Thomas Reid argues that both perception and memory involve a conception of an object and usually cause a corresponding belief. According to defenders of the constitutive interpretation, such as Rebecca Copenhaver, the belief is constitutive of acts of perception and memory. I instead argue for a causal interpretation: although in normal circumstances perceiving and remembering cause a corresponding belief, the belief is not constitutive of perception or memory. Copenhaver's strongest argument for the constitutive interpretation is that perception essentially represents objects (...) as present, while memory essentially represents objects as past; since such tense markers can only occur within the beliefs, the beliefs must be an essential aspect of perception and memory. I argue, in contrast, that temporal markers are contained in our conceptions of objects, so beliefs do not play an essential role in distinguishing between perception and memory. Such a reading presupposes a “thick” interpretation of what Reid means by a conception, according to which a Reidian conception is a mode of presentation of the object apprehended. (shrink)

This chapter has two main sections. In the first section I briefly sketch Immanuel Kant’s moral theory as laid out in his Groundwork of the Metaphysics of Morals (1785). I explain Kant’s claim that morality must be grounded on what he calls a categorical imperative and examine his three formulations of this categorical imperative. In the second section I explain the distinction between “deontological” and “teleological” ethical theories. Kantian ethics is often presented as the paradigm example of a deontological ethical (...) theory, but I question whether Kant’s ethics should be understood as purely deontological. (shrink)

Color-motion asynchrony (CMA) refers to an apparent lag of direction of motion when a dynamic stimulus changes both color and direction at the same time. The subjective order of simultaneous events, however, is not only perceptual but also subject to illusions during voluntary actions. Self-initiated actions, for example, seem to precede their sensory outcomes following an adaptation to a delay between the action and the sensory feedback. Here, we demonstrate that the extent of the apparent asynchrony can be substantially reduced (...) when direction change is induced by a voluntary key press following a delay adaptation regime. We also show that the reduced color-motion asynchrony effect size following a motor-sensory recalibration is not a result of a change in the onset of perceived direction change relative to that of the color. This is particularly important as it implies, for the first time in the literature, that voluntary action is not only important in forming action-sensory outcome associations but may also act as a binding factor between the two perceptual features of a sensory event. (shrink)

Event concepts are unstructured atomic concepts that apply to event types. A paradigm example of such an event type would be that of diaper changing, and so a putative example of an atomic event concept would be DADDY'S-CHANGING-MY-DIAPER.1 I will defend two claims about such concepts. First, the conceptual claim that it is in principle possible to possess a concept such as DADDY'S-CHANGING-MY-DIAPER without possessing the concept DIAPER. Second, the empirical claim that we actually possess such concepts and that they (...) play an important role in our cognitive lives. The argument for the empirical claim has the form of an inference to the best explanation and is aimed at those who are already willing to attribute concepts and beliefs to infants and nonhuman animals. Many animals and prelinguistic infants seem capable of re-identifying event-types in the world, and they seem to store information about things happening at particular times and places. My account offers a plausible model of how such organisms are able to do this without attributing linguistically structured mental states to them. And although language allows adults to form linguistically structured mental representations of the world, there is no good reason to think that such structured representations necessarily replace the unstructured ones. There is also no good reason for a philosopher who is willing to explain the behavior of an organism by appealing to atomic concepts of individuals or kinds to not use a similar form of explanation when explaining the organism's capacity to recognize events. -/- We can form empirical concepts of individuals, kinds, properties, event-types, and states of affairs, among other things, and I assume that such concepts function like what François Recanati calls ‘mental files’ or what Ruth Millikan calls ‘substance concepts’ (Recanati 2012; Millikan 1999, 2000, 2017). To possess such a concept one must have a reliable capacity to re-identify the object in question, but this capacity of re-identification does not fix the reference of the concept. Such concepts allow us to collect and utilize useful information about things that we re-encounter in our environment. We can distinguish between a perception-action system and a perception-belief system, and I will argue that empirical concepts, including atomic event concepts, can play a role in both systems. The perception-action system involves the application of concepts in the service of (often skilled) action. We can think of the concept as a mental file containing motor-plans that can be activated once the individual recognizes that they are in a certain situation. In this way, recognizing something (whether an object or an event) as a token of a type, plays a role in guiding immediate action. The perception-belief system, in contrast, allows for the formation of beliefs that can play a role in deliberation and planning and in the formation of expectations. I distinguish between two particular types of belief which I call where-beliefs and when-beliefs, and I argue that we can model the formation of such perceptual beliefs in nonlinguistic animals and human infants in terms of the formation of a link between an empirical concept and a position on a cognitive map. According to the account offered, seemingly complex beliefs, such as a baby's belief that Daddy changed her diaper in the kitchen earlier, will not be linguistically structured. If we think that prelinguistic infants possess such concepts and are able to form such beliefs, it is likely that adults do too. The ability to form such beliefs does not require the capacity for public language, and we can model them in nonlinguistic terms; thus, we have no good reason to think of such beliefs as propositional attitudes. Of course, we can use sentences to refer to such beliefs, and thus it is possible to think of such beliefs as somehow relations to propositions. But it is not clear to me what is gained by this as we have a perfectly good way to think about the structure of such beliefs that does not involve any appeal to language. (shrink)

