For Kant, inquiry into nature properly requires seeking to explain all material wholes merely mechanically, in terms of their parts. There is no consensus on how he justifies this Principle of Mechanism. I argue that Kant seeks to derive this claim about part and wholes neither from his laws or mechanics, nor from the mere discursivity of our understanding (two standard options in the literature), but instead from a priori principles laid out in the first Critique, which govern parts, wholes, (...) and magnitudes. These principles are also fundamental to Kant’s account of mathematics. Therefore, Kant’s Principle of Mechanism and his philosophy of mathematics have common foundations. (shrink)

I am going to argue for a robust realism about magnitudes, as irreducible elements in our ontology. This realistic attitude, I will argue, gives a better metaphysics than the alternatives. It suggests some new options in the philosophy of science. It also provides the materials for a better account of the mind’s relation to the world, in particular its perceptual relations.

This paper addresses a number of closely related questions concerning Kant's model of intentionality, and his conceptions of unity and of magnitude [Gröβe]. These questions are important because they shed light on three issues which are central to the Critical system, and which connect directly to the recent analytic literature on perception: the issues are conceptualism, the status of the imagination, and perceptual atomism. In Section 1, I provide a sketch of the exegetical and philosophical problems raised by Kant's (...) views on these issues. I then develop, in Section 2, a detailed analysis of Kant's theory of perception as elaborated in both the Critique of Pure Reason and the Critique of Judgment; I show how this analysis provides a preliminary framework for resolving the difficulties raised in Section 1. In Section 3, I extend my analysis of Kant's position by considering a specific test case: the Axioms of Intuition. I contend that one way to make sense of Kant's argument is by juxtaposing it with Russell's response to Bradley's regress; I focus in particular on the concept of ‘unity’. Finally, I offer, in Section 4, a philosophical assessment of the position attributed to Kant in Sections 2 and 3. I argue that, while Kant's account has significant strengths, a number of key areas remain underdeveloped; I suggest that the phenomenological tradition may be read as attempting to fill precisely those gaps. (shrink)

This paper introduces the reader to Meinong's work on the metaphysics of magnitudes and measurement in his Über die Bedeutung des Weber'schen Gesetzes. According to Russell himself, who wrote a review of Meinong's work on Weber's law for Mind, Meinong's theory of magnitudes deeply influenced Russell's theory of quantities in the Principles of Mathematics. The first and longest part of the paper discusses Meinong's analysis of magnitudes. According to Meinong, we must distinguish between divisible and indivisible magnitudes. He argues that (...) relations of distance, or dissimilarity, are indivisible magnitudes that coincide with divisible magnitudes called "stretches". The second part of the paper is concerned with Meinong's account of measurement as a comparison of parts. According to Meinong, since measuring consists in comparing parts only divisible magnitudes are directly measurable. Indivisible magnitudes can only be measured indirectly, by measuring the divisible stretches that coincide with them. (shrink)

In the first Critique, Kant attempts to prove what we can call the "Principle of Intensive Magnitudes," according to which every possible object of experience will possess a determinate "degree" of reality. Curiously, Kant argues for this principle by inferring from a psychological premise about internal sensations (they have intensive magnitudes) to a metaphysical thesis about external objects (they also have intensive magnitudes). Most commentators dismiss the argument as a failure. In this article I give a reconstruction of Kant's argument (...) that attempts to rehabilitate the argument back into his broader transcendental theory of experience. I argue that we can make sense of the argument's central inference by appeal to Kant's theory of empirical intuition and by an analysis of the way in which Kant thinks sensory matter constitutes our most basic representations of objects. (shrink)

Dustin Stokes argues for the existence of orectic penetration, a phenomenon in which a desire-like state penetrates our perceptual experience. His candidate for a case of orectic penetration is the most convincing candidate presented thus far. It is argued here that his candidate and his further arguments for the existence of orectic penetration do not support the claim that orectic penetration takes place. As a result, it is concluded that there are no convincing cases of desire-like states penetrating perceptual experience.

I offer a critique of Melissa Zinkin’s reading of Kant’s analysis of aesthetic judgment. She argues that in judgments of taste the imagination is freed from its determinate relation with the understanding because the form of intuition in which beauty is apprehended is different from the form of intuition employed in determinate judgment. By distinguishing between an extensive and intensive form of intuition, this interpretation is able to explain why the apprehension of beauty cannot be subsumed under a concept. But (...) I contest Zinkin’s identification of the sensus communis with this intensive form of intuition. I then substantiate two interrelated claims: that we can account for the genesis of the sensus communis by distinguishing between an intensive and an extensive form of time, and that we can avoid making the sensus communis atemporal by showing that it resides within an intensive form of time as a condition for its possibility, thereby structuring Kant’s account of the sensus communis securely within the critical framework. (shrink)

