Scientists depend on complex computational systems that are often ineliminably opaque, to the detriment of our ability to give scientific explanations and detect artifacts. Some philosophers have s...

This article examines the complaint that arbitrary algorithmic decisions wrong those whom they affect. It makes three contributions. First, it provides an analysis of what arbitrariness means in this context. Second, it argues that arbitrariness is not of moral concern except when special circumstances apply. However, when the same algorithm or different algorithms based on the same data are used in multiple contexts, a person may be arbitrarily excluded from a broad range of opportunities. The third contribution is to explain (...) why this systemic exclusion is of moral concern and to offer a solution to address it. (shrink)

I defend an account of sexual orientation, understood as a reflexive disposition to be sexually attracted to people of a particular biological Sex or Sexes. An orientation is identified in terms of two aspects: the Sex of the subject who has the disposition, and whether that Sex is the same as, or different to, the Sex to which the subject is disposed to be attracted. I explore this account in some detail and defend it from several challenges. In doing so, (...) I provide a theoretical framework that justifies our continued reference to Sex-directed sexual orientation as an important means of classifying human subjects. (shrink)

The author addresses speech restrictions on campuses, the axiom “A is A” as it applies to men and women, Roe v. Wade and its effect on examining the definition of personhood, and how this examination may have contributed to the anti-conceptual mentality that was already under way on campuses and elsewhere.

This paper examines rights and the protection of rights from both the minarchist and the anarchist perspectives. The former relies on Objectivist perspectives and the latter relies primarily on Murray Rothbard’s views. My view is that government protection as put forth by Objectivists is coercive, as are all methods of financing. However, under anarcho-capitalism, children who have been killed or abused by their caregivers do not have equal protection under the law. The principle of equal protection is one with which (...) both Objectivists and Rothbard agree. A case is made for government protection of rights under those circumstances. In addition, a case is made for positive rights to parental care for children, and also for government protection of those rights if they have been violated by their caregivers. I also argue for government oversight in instances when the rights of children have been violated and as a consequence the children have no alternative means of care. (shrink)

This article considers the meanings of “life” within Objectivist ethics. It distinguishes between life lived moment to moment and life-as-a-whole. It examines life's finality as related to life being the ultimate value. It questions whether one “lives to consume” or “consumes to live” from a desert island perspective. It discusses what one's whole life entails within the context of decision making. It looks at decisions between competing values. Finally, it discusses the distinction between ethical and ethically neutral actions and suggests (...) ways in which inquiries regarding these may be approached. (shrink)

Cosmopolitanism is an ancient concept whose meaning and significance have shifted over the last two millennia. Most recently, cosmopolitanism has been resurrected to mean “world citizenship” – a renunciation of one’s national identity for the sake of the universal human family. While such an endeavor seems as though it should correspond to Catholic social thought, its iterations in academia and elsewhere have resulted in a preoccupation with personal identity and political doctrine rather than love. Cosmopolitanism is complex and harbors many (...) weaknesses in both theory and practice. Considered in relation to universalism in Catholic social thought, one weakness is thrown into specific relief: cosmopolitanism as a personal identity or political doctrine lacks a unified philosophy of the human person. This essay recasts the desire to form solidarity across national boundaries as universalism within Trinitarian anthropology and discusses accompaniment as exemplary of the love this thought system requires. (shrink)

The existence of various sufferings has long been thought to pose a problem for the existence of a personal God: the Problem of Evil. In this paper, we propose an original version of POE, in which the geographic distribution of sufferings and of opportunities for flourishing or suffering is better explained if the universe, at bottom, is indifferent to the human condition than if, as theists propose, there is a personal God from whom the universe originates: the Problem of Geography. (...) POG moves beyond previous versions of POE because traditional responses to POE are less effective as responses to POG than they are to other versions of POE. (shrink)

: The purpose of this paper is to address from a normative perspective issues raised by John Mueller in Redeeming Economics: Rediscovering the Missing Element. Mueller criticizes economists, including Austrians, for failing to properly address unilateral transfers—in particular, charity, childcare, and crime—in economic thought. Mueller challenges economist Gary Becker’s position that giving increases the […] The post “Charity, Childcare, and Crime: From Objectivist Ethics to the Austrian School” appeared first on Libertarian Papers.

