We introduce an Automatic Theorem Prover (ATP) of a dual tableau system for a relational logic for order of magnitude qualitative reasoning, which allows us to deal with relations such as negligibility, non-closeness and distance. Dual tableau systems are validity checkers that can serve as a tool for verification of a variety of tasks in order of magnitude reasoning, such as the use of qualitative sum of some classes of numbers. In the design of (...) our ATP, we have introduced some heuristics, such as the so called phantom variables, which improve the efficiency of the selection of variables used un the proof. (shrink)

Qualitative Reasoning (QR) is an area of research within Artificial Intelligence that automates reasoning and problem solving about the physical world. QR research aims to deal with representation and reasoning about continuous aspects of entities without the kind of precise quantitative information needed by conventional numerical analysis techniques. Order-of-magnitude Reasoning (OMR) is an approach in QR concerned with the analysis of physical systems in terms of relative magnitudes. In this paper we consider the logic (...) OMR_N for order-of-magnitude reasoning with the bidirectional negligibility relation. It is a multi-modal logic given by a Hilbert-style axiomatization that reflects properties and interactions of two basic accessibility relations (strict linear order and bidirectional negligibility). Although the logic was studied in many papers, nothing was known about its decidability. In the paper we prove decidability of OMR N by showing that the logic has the strong finite model property. (shrink)

We present a relational proof system in the style of dual tableaux for a multimodal propositional logic for order of magnitude qualitative reasoning to deal with relations of negligibility, non-closeness, and distance. This logic enables us to introduce the operation of qualitative sum for some classes of numbers. A relational formalization of the modal logic in question is introduced in this paper, i.e., we show how to construct a relational logic associated with the logic for order-of- (...) class='Hi'>magnitude reasoning and its dual tableau system which is a validity checker for the modal logic. For that purpose, we define a validity preserving translation of the modal language into relational language. Then we prove that the system is sound and complete with respect to the relational logic defined as well as with respect to the logic for order of magnitude reasoning. Finally, we show that in fact relational dual tableau does more. It can be used for performing the four major reasoning tasks: verification of validity, proving entailment of a formula from a finite set of formulas, model checking, and verification of satisfaction of a formula in a finite model by a given object. (shrink)

We present a relational proof system in the style of dual tableaux for the relational logic associated with a multimodal propositional logic for order of magnitude qualitative reasoning with a bidirectional relation of negligibility. We study soundness and completeness of the proof system and we show how it can be used for verification of validity of formulas of the logic.

According to proponents of the generalized magnitude system proposal (GMS), SNARC-like effects index spatial mappings of magnitude and provide crucial evidence for the existence of a GMS. Casasanto and Pitt (2019) have argued that these effects, instead, reflect mappings of ordinality, which people compute on the basis of differences among stimuli that vary either qualitatively (e.g., musical pitches) or quantitatively (e.g., dots of different sizes). In response to our paper, Prpic et al. (2021) argued that both magnitude (...) and ordinality play a role in SNARC-like effects. Here, we address each of their arguments and conclude that magnitude is relevant to these effects only insofar as it serves as a basis for ordinality. For this reason and others, SNARC or SNARC-like effects cannot provide evidence for the putative generalized magnitude system. (shrink)

In this paper, we focus on a logical approach to the important notion of closeness, which has not received much attention in the literature. Our notion of closeness is based on the so-called proximity intervals, which will be used to decide the elements that are close to each other. Some of the intuitions of this definition are explained on the basis of examples. We prove the decidability of the recently introduced multimodal logic for closeness and, then, we show some capabilities (...) of the logic with respect to expressivity in order to denote particular positions of the proximity intervals. (shrink)

This article suggests that we are in the midst of a profound dimensional shift in our rational capacity to process reality, and seeks to articulate the implications of this evolutionary shift to global reason for our scientific enterprise. As we enter the 21st century it is unmistakably clear that we are in the midst of an unprecedented shift in the human condition - a global renaissance that affects every aspect of our cultural lives, our self-understanding, and, of course, our rational (...) enterprise. This evolutionary transformation, when seen through the expanded global lens, has been emerging through the ages on a global scale. In this brief reflection I suggest that this advance in our technology of mind is of an order of magnitude that is so radical and comprehensive that the very concept of a person, of what it means to be human, of our encounter with Reality and all our hermeneutical arts, including the sciences, are likewise taken to a higher global dimension. I suggest that the diverse voices included in this special edition are best situated in the context of this global awakening of reason, scientific knowing, and the holistic worldview. (shrink)

This paper presents a formalism that combines useful properties of both logic and probabilities. Like logic, the formalism admits qualitative sentences and provides symbolic machinery for deriving deductively closed beliefs and, like probability, it permits us to express if-then rules with different levels of firmness and to retract beliefs in response to changing observations. Rules are interpreted as order-of-magnitude approximations of conditional probabilities which impose constraints over the rankings of worlds. Inferences are supported by a unique priority ordering (...) on rules which is syntactically derived from the knowledge base. This ordering accounts for rule interactions, respects specificity considerations and facilitates the construction of coherent states of beliefs. Practical algorithms are developed and analyzed for testing consistency, computing rule ordering, and answering queries. Imprecise observations are incorporated using qualitative versions of Jeffrey's rule and Bayesian updating, with the result that coherent belief revision is embodied naturally and tractably. Finally, causal rules are interpreted as imposing Markovian conditions that further constrain world rankings to reflect the modularity of causal organizations. These constraints are shown to facilitate reasoning about causal projections, explanations, actions and change. (shrink)

