Die Frage nach der Legitimität staatlicher Strafe ist Gegenstand einer anhaltenden und bisweilen ausufernden Diskussion, die inzwischen eine kaum noch überschaubare Fülle von Texten im rechts- und moralphilosophischen, staatstheoretischen und strafrechtlichen Schrifttum hervorgebracht hat. Mit Benthams utilitaristischem Prinzip des größten Glücks der größten Zahl und des im Retributivismus entscheidenden intrinsischen Unwertes der Tat als Anknüpfungspunkt der Strafe sowie dessen prominentesten Vertreter Kant werden die verschiedenen Strafkonzeptionen vorgestellt - einschließlich jenen, in denen beide Elemente miteinander verknüpft sind - wie etwa im (...) Strafziel der Resozialisierung. Darüber hinaus werden die unterschiedlichen staatstheoretischen Modelle, die dem utilitaristischen und retributivistischen Ansatz entsprechen im einzelnen entfaltet. Die Anwort auf die Frage nach der Vereinigung der Zweckbestimmungen staatlichen Strafens mit den fundamentalen Vorstellungen über Freiheit, Verantwortlichkeit, Schuldfähigkeit und damit Personalität, wie sie innerhalb des gedanklichen Horizontes einer staatlichen Gemeinschaft konsensfähig sind, bleibt jedoch zwangsläufig offen. (shrink)

Quick, accessible, compact guide to understanding key political concepts. Contents include: Liberty, Justice, Equality, Human rights, Social contract, Democracy, Monarchy, Anarchism, Capitalism, Socialism, Nationalism and Globalisation.

This article argues that existing approaches to programming ethical AI fail to resolve a serious moral-semantic trilemma, generating interpretations of ethical requirements that are either too semantically strict, too semantically flexible, or overly unpredictable. This paper then illustrates the trilemma utilizing a recently proposed ‘general ethical dilemma analyzer,’ GenEth. Finally, it uses empirical evidence to argue that human beings resolve the semantic trilemma using general cognitive and motivational processes involving ‘mental time-travel,’ whereby we simulate different possible pasts and futures. I (...) demonstrate how mental time-travel psychology leads us to resolve the semantic trilemma through a six-step process of interpersonal negotiation and renegotiation, and then conclude by showing how comparative advantages in processing power would plausibly cause AI to use similar processes to solve the semantic trilemma more reliably than we do, leading AI to make better moral-semantic choices than humans do by our very own lights. (shrink)

Many of Margaret Cavendish’s criticisms of Thomas Hobbes in the Philosophical Letters (1664) relate to the disorder and damage that she holds would result if Hobbesian pressure were the cause of visual perception. In this paper, I argue that her “two men” thought experiment in Letter IV is aimed at a different goal: to show the explanatory potency of her account. First, I connect Cavendish’s view of visual perception as “patterning” to the “two men” thought experiment in Letter IV. Second, (...) I provide a potential reply on Hobbes’s behalf that appeals to physiological differences between perceivers’ sense organs, drawing upon Hobbes’s optics in De homine. Third, I argue that such a reply would misunderstand Cavendish’s objective of showing the limited explanatory resources available in understanding visual perception as pressing when compared to her view of visual perception as patterning. (shrink)

In this article I have two primary goals. First, I present two recent views on the distinction between knowledge-that and knowledge-how (Stanley and Williamson, The Journal of Philosophy 98(8):411–444, 2001; Hetherington, Epistemology futures, 2006). I contend that neither of these provides conclusive arguments against the distinction. Second, I discuss studies from neuroscience and experimental psychology that relate to this distinction. Having examined these studies, I then defend a third view that explains certain relevant data from these studies by positing the (...) double dissociation of knowledge-that and knowledge-how and that is also able to do explanatory work elsewhere. (shrink)