Deafferented subjects, while lacking proprioceptive awareness of much of their bodies, are nevertheless able to use their bodies in basic action. Sustained visual contact with the body parts of which they are no longer proprioceptively aware enables them to move these parts in a controlled way. This might be taken to straightforwardly show that proprioceptive awareness is inessential to bodily action. I, however, argue that this is not the case. Proprioceptive awareness figures essentially in our self-conscious unity as practical subjects. (...) Recognizing this allows us to better understand the nature of the impairment with which deafferented subjects live. (shrink)

This paper concerns the familiar topic of whether we can have genuinely emotional responses such as pity and fear to characters and situations we believe to be fictional1. As is well known, Kendall Walton responds in the negative (Walton (1978); (1990): 195-204 and Chapter 7; (1997)). That is, he is an ‘irrealist’ about emotional responses to fiction (the term is Gaut’s (2003): 15), arguing that such responses should be construed as quasiemotions (Walton (1990): 245), of which their possessor imagines that (...) they are genuine emotions. This is not to deny that an experience in response to a fiction may have a phenomenology very like a given emotion, but to insist that, nonetheless, such responses are not real instances of the emotions which they resemble (Walton (1997)). So, in his most famous example, Charles, who experiences fear-like emotion in relation to a film which depicts the approach of evil slime, does not, despite appearances, experience genuine fear towards the slime, but only quasi-fear (Walton (1990): 195-204)2. Walton’s view presupposes the following view about the nature of emotion3. (shrink)

My topic is a certain view about mental images: namely, the ‘Multiple Use Thesis’. On this view, at least some mental image-types, individuated in terms of the sum total of their representational content, are potentially multifunctional: a given mental image-type, individuated as indicated, can serve in a variety of imaginative-event-types. As such, the presence of an image is insufficient to individuate the content of those imagination-events in which it may feature. This picture is argued for, or (more usually) just assumed (...) to be true, by Christopher Peacocke, Michael Martin, Paul Noordhof, Bernard Williams, Alan White, and Tyler Burge. It is also presupposed by more recent authors on imagination such as Amy Kind, Peter Kung and Neil Van Leeuwen. I reject various arguments for the Multiple Use Thesis, and conclude that instead we should endorse SINGLE: a single image-type, individuated in terms of the sum total of its intrinsic representational content, can serve in only one imagination event-type, whose content coincides exactly with its own, and is wholly determined by it. Plausibility aside, the interest of this thesis is also in its iconoclasm, as well as the challenge it poses for the diverse theories that rest on the truth of the Multiple Use Thesis. (shrink)

Some economists, notably Gary Becker, claim that economic analysis is applicable to any decision, ethical or otherwise. Ethical principles within Objectivist Ethics are based on long-range success— life being the measure of success. This paper examines these different approaches to decision-making. Decision theory and Rand's Benevolent Universe Premise form the basis for the analysis.

This dissertation examines the influence of Cambridge Platonism and materialist philosophy on Mary Astell's early feminism. More specifically, I argue that Astell co-opts Descartes's theory of regulating the passions in his final publication, The Passions of the Soul, to articulate a comprehensive, Enlightenment and body friendly theory of feminine self-esteem that renders her feminism modern. My analysis of Astell's theory of feminine self-esteem follows both textual and contextual cues, thus allowing for a reorientation of her early feminism vis-a-vis contemporary feminist (...) theory . An entire chapter in the dissertation is devoted to Astell's use of Descartes's theory of regulating the passions to render women more substantial and inherently worthy. This rendering becomes more concrete in Astell's feminist framework as she employs the language of the social contract in her fourth publication, Reflections Upon Marriage, to depict wives as contractual slaves. I argue that her assertion concerning women's slavery is theoretically consistent when read in light of her theory of feminine self-esteem, since this theory is based on the Enlightenment principles of self-mastery, independence and self-preservation. Further, I align Astell's early feminism in a dialogic sense with the Continental "querelle des femmes," especially as presented in writings by Christine de Pizan and Agrippa. Astell, I argue, contributes to the "querelle" by framing the feminist problem she wishes to solve concerning women's equality in a robust , philosophical manner that uncannily prefigures Wollstonecraft's call for the universalization of human virtues and the reform of of women's education. (shrink)

Letheby’s book is an engaging and crystal-clear exploration of the philosophical issues raised by the use of psychedelic drugs. In this paper, we focus on the epistemological issues Letheby examines in chapter 8 and argue that his analysis requires an agency-first approach to epistemic evaluation. On an agency-first approach, epistemic evaluation is about identifying the skills agents needs to acquire in order to pursue and fulfil their epistemic goals.

