenna, John of Jandun, Nicole Oresme, and Sayf al-Din al-Amidi, among others. The result of this is a coherent collection that attacks a well-defined topic from a wide range of perspectives and across philosophical traditions. (shrink)

The view that living beings as well as plant-based medicaments possess causal properties that are caused by the causal properties of their constituents, without being reducible to the combination of the causal properties of these constituents goes back to ancient thinkers such as Alexander of Aphrodisias and Johannes Philoponus. In the early modern period, this view was not only criticized by natural philosophers taking a reductionist stance; it was also criticized by Neo-Platonic thinkers such as Jean Fernel. One (...) of the relatively few early modern natural philosophers who adopted an emergentist position was Jacob Schegk. The present article discusses whether Schegk’s analysis of the structure of plants and medicaments offers the theoretical resources required to answer Fernel’s critique of the tradition going back to Alexander. In particular, it examines whether Schegk’s account of synchronic upward causation and diachronic downward causation could offer solutions to two interrelated problems identified by Fernel: the question of whether a mere aggregates of material particles could form a composite that possesses substantiality, not only accidental unity; and the question of whether multitudes of material particles could bring forth simple forms, whose existence seems to be presupposed by powers that cannot be ascribed to the constituents. (shrink)

In his early metaphysics, Leibniz interprets the results of Santorio’s quantitative methods as supporting the possibility of the natural immortality of human beings. A closer look into Santorio’s more theoretically oriented medical writings reveals that he vehemently rejected the idea of natural immortality. Still, it may be interesting to ask what the theoretical differences between the natural philosophies of Santorio and the early Leibniz are that could explain their diverging attitudes toward the possibility of natural immortality. I will argue for (...) two claims: (1) Santorio but not the early Leibniz, makes use of emergentist ideas along lines developed by Alexander of Aphrodisias and Galen. (2) The early Leibniz, but not Santorio, uses the concept of emanative causation to characterize the relation between the soul and its potencies. (shrink)

L'esistenza del commento di Alessandro di Afrodisia al De generatione aristotelico, perduto nella versione greca e nella traduzione araba, è attestata da numerose fonti arabe, tra le quali Averroè, nel suo commento alla stessa opera. L'A. rintraccia la presenza, la tipologia e la distribuzione delle citazioni tratte dal commento di Alessandro nel Kitab al-Tasrif, un'opera del corpus alchemico attribuita a Gabir ibn Hayyan. Secondo l'A., la sezione interessata dalle citazioni assembla tre diversi tipi di testi: 1) lemmi del De generatione (...) in traduzione araba; 2) frammenti lacunosi della traduzione araba del commento di Alessandro; 3) interventi di collegamento. Una più ampia discussione si trova in un saggio visibile sulla pagina "publicationslist" dell'autore: "Alessandro di Afrodisia sulle 'contrarietà tangibili' (De gen. et corr. II.2): fonti greche e arabe a confronto" in: Aristotele e Alessandro di Afrodisia nella tradizione araba, a c. di C. D'Ancona e G. Serra, “Il Poligrafo”, Padova 2002, pp. 151-189. Notasi che il testo ricostruito di Alessandro in GC 2.2-5 è stato pubblicato da E. Gannagé nella serie ACA, che però non menziona il contributo di SF, dalla cui iniziativa, dalle cui analisi e dalla cui ricostruzione integrale, svolta sul manoscritto arabo Paris. 5099, la ricerca prese l'avvio. (shrink)

ABSTRACT: This paper traces the earliest development of the most basic principle of deduction, i.e. modus ponens (or Law of Detachment). ‘Aristotelian logic’, as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as ‘hypothetical syllogisms’. However, Aristotle did not discuss such arguments, nor did he call any (...) arguments ‘hypothetical syllogisms’. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them ‘hypothetical syllogisms’; nor did they describe them as ponendo ponens, etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle’s logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called ‘hypothetical syllogisms’? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle’s dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle’s logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories. (shrink)

