While it seems to be evident that the vision of the eternal return of the same is the solution to the riddle mentioned in "On the vision and the riddle," exactly what constitutes the riddle is anything but clear. Li ke all good riddles the solution demands a paradigm shift. Nietzsche's riddle is solved by a radical rethinking of the concept of time, from a straight line to a circle. I give a detailed account of how Nietzsche's riddle is formulated (...) in such a way tha t the eternal return of the same is the only possible solution. (shrink)

Nietzsche announces his intentions to publish a “physiology of aesthetics”, namely a naturalistic explanation for how aesthetic judgements are grounded in the physiology of both the one experiencing the work, and the creator of it. But as well as the physiological reduction of aesthetic judgements, Nietzsche in many places across his oeuvre frames the apparatus of physiology, especially the prescriptive dimension of self-cultivation, in terms amenable to being treated as ‘aesthetic’. The first section will mount a (re-) defense of the (...) use of aestheticized language for discussing Nietzschean self-cultivation. The second section demonstrates an aesthetic evaluation of capacities that make possible the acquisition and removal of instinctual components, ultimately arguing for Nietzsche’s qualified indeterminism regarding the capacity for self-cultivation. The third section will assess the pres- ence of another aesthetic measure, this time in terms of envisaging one’s psycho-physiology by reference to an external spectacle. The final section discusses metaethical questions stemming from Nietzsche’s prescriptive language regarding the aestheticization of our physiology. (shrink)

Orthodox semantics for natural language modals give rise to two puzzles for their interactions with disjunction: Ross’s puzzle and the puzzle of free choice permission. It is widely assumed that each puzzle can be explained in terms of the licensing of ‘Diversity’ inferences: from the truth of a possibility or necessity modal with an embedded disjunction, hearers infer that each disjunct is compatible with the relevant set of worlds. I argue that Diversity inferences are too weak to explain the full (...) range of data. Instead, I argue, modals with embedded disjunctions license ‘Independence’ inferences: from the truth of a modal with an embedded disjunction, hearers infer that each disjunct is an independent alternative among the relevant set of worlds. I then develop a bilateral inquisitive semantics for modals that predicts the validity of these Independence inferences. My account vindicates common intuitions about both Ross’s puzzle and the puzzle of free choice permission, and explains the full range of data. (shrink)

Angell's logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC by Ferguson, and by a 16-valued matrix by Fine. We show that the former is the image of a surjective homomorphism from the latter, i.e., an epimorphic image. The epimorphism was found with the help of MUltlog, which also provides a tableau calculus for NC extended by quantifiers that generalize conjunction and disjunction.

This analysis shows Cantor's diagonal definition in his 1891 paper was not compatible with his horizontal enumeration of the infinite set M. The diagonal sequence was a counterfeit which he used to produce an apparent exclusion of a single sequence to prove the cardinality of M is greater than the cardinality of the set of integers N.

We provide a philosophical reconstruction and analysis of the debate on the scientific status of cosmic inflation that has played out in recent years. In a series of critical papers, Ijjas et al. have questioned the scientificality of the current views on cosmic inflation. Proponents of cosmic inflation have in turn defended the scientific credentials of their approach. We argue that, while this defense, narrowly construed, is successful against Ijjas et al., the latter's reasoning does point to a significant epistemic (...) issue that arises with respect to inflation. A broadening of the concept of theory assessment is needed to address that issue in an adequate way. (shrink)

So-called 'Frege cases' pose a challenge for anyone who would hope to treat the contents of beliefs (and similar mental states) as Russellian propositions: It is then impossible to explain people's behavior in Frege cases without invoking non-intentional features of their mental states, and doing that seems to undermine the intentionality of psychological explanation. In the present paper, I develop this sort of objection in what seems to me to be its strongest form, but then offer a response to it. (...) I grant that psychological explanation must invoke non-intentional features of mental states, but it is of crucial importance which such features must be referenced. -/- It emerges from a careful reading of Frege's own view that we need only invoke what I call 'formal' relations between mental states. I then claim that referencing such 'formal' relations within psychological explanation does not undermine its intentionality in the way that invoking, say, neurological features would. The central worry about this view is that either (a) 'formal' relations bring narrow content in through back door or (b) 'formal' relations end up doing all the explanatory work. Various forms of each worry are discussed. The crucial point, ultimately, is that the present strategy for responding to Frege cases is not available either to the 'psycho-Fregean', who would identify the content of a belief with its truth-value, nor even to someone who would identify the content of a belief with a set of possible worlds. It requires the sort of rich semantic structure that is distinctive of Russellian propositions. There is therefore no reason to suppose that the invocation of 'formal' relations threatens to deprive content of any work to do. (shrink)

Priest has provided a simple tableau calculus for Chellas's conditional logic Ck. We provide rules which, when added to Priest's system, result in tableau calculi for Chellas's CK and Lewis's VC. Completeness of these tableaux, however, relies on the cut rule.

