Non-Archimedean population axiologies – also known as lexical views – claim (i) that a sufficient number of lives at a very high positive welfare level would be better than any number of lives at a very low positive welfare level and/or (ii) that a sufficient number of lives at a very low negative welfare level would be worse than any number of lives at a very high negative welfare level. Such axiologies are popular because they can avoid the (Negative) (...) Repugnant Conclusion and satisfy the adequacy conditions given in the central impossibility result in population axiology due to Gustaf Arrhenius. I provide a novel argument against them which appeals to the way that good and bad lives can intuitively outweigh one other. (shrink)

We prove a representation theorem for preference relations over countably infinite lotteries that satisfy a generalized form of the Independence axiom, without assuming Continuity. The representing space consists of lexicographically ordered transfinite sequences of bounded real numbers. This result is generalized to preference orders on abstract superconvex spaces.

In 1980 F. Wattenberg constructed the Dedekind completion

d of the Robinson non-archimedean field

and established basic algebraic properties of

d [6]. In 1985 H. Gonshor established further fundamental properties of

d [7].In [4] important construction of summation of countable sequence of Wattenberg numbers was proposed and corresponding basic properties of such summation were considered. In this paper the important applications of the Dedekind completion

d in transcendental number theory were considered. We dealing using set theory ZFC
(
-model of (...) ZFC).Given an class of analytic functions of one complex variable f  

z, we investigate the arithmetic nature of the values of fz at transcendental points en, n  .Main results are: (i) the both numbers e
 and e   are irrational, (ii) number ee is transcendental. Nontrivial generalization of the Lindemann- Weierstrass theorem is obtained. (shrink)

After generalizing the Archimedean property of real numbers in such a way as to make it adaptable to non-numeric structures, we demonstrate that the real numbers cannot be used to accurately measure non-Archimedean structures. We argue that, since an agent with Artificial General Intelligence (AGI) should have no problem engaging in tasks that inherently involve non-Archimedean rewards, and since traditional reinforcement learning rewards are real numbers, therefore traditional reinforcement learning probably will not lead to AGI. We indicate (...) two possible ways traditional reinforcement learning could be altered to remove this roadblock. (shrink)

Metaethics is traditionally understood as a non-moral discipline that examines moral judgements from a standpoint outside of ethics. This orthodox understanding has recently come under pressure from anti-Archimedeans, such as Ronald Dworkin and Matthew Kramer, who proclaim that rather than assessing morality from an external perspective, metaethical theses are themselves substantive moral claims. In this paper, I scrutinise this anti-Archimedean challenge as applied to the metaethical position of expressivism. More precisely, I examine the claim that expressivists do not avoid (...) moral commitments when accounting for moral thought, but instead presuppose them; they do not look at ethics from the outside, but operate from within ethics. This paper defends the non-moral status of expressivism against anti-Archimedeanism by rejecting a new anti-Archimedean challenge which, on the basis of Hume’s Law, aims to exploit expressivist explanations of supervenience in order to show that expressivism is a substantive moral position. (shrink)

We study the representation of sets of desirable gambles by sets of probability mass functions. Sets of desirable gambles are a very general uncertainty model, that may be non-Archimedean, and therefore not representable by a set of probability mass functions. Recently, Cozman (2018) has shown that imposing the additional requirement of even convexity on sets of desirable gambles guarantees that they are representable by a set of probability mass functions. Already more that 20 years earlier, Seidenfeld et al. (1995) (...) gave an axiomatisation of binary preferences—on horse lotteries, rather than on gambles—that also leads to a unique representation in terms of sets of probability mass functions. To reach this goal, they use two devices, which we will call ‘SSK–Archimedeanity’ and ‘SSK–extension’. In this paper, we will make the arguments of Seidenfeld et al. (1995) explicit in the language of gambles, and show how their ideas imply even convexity and allow for conservative reasoning with evenly convex sets of desirable gambles, by deriving an equivalence between the SSK–Archimedean natural extension, the SSK–extension, and the evenly convex natural extension. (shrink)

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

Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general.

We provide an intuitive motivation for the hyperreal numbers via electoral axioms. We do so in the form of a Socratic dialogue, in which Protagoras suggests replacing big-oh complexity classes by real numbers, and Socrates asks some troubling questions about what would happen if one tried to do that. The dialogue is followed by an appendix containing additional commentary and a more formal proof.