I discuss the role of translatability in philosophical justification. I begin by discussing and defending Thomas Reid’s account of the role that facts about comparative linguistics can play in philosophical justification. Reid believes that common sense offers a reliable but defeasible form of justification. We cannot know by introspection, however, which of our judgments belong to common sense. Judgments of common sense are universal, and so he argues that the strongest evidence that a judgment is a part of common sense (...) is that it is to be found in all languages. For Reid, then, evidence that a certain distinction is to be found in all languages is evidence that the distinction is part of common sense rather than being a common local prejudice. From such a perspective, empirical work in comparative linguistics can play a defeasible justificatory role in philosophical arguments. I contrast Reid’s position with the more radical position of defenders of the Natural Semantic Metalanguage approach, such as Anna Wierzbicka, who argues that only judgments that are translatable into all natural languages are justifiable. I show how such a position is rooted in an implausible view, although one common among cognitive scientists and linguistics, about the nature of concepts, which does not allow for novel concepts. (shrink)

On the surface Kant himself seems quite clear about who is deserving of respect: The morally relevant others are all “rational, free beings” or all “human beings.” It is clear, however, that Kant does not want to identify “human beings” in this sense with members of a particular biological species, for he is explicitly open to the idea that there might be non-biologically human rational beings. Thus, for example he is explicitly open to the possibility of extraterrestrial rational beings, who (...) would not be members of the same biological species as us, but who would, presumably be worthy of respect. And it would seem possible that there are members of our biological species who are not “human” in the morally relevant sense. Given these facts, a Kantian needs to give some account of how we are to recognize who or what counts as “human” in the morally relevant sense. I argue that to be “human” in the morally relevant sense is to have the capacity for morality, and that this involves: (a) the capacity to recognize others as ends rather than merely as means and (b) the capacity to enter into relations of ethical community with us. I defend a position I name moral reliabilism. According to this position: (a) We have a quasi-perceptual capacity to directly ascribe moral status to various bits of the world around us. I will argue that this capacity is best thought of in Gibsonian terms as a capacity to pick up on certain types of social affordances; morally relevant others have the capacity to engage in ethical interaction with us, and recognizing the humanity of others involves picking up on this capacity. Those beings who are “human” in the morally relevant sense, then, afford interaction based on mutual respect. (b) We should assume as a postulate of practical reason that this capacity is reliable (although fallible). (shrink)

The central idea behind this paper is the claim that Kant's moral idea of a realm of ends is modeled on the category of community examined in his theoretical works, and that understanding Kant's account of the category of community helps us understand certain features of the idea of a realm of ends, and in particular the fact that a member of a realm of ends must be an autonomous agent. For Kant the idea of a community is essentially the (...) idea of a multitude of individuals in interaction and in this paper I will attempt to show why Kant believes that only autonomous individuals can interact. (shrink)

A fully cross-referenced A-Z reference guide to the ideas and work of Immanuel Kant - one of the most important figures in Western Philosophy.

