This paper discusses some of the ways in which circular definitions and circular explanations entail or fail to entail infinite regresses. And since not all infinite regresses are vicious, a few criteria of viciousness are examined in order to determine when the entailment of a regress refutes a circular definition or a circular explanation.

이 글은 『지성 교정론』의 미완의 이유로 제기된 다양한 가설들 가운데 방법이라는 기획 자체의 문제를 다룬다. 스피노자는 가상의 반박자의 입을 빌려 방법의 기획에 다음과 같은 치명적 문제를 제기한다. 첫째, 올바른 방법을 마련하려면 그것을 마련할 올바른 방법이, 또 이를 발견할 올바른 방법 등등이 필요하지 않은가? (무한퇴행의 문제) 둘째, 방법의 출발점인 주어진 참된 관념의 참됨은 어떻게 보증하는가? (진리의 보증 문제) 셋째, 진리는 스스로 참됨을 드러내는데 인식 과정과 별도로 방법이 왜 필요한가? (방법의 필요 문제) 스피노자는 인식에 대한 방법의 내재성과 진리의 자기현시를 통해 앞의 두 (...) 물음에 답함과 동시에, 스스로를 베이컨 및 데카르트의 입장과 차별화한다. 단 마지막 문제는 내가 보기에 충분히 답변되지 않았으며, 나는 여기에 논고가 미완으로 남은 이유가 함축되어 있다고 본다. 곧 방법 논의는 한편으로는 관념들의 발생적 원인에 대한 논의로 대체되어야 했고, 다른 한편으로는 진리의 자기현시를 가로막는 편견이나 정념의 치유에 대한 논의로 대체되어야 했다. (shrink)

Dispositional monism is the view that natural properties and relations are ‘pure powers’. It is objected that dispositional monism involves some kind of vicious or otherwise unpalatable regress or circularity. I examine ways of making this objection precise. The most pressing interpretation is that is fails to make the identities of powers determinate. I demonstrate that this objection is in error. It does however puts certain constraints on what the structure of fundamental properties is like. I show what a (...) satisfactory structure would be. (shrink)

Influenced by the Wittgensteinian slogan “Don’t look for the meaning, look for the use,” ordinary language philosophers aimed to defuse various philosophical problems by analyzing key words in terms of what they are used to do or the conditions for appropriately using them. Although Moore, Grice and Searle exposed this error – mixing pragmatics with semantics – it still gets committed, now to a different end. Nowadays the aim is to reckon with the fact that the meanings of a great (...) many sentences underdetermine what we would normally mean in using them – even if the sentence is free of indexicality, ambiguity, and vagueness. This can be so because the sentence expresses a “minimal” proposition or even because it doesn’t fully express any proposition. Many theorists are led to defend “truth-conditional pragmatics” (or linguistic “contextualism”), to find a hidden indexical in every syntactic nook or semantic cranny, or otherwise to pay undue respect to seemingly semantic intuitions and intentions. This paper identifies various such moves and explains what’s regressive about them. (shrink)

Is structure a fundamental and indispensable part of the world? Is the question of ontology a question about structure? Structure is a central notion in contemporary metaphysics [Sider 2011. Writing the Book of the World. Oxford: Clarendon Press]. Realism about structure claims that the question of ontology is about the fundamental and indispensable structure of the world. In this paper, I present a criticism of the metaphysics of realism about structure based on a version of Russell’s famous regress argument (...) against nominalism [Russell 1911. “On the Relation of Universals and Particular.” In Logic & Knowledge. Reprint, London: George Allen & Unwin]. First, I argue that the three general tests for the fundamentality of structure proposed by realism about structure rely on a particular empirical test for structure, namely, the so-called ‘similarity test for structure.’ Second, I argue that the similarity test is not well-founded because it leads to a vicious regress. Third, I argue that the regress affects the whole metaphysics of realism about structure, and that no structural notion can be said to be fundamental in connection with any of the other tests. Lastly, I argue that the question of ontology as a question about structure is not substantive. (shrink)