The book presents logical foundations of dual tableaux together with a number of their applications both to logics traditionally dealt with in mathematics and philosophy (such as modal, intuitionistic, relevant, and many-valued logics) and to various applied theories of computational logic (such as temporal reasoning, spatial reasoning, fuzzy-set-based reasoning, rough-set-based reasoning, order-of magnitude reasoning, reasoning about programs, threshold logics, logics of conditional decisions). The distinguishing feature of most of these applications is that (...) the corresponding dual tableaux are built in a relational language which provides useful means of presentation of the theories. In this way modularity of dual tableaux is ensured. We do not need to develop and implement each dual tableau from scratch, we should only extend the relational core common to many theories with the rules specific for a particular theory. (shrink)

How do people stretch their understanding of magnitude from the experiential range to the very large quantities and ranges important in science, geopolitics, and mathematics? This paper empirically evaluates how and whether people make use of numerical categories when estimating relative magnitudes of numbers across many orders of magnitude. We hypothesize that people use scale words—thousand, million, billion—to carve the large number line into categories, stretching linear responses across items within each category. If so, discontinuities in position and (...) response time are expected near the boundaries between categories. In contrast to previous work that suggested only that a minority of college undergraduates employed categorical boundaries, we find that discontinuities near category boundaries occur in most or all participants, but that accurate and inaccurate participants respond in opposite ways to category boundaries. Accurate participants highlight contrasts within a category, whereas inaccurate participants adjust their responses toward category centers. (shrink)

In this issue of Philosophical Studies, Richard Arneson, Jonathan Quong and Robert Talisse contribute papers discussing The Order of Public Reason (OPR). All press what I call “agent-type challenges” to the project of OPR. In different ways they all focus on a type (or types) of moral (or sometimes not-so-moral) agent. Arneson presents a good person who is so concerned with doing the best thing she does not truly endorse social morality; Quong a bad person who rejects it and (...) violates the basic rights of others, and Talisse a morally ugly person, a hypocrite, who criticizes others for failing to do what he does not do. All suggest that OPR does not give a satisfying account of what we are to say to, or how we should act towards, such agents. In my response I highlight some core concerns of OPR, while also seeking to show that OPR does not say quite what they think it says, and it often leaves them room for saying what they would like to say about such agents. (shrink)

Between Summits I and II, media ethics established its legitimacy, summarized into recommendations for the field's future fluorescence. This history points to the challenges through which media ethics moves to another order of magnitude. A historical map of media ethics scholarship since 1980 divides into 5 domains, and each is introduced: theory, social philosophy, religious ethics, technology, and truth. From this content analysis of the literature, an agenda emerges for research and academic study that can raise media ethics (...) to a higher level. (shrink)

The purpose of this work is to elaborate an empirically grounded mathematical model of the magnitude of consequences component of "moral intensity", 366, 1991) that can be used to evaluate different ethical situations. The model is built using the analytical hierarchy process and empirical data from the legal profession. One contribution of our work is that it illustrates how AHP can be applied in the field of ethics. Following a review of the literature, we discuss the development of the (...) model. We then illustrate how the model can be used to rank-order three well-known ethical reasoning cases in terms of the magnitude of consequences. The work concludes with implications for theory, practice, and future research. Specifically we discuss how this work extends the previous work by Collins regarding the nature harm variable. We also discuss the contribution this work makes in the development of ethical scenarios used to test hypotheses in the field of business ethics. Finally, we discuss how the model can be used for after-action review, contribute to organizational learning, train employees in ethical reasoning, and aid in the design and development of decision support systems that support ethical reasoning. (shrink)