An interdisciplanary collection of essays focused on Kant's work on the concept of community.

Many readers of Kant’s ethical writings take him to be primarily concerned with offering guidelines for action. At the least, they write about Kant as if this were the purpose of his ethical writings. For example, Christine Korsgaard, in her influential article Kant’s Analysis of Obligation: The Argument of Groundwork I, writes that, ‘‘the argument of Groundwork I is an attempt to give what I call a ‘motivational analysis’ of the concept of a right action, in order to discover what (...) that concept applies to, that is, which actions are right.’’ Similar comments are not hard to find in the secondary literature. This, however, is a fundamentally misguided way of reading Kant, since he repeatedly asserts that we do not need to do moral philosophy in order to discover which actions are right. We already know how to behave morally and do not need philosophers to tell us this. ‘‘Common human reason,’’ Kant argues, ‘‘knows very well how to distinguish in every case that comes up what is good and what is evil, what is in conformity to duty or contrary to duty.’’ Because people with pre-philosophical understanding know how to act morally, the purpose of moral philosophy cannot be to provide us with a set of rules for correct behavior. If we take Kant’s claims about common human reason seriously, then his aim in the Groundwork of the Metaphysics of Morals cannot be to discover which actions are right. (shrink)

Kant and Leibniz are interested in explaining how a number of individuals can come together and form a single unified composite substance. Leibniz does not have a convincing account of how this is possible. In his pre-critical writings and in his later metaphysics lectures, Kant is committed to the claim that the idea of a world is the idea of a real whole, and hence is the idea of a composite substance. This metaphysical idea is taken over into his ethical (...) writings and becomes the idea of a realm of ends. I explain why a realm of ends, should be thought of as both a unum per se and as a real whole. A realm of ends is a whole of individuals unified by laws they have given themselves, that is, it is a community of autonomous individuals. Only such a community can be thought of as a composite individual. Such a whole will be real rather than ideal because the source of the unity of the whole is intrinsic to the whole, for what gives unity to the realm are laws and the sources of the laws are the individual members of the whole. It will be a unum per se because both the laws and the individuals constituting the realm are incomplete without one another. If this reading is correct, this requires a fundamental reevaluation of Kant’s notion of autonomy. To be autonomous is not, primarily, to be understood in terms of ruling oneself, but instead must be thought of primarily in terms of being a generative source of laws for an ideal community. (shrink)

The ideal of the United Nations was first put forward by Immanuel Kant in his 1795 essay Perpetual Peace. Kant, in the tradition of Locke and Rousseau is a liberal who believes that relations between individuals can either be based upon law and consent or upon force and violence. One way that such the ideal of world peace could be achieved would be through the creation of a single world state, of which every human being was a citizen. Such an (...) ideal was advocated by a number of eighteenth century liberals. Kant, however, rejects this ideal and instead argues that the universal rule of law can be achieved through the establishment a federation of independent states. I examine the relevance of Kant’s arguments today, focusing on two questions: Firstly, as advocates of the rule of law, why advocate a federation of independent nations rather than a single world state. Secondly, is this ideal realizable? Is Kant right to think that republics are natural and are likely to live peacefully with one another? Kant’s arguments on this issue have been taken up again in recent decades by defenders of the theory of the “democratic peace”, the theory that democracies are more likely to live at peace with one another. (shrink)