A new non-Archimedean approach to interacted quantum fields is presented. In proposed approach, a field operator φ(x,t) no longer a standard tempered operator-valued distribution, but a non-classical operator-valued function. We prove using this novel approach that the quantum field theory with Hamiltonian P(φ)_4 exists and that the corresponding C^*­ algebra of bounded observables satisfies all the Haag-Kastler axioms except Lorentz covariance. We prove that the λ(φ^2n )_4,n≥2 quantum field theory models are Lorentz covariant.

A new non-Archimedean approach to interacted quantum fields is presented. In proposed approach, a field operator φ(x,t) no longer a standard tempered operator-valued distribution, but a non-classical operator-valued function. We prove using this novel approach that the quantum field theory with Hamiltonian P(φ)_4 exists and that the corresponding C^*­ algebra of bounded observables satisfies all the Haag-Kastler axioms except Lorentz covariance. We prove that the λ(φ^4 )_4 quantum field theory model is Lorentz covariant.

This dissertation is a contribution to formal and computational philosophy. -/- In the first part, we show that by exploiting the parallels between large, yet finite lotteries on the one hand and countably infinite lotteries on the other, we gain insights in the foundations of probability theory as well as in epistemology. Case 1: Infinite lotteries. We discuss how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. The solution boils down to the introduction (...) of infinitesimal probability values, which can be achieved using non-standard analysis. Our solution can be generalized to uncountable sample spaces, giving rise to a Non-Archimedean Probability (NAP) theory. Case 2: Large but finite lotteries. We propose application of the language of relative analysis (a type of non-standard analysis) to formulate a new model for rational belief, called Stratified Belief. This contextualist model seems well-suited to deal with a concept of beliefs based on probabilities ‘sufficiently close to unity’. -/- The second part presents a case study in social epistemology. We model a group of agents who update their opinions by averaging the opinions of other agents. Our main goal is to calculate the probability for an agent to end up in an inconsistent belief state due to updating. To that end, an analytical expression is given and evaluated numerically, both exactly and using statistical sampling. The probability of ending up in an inconsistent belief state turns out to be always smaller than 2%. (shrink)

The repugnant conclusion poses a conundrum in population ethics that has evaded satisfactory solution for four decades. In this article, I show that the repugnant conclusion can be avoided without sacrificing key moral intuitions. This is achieved using non-Archimedean orders, which admit the possibility of pairs of goods for which no amount of one is better than a single unit of the other. I show that with minimal assumptions, not only are such goods sensible, they are compulsory. I show (...) that utilitarianism and expected utility theory in their canonical forms are not in general suitable in this setting, and using these tools naively can lead to ethical errors that are arbitrarily serious. Multi-dimensional lexicographic expected utility representations may be required. I use fuzzy sets to show that there needn't be a clear boundary separating goods that are not Archimedean equivalent. (shrink)

This paper deals with Natorp’s version of the Marburg mathematical philosophy of science characterized by the following three features: The core of Natorp’s mathematical philosophy of science is contained in his “knowledge equation” that may be considered as a mathematical model of the “transcendental method” conceived by Natorp as the essence of the Marburg Neo-Kantianism. For Natorp, the object of knowledge was an infinite task. This can be elucidated in two different ways: Carnap, in the Aufbau, contended that this endeavor (...) can be divided into two distinct parts, namely, a finite “constitution” of the object of knowledge and an infinite incompletable empirical description. In contrast, and more in the original spirit of Cohen and Natorp, the physicist and philosopher Margenau in The Nature of Physical Reality (Margenau. 1950) conceived the infinity of this “Aufgabe” as an infinite dialectical process, in which relative “data” and “conceptual constructs” determine each other. This dialectical process eliminates the dichotomy between Anschauung and Begriff that distinguished the Marburg Neo-Kantianism from Kantian orthodoxy, namely, the abandonment of the difference between intuition and concept. Finally, the paper deals with the non-Archimedean geometrical systems that played a central role in Natorp’s defence of Cohen’s “infinitesimal” metaphysics. (shrink)

A probability distribution is regular if no possible event is assigned probability zero. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “isomorphic” events are not in fact isomorphic, but Howson is speaking (...) of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