This chapter presents a re-understanding of the contents of our analog magnitude representations (e.g., approximate duration, distance, number). The approximate number system (ANS) is considered, which supports numerical representations that are widely described as fuzzy, noisy, and limited in their representational power. The contention is made that these characterizations are largely based on misunderstandings—that what has been called “noise” and “fuzziness” is actually an important epistemic signal of confidence in one’s estimate of the value. Rather than the ANS having (...) noisy or fuzzy numerical content, it is suggested that the ANS has exquisitely precise numerical content that is subject to epistemic limitations. Similar considerations will arise for other analog representations. The chapter discusses how this new understanding of ANS representations recasts the learnability problem for number and the conceptual changes that children must accomplish in the number domain. (shrink)

The philosophy of mathematics has been accused of paying insufficient attention to mathematical practice: one way to cope with the problem, the one we will follow in this paper on extensive magnitudes, is to combine the `history of ideas' and the `philosophy of models' in a logical and epistemological perspective. The history of ideas allows the reconstruction of the theory of extensive magnitudes as a theory of ordered algebraic structures; the philosophy of models allows an investigation into the way epistemology (...) might affect relevant mathematical notions. The article takes two historical examples as a starting point for the investigation of the role of numerical models in the construction of a system of non-Archimedean magnitudes. A brief exposition of the theories developed by Giuseppe Veronese and by Rodolfo Bettazzi at the end of the 19th century will throw new light on the role played by magnitudes and numbers in the development of the concept of a non-Archimedean order. Different ways of introducing non-Archimedean models will be compared and the influence of epistemological models will be evaluated. Particular attention will be devoted to the comparison between the models that oriented Veronese's and Bettazzi's works and the mathematical theories they developed, but also to the analysis of the way epistemological beliefs affected the concepts of continuity and measurement. (shrink)

One vexing question for Desire Satisfactionism is this: At what time do you benefit from a satisfied desire? Recently Eden Lin has proposed an intriguing answer. On this proposal – Asymmetrism – when past-directed desires are satisfied, the time interval during which you benefit is the time of the desire; and, when future-directed desires are satisfied, the time interval during which you benefit is the time of the object. In this essay, I argue that Asymmetrism forces us to give implausible (...) answers to a different question: To what extent does a given satisfied desire benefit you? (shrink)

The problem of the intensification and remission of qualities was a crux for philosophical, theological, and scientific thought in the Middle Ages. It was raised in Antiquity with this remark of Aristotle: some qualities, as accidental beings, admit the more and the less. Admitting more and less is not a trivial property, since it belongs neither to every category of being, nor to every quality. Rather it applies only to states and dispositions such as virtue, to affections of bodies such (...) as heat and sweetness, and to affections of soul such as anger. However, the property of admitting more and less was a matter of importance for the qualitative physics that had reigned up to about the time of Descartes, a physics which was concerned with concepts such as heat, coldness, lightness, heaviness, and so on. (shrink)

Why did God create a vast universe? Various answers are discussed and rejected: a) for its beauty; b) to instill a sense of the sublime in his intelligent creatures; c) to demonstrate his glory, d) to provide a home for extraterrestrial species; e) to guarantee that the natural emergence of (intelligent) life, though extremely rare, happens nonetheless somewhere; f) for no reason at all, because the human notion of efficiency does not apply to God’s actions. Instead, the paper suggests that (...) the universe is intended for Space settlements. Several objections to this proposal are considered and deemed unconvincing. (shrink)

Kant's account of space as an infinite given magnitude in the Critique of Pure Reason is paradoxical, since infinite magnitudes go beyond the limits of possible experience. Michael Friedman's and Charles Parsons's accounts make sense of geometrical construction, but I argue that they do not resolve the paradox. I argue that metaphysical space is based on the ability of the subject to generate distinctly oriented spatial magnitudes of invariant scalar quantity through translation or rotation. The set of determinately oriented, (...) constructed geometrical spaces is a proper subset of metaphysical space, thus, metaphysical space is infinite. Kant's paradoxical doctrine of metaphysical space is necessary to reconcile his empiricism with his transcendental idealism. (shrink)

This paper investigates Hume's theory of the perception of spatial magnitude or size as developed in the _Treatise<D>, as well as its relation to his concepts of space and geometry. The central focus of the discussion is Hume's espousal of the 'composite' hypothesis, which holds that perceptions of spatial magnitude are composed of indivisible sensible points, such that the total magnitude of a visible figure is a derived by-product of its component parts. Overall, it will be argued (...) that a straightforward reading of this hypothesis fails to do full justice to the complexity of Hume's theory of spatial perception and geometry, and that a more adequate treatment must also admit an important role for the more direct process of spatial magnitude perception which he dubs 'intuition'. (shrink)