In this paper I focus on the work of Sayyid Qutb and in particular his book Milestones, which is often regarded as the Communist Manifesto of Islamic fundamentalism. This paper has four main sections. First I outline Qutb’s political position and in particular examine his advocacy of offensive jihad. In section two I argue that there are a number of tendencies that make his position potentially more liberal that it is often taken to be. I here argue that there are (...) at least six reasons why Qutb’s position is not intrinsically as anti-liberal as it might at first appear. First, many western liberals, influenced by the social contract tradition, regard the legitimacy of their societies as based on popular sovereignty. Qutb, however, regards a society based on popular sovereignty, where law emerges from the will of man rather than the will of God, as a form of tyranny, so it would seem that he is in principle opposed to Western liberal societies. It is not clear, however, that we, or Islamic fundamentalist, need to regard Western liberal societies as based on popular sovereignty, for it is always possible to interpret Western political institutions through the lens of natural law theory, which was one of the main sources of the liberal tradition. In this section I will compare Qutb’s political philosophy with that of Aquinas to illustrate this point and suggest the possibility of secularists and puritan Islamists being able to form an overlapping consensus on the legitimacy of liberal Western societies. Secondly, there is an analogue to the social contract in Qutb’s own position as he believes that legitimate authority requires the free submission of the governed. Thirdly, Qutb is in principle a fallibilist about human reason; this fallibilism extends even to our capacity to interpret divine revelation. Fourthly, Islamic universalism requires that Muslims regard enemies they might be fighting as potential converts. Fifthly, Qutb, like most Sunni fundamentalists, is an implacable enemy of theocracy. And finally, Qutb is a gradualist. In the third section I argue that the real danger for liberal societies from believers in a position like Qutb’s is sociological rather than intrinsic to the ideology – specifically, that there is a danger that such groups may develop in a ‘Leninist’ direction. In the final section I argue that one of the main reasons for this danger is the lack of a consensus in the Islamic world about what it is to be a good, or even a true, Muslim, and that the slow emergence of some sort of consensus will require a vigorous public debate amongst Muslims. Western liberals should welcome such debate rather than fearing such, and should do all they can to ensure that civil society, both in Western societies and in predominantly Islamic societies, is open to such debate. (shrink)

This paper examines Timothy Williamson's recent 'expertise defense' of armchair philosophy mounted by skeptical experimental philosophers. The skeptical experimental philosophers argue that the methodology of traditional 'armchair' philosophers rests up trusting their own intuitions about particular problem cases. Empirical studies suggest that these intuitions are not generally shared and that such intuitions are strongly influenced factors that are not truth conducive such as cultural background or whether or not the question is asked in a messy or tidy office. Williamson's response (...) is that the skeptical armchair philosophers trust the expertise of the social scientists, as they trust and use the methods of the social sciences to undermine trust in the judgment of armchair philosophers. Given this, the burden of proof is on the skeptical experimental philosopher to give us a reason to doubt the expertise of the armchair philosopher. I examine how our understanding of the history of philosophy is significant in this context. And suggest that prevalent false beliefs about the history of philosophy can lead to mistrust of the expertise of philosophers. (shrink)

In this paper I examine the genesis of Kant’s conception of a realm of ends, arguing that Kant first started to think of morality in terms of striving to be a member of a realm of ends, understood as an ideal community, in the early 1760s, and that he was influenced in this by his encounter with the Swedish mystic Emanuel Swedenborg. In 1766 Kant published Dreams of a Spirit Seer, a commentary on Swedenborg’s magnum opus, Heavenly Secrets. Most commentators (...) take Kant’s attitude towards Swedenborg to have been entirely negative, and argue that, at the most, Kant’s encounter with him had a purely negative impact on Kant’s development, inducing him to reject certain of his early metaphysical positions. I argue, in contrast, that Swedenborg had a positive influence on Kant’s development, particularly on his ethics, for Kant’s conception of a realm of ends is modeled on Swedenborg’s conception of heaven as a community of spirits governed by moral laws. (shrink)