The dominant theory of the evolution of moral cognition across a variety of fields is that moral cognition is a biological adaptation to foster social cooperation. This chapter argues, to the contrary, that moral cognition is likely an evolutionary exaptation: a form of cognition where neurobiological capacities selected for in our evolutionary history for a variety of different reasons—many unrelated to social cooperation—were put to a new, prosocial use after the fact through individual rationality, learning, and the development and transmission (...) of social norms. This chapter begins with a brief overview of the emerging behavioral neuroscience of moral cognition. It then outlines a novel theory of moral cognition that I have previously argued explains these findings better than alternatives. Finally, it shows how the evidence for this theory of moral cognition and human evolutionary history together suggest that moral cognition is likely not a biological adaptation. Instead, like reading sheet music or riding a bicycle, moral cognition is something that individuals learn to do—in this case, in response to sociocultural norms created in our ancestral history and passed down through the ages to enable cooperative living. (shrink)

Kant’s revolutionary new approach to philosophy was accompanied by the introduction of a largely novel terminology. With the Kant-Lexikon, a lexical reference gives the modern reader access to his work on the basis of present-day editions and takes into account 20th century and contemporary research and advances in lexicology. The Kant-Lexikon includes 2395 entries authored by 221 scholars.

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)

Marcus Giaquinto presents an investigation into the different kinds of visual thinking involved in mathematical thought, drawing on work in cognitive psychology, philosophy, and mathematics. He argues that mental images and physical diagrams are rarely just superfluous aids: they are often a means of discovery, understanding, and even proof.

In the de Officiis we have, save for the latter Philippics, the great orator's last contribution to literature. The last, sad, troubled years of his busy life could not be given to his profession; and he turned his never-resting thoughts to the second love of his student days and made Greek philosophy a possibility for Roman readers. The senate had been abolished; the courts had been closed. His occupation was gone; but Cicero could not surrender himself to idleness. In those (...) days of distraction (46-43 b.c.) he produced for publication almost as much as in all his years of active life.The liberators had been able to remove the tyrant, but they could not restore the republic. Cicero's own life was in danger from the fury of mad Antony and he left Rome about the end of March, 44 b.c. He dared not even stop permanently in any one of his various country estates, but, wretched, wandered from one of his villas to another nearly all the summer and autumn through. He would not suffer himself to become a prey to his overwhelming sorrow at the death of the republic and the final crushing of the hopes that had risen with Caesar's downfall, but worked at the highest tension on his philosophical studies. (shrink)

Peer review is often taken to be the main form of quality control on academic research. Usually journals carry this out. However, parts of maths and physics appear to have a parallel, crowd-sourced model of peer review, where papers are posted on the arXiv to be publicly discussed. In this paper we argue that crowd-sourced peer review is likely to do better than journal-solicited peer review at sorting papers by quality. Our argument rests on two key claims. First, crowd-sourced peer (...) review will lead on average to more reviewers per paper than journal-solicited peer review. Second, due to the wisdom of the crowds, more reviewers will tend to make better judgments than fewer. We make the second claim precise by looking at the Condorcet Jury Theorem as well as two related jury theorems developed specifically to apply to peer review. (shrink)

This book treats modal logic as a theory, with several subtheories, such as completeness theory, correspondence theory, duality theory and transfer theory and is intended as a course in modal logic for students who have had prior contact with modal logic and who wish to study it more deeply. It presupposes training in mathematical or logic. Very little specific knowledge is presupposed, most results which are needed are proved in this book.

