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 (...) class='Hi'>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)

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)

The Language of Thought Hypothesis is often taken to have the fatal flaw that it generates an explanatory regress. The language of thought is invoked to explain certain features of natural language (e.g., that it is learned, understood, and is meaningful), but, according to the regress argument, the language of thought itself has these same features and hence no explanatory progress has been made. We argue that such arguments rely on the tacit assumption that the entire motivation (...) for the language of thought consists in explaining the explanandum that allegedly generates the regress. But this tacit assumption is simply false. The Language of Thought Hypothesis is a cogent view and one with considerable explanatory advantages. (shrink)

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.

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)

In this dissertation we discuss infinite regress arguments from both a historical and a logical perspective. Throughout we deal with arguments drawn from various areas of philosophy. ;We first consider the regress generating portion of the argument. We find two main ways in which infinite regresses can be developed. The first generates a regress by defining a relation that holds between objects of some kind. An example of such a regress is the causal (...) class='Hi'>regress used in some versions of the Cosmological Argument. The second sort of regress is generated by defining a certain procedure that can be repeated indefinitely many times. This will often be a procedure of analysis or of explanation. ;We then argue that for purposes of discussing regressive viciousness it is helpful to divide regresses into two main types. One type raises primarily epistemological issues. In this class we find the regress of justification often used in foundational arguments in epistemology. We also discuss certain arguments that treat theories of predication as attempts to explain predication. Our other class contains those regresses that raise primarily metaphysical problems. This class includes the causal regress as well as those arguments concerned with predication as an ontological problem. ;We agree with some philosophers that one problem that arises in the case of vicious regression is circularity. We show how this problem can be generalized to include other apparently non-circular regresses. The other main problem in epistemological regresses arises as a result of certain conditions that are placed on the relation involved. We look in detail at the epistemological justification regress to illustrate this last point. ;With respect to metaphysical regresses we again find several types of viciousness arguments. One problem is whether the infinite collection required for the regress is even possible. Another problem is whether an infinite number of events can occur in a finite time. These we deal with only briefly. The main difficulty with these regresses, considered as regresses and not just as infinite sets, again turns out to be certain conditions built into the relation involved. We focus on some arguments about causal regression to illustrate this point. ;Finally, we find no absolutely general conditions for regressive viciousness. There is, however, a certain limited range of ways in which a regress may be vicious. We make these ways explicit. (shrink)

Infinite regress arguments are used by philosophers as methods of refutation. A hypothesis is defective if it generates an infinite series when either such a series does not exist or its supposed existence would not serve the explanatory purpose for which it was postulated.

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 the literature, regress arguments often take one of two different forms: either they conclude that a given solution fails to solve any problem of a certain kind (the strong conclusion), or they conclude that a given solution fails to solve all problems of a certain kind (the weaker conclusion). This gives rise to a logical problem: do regresses entail the strong or the weaker conclusion, or none? In this paper I demonstrate that regress arguments can (...) in fact take both forms, and clearly set out the logical difference between them. Throughout the paper, I confine myself to metaphysical examples from the early Russell. Only now that we know they are valid can we start to discuss whether they are sound. (shrink)

This paper critically evaluates the regress argument for infinitism. The dialectic is essentially this. Peter Klein argues that only an infinitist can, without being dogmatic, enhance the credibility of a questioned non-evident proposition. In response, I demonstrate that a foundationalist can do this equally well. Furthermore, I explain how foundationalism can provide for infinite chains of justification. I conclude that the regress argument for infinitism should not convince us.

I argue that Cartesian skepticism about the external world leads to a vicious regress of skeptical attitudes, the only principled and unproblematic response to which requires refraining from taking the very first skeptical step.

