It has recently been argued that foundationalists, those who take grounding to be well-founded, should not understand the well-foundedness of grounding as the condition that every grounding chain terminates in the downward direction, because this interpretation of well-foundedness fails to correctly classify certain complex grounding structures. Some structures that plausibly would be acceptable to the foundationalist are classified as not well-founded and others that plausibly would not be acceptable to the foundationalist are classified as (...) well-founded. In this paper I provide a characterisation of well-foundedness in terms of termination that correctly characterises all these difficult cases. This acts as a response to these recent arguments. Furthermore, it allows us to better evaluate their importance: these arguments have not shown that foundationalists are wrong to harbour the intuition that grounding chains must terminate in the downward direction, rather, they have shown that foundationalists need to be more clear about this intuition and how it is born out in more complex grounding structures. (shrink)

A number of philosophers think that grounding is, in some sense, well-founded. This thesis, however, is not always articulated precisely, nor is there a consensus in the literature as to how it should be characterized. In what follows, I consider several principles that one might have in mind when asserting that grounding is well-founded, and I argue that one of these principles, which I call ‘full foundations’, best captures the relevant claim. My argument is by the process of (...) elimination. For each of the inadequate principles, I illustrate its inadequacy by showing either that it excludes cases that should not be ruled out by a well-foundedness axiom for grounding, or that it admits cases that should be ruled out. (shrink)

Tarski [5] showed that for any set X, its set w(X) of well-orderable subsets has cardinality strictly greater than that of X, even in the absence of the axiom of choice. We construct a Fraenkel-Mostowski model in which there is an infinite strictly descending sequence under the relation |w (X)| = |Y|. This contrasts with the corresponding situation for power sets, where use of Hartogs' ℵ-function easily establishes that there can be no infinite descending sequence under the relation |P(X)| (...) = |Y|. (shrink)

We highlight that the connection of well-foundedness and recursive definitions is more than just convenience. While the consequences of making well-foundedness a sufficient condition for the existence of hierarchies have been extensively studied, we point out that well-foundedness is a necessary condition for the existence of hierarchies e.g. that even in an intuitionistic setting α⊢wfwhereα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${_\alpha \vdash \mathsf{wf}\, {\rm where}\, _\alpha}$$\end{document} stands for the iteration of Π10\documentclass[12pt]{minimal} (...) \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi^0_1}$$\end{document} comprehension along some ordinal α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha}$$\end{document} and wf\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{wf}}$$\end{document} stands for the well-foundedness of α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\alpha}$$\end{document}. (shrink)

A foundational algebra ( , f, ) consists of a hemimorphism f on a Boolean algebra with a greatest solution to the condition f(x). The quasi-variety of foundational algebras has a decidable equational theory, and generates the same variety as the complex algebras of structures (X, R), where f is given by R-images and is the non-wellfounded part of binary relation R.The corresponding results hold for algebras satisfying =0, with respect to complex algebras of wellfounded binary relations. These algebras, however, (...) generate the variety of all ( ,f) with f a hemimorphism on ). (shrink)

Typed feature structures are used extensively for the specification of linguistic information in many formalisms. The subsumption relation orders TFSs by their information content. We prove that subsumption of acyclic TFSs is well founded, whereas in the presence of cycles general TFS subsumption is not well founded. We show an application of this result for parsing, where the well-foundedness of subsumption is used to guarantee termination for grammars that are off-line parsable. We define a new version (...) of off-line parsability that is less strict than the existing one; thus termination is guaranteed for parsing with a larger set of grammars. (shrink)

Those who wish to claim that all facts about grounding are themselves grounded (“the meta-grounding thesis”) must defend against the charge that such a claim leads to infinite regress and violates the well-foundedness of ground. In this paper, we defend. First, we explore three distinct but related notions of “well-founded”, which are often conflated, and three corresponding notions of infinite regress. We explore the entailment relations between these notions. We conclude that the meta-grounding thesis need not lead (...) to tension with any of the three notions of “well-founded”. Finally, we explore the details of and motivations for further conditions on ground that one might add to generate a conflict between the meta-grounding thesis and a well-founded constraint. We explore these topics by developing and utilizing a formal framework based on the notion of a grounding structure. (shrink)