ABSTRACT: In contemporary discussions of freedom in Stoic philosophy we often encounter the following assumptions: (i) the Stoics discussed the problem of free will and determinis; (ii) since in Stoic philosophy freedom of the will is in the end just an illusion, the Stoics took the freedom of the sage as a substitute for it and as the only true freedom; (iii) in the c. 500 years of live Stoic philosophical debate, the Stoics were largely concerned with the same philosophical (...) problems of freedom. In this paper I argue that (i) can be upheld only in a very restricted way; (ii) is altogether untenable; and regarding (iii), that, although there may have occurred little change in the Stoic philosophical position on freedom over the centuries, we can detect more than one transformation of the philosophical problems that were at the forefront of the discussion. Moreover, that all the conceptions and problems of freedom were linked to Stoic ethics, and that the differences between them become transparent when one considers their various roles in this context. (shrink)

A new translation and edition of Aristotle's Protrepticus (with critical comments on the fragments) -/- Welcome -/- The Protrepticus was an early work of Aristotle, written while he was still a member of Plato's Academy, but it soon became one of the most famous works in the whole history of philosophy. Unfortunately it was not directly copied in the middle ages and so did not survive in its own manuscript tradition. But substantial fragments of it have been preserved in several (...) works by Iamblichus of Chalcis, a third century A.D. neo-Pythagorean philosopher and educator. On the basis of a close study of Iamblichus' extensive use and excerption of Aristotle's Protrepticus, it is possible to reconstruct the backbone of the lost work, and then to flesh it out with the other surviving reports about the work from antiquity (for example in Alexander of Aphrodisias and other ancient commentators on Aristotle). It is also possible to identify several papyrus fragments of the work, and many references and literary allusions in later authors, especially Cicero, whose own lost dialogue Hortensius was a defense of philosophy modeleld on Aristotle's. (shrink)

ABSTRACT: One-page entry on freedom in the philosophical (as opposed to political) sense in antiquity, noting (among other things) that a notion of freedom of choice that requires that the person not be causally predetermined in his/her actions is developed only in the 1st-3rd cents. CE in Alexander of Aphrodisias, building on elements of Aristotelian ethics and logic, Stoic psychology and perhaps Christian and Middle Platonic influences. Both German version (1998) and English translation (2011).