While feminist critiques of AI are increasingly common in the scholarly literature, they are by no means new. Alison Adam’s Artificial Knowing (1998) brought a feminist social and epistemological stance to the analysis of AI, critiquing the symbolic AI systems of her day and proposing constructive alternatives. In this paper, we seek to revisit and renew Adam’s arguments and methodology, exploring their resonances with current feminist concerns and their relevance to contemporary machine learning. Like Adam, we ask how new AI (...) methods could be adapted for feminist purposes and what role new technologies might play in addressing concerns raised by feminist epistemologists and theorists about algorithmic systems. In particular, we highlight distributed and federated learning as providing partial solutions to the power-oriented concerns that have stymied efforts to make machine learning systems more representative and pluralist. (shrink)

This paper reviews some points of agreement between Objectivism and the Austrian school of economics. It also discusses some of my points of departure with Objectivism. One such is Rand’s justification for holding life as man’s ultimate value. I present a case that the recognition of death’s inevitability is needed to establish life as man’s ultimate value. Although death’s inevitability is implicit within Objectivist ethics (in its emphasis on a person’s entire life), the focus of Rand’s discussion of the ultimate (...) value is on life’s contingency, not its limitedness. I present an example comparing a being with a contingent and limited life to a being with a contingent but potentially endless life. This illustrates the function of life’s limitedness in valuation. I qualify my position somewhat by exploring one way in which a being with a contingent but potentially endless life may value his life as a whole. I also explain that a being with an endless life might have no ultimate value, but could have an endless number of goals. Finally, I discuss a desert-island scenario that supports the noninterference principle. (shrink)

In the exploratory study reported here, we tested the efficacy of an intervention designed to train teenagers with Möbius syndrome (MS) to increase the use of alternative communication strategies (e.g., gestures) to compensate for their lack of facial expressivity. Specifically, we expected the intervention to increase the level of rapport experienced in social interactions by our participants. In addition, we aimed to identify the mechanisms responsible for any such increase in rapport. In the study, five teenagers with MS interacted with (...) three naïve participants without MS before the intervention, and with three different naïve participants without MS after the intervention. Rapport was assessed by self-report and by behavioral coders who rated videos of the interactions. Individual non-verbal behavior was assessed via behavioral coders, whereas verbal behavior was automatically extracted from the sound files. Alignment was assessed using cross recurrence quantification analysis and mixed-effects models. The results showed that observer-coded rapport was greater after the intervention, whereas self-reported rapport did not change significantly. Observer-coded gesture and expressivity increased in participants with and without MS, whereas overall linguistic alignment decreased. Fidgeting and repetitiveness of verbal behavior also decreased in both groups. In sum, the intervention may impact non-verbal and verbal behavior in participants with and without MS, increasing rapport as well as overall gesturing, while decreasing alignment. (shrink)

The issue of whether or not there are visual arguments has been an issue in informal logic and argumentation theory at least since 1996. In recent years, books, sections of prominent conferences and special journals issues have been devoted to it, thus significantly raising the profile of the debate. In this paper I will attempt to show how the views of the later Wittgenstein, particularly his views on images and the no- tion of “picturing”, can be brought to bear on (...) the question of whether there are such things as “purely visual” arguments. I shall draw on Wittgenstein’s remarks in the Blue and Brown Books and in Philosophical Investigations in order to argue that al- though visual images may occur as elements of argumentation, broadly conceived, it is a mistake to think that there are purely visual arguments, in the sense of illative moves from premises to conclusions that are conveyed by images alone, without the support or framing of words. (shrink)

In her 2007 paper, “Argument Has No Function” Jean Goodwin takes exception with what she calls the “explicit function claims”, arguing that not only are function-based accounts of argumentation insufficiently motivated, but they fail to ground claims to normativity. In this paper I stake out the beginnings of a functionalist answer to Goodwin.