This article reviews and criticizes Joseph Heath’s market failures approach (MFA) to business ethics. Our criticism is organized into three sections. First, we argue that, even under the ideal assumptions of perfect competition, when markets generate Pareto-efficient distributions, Heath’s approach does not rule out significant harms. Second, we show that, under nonideal conditions, the MFA is either too demanding, if efficiency is to be attained, or not sufficiently demanding, if the goal of Pareto efficiency is abandoned. Finally, we argue that (...) Heath’s appeal to regulations and specific moral requirements as a remedy for market failures is unlikely to safeguard efficiency and exposes a number of general worries regarding the moral force of the MFA. We end this article with a constructive suggestion on how to adjust the MFA to avoid these problems while preserving its contractualist and Paretian spirit. (shrink)

David Hilbert's finitistic standpoint is a conception of elementary number theory designed to answer the intuitionist doubts regarding the security and certainty of mathematics. Hilbert was unfortunately not exact in delineating what that viewpoint was, and Hilbert himself changed his usage of the term through the 1920s and 30s. The purpose of this paper is to outline what the main problems are in understanding Hilbert and Bernays on this issue, based on some publications by them which have so far received (...) little attention, and on a number of philosophical reconstructions of the viewpoint (in particular, by Hand, Kitcher, and Tait). (shrink)

Some years ago, Machery, Mallon, Nichols, and Stich reported the results of experiments that reveal, they claim, cross-cultural differences in speaker’s ‘intuitions’ about Kripke’s famous Gödel–Schmidt case. Several authors have suggested, however, that the question they asked their subjects is ambiguous between speaker’s reference and semantic reference. Machery and colleagues have since made a number of replies. It is argued here that these are ineffective. The larger lesson, however, concerns the role that first-order philosophy should, and more importantly should not, (...) play in the design of such experiments and in the evaluation of their results. (shrink)

This paper formalizes part of the cognitive architecture that Kant develops in the Critique of Pure Reason. The central Kantian notion that we formalize is the rule. As we interpret Kant, a rule is not a declarative conditional stating what would be true if such and such conditions hold. Rather, a Kantian rule is a general procedure, represented by a conditional imperative or permissive, indicating which acts must or may be performed, given certain acts that are already being performed. These (...) acts are not propositions; they do not have truth-values. Our formalization is related to the input/ output logics, a family of logics designed to capture relations between elements that need not have truth-values. In this paper, we introduce KL3 as a formalization of Kant’s conception of rules as conditional imperatives and permissives. We explain how it differs from standard input/output logics, geometric logic, and first-order logic, as well as how it translates natural language sentences not well captured by first-order logic. Finally, we show how the various distinctions in Kant’s much-maligned Table of Judgements emerge as the most natural way of dividing up the various types and sub-types of rule in KL3. Our analysis sheds new light on the way in which normative notions play a fundamental role in the conception of logic at the heart of Kant’s theoretical philosophy. (shrink)

Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial (...) successes, and generated important advances in logical theory and metatheory, both at the time and since. The article discusses the historical background and development of Hilbert’s program, its philosophical underpinnings and consequences, and its subsequent development and influences since the 1930s. (shrink)

The Dutch Book Argument for Probabilism assumes Ramsey's Thesis (RT), which purports to determine the prices an agent is rationally required to pay for a bet. Recently, a new objection to Ramsey's Thesis has emerged (Hedden 2013, Wronski & Godziszewski 2017, Wronski 2018)--I call this the Expected Utility Objection. According to this objection, it is Maximise Subjective Expected Utility (MSEU) that determines the prices an agent is required to pay for a bet, and this often disagrees with Ramsey's Thesis. I (...) suggest two responses to Hedden's objection. First, we might be permissive: agents are permitted to pay any price that is required or permitted by RT, and they are permitted to pay any price that is required or permitted by MSEU. This allows us to give a revised version of the Dutch Book Argument for Probabilism, which I call the Permissive Dutch Book Argument. Second, I suggest that even the proponent of the Expected Utility Objection should admit that RT gives the correct answer in certain very limited cases, and I show that, together with MSEU, this very restricted version of RT gives a new pragmatic argument for Probabilism, which I call the Bookless Pragmatic Argument. (shrink)