Aristotle says that ὑπαρχειν has as many senses as ‘to be true’ (PrA. , A, 36, 48b2-9) and as many ways as there are different categories. (PrA., A, 37, 49a6-9) This may mean that for every ‘is’ there is a ὑπαρχειν. Τhe reason is that Aristotle uses ὑπαρχειν in converse direction of ‘is’. The equal statement of ‘A is B’ with ὑπαρχειν is ‘B ὑπαρχει to A.’ Allen Bāck points to the difference between the use of the verb with dative (...) case and its use with a subject alone in Greek language. When it is used with the dative, it retains its basic meaning, that is, ‘be already present’ or ‘exist really.’ ‘So to say that P belongs to S is to say that P exists in S, or, if you like, that P has its being in S.’ He believes that Aristotle uses this construction to insist that primary substances alone are the fundamental being and all other things only are ‘in’ substances. Thus, when the verb is used with the dative, it expresses dependent substance relation. But when it is used with a subject alone, e.g. in ‘S ὑπάρχει,’ it expresses that the subject really exists. (OI., 17a24 and 17b2) Thus, while it is the subject which is said to be the predicate, it is the predicate which ὑπάρχει to the subject. The formula of ‘τὸ Α ὑπάρχει τῷ Β’ is equivalent to ‘τὸ Β ἐστι Α.’ He uses the word for the predication of a category on substance (e.g. Met., α, 993b24-25; Met., Z, 1029a15-16; Cat., 5, 3b24-25), the predication of secondary substance on primary substance (e.g. Met., Z, 1038b21-23; Cat., 5, 2a14-19), the predication of primary substance on nothing else but itself (e.g. Met., Z, 1040b23-24), the belonging of a verb to the subject, the belonging of axioms to a single science (Met., 1005a22-23) , the belonging of PNC to all things that are (Met., IV, 3) , in the sense of really existing (Cael. 297b22, Met., 1041b4. Cf. B503, 125-126) or merely in the sense of the predication of a predicate on a subject (e.g. OI., I, 5, 17a22-24) and especially and much more repeatedly than anywhere else in his discussion of syllogism. (e.g. PrA., A, 36, 48a40-b2; PrA., B, 22, 67b28-30; PrA., A, 24a26-28) It is also used in some related senses like mere belonging (e.g. Met., A, 989a10-14; K, 1060a9-10) or to be there. (So., B, 5, 417b23-26) Some of its derived forms are also used by Aristotle. For example, ἐνυπαρχον in the sense of the thing that is ‘in’ something; (e.g. Met., A, 991a13-16; Met., Z, 1038b29-33 and 1039a3-5) ὑπερέχον in the sense of that which contains and ὑπερεχόμενον in the sense of that which is contained in something else. (e.g. Met., Δ, 1020b26-28) In a sense, the extent of the application of ὑπαρχειν is wider than ‘is’ since it is not restricted to the nominative form in which ‘is’ is used but is applicable to other cases as well: ‘For ‘That does not belong to this’ does not always mean that ‘This is not that’ but sometimes that ‘this is not of that’ or ‘for that.’ (PsA., A, 36, 48b28-33) Allen Bāck (B503, 124) points that in the Prior Analytics Aristotle uses ‘ὑπάρχει τῷ’ and ‘κατηγορεῖσθαι κατά’ interchangeably. (e.g. at 25b37-26a4) Referring to its converse construction in respect of μετέχει (if A belongs to B, then B participates in A) as a probable reason that it may have Platonist foundations. But the question is: why does Aristotle uses this construction (B belongs to A) instead of simply saying A is B? Alexander of Aphrodisias (Apr 54.21-29) wonders why Aristotle had to adhere to such artificial language, entirely unnatural for ordinary speakers of Greek. As Jonathan Barnes points out, all the three formulas of ‘τὸ Α ὑπάρχει τῷ Β,’ ‘τὸ Α κατηγορεῖται κατὰ τοῦ Β’ and ‘τὸ Α λέγεται κατὰ τοῦ Β’ are artificial in the sense that no Greek who wanted to say that pleasure was good would normally have expressed himself by way of any of them.’ Bāck thinks Aristotle may have used it ‘to stress the primacy of primary substances as the ultimate subjects.’ He also mentions the probability that it may be to emphasize that the terms are being coupled in predication without any existence condition, a suggestion he is not himself inclined with. Robin Smith notes for Aristotle that ‘belonging to’ construction is wider than ‘predicated of’ construction because it can be used for cases that cannot easily be treated as categorical sentences. While predication is restricted to cases in which the subject term is in the nominative case, belonging can indicate, as he quotes Mignucci (480-481), ‘any possible grammatical construction for a predicative relation’ . (shrink)

This article faces the classic problem of the interpretation of what Aristotle calls in de An. III, 5 “the intellect that produces all things”, which is commonly named agent intellect. Historically, there have been two approaches: one that goes back to Alexander of Aphrodisias, who associates the agent intellect with the unmoved mover and the divinity, and another one, associated with Theophrastus but whose major representatives are Philoponus and St. Thomas of Aquinas, who consider that agent intellect is (...) an exclusively human faculty. This last interpretation has been the most accepted historically. Nevertheless, in recent years there has been a resurgence of interpretations of the agent intellect as divine (Caston, Frede, Burnyeat, and others). What we want to demonstrate in this article is that this revival, more than responding to a reinterpretation of the agent intellect, is due to a different understanding of the divinity in Aristotle’s philosophy, which supposes immanent characteristics closer to the human intellect. (shrink)