Formalizing Euclid’s first axiom. Bulletin of Symbolic Logic. 20 (2014) 404–5. (Coauthor: Daniel Novotný) -/- Euclid [fl. 300 BCE] divides his basic principles into what came to be called ‘postulates’ and ‘axioms’—two words that are synonyms today but which are commonly used to translate Greek words meant by Euclid as contrasting terms. -/- Euclid’s postulates are specifically geometric: they concern geometric magnitudes, shapes, figures, etc.—nothing else. The first: “to draw a line from any point to any point”; the last: the (...) parallel postulate. -/- Euclid’s axioms are general principles of magnitude: they concern geometric magnitudes and magnitudes of other kinds as well even numbers. The first is often translated “Things that equal the same thing equal one another”. -/- There are other differences that are or might become important. -/- Aristotle [fl. 350 BCE] meticulously separated his basic principles [archai, singular archê] according to subject matter: geometrical, arithmetic, astronomical, etc. However, he made no distinction that can be assimilated to Euclid’s postulate/axiom distinction. -/- Today we divide basic principles into non-logical [topic-specific] and logical [topic-neutral] but this too is not the same as Euclid’s. In this regard it is important to be cognizant of the difference between equality and identity—a distinction often crudely ignored by modern logicians. Tarski is a rare exception. The four angles of a rectangle are equal to—not identical to—one another; the size of one angle of a rectangle is identical to the size of any other of its angles. No two angles are identical to each other. -/- The sentence ‘Things that equal the same thing equal one another’ contains no occurrence of the word ‘magnitude’. This paper considers the problem of formalizing the proposition Euclid intended as a principle of magnitudes while being faithful to the logical form and to its information content. (shrink)

Scholars working on Kant’s Anticipations of Perception generally attribute to him an argument that invalidly infers that objects have degrees of intensive magnitude from the premise that sensations do. I argue that this rests on an incorrect disambiguation of Kant’s use of Empfindung as referring to the mental states that are our sensings, rather than the objects that are thereby sensed. Kant’s real argument runs as follows. The difference between a representation of an empty region of space and/or time (...) and a representation of that same region as occupied by an object entails that, in addition to their extensive magnitude, objects must be represented as having a matter variable in intensive magnitude. Since it is the presence of sensation in a cognition that marks the difference between representing only the extensive magnitude of the object and the object as a whole, it is sensation that represents its intensive magnitude. (shrink)

Building on Christopher Peacocke’s account of analog perceptual contentand my own account of analog perceptual vehicles, I defend three claims: that theperception of magnitudes often has analog contents; that the perception of magni-tudes often has analog vehicles; and that the first claim is true in virtue of the second—that is, the analog vehicles help to ground the analog contents.

Online shaming is a subject of import for social philosophy in the Internet age, and not simply because shaming seems generally bad. I argue that social philosophers are well-placed to address the imaginal relationships we entertain when we engage in social media; activity in cyberspace results in more relationships than one previously had, entailing new and more responsibilities, and our relational behaviors admit of ethical assessment. I consider the stresses of social media, including the indefinite expansion of our relationships and (...) responsibilities, and the gap between the experiences of those shamed and the shamers’ appreciation of the magnitude of what they do when they shame; I connect these to the literature suggesting that some intuitions fail to guide our ethics. I conclude that we each have more power than we believe we do or than we think carefully about exerting in our online imaginal relations. Whether we are the shamers or the shamed, we are unable to control the extent to which intangible words in cyberspace take the form of imaginal relationships that burden or brighten our self-perceptions. (shrink)

Although symmetry has been discussed in terms of a major law of perceptual organization since the early conceptual efforts of the Gestalt school (Wertheimer, Metzger, Koffka and others), the first quantitative measurements testing for effects of symmetry on processes of Gestalt formation have seen the day only recently. In this study, a psychophysical rating study and a “foreground”-“background” choice response time experiment were run with human observers to test for effects of bilateral symmetry on the perceived strength of figure-ground in (...) triangular Kanizsa configurations. Displays with and without bilateral symmetry, identical physically-specified-to-total contour ratio, and constant local contrast intensity within and across conditions, but variable local contrast polarity and variable orientation in the plane, were presented in a random order to human observers. Configurations with bilateral symmetry produced significantly stronger figure-ground percepts reflected by greater subjective magnitudes and consistently higher percentages of “foreground” judgments accompanied by significantly shorter response times. These effects of symmetry depend neither on the orientation of the axis of symmetry, nor on the contrast polarity of the physical inducers. It is concluded that bilateral symmetry, irrespective of orientation, significantly contributes to the, largely sign-invariant, visual mechanisms of figure-ground segregation that determine the salience of figure-ground in perceptually ambiguous configurations. (shrink)

The purpose of this article is to present Lisa Shabel's interpretive proposal that relates algebra to symbolic constructions. This briefly covers the problem of the status of algebra and how some of the interpretations given relate it to the numerical calculation. Subsequently, by the hand of Shabel and with an eye on the mathematical practice of Cristian Wolff, the ways of proceeding algebraically in the eighteenth century will be identified and then analyze the two meanings of the term “magnitude”. (...) Finally, algebra is related to a construction in accordance with the a priori concepts, certain rules and which it has its referent. Such a type of construction defines what Kant understands by symbolic construction. (shrink)