Kantian ethics today is dominated followers of Rawls, many of them his former students. Following Rawls they interpret Kant as a moral constructivist who defines the good in terms of the reasonable. Such readings give priority to the first formulation of the categorical imperative and argue that the other two formulations are (ontologically or definitionally) dependent upon it. In contrast the aim of my paper will be to show that Kant should be interpreted firstly as a moral idealist and secondly (...) as, it least in a certain sense a particularist who takes morality to involve the exercise of recognitional capacities rather than following principles or rules. In claiming that Kant is a moral idealist we won’t mean to imply that he is an anti-realist, indeed we believe that he is a realist. Instead, by ‘moral idealism’ it is meant the position that maintains that to be moral is to instantiate an ideal. And so understood moral idealism can be seen as offering an alternative to both constructivism and utilitarianism. (shrink)

There are at least five ‘core’ notions of community found in Kant's works: 1. The scientific notion of interaction. This concept is introduced in the Third Analogy and developed in the Metaphysical Foundations of Natural Science. 2. A metaphysical idea. The idea of a world of individuals (monads) in interaction. This idea was developed in Kant’s precritical period and can be found in his metaphysics lectures. 3. A moral ideal. The idea of a realm of ends. 4. A political ideal. (...) The idea of a juridical community (or community of communities) governed by juridical laws. 5. A theological ideal. What Kant calls ‘the kingdom of heaven’, and which can be thought of as a community of holy beings, or angels. In this paper I focus on the relationship between the first, second and fourth of these notions. My argument is that Kant’s notion of a juridical community governed by juridical laws is modelled on the metaphysical idea of the world. This metaphysical idea of a world is, in turn, modelled on the category of community introduced in the first Critique and developed in his logic lectures. (shrink)

This thesis examines the theoretical foundations of Kant's moral philosophy. I argue that Kant's moral ideal of a kingdom of ends is to be identified with the theoretical idea of a community, and that this idea can be traced back to the category of community introduced in his table of categories. In particular I argue that, for the mature Kant, the only application of the theoretical idea of community is the moral idea of a kingdom of ends, the only way (...) we can conceive of a kingdom of ends is as a political community governed by juridical laws, and the only way we can conceive of a member of a community is as an autonomous agent. To support my interpretation I show how an understanding of Kant's theoretical work on community and interaction helps us understand the motivation behind the theory of property Kant offers in the Metaphysics of Morals. In addition, I trace the development of Kant's ethics back to his reading of Swedenborg in the early 1760s. (shrink)

Kant and the Concept of Community, edited by Charlton Payne and Lucas Thorpe, gathers together some of the best known figures in contemporary Kant scholarship. This fine collection traces Kant’s concept of community from its Precritical roots to its role in The Critique of Pure Reason, before going on to investigate the subsequent transformations it would undergo in Kant’s later works on ethics, religion, history, politics, and aesthetics. With very few exceptions, all of the essays in this collection (...) are interesting and informative, with signature pieces by Béatrice Longuenesse, Paul Guyer, Allen Wood, Onora O’Neill, and Susan Shell. This is a highly recommended collection suitable for advanced undergraduates, graduate students, and professionals. (shrink)

Sets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naïve and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the graph (...) conception. In addition, he presents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics. (shrink)

Translation of passages of Aristotle's De Anima into Portuguese. The passages are these: I.1, I.4 (the 'Rylean passage'); II.1-6; III.1-8. The translation is preliminary.

Translation of Aristotle's Posterior Analytics I into Portuguese, with a few notes, experimental glossary and introduction. The translation, which was made at 2003/4, was preliminary and its publication was intended to provide a didactic tool for courses as well as a provisional resource in research seminars. It needs some revision. I am currently working (slowly...) on the revision of the translation and a new revised one will surely appear at some point.