This article argues that diverse theorists have reasons to theorize about fairness in nonideal conditions, including theorists who reject fairness in ideal theory. It then develops a new all-purpose model of ‘nonideal fairness.’ §1 argues that fairness is central to nonideal theory across diverse ideological and methodological frameworks. §2 then argues that ‘nonideal fairness’ is best modeled by a nonideal original position adaptable to different nonideal conditions and background normative frameworks (including anti-Rawlsian ones). §3 then argues that the parties to (...) the model have grounds to seek a variety of remedial social, legal, cultural, and economic ‘nonideal primary goods’ for combating injustice, as well as grounds to distribute these goods in an equitable and inclusive manner. Finally, I illustrate how the model indexes the nonideal primary goods it justifies to different nonideal contexts and background normative frameworks, illustrating why diverse theorists should find the model and its output principles attractive. (shrink)

Presenting the first step-by-step commentary on Husserl’s Ideas I, Marcus Brainard’s Belief and Its Neutralization provides an introduction not only to this central work, but also to the whole of transcendental phenomenology. Brainard offers a clear and lively account of each key element in Ideas I, along with a novel reading of Husserl, one which may well cause scholars to reconsider many long-standing views on his thought, especially on the role of belief, the effect and scope of the epoché, (...) and the significance of the universal neutrality modification. (shrink)

Following in a psychological and musicological tradition beginning with Leonard Meyer, and continuing through David Huron, we present a functional, cognitive account of the phenomenon of expectation in music, grounded in computational, probabilistic modeling. We summarize a range of evidence for this approach, from psychology, neuroscience, musicology, linguistics, and creativity studies, and argue that simulating expectation is an important part of understanding a broad range of human faculties, in music and beyond.

In the Critique of Pure Reason, Kant famously criticizes traditional metaphysics and its proofs of immortality, free will and God's existence. What is often overlooked is that Kant also explains why rational beings must ask metaphysical questions about 'unconditioned' objects such as souls, uncaused causes or God, and why answers to these questions will appear rationally compelling to them. In this book, Marcus Willaschek reconstructs and defends Kant's account of the rational sources of metaphysics. After carefully explaining Kant's conceptions (...) of reason and metaphysics, he offers detailed interpretations of the relevant passages from the Critique of Pure Reason in which Kant explains why reason seeks 'the unconditioned'. Willaschek offers a novel interpretation of the Transcendental Dialectic, pointing up its 'positive' side, while at the same time it uncovers a highly original account of metaphysical thinking that will be relevant to contemporary philosophical debates. (shrink)

Marcus Aurelius' Meditations is a private notebook of philosophical reflections with universal significance. Drawing on Stoic philosophy, Marcus confronts challenges that affect us all in our struggle to live meaningful lives. This edition includes a selection of Marcus' correspondence with his tutor Fronto which complements the Meditations.

We argue that many intuitions do not have conscious propositional contents. In particular, many of the intuitions had in response to philosophical thought experiments, like Gettier cases, do not have such contents. They are more like hunches, urgings, murky feelings, and twinges. Our view thus goes against the received view of intuitions in philosophy, which we call Mainstream Propositionalism. Our positive view is that many thought-experimental intuitions are conscious, spontaneous, non-theoretical, non-propositional psychological states that often motivate belief revision, but they (...) require interpretation, in light of background beliefs, before a subject can form a propositional judgment as a consequence of them. We call our view Interpretationalism. We argue (i) that Interpretationalism avoids the problems that beset Mainstream Propositionalism and (ii) that our view meshes well with empirical results in contemporary cognitive science. (shrink)

Liberalism is often claimed to be at odds with feminism and critical race theory (CRT). This article argues, to the contrary, that Rawlsian liberalism supports the central commitments of both. Section 1 argues that Rawlsian liberalism supports intersectional feminism. Section 2 argues that the same is true of CRT. Section 3 then uses Young’s ‘Five Faces of Oppression’—a classic work widely utilized in feminism and CRT to understand and contest many varieties of oppression—to illustrate how Rawlsian liberalism supports diverse feminist (...) and CRT projects, and why it may be critical to achieve solidarity between feminism, CRT, and Rawlsian liberalism. Finally, Section 4 responds to five objections. (shrink)