According to Johansson (2009: 22) an infinite regress is vicious just in case “what comes first [in the regress-order] is for its definition dependent on what comes afterwards.” Given a few qualifications (to be spelled out below (section 3)), I agree. Again according to Johansson (ibid.), one of the consequences of accepting this way of distinguishing vicious from benign regresses is that the so-called Russellian Resemblance Regress (RRR), if generated in a one-category trope-theoretical framework, is vicious and (...) that, therefore, the existence of tropes only makes sense if trope-theory is understood (minimally) as a two-category theory which accepts, besides the existence of tropes, also the existence of at least one universal: resemblance.1 I disagree. But how can that be? How can Johansson and I agree about what distinguishes a vicious from a benign regress, yet disagree about which regresses are vicious and which are benign? In this paper I attempt to answer that question by first setting out and defending the sense of viciousness which both Johansson and I accept, only to then argue that to be able to determine if a particular regress is vicious in this sense, more than features intrinsic to the regress itself must be taken into account. This is why, although the RRR as originally set out by Russell is vicious, the seemingly identical resemblance regress which ensues in a one-category (standard) trope-theoretical context is not (provided, that is, that we accept certain views about how the nature of tropes relates to the resemblance between tropes, and given that we set our theory in a truthmaker theoretical framework – all of which are standard assumptions for proponents of (the standard-version of) the trope-theory).2. (shrink)

This paper explains what an infinite regress argument is. Part 1 contains some examples of infinite regress arguments. Part 2 presents a schema for all such arguments an defines an infinite regress argument as one that approximates to the schema. Part 3 tests the schema on the examples. Part 4 contrasts my account of infinite regress arguments with that given by Passmore and shows that Passmore's theory succumbs to objections. Part 5 distinguishes an (...) infinite regress argument from an infinite regress and defines an infinite regress. Part 6 explains the dyslogistic force of 'infinite regress'. (shrink)

What is it for a particular to have a property? many proposed analyses of this situation may be called relational accounts. The particular has some relation, R, To some entity p. R may be the relation of falling under, Being a member of, Resembling or "participating." p may be a predicate, A concept, A class, A paradigm instance or a form. A number of arguments seek to prove that all these accounts are involved in various vicious infinite regresses. These (...) arguments are classified, Their resemblances and differences noted, And their soundness assessed. (edited). (shrink)

In this discussion note, I aim to reconstruct and assess Korsgaard's recent attempt to extend her regress argument. I begin, in section 1, with a brief recapitulation of the regress argument. Then, in section 2, I turn to the extension. I argue that the extension does not work because Korsgaard cannot rule out the possibility--a possibility for which there is both empirical evidence and argumentative pressure coming directly from the original regress--that we value animality in ourselves qua (...) animality of rational beings. (shrink)

This paper reconstructs Reid 's responses to regress arguments against the possibility of free will, highlighting the role played by long-term decisions in the explanation of paradigmatic free actions on Reid 's account. In addition to reconstructing Reid 's response to the two versions of the regress argument that he explicitly discusses, I also construct a Reidian response to Galen Strawson's contemporary version of the regress argument. The depth of Reid 's position is most apparent in (...) the resources it provides for responding to this sophisticated articulation of a traditional argument against freedom of the will. (shrink)

I describe the general structure of most infinite regress arguments; introduce some basic vocabulary; present a working hypothesis of the nature and derivation of an infinite regress; apply this working hypothesis to various infinite regress arguments to explain why they fail to entail an infinite regress; describe a common mistake in attempting to derive certain infinite regresses; and examine how infinite regresses function as a premise.

Many take the claim that you cannot ‘get’ an ‘ought’ from an ‘is’ to imply that non- moral beliefs are by themselves incapable of justifying moral beliefs. I argue that this is a mistake and that the position that moral beliefs are justified exclusively by non-moral beliefs—a view that I call moral inferentialism—presents an attractive non-sceptical moral epistemology.