This article shows the origin of the famous Aristotelian expression τὸ τί ἦν εἶναι in everyday language. The expression is analysable in τὸ εἶναι and τί ἦν, and this part is the core of the common language question τουτὶ τί ἦν; or τουτὶ τί ἦν τὸ πρᾶγμα; always in imperfect form. This question is often found in Aristophanes’ comedies, which represent common Attic language. The imperfect ἦν is noted as a common Attic form indicating the present already by early comentators (...) of Aristotle as Alexander of Aphrodisias, the scholia to Aristophanes, later by Budaeus, but also in the modern Greek Lexikon of D. Demetrakos. Therefore not the imperfect is the problem, by mere embarrassement it was called "philosophic." The situations in the Aristophanean comedies, in which the question occurs, show that the thing about which somebody asks, is present, in front of the speaker, that it is an individual thing and something absolutly unexspected. The questioner will ask "What on the whole is this?" He asks about the first ground of being of the thing. The term τὸ τί ἦν εἶναι quotes only the use of εἶναι in this question in common language (like many other terms are quotations as τὸ τί ἐστίν; τὸ οὗ ἕνεκα etc.) and may be paraphrased by "Think of ’to be’ as you use it in the question ’What at all is this?’ " See also my article: Sonderegger (2001). Zur Sprachform des Ausdrucks to ti en einai. Rheinisches Museum Für Philologie 144:113–122. -/- The consequences of this linguistic finding can be found in my comments on Metaphysik Z and Metaphysics Λ (English version from 2020). (shrink)

Contemporary work on Boethius' Consolation of Philosophy often overlooks a discussion in CP.V.3 of a Peripatetic strategy for dissolving theological fatalism. Boethius’ treatment of this strategy and the lesson it provides about divine foreknowledge requires a reorientation of our understanding of the Consolation text. The result is that it is not foreknowledge nor any other temporally-conditioned knowledge that motivates Boethian concern but divine knowledge simpliciter.

This paper looks at the causal activity of the unmoved mover of Aristotle. The author affirms both the efficient causality of God and his teleological role. He thinks that the principal character, by describing God, is ‘thinking on thinking’. That means his most important factor to act cannot only ‘be aimed’ but must also ‘be thought’. There are many new texts to defend such as an efficient causal interpretation and also various philosophical arguments to support final causality.

In this work we show that our self-awareness and perception may be successfully explained using two dimensional holistic structures with closed topology embedded into our brains - elastic membranes. These membranes are able to preserve their structure during conscious processes. Their elastic oscillations may be associated with our perceptions, where the frequency of the oscillations is responsible for the perception of different colors, sounds and other stimuli, while the amplitude of the oscillations is responsible for the feeling of a distance. (...) According to the model the squeezed regions of a membrane correspond to the brain zones involved into awareness and attention. The model may be useful for prediction, explanation and interpretation of various conscious phenomena. (shrink)

Do we live in a computer simulation? I will present an argument that the results of a certain experiment constitute empirical evidence that we do not live in, at least, one type of simulation. The type of simulation ruled out is very specific. Perhaps that is the price one must pay to make any kind of Popperian progress.

I propose an approach to liar and Curry paradoxes inspired by the work of Roger Swyneshed in his treatise on insolubles (1330-1335). The keystone of the account is the idea that liar sentences and their ilk are false (and only false) and that the so-called ''capture'' direction of the T-schema should be restricted. The proposed account retains what I take to be the attractive features of Swyneshed's approach without leading to some worrying consequences Swyneshed accepts. The approach and the resulting (...) logic (called ''Swynish Logic'') are non-classical, but are consistent and compatible with many elements of the classical picture including modus ponens, modus tollens, and double-negation elimination and introduction. It is also compatible with bivalence and contravalence. My approach to these paradoxes is also immune to an important kind of revenge challenge that plagues some of its rivals. (shrink)

A supplemental document for "The Logic of Hyperlogic. Part A: Foundations".

We propose that, for the purpose of studying theoretical properties of the knowledge of an agent with Artificial General Intelligence (that is, the knowledge of an AGI), a pragmatic way to define such an agent’s knowledge (restricted to the language of Epistemic Arithmetic, or EA) is as follows. We declare an AGI to know an EA-statement φ if and only if that AGI would include φ in the resulting enumeration if that AGI were commanded: “Enumerate all the EA-sentences which you (...) know.” This definition is non-circular because an AGI, being capable of practical English communication, is capable of understanding the everyday English word “know” independently of how any philosopher formally defines knowledge; we elaborate further on the non-circularity of this circular-looking definition. This elegantly solves the problem that different AGIs may have different internal knowledge definitions and yet we want to study knowledge of AGIs in general, without having to study different AGIs separately just because they have separate internal knowledge definitions. Finally, we suggest how this definition of AGI knowledge can be used as a bridge which could allow the AGI research community to import certain abstract results about mechanical knowing agents from mathematical logic. (shrink)