In order to ward off the global threat of a regress of justification, Brandom argues that some claims in our linguistic practices must be treated as “innocent until proven guilty’, i.e. participants must be treated as prima facie entitled when making them. Examples he gives include claims such as “There have been black dogs” and “I have ten fingers”. Brandom calls this idea “the default and challenge structure of entitlement”. In On Certainty, Wittgenstein argues that there are basic certainties (...) (“hinge propositions” or “hinges”) such as “The world existed long before I was born” or “This is a tree” that cannot be meaningfully doubted because they provide the basic frameworks for our language–games in the first place. The aim of this article is threefold. First, it offers an understanding of Brandom’s philosophical project in the light of Wittgenstein’s On Certainty. Secondly, it shows how Brandom may help to elucidate some of the more mysterious passages in Wittgenstein’s “third masterpiece”. Thirdly, it outlines a sketch of a promising solution to an old philosophical riddle. (shrink)

If an argument can be reconstructed in at least two different ways, then which reconstruction is to be preferred? In this paper I address this problem of argument reconstruction in terms of Ryle’s infinite regress argument against the view that knowledge-how requires knowledge-that. First, I demonstrate that Ryle’s initial statement of the argument does not fix its reconstruction as it admits two, structurally different reconstructions. On the basis of this case and infinite regress arguments generally, I defend a (...) revisionary take on argument reconstruction: argument reconstruction is mainly to be ruled by charity (viz. by general criteria which arguments have to fulfil in order to be good arguments) rather than interpretation. (shrink)

This book on infinite regress arguments provides (i) an up-to-date overview of the literature on the topic, (ii) ready-to-use insights for all domains of philosophy, and (iii) two case studies to illustrate these insights in some detail. Infinite regress arguments play an important role in all domains of philosophy. There are infinite regresses of reasons, obligations, rules, and disputes, and all are supposed to have their own moral. Yet most of them are involved in controversy. Hence the question (...) is: what exactly is an infinite regress argument, and when is such an argument a good one? (shrink)

Infinite regress arguments are part of a philosopher's tool kit of argumentation. But how sharp or strong is this tool? How effectively is it used? The typical presentation of infinite regress arguments throughout history is so succinct and has so many gaps that it is often unclear how an infinite regress is derived, and why an infinite regress is logically problematic, and as a result, it is often difficult to evaluate infinite regress arguments. These consequences (...) of our customary way of using this tool indicate that there is a need for a theory to re-orient our practice. My general approach to contribute to such a theory, consists of collecting and evaluating as many infinite regress arguments as possible, comparing and contrasting many of the formal and non-formal properties, looking for recurring patterns, and identifying the properties that appeared essential to those patterns. Two very general questions guided this work: How are infinite regresses generated in infinite regress arguments? How do infinite regresses logically function as premises in an argument? In answering these questions I clarify the notion of an infinite regress; identify different logical forms of infinite regresses; describe different kinds of infinite regress arguments; distinguish the rhetoric from the logic in infinite regress arguments; and suggest ways of improving our discussion and our practice of constructing and evaluating these arguments. (shrink)

This paper presents a slightly modified version of the compositional semantics proposed in Events and Semantic Architecture (OUP 2005). Some readers may find this shorter version, which ignores issues about vagueness and causal constructions, easier to digest. The emphasis is on the treatments of plurality and quantification, and I assume at least some familiarity with more standard approaches.

In his paper "Undecidability without arithmetization," Andrzej Grzegorczyk introduces a theory of concatenation $\mathsf{TC}$. We show that pairing is not definable in $\mathsf{TC}$. We determine a reasonable extension of $\mathsf{TC}$ that is sequential, that is, has a good sequence coding.

Plausibly, no agent ever performs an action without some desire to perform that action. If so, a regress argument shows that, given incompatibilism, we are only rarely free. The argument sidesteps recent objections to this thesis.

Infinite regress arguments play an important role in many distinct philosophical debates. Yet, exactly how they are to be used to demonstrate anything is a matter of serious controversy. In this paper I take up this metaphilosophical debate, and demonstrate how infinite regress arguments can be used for two different purposes: either they can refute a universally quantified proposition (as the Paradox Theory says), or they can demonstrate that a solution never solves a given problem (as the Failure (...) Theory says). In the meantime, I show that Black’s view on infinite regress arguments (1996, this journal) is incomplete, and how his criticism of Passmore can be countered. (shrink)

We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.