Peter Klein has taken Aristotle’s regress argument for foundationalism as a point of departure for developing a view he calls ‘infinitism’. In this paper, I offer a critique of Klein’s view. I argue for three main conclusions. First, Klein’s response to the regress argument for foundationalism is neither infinitism nor foundationalism but a distinct position I call the “unjustified foundations” view. Second, Klein’s “unjustified foundations” view is subject to some serious problems that make it inferior to foundationalism. Third, (...) Klein’s objections to foundationalism fail to knock it from its place of superiority over the “unjustified foundations” view. Before defending these three conclusions in sections 3-5, I begin with an account of the regress argument for foundationalism in section 1 and with a brief presentation of Klein’s views in section 2. (shrink)

Infinite regress arguments are a powerful tool in Aristotle, but this style of argument has received relatively little attention. Improving our understanding of infinite regress arguments has become pressing since recent scholars have pointed out that it is not clear whether Aristotle’s infinite regress arguments are, in general, effective or indeed what the logical structure of these arguments is. One obvious approach would be to hold that Aristotle takes infinite regress arguments (...) to be per impossibile arguments, which derive an infinite sequence. Due to his finitism, Aristotle then rejects such a sequence as impossible. This paper argues that this obvious approach does not work, even for its most amenable cases. The paper argues instead that infinite regress arguments involve domain-specific infinities, and so there is not a general finitism which underpins infinite regress arguments in Aristotle, but rather domain-specific reasons that there cannot be an infinite number of entities in each domain in which Aristotle invokes an infinite regress argument. (shrink)

Many philosophers reject the Language of Thought Hypothesis (LOT) on the grounds that is leads to an explanatory regress problem. According to this line of argument, LOT is invoked to explain certain features of natural language, but the language of thought has the very same features and consequently no explanatory progress has been made. In an earlier paper (“Regress Arguments against the Language of Thought”, Analysis 57.1), we argued that this regress argument doesn’t work and that (...) even proponents of LOT have given the regress argument too much credit. In this paper, we extend our critique of the regress argument against LOT by responding to J. Knowles’s commentary of our earlier paper (in “The Language of Thought and Natural Language Understanding”, Analysis 58.4). (shrink)

H. Collins has challenged the empiricist understanding of experimentation by identifying what he thinks constitutes the experimenter’s regress: an instrument is deemed good because it produces good results, and vice versa. The calibration of an instrument cannot alone validate the results: the regressive circling is broken by an agreement essentially external to experimental procedures. In response, A. Franklin has argued that calibration is a key reasonable strategy physicists use to validate production of results independently of their interpretation. The physicists’ (...) arguments about the merits of calibration are not coextensive with the interpretation of results, and thus an objective validation of results is possible. I argue, however, that the in-situ calibrating and measurement procedures and parameters at the Large Hadron Collider are closely and systematically interrelated. This requires empiricists to question their insistence on the independence of calibration from the outcomes of the experiment and rethink their position. Yet this does not leave the case of in-situ calibration open to the experimenter’s regress argument; it is predicated on too crude a view of the relationship between calibration and measurement that fails to capture crucial subtleties of the case. (shrink)

Context: Is non-dualist epistemology, based on the unity of descriptions and objects, logically consistent? Problem: What is the status of the infinite regresses that the non-dualist Josef Mitterer, in his book The Beyond of Philosophy, censures in dualist thought? Their academic discussion is still in its infancy. Method: An attempt to reconstruct and differentiate Mitterer’s infinite regress accusations against dualism (originating from the 1970s) with today’s means and distinctions. Results: A weak and a strong linguistic principle are presented (non-dualism (...) being subsumed under the strong linguistic principle), which are defined as such depending on whether the infinite regresses of dualism are interpreted as benign or as vicious. Implications: Further penetrating investigation of the infinite regresses highlighted by Mitterer is of crucial importance because these regresses have not yet been discussed and classified in relevant current publications on infinite regress arguments by authors such as Rescher or Gratton. Such proper classification is indispensable, however, if the value of the non-dualist alternative to, and its critique of, dualist thought is to be assessed adequately. (shrink)