ABSTRACT Kant famously claims that we have all freely chosen evil. This paper offers a novel account of the much-debated justification for this claim. I reconstruct Kant’s argument from his affirmation that we all have a price – we can all succumb to temptation. I argue that this follows a priori from a theoretical principle of the Critique of Pure Reason, namely that all empirical powers have a finite, changeable degree, an intensive magnitude. Because of this, our reason can (...) always be overpowered by sensible inclinations. Kant moreover holds that this necessary feature of our moral psychology should not have been the case: We ought to instead be like the divine human being, for whom the moral law yields a greater incentive than any possible temptation. On Kant’s view, we are thus responsible for having a price, and the synthetic a priori fact that we do proves that we each made an initial choice of evil. (shrink)

Achievements have recently begun to attract increased attention from value theorists. One recurring idea in this budding literature is that one important factor determining the magnitude or value of an achievement is the amount of effort the achiever invested. The aim of this paper is to present the most plausible version of this idea. This advances the current state of debate where authors are invoking substantially different notions of effort and are thus talking past each other. While the concept (...) of effort has been invoked in the philosophical analysis of a number of important concepts such as desert, attention, competence, and distributive justice, it has hardly ever been analyzed itself. This paper makes headway in this regard by discussing three ambiguities in the everyday notion of effort. It continues to develop two accounts of effort and shows how both of them are achievement-enhancing. (shrink)

In the wake of the spectacular success of Miranda Fricker's Epistemic Injustice, philosophers have paid a great deal of attention to testimonial injustice. Testimonial injustice occurs when recipients of testimony discount it in virtue of its source: usually, their social identity. The remedy for epistemic injustice is almost always listening better and giving greater weight to the testimony we hear, on most philosophers' implicit or explicit view. But Fricker identifies another kind of epistemic injustice: hermeneutical injustice. This kind of injustice (...) occurs when someone can't articulate their own experience or understand their situation for lack of the hermeneutical tools. There is a possible tension between these kinds of injustice, we suggest: sincere testimony may be misleading (may fail to identify significant harms the testfier is subject, or may fail to register its magnitude, or to categorize it as the kind of harm it is) in virtue of a lack of hermeneutical resources. This tension raises the possibility that there are situations in which experts - those who possess hermeneutical tools - may be able to correct the testimony of those who experience harms in virtue of their identity. In this paper, we identify possible cases in which epistemic injustice might be reduced through such correction: in which an increase in testimonial injustice might serve to decrease it in the longer run, for example. We also suggest how the obvious dangers of a too great readiness to see testimony as in need of expert correction might be mitigated, and how the expert might suggest corrections without ceasing to listen. (shrink)

There are at least two threads in our thought and talk about rationality, both practical and theoretical. In one sense, to be rational is to respond correctly to the reasons one has. Call this substantive rationality. In another sense, to be rational is to be coherent, or to have the right structural relations hold between one’s mental states, independently of whether those attitudes are justified. Call this structural rationality. According to the standard view, structural rationality is associated with a distinctive (...) set of requirements that mandate or prohibit certain combinations of attitudes, and it’s in virtue of violating these requirements that incoherent agents are irrational. I think the standard view is mistaken. The goal of this paper is to explain why, and to motivate an alternative account: rather than corresponding to a set of law-like requirements, structural rationality should be seen as corresponding to a distinctive kind of pro tanto rational pressure—i.e. something that comes in degrees, having both magnitude and direction. Something similar is standardly assumed to be true of substantive rationality. On the resulting picture, each dimension of rational evaluation is associated with a distinct kind of rational pressure—substantive rationality with (what I call) justificatory pressure and structural rationality with attitudinal pressure. The former is generated by one’s reasons while the latter is generated by one’s attitudes. Requirements turn out to be at best a footnote in the theory of rationality. (shrink)

The singularity hypothesis is a radical hypothesis about the future of artificial intelligence on which self-improving artificial agents will quickly become orders of magnitude more intelligent than the average human. Despite the ambitiousness of its claims, the singularity hypothesis has been defended at length by leading philosophers and artificial intelligence researchers. In this paper, I argue that the singularity hypothesis rests on scientifically implausible growth assumptions. I show how leading philosophical defenses of the singularity hypothesis (Chalmers 2010, Bostrom 2014) (...) fail to overcome the case for skepticism. I conclude by drawing out philosophical implications of this discussion for our understanding of consciousness, personal identity, digital minds, existential risk, and ethical longtermism. GPI Working Paper No . 19-2022. (shrink)