Conventional wisdom has it that truth is always evaluated using our actual linguistic conventions, even when considering counterfactual scenarios in which different conventions are adopted. This principle has been invoked in a number of philosophical arguments, including Kripke’s defense of the necessity of identity and Lewy’s objection to modal conventionalism. But it is false. It fails in the presence of what Einheuser (2006) calls c-monsters, or convention-shifting expressions (on analogy with Kaplan’s monsters, or context-shifting expressions). We show that c-monsters naturally (...) arise in contexts, such as metalinguistic negotiations, where speakers entertain alternative conventions. We develop an expressivist theory—inspired by Barker (2002) and MacFarlane (2016) on vague predications and Einheuser (2006) on counterconventionals—to model these shifts in convention. Using this framework, we reassess the philosophical arguments that invoked the conventional wisdom. (shrink)

Distributive justice deals with allocations of goods and bads within a group. Different principles and results of distributions are seen as possible ideals. Often those normative approaches are solely framed verbally, which complicates the application to different concrete distribution situations that are supposed to be evaluated in regard to justice. One possibility in order to frame this precisely and to allow for a fine-grained evaluation of justice lies in formal modelling of these ideals by metrics. Choosing a metric that is (...) supposed to map a certain ideal has to be justified. Such justification might be given by demanding specific substantiated axioms, which have to be met by a metric. This paper introduces such axioms for metrics of distributive justice shown by the example of needs-based justice. Furthermore, some exemplary metrics of needs-based justice and a three dimensional method for visualisation of non-comparative justice axioms or evaluations are presented. Therewith, a base worth discussing for the evaluation and modelling of metrics of distributive justice is given. (shrink)

Mathematics is everywhere and yet its objects are nowhere. There may be five apples on the table but the number five itself is not to be found in, on, beside or anywhere near the apples. So if not in space and time, where are numbers and other mathematical objects such as perfect circles and functions? And how do we humans discover facts about them, be it Pythagoras’ Theorem or Fermat’s Last Theorem? The metaphysical question of what numbers are and the (...) epistemological question of how we know about them are central to the philosophy of mathematics. These and related philosophical questions are of particular interest because of mathematics’ unusual status. Mathematics is exceptional in that, on the one hand, it appears unhesitatingly true—no one doubts that 2 + 3 = 5—but on the other, as just noted, it is not about the physical world. This ambivalent status is what gives the philosophy of mathematics its special interest. The philosophy of mathematics is also one of the oldest academic fields, more or less coeval with philosophy itself. But contemporary philosophy of mathematics is rather different from its pre-twentieth-century antecedents, largely for three reasons. The first is that since the seventeenth century, mathematics has become integral to science. Science has over the past few centuries become increasingly mathematical, and indeed the fundamental science of nature, physics, is today recognised as a branch of applied mathematics. The second is that mathematics underwent a transformation in the course of nineteenth century: having started the century as a rather traditional-looking science of quantity it emerged a hundred years later a radically transformed abstract theory of structure. The final factor in the transformation of the philosophy of mathematics is the rise of modern logic. Developed by Frege, Cantor and others in the late nineteenth century, modern logic pervades contemporary mathematics, philosophy and computer science, and has had an immeasurable effect on the philosophy of mathematics. These volumes will collect the major works in this major field, with a focus on the last few decades. The anthology will include technical work, which interprets philosophically significant mathematical results or subfields of mathematics, as well as purely philosophical writing, aimed at those without advanced mathematics. The collection should be of interest to both philosophers and mathematicians, as well as to anyone who is susceptible to wondering what the main intellectual tool used in science, economics and finance, and indeed everyday life is ultimately about. (shrink)