Margaret Cavendish is widely known as a materialist. However, since Cavendishian matter is always in motion, “matter” and “motion” are equally important foundational concepts for her natural philosophy. In Philosophical Letters (1664), she takes to task her materialist rival Thomas Hobbes by assaulting his account of accidents in general and his concept of “rest” in particular. In this article, I argue that Cavendish defends her continuous-motion view in two ways: first, she claims that her account avoids seeing accidents as capable (...) of generation and annihilation, which she argues is inconceivable; and second, she contends that according to Hobbes’s own view “rest” is an absurd conception since it cannot be drawn from experience. Beyond its function as a defense, I claim that Cavendish’s focused criticism of “rest” shows that she is a perceptive reader of Hobbes’s natural philosophy, insofar as her criticisms undercut the two a priori principles of Hobbesian physics. Finally, I show how her views developed in more detail in Philosophical and Physical Opinions (1663) and Observations upon Experimental Philosophy ([1666] 2001) avoid the worries she raises for Hobbesian materialism. (shrink)

Biometric facial recognition is an artificial intelligence technology involving the automated comparison of facial features, used by law enforcement to identify unknown suspects from photographs and closed circuit television. Its capability is expanding rapidly in association with artificial intelligence and has great potential to solve crime. However, it also carries significant privacy and other ethical implications that require law and regulation. This article examines the rise of biometric facial recognition, current applications and legal developments, and conducts an ethical analysis of (...) the issues that arise. Ethical principles are applied to mediate the potential conflicts in relation to this information technology that arise between security, on the one hand, and individual privacy and autonomy, and democratic accountability, on the other. These can be used to support appropriate law and regulation for the technology as it continues to develop. (shrink)

This paper investigates the relation of the Calculus of Individuals presented by Henry S. Leonard and Nelson Goodman in their joint paper, and an earlier version of it, the so-called Calculus of Singular Terms, introduced by Leonard in his Ph.D. dissertation thesis Singular Terms. The latter calculus is shown to be a proper subsystem of the former. Further, Leonard’s projected extension of his system is described, and the definition of an intensional part-relation in his system is proposed. The final section (...) discusses to what extend Goodman might have contributed to the formulation of the Calculus of Individuals. (shrink)

I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the ‘that’) with causal principles from geometry (the ‘why’). My argument shows (...) that Hobbesian natural philosophy relies upon suppositions that bodies plausibly behave according to these borrowed causal principles from geometry, acknowledging that bodies in the world may not actually behave this way. First, I consider Hobbes's relation to Aristotelian mixed mathematics and to Isaac Barrow's broadening of mixed mathematics in Mathematical Lectures (1683). I show that for Hobbes maker's knowledge from geometry provides the ‘why’ in mixed-mathematical explanations. Next, I examine two explanations from De corpore Part IV: (1) the explanation of sense in De corpore 25.1-2; and (2) the explanation of the swelling of parts of the body when they become warm in De corpore 27.3. In both explanations, I show Hobbes borrowing and citing geometrical principles and mixing these principles with appeals to experience. (shrink)

Several recent commentators argue that Thomas Hobbes’s account of the nature of science is conventionalist. Engaging in scientific practice on a conventionalist account is more a matter of making sure one connects one term to another properly rather than checking one’s claims, e.g., by experiment. In this paper, I argue that the conventionalist interpretation of Hobbesian science accords neither with Hobbes’s theoretical account in De corpore and Leviathan nor with Hobbes’s scientific practice in De homine and elsewhere. Closely tied to (...) the conventionalist interpretation is the deductivist interpretation, on which it is claimed that Hobbes believed sciences such as optics are deduced from geometry. I argue that Hobbesian science places simplest conceptions as the foundation for geometry and the sciences in which we use geometry, which provides strong evidence against both the conventionalist and deductivist interpretations. (shrink)

This paper demonstrates something that Kant notoriously claimed to be possible, but which Kant scholars today widely believe to be impossible: unification of all three formulations of the Categorical Imperative. Part 1 of this paper tells a broad-brush story of how I understand Kant’s theory of practical reason and morality, showing how the three formulations of the Categorical Imperative appear to be unified. Part 2 then provides clear textual support for each premise in the argument for my interpretation.