The standard version of sufficientarianism maintains that providing people with enough, or as close to enough as is possible, is lexically prior to other distributive goals. This article argues that this is excessive – more than distributive justice allows – in four distinct ways. These concern the magnitude of advantage, the number of beneficiaries, responsibility and desert, and above-threshold distribution. Sufficientarians can respond by accepting that providing enough unconditionally is more than distributive justice allows, instead balancing sufficiency against other (...) considerations. (shrink)

We make physical efforts when we swim, carry shopping bags, push heavy doors, or cycle up hills. A growing concern among philosophers and scientists in related fields is the absence of a well-defined concept for physical efforts. This paper addresses this issue by presenting a force-based definition of physical efforts. In Sect. 1, we explore the shortcomings of existing definitions of effort. Section 2 introduces the force-based account of efforts according to which making an effort consists in exerting a force (...) so as to make an object move or stay at rest. Section 3 introduces three central distinctions stemming from the account: failed vs. successful efforts; resisted vs. unresisted efforts; and efforts vs. effortful actions. Section 4 presents a key objection, to the effect that the force-based theory cannot account for the difficulty of efforts: efforts usually feel difficult, but effort’s difficulty is not always a function of the magnitude of force(s) exerted. Section 5 argues that the most in-depth account of difficulty so far, that developed by Bradford ( 2015 ), cannot account for the difficulty of efforts. Sections 6 & 7 develop a novel account of effort’s difficulty. (shrink)

Phineas Gage’s story is typically offered as a paradigm example supporting the view that part of what matters for personal identity is a certain magnitude of similarity between earlier and later individuals. Yet, reconsidering a slight variant of Phineas Gage’s story indicates that it is not just magnitude of similarity, but also the direction of change that affects personal identity judgments; in some cases, changes for the worse are more seen as identity-severing than changes for the better of (...) comparable magnitude. Ironically, thinking carefully about Phineas Gage’s story tells against the thesis it is typically taken to support. (shrink)

The EU proposal for the Artificial Intelligence Act (AIA) defines four risk categories: unacceptable, high, limited, and minimal. However, as these categories statically depend on broad fields of application of AI, the risk magnitude may be wrongly estimated, and the AIA may not be enforced effectively. This problem is particularly challenging when it comes to regulating general-purpose AI (GPAI), which has versatile and often unpredictable applications. Recent amendments to the compromise text, though introducing context-specific assessments, remain insufficient. To address (...) this, we propose applying the risk categories to specific AI scenarios, rather than solely to fields of application, using a risk assessment model that integrates the AIA with the risk approach arising from the Intergovernmental Panel on Climate Change (IPCC) and related literature. This model enables the estimation of the magnitude of AI risk by considering the interaction between (a) risk determinants, (b) individual drivers of determinants, and (c) multiple risk types. We use large language models (LLMs) as an example. (shrink)

The personal identity relation is of great interest to philosophers, who often consider fictional scenarios to test what features seem to make persons persist through time. But often real examples of neuroscientific interest also provide important tests of personal identity. One such example is the case of Phineas Gage – or at least the story often told about Phineas Gage. Many cite Gage’s story as example of severed personal identity; Phineas underwent such a tremendous change that Gage “survived as a (...) different man.” I discuss a recent empirical finding about judgments about this hypothetical. It is not just the magnitude of the change that affects identity judgment; it is also the negative direction of the change. I present an experiment suggesting that direction of change also affects neuroethical judgments. I conclude we should consider carefully the way in which improvements and deteriorations affect attributions of personal identity. This is particularly important since a number of the most crucial neuroethical decisions involve varieties of cognitive enhancements or deteriorations. (shrink)

People sometimes explain behavior by appealing to an essentialist concept of the self, often referred to as the true self. Existing studies suggest that people tend to believe that the true self is morally virtuous; that is deep inside, every person is motivated to behave in morally good ways. Is this belief particular to individuals with optimistic beliefs or people from Western cultures, or does it reflect a widely held cognitive bias in how people understand the self? To address this (...) question, we tested the good true self theory against two potential boundary conditions that are known to elicit different beliefs about the self as a whole. Study 1 tested whether individual differences in misanthropy—the tendency to view humans negatively—predict beliefs about the good true self in an American sample. The results indicate a consistent belief in a good true self, even among individuals who have an explicitly pessimistic view of others. Study 2 compared true self-attributions across cultural groups, by comparing samples from an independent country and a diverse set of interdependent countries. Results indicated that the direction and magnitude of the effect are comparable across all groups we tested. The belief in a good true self appears robust across groups varying in cultural orientation or misanthropy, suggesting a consistent psychological tendency to view the true self as morally good. (shrink)