A growing number of philosophers are concerned with the epistemic status of culturally nurtured beliefs, beliefs found especially in domains of morals, politics, philosophy, and religion. Plausibly, worries about the deep impact of cultural contingencies on beliefs in these domains of controversial views is a question about well-foundedness: Does it defeat well-foundedness if the agent is rationally convinced that she would take her own reasons for belief as insufficiently well-founded, or would take her own belief (...) as biased, had she been nurtured in a different psychographic community? This chapter will examine the proper scope and force of this epistemic location problem. It sketches an account of well and ill-founded nurtured belief based upon the many markers of doxastic strategies exhibiting low to high degrees of inductive risk: the moral and epistemic risk of ‘getting it wrong’ in an inductive context of inquiry. (shrink)

According to Alan Millar, justified beliefs are well-founded beliefs. Millar cashes out the notion of well-foundedness in terms of having an adequate reason to believe something and believing it for that reason. To make his account of justified belief compatible with perceptual justification he appeals to the notion of recognitional ability. It is argued that, due to the fact that Millar’s is a knowledge-first view, his appeal to recognitional abilities fails to offer an explanatory account of familiar (...) cases in the literature and, as a consequence, of the notion of perceptual justification. (shrink)

The generality problem is perhaps the most notorious problem for process reliabilism. Several recent responses to the generality problem have claimed that the problem has been unfairly leveled against reliabilists. In particular, these responses have claimed that the generality problem is either (i) just as much of a problem for evidentialists, or (ii) if it is not, then a parallel solution is available to reliabilists. Along these lines, Juan Comesaña has recently proposed solution to the generality problem—well-founded reliabilism. According (...) to Comesaña, the solution to the generality problem lies in solving the basing problem, such that any solution to the basing problem will give a solution to the generality problem. Comesaña utilizes Conee and Feldman’s evidentialist account of basing (Conee and Feldman’s well-foundedness principle) in forming his version of reliabilism. In this paper I show that Comesaña’s proposed solution to the generality problem is inadequate. Well-founded reliabilism both fails to solve the generality problem and subjects reliabilism to new damning verdicts. In addition, I show that evidentialism does not face any parallel problems, so the generality problem remains a reason to prefer evidentialism to reliabilism. (shrink)

Gaisi Takeuti extended Gentzen's work to higher-order case in 1950's–1960's and proved the consistency of impredicative subsystems of analysis. He has been chiefly known as a successor of Hilbert's school, but we pointed out in the previous paper that Takeuti's aimed to investigate the relationships between "minds" by carrying out his proof-theoretic project rather than proving the "reliability" of such impredicative subsystems of analysis. Moreover, as briefly explained there, his philosophical ideas can be traced back to Nishida's philosophy in Kyoto's (...) school. For the proving the consistency of such systems, it is crucial to prove the well-foundedness of ordinals called "ordinal diagrams" developed for it. Takeuti presented such arguments several times in order to show that they are admitted in his stand point. As a starting point of investigating his finitist stand point, we formulate the system of ordinal notations up to ε0 and reconstruct the well-foundedness arguments of them. (shrink)

Should a philosophical account of perceptual knowledge accord a justificatory role to sensory experiences? This discussion raises problems for an affirmative answer and sets out an alternative account on which justified belief is conceived as well-founded belief and well-foundedness is taken to depend on knowledge. A key part of the discussion draws on a conception of perceptual-recognitional abilities to account for how perception gives rise both to perceptual knowledge and to well-founded belief.