On a prominent family of views about the justification of legitimate policy-making (_public justification views_), considerations about the rights and well-being of nonhuman animals can only play a derivative role at best. On these views, these considerations matter only if they can figure in the content of the public reasons that citizens can offer each other. This thesis I call the Indirect View. Some authors have argued that this constitutes a reason to reject the ideal of public justification, or at (...) least to qualify it. It is unclear, however, whether public justification theorists will be persuaded by this. In this paper, I argue that they should. In order to do so, I focus on three justifications of the ideal of public justification that have been offered in the literature (justice, our reactive attitudes, and civic friendship), and contend that none of them supports the Indirect View. In some cases, this is because the value in question (e.g. justice) might indeed be extended to animals. In other cases, this is because there is often a trade-off between the values in play and considerations about the rights and well-being of animals in which the former do not always outweigh the latter. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.3 (2003) 415-416 [Access article in PDF] Tad M. Schmaltz. Radical Cartesianism: The French Reception of Descartes. Cambridge: Cambridge University Press, 2002. Pp. xiv + 288. Cloth, $65.00.More than fifty years ago Richard H. Popkin urged historians of philosophy to work on secondary figures in philosophy, in part for their own sake, but also because the true shape of philosophy and the development (...) of major figures can be understood only through examination of the intellectual milieu out of which they arose. Among others he specifically mentioned Robert Desgabets, Jean Du Hamel, Simon Foucher, Pierre-Daniel Huet, Pierre-Sylvain Regis, and Henricus Regius. Now in Radical Cartesianism, Tad Schmaltz has provided a masterful and erudite study of these and other philosophers who are minor now but were major in their day. The importance of this study is not just that it illuminates the metaphysics of Descartes, Spinoza, and Malebranche, and clarifies the relationship of these philosophers to Arnauld, Jansenism, Plato, and the Aristotelian scholasticism of the day, but also that it opens to view an intricate and significant body of thought. The radical Cartesianism Schmaltz examines addresses and provides solutions to problems of the relationship between mind and body, between man and God, and between ideas and the external world that continue to engage philosophers today. Schmaltz concludes his study with the suggestion that these philosophers might have had more latter-day influence if larger historical events, in particular the death of Louis XIV and the subsequent relaxation of attacks on Jansenism (and on supposed Jansenist Cartesianism) had not led to interest in matters other than the Eucharist and the nature of the soul that were major issues among the radical Cartesians and their opponents.But were any of these radical Cartesians actually Cartesians? If, as Schmaltz says, the metaphysical core of Cartesianism is Descartes's doctrine that "the essence of body consists in extension and that the essence of mind consists in thought" (10), then most of his followers were not radical Cartesians, but rather heretical Cartesians. They rebelled against as many of Descartes's doctrines as they accepted. Schmaltz's careful expositions, analyses, comparisons, correlations, and extrapolations of their arguments and positions make up the bulk of his book. The detail, command of the material, insight, and breadth of Schmaltz's exposition is on an order of magnitude above previous work on these figures and will stand for a long time as a challenge to the next few generations of scholars.But if so many of these figures alter Descartes's metaphysics so radically, why do they still designate themselves as Cartesians? The major reason is that while Cartesian metaphysics was in disarray, Cartesian science was flourishing. Regius is the model. He said (directly to Descartes) that metaphysics is inessential to science, that matters of God and certainty about the existence of the external world could and should be left to faith. What was liberating during the third quarter of the century in The Netherlands and in the fourth quarter in France was Descartes's scientific method of posing hypotheses and testing them with experiments. You will never get certainty this way, but already science was advancing by leaps and bounds. Christian Huygens, who as a boy had known Descartes, belittled the man's metaphysics, but was one of the greatest and most successful practitioners of the [End Page 415] Cartesian scientific method of his time. What remains to be written is a study of late-seventeenth-century Cartesian science that is as excellent and comprehensive as Schmaltz's study of the Cartesian metaphysics of the time. Here are some problems Descartes set up that are of particular concern to the philosophers of the time. If God can do anything, even make contradictions true, then why could he not make you think you exist even when you do not? How could you think of something that does not exist? Because your thoughts have a temporal dimension, and time depends on motion, and motion pertains only to material bodies, how could you... (shrink)

We argue that, in order to explain the relative strengths of our reasons to contribute to different collective endeavours, approaches to the ethics of collective action must understand the strengths of our reasons to make a given contribution as proportional to its expected benefits, or its chances of bringing about benefits in proportion to their magnitudes. The view that most clearly meets this proportionality requirement is the expected consequences approach, which identifies our reasons to perform an act with its (...) expected benefits. We contend that views other than the expected consequences approach must similarly proportion the expected degrees of what they take to be reason-giving features of a contribution – such as its virtuousness, appropriate expression, support by considerations of fairness, or helping without making a difference – to the contribution’s expected benefits. The proportionality requirement explains why we should spend more time participating in strategic social, political, and labour movement activities, while avoiding unproductive conflicts and merely performative activities. We conclude that the proportionality requirement, and the ability of views other than the expected consequences approach to meet it, are important for thinking and communicating about the ethics of collective action in ways that are simultaneously most compelling and most strategic. (shrink)

In this innovative and important work, Gerald Gaus advances a revised and more realistic account of public reason liberalism, showing how, in the midst of fundamental disagreement about values and moral beliefs, we can achieve a moral and political order that treats all as free and equal moral persons. The first part of this work analyzes social morality as a system of authoritative moral rules. Drawing on an earlier generation of moral philosophers such as Kurt Baier and Peter Strawson (...) as well as current work in the social sciences, Gaus argues that our social morality is an evolved social fact, which is the necessary foundation of a mutually beneficial social order. The second part considers how this system of social moral authority can be justified to all moral persons. Drawing on the tools of game theory, social choice theory, experimental psychology and evolutionary theory, Gaus shows how a free society can secure a moral equilibrium that is endorsed by all, and how a just state respects, and develops, such an equilibrium. (shrink)