It is widely acknowledged that susceptibility to suitable emotional responses is part of what it is to value something. Indeed, the value of at least some things calls for such emotional responses – if we lack them, we don’t respond appropriately to their value. In this paper, I argue that susceptibility to anger is an essential component of valuing other people, ourselves, and our relationships. The main reason is that various modes of valuing, such as respect, self-respect, and love, ground (...) normative expectations towards others and ourselves. And holding someone accountable for violating legitimate normative expectations involves emotions from the anger family, such as resentment and indignation. I hold that such forms of anger, which aim at getting the target to conform to expectations or lower their unduly elevated status, are neither inherently problematic or dispensable parts of the package of attitudes involved in valuing. Finally, thinking about anger’s role in valuing also helps see when it is out of place or immature – roughly, it is often excessive, because we easily exaggerate the magnitude of the value involved, the harm or threat to it, or the degree of the target’s moral responsibility. (shrink)

It seems like we care about at least two features of our credence function: gradational-accuracy and verisimilitude. Accuracy-first epistemology requires that we care about one feature of our credence function: gradational-accuracy. So if you want to be a verisimilitude-valuing accuracy-firster, you must be able to think of the value of verisimilitude as somehow built into the value of gradational-accuracy. Can this be done? In a recent article, Oddie has argued that it cannot, at least if we want the accuracy measure (...) to be proper. I argue that it can. 1Introduction2Some Nuts and Bolts3First Attempts4Oddie’s Constraint5The Good5.1Proximity over the disagreement metric 5.2Proximity over the magnitude metric 6The Bad and the Ugly 7Some More Good: The Role of Evenness of Distribution 8Some More Bad: Which Propositions to Privilege? 9Concluding Thoughts: Accuracy and Practical Value. (shrink)

Visual illusions of number provide a means of investigating the rules and principles through which approximate number representations are formed. Here, we investigated the developmental trajectory of an important numerical illusion – the connectedness illusion, wherein connecting pairs of items with thin lines reduces their perceived number without altering continuous attributes of the collections. We found that children as young as 5 years of age are affected by the illusion and that the magnitude of the effect increased into adulthood. (...) Moreover, individuals with greater numerical acuity exhibited stronger connectedness illusions after controlling for age. Overall, these results suggest the approximate number system expects to enumerate over bounded wholes and doing so is a signature of its optimal functioning. (shrink)

Our pains can be more or less intense, our mental imagery can be more or less vivid, our perceptual experiences can be more or less striking. These degrees of intensity of conscious experiences are all manifestations of a phenomenal property I call mental strength. In this article, I argue that mental strength is a domain-general phenomenal magnitude; in other words, it is a phenomenal quantity shared by all conscious experiences that explains their degree of felt intensity. Mental strength has (...) been largely overlooked in favor of mental states’ type, representational contents, domain-specific phenomenology, or processes such as attention. Considering mental strength in our reflections about the mind illuminates debates about the relation of representational contents and phenomenal character, and it also helps address questions about the structure and functions of consciousness. Mental strength provides a unifying construct to model what is shared in the phenomenology of different types of conscious experiences. (shrink)

The EU Artificial Intelligence Act (AIA) defines four risk categories for AI systems: unacceptable, high, limited, and minimal. However, it lacks a clear methodology for the assessment of these risks in concrete situations. Risks are broadly categorized based on the application areas of AI systems and ambiguous risk factors. This paper suggests a methodology for assessing AI risk magnitudes, focusing on the construction of real-world risk scenarios. To this scope, we propose to integrate the AIA with a framework developed by (...) the Intergovernmental Panel on Climate Change (IPCC) reports and related literature. This approach enables a nuanced analysis of AI risk by exploring the interplay between (a) risk determinants, (b) individual drivers of determinants, and (c) multiple risk types. We further refine the proposed methodology by applying a proportionality test to balance the competing values involved in AI risk assessment. Finally, we present three uses of this approach under the AIA: to implement the Regulation, to assess the significance of risks, and to develop internal risk management systems for AI deployers. (shrink)

Humans and other animals have an evolved ability to detect discrete magnitudes in their environment. Does this observation support evolutionary debunking arguments against mathematical realism, as has been recently argued by Clarke-Doane, or does it bolster mathematical realism, as authors such as Joyce and Sinnott-Armstrong have assumed? To find out, we need to pay closer attention to the features of evolved numerical cognition. I provide a detailed examination of the functional properties of evolved numerical cognition, and propose that they prima (...) facie favor a realist account of numbers. (shrink)

Developing earlier studies of the system of numbers in Mundurucu, this paper argues that the Mundurucu numeral system is far more complex than usually assumed. The Mundurucu numeral system provides indirect but insightful arguments for a modular approach to numbers and numerals. It is argued that distinct components must be distinguished, such as a system of representation of numbers in the format of internal magnitudes, a system of representation for individuals and sets, and one-to-one correspondences between the numerosity expressed by (...) the number and its metrics. It is shown that while many-number systems involve a compositionality of units, sets and sets composed of units, few-number languages, such as Mundurucu, do not have access to sets composed of units in the usual way. The nonconfigurational character of the Mundurucu language, which is related to a property for which we coin the term 'low compositionality power', accounts for this and explains the curious fact that Mundurucus make use of marked one-to-one correspondence strategies in order to overcome the limitations of the core system at the perceptual/motor interface of the language faculty. We develop an analysis of a particular construction, parallel numbers, which has not been studied before, elucidating the whole system. This analysis, we argue, sheds new light on classical philosophical, psychological and linguistic debates about numbers and numerals and their relation to language, and more particularly, sheds light on few-number languages. (shrink)

Aristotle is said to have held that any kind of actual infinity is impossible. I argue that he was a finitist (or "potentialist") about _magnitude_, but not about _plurality_. He did not deny that there are, or can be, infinitely many things in actuality. If this is right, then it has implications for Aristotle's views about the metaphysics of parts and points.