I claim that there is pro tanto moral reason for parents to not raise their child on a vegan diet because a vegan diet bears a risk of harm to both the physical and the social well-being of children. After giving the empirical evidence from nutrition science and sociology that supports this claim, I turn to the question of how vegan parents should take this moral reason into account. Since many different moral frameworks have been used to argue for veganism, (...) this is a complex question. I suggest that, on some of these moral frameworks, the moral reason that some parents have for not raising their child on a vegan diet on account of this risk is plausibly as strong as the reason they have for raising their child on a vegan diet. In other words, the moral reason I outline is weighty enough to justify some vegan parents in plausibly finding it permissible to not raise their child on a vegan diet. (shrink)

The nature of light is a focus of Thomas Hobbes’s natural philosophical project. Hobbes’s explanation of the light of lucid bodies differs across his works, from dilation and contraction in Elements of Law to simple circular motions in De corpore. However, Hobbes consistently explains perceived light by positing that bodily resistance generates the phantasm of light. In Letters I.XIX–XX of Philosophical Letters, fellow materialist Margaret Cavendish attacks the Hobbesian understanding of both lux and lumen by claiming that Hobbes has illicitly (...) made abstractions from matter. In this paper, I argue that Cavendish’s criticisms rely on an incorrect understanding of the nature of Hobbesian geometry and the role it plays in Hobbes’s natural philosophy. Rather than understanding geometry as wholly abstract, Hobbes attempts to ground geometry in different ways of considering bodies and their motions. Furthermore, Hobbes’s own criticisms of abstraction suggest that he would share many of the worries she raises but deny that he falls prey to them. (shrink)

Marcus Tullius Cicero (106 BC-43 BC) was a Roman statesman, lawyer, political theorist, philosopher, and Roman constitutionalist. He is widely considered one of Rome's greatest orators and prose stylists. He is generally perceived to be one of the most versatile minds of ancient Rome. He introduced the Romans to the chief schools of Greek philosophy and created a Latin philosophical vocabulary, distinguishing himself as a linguist, translator, and philosopher. An impressive orator and successful lawyer, he probably thought his political (...) career his most important achievement. Today, he is appreciated primarily for his humanism and philosophical and political writings. Although a great master of Latin rhetoric and composition, Cicero was not Roman in the traditional sense, and was quite self-conscious of this for his entire life. He was declared a "righteous pagan" by the early Catholic Church, and therefore many of his works were deemed worthy of preservation. Saint Augustine and others quoted liberally from his works On the Republic and On the Laws, and it is due to this that we are able to recreate much of the work from the surviving fragments. (shrink)

Marcus Giaquinto tells the compelling story of one of the great intellectual adventures of the modern era: the attempt to find firm foundations for mathematics. From the late nineteenth century to the present day, this project has stimulated some of the most original and influential work in logic and philosophy.

This paper examines Hobbes’s criticisms of Robert Boyle’s air-pump experiments in light of Hobbes’s account in _De Corpore_ and _De Homine_ of the relationship of natural philosophy to geometry. I argue that Hobbes’s criticisms rely upon his understanding of what counts as “true physics.” Instead of seeing Hobbes as defending natural philosophy as “a causal enterprise … [that] as such, secured total and irrevocable assent,” 1 I argue that, in his disagreement with Boyle, Hobbes relied upon his understanding of natural (...) philosophy as a mixed mathematical science. In a mixed mathematical science one can mix facts from experience with causal principles borrowed from geometry. Hobbes’s harsh criticisms of Boyle’s philosophy, especially in the _Dialogus Physicus, sive De natura aeris_, should thus be understood as Hobbes advancing his view of the proper relationship of natural philosophy to geometry in terms of mixing principles from geometry with facts from experience. Understood in this light, Hobbes need not be taken to reject or diminish the importance of experiment/experience; nor should Hobbes’s criticisms in _Dialogus Physicus_ be understood as rejecting experimenting as ignoble and not befitting a philosopher. Instead, Hobbes’s viewpoint is that experiment/experience must be understood within its proper place – it establishes the ‘that’ for a mixed mathematical science explanation. (shrink)