In standard probability theory, probability zero is not the same as impossibility. But many have suggested that only impossible events should have probability zero. This can be arranged if we allow infinitesimal probabilities, but infinitesimals do not solve all of the problems. We will see that regular probabilities are not invariant over rigid transformations, even for simple, bounded, countable, constructive, and disjoint sets. Hence, regular chances cannot be determined by space-time invariant physical laws, and regular credences cannot satisfy seemingly reasonable (...) symmetry principles. Moreover, the examples here are immune to the objections against Williamson’s infinite coin flips. (shrink)

Quasi-realist expressivists have developed a growing liking for minimalism about truth. It has gone almost unnoticed, though, that minimalism also drives an anti-Archimedean movement which launches a direct attack on expressivists’ non-moral self-image by proclaiming that all metaethical positions are built on moral grounds. This interplay between expressivism, minimalism and anti-Archimedeanism makes for an intriguing metaethical encounter. As such, the first part of this dissertation examines expressivism’s marriage to minimalism and defends it against its critics. The second part then (...) turns to the anti-Archimedean challenge to expressivism and shows how to ward off this challenge by securing expressivism’s non-moral, metaethical status without having to abandon minimalism about truth. (shrink)

The nature of state governance in consolidated liberal democracies has important implications for the ideal theory debate. The states of these societies are polycentric. Decision-making power within them is disaggregated across multiple sites. This rules out one major justification for ideal theory. On this influential view, the ideal furnishes a blueprint of the morally perfect society that we should strive to realise. This justification is not viable in consolidated liberal democracies because their states lack an Archimedean point from which (...) the institutional structure as a whole can be designed to accord with the true ideal – whichever it might be. However, knowledge of the ideal can still aid agents in those societies to determine the worth of more modest political objectives other than the ideal itself. (shrink)

What effect has finding the Archimedean point in ourselves had on how we look at ethics? The modern era of philosophy began with Descartes finding within himself an unshakable point from which to pursue knowledge of the world and himself. This intellectual alienation from the world into the universal mathematical structures of the human mind has led to a reversal where, henceforth, production, rather than contemplation, of knowledge became epistemologically superior. Guided by Hannah Arendt’s discussion of the Archimedean (...) point and Earth alienation in the Human Condition, I will argue that this scientific form of thinking made its way into ethical investigation in the age of modern philosophy. Furthermore, I will provide an analysis of Kant’s categorical imperative and John Stuart Mill’s utilitarianism to show that despite modern science’s success in elucidating universal laws of nature, a scientific approach to ethics has not universalized our judgments of good and evil. (shrink)

According to the orthodox account of meaning and translation in the literature, meaning is a property of expressions of a language, and translation is a matching of synonymous expressions across languages. This linguistic account of translation gives rise to well-known skeptical conclusions about translation, objectivity, meaning and truth, but it does not conform to our best translational practices. In contrast, I argue for a textual account of meaning based on the concept of a TEXT-TYPE that does conform to our best (...) translational practices. With their semantic function in view, text-types are Archimedean points for their respective disciplines. The text-type of philosophy is no exception. Culture-transcendent conceptual analysis can proceed on firm footing without having to deny the reality of radical cultural and linguistic difference by treating components of text-types as the concepts to be analyzed. Analyses of central philosophical concepts are provided as a means of adjudicating philosophical controversy. (shrink)

Archimedes of Syracuse has long provided a touchstone for considering how we make and acquire knowledge. Since the early Roman chroniclers of Archimedes’ life, and especially intensively since Descartes, scholars have described, sought, or derided the Archimedean point, defining and redefining its epistemic role. “Knowledge,” at least within modernity, is rhetorically tied to the figure of the Archimedean point, a place somewhere outside a regular and constrained world of experience. If this figure still leads to useful ways of (...) thinking about knowing, we are left with the question of how different modes of making knowledge approach their “Archimedean” points. The question is especially important today as a renewed .. (shrink)

Lexical views in population axiology can avoid the Repugnant Conclusion without violating Transitivity or Separability. However, they imply a dilemma: either some good life is better than any number of slightly worse lives, or else the ‘at least as good as’ relation on populations is radically incomplete. In this paper, I argue that Archimedean views face an analogous dilemma. I thus conclude that the lexical dilemma gives us little reason to prefer Archimedean views. Even if we give up (...) on lexicality, problems of the same kind remain. (shrink)

We study whether it is possible to generalise Seidenfeld et al.’s representation result for coherent choice functions in terms of sets of probability/utility pairs when we let go of Archimedeanity. We show that the convexity property is necessary but not sufficient for a choice function to be an infimum of a class of lexicographic ones. For the special case of two-dimensional option spaces, we determine the necessary and sufficient conditions by weakening the Archimedean axiom.

Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. Specifically, (...) a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff’s representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics. This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics. (shrink)

This chapter identifies a novel family of metaethical theories that are non-descriptive and that aim to explain the action-guiding qualities of normative thought and language. The general strategy is to consider different relations language might bear to a given content, where we locate descriptivity (or lack of it) in these relations, rather than locating it in a theory that begins with the expression of states of mind, or locating it in a special kind of content that is not way-things-might-be content. (...) One such view is sketched, which posits two different content-fixing cognitive roles for bits of language. One role fixes a descriptive relation to content and another role fixes a non-descriptive relation to content. In addition to non-descriptivity and action guidance, the chapter briefly considers the appearance of mind-independent authoritative force, disagreement, and Frege–Geach concerns. (shrink)

A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of this paper is (...) to show that a large class of non-classical logics are strong enough to formulate their own model theory in a corresponding non-classical set theory. Specifically I show that adequate definitions of validity can be given for the propositional calculus in such a way that the metatheory proves, in the specified logic, that every theorem of the propositional fragment of that logic is validated. It is shown that in some cases it may fail to be a classical matter whether a given sentence is valid or not. One surprising conclusion for non-classical accounts of vagueness is drawn: there can be no axiomatic, and therefore precise, system which is determinately sound and complete. (shrink)

Based on three recently published books on climate justice, this article reviews the field of climate ethics in light of developments of international climate politics. The central problem addressed is how idealised normative theories can be relevant to the political process of negotiating a just distribution of the costs and benefits of mitigating climate change. I distinguish three possible responses, that is, three kinds of non-ideal theories of climate justice: focused on (1) the injustice of some agents not doing their (...) part; (2) the policy process and aiming to be realistic; and (3) grievances related to the transition to a clean-energy economy. The methodological discussion underpinning each response is innovative and should be of interest more generally, even though it is still underdeveloped. The practical upshot, however, is unclear: even non-ideal climate justice may be too disconnected from the fast-moving and messy climate circus. (shrink)

Safety principles in epistemology are often hailed as providing us with an explanation of why we fail to have knowledge in Gettier cases and lottery examples, while at the same time allowing for the fact that we know the negations of sceptical hypotheses. In a recent paper, Sinhababu and Williams have produced an example—the Backward Clock—that is meant to spell trouble for safety accounts of knowledge. I argue that the Backward Clock case is, in fact, unproblematic for the more sophisticated (...) formulations of safety in the literature. However, I then proceed to construct two novel examples that turn out problematic for those formulations—one that provides us with a lottery-style case of safe ignorance and one that is a straightforward case of unsafe knowledge. If these examples succeed, then safety as it is usually conceived in the current debate cannot account for ignorance in all Gettier and lottery-style cases, and neither is it a necessary condition for knowledge. I conclude from these troublesome examples that modal epistemologists ought to embrace a much more simple and non-reductive version of safety, according to which the notion of similarity between possible worlds that determines in which worlds the subject must believe truly is an epistemic notion that cannot be defined or reduced to notions independent of knowledge. The resulting view is shown to also lead to desirable results with respect to lottery cases, certain quantum phenomena, and a puzzling case involving a cautious brain-in-a-vat. (shrink)

It is widely accepted that the ethical supervenes on the natural, where this is roughly the claim that it is impossible for two circumstances to be identical in all natural respects, but different in their ethical respects. This chapter refines and defends the traditional thought that this fact poses a significant challenge to ethical non-naturalism, a view on which ethical properties are fundamentally different in kind from natural properties. The challenge can be encapsulated in three core claims which the chapter (...) defends: that a defensible non-naturalism is committed to the supervenience of the ethical, that this commits the non-naturalist to a brute necessary connection between properties of distinct kinds, and that commitment to such brute connections counts against the non-naturalist’s view. Each of these claims has recently been challenged. Against Nicholas Sturgeon’s recent doubts about the dialectical force of supervenience, this chapter defends a supervenience thesis as deserving to be common ground among ethical realists. It is then argued that attempts to explain supervenience on behalf of the non-naturalist either fail as explanations, generate near-identical explanatory burdens elsewhere, or appeal to commitments that are inconsistent with core motivations for non-naturalism. The chapter concludes that, suitably refined, the traditional argument against nonnaturalism from supervenience is alive and well. (shrink)

This article argues that non-consensual vaccination is morally impermissible, for the same reasons for which sexual assault is not permissible. Likewise, mandatory vaccination is morally akin to sexual harassment, and therefore is not to be allowed.