Gerald Gaus’s latest book achieves a remarkable, definitive development of the public reason project whose roots can be traced back to Locke and Kant and which had already attained its full expression in the later writing of John Rawls—or so we had thought! In fact Gaus takes a long step beyond Rawls.Gaus (2011). Page numbers enclosed in parentheses of the text refer to this book. For John Rawls on public reason, see especially his A Theory of Justice (1999); also Rawls (...) (1996). In my view we should have a raised eyebrows response to the public reason project, but this does not gainsay Gaus’s achievement in rigorously working out its implications. The book develops an account of the justified imposition of moral constraints and, following that, of justified political arrangements. These comments focus on the former.SummaryLike any genuinely original work, this one admits of quick summary. In everyday life, people make moral demands on each other, and claim a special authority in making. (shrink)

Much of cognitive psychology focuses on effects measured in tens of milliseconds while significant educational outcomes take tens of hours to achieve. The task of bridging this gap is analyzed in terms of Newell's (1990) bands of cognition—the Biological, Cognitive, Rational, and Social Bands. The 10 millisecond effects reside in his Biological Band while the significant learning outcomes reside in his Social Band. The paper assesses three theses: The Decomposition Thesis claims that learning occurring at the Social Band can be (...) reduced to learning occurring at lower bands. The Relevance Thesis claims that instructional outcomes at the Social Band can be improved by paying attention to cognition at the lower bands. The Modeling Thesis claims that cognitive modeling provides a basis for bridging between events on the small scale and desired outcomes on the large scale. The unit-task level, at the boundary of the Cognitive and Rational Bands, is useful for assessing these theses. There is good evidence for all three theses in efforts that bridge from the unit-task level to educational applications. While there is evidence for the Decomposition Thesis all the way down to the 10 millisecond level, more work needs to be done to establish the Relevance Thesis and particularly the Modeling Thesis at the lower levels. (shrink)

Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. The usual representation of the quantum algorithm is limited to the process of solving the problem. We extend it to the process of setting the problem. The number of the drawer with the ball becomes a unitary transformation of the random outcome of the preparation (...) measurement. This extended, time-symmetric, representation brings in relational quantum mechanics. It is with respect to Bob and any external observer and cannot be with respect to Alice. It would tell her the number of the drawer with the ball before she opens any drawer. To Alice, the projection of the quantum state due to the preparation measurement should be retarded at the end of her search; in the input state of the search, the drawer number is determined to Bob and undetermined to Alice. We show that, mathematically, one can ascribe any part of the selection of the random outcome of the preparation measurement to the final Alice’s measurement. Ascribing half of it explains the speedup of the present algorithm. This leaves the input state to Bob unaltered and projects that to Alice on a state of lower entropy where she knows half of the number of the drawer with the ball in advance. The quantum algorithm turns out to be a sum over histories in each of which Alice knows in advance that the ball is in a pair of drawers and locates it by opening one of the two. In the sample of quantum algorithms examined, the part of the random outcome of the initial measurement selected by the final measurement is one half or slightly above it. Conversely, given an oracle problem, the assumption it is one half always corresponds to an existing quantum algorithm and gives the order of magnitude of the number of oracle queries required by the optimal one. (shrink)

About forty years ago, when print media were still in their ascendancy, Marshall McLuhan argued that all media are extensions of the senses and that the rational view of the world associated with print is being replaced by a world-view associated with electronic media that stresses feelings and emotions. In 2003 researchers from the School of Information Management Sciences at Berkeley estimated that five exabytes of information had been generated in the previous year, equivalent to 37,000 times the holdings of (...) the Library of Congress and that 92.00% of this was on magnetic media, mostly hard disks, while only 0.01% was in print. This SIMS estimate could be wrong by several orders of magnitude and it would still be clear that the era of the printed word is waning rapidly. We are well-advised to pay attention to McLuhan’s suggestionthat electronic media change how we think and how we feel.Sense of place and virtual reality are both inextricably caught up in this cultural-technological upheaval. I have written about the concept of ‘place’ from a phenomenological perspective for many years and have achieved a reasonable understanding of its subtleties, but I have a limited knowledge of digital virtual reality and its technical attributes. Nevertheless, it seems to me that a mutual interaction is at work between what might be called ‘real’ place and virtual places, that digital virtual reality shares characteristics with other electronic media and that our experiences of real places are being changed those same media. This essay explores these issues particularlyfrom the perspective of the distinction between spirit of place and sense of place. (shrink)

For the most part, this is a fairly literal translation, but I have opted for a few English idioms for the sake of readability. In that spirit, I have kept the original punctuation, which results in very long sentences, but I have inserted paragraph breaks for readability. I mark these inserted breaks with this sign [¶]; unmarked breaks are in the original. In addition to providing the French for difficult translations, I also interpolate a few English words for readability. Simondon’s (...) notes appear as footnotes; translator’s notes as endnotes. (shrink)

We introduce a multimodal logic for order of magnitude reasoning which considers a new logic-based alternative to the notion of closeness, we provide an axiom system and prove its soundness and completeness.

Critical notice of The Order of Public Reason by Gerald Gaus.