Number words seemingly function both as adjectives attributing cardinality properties to collections, as in Frege’s ‘Jupiter has four moons’, and as names referring to numbers, as in Frege’s ‘The number of Jupiter’s moons is four’. This leads to what Thomas Hofweber calls Frege’s Other Puzzle: How can number words function as modifiers and as singular terms if neither adjectives nor names can serve multiple semantic functions? Whereas most philosophers deny that one of these uses is genuine, we instead argue that (...) number words, like many related expressions, are polymorphic, having multiple uses whose meanings are systematically related via type shifting. (shrink)

Much of our information comes to us indirectly, in the form of conclusions others have drawn from evidence they gathered. When we hear these conclusions, how can we modify our own opinions so as to gain the benefit of their evidence? In this paper we study the method known as geometric pooling. We consider two arguments in its favour, raising several objections to one, and proposing an amendment to the other.

There are three main moral theories: virtue ethics, the deontological approach and utilitarianism. The concern here is how they interrelate, why they come into focus at different times and places, and how they are configured in their application to a modern democratic society. Person-oriented virtue ethics was the dominant understanding in Ancient Greece but within the Western tradition this was later subordinated to the monotheism of Ancient Judaism as modified by Christianity. Of growing importance by the eighteenth century was rights (...) theory which was often still situated religiously. Kant’s principle of the categorical imperative has been highly influential but was challenged by the emerging nature of industrial and capitalist society. Utilitarianism, within which the moral rightness of activity resides in its tendency to promote happiness or unhappiness, represented the decisive move from the transcendental to the immanent approach. Although all three approaches to moral theory continue to be relevant to identifiable situations and aspects of modern society, there has been a substantial turn towards a heavily modified utilitarianism associated with parliamentary democracy and market economies founded on property ownership. The root cause of this is the ability of utilitarianism, as opposed to the other approaches, to handle considerations of number and probability. The concept of utility is fundamental in economics but the idea has evolved away from its origins to mean “preference”. There is a sense in which the straightforward appeal of basic utilitarianism has been “leased out” in modified form to a set of institutional arrangements. Certain “pressure points” in a modern society are noted which pose particular problems pertinent to moral theory. Bernard Williams argues persuasively for an appropriately modified form of virtue ethics. (shrink)

If a Zen Master kills a kitten, and does not hear its scream, does it make a sound? In this essay, I use the Zen story of Master Nansen's killing of a kitten as an entree into a reflection on the Zen experience of enlightenment. I argue that the story of Nansen and the cat, as presented in the Zen tradition, raises many questions and problems that must be resolved if we are to envision the enlightenment experience in a clear (...) way. (shrink)

In this brief essay, I argue that Anselm's ontological argument for the existence of God achieves its effect through the verbal equivalent of a magician's "sleight-of-hand." More technically, the argument commits the informal fallacy of equivocation. I provide a brief analysis of the argument's text to demonstrate this.

The political philosophy originates from the reflections of crisis, risks and threats which society faces to. The author understands environmentalism as a tendency of current political philosophy which starts from the reflections of causes and possible effects of global environmental crisis as one of the most serious threats to the existential preconditions of current political system and global civilization at all. Considering the changes in social, technological and environmental starting conditions of the existence of economic-political system – that are consequences (...) of the transition from stable geologic-climate era of Holocene to unstable era of anthropocene – it is necessary to reconsider once more the basic premises, imperatives and conceptual frames of current economic-political system. The outlines of current economic-political system in philosophical frame were laid out by founders of modern political thinking while we can identify some of basic premises of environmentalism and also concepts relevant to the reflection of current threats and risks in some of their works. Author considers the concept of civil and human rights, the concept of natural state and the concept of social contract to be suitable for the reflection of the crisis of current economic-political system regarding environmentalism. Afterwards, the author formulates in what meanings are these concepts actual also for anthropocene. In conclusion, the author´s hypothesis is that the political philosophy of 21st century must reflect the environmental preconditions and limits of existence and forms of economic-political system and, at the same time, it must take into account that any economic and social activities have influence on the quality and sustainability of environment. (shrink)