We construct by diagonalization a non-well-founded primitive recursive tree, which is well-founded for co-r.e. sets, provable in Σ1 0. It follows that the supremum of order-types of primitive recursive well-orderings, whose well-foundedness on co-r.e. sets is provable in Σ1 0, equals the limit of all recursive ordinals ω1 ck . RID=""ID="" Mathematics Subject Classification (2000): 03B30, 03F15 RID=""ID="" Supported by the Deutschen Akademie der Naturforscher Leopoldina grant #BMBF-LPD 9801-7 with funds from the Bundesministerium für Bildung, (...) Wissenschaft, Forschung und Technologie. RID=""ID="" I would like to thank A. SETZER for his hospitality during my stay in Uppsala in December 1998 – these investigations are inspired by a discussion with him; S. BUSS for his hospitality during my stay at UCSD and for valuable remarks on a previous version of this paper; and M. MÖLLERFELD for remarks on a previous title. (shrink)

This paper investigates provability and non-provability of well-foundedness of ordinal notations in weak theories of bounded arithmetic. We define a notion of well-foundedness on bounded domains. We show that T21 and S22 can prove the well-foundedness on bounded domains of the ordinal notations below 0 and Γ0. As a corollary, the class of polynomial local search problems, PLS, can be augmented with cost functions that take ordinal values below 0 and Γ0 without increasing the (...) class PLS. (shrink)

This paper investigates provability and non-provability of well-foundedness of ordinal notations in weak theories of bounded arithmetic. We define a notion of well-foundedness on bounded domains. We show that T21 and S22 can prove the well-foundedness on bounded domains of the ordinal notations below 0 and Γ0. As a corollary, the class of polynomial local search problems, PLS, can be augmented with cost functions that take ordinal values below 0 and Γ0 without increasing the (...) class PLS. (shrink)

Introduction -- Elucidating complexity theories -- Complexity in the natural sciences -- Complexity in social theory -- Towards transdisciplinarity -- Complexity in philosophy: complexification and the limits to knowledge -- Complexity in ethics -- Earth in the anthropocene -- Complexity and climate change -- American dreams, ecological nightmares and new visions -- Complexity and sustainability: wicked problems, gordian knots and synergistic solutions -- Conclusion.

In Improvisation, Samuel Wells defines improvisation in the theater as "a practice through which actors seek to develop trust in themselves and one another in order that they may conduct unscripted dramas without fear." Sounds a lot like life, doesn't it? Building trust, overcoming fear, conducting relationships, and making choices--all without a script. Wells establishes theatrical improvisation as a model for Christian ethics, a matter of "faithfully improvising on the Christian tradition." He views the Bible not as a "script" but (...) as a "training school" that shapes the habits and practices of the Christian community. Drawing on scriptural narratives and church history, Wells explains six practices that characterize both improvisation and Christian ethics. His model of improvisation reinforces the goal of Christian ethics--to teach Christians to "embody their faith in the practices of discipleship all the time."--Publisher description. (shrink)

It is widely held that, in his pre-Critical works, Kant endorsed a necessitation account of laws of nature, where laws are grounded in essences or causal powers. Against this, I argue that the early Kant endorsed the priority of laws in explaining and unifying the natural world, as well as their irreducible role in in grounding natural necessity. Laws are a key constituent of Kant’s explanatory naturalism, rather than undermining it. By laying out neglected distinctions Kant draws among types (...) of natural law, grounding relations, and ontological levels, I show that his early works present a coherent and sophisticated laws-first account of the natural order. (shrink)

The story of God -- The story of the church -- The story of ethics -- The story of Christian ethics -- Universal ethics -- Subversive ethics -- Ecclesial ethics -- Good order -- Good life -- Good relationships -- Good beginnings and endings -- Good earth.

Contemporary metaphysicians have been drawn to a certain attractive picture of the structure of the world. This picture consists in classical mereology, the priority of parts over wholes, and the well-foundedness of metaphysical priority. In this short note, I show that this combination of theses entails superatomism, which is a significant strengthening of mereological atomism. This commitment has been missed in the literature due to certain sorts of models of mereology being overlooked. But the entailment is an important (...) one: we must either accept superatomism or reject one (or other) of the most widespread theses of contemporary metaphysics. (shrink)

I reconstruct J. H. Lambert’s views on how practical grounds relate to epistemic features, such as certainty. I argue, first, that Lambert’s account of moral certainty does not involve any distinctively practical influence on theoretical belief. However, it does present an interesting form of fallibilism about justification as well as a denial of a tight link between knowledge and action. Second, I argue that for Lambert, the persistence principle that underwrites induction is supported by practical reasons to believe; this (...) indicates that Lambert is a moderate pragmatist about reasons for theoretical belief. (shrink)