In the heart of southeast Texas, an industrial powerhouse often referred to as the 'Golden Triangle', the oil refineries and petrochemical plants stand as stalwart testaments to the region's economic evolution. Interestingly, before the discovery of oil at Spindletop, the lumber and cattle industries powered this region's economy. A profound shift occurred when the Lucas Gusher, a fountain of oil spurting thousands of feet into the air, struck the lands of Spindletop Hill on January 10, 1901. This remarkable discovery of (...) the Spindletop oilfield on a slat dome formation south of Beaumont, Texas, marked the birth of the modern petroleum industry and fundamentally transformed the region's geopolitical, economic, and cultural landscapes. People from all over the country relocated to Gladys City and Beaumont in search of work and new opportunities, creating a boomtown as the town's population swelled from 10,000 to 50,000. The newfound urbanization brought by the oil industry transformed the town and the surrounding areas, creating a ripple effect across the region that would be felt for generations to come. The surge in oil-driven economic activity transmuted the region into a vibrant nexus of commerce, with the oil industry emerging as a critical architect of growth and advancement. This newfound affluence incited by the petroleum sector ushered in an era of economic diversification, laying the groundwork for industrialization’s further evolution. The Spindletop Oil Fields not only underscored the United States’ ascent as the foremost petroleum-producing nation but also signaled the nation’s initiation into the Petroleum Age. It was Spindletop that solidified its position as America’s first significant oil field, becoming an enduring symbol of its industrial might. By 1985, over 153,000,000 barrels of oil had been produced and extracted from the Spindletop oil fields, underscoring the magnitude of this extraordinary resource. (shrink)

This research investigates 3- and 5-year-olds' relative fairness in distributing small collections of even or odd numbers of more or less desirable candies, either with an adult experimenter or between two dolls. The authors compare more than 200 children from around the world, growing up in seven highly contrasted cultural and economic contexts, from rich and poor urban areas, to small-scale traditional and rural communities. Across cultures, young children tend to optimize their own gain, not showing many signs of self-sacrifice (...) or generosity. Already by 3 years of age, self-optimizing in distributive justice is based on perspective taking and rudiments of mind reading. By 5 years, overall, children tend to show more fairness in sharing. What varies across cultures is the magnitude of young children's self-interest. More fairness (less self-interest) in distributive justice is evident by children growing up in small-scale urban and traditional societies thought to promote more collective values. (shrink)

Aristotle offers several arguments in Physics viii.8 for his thesis that, when something moves back and forth, it does not undergo a single motion. These arguments occur against the background of a sophisticated theory, expounded in Physics v—vi, of the basic structure of motions and of other continuous entities such as times and magnitudes. The arguments in Physics viii.8 stand in a complex relation to that theory. On the one hand, Aristotle evidently relies on the theory in a number of (...) crucial steps. Yet in other steps he seems to contradict or misapply the theory. This situation offers the occasion to examine Aristotle’s views about some fundamentals in the metaphysics of motion, while also raising questions about the unity of the text which has come down to us as the Physics. (shrink)

Selection against embryos that are predisposed to develop disabilities is one of the less controversial uses of embryo selection technologies. Many bio-conservatives argue that while the use of ESTs to select for non-disease-related traits, such as height and eye-colour, should be banned, their use to avoid disease and disability should be permitted. Nevertheless, there remains significant opposition, particularly from the disability rights movement, to the use of ESTs to select against disability. In this article we examine whether and why the (...) state could be justified in restricting the use of ESTs to select against disability. We first outline the challenge posed by proponents of ‘liberal eugenics’. Liberal eugenicists challenge those who defend restrictions on the use of ESTs to show why the use of these technologies would create a harm of the type and magnitude required to justify coercive measures. We argue that this challenge could be met by adverting to the risk of harms to future persons that would result from a loss of certain forms of cognitive diversity. We suggest that this risk establishes a pro tanto case for restricting selection against some disabilities, including dyslexia and Asperger's syndrome. (shrink)

Some experts have argued that patients should routinely be told the specific magnitude and absolute probability of potential risks and benefits of screening tests. This position is motivated by the idea that framing risk information in ways that are less precise violates the ethical principle of respect for autonomy and its application in informed consent or shared decisionmaking. In this Perspective, we consider a number of problems with this view that have not been adequately addressed. The most important challenges (...) stem from the danger that patients will misunderstand the information or have irrational responses to it. Any initiative in this area should take such factors into account and should consider carefully how to apply the ethical principles of respect for autonomy and beneficence. (shrink)