This paper introduces and evaluates two contemporary approaches of neo-logicism. Our aim is to highlight the differences between these two neo-logicist programmes and clarify what each projects attempts to achieve. To this end, we first introduce the programme of the Scottish school – as defended by Bob Hale and Crispin Wright1 which we believe to be a..

According to Ole Hjortland, Timothy Williamson, Graham Priest, and others, anti-exceptionalism about logic is the view that logic “isn’t special”, but is continuous with the sciences. Logic is revisable, and its truths are neither analytic nor a priori. And logical theories are revised on the same grounds as scientific theories are. What isn’t special, we argue, is anti-exceptionalism about logic. Anti-exceptionalists disagree with one another regarding what logic and, indeed, anti-exceptionalism are, and they are at odds with naturalist philosophers of (...) logic, who may have seemed like natural allies. Moreover, those internal battles concern well-trodden philosophical issues, and there is no hint as to how they are to be resolved on broadly scientific grounds. We close by looking at three of the founders of logic who may have seemed like obvious enemies of anti-exceptionalism—Aristotle, Frege, and Carnap—and conclude that none of their positions is clearly at odds with at least some of the main themes of anti-exceptionalism. We submit that, at least at present, anti-exceptionalism is too vague or underspecified to characterize a coherent conception of logic, one that stands opposed to more traditional approaches. (shrink)

This paper shows that several live philosophical and scientific hypotheses – including the holographic principle and multiverse theory in quantum physics, and eternalism and mind-body dualism in philosophy – jointly imply an audacious new theory of free will. This new theory, "Libertarian Compatibilism", holds that the physical world is an eternally existing array of two-dimensional information – a vast number of possible pasts, presents, and futures – and the mind a nonphysical entity or set of properties that "read" that physical (...) information off to subjective conscious awareness (in much the same way that a song written on an ordinary compact-disc is only played when read by an outside medium, i.e. a CD-player). According to this theory, every possible physical “timeline” in the multiverse may be fully physically deterministic or physically-causally closed but each person’s consciousness still entirely free to choose, ex nihilo, outside of the physical order, which physically-closed timeline is experienced by conscious observers. Although Libertarian Compatibilism is admittedly fantastic, I show that it not only follows from several live scientific and philosophical hypotheses, I also show that it (A) is a far more explanatorily powerful model of quantum mechanics than more traditional interpretations (e.g. the Copenhagen, Everett, and Bohmian interpretations), (B) makes determinate, testable empirical predictions in quantum theory, and finally, (C) predicts and explains the very existence of a number of philosophical debates and positions in the philosophy of mind, time, personal identity, and free will. First, I show that whereas traditional interpretations of quantum mechanics are all philosophically problematic and roughly as ontologically “extravagant” as Libertarian Compatibilism – in that they all posit “unseen” processes – Libertarian Compatibilism is nearly identical in structure to the only working simulation that human beings have ever constructed capable of reproducing (and so explaining) every general feature of quantum mechanics we perceive: namely, massive-multiplayer-online-roleplaying videogames (or MMORPGs). Although I am not the first to suggest that our world is akin to a computer simulation, I show that existing MMORPGs (online simulations we have already created) actually reproduce every general feature of quantum mechanics within their simulated-world reference-frames. Second, I show that existing MMORPGs also replicate (and so explain) many philosophical problems we face in the philosophy of mind, time, personal identity, and free will – all while conforming to the Libertarian Compatibilist model of reality. -/- I conclude, as such, that as fantastic and metaphysically extravagant as Libertarian Compatibilism may initially seem, it may well be true. It explains a number of features of our reality that no other physical or metaphysical theory does. (shrink)