Rescorla (Erkenntnis, 2020) has recently pointed out that the standard arguments for Bayesian Conditionalization assume that whenever I become certain of something, it is true. Most people would reject this assumption. In response, Rescorla offers an improved Dutch Book argument for Bayesian Conditionalization that does not make this assumption. My purpose in this paper is two-fold. First, I want to illuminate Rescorla’s new argument by giving a very general Dutch Book argument that applies to many cases of updating beyond those (...) covered by Conditionalization, and then showing how Rescorla’s version follows as a special case of that. Second, I want to show how to generalise R. A. Briggs and Richard Pettigrew’s Accuracy Dominance argument to avoid the assumption that Rescorla has identified (Briggs and Pettigrew in Noûs, 2018). In both cases, these arguments proceed by first establishing a very general reflection principle. (shrink)

As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell’s Paradox being derivable in it.This system is, except for minor differ...

The aim of this study is to identify the key terms and arguments of J. Lovelock՚s sustainable retreat concept and their analysis with emphasize on the consequences of this concept for political, social and environmental thinking. J. Lovelock points out that considering rapid and complex changes in global environment, marked by the term Anthropocene; we do not have enough time and sources to realize the sustainable development concept. For that reason, it is, according to him, necessary to formulate sustainable retreat (...) concept as a strategy which will allow to prepare for climate change in a way that not only a man as a biological specie, but also civilized society could survive. Even basic theses of this concept indicate a need to revalue majority political concepts, mainly concepts of sovereignty, citizenship, also the freedom of movement and residence, freedom of business and consume, which are fundamentals of neoliberal economic-political system. Retreat expects elaborated and organized migration to beforehand chosen and arranged areas. Opposite to retreat is mass escape chaos that reduces human relations to fight for survival. As J. Lovelock proposed in his sustainable retreat concept, relocating people from areas affected by climate changes to climate oases would mean that rich northern countries give up their current, in fact, isolationistic politics that refuses climate migrants. Therefore the sustainable retreat concept requires much greater competence and mainly willingness to cooperate not only on national, but also on international and global level more than humanity is able to do it currently. (shrink)

The pantheist ontology of Baruch Spinoza (b.1632 – d.1677) is an attempt to deny the accountability of political evil. -/- Spinoza’s instinct for statist control and his distrust of the common man are displayed in Theological-Political Treatise (published 1670). His masterwork, Ethics (published posthumously in 1677), is a bold attempt (in the guise of ontology) to classify minds and bodies as attributes of the State. -/- In Ethics, Spinoza ‘outlaws’ any vantage point from which we can address or protest the (...) kind of ‘perfect power’ -- and its attendant evils -- that constitute the essence and existence of the State. (shrink)

C. Stephen Layman contends that an argument supporting theism over naturalism can be constructed based on three defensible, non–question-begging premises about the moral order. Previous critics of Layman’s argument have challenged the truth of these premises. We stipulate them arguendo but go on to show that there is a deeper problem: a fourth premise introduced to complete the argument—the “completion premise,” as we call it—is true only if we assume that God exists or we concede that there is no afterlife. (...) We close with suggestions for how Layman’s argument must be strengthened to meet with dialectical success. (shrink)

In this paper, we attempt to show that if Plantinga’s free will defence succeeds, his O Felix Culpa theodicy fails. For if every creaturely essence suffers from transworld depravity, then given that Jesus has a creaturely essence (as we attempt to show), it follows that Incarnation and Atonement worlds cannot be actualized by God, in which case we have anything but a felix culpa.