The phenomenon of regression toward the mean is notoriously liable to be overlooked or misunderstood; regression fallacies are easy to commit. But even when regression phenomena are duly recognized, it remains perplexing how they can feature in explanations. This article develops a philosophical account of regression explanations as “statistically autonomous” explanations that cannot be deepened by adducing details about causal histories, even if the explananda as such are embedded in the causal structure of the world. That regression explanations have statistical (...) autonomy was first suggested by Ian Hacking and has recently been defended and elaborated by André Ariew, Yasha Rohwer, and Collin Rice. However, I will argue that these analyses fail to capture what regression’s statistical autonomy consists in and how it sets regression explanations apart from other kinds of explanation. The alternative account I develop also shows what is amiss with a recent denial of regression’s statistical autonomy. Marc Lange has argued that facts that can be explained as regression phenomena can in principle also be explained by citing a conjunction of causal histories. The account of regression explanation developed here shows that his argument is based on a misunderstanding of the nature of statistical autonomy. (shrink)

We consider weak theories of concatenation, that is, theories for strings or texts. We prove that the theory of concatenation WTC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}^{-\varepsilon}}$$\end{document}, which is a weak subtheory of Grzegorczyk’s theory TC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{TC}^{-\varepsilon}}$$\end{document}, is a minimal essentially undecidable theory, that is, the theory WTC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}^{-\varepsilon}}$$\end{document} is essentially undecidable and if one omits an axiom scheme from WTC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} (...) \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}^{-\varepsilon}}$$\end{document}, then the resulting theory is no longer essentially undecidable. Moreover, we give a positive answer to Grzegorczyk and Zdanowski’s conjecture that ‘The theory TC-ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{TC}^{-\varepsilon}}$$\end{document} is a minimal essentially undecidable theory’. For the alternative theories WTC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{WTC}}$$\end{document} and TC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{TC}}$$\end{document} which have the empty string, we also prove that the each theory without the neutrality of ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon}$$\end{document} is to be such a theory too. (shrink)

The best extant statement of the epistemic regress problem makes assumptions that are too strong. An improved version assumes only that that reasons require support, that no proposition is supported only by endless regresses of reasons, and that some proposition is supported. These assumptions are individually plausible but jointly inconsistent. Attempts to explain support by means of unconceptualized sensations, contextually immunized propositions, endless regresses, and holistic coherence all require either additional reasons or an external condition on support that is (...) arbitrary from the believer's own point of view. (shrink)

This article looks at Galton's regression to the mean from several traditionally unrelated but interwoven venues: as a law of trait heredity; as a statistical artifact infiltrating careless research designs; as an illustration of cognitive bias. Hereditarians argue for the first of these, disputed by biogeneticists, who view R to M as a mere correlate of generational traits decline. Research designers busy themselves with the second perspective, but to explain the concept, cavalierly adduce various organismic states that sum as "error (...) variance" Research on subjective probability finds R to M in unexpected places. Across these contexts, the weight of argument falls on R to M's confounding rather than causal role in vexing data analysis. 2012 APA, all rights reserved). (shrink)

This paper considers the possibility of prediction in land use planning, and the use of statistical research methods in analyses of relationships between urban form and travel behaviour. Influential writers within the tradition of critical realism reject the possibility of predicting social phenomena. This position is fundamentally problematic to public planning. Without at least some ability to predict the likely consequences of different proposals, the justification for public sector intervention into market mechanisms will be frail. Statistical methods like regression analyses (...) are commonly seen as necessary in order to identify aggregate-level effects of policy measures, but are questioned by many advocates of critical realist ontology. Using research into the relationship between urban structure and travel as an example, the paper discusses relevant research methods and the kinds of prediction necessary and possible in spatial planning of urban development. Finally, the political implications of positions within theory of science rejecting the possibility of predictions about social phenomena are addressed. (shrink)

The epistemic regress problem is about the possibility of having beliefs that are based on evidence. The problem of the criterion is about the possibility of having beliefs that are based on general standards for distinguishing what is true from what is false. These problems are similar. Each is constituted by a set of propositions about epistemically valuable relational properties—being supported by evidence and being authorized by a criterion of truth—that are individually plausible but jointly inconsistent, a paradox. The (...) propositions that constitute one problem have the same forms as the propositions that constitute the other. In particular, each problem turns on the claim that a belief can have a valuable relational property only by means of an endless regress and that this requirement cannot be satisfied. Finally, since evidence and criteria are kinds of reasons, each problem is about the possibility of having beliefs that are based on reasons. (shrink)

That a philosophical thesis entails a vicious regress is commonly taken to be decisive evidence that the thesis is false. In this paper, I argue that the existence of a vicious regress is insufficient to reject a proposed analysis provided that certain constraints on the analysis are met. When a vicious regress is present, some further consequence of the thesis must be established that, together with the presence of the vicious regress, shows the thesis to be (...) false. The argument is provided largely through the examination of Michael Bergmann's vicious regress argument against strong awareness internalism and a partial defense of that thesis against Bergmann. (shrink)