Visual thinking -- visual imagination or perception of diagrams and symbol arrays, and mental operations on them -- is omnipresent in mathematics. Is this visual thinking merely a psychological aid, facilitating grasp of what is gathered by other means? Or does it also have epistemological functions, as a means of discovery, understanding, and even proof? By examining the many kinds of visual representation in mathematics and the diverse ways in which they are used, Marcus Giaquinto argues that visual thinking (...) in mathematics is rarely just a superfluous aid; it usually has epistemological value, often as a means of discovery. Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis. He shows how we can discern abstract general truths by means of specific images, how synthetic a priori knowledge is possible, and how visual means can help us grasp abstract structures. Visual Thinking in Mathematics reopens the investigation of earlier thinkers from Plato to Kant into the nature and epistemology of an individual's basic mathematical beliefs and abilities, in the new light shed by the maturing cognitive sciences. Clear and concise throughout, it will appeal to scholars and students of philosophy, mathematics, and psychology, as well as anyone with an interest in mathematical thinking. (shrink)

The status of the laws of nature in Hobbes’s Leviathan has been a continual point of disagreement among scholars. Many agree that since Hobbes claims that civil philosophy is a science, the answer lies in an understanding of the nature of Hobbesian science more generally. In this paper, I argue that Hobbes’s view of the construction of geometrical figures sheds light upon the status of the laws of nature. In short, I claim that the laws play the same role as (...) the component parts – what Hobbes calls the “cause” – of geometrical figures. To make this argument, I show that in both geometry and civil philosophy, Hobbes proceeds by a method of synthetic demonstration as follows: 1) offering a thought experiment by privation; 2) providing definitions by explication of “simple conceptions” within the thought experiment; and 3) formulating generative definitions by making use of those definitions by explication. In just the same way that Hobbes says that the geometer should “put together” the parts of a square to learn its cause, I argue that the laws of nature are the cause of peace. (shrink)

We give an overview of some remarkable connections between symmetric informationally complete measurements and algebraic number theory, in particular, a connection with Hilbert’s 12th problem. The paper is meant to be intelligible to a physicist who has no prior knowledge of either Galois theory or algebraic number theory.

A wide range of non-pharmaceutical interventions (NPIs) have been introduced to stop or slow down the COVID-19 pandemic. Examples include school closures, environmental cleaning and disinfection, mask mandates, restrictions on freedom of assembly and lockdowns. These NPIs depend on coercion for their effectiveness, either directly or indirectly. A widely held view is that coercive policies need to be publicly justified—justified to each citizen—to be legitimate. Standardly, this is thought to entail that there is a scientific consensus on the factual propositions (...) that are used to support the policies. In this paper, we argue that such a consensus has been lacking on the factual propositions justifying most NPIs. Consequently, they would on the standard view be illegitimate. This is regrettable since there are good reasons for granting the state the legitimate authority to enact NPIs under conditions of uncertainty. The upshot of our argument is that it is impossible to have both the standard interpretation of the permissibility of empirical claims in public justification and an effective pandemic response. We provide an alternative view that allows the state sufficient room for action while precluding the possibility of it acting without empirical support. (shrink)