In their seeking of simplicity, scientists fall into the error of Whitehead's "fallacy of misplaced concreteness." They mistake their abstract concepts describing reality for reality itself--the map for the territory. This leads to dogmatic overstatements, paradoxes, and mysteries such as the deep incompatibility of our two most fundamental physical theories--quantum mechanics and general relativity. To avoid such errors, we should evoke Whitehead's conception of the universe as a universe-in-process, where physical relations perpetually beget new physical relations. Today, the most promising (...) interpretations of quantum mechanics exemplify this Whiteheadian idea, formalizing physical systems, and the universe itself, as ongoing histories of actualizations of potential states, where actual states and potential states exist in mutually implicative relation as two separate categories of reality—an idea first proposed by Aristotle and rehabilitated by Heisenberg. In these interpretations, the classical conception of a history as a derivative story about fundamental physical objects is reversed: the classical physical object becomes the derivative story about fundamental histories of quantum states. The consistent histories interpretation of Robert Griffiths and the decoherent histories interpretation of Roland Omnès are cardinal examples of this approach to quantum mechanics. Another example, the relational realist interpretation, begins with the decoherent histories approach and formalizes it explicitly as a Whiteheadian interpretation, taking his “algebraic method” and applying it to quantum mechanics via algebraic topology. This branch of mathematics can be thought of as a “de-concretized” geometry in that it focuses only on the logical relations among objects and regions (and relations of these relations) rather than the fixed magnitudes of lines, planes, and other such rigid intervals. It has all the robust logical structure of geometry yet allows for an elasticity of relations that makes topological mathematical structures inherently immune misplaced concretization. (shrink)

This study forms a part of a larger investigation of the influence of the philosophy of Heraclitus of Ephesus on modern poetry. T. S. Eliot, to mention the best known of the many poets inspired by Heraclitus, selected two Heraclitus fragments (B 2 and B 60) as epigraphs for his “Burnt Norton”, the first of his Four Quartets. Eliot explained that he was drawn to the fragments because of their ‘ambiguity’ and ‘extraordinary poetic suggestiveness’. Similarly, in ‘This Solitude of Cataracts’, (...) Wallace Stevens spoke of ‘the flecked river which kept flowing and never the same way twice’ and elsewhere noted the ‘inherently poetic quality’ of many Heraclitean sayings. To gain some sense of the nature and magnitude of Heraclitus’ legacy for modern poetry we must first explore his vision of ‘a fiery cosmos being kindled in measures and extinguished in measures’ and a river into which one cannot step twice. -/- . (shrink)

This paper investigates the relationships between organizational change and trust in management. It is argued that organizational change represents a critical episode for the production and destruction of trust in management. Although trust in management is seen as a semi stable psychological state, changes in organizations make trust issues salient and organizational members attend to and process trust relevant information resulting in a reassessment of their trust in management. The direction and magnitude of change in trust is dependent on (...) a set of change dimensions that reflect trust relevant experiences and information. We distinguish between dimensions related to trust relevant consequences of the change and trust relevant aspects of how the change process is performed. Empirical results indicate that increases in post change emotional stress and the use of referential accounts for justifying change are both negatively related to post change trust in management. The use of ideological accounts and participation were found to be positively related to post change trust in management, so was perceived decision quality. Findings also indicate that the effects of change on trust are negatively moderated by tenure. (shrink)

This article argues that if panpsychism is true, then there are grounds for thinking that digitally-based artificial intelligence may be incapable of having coherent macrophenomenal conscious experiences. Section 1 briefly surveys research indicating that neural function and phenomenal consciousness may be both analog in nature. We show that physical and phenomenal magnitudes—such as rates of neural firing and the phenomenally experienced loudness of sounds—appear to covary monotonically with the physical stimuli they represent, forming the basis for an analog relationship between (...) the three. Section 2 then argues that if this is true and micropsychism—the panpsychist view that phenomenal consciousness or its precursors exist at a microphysical level of reality—is also true, then human brains must somehow manipulate fundamental microphysical-phenomenal magnitudes in an analog manner that renders them phenomenally coherent at a macro level. However, Sect. 3 argues that because digital computation abstracts away from microphysical-phenomenal magnitudes—representing cognitive functions non-monotonically in terms of digits—digital computation may be inherently incapable of realizing coherent macroconscious experience. Thus, if panpsychism is true, digital AI may be incapable of achieving phenomenal coherence. Finally, Sect. 4 briefly examines our argument’s implications for Tononi’s Integrated Information Theory theory of consciousness, which we contend may need to be supplanted by a theory of macroconsciousness as analog microphysical-phenomenal information integration. (shrink)