In this paper I begin by examining Fogelin’s account of deep disagreement. My contention is that this account is so deeply flawed as to cast doubt on the possibility that such deep disagreements actually happen. Nevertheless, I contend that the notion of deep disagreement itself is a useful theoretical foil for thinking about argumentation. The second part of this paper makes this case by showing how thinking about deep disagreements from the perspective of rhetoric, Walton-style argumentation theory, computation, and normative (...) pragmatics can all yield insights that are useful no matter what one’s orientation within the study of argument. Thus, I conclude that deep disagreement –even if it were to turn out that there are no real-world occurrences of it to which we can point–is useful for theorists of argumentation. In this wise, deep disagreement poses a theoretical challenge for argumentation theory not unlike that posed by radical skepticism for traditional epistemology. (shrink)

I argue that there are slurs that are distinctly derogatory insofar as they only derogate their target’s epistemic faculties or capacities qua group member. I call these slurs epistemic slurs. Given that slur theories should explain the derogatory nature of all slurs, any comprehensive slur theory should be able to explain the derogatory nature of the epistemic slurs. I argue, however, that two particular expressivist theories of slurs cannot explain their distinctive derogatory nature. The epistemic slurs thus constitute a novel (...) explanatory problem for these expressivist slur theories. Yet I argue that a semantic theory of slurs, combinatorial externalism, can explain the distinctive derogatory nature of the epistemic slurs in which case these slurs constitute a novel explanatory advantage for combinatorial externalism. Whether the epistemic slurs constitute a novel explanatory problem or advantage for any other slur theories remains to be seen. (shrink)

In his recent book Bad Beliefs and Why They Happen to Good People, Neil Levy argues that conspiracy theories result from the same rational processes that underlie epistemic success. While we think many of Levy’s points are valuable, like his criticism of the myth of individual cognition and his emphasis on the importance of one’s social epistemic environment, we believe that his account overlooks some important aspects. We argue that social deference is an active process, and as such can be (...) helped or hindered by epistemic virtues and vices. With this in mind, holders of bad beliefs acquire more responsibility than is considered by Levy. (shrink)

This sequel to Exploring Maori Values develops the idea that humans can and need to become 'people of the land' in the Maori sense, developing a harmonious interdependence with the environment in which we live rather than continuing to dominate it. Although arising out of Maori concepts, this is a model for human life which is available to any culture.

The turn of the nineteenth century marked a rich and exciting explosion of philosophical energy and talent. The enormity of the revolution set off in philosophy by Immanuel Kant was comparable, in Kant's own estimation, with the Copernican Revolution that ended the Middle Ages. The movement he set in motion, the fast-moving and often cantankerous dialectic of "German Idealism," inspired some of the most creative philosophers in modern times: including G. W. F. Hegel and Arthur Schopenhauer as well as those (...) who reacted against Kant--Marx and Kierkegaard, for example. This volume traces the emergence of German Idealism from Kant and his predecessors through the first half of the nineteenth century, ending with the irrationalism of Kierkegaard. It provides a broad, scholarly introduction to this period for students of philosophy and related disciplines, as well as some original interpretations of these authors. Also included is a glossary of technical terms as well as a chronological table of philosophical, scientific and other important cultural events. (shrink)

In "Exploring 'Atlas Shrugged': Ayn Rand’s Magnum Opus (2021)," Edward W. Younkins has compiled several of his essays on Ayn Rand's novel "Atlas Shrugged." The volume leads with an “Introduction” that contextualizes the importance of "Atlas Shrugged" and provides a detailed overview of each chapter. Chapter 1 gives a synopsis of the novel. Chapter 2 examines "Atlas Shrugged" as both philosophy and literature. In Chapter 3, Younkins looks at it as a treatise on economics before turning in Chapter 4 to (...) consider it as a story about business. Chapter 5 discusses it as a novel about and a blueprint for social change. In the “Appendix,” Younkins provides an overview of the philosophy of Objectivism. "Exploring 'Atlas Shrugged': Ayn Rand’s Magnum Opus" is a significant contribution and highly recommended for instructors, students, and the general reader. Younkins’s volume can serve as an instructor’s resource for those teaching "Atlas Shrugged," as a companion text for students in those courses, or as a stand-alone book for readers who are familiar with the book and are interested in a fresh examination of this timeless novel from a thematic, structural, and character-development point of view. (shrink)

