Infinite Regress Research Articles

Self-Representation in Girard's System U

In 1991, Pfenning and Lee studied whether System F could support a typed self-interpreter. They concluded that typed self-representation for System F "seems to be impossible", but were able to represent System F in F ω . Further, they found that the representation of F ω requires kind polymorphism, which is outside F ω . In 2009, Rendel, Ostermann and Hofer conjectured that the representation of kind-polymorphic terms would require another, higher form of polymorphism. Is this a case of infinite regress? We show that it is not and present a typed self-representation for Girard's System U, the first for a λ-calculus with decidable type checking. System U extends System F ω with kind polymorphic terms and types. We show that kind polymorphic types (i.e. types that depend on kinds) are sufficient to "tie the knot" -- they enable representations of kind polymorphic terms without introducing another form of polymorphism. Our self-representation supports operations that iterate over a term, each of which can be applied to a representation of itself. We present three typed self-applicable operations: a self-interpreter that recovers a term from its representation, a predicate that tests the intensional structure of a term, and a typed continuation-passing-style (CPS) transformation -- the first typed self-applicable CPS transformation. Our techniques could have applications from verifiably type-preserving metaprograms, to growable typed languages, to more efficient self-interpreters.

A Duet for one.

This paper considers communication in terms of inference about the behaviour of others (and our own behaviour). It is based on the premise that our sensations are largely generated by other agents like ourselves. This means, we are trying to infer how our sensations are caused by others, while they are trying to infer our behaviour: for example, in the dialogue between two speakers. We suggest that the infinite regress induced by modelling another agent - who is modelling you - can be finessed if you both possess the same model. In other words, the sensations caused by others and oneself are generated by the same process. This leads to a view of communication based upon a narrative that is shared by agents who are exchanging sensory signals. Crucially, this narrative transcends agency - and simply involves intermittently attending to and attenuating sensory input. Attending to sensations enables the shared narrative to predict the sensations generated by another (i.e. to listen), while attenuating sensory input enables one to articulate the narrative (i.e. to speak). This produces a reciprocal exchange of sensory signals that, formally, induces a generalised synchrony between internal (neuronal) brain states generating predictions in both agents. We develop the arguments behind this perspective, using an active (Bayesian) inference framework and offer some simulations (of birdsong) as proof of principle.

The Concept of Free Will as an Infinite Metatheoretic Recursion

It is argued that the concept of will, like the concept of truth in formal languages, requires a separation between an object level and a meta-level for being consistently defined. The Jamesian two stage model, which deconstructs into the causally open free stage with its closure in the will stage, is implicitly a move in this direction. However, to avoid the dilemma of determinism, additionally requires an infinite regress of causal meta-stages, making choice a hypertask. We use this model to define of the rationalist-compatibilist type. This is shown to provide a natural three-way distinction between quantum indeterminism, freedom and will, applicable respectively to artificial intelligence (AI), animal agents and human agents. We propose that the causal hierarchy in our model corresponds to a hierarchy of Turing uncomputability. Possible neurobiological and behavioral tests to demonstrate experimentally are suggested. Ramifications of the model for physics, evolutionary biology, neuroscience, neuropathological medicine and moral philosophy are briefly outlined.

The quest for the legitimacy of the people

This article addresses the problem of ‘the legitimacy of the people’, that is, what constitutes the legitimate demarcation of the political units within which democracy is practiced? It is commonplace among philosophers to argue that this problem cannot be solved by appeal to democratic procedure because every attempt to do so results in an infinite regress. Based on a social contract theoretical analysis of the problem, this view is rejected. Although contract theorists have ignored the problem of the legitimacy of the people, this article nevertheless argues for one specific, and currently dominant, type of contract view – ‘contractarianism’ – that it contains the conceptual tools to solve it. In a contractarian view, the people are understood as a cooperative venture for mutual advantage and accordingly consist of only those individuals for whom it is mutually beneficial to bind themselves to one another. It is argued that contractarianism offers a procedurally democratic solution to the problem of the legitimacy of the people that does not cause an infinite regress. Furthermore, this article refutes a classic criticism of contractarianism’s account of moral standing. Finally, the article demonstrates contractarianism’s practical implications for one specific articulation of the problem of the legitimacy of the people, namely, immigration.