Logical pluralism is the theory that there is more than one right logic. Logical instrumentalism is the view that a logic is a correct logic if it can be used to fruitfully pursue some deductive inquiry. Logical instrumentalism is a version of logical pluralism, since more than one logic can be used fruitfully. In this paper, I will show that a logical instrumentalist must accept linear logic as a correct logic, since linear logic is useful for studying natural language syntax. (...) I further show that this means that the logical instrumentalist must accept a wide range of connectives, in particular concatenation. I end by explaining why this is a feature rather than a bug. (shrink)

This paper uses a schema for infinite regress arguments to provide a solution to the problem of the infinite regress of justification. The solution turns on the falsity of two claims: that a belief is justified only if some belief is a reason for it, and that the reason relation is transitive.

In the last decade, the familiar problem of the regress of reasons has returned to prominent consideration in epistemology. And with the return of the problem, evaluation of the options available for its solution is begun anew. Reason’s regress problem, roughly put, is that if one has good reasons to believe something, one must have good reason to hold those reasons are good. And for those reasons, one must have further reasons to hold they are good, and so (...) a regress of reasons looms. In this new study, Aikin presents a full case for infinitism as a response to the problem of the regress of reasons. Infinitism is the view that one must have a non-terminating chain of reasons in order to be justified. The most defensible form of infinitism, he argues, is that of a mixed theory – that is, epistemic infinitism must be consistent with and integrate other solutions to the regress problem. (shrink)

How should you decide what to do when you’re uncertain about basic normative principles? A natural suggestion is to follow some "second-order:" norm: e.g., obey the most probable norm or maximize expected choiceworthiness. But what if you’re uncertain about second-order norms too—must you then invoke some third-order norm? If so, any norm-guided response to normative uncertainty appears doomed to a vicious regress. This paper aims to rescue second-order norms from the threat of regress. I first elaborate and defend (...) the claim some philosophers have made that the regress problem forces us to accept normative externalism, the view that at least one norm is incumbent on all agents regardless of their normative beliefs. But, I then argue, we need not accept externalism about first-order norms, thus closing off any question of how agents should respond to normative uncertainty. Rather, we can head off the threat of regress by ascribing external force to a single second-order norm: the enkratic principle. (shrink)

Is the content of our thoughts determined by norms such as ‘if I know that p, then I ought to believe that p’? Glüer & Wikforss (2009a) set forth a regress argument for a negative answer. The aim of this paper is to clarify and evaluate this argument. In the first part I show how it (just like an argument from Wittgenstein 1953) can be taken as an instance of an argument schema. In the second part, I evaluate the (...) relevant premises in some detail, and argue that the dialectical situation is slightly more complicated than a ‘dilemma of regress and idleness’, as Glüer & Wikforss have dubbed it. (shrink)

Saul Kripke recently has published an interpretation of the later Wittgenstein's rule-following problem as a "sceptical paradox," the conclusion of which is that language is impossible. In this dissertation, I document the history of the rule-following problem in Wittgenstein's writings, thereby providing a historical perspective not provided by Kripke. In chapters I and II, I develop a broadly Kantian interpretation of the epistemology of the Tractatus. My interpretation conflicts both with interpretations according to which the Tractatus implicitly embodies an empiricist (...) epistemology or no epistemology at all and with idealist readings. In chapter III, I extend the comparison between Wittgenstein and Kant, arguing that there is an important sense in which the notion of thought is fundamental in the Tractatus. My interpretation conflicts with interpretations according to which the Tractarian theory of meaning requires a mental act of "dubbing" which correlates signs and objects as well as with interpretations according to which nothing mental is presupposed. On one hand, chapters I-III can be read independently of chapters IV and V as an interpretation of some aspects of the Tractatus. On the other hand, these chapters lay the groundwork for my argument in chapter IV that the rule-following problem in the Philosophical Investigations is a general and forceful restatement of the problem of an infinite regress of interpretations to which the Tractarian theory of meaning was supposed to provide a solution. For various reasons, which I recount, Wittgenstein became dissatisfied with his early answer, and the problem reappears in his later work. Finally, in chapter V, I present and evaluate Kripke's interpretation of the rule-following problem from the historical perspective developed in the preceding chapters. I suggest that Kripke fails to see that it is a carry-over of a problem with which Wittgenstein wrestled in the Tractatus. In addition, although he recognizes that the later Wittgenstein believes that no fact or process could account for our ability to represent the world, he does not show clearly why Wittgenstein believes that this is so. (shrink)