Scholarly processes play a pivotal role in discovering, challenging, improving, advancing, synthesizing, codifying, and disseminating knowledge. Since the 17th Century, both the quality and quantity of knowledge that scholarship has produced has increased tremendously, granting academic research a pivotal role in ensuring material and social progress. Artificial Intelligence (AI) is poised to enable a new leap in the creation of scholarly content. New forms of engagement with AI systems, such as collaborations with large language models like GPT-3, offer affordances that (...) will change the nature of both the scholarly process and the artifacts it produces. (shrink)

It is argued that medical science requires a classificatory system that (a) puts functions in the taxonomic center and (b) does justice ontologically to the difference between the processes which are the realizations of functions and the objects which are their bearers. We propose formulae for constructing such a system and describe some of its benefits. The arguments are general enough to be of interest to all the life sciences.

It is argued that medical science requires a classificatory system that (a) puts functions in the taxonomic center and (b) does justice ontologically to the difference between the processes which are the realizations of functions and the objects which are their bearers. We propose formulae for constructing such a system and describe some of its benefits. The arguments are general enough to be of interest to all the life sciences.

The current informal practice of pharmacometrics as a combination art and science makes it hard to appreciate the role that informatics can and should play in the future of the discipline and to comprehend the gaps that exist because of its absence. The development of pharmacometric informatics has important implications for expediting decision making and for improving the reliability of decisions made in model-based development. We argue that well-defined informatics for pharmacometrics can lead to much needed improvements in the efficiency, (...) effectiveness, and reliability of the pharmacometrics process. The purpose of this paper is to provide a description of the pervasive yet often poorly appreciated role of informatics in improving the process of data assembly, a critical task in the delivery of pharmacometric analysis results. First, we provide a brief description of the pharmacometric analysis process. Second, we describe the business processes required to create analysis-ready data sets for the pharmacometrician. Third, we describe selected informatic elements required to support the pharmacometrics and data assembly processes. Finally, we offer specific suggestions for performing a systematic analysis of existing challenges as an approach to defi ning the next generation of pharmacometric informatics. (shrink)

This is a critical review of David Patterson's book Anti-Semitism and Its Metaphysical Origins (2015). In this review, I present the author's new explanation of the roots of anti-Semitism, which he finds in the anti-Semite's desire to become like God himself. Patterson's explanation makes an anti-Semite of all those who partake in the "Western rationalist project," especially philosophers (including Jewish philosophers such as Spinoza, Hermann Cohen, and Marx), but also Islamists and anti-Zionist Jews. I criticize Patterson on (...) two fronts: First, his "metaphysical" explanation relies on a petitio principii. Second, he should have argued his stance against that of Zeev Sternhell's thesis, according to which Western anti-Semitism is rooted, not in Western rationalism, but rather in the Western anti-rationalist (anti-Enlightenment) movement. (shrink)

I argue that Kathleen Stock omits crucial information in her 2021 book Material Girls, when she debates with Thomas Laqueur, information which enables readers to appreciate the excitement in relation to his historical discovery. I argue further that this is more than just a communicational problem. I then present a reason for rejecting the theory Laqueur uncovers: the initially strange theory that there is just one sex. But I argue that the one sex theory is unlikely to be killed (...) off by this reason. I also raise a concern about Stock’s interpretation of Mrs. Gaskell’s Cranford. The writing style here is influenced by an essay by a medic. (shrink)

I consider Kathleen Stock’s response to trans-rights claims which appeals to the concept of immersion in a fiction. I propose that some fictional personas, however artificial they seem, are fixed points within a subject’s system. That fiction is there come what may.

How well do we understand our own societies? In this paper, I raise quite obvious puzzles for Diego Gambetta and Gloria Origgi’s depiction of Italy as a kakonomy and Kathleen Stock’s depiction of ordinary people.

This paper responds to Kathleen Stock’s attempt to explain a puzzling fact, at least from her standpoint: widespread assertions that some people who are biologically male are women and some people who are biologically female are men. She regards these assertions as made while immersed in a fiction. Stock rejects an alternative explanation – that a lot of these people have read Judith Butler or 1970s feminism. Clarifying that explanation reveals it to be not so easy to dismiss.

This is a one page handout identifying some notable omissions from her brief history of gender identity theory.