to appear in Lambert, E. and J. Schwenkler (eds.) Transformative Experience (OUP) -/- L. A. Paul (2014, 2015) argues that the possibility of epistemically transformative experiences poses serious and novel problems for the orthodox theory of rational choice, namely, expected utility theory — I call her argument the Utility Ignorance Objection. In a pair of earlier papers, I responded to Paul’s challenge (Pettigrew 2015, 2016), and a number of other philosophers have responded in similar ways (Dougherty, et al. 2015, Harman (...) 2015) — I call our argument the Fine-Graining Response. Paul has her own reply to this response, which we might call the Authenticity Reply. But Sarah Moss has recently offered an alternative reply to the Fine-Graining Response on Paul’s behalf (Moss 2017) — we’ll call it the No Knowledge Reply. This appeals to the knowledge norm of action, together with Moss’ novel and intriguing account of probabilistic knowledge. In this paper, I consider Moss’ reply and argue that it fails. I argue first that it fails as a reply made on Paul’s behalf, since it forces us to abandon many of the features of Paul’s challenge that make it distinctive and with which Paul herself is particularly concerned. Then I argue that it fails as a reply independent of its fidelity to Paul’s intentions. (shrink)

Longtermism is the view that the most urgent global priorities, and those to which we should devote the largest portion of our resources, are those that focus on (i) ensuring a long future for humanity, and perhaps sentient or intelligent life more generally, and (ii) improving the quality of the lives that inhabit that long future. While it is by no means the only one, the argument most commonly given for this conclusion is that these interventions have greater expected goodness (...) per unit of resource devoted to them than each of the other available interventions, including those that focus on the health and well-being of the current population. In this paper, I argue that, even if we grant the consequentialist ethics upon which this argument depends, and even if we grant one of the axiologies that are typically paired with that ethics to give the argument, we are not morally required to choose an option that maximises expected utility; indeed, we might not even be permitted to do so. Instead, I will argue, if the argument's consequentialism is correct, we should choose using a decision theory that is sensitive to risk, and allows us to give greater weight to worse-case outcomes than expected utility theory does. And, I will show, such decision theories do not always recommend longtermist interventions. Indeed, sometimes, they recommend exactly the opposite: sometimes, they recommend hastening human extinction. Many, though not all, will take this as a reductio of the consequentialism or the axiology of the argument. I remain agnostic on the conclusion we should draw. (shrink)

Derek Parfit was one of the most important and influential moral philosophers of the late 20th and early 21st centuries. This Element offers a critical introduction to his wide-ranging ethical thought, focusing especially on his two most significant works, Reasons and Persons and On What Matters, and their contribution to the consequentialist moral tradition. Topics covered include: rationality and objectivity, distributive justice, self-defeating moral theories, Parfit's Triple Theory, personal identity, and population ethics.

An investigation of Frege's various contributions to the study of language, focusing on three of his most famous doctrines: that concepts are unsaturated, that sentences refer to truth-values, and that sense must be distinguished from reference.

Epistemologists who study credences have a well-developed account of how you should change them when you learn new evidence; that is, when your body of evidence grows. What's more, they boast a diverse range of epistemic and pragmatic arguments that support that account. But they do not have a satisfactory account of when and how you should change your credences when you become aware of possibilities and propositions you have not entertained before; that is, when your awareness grows. In this (...) paper, I consider the arguments for the credal epistemologist's account of how to respond to evidence, and I ask whether they can help us generate an account of how to respond to awareness growth. The results are surprising: the arguments that all support the same norms for responding to evidence growth support a number of different norms when they are applied to awareness growth. Some of these norms seem too weak, others too strong. I ask what we should conclude from this, and argue that our credal response to awareness growth is considerably less rigorously constrained than our credal response to new evidence. (shrink)

Mathematical formalism is the the view that numbers are "signs" and that arithmetic is like a game played with such signs. Frege's colleague Thomae defended formalism using an analogy with chess, and Frege's critique of this analogy has had a major influence on discussions in analytic philosophy about signs, rules, meaning, and mathematics. Here I offer a new interpretation of formalism as defended by Thomae and his predecessors, paying close attention to the mathematical details and historical context. I argue that (...) for Thomae, the formal standpoint is an _algebraic perspective_ on a domain of objects, and a "sign" is not a linguistic expression or mark, but a representation of an object within that perspective. Thomae exploits a shift into this perspective to give a purely algebraic construction of the real numbers from the rational numbers. I suggest that Thomae's chess analogy is intended to provide a model for such shifts in perspective. (shrink)

This essay outlines one way to conceptualise the relation between cultural identity, collective memory, and artifacts. It starts by characterising the notion of cultural identity as our membership to cultural groups and briefly explores the relation between cultural and narrative identity (section 2). Next, it presents how human memory is conceptualised on an individual and collective level (section 3) and then distinguishes between small-scale and large-scale collective memory (section 4). Having described cultural identity and collective memory, it argues that cultural (...) identity is materialised in the environment when we retrieve and construct collective memories by integrating information from our biological memory with information in artifacts or in other people’s embodied brains (section 5). This essay ends with analysing how materialised cultural identities are constructed by using a niche construction approach from evolutionary biology (section 6). (shrink)