On Malcolm Schofield’s highly influential reading of the Similarity Regress in Part I of the Parmenides, the problem that the Regress poses is explanatory. Socrates posited the Similarity Form in order to explain why similar things are similar: similar things are similar because they participate in the Form Similarity as copies of the same original. Yet, the Similarity Regress generates an infinite series of Similarity Forms such that explanation is deferred ad infinitum. Schofield provides a philosophical incentive (...) for adopting his reading. He argues that the treatment of similarity in Part II of the dialogue yields a complete explanation of similarity. If we adopt this account, we can avoid the Similarity Regress altogether since a Form of Similarity is not needed in order to explain why similar things are similar. Thus, his interpretation has a hugely important philosophical pay-off. However, there is a different way to read the argument. Socrates claims that each Form is only one. Yet, the Similarity Regress is an argument that generates an infinite series of Similarity Forms. This results in a violation of the principle of non-contradiction: there is both only one Similarity Form and infinitely many Similarity Forms. Yet, anything that is incompatible with the principle of non-contradiction is surely absurd. Nobody, as far as I am aware, has explored whether this reading also has philosophical pay-off if we look at it together with similarity in Part II. However, should this interpretation pay off, it would be a viable alternative to Schofield’s. In this paper, I explore both views in the context of the treatment of similarity in Part II of the Parmenides. I argue for an account of similarity that differs from Schofield’s. Although my account is not wholly dismissive of Schofield’s, it renders the pay-off of Schofield’s account less appealing than he suggests. Furthermore, I show that the account of similarity in Part II also yields important lessons for the proponent of the alternative reading of the Similarity Regress: similarity as treated in Part II simply leads to further infinite regresses, thereby pushing us to consider rejecting the account of similarity in Part II too and to look for some other account intead. (shrink)

This paper presents a regress challenge to the selective psychological debunking of moral judgments. A selective psychological debunking argument conjoins an empirical claim about the psychological origins of certain moral judgments to a theoretical claim that these psychological origins cannot track moral truth, leading to the conclusion that the moral judgments are unreliable. I argue that psychological debunking arguments are vulnerable to a regress challenge, because the theoretical claim that ‘such-and-such psychological process is not moral-truth-tracking’ relies upon moral (...) judgments. We must then ask about the psychological origins of these judgments, and then make a further evaluative judgment about these psychological origins… and so on. This chain of empirical and evaluative claims may continue indefinitely and, I will argue, proponents of the debunking argument are in a dialectical position where they may not simply call a halt to the process. Hence, their argument cannot terminate, and its debunking conclusion cannot be upheld. (shrink)

We define a new theory of concatenation WTC which is much weaker than Grzegorczyk's well-known theory TC. We prove that WTC is mutually interpretable with the weak theory of arithmetic R. The latter is, in a technical sense, much weaker than Robinson's arithmetic Q, but still essentially undecidable. Hence, as a corollary, WTC is also essentially undecidable.

In this paper I argue that the infinite regress of resemblance is vicious in the guise it is given by Russell but that it is virtuous if generated in a (contemporary) trope theoretical framework. To explain why this is so I investigate the infinite regress argument. I find that there is but one interesting and substantial way in which the distinction between vicious and virtuous regresses can be understood: The Dependence Understanding. I argue, furthermore, that to be able (...) to decide whether an infinite regress exhibits a dependence pattern of a vicious or a virtuous kind, facts about the theoretical context in which it is generated become essential. It is precisely because of differences in context that he Russellian resemblance regress is vicious whereas its trope theoretical counterpart is not. (shrink)

The paper aims to elucidate in better detail than before the dispute about whether or not dispositional monism—the view that all basic properties are pure powers—entails a vicious infinite regress. Particular focus is on Alexander Bird's and George Molnar's attempts to show that the arguments professing to demonstrate a vicious regress are inconclusive because they presuppose what they aim to prove, notably that powers are for their nature dependent on something else. I argue that Bird and Molnar are (...) mistaken. It is true that dispositional monism is popularly assumed to characterize powers as dependent entities, but this is not what the arguments aim to prove. They merely aim to demonstrate that it would be absurd to assume that all properties are dependent in this way. Finally, it is argued that there is an unresolved tension in Bird's and Molnar's accounts of powers. They characterize them as being for their nature dependent on the manifestations that they are for, and yet ontologically independent of those same manifestations. Until that tension is resolved, their accounts are not equipped to remove the threat of vicious regress. (shrink)