I begin by outlining Du Châtelet’s ontology of mathematical objects: she is an idealist, and mathematical objects are fictions dependent on acts of abstraction. Next, I consider how this idealism can be reconciled with her endorsement of necessary truths in mathematics, which are grounded in essences that we do not create. Finally, I discuss how mathematics and physics relate within Du Châtelet’s idealism. Because the primary objects of physics are partly grounded in the same kinds of acts as yield mathematical (...) objects, she thinks we are sometimes licensed in drawing conclusions about physical things from mathematical premises. (shrink)

The 'Why ain'cha rich?' argument for one-boxing in Newcomb's problem allegedly vindicates evidential decision theory and undermines causal decision theory. But there is a good response to the argument on behalf of causal decision theory. I develop this response. Then I pose a new problem and use it to give a new 'Why ain'cha rich?' argument. Unlike the old argument, the new argument targets evidential decision theory. And unlike the old argument, the new argument is sound.

I argue that Émilie Du Châtelet breaks with Christian Wolff regarding the scope and epistemological content of the principle of sufficient reason, despite his influence on her basic ontology and their agreement that the principle of sufficient reason has foundational importance. These differences have decisive consequences for the ways in which Du Châtelet and Wolff conceive of science.

Du Châtelet holds that mathematical representations play an explanatory role in natural science. Moreover, she writes that things proceed in nature as they do in geometry. How should we square these assertions with Du Châtelet’s idealism about mathematical objects, on which they are ‘fictions’ dependent on acts of abstraction? The question is especially pressing because some of her important interlocutors (Wolff, Maupertuis, and Voltaire) denied that mathematics informs us about the properties of material things. After situating Du Châtelet in this (...) debate, this chapter argues, first, that her account of the origins of mathematical objects is less subjectivist than it might seem. Mathematical objects are non-arbitrary, public entities. While mathematical objects are partly mind-dependent, so are material things. Mathematical objects can approximate the material. Second, it is argued that this moderate metaphysical position underlies Du Châtelet’s persistent claims that mathematics is required for certain kinds of general knowledge, including in natural science. The chapter concludes with an illustrative example: an analysis of Du Châtelet’s argument that matter is continuous. A key premise in the argument is that mathematical representations and material nature correspond. (shrink)

I examine Du Châtelet’s methodology for physics and metaphysics through the lens of her engagement with Newton’s Rules for Reasoning in Natural Philosophy. I first show that her early manuscript writings discuss and endorse these Rules. Then, I argue that her famous published account of hypotheses continues to invoke close analogues of Rules 3 and 4, despite various developments in her position. Once relevant experimental evidence and some basic constraints are met, it is legitimate to inductively generalize from observations; general (...) hypotheses can thereafter be assumed as true until contrary experiments show otherwise. I conclude by arguing that this account of induction plays an essential role in her metaphysics, both in an argument for simple substances—which has an inductive premise—and in her attempt to distinguish acceptable and unacceptable metaphysical commitments. (shrink)

The principle of informed consent obligates physicians to explain possible side effects when prescribing medications. This disclosure may itself induce adverse effects through expectancy mechanisms known as nocebo effects, contradicting the principle of nonmaleficence. Rigorous research suggests that providing patients with a detailed enumeration of every possible adverse event—especially subjective self-appraised symptoms—can actually increase side effects. Describing one version of what might happen (clinical “facts”) may actually create outcomes that are different from what would have happened without this information (another (...) version of “facts”). This essay argues that the perceived tension between balancing informed consent with nonmaleficence might be resolved by recognizing that adverse effects have no clear black or white “truth.” This essay suggests a pragmatic approach for providers to minimize nocebo responses while still maintaining patient autonomy through “contextualized informed consent,” which takes into account possible side effects, the patient being treated, and the particular diagnosis involved. (shrink)