Many philosophers believe that the relationship between a parent and a child is objectively valuable, but few believe that there is any objective value in first creating a child in order to parent her. But if it is indeed true that all of the objective value of procreative-parenting comes from parenting, then it is hard to see how procreative-parenting can overcome two particularly pressing philosophical challenges. A first challenge is to show that it is morally permissible for prospective parents (...) to procreate given that adoption takes us much closer to both environmental and social justice. A second challenge is to show that it is morally permissible for biological parents to parent their biological child given that other prospective parents are willing and able to do a much better job at furthering the child's interests. In this essay, I argue that there is value in procreative-parenting, and that this value is of sufficient magnitude so as to block both the case against procreation and the case in favour of child re-distribution. (shrink)

Aristotle’s philosophy of geometry is widely interpreted as a reaction against a Platonic realist conception of mathematics. Here I argue to the contrary that Aristotle is concerned primarily with the methodological question of how universal inferences are warranted by particular geometrical constructions. His answer hinges on the concept of abstraction, an operation of “taking away” certain features of material particulars that makes perspicuous universal relations among magnitudes. On my reading, abstraction is a diagrammatic procedure for Aristotle, and it is through (...) imagined variation of diagrams that one can universalize spatial inferences. In order to shift the discussion of Aristotle’s work on geometry from ontological to methodological questions, I argue in the first section that geometrical properties for Aristotle are necessary accidents of the particulars, canonically diagrams, in which they inhere. I then consider a line of research that shows how diagrams in ancient geometry are not illustrations of the textual proof but are in part constitutive of geometrical inference, an insight I claim can shed light on Aristotle’s philosophical project. Next I substantiate this assertion by giving an alternative interpretation of abstraction according to which it is a diagrammatic procedure that allows a part of a particular diagram to stand in for a universal. In the last section, I consider Aristotle’s account of mathematical cognition, arguing that there is evidence for the view that imagination is necessary both for the construction of figures, and for their presentation as abstractions subject to universal inference. (shrink)

This paper proposes Gilbert Simondon’s ontogenetic theory of individuation as an overarching framework for multilevel semiosis. What renders this theory suitable for this role is the fact that it shares a significant part of its heritage with biosemiotics, which provides compatibility between them. Unlike many philosophers who have worked on individuation, Simondon envisages a general process of individuation that starts with a metastable preindividual. This process ultimately constitutes an axiomatisation of ontogenesis and manifests itself in three basic modes: physical, vital (...) and psycho-collective. In any of these modes a transductive operation is at work resolving the disparities of the preindividual whereby new structures emerge. Depending on the mode of individuation, the emerging structures can create new disparities that ask for further individuation. Simondon refers to such conversion of structure to operation and vice versa as allagmatics. He also extends his theory to scientific methodology establishing a healthy balance between reductionism and holism. His theory can be used to amend Peircean metaphysics to improve its compatibility with contemporary scientific discourse. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Peter Singer’s ChallengeEugene GoodheartThe politicizing of the Terri Shiavo case has made it difficult to think clearly and judiciously (as distinguished from judicially) about what it means to decide to end the life of a terminally ill or disabled person. Can we take seriously the rhetoric of the sanctity of human life from the mouths of exponents of the death penalty? And yet there are those who consistently and (...) in good faith hold euthanasia in whatever form morally anathema. Many of those who share this view have expressed disapproval of government intervention in the Shiavo case. They cannot be accused of having a political agenda. Over the years, philosopher Peter Singer has made the case for euthanasia most forcefully. This may be a good time to consider critically his arguments, free of the immediate tumult surrounding the Shiavo case. Such consideration may even help us in our understanding of the issues involved in that case.Singer has been variously characterized as "the most controversial," "the most influential" and "the most notorious" philosopher in the world. His books cover a wide range of ethical issues, from animal liberation to euthanasia (including infanticide), and from globalization to the workings of George W. Bush's mind. The controversy, influence and notoriety come from positions he has taken, with a candor that one rarely finds in the work of a respectable philosopher, on the most sensitive issues of life and death. Whether or not one is in agreement with his views (I am not, as will soon become evident), they are argued with a provocative clarity and consistency. A radical advocate of animal [End Page 238] rights, he wants to dissolve the species distinction between human beings and non-human animals. An advocate of euthanasia and infanticide, he substitutes the commandment that honors the sanctity of human life for one that sanctifies the quality of life. In both instances, human beings are being denied a privileged place in the world simply by virtue of being human.If, as Copernicus demonstrated, the universe is not earth-centered, and if, as Darwin has shown, human beings are not the separate creation of God, there can be no justification for providing human beings with a separate ethical system, often at the expense of non-human animals. Singer calls this speciesism and analogizes it to racism. In Rethinking Life and Death: The Collapse of Our Traditional Ethics (New York: St. Martin's Griffin, 1994), he argues against speciesism that in their susceptibility to pain and pleasure, in their capacity for consciousness and even in certain instances a rudimentary self-consciousness, animals deserve to be treated with the same consideration as human beings. He does not deny the superior capacities of human beings, but he views the differences between human and non-human animals as differences in degree and not kind. He provides the following memorable account of the gorilla Koko:She communicates in sign language, using a vocabulary of over 1000 words. She also understands spoken English and often carries on 'bilingual' conversation, responding in sign to questions asked in English. She is learning the letters of the alphabet, and can read some printed words, including her own name. She has achieved scores between 85 and 95 on the Stanford-Binet Intelligence Test.talk about what happens when one dies, but she becomes fidgety and uncomfortable when asked to discuss her own death or the death of her companions. She displays a wonderful gentleness with kittens and other small animals. She has even expressed empathy for others seen only in pictures.(p. 181)Why then should animals (Koko is unusual but not alone in these capacities) not be accorded the same ethical consideration as human beings? The differences between human and non-human animals in intelligence, linguistic and symbolic capacity, consciousness and self-consciousness may be a difference in degree, but of such an order of magnitude that quantity becomes quality. To say that non-human animals have 98% of DNA in common with human beings tells us nothing of the effective intellectual superiority of human beings. No matter. Singer provides a deeper reason for his anti-speciesism. "Whether or not dogs and pigs [animals... (shrink)