A system of logic usually comprises a language for which a model-theory and a proof-theory are defined. The model-theory defines the semantic notion of model-theoretic logical consequence (⊨), while the proof-theory defines the proof- theoretic notion of logical consequence (or logical derivability, ⊢). If the system in question is sound and complete, then the two notions of logical consequence are extensionally equivalent. The concept of full formalization is a more restrictive one and requires in addition the preservation of the standard (...) meanings of the logical terms in all the admissible interpretations of the logical calculus, as it is proof-theoretically defined. Although classical first-order logic is sound and complete, its standard formalizations fall short to be full formalizations since they allow non-intended interpretations. This fact poses a challenge for the logical inferentialism program, whose main tenet is that the meanings of the logical terms are uniquely determined by the formal axioms or rules of inference that govern their use in a logical calculus, i.e., logical inferentialism requires a categorical calculus. This paper is the first part of a more elaborated study which will analyze the categoricity problem from its beginning until the most recent approaches. I will first start by describing the problem of a full formalization in the general framework in which Carnap (1934/1937, 1943) formulated it for classical logic. Then, in sections IV and V, I shall discuss the way in which the mathematicians B.A. Bernstein (1932) and E.V. Huntington (1933) have previously formulated and analyzed it in algebraic terms for propositional logic and, finally, I shall discuss some critical reactions Nagel (1943), Hempel (1943), Fitch (1944), and Church (1944) formulated to these approaches. (shrink)

In a previous article on cosmological arguments, I have put forward a few examples of complete infinite and circular explanations, and argued that complete non-wellfounded explanations such as these might explain the present state of the world better than their well-founded theistic counterparts (Billon, 2021). Although my aim was broader, the examples I gave there implied merely causal explanations. In this article, I would like to do three things: • Specify some general informative conditions for complete and incomplete non-wellfounded causal (...) explanations that can be used to assess candidate explanations and to generate new examples of complete non-wellfounded explanations. • Show that these conditions, which concern chains of causal explanations, easily generalize to chains of metaphysical, grounding explanations and even to chains involving other “determination relations” such as supervenience. • Apply these general conditions to the recent debates against the existence of nonwellfounded chains of grounds and show, with a couple of precise examples, that the latter can be complete, and that just like in the case of causal explanations, non-wellfoundedness can in fact be an aset rather than a liability. (shrink)

Aesthetic non-naturalism is the view that there are objective aesthetic truths that hold in virtue of sui generis facts. This view is seldom explicitly endorsed in philosophical aesthetics. I argue that many aestheticians should treat it as the view to beat, since (a) their commitments favour aesthetic realism, (b) non-naturalistic forms of aesthetic realism are particularly promising and (c) non-naturalists have reasonable answers to four important objections.

Derek Parfit defended Non-Realist Cognitivism. It is an open secret that this metaethical theory is often thought at best puzzling and at worst objectionably unclear. Employing truthmaker theory, I provide an account of Non-Realist Cognitivism that dispels charges of objectionable unclarity, clarifies how to assess it, and explains why, if plausible, it would be an attractive theory. I develop concerns that the theory involves cheating into an objection that ultimately reveals Non-Realist Cognitivism faces a dilemma. Whether it can escape demands (...) further attention. In bridging metaethics and the truthmaking literature, I illustrate the importance of greater meta-metaphysical reflection in metaethics. (shrink)

Bioart is a form of hybrid artistico-scientific practices in contemporary art that involve the use of bio-materials (such as living cells, tissues, organisms) and scientific techniques, protocols, and tools. Bioart-works embody vulnerability (intrinsic to all beings) and depend on (bio)technologies that allow these creations to come into being, endure and flourish but also discipline them. This article focuses on ‘semi-living’ sculptures by The Tissue Culture and Art Project (TC&A). TC&A’s artworks consist of bioengineered mammal tissues grown over biopolymer scaffoldings of (...) different shapes and require sterile conditions of a bioreactor and constant care in order to survive. The article explores how bioart-works are always already intertwined with multiple (bio)technologies and techniques of care and labour, forming specific feminist technoecologies that challenge conventional bioscientific and cultural imaginaries of embodiment and the relation between physis and techné. TC&A’s sculptures expose life as the non/living: the processual enmeshment of the organic and inorganic, living and non-living, and growth and decay. The article argues that thinking with and through the feminist technoecologies of bioart mobilises philosophical inventiveness: not only does it problematise the entwinement of technology and biomatter and of culture and nature, but it also prompts us to rethink the ontology of life. (shrink)