In Metaphysics Z 8 Aristotle offers an infinite regress argument to deny that forms come to be. Briefly put, the argument states that, if we assume that every time an x composed of matter (m1) and form (f1) comes to be, f1 also comes to be, then there would be infinitely many xs coming to be – for f1 would itself be a compound, if it comes to be, and the same reasoning would in turn apply to it. This (...) argument has great significance in the history of philosophy, for some later thinkers take Aristotle to allow or make room for the creation ex nihilo of forms. However, the only direct Greek engagement with this argument in its proper context is provided by Asclepius of Tralles’ commentary on Book Z. A close study of Asclepius’ interpretation shows that he endorsed the argument on the tacit condition that it refers to the forms αὐτὰ καθ’ αὑτά as different from both Platonic Ideas and enmattered forms. At the same time, however, its elaboration includes alongside forms αὐτὰ καθ’ αὑτά also eternal separate forms and generated forms. His reconstruction also displays a sophisticated toning-down of the potential disagreements between Plato and Aristotle on the conception of pre-existing form which is assumed in the argument. Asclepius’ interpretation offers yet further proof of the commentators’ camouflaged and stratified way of tackling philosophical issues of paramount importance. (shrink)

This compact booklet addresses informal logical aspects of infinite regress arguments. We know what infinite regress arguments are from such examples as Plato’s Third Man problem. It is presented here for tradition sake in its original formulation, where for convenience ‘man’ does duty for ‘human being’. Plato’s theory of abstract Ideas or Forms, in order to explain how it is that Phaedo and Meno are both men, posits their belonging to, participating in or falling under a (...) higher ideal abstract universal Man. The theory thereby takes the first irreversible step toward an infinite regress of ideal abstract universal men of increasingly higher order, beginning with the third MAN, for which there seems to be no legitimating explanatory rationale. A further example, to have several on hand, is the infinite regress that occurs on the assumption that every occurrent event has a temporally prior cause, or, simply, that every event has a cause that is also an event. The logical structure, class .. (shrink)

The three classic regress problems (the Extensive Regress of states, the Intensive Regress of contents, and the Fichte-Henrich-Shoemaker Regress of de se beliefs) related to the Self-Awareness Thesis (that one’s conscious states are the ones that one is aware of being in) can all be elegantly resolved by a self-acquaintance postulate. This resolution, however, entails that consciousness has an irreducibly circular structure and that self-acquaintance should not be conceived of in terms of an independent entity bearing (...) an external or mediated relation to itself but rather in terms of a realized relation-instance relating to itself as well as to something other than itself. Consciousness, on this account, has a categorially curious status. It is like a relation-particular hybrid. This can be formalized in terms of the theory of hypersets, which in turn can be used to elucidate the problem of individuality, one source of the conceptual difficulty with adequately characterizing de se content. (shrink)

This dissertation is on infinite regress arguments in philosophy. Its main goals are to explain what such arguments from many distinct philosophical debates have in common, and to provide guidelines for using and evaluating them. Two theories are reviewed: the Paradox Theory and the Failure Theory. According to the Paradox Theory, infinite regress arguments can be used to refute an existentially or universally quantified statement (e.g. to refute the statement that at least one discussion is (...) settled, or the statement that discussions are settled only if there is an agreed-upon criterion to settle them). According to the Failure Theory, infinite regress arguments can be used to demonstrate that a certain solution fails to solve an existentially or universally quantified problem (e.g. to demonstrate that a certain solution fails to settle all discussions, or that it fails to settle even one discussion). In the literature, the Paradox Theory is fairly well-developed, and this dissertation provides the Failure Theory with the same tools. (shrink)

In recent years a great deal of scholarly and philosophical discussion has been devoted to the interpretation and evaluation of the regress arguments which Parmenides is made to deploy against the theory of Ideas in the first part of the dialogue which takes its name from him. By contrast, scarcely anything has been written about the infinite regress argument which Parmenides presents at the start of the second of the deductions which make up the dialogue's second part. (...) Yet while it may contain less to reward the philosopher than the earlier regresses, it can hardly fail to perplex the scholar. (shrink)

In recent years a great deal of scholarly and philosophical discussion has been devoted to the interpretation and evaluation of the regress arguments which Parmenides is made to deploy against the theory of Ideas in the first part of the dialogue which takes its name from him. By contrast, scarcely anything has been written about the infinite regress argument which Parmenides presents at the start of the second of the deductions which make up the dialogue's second part. (...) Yet while it may contain less to reward the philosopher than the earlier regresses, it can hardly fail to perplex the scholar. (shrink)

The aim of this paper is to examine the medieval posterity of the Aristotelian and Pyrrhonian treatments of the infinite regress argument. We show that there are some possible Pyrrhonian elements in Autrecourt's epistemology when he argues that the truth of our principles is merely hypothetical. By contrast, Buridan's criticisms of Autrecourt rely heavily on Aristotelian material. Both exemplify a use of scepticism.