Kant’s investigations into so‐called a priori judgments of pure mathematics in the Critique of Pure Reason (KrV) are mainly confined to geometry and arithmetic both of which are grounded on our pure forms of intuition, space, and time. Nevertheless, as regards notions such as irrational numbers and continuous magnitudes, such a restricted account is crucially problematic. I argue that algebra can play a transcendental role with respect to the two pure intuitive sciences, arithmetic and geometry, as the condition of their (...) possibility. It follows that Kant’s schematism of the concept of magnitude ought to be quantitatively represented in algebraic formulas in general, and also undergo several modifications in order to suit continuities. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Global Empires and The Roman ImperiumBrent D. ShawP. Fibiger Bang, C. A. Bayly, and W. Scheidel, eds. The Oxford World History of Empire. 2 vols. Oxford: Oxford University Press, 2021; xxviii + 552 pp.; xxxiv + 1,318 pp.The volumes under review are an impressive if unequal diptych. The first, the slimmer of the two, entitled "The Imperial Experience," comprises a series of analytical studies on the creation, management, and (...) ideologies of empires, and forms of resistance to them. The second, "The History of Empires," is a forbidding tome of forty-four specific studies of individual empires and imperial ventures, from Ur III and Middle Kingdom Egypt to the Mongols and the British, ending, naturally, with America's "global imperium." In the analytics, the usual suspects, including Michael Doyle, Frederick Cooper and Jane Burbank, are on display; and the conceptual approaches of Michael Mann and Ernest Gellner are favorite points d'appui. For premodern empires, the ideas of the Maghribi thinker Ibn Khaldūn provide a different focus, so it is heartening to see Bang and others applying them more consistently (e.g., 1:13, 40, 326–9; 2:162, 246–8, 253). Especially for premodern empires, these volumes can be seen as an extension of earlier handbooks devoted to the state, one devoted to the ancient Near Eastern and Mediterranean state and another on ancient empires.1 As an aspect of world history, the endeavor is the culmination of a decades-long project on the history of empires fronted by Peter Bang.2 He has usefully produced detailed historical introductions not only to both volumes, but also to the subsections in each of them. Perhaps not surprisingly, empire turns out to be a virile enterprise. As Ian Morris notes, "the story of empire... is so strongly gendered that it [End Page 505] seems reasonable to call rulers and commanders 'he' throughout" (1:162 n. 14). The muscular subject is mirrored by its principal actors and by its students. All the editors are men. Reflecting the same balance, out of the forty-five authors of individual studies in the large history of empires volume, there are five (lonely) female voices. In both volumes, women as subjects of empire are, for all intents and purposes, absent.3From the perspective of an historian who has actually worked on the history of an empire, it must be plainly stated that almost all of the theories, adequately reviewed by Bang (1:20–48), are worth about as much as the paper or pixilated screens on which they have been written. Obvious and serious exceptions to every one of the definitions and hypotheticals abound. In fact, a fair number of the exemplary histories in the second volume do not obey the strictures of most of the theories advanced in the first. So it is with a sense of relief that one turns from theory to the hard quantities offered by Walter Scheidel (1:chap. 2). To a considerable degree, his analysis depends on the well-known measurements made by Rein Taagepera. Rather alarmingly, Taagepera counted as an empire "any large sovereign political entity whose components are not sovereign," say, like the well-known empires of Algeria, Finland, or Canada.4 What an analysis of these global entities confirms is that size or orders of magnitude mattered, and that the first entities to count as empires emerged in the 7th to 5th centuries bce in southwestern Asia (1:53; 2:161, 245). The neo-Assyrian empire was the first super-large territorial state and its successor, the Achaemenid empire, was the first "hyper-power without rival" (1:172; 2:83, 111, 161). Subsequent premodern empires were able to reach higher levels of millions of square kilometers of territory and larger populations of dozens of millions of subjects nominally under their aegis. The magnitudes reached by a given generation of super-states set base-lines above which a successor might be able to reach greater sophistication of rule, numbers of subjects, and extent of territory. In some cases, being able to piggy-back on existing empires, they were able to skip early developmental stages and to advance quickly to imperial status, as a succession... (shrink)

This is a book review of Gerald Gaus's book The Order of Public Reason: A Theory of Freedom and Morality in a Diverse and Bounded World.