There are important similarities between the epistemic regress problem and the problem of the criterion. Each turns on plausible principles stating that epistemic reasons must be supported by epistemic reasons but that having reasons is impossible if that requires having endless regresses of reasons. These principles are incompatible with the possibility of reasons, so each problem is a paradox. Whether there can be an antiskeptical solution to these paradoxes depends upon the kinds of reasons that we need in order (...) to attain our epistemic goals. This article explains the problems and considers the ways in which two different conceptions of human flourishing support the value of different kinds of reasons. One conception requires reasons that allow an easy solution to these paradoxes. The other—rational autonomy—requires reasons that depend upon endless regresses. So we cannot have the kinds of fully transparent reasons required for rational autonomy. (shrink)

We prove that a variant of Robinson arithmetic $\mathsf{Q}$ with nontotal operations is interpretable in the theory of concatenation $\mathsf{TC}$ introduced by A. Grzegorczyk. Since $\mathsf{Q}$ is known to be interpretable in that nontotal variant, our result gives a positive answer to the problem whether $\mathsf{Q}$ is interpretable in $\mathsf{TC}$. An immediate consequence is essential undecidability of $\mathsf{TC}$.

In a regressive tax system, lower-income taxpayers pay larger percentages of their incomes in taxes compared to higher-income taxpayers. Although most policymakers and citizens view regressive taxation as generally unfair and unethical, the U.S. tax system taxes wage, salary, and self-employment income in a manner that deliberately subjects lower-income taxpayers to marginal tax rates that are greater than those imposed on higher-income taxpayers. As a result, some lower-income taxpayers pay a larger percentage of their income in taxes than higher-income taxpayers. (...) In this essay, we argue that this regressiveness in the taxation of salaried income is unfair and unethical. We then evaluate President Obama’s social security plan, which would retain most of the current tax system’s regressive structure. Finally, we offer two simple alternative proposals that are non-regressive, and thus more fair and ethical approaches to the taxation of salaried income. (shrink)

Regress arguments have convinced many that reasoning cannot require beliefs about what follows from what. In this paper I argue that this is a mistake. Regress arguments rest on dubious (although deeply entrenched) assumptions about the nature of reasoning — most prominently, the assumption that believing p by reasoning is simply a matter of having a belief in p with the right causal ancestry. I propose an alternative account, according to which beliefs about what follows from what play (...) a constitutive role in reasoning. (shrink)

There are (at least) four numbers of physical and cosmological significance, whose inferred values, when expressed in mass units, cluster in a window below 1 eV. There are: the neutrino mass, the neutrino chemical potential, the cosmological constant, and the size of two extra dimensions (if the fundamental scale of gravity is 1–10 TeV). In this note, we imagine ways in which these four numbers could all be connected.

Recent work by Peijnenburg, Atkinson, and Herzberg suggests that infinitists who accept a probabilistic construal of justification can overcome significant challenges to their position by attending to mathematical treatments of infinite probabilistic regresses. In this essay, it is argued that care must be taken when assessing the significance of these formal results. Though valuable lessons can be drawn from these mathematical exercises (many of which are not disputed here), the essay argues that it is entirely unclear that the form of (...) infinitism that results meets a basic requirement: namely, providing an account of infinite chains of propositions qua reasons made available to agents. (shrink)

In this work we propose an encoding of Reiter’s Situation Calculus solution to the frame problem into the framework of a simple multimodal logic of actions. In particular we present the modal counterpart of the regression technique. This gives us a theorem proving method for a relevant fragment of our modal logic.

Wolff’s relation to Leibniz and Kant’s relation to both are notoriously vexed questions. First, this paper argues that Wolff’s most serious departure from Leibniz consists in his (so far overlooked) rejection of the latter’s infinitism. Second, it contends that the controversies that surrounded Wolff’s early acceptance of infinite causal regress and prompted his conversion to finitism played a prominent role in shaping the theses of Kant’s Antinomies. Whereas Leibniz and the early Wolff considered infinite regress to provide support (...) for the contingency of the world and the existence of God, Wolff’s enemies condemned it as Spinozistic. After Wolff, the claim that an infinite chain of causes is impossible became the standard view among both Wolffian and anti-Wolffian metaphysicians. (shrink)