Crispin Wright maintains that the architecture of perceptual justification is such that we can acquire justification for our perceptual beliefs only if we have antecedent justification for ruling out any sceptical alternative. Wright contends that this principle doesn’t elicit scepticism, for we are non-evidentially entitled to accept the negation of any sceptical alternative. Sebastiano Moruzzi has challenged Wright’s contention by arguing that since our non-evidential entitlements don’t remove the epistemic risk of our perceptual beliefs, they don’t actually enable us to (...) acquire justification for these beliefs. In this paper I show that Wright’s responses to Moruzzi are ineffective and that Moruzzi’s argument is validated by probabilistic reasoning. I also suggest that Wright cannot answer Moruzzi’s challenge without weakening the support available for his conception of the architecture of perceptual justification. (shrink)

In Posterior Analytics 71b9 12, we find Aristotle’s definition of scientific knowledge. The definiens is taken to have only two informative parts: scientific knowledge must be knowledge of the cause and its object must be necessary. However, there is also a contrast between the definiendum and a sophistic way of knowing, which is marked by the expression “kata sumbebekos”. Not much attention has been paid to this contrast. In this paper, I discuss Aristotle’s definition paying due attention to this contrast (...) and to the way it interacts with the two conditions presented in the definiens. I claim that the “necessity” condition ammounts to explanatory appropriateness of the cause. (shrink)

In this paper, we develop an impure somatic theory of emotion, according to which emotions are constituted by the integration of bodily perceptions with representations of external objects, events, or states of affairs. We put forward our theory by contrasting it with Prinz's pure somatic theory, according to which emotions are entirely constituted by bodily perceptions. After illustrating Prinz's theory and discussing the evidence in its favor, we show that it is beset by serious problems—i.e., it gets the neural correlates (...) of emotion wrong, it isn't able to distinguish emotions from bodily perceptions that aren't emotions, it cannot account for emotions being directed towards particular objects, and it mischaracterizes emotion phenomenology. We argue that our theory accounts for the empirical evidence considered by Prinz and solves the problems faced by his theory. In particular, we maintain that our theory gives a unified and principled account of the relation between emotions and bodily perceptions, the intentionality of emotions, and emotion phenomenology. (shrink)

I discuss what Aristotle means when he say that scientific demonstration must proceed from necessary principles. I argue that, for Aristotle, scientific demonstration should not be reduced to sound deduction with necessary premises. Scientific demonstration ultimately depends on the fully appropriate explanatory factor for a given explanandum. This explanatory factor is what makes the explanandum what it is. Consequently, this factor is also unique. When Aristotle says that demonstration must proceed from necessary principles, he means that each demonstration requires the (...) principle that is the necessary one for the fully appropriate explanation of its explanandum. This picture also provides a key to understand Aristotle's thesis that scientific explanation depends on essences: it is the essence of the attribute to be explained that should be stated as the fully appropriate explanatory factor. (shrink)

Translation of Aristotle's Physics I-II into Portuguese, with commentaries. Tradução para o português dos livros I e II da Física de Aristóteles, com comentários.

Experiences like pains, pleasures, and emotions have affective phenomenal character: they feel pleasant or unpleasant. Imperativism proposes to explain affective phenomenal character by appeal to imperative content, a kind of intentional content that directs rather than describes. We argue that imperativism is on the right track, but has been developed in the wrong way. There are two varieties of imperativism on the market: first-order and higher-order. We show that neither is successful, and offer in their place a new theory: reflexive (...) imperativism. Our proposal is that an experience P feels pleasant in virtue of being constituted by a Command with reflexive imperative content, while an experience U feels unpleasant in virtue of being constituted by a Command with reflexive imperative content : More of P!Less of U! If you need a slogan: experiences have affective phenomenal character in virtue of commanding us Get more of me! Get less of me! (shrink)

I review recent work on Phenomenal Conservatism, the position introduced by Michael Huemer according to which if it seems that P to a subject S, in the absence of defeaters S has thereby some degree of justification for believing P.