SummaryThe present paper deals with the determination of the size and charge of a single submicroscopic particle, measured in a small horizontal condenser of a diameter of approximately 8 mm., using the author's method first stated April 1910. To obtain the highest sensitivity, author used solid particles of an order of magnitude under 3 × 10–5 cm. and found charges less than that of the electron. Various objections were raised against his findings, namely that the particles investigated were (...) not spheres, and that their density was not that of the macroscopic substance, so that his findings of charges less than the electronic charge were merely imaginary. The author has succeeded in precipitating and measuring a particle after having observed it in the condenser under normal and also very high gas pressures. The particles were shown to be perfect spheres. A new method is indicated whereby it is possible to determine the size of sub-microscopic spheres by pushing together two equal spheres with a micromanipulator; the two diffraction disks overlap and render it very easy to determine the actual size. It is also possible to show that the density of each individual sphere is that of the macroscopic substance, since it can be computed easily from the velocity of fall at high gas pressures. These two data being accurately determined, the author still found charges considerably less than the electronic charge, and the deviations are too great to be accounted for by errors of observation. The reason that the author has used a solid substance and not oil, which is a liquid, was in the first place, that liquids evaporate, and therefore do not yield correct results, and secondly, because liquid spheres are not certain to preserve their sphericity when precipitated. Thus charges less than that of the electron are to be considered as actually existing. (shrink)

This is a review of Gerald Gaus's recent book, _The Order of Public Reason_.

The purpose of this essay is to show that there was one person, perhaps only one, who developed a rigorously scientific cosmology nearly two thousand years ago. Cosmology is the largest of all subjects, with a long history, and the cosmology considered here is the one that endured for the longest part, nearly three-quarters, of that history. By cosmology I mean a description of the universe as a whole and of the arrangement of its principal parts. But by scientific cosmology, (...) I mean something more. For a cosmology to be considered scientific, three criteria must be met: it must be quantitative, physical, and empirical. Quantitative means that it must assign some scale of distances and sizes to its parts. Physical means that it must rest upon some kind of physical or mechanical principles, causes, for the ordering and motion of its parts. Finally, empirical means that it must either be derived from observation or, if derived theoretically, as from physical or mechanical principles, it must be confirmed by observation. I set out these criteria, which may not be exclusive or exhaustive but are surely within reason, in order to define our subject and exclude mythological or theological cosmologies, which generally meet none of the criteria, and philosophical cosmologies, as those of Plato, Aristotle, and Descartes, which may meet one or two in some way, although not rigorously, but surely do not meet all three. I am not concerned with whether the cosmology or the criteria upon which it is based are correct. Compared to our present understanding, the scale may be off by orders of magnitude, the physics may be entirely mistaken, and the observations may be inaccurate. But if all three are present I would call the cosmology scientific, and if not I would not call the cosmology scientific. (shrink)

This dissertation examines Kant's transcendental idealism with respect to his account of natural forces. Although force plays a crucial role in Kant's pre-critical writings, especially in his argument against Leibniz's pre-established harmony, it is conspicuously absent in the Critique of Pure Reason . I argue that force has to be excluded once Kant's philosophy takes its "critical turn" in order for his transcendental argument to be able to prove that the categories of thought apply to objects of experience. In (...) order for the forms of thought to apply to the matter of sensibility, both thought and sensible intuition must not only be forms of unity, or unified forms, but also uniform in quality and capable of being measured in terms of extensive magnitudes. Force, on the other hand, is an intensive magnitude which is measured not in terms of homogeneous units, but in terms of degrees. It must be excluded from Kant's critical philosophy since the coherence of the experience that Kant seeks to justify requires the uniformity and consistency of the subject, the ground of knowledge. Nevertheless, the concept of force can still be found to be "at work" in the Critique of Pure Reason in Kant's schematism of the categories of quality and the principle of the anticipations of perception which are based on this schematism. In order for a quality to be predicated of an object it must have an impact on the subject and become an object of attention. Kant's controversial discussion of judgments of perception in the Prolegomena, can be understood as his attempt to incorporate force into his ontology by introducing a new category of thought, that of analogy. In the case of analogy, I argue, the copula of the judgment is not that of being but is that of force itself. This form of judgment ultimately becomes the reflective judgment in Kant's Critique of Judgment, which makes explicit the form of thought that would make the experience of force possible. (shrink)