Drawing mainly from the Tractatus Logico-Philosophicus and his middle period writings, strategic issues and problems arising from Wittgenstein’s philosophy of mathematics are discussed. Topics have been so chosen as to assist mediation between the perspective of philosophers and that of mathematicians on their developing discipline. There is consideration of rules within arithmetic and geometry and Wittgenstein’s distinctive approach to number systems whether elementary or transfinite. Examples are presented to illuminate the relation between the meaning of an arithmetical generalisation or theorem (...) and its proof. An attempt is made to meet directly some of Wittgenstein’s critical comments on the mathematical treatment of infinity and irrational numbers. (shrink)

In December of 2013, my Dad died of advanced Alzheimer's and a condition called Myasthenia Gravis. This is a selection of journal entries I made over the course of the two years leading up to my Dad's death. It is not a philosophical essay, but a personal reflection, in "real time" so to speak, on the nature of the dying process in relation to questions of faith, hope, despair, and the meaning of a man's life. I offer it here for (...) any who might find it worthwhile. (shrink)

In this paper, we seek a reliabilist account of justified credence. Reliabilism about justified beliefs comes in two varieties: process reliabilism (Goldman, 1979, 2008) and indicator reliabilism (Alston, 1988, 2005). Existing accounts of reliabilism about justified credence comes in the same two varieties: Jeff Dunn (2015) proposes a version of process reliabilism, while Weng Hong Tang (2016) offers a version of indicator reliabilism. As we will see, both face the same objection. If they are right about what justification is, it (...) is mysterious why we care about justification, for neither of the accounts explains how justification is connected to anything of epistemic value. We will call this the Connection Problem. I begin by describing Dunn’s process reliabilism and Tang’s indicator reliabilism. I argue that, understood correctly, they are, in fact, extensionally equivalent. That is, Dunn and Tang reach the top of the same mountain, albeit by different routes. However, I argue that both face the Connection Problem. In response, I offer my own version of reliabilism, which is both process and indicator, and I argue that it solves that problem. Furthermore, I show that it is also extensionally equivalent to Dunn’s reliabilism and Tang’s. Thus, I reach the top of the same mountain as well. (shrink)

In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing---using only so-called finitistic principles---that these formalizations are free of contradictions. ;In the area of logic, the Hilbert school accomplished major advances both in introducing new systems of logic, and in developing central metalogical notions, such as completeness and decidability. The analysis of unpublished material presented (...) in Chapter 2 shows that a completeness proof for propositional logic was found by Hilbert and his assistant Paul Bernays already in 1917--18, and that Bernays's contribution was much greater than is commonly acknowledged. Aside from logic, the main technical contribution of Hilbert's Program are the development of formal mathematical theories and proof-theoretical investigations thereof, in particular, consistency proofs. In this respect Wilhelm Ackermann's 1924 dissertation is a milestone both in the development of the Program and in proof theory in general. Ackermann gives a consistency proof for a second-order version of primitive recursive arithmetic which, surprisingly, explicitly uses a finitistic version of transfinite induction up to www . He also gave a faulty consistency proof for a system of second-order arithmetic based on Hilbert's &egr;-substitution method. Detailed analyses of both proofs in Chapter 3 shed light on the development of finitism and proof theory in the 1920s as practiced in Hilbert's school. ;In a series of papers, Charles Parsons has attempted to map out a notion of mathematical intuition which he also brings to bear on Hilbert's finitism. According to him, mathematical intuition fails to be able to underwrite the kind of intuitive knowledge Hilbert thought was attainable by the finitist. It is argued in Chapter 4 that the extent of finitistic knowledge which intuition can provide is broader than Parsons supposes. According to another influential analysis of finitism due to W. W. Tait, finitist reasoning coincides with primitive recursive reasoning. The acceptance of non-primitive recursive methods in Ackermann's dissertation presented in Chapter 3, together with additional textual evidence presented in Chapter 4, shows that this identification is untenable as far as Hilbert's conception of finitism is concerned. Tait's conception, however, differs from Hilbert's in important respects, yet it is also open to criticisms leading to the conclusion that finitism encompasses more than just primitive recursive reasoning. (shrink)