Book review of Gratton's Infinite Regress Arguments.

In this paper I fix a typical regress argument, locate a typical gap in the argument, and try to supply a number of gap-filling readings of its first premise.

I propose a counterfactual theory of infinite regress arguments. Most theories of infinite regress arguments present infinite regresses in terms of indicative conditionals. These theories direct us to seek conditions under which an infinite regress generates an infinite inadmissible set. Since in ordinary language infinite regresses are usually expressed by means of infinite sequences of counterfactuals, it is natural to expect that an analysis of infinite regress arguments should be based on a theory (...) of counterfactuals. The Stalnaker–Lewis theory of counterfactuals, augmented with some fundamental notions from metric-spaces, provides a basis for such an analysis of infinite regress arguments. Since the technique involved in the analysis is easily adaptable to various analyses, it facilitates a rigorous comparison among conflicting philosophical analyses of any given infinite regress. (shrink)

I investigate various logical and contextual factors involved in the derivation and use of infinite regresses in infinite regress arguments. I discuss the concept of a regress; identify different kinds of infinite regresses; clarify the core structure of most infinite regress arguments; use the logic of binary relations to explain the derivation of the most common kind of infinite regress encountered in my research; explain how circular definitions and circular explanations entail infinite regresses; discuss (...) the rhetorical features of infinite regress arguments that are presented or analyzed in terms of recurring questions and answers; examine different conditions under which an infinite regress is used to refute a statement; identify different structures of infinite regress arguments that are presented or analyzed in terms of recurring problems and solutions. (shrink)

Howard Robinson's *From the Knowledge Argument to Mental Substance* contains two quite different arguments from the vagueness of composite objects to the conclusion that I am not a physical object at all. One of them, developed over the course of several chapters, takes the following form: All composite physical objects (and only composite physical objects are candidates to be a human being) are non-fundamental; non-fundamental things are inevitably vague in various ways; this vagueness shows that we must "make a (...) conceptual interpretation of them", treating them as "artefacts of conceptualisation"; and this in turn precludes our identifying ourselves with any such things. Some interesting morals fall out of close consideration of Robinson's argument; but, in the end, materialists can reasonably resist it. (shrink)

There is an argument according to which there must be something nonrelationally valuable for anything to be of value. The chains of dependence between values must come to an end, and humanity meets the specifications. I explore alternatives to terminating a regress in nonrelational value and give reason to reject the “borrowing” conception of relational value that drives the argument. I doubt that the nonrelational value of humanity can be secured by an argument from the structure of value, but (...) I am optimistic about the prospects for explaining our value relationally and give reason to favor a reflexive relational model. (shrink)

This paper concerns connection between knowing or accepting a logical principle such as Modus Ponens and actions of reasoning involving it. Discussions of this connection typically mention the so-called ‘Lewis Carroll Regress’ and there is near consensus that the regress shows something important about it. Also, although the regress explicitly concerns logic, many philosophers think that it establishes a more general truth, about the structurally similar connection between epistemic or practical principles and actions involving them. This paper’s (...) first aim is to address key interpretations Carroll’s regress as clearly as possible so as to show precisely how it might be relevant to questions concerning the connection between logical knowledge and reasoning, and, more broadly, to discussions of how epistemic or practical principles may be action-guiding. Its second aim is to show that the regress fails to establish anything of substance about the connection between logical knowledge and reasoning, or any other structurally similar relation, unless substantive, contentious and typically undefended assumptions are made. The consensus is thus on shaky ground. (shrink)