This paper situates Wittgenstein in what is known as the causalism/anti-causalism debate in the philosophy of mind and action and reconstructs his arguments to the effect that reasons are not a species of causes. On the one hand, the paper aims to reinvigorate the question of what these arguments are by offering a historical sketch of the debate showing that Wittgenstein's arguments were overshadowed by those of the people he influenced, and that he came to be seen as an anti-causalist (...) for reasons that are in large part extraneous to his thought. On the other hand, the paper aims to recover the arguments scattered in Wittgenstein's own writings by detailing and defending three lines of argument distinguishing reasons from causes. The paper concludes that Wittgenstein's arguments differ from those of his immediate successors; that he anticipates current anti-psychologistic trends; and that he is perhaps closer to Davidson than historical dialectics suggest. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Refugees of a Crisis in ReferenceHolocaust Memoir and the Deconstruction of Paul de ManPatrick Lawrence (bio)Since discovery of Paul de Man’s wartime journalism, the debate over perceived ethical deficiencies in the philosophies of postmodernism in general, and deconstruction in particular, has intensified. At times more or less vitriolic or persuasive, this debate has brought about a crisis of scholarship to accompany the crisis of reference that is one of (...) its central points.1 At the horizon of the discussion is the Holocaust and its potential to reform modes of representation. As Jeremy Varon notes in his essay “Probing the Limits of the Politics of Representation”:the premises and insights of a variety of discourses, notably postructuralism [sic], deconstruction, psychoanalysis in its newer versions, metahistory, and postmodern theory in general, have at once been applied to and checked against the Holocaust. Such discourses often approach the Holocaust as a kind of limit case that tests the strengths and weaknesses of their various interpretive strategies.(Varon 84)It seems natural because of its (perhaps incomprehensible) magnitude and significance that the Holocaust should occasion self-testing and soul searching on the part of a variety of discourses, notably those that already inclined to such activities.2 Because of its status as at once radically historical and radically ahistorical (in that its import for history cannot be denied, but that the scope of its horror may transform notions of historicity), the Holocaust calls for a reassessment of all aesthetic, poetic, and theoretical paradigms. In the context of such novel and difficult historicity, the problematization of reference that de Manian deconstruction occasions takes on new and complex implications that need particular attention. This is especially important because, like American deconstruction, artistic representations of the Holocaust also assert a new, problematic relationship with their referent.My intention is not to delve into this debate exhaustively. Rather, I attempt an understanding of the problems of some specific critical-theoretical tenets proposed by Paul de Man as they interact with Holocaust memoirs. Doing so may be a way to understand the larger issue by exploring its expression in a narrow vein: that of literature. Holocaust memoirs as a group have been read as making new claims about their relation to a particular referent—about the inability of fully representing the Holocaust in existing modes—but they also make simultaneous claims about the utter necessity of attempting to do so. It will be helpful to see how this revolution of the relationship of [End Page 17] writing to its referent is perhaps at odds with that other similar revolution, that of deconstruction. I also attempt to put this potential conflict into a frame that may elucidate the reasons for their disconnect, using Lyotard’s well-known attempt at establishing an order of postmodern ethics: The Differend, as well as approaches to trauma and memory suggested by Derrida.My aim here is also not to delve into judgments of guilt or innocence with respect to de Man himself and his activities during World War II. I instead venture into the ways, both positive and negative, but inherently problematic, that his writings come into contact with an event recognized by many as a limit event, one that demands recognition of its historicity, even as it engenders a body of literature that expresses the difficulty of understanding the event itself.There is much in de Man’s writings that forces us to consider the restraints and potential of the means of construction of written texts. Exploring this can lead toward a better understanding of the way that individual texts create and manipulate meaning. To this end, much can be gained from de Manian criticism that makes apparent the contradictory tendency of linguistic constructions to indicate something outside themselves (their referential potential), even while their structures and conventions cast in doubt the reality of this “something.” One makes use of this discourse, not in the hopes of destroying the privilege of referentiality that underlies the structures of testimony, victimization, and trauma, but in the hopes of finding a way for the discourse of memoir (and autobiography) to be reconciled with the discourse of deconstruction in such a way that... (shrink)

In theCritique of Pure Reason,Kant argues for two principles that concern magnitudes. The first is the principle that ‘All intuitions are extensive magnitudes,’ which appears in the Axioms of Intuition (B202); the second is the principle that ‘In all appearances the real, which is an object of sensation, has an intensive magnitude, that is, a degree,’ which appears in the Anticipations of Perception (B207). A circle drawn in geometry and the space occupied by an object such as a book (...) are paradigm examples of extensive magnitudes, while the intensity of a light is a paradigm example of an intensive magnitude. These principles justify and explain the possibility of applying mathematics to objects of experience. The Axioms principle also explains the possibility of any mathematical cognition at all. (shrink)

Computers may help us to better understand (not just verify) arguments. In this article we defend this claim by showcasing the application of a new, computer-assisted interpretive method to an exemplary natural-language ar- gument with strong ties to metaphysics and religion: E. J. Lowe’s modern variant of St. Anselm’s ontological argument for the existence of God. Our new method, which we call computational hermeneutics, has been particularly conceived for use in interactive-automated proof assistants. It aims at shedding light on the (...) meanings of words and sentences by framing their inferential role in a given argument. By employing automated theorem reasoning technology within interactive proof assistants, we are able to drastically reduce (by several orders of magnitude) the time needed to test the logical validity of an argu- ment’s formalization. As a result, a new approach to logical analysis, inspired by Donald Davidson’s account of radical interpretation, has been enabled. In computational hermeneutics, the utilization of automated reasoning tools ef- fectively boosts our capacity to expose the assumptions we indirectly commit ourselves to every time we engage in rational argumentation and it fosters the explicitation and revision of our concepts and commitments. (shrink)