I discuss methodology in epistemology. I argue that settling the facts, even the epistemic facts, fails to settle the questions of intellectual policy at the center of our epistemic lives. An upshot is that the standard methodology of analyzing concepts like knowledge, justification, rationality, and so on is misconceived. More generally, any epistemic method that seeks to issue in intellectual policy by settling the facts, whether by way of abductive theorizing or empirical investigation, no matter how reliable, is inapt. The (...) argument is a radicalization of Moore’s Open Question Argument. I conclude by considering the ramifications of this conclusion for the debate surrounding “Modal Security”, a proposed necessary condition on undermining defeat. (shrink)

The boundaries of social categories are frequently altered to serve normative projects, such as social reform. Griffiths and Khalidi argue that the value-driven modification of categories diminishes the epistemic value of social categories. I argue that concerns over value-modified categories stem from problematic assumptions of the value-free ideal of science. Contrary to those concerns, non-epistemic value considerations can contribute to the epistemic improvement of a scientific category. For example, the early history of the category infantile autism shows how non-epistemic value (...) considerations can contribute to delimiting and establishing infantile autism as a distinct category in mainstream psychiatry. In the case of infantile autism, non-epistemic considerations have led to a new interpretation of existing data, the expansion of research to include biology, and the creation of diagnostic criteria that further contribute to collecting relevant data. Given this case study, it can be argued that non-epistemic values can improve our knowledge of scientific categories. (shrink)

While there is considerable disagreement on the precise nature of material objecthood, it is standardly assumed that material objects must be spatial. In this paper, I provide two arguments against this assumption. The first argument is made from largely a priori considerations about modal plenitude. The possibility of non-spatial material objects follows from commitment to certain plausible principles governing material objecthood and plausible principles regarding modal plenitude. The second argument draws from current philosophical discussions regarding theories of quantum gravity and (...) the emergence of spacetime. When it is appreciated what possible worlds these current theories commit us to, the possibility of non-spatial material objects will follow. Thus, either route will lead us to the possibility of non-spatial material objects. The significance of this result is that we need to revise our accounts of material objecthood to both accommodate these possibilities and the theories that lead to them. (shrink)

Direct epistemic consequentialism is the idea that X is epistemically permissible iff X maximizes epistemic value. It has received lots of attention in recent years and is widely accepted by philosophers to have counterintuitive implications. There are various reasons one might suspect that the relevant intuitions will not be widely shared among non-philosophers. This paper presents an initial empirical study of ordinary intuitions. The results of two experiments demonstrate that the counterintuitiveness of epistemic consequentialism is more than a philosophers' worry---the (...) folk seem to agree! (shrink)

This essay examines the role of non-existent objects in "epistemological ontology" — the study of the entities that make thinking possible. An earlier revision of Meinong's Theory of Objects is reviewed, Meinong's notions of Quasisein and Außersein are discussed, and a theory of Meinongian objects as "combinatorially possible" entities is presented.

Non‐Humean theories of natural necessity invoke modally‐laden primitives to explain why nature exhibits lawlike regularities. However, they vary in the primitives they posit and in their subsequent accounts of laws of nature and related phenomena (including natural properties, natural kinds, causation, counterfactuals, and the like). This article provides a taxonomy of non‐Humean theories, discusses influential arguments for and against them, and describes some ways in which differences in goals and methods can motivate different versions of non‐Humeanism (and, for that matter, (...) Humeanism). In short, this article provides an introduction to non‐Humeanism concerning the metaphysics of laws of nature and natural necessity. (shrink)