We are able to participate in countless different sorts of social practice. This indefinite set of capacities must be explainable in terms of a finite stock of capacities. This paper compares and contrasts two different explanations. A standard decomposition of the capacity to participate in social practices goes something like this: the interpreter arrives on the scene with a stock of generic practice-types. He looks at the current scene to fill-in the current tokens of these types. He looks at the (...) current state of these practice tokens to see what actions are available to him. He uses his current desires to choose between these various possible actions. I argue that this standard explanation is defective, drawing on arguments by Searle and Wittgenstein and Garfinkel. I propose an alternative explanation, in which the participants must continually show each other the state of the scene in order to maintain the scene’s intelligibility. I provide a simple formal language in which to describe this alternative approach, in which we can state quite precisely what someone is doing when they participate in a practice. This language is related to both deontic and epistemic logics, but it is much simpler – it does not include the classic propositional connectives, and it is driven by a very different set of assumptions. The inspirations for this formal language are Searle’s analysis of directions of fit, Wittgenstein’s remarks on rule-following and Garfinkel’s ethnomethodology. (shrink)

One goal of this paper is to argue that autobiographical memories are extended and distributed across embodied brains and environmental resources. This is important because such distributed memories play a constitutive role in our narrative identity. So, some of the building blocks of our narrative identity are not brain-bound but extended and distributed. Recognising the distributed nature of memory and narrative identity, invites us to find treatments and strategies focusing on the environment in which dementia patients are situated. A second (...) goal of this paper is to suggest various of such strategies, including lifelogging technologies such as SenseCams, life story books, multimedia biographies, memory boxes, ambient intelligence systems, and virtual reality applications. Such technologies allow dementia patients to remember their personal past in a way that wouldn’t be possible by merely relying on their biological memory, in that way aiding in preserving their narrative identity and positively contributing to their sense of well-being. (shrink)

This paper discusses Frege's account of definition by induction in Grundgesetze and the two key theorems Frege proves using it.

Critical examination of possible socio-political Anthropocene consequences leads to the conclusion that the sustainable development concept is not an adequate answer for current threats and risks. An effort to implement the sustainable development concept can even make climate changes and other forms of nature devastation worse, as it turns out on ongoing greenhouse gas concentrations growth in the atmosphere, despite obligations that result to all states of the world from Paris agreement. The climate change rate and range of plant and (...) animal species extinction confirms J. Lovelock´s thesis that humanity does not have enough time and, most likely, enough sources to implement the sustainable development concept and, as B. Latour points out, we do not have a big enough planet. Therefore, it is necessary to think about a retreat – to areas that are likely to stay livable even after the sea level rise and desertification; it is necessary to think about how to move millions of people from areas flooded by sea or parched by desert; to think about a change of our current way of life, of production of food and energy so that not only humankind as animal species would continue, but also our civilization and its technological and organizational knowledge. Even basic theses based on this concept indicate a need to reassess most political concepts, mainly the concepts of sovereignty, citizenship, but also those of freedom of movement and residence, freedom of business and consume, which work as fundamentals of the neoliberal economic-political system. Retreat expects complex and organized migration to beforehand chosen and arranged areas. Opposite to retreat is mass escape chaos that reduces human relations to fight for survival. As J. Lovelock proposed in his sustainable retreat concept, relocating people from areas affected by climate changes to climate oases would mean that rich northern countries give up their current, in fact, isolationistic politics of refusing climate migrants. Therefore, the concept of sustainable retreat requires much greater competence and especially willingness to cooperate not only nationally, but also internationally and globally, in addition to what humanity is capable of doing today. (shrink)

This paper applies a virtue epistemology approach to using the Internet, as to improve our information-seeking behaviours. Virtue epistemology focusses on the cognitive character of agents and is less concerned with the nature of truth and epistemic justification as compared to traditional analytic epistemology. Due to this focus on cognitive character and agency, it is a fruitful but underexplored approach to using the Internet in an epistemically desirable way. Thus, the central question in this paper is: How to use the (...) Internet in an epistemically virtuous way? Using the work of Jason Baehr, it starts by outlining nine intellectual or epistemic virtues: curiosity, intellectual autonomy, intellectual humility, attentiveness, intellectual carefulness, intellectual thoroughness, open-mindedness, intellectual courage and intellectual tenacity. It then explores how we should deploy these virtues and avoid the corresponding vices when interacting with the Internet, particularly search engines. Whilst an epistemically virtuous use of the Internet will not guarantee that one will acquire true beliefs, understanding or even knowledge, it will strongly improve one’s information-seeking behaviours. The paper ends with arguing that teaching and assessing online intellectual virtues should be part of school and university curricula, perhaps embedded in critical thinking courses, or even better, as individual units. (shrink)