Theorists have long debated whether John Rawls’ conception of justice as fairness can be extended to nonideal (i.e. unjust) social and political conditions, and if so, what the proper way of extending it is. This paper argues that in order to properly extend justice as fairness to nonideal conditions, Rawls’ most famous innovation – the original position – must be reconceived in the form of a “nonideal original position.” I begin by providing a new analysis of the ideal/nonideal theory distinction (...) within Rawls’ theoretical framework. I then systematically construct a nonideal original position, showing that although its parties must have Rawls’ principles of ideal justice and priority relations as background aims, the parties should be entirely free to weigh those aims against whatever burdens and benefits they might face under nonideal conditions. Next, I show that the parties ought to aim to secure for themselves a special class of nonideal primary goods: all-purpose goods similar to Rawls’ original primary goods, but which in this case are all-purpose goods individuals might use to (A) promote Rawlsian ideals under nonideal conditions, (B) weigh Rawls’ principles of ideal justice and priority relations against whatever burdens and benefits they might face under nonideal conditions, and (C) effectively pursue their most favored weighting thereof. I then defend a provisional list of nonideal primary goods which include opportunities to participate effectively in equitable and inclusive grassroots reform movements guided by a series of substantive aims. Finally, I briefly speculate on how the parties to the nonideal original position might deliberate to principles of nonideal justice for distributing nonideal primary goods, suggesting that those goods should be distributed in proportion to unjust disadvantage. (shrink)

In this paper we will study the properties of the least extension n(Λ) of a given intermediate logic Λ by a strong negation. It is shown that the mapping from Λ to n(Λ) is a homomorphism of complete lattices, preserving and reflecting finite model property, frame-completeness, interpolation and decidability. A general characterization of those constructive logics is given which are of the form n(Λ). This summarizes results that can be found already in [13, 14] and [4]. Furthermore, we determine the (...) structure of the lattice of extensions of n(LC). (shrink)

The theory of mind (ToM) deficit associated with autism spectrum disorder has been a central topic in the debate about the modularity of the mind. In a series of papers, Philip Gerrans and Valerie Stone argue that positing a ToM module does not best explain the deficits exhibited by individuals with autism (Gerrans 2002; Stone & Gerrans 2006a, 2006b; Gerrans & Stone 2008). In this paper, I first criticize Gerrans and Stone’s (2008) account. Second, I discuss various studies of individuals (...) with autism and argue that they are best explained by positing a higher-level, domain-specific ToM module. (shrink)

To what extent are authors morally culpable for harms caused by their published work? Can authors be culpable even if their ideas are misused, perhaps because they failed to take precautions to prevent harmful misinterpretations? Might authors be culpable even if they do take precautions—if, for example, they publish ideas that others can be reasonably expected to put to harmful uses, precautions notwithstanding? Although complete answers to these questions depend upon controversial views about the right to free speech, this paper (...) argues that five notions from philosophy of law and legal practice—liability, burden of proof, legal causation, mens rea, and reasoning by precedent—can be adapted to provide an attractive moral framework for determining whether an author’s work causes harm, whether and how culpable the author is for causing such harm, steps authors may take to immunize themselves from culpability, and how to responsibly develop new rules for publishing ethics. (shrink)

The paper argues that ‘All varieties of gratitude are only overall fitting when targeted towards agents,’ for instance that any variety of gratitude for the beautiful sunset is only overall fitting if a supernatural agent such as God exists. The first premise is that ‘Prepositional gratitude is overall fitting only when targeted towards agents.’ For this premise, intuitive judgments are offered. The second premise is that ‘Prepositional gratitude is the paradigmatic variety of gratitude.’ For this premise, an aspect of the (...) common consent of philosophers about gratitude is noted and the metaphysical basicness of prepositional gratitude is argued for. This gives the intermediate conclusion that ‘The paradigmatic variety of gratitude is overall fitting only when targeted towards agents.’ The fourth premise is that ‘If the paradigmatic variety of gratitude is overall fitting only when targeted towards agents, then all varieties of gratitude are overall fitting only when targeted towards agents.’ To supply the conditional of this premise, the Paradigmatic Fittingness Principle is offered, which states that ‘Paradigmatic emotions set the fittingness conditions for their non-paradigmatic varieties.’ This principle is argued for by noting that it vindicates some popular and plausible intuitive judgements and gives an error theory of why one might think that gratitude could be fittingly targeted towards non-agents, and by suggesting the absence of any other plausible source of fittingness conditions for non-paradigmatic emotions. (shrink)