The categoricity problem for a system of logic reveals an asymmetry between the model-theoretic and the proof-theoretic resources of that logic. In particular, it reveals prima facie that the proof-theoretic instruments are insufficient for matching the envisaged model-theory, when the latter is already available. Among the proposed solutions for solving this problem, some make use of new proof-theoretic instruments, some others introduce new model-theoretic constrains on the proof-systems, while others try to use instruments from both sides. On the proof-theoretical side, (...) two main approaches for solving the categoricity problem for propositional classical logic consist in the enforcement of the formal systems of this logic by introducing rules of inference of a new kind. A multiple-conclusions logic allows rules of inference with more than one conclusion, while a bilateralist system contains rules of inference formulated in terms of assertion and rejection. Both these approaches reveal interesting formal features of logical reasoning. This paper analyses some of the advantages and limitations of these two approaches as solutions for a full formalization of logic, i.e., for a categorical formalization. (shrink)

This article aims to highlight the extent to which Kant’s account of belief draws on the views of his contemporaries. Situating the non-evidentialist features of Crusius’s account of belief within his broader account, I argue that they include antecedents to both Kant’s distinction between pragmatic and moral belief and his conception of a postulate of pure practical reason. While moving us closer to Kant’s arguments for the first postulate, however, both Crusius’s and Meier’s arguments for the immortality of the soul (...) fail to anticipate the most important aspect of their Kantian counterparts. Developing the non-evidentialist features of Basedow’s account of belief, I distinguish it from its Pascalian and Jamesian relatives and argue that it is the clearest antecedent to Kant’s arguments for the first and second postulates. Finally, I consider the development of Kant’s account of belief after the first Critique in light of the foregoing, and discuss the broader implications of my analysis. (shrink)

This paper establishes that the occasional identity relation and the contingent identity relation are both non-transitive and as such are not properly classified as identity relations. This is achieved by appealing to cases where multiple fissions and fusions occur simultaneously. These cases show that the contingent and occasional identity relations do not even satisfy the time-indexed and world-indexed versions of the transitivity requirement and hence are non-transitive relations.

Consciousness-based approaches to non-human moral status maintain that consciousness is necessary for (some degree or level of) moral status. While these approaches are intuitive to many, in this paper I argue that the judgment that consciousness is necessary for moral status is not secure enough to guide policy regarding non-humans, that policies responsive to the moral status of non-humans should take seriously the possibility that psychological features independent of consciousness are sufficient for moral status. Further, I illustrate some practical consequences (...) of calling consciousness-based views into question. (shrink)

Frege-Geach worries about embedding and composition have plagued metaethical theories like emotivism, prescriptivism and expressivism. The sharpened point of such criticism has come to focus on whether negation and inconsistency have to be understood in descriptivist terms. Because they reject descriptivism, these theories must offer a non-standard account of the meanings of ethical and normative sentences as well as related semantic facts, such as why certain sentences are inconsistent with each other. This paper fills out such a solution to the (...) negation problems, following some of the original emotivist ideas about the interplay of interests in conversation. We communicate both to share information and coordinate our actions, and we use distinctively normative language like deontic ‘must’ and ‘may’ to negotiate what people are to do. The kinds of disagreement involved in such negotiation can illuminate the issues with negation and inconsistency. This paper outlines a dynamic semantic system in which these ideas can bear fruit, developing the scorekeeping model of conversation. The result is clarification about what Frege-Geach worries can mean for nondescriptive semantics. (shrink)

In this article, I present two objections against the view that aesthetic judgements – that is, judgemental ascriptions of aesthetic qualities like elegance or harmony – are justified non‐inferentially. The first is that this view cannot make sense of our practice to support our aesthetic judgements by reference to lower‐level features of the objects concerned. The second objection maintains that non‐inferentialism about the justification of aesthetic judgements cannot explain why our aesthetic interest in artworks and other objects is limited to (...) only some of their lower‐level features that realise their higher‐level aesthetic qualities. Although my concern with the view that aesthetic judgements are subject to non‐inferential justification is very general, my discussion is primarily structured around Sibley's well‐developed and influential version of this view. (shrink)

The authors of this book reconstruct the philosophical, methodological and theoretical assumptions of non-Marxian historical materialism, a theory of historical process authored by Leszek Nowak (1943-2009), a co-founder of the Poznań School of Methodology. In the first part of the book, philosophical assumptions of this theory are compared with the concepts of Robert Nozick, Immanuel Wallerstein, André Gunder Frank and analytical Marxism. In the second part, non-Marxian historical materialism is compared with the concepts of Eva Etzioni-Halevy, Andrzej Falkiewicz, Robert Michels, (...) Vilfredo Pareto, Theda Skocpol and Karl August Wittfogel. (shrink)