Is the societal-level of analysis sufficient today to understand the values of those in the global workforce? Or are individual-level analyses more appropriate for assessing the influence of values on ethical behaviors across country workforces? Using multi-level analyses for a 48-society sample, we test the utility of both the societal-level and individual-level dimensions of collectivism and individualism values for predicting ethical behaviors of business professionals. Our values-based behavioral analysis indicates that values at the individual-level make a more significant contribution to (...) explaining variance in ethical behaviors than do values at the societal-level. Implicitly, our findings question the soundness of using societal-level values measures. Implications for international business research are discussed. (shrink)

It has been known for a few years that no more than Pi-1-1 comprehension is needed for the proof of "Frege's Theorem". One can at least imagine a view that would regard Pi-1-1 comprehension axioms as logical truths but deny that status to any that are more complex—a view that would, in particular, deny that full second-order logic deserves the name. Such a view would serve the purposes of neo-logicists. It is, in fact, no part of my view that, say, (...) Delta-3-1 comprehension axioms are not logical truths. What I am going to suggest, however, is that there is a special case to be made on behalf of Pi-1-1 comprehension. Making the case involves investigating extensions of first-order logic that do not rely upon the presence of second-order quantifiers. A formal system for so-called "ancestral logic" is developed, and it is then extended to yield what I call "Arché logic". (shrink)

David Rosenthal explains conscious mentality in terms of two independent, though complementary, theories—the higher-order thought (“HOT”) theory of consciousness and quality-space theory (“QST”) about mental qualities. It is natural to understand this combination of views as constituting a kind of representationalism about experience—that is, a version of the view that an experience’s conscious character is identical with certain of its representational properties. At times, however, Rosenthal seems to resist this characterization of his view. We explore here whether and to what (...) extent it makes sense to construe Rosenthal’s views as representationalist. Our goal is not merely terminological—discerning how best to use the expression ‘representationalism’. Rather, we argue that understanding Rosenthal’s account as a kind of representationalism permits us not only to make sense of broader debates within the philosophy of mind, but also to extend and clarify aspects of the view itself. (shrink)

This paper explores the relationship between Hume's Prinicple and Basic Law V, investigating the question whether we really do need to suppose that, already in Die Grundlagen, Frege intended that HP should be justified by its derivation from Law V.

ABSTRACT In ‘Scorekeeping in a Pornographic Language Game’, Rae Langton and Caroline West borrow ideas from David Lewis to attempt to explain how pornography might subordinate and silence women. Pornography is supposed to express certain misogynistic claims implicitly, through presupposition, and to convey them indirectly, through accommodation. I argue that the appeal to accommodation cannot do the sort of work Langton and West want it to do: Their case rests upon an overly simplified model of that phenomenon. I argue further (...) that, once we are clear about why Langton and West's account fails, a different and more plausible account of pornography's influence emerges. (shrink)

Abstract Tom Dougherty observes that challenges to counting the numbers often cite John Taurek’s 1977 article, “Should the Numbers Count.” Dougherty, though sympathetic to Taurek’s (and others) critique of consequentialism’s aggregating good across individuals, defends a non-consequentialist principle for addition he calls “the Ends Principle. Take the case (he labels “Drug”) when an agent, possessing a dose of a lifesaving drug, can save one person with the entire dose, or two people, each of whom only need half the dose. Dougherty (...) argues that a rational agent, summing her altruistic goals (three), but unable to save all three, will save two. I give two criticisms of Dougherty’s paper. (1) He hasn’t ruled out, though acknowledging, the equal chance principle as deontological grounds for deciding Drug. (2) An agent using the Ends Principle in Drug, as he formulates it, will not have the requisite aims to make use of the Principle. I also consider an issue, little discussed, the conditions for aggregation in general. (shrink)