Aristotle contrasts episteme and doxa through the key notions of universal and necessary. These notions have played a central role in Aristotle’s characterization of scientific knowledge in the previous chapters of APo. They are not spelled out in APo I.33, but work as a sort of reminder that packs an adequate characterization of scientific knowledge and thereby gives a highly specified context for Aristotle’s contrast between episteme and doxa. I will try to show that this context introduces a contrast in (...) terms of explanatory claims: on the one hand, episteme covers those claims which capture explanatory connections that are universal and necessary and thereby deliver scientific understanding; on the other hand, doxa covers the explanatory attempts that fail at doing so. (shrink)

I examine Aristotle’s definition of scientific knowledge in Posterior Analytics 71b 9-12 and try to understand how it relates to the sophistical way of knowing and to "kata sumbebekos knowledge". I claim that scientific knowledge of p requires knowing p by its appropriate cause, and that this appropriate cause is a universal (katholou) in the restricted sense Aristotle proposes in 73b 26-27 ff., i.e., an attribute coextensive with the subject (an extensional feature) and predicated of the subject in itself (an (...) intensional feature). Kata sumbebekos knowledge, on the other hand, can occur even when the predicate of a conclusion is coextensive with its subject and is proved by a convertible meson which is not the most appropriate from an explanatory standpoint. (shrink)

Analyzing geometric properties of high-dimensional loss functions, such as local curvature and the existence of other optima around a certain point in loss space, can help provide a better understanding of the interplay between neural network structure, implementation attributes, and learning performance. In this work, we combine concepts from high-dimensional probability and differential geometry to study how curvature properties in lower-dimensional loss representations depend on those in the original loss space. We show that saddle points in the original space are (...) rarely correctly identified as such in expected lower-dimensional representations if random projections are used. The principal curvature in the expected lower-dimensional representation is proportional to the mean curvature in the original loss space. Hence, the mean curvature in the original loss space determines if saddle points appear, on average, as either minima, maxima, or almost flat regions. We use the connection between expected curvature in random projections and mean curvature in the original space (i.e., the normalized Hessian trace) to compute Hutchinson-type trace estimates without calculating Hessian-vector products as in the original Hutchinson method. Because random projections are not suitable to correctly identify saddle information, we propose to study projections along dominant Hessian directions that are associated with the largest and smallest principal curvatures. We connect our findings to the ongoing debate on loss landscape flatness and generalizability. Finally, for different common image classifiers and a function approximator, we show and compare random and Hessian projections of loss landscapes with up to about 7×10^6 parameters. (shrink)

I discuss the exact meaning of the thesis according to which the object of scientific knowledge is necessary. The thesis is expressed by Aristotle in the Posterior Analytics, in his definition of scientific knowledge. The traditional interpretation understands this definition as depending on two parallel and independent requirements, the causality requirement and the necessity requirement. Against this interpretation, I try to show, through the examination of several passages that refer to the definition of scientific knowledge, that the necessity requirement specifies (...) more exactly the causality requirement: what cannot be otherwise is the explanatory relation between the explanandum and the cause by which it is what it is. (shrink)

I focus on a key argument for global external world scepticism resting on the underdetermination thesis: the argument according to which we cannot know any proposition about our physical environment because sense evidence for it equally justifies some sceptical alternative (e.g. the Cartesian demon conjecture). I contend that the underdetermination argument can go through only if the controversial thesis that conceivability is per se a source of evidence for metaphysical possibility is true. I also suggest a reason to doubt that (...) conceivability is per se a source of evidence for metaphysical possibility, and thus to doubt the underdetermination argument. (shrink)

This book uses mathematical models of language to explain why there are certain gaps in language: things that we might expect to be able to say but can't. For instance, why can we say I ran for five minutes but not *I ran to the store for five minutes? Why is five pounds of books acceptable, but *five pounds of book not acceptable? What prevents us from saying *sixty degrees of water to express the temperature of the water in a (...) swimming pool when sixty inches of water can express its depth? And why can we not say *all the ants in my kitchen are numerous? The constraints on these constructions involve concepts that are generally studied separately: aspect, plural and mass reference, measurement, and distributivity. In this book, Lucas Champollion provides a unified perspective on these domains, connects them formally within the framework of algebraic semantics and mereology, and uses this connection to transfer insights across unrelated bodies of literature and formulate a single constraint that explains each of the judgments above. (shrink)