The result of the doctoral work of the author, this volume reflects well her painstaking eff orts of the investigative trail into the life of Sir John Woodroffe. This book gives a concise yet overall view of the large and multifarious canvas of the personality that Woodroffe was. Including rare photographs, facsimiles of letters and notes, an elaborate bibliography and index, this book fills a void by fulfilling the long-felt need of a good biography of a soul, who preferred to (...) remain anonymous and speak to the world only through this writings under his pen name, Arthur Avalon. (shrink)

Some Anglophone legal theorists look to analytic philosophy for core presuppositions. For example, the epistemological theories of Ludwig Wittgenstein and Willard Quine shape the theories of Dennis Patterson and Brian Leiter, respectively. These epistemologies are anti-foundational since they reject the kind of certain grounding that is exemplified in Cartesian philosophy. And, they are coherentist in that they seek to legitimate truth-claims by reference to entire linguistic systems. While these theories are insightful, the current context of information and communication technologies (...) (ICT) has created new informational concepts and issues. As a result, the analytic epistemologies are increasingly challenged by alternative perspectives. One such alternative is Structural Realism (SR), which is influential among the natural sciences, and especially physics. “Informational Structural Realism,” (ISR) is a variant of SR that was introduced by Luciano Floridi. Unlike the coherentist theories, ISR promotes examination of the connections among types of information and informational structures. It is an important shift for legal theory today, since the challenges that the ICT presents have to do with pattern recognition across vast domains of diverse data. An informational jurisprudence is now required to understand the issues emerging from the ICT. (shrink)

Philosophical exploration of individualism and externalism in the cognitive sciences most recently has been focused on general evaluations of these two views (Adams & Aizawa 2008, Rupert 2008, Wilson 2004, Clark 2008). Here we return to broaden an earlier phase of the debate between individualists and externalists about cognition, one that considered in detail particular theories, such as those in developmental psychology (Patterson 1991) and the computational theory of vision (Burge 1986, Segal 1989). Music cognition is an area in (...) the cognitive sciences that has received little attention from philosophers, though it has relatively recently been thrown into the externalist spotlight (Cochrane 2008, Kruger 2014, Kersten forthcoming). Given that individualism can be thought of as a kind of paradigm for research on cognition, we provide a brief overview of the field of music cognition and individualistic tendencies within the field (sections 2 and 3) before turning to consider externalist alternatives to individualistic paradigms (section 4-5) and then arguing for a qualified form of externalism about music cognition (section 6). (shrink)

The moral status of sexbots was analyzed while using consequentialism and feminism as the guiding frameworks. Sexbots are humanoid robots with a certain level of AI that represents personality-scripts. The thesis contained three main questions: A) What moral pain points can be identified in producing and using sex bots? B) Is it necessary to conclude from these moral issues that these practices are inherently immoral? C) What ethical conditions and contexts can be formulated in which sex bots can be used (...) and used positively and morally? -/- First of all a brief summary is given on the psychology behind our relationships with robots/sexbots to show the weight of the dynamics behind this relationship between sexual subject and the sexual technology of sexbots. Second, The Campaign Against Sex Robots from Richardson was used as a starting point to explore a more contextual approach of the moral uses and designs of sexbots. The claims about what sexbots represent and what possible effects they have were analyzed to find an opening that does not a priori ban the production of sexbots (as Richardson postulates). -/- Through the thesis, tentative explorations of moral designs and uses of sexbots can be found. This includes an analysis on the hardware and software behind a sexbot going from scripts and programming concerning consent and designs that are meant for different (for example; therapeutical) contexts. To conclude, the use of a non-essentialistic feminist new-materialism was used for a first exploration of the political value of sexbots as tools of empowerment, instead of oppression. (shrink)

Kathleen Touchstone's Then Athena Said: Unilateral Transfers and the Transformation of Objectivist Ethics is an intriguing book on unilateral transfers within the context of Objectivism. Touchstone examines Rand's primary social ethic, the Trader Principle—the bilateral exchange of value between independent equals. In reconsidering Rand's thoughts, she raises many arguments and provides thought-provoking insights especially on charity, reproductivity, retaliation and rights. Touchstone reinterprets Objectivism through the prism of economics, applying economic tools such as consumer theory, capital theory, game theory, and (...) decision making under uncertainty to address the questions she raises. (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)