Many philosophers of science are ontologically committed to a lush rainforest of special science entities ), but are often reticent about the criteria that determine which entities count as real. On the other hand, the metaphysics literature is much more forthcoming about such criteria, but often links ontological commitment to irreducibility. We argue that the irreducibility criteria are in tension with scientific realism: for example, they would exclude viruses, which are plausibly theoretically reducible and yet play a sufficiently important role (...) in scientific accounts of the world that they should be included in our ontology. In this paper, we show how the inhabitants of the rainforest can be inoculated against the eliminative threat of reduction: by demonstrating that they are emergent. According to our account, emergence involves a screening off condition as well as novelty. We go on to demonstrate that this account of emergence, which is compatible with theoretical reducibility, satisfies common intuitions concerning what should and shouldn't count as real: viruses are emergent, as are trouts and turkeys, but philosophically gerrymandered objects like trout-turkeys do not qualify. (shrink)

This is an introduction to the volume "Explanation Beyond Causation: Philosophical Perspectives on Non-Causal Explanations", edited by A. Reutlinger and J. Saatsi (OUP, forthcoming in 2017). -/- Explanations are very important to us in many contexts: in science, mathematics, philosophy, and also in everyday and juridical contexts. But what is an explanation? In the philosophical study of explanation, there is long-standing, influential tradition that links explanation intimately to causation: we often explain by providing accurate information about the causes of the (...) phenomenon to be explained. Such causal accounts have been the received view of the nature of explanation, particularly in philosophy of science, since the 1980s. However, philosophers have recently begun to break with this causal tradition by shifting their focus to kinds of explanation that do not turn on causal information. The increasing recognition of the importance of such non-causal explanations in the sciences and elsewhere raises pressing questions for philosophers of explanation. What is the nature of non-causal explanations - and which theory best captures it? How do non-causal explanations relate to causal ones? How are non-causal explanations in the sciences related to those in mathematics and metaphysics? This volume of new essays explores answers to these and other questions at the heart of contemporary philosophy of explanation. The essays address these questions from a variety of perspectives, including general accounts of non-causal and causal explanations, as well as a wide range of detailed case studies of non-causal explanations from the sciences, mathematics and metaphysics. (shrink)

The paper takes up Bell's “Everett theory” and develops it further. The resulting theory is about the system of all particles in the universe, each located in ordinary, 3-dimensional space. This many-particle system as a whole performs random jumps through 3N-dimensional configuration space – hence “Tychistic Bohmian Mechanics”. The distribution of its spontaneous localisations in configuration space is given by the Born Rule probability measure for the universal wavefunction. Contra Bell, the theory is argued to satisfy the minimal desiderata for (...) a Bohmian theory within the Primitive Ontology framework. TBM's formalism is that of ordinary Bohmian Mechanics, without the postulate of continuous particle trajectories and their deterministic dynamics. This “rump formalism” receives, however, a different interpretation. We defend TBM as an empirically adequate and coherent quantum theory. Objections voiced by Bell and Maudlin are rebutted. The “for all practical purposes”-classical, Everettian worlds exist sequentially in TBM. In a temporally coarse-grained sense, they quasi-persist. By contrast, the individual particles themselves cease to persist. (shrink)

Existence of state-supported academies of science is a distinctive feature of the fundamental-science organization in Ukraine. Their research staff is divided into two groups: (i) personal members (academicians and corresponding members) and the rest of the researchers. First-group members have numerous economic and status privileges. It is officially purported that personal members are scientifically qualified than their colleagues. We analyzed this hypothesis on the basis of international indicators of the scientifi c activity (numbers of publications in the international peer-reviewed journals (...) and citations in them). The indicators testify that there are no distinctions between representatives of both groups being of the same age and qualifi cation. A conclusion is made that the lifelong privileges of the first group are ill-founded. (shrink)

This article examines two questions about scientists’ search for knowledge. First, which search strategies generate discoveries effectively? Second, is it advantageous to diversify search strategies? We argue pace Weisberg and Muldoon, “Epistemic Landscapes and the Division of Cognitive Labor”, that, on the first question, a search strategy that deliberately seeks novel research approaches need not be optimal. On the second question, we argue they have not shown epistemic reasons exist for the division of cognitive labor, identifying the errors that led (...) to their conclusions. Furthermore, we generalize the epistemic landscape model, showing that one should be skeptical about the benefits of social learning in epistemically complex environments. (shrink)