For Émilie Du Châtelet, I argue, a central role of the principle of sufficient reason is to discriminate between better and worse explanations. Her principle of sufficient reason does not play this role for just any conceivable intellect: it specifically enables understanding for minds like ours. She develops this idea in terms of two criteria for the success of our explanations: “understanding how” and “understanding why.” These criteria can respectively be connected to the determinateness and contrastivity of explanations. The crucial (...) role Du Châtelet’s principle of sufficient reason plays in identifying good explanations is often overlooked in the literature, or else run together with questions about the justification and likelihood of explanations. An auxiliary goal of the article is to situate Du Châtelet’s principle of sufficient reason with respect to some of the general epistemological and metaphysical commitments of her Institutions de Physique, clarifying how it fits into the broader project of that work. (shrink)

Adam Smith is respected as the father of contemporary economics for his work on systemizing classical economics as an independent field of study in The Wealth of Nations. But he was also a significant moral philosopher of the Scottish Enlightenment, with its characteristic concern for integrating sentiments and rationality. This article considers Adam Smith as a key moral philosopher of commercial society whose critical reflection upon the particular ethical challenges posed by the new pressures and possibilities of commercial society remains (...) relevant today. The discussion has three parts. First I address the artificial separation between self-interest and morality often attributed to Smith, in which his work on economics is stripped of its ethical context. Second I outline Smith’s ethical approach to economics, focusing on his vigorous but qualified defence of commercial society for its contributions to prosperity, justice, and freedom. Third I outline Smith’s moral philosophy proper as combining a naturalistic account of moral psychology with a virtue ethics based on propriety in commercial society. (shrink)

Whether or not capitalism is compatible with ethics is a long standing dispute. We take up an approach to virtue ethics inspired by Adam Smith and consider how market competition influences the virtues most associated with modern commercial society. Up to a point, competition nurtures and supports such virtues as prudence, temperance, civility, industriousness and honesty. But there are also various mechanisms by which competition can have deleterious effects on the institutions and incentives necessary for sustaining even these most commercially (...) friendly of virtues. It is often supposed that if competitive markets are good, more competition must always be better. However, in the long run competition enhancing policies that neglect the nurturing and support of the bourgeois virtues may undermine the continued flourishing of modern commercial society. (shrink)

Draft for presentation at the 14th International Kant-Congress, September 2024. -/- Abstract: Kant claims we intuit infinite space. There’s a problem: Kant thinks full awareness of infinite space requires synthesis—the act of putting representations together and comprehending them as one. But our ability to synthesize is finite. Tobias Rosefeldt has argued in a recent paper that Kant’s notion of decomposing synthesis offers a solution. This talk criticizes Rosefeldt’s approach. First, Rosefeldt is committed to nonconceptual yet determinate awareness of (potentially) infinite (...) space, but I argue that such awareness is (1) prima facie implausible, as well as contravened by textual evidence from Kant’s (2a) definitions of ‘infinity’ and (2b) account of geometrical construction. Second, scrutiny of how Kant thinks awareness of potential infinity is afforded by geometrical construction (e.g., extending a line segment ad indefinitum) indicates no essential role for decomposing synthesis. Familiar synthesis from parts to wholes is sufficient. (shrink)

The crisis in the meaning of freedom -- What is freedom? -- Limiting freedom -- Freedom and justice -- Why we should accept this view of freedom -- Conditions that make us more free -- Applying the theory to the real world --Conclusion -- Appendix for professional philosophers -- Notes.

There is a tension in Emilie Du Châtelet’s thought on mathematics. The objects of mathematics are ideal or fictional entities; nevertheless, mathematics is presented as indispensable for an account of the physical world. After outlining Du Châtelet’s position, and showing how she departs from Christian Wolff’s pessimism about Newtonian mathematical physics, I show that the tension in her position is only apparent. Du Châtelet has a worked-out defense of the explanatory and epistemic need for mathematical objects, consistent with their metaphysical (...) nonfundamentality. I conclude by sketching how Du Châtelet’s conception of mathematical indispensability differs interestingly from many contemporary approaches. (shrink)