Mobius’ edge: Infinite regress in the resource-based and dynamic capabilities views

The study of strategic organization involves many delicious ironies, one of which is the goal to prescribe general paths to sustainable competitive advantage. Twenty years after Collis and a few good men and women originally exposed and confronted the infinite regress problem in the resource-/capabilities-based theories, we revisit this problem to resolve it. We consider the linkages between the infinite hierarchical levels that form the paths to the origins of sustainable competitive advantages in both the resource-based view and the dynamic capabilities view. We find that there are logical factors that limit the number of levels that need to be traversed to reach the origins. We discuss the implications to academics, managers and policy-makers from our resolution to the infinite regress problem to provide a more crystal clear understanding of the strenuous objective that continues to challenge all strategic theory.

Why Law Matters - A Debate

This is a debate between Lorenzo Zucca and Alon Harel on the nature of constitutionalism. Traditionally constitutions and judicial review are considered to be instruments to protect rights or justice. In his book Why Law matters Harel develops a non-instrumentalist account of legal institutions and procedures. It argues that various legal and political institutions that are often perceived as contingent means to the realization of valuable ends are necessary components of a just society, namely that they matter as such. Part III of Why Law Matters defends a non-instrumentalist defense of constitutionalism (robust constitutionalism). More particularly it defends two aspects of constitutionalism: binding constitutional directives and judicial review.Zucca rejects this view and defends robust instrumentalism; he argues that constitutions and judicial review are means to bring about social coordination. Zucca raises several objections against binding constitutionalism. He argues that: Harel’s understanding of constitutional entrenchment is flawed; Harel’s argument suffers from infinite regress and Harel’s reliance on republicanism exposes his argument to forceful objections. He further argues that Harel’s theory of judicial review is ultimately an instrumentalist one and that Harel’s understanding of the role of judges is too limited. The debate touches upon fundamental questions of constitutional theory: is the constitution a means to protect rights or democracy or is it a component of justice? Should the desirability of judicial review hinge only on the instrumental contribution of judges in protecting rights or does judicial review rest also on the very opportunity that individuals have to challenge the state?

William Ockham on the Scope and Limits of Consciousness

William Ockham (ca. 1287-1347) holds what nowadays would be characterized as a “higher-order perception” theory of consciousness. Historically speaking, one of the most persistent objections to this type of theory is the charge that it gives rise to an infinite regress in higher-order states. In this paper, I examine Ockham’s efforts to respond to the regress problem, focusing in particular on his attempts to restrict the scope of consciousness so as to avoid it. In his earlier writings, Ockham holds that we are conscious only of those states to which we explicitly attend. This view, I go on to argue, is inadequate on both phenomenological and philosophical grounds. Interestingly, and perhaps for this very reason, in later works, Ockham goes on to develop an alternative explanation for his account of the limited scope of consciousness.

The infinite regression illusion reveals dissociation between perception and action

The infinite regression illusion reveals dissociation between perception and action

Infinite order cross-validated local polynomial regression

Many practical problems require nonparametric estimates of regression functions, and local polynomial regression has emerged as a leading approach. In applied settings practitioners often adopt either the local constant or local linear variants, or choose the order of the local polynomial to be slightly greater than the order of the maximum derivative estimate required. But such ad hoc determination of the polynomial order may not be optimal in general, while the joint determination of the polynomial order and bandwidth presents some interesting theoretical and practical challenges. In this paper we propose a data-driven approach towards the joint determination of the polynomial order and bandwidth, provide theoretical underpinnings, and demonstrate that improvements in both finite-sample efficiency and rates of convergence can thereby be obtained. In the case where the true data generating process (DGP) is in fact a polynomial whose order does not depend on the sample size, our method is capable of attaining the n rate often associated with correctly specified parametric models, while the estimator is shown to be uniformly consistent for a much larger class of DGPs. Theoretical underpinnings are provided and finite-sample properties are examined.

The Paradox of Adjudication

Building on the work of Oren Perez (2006), this work is the first full-length paper to explore the problem of infinite regress in the process of adjudication (i.e. the problem of deciding to decide) and is organized as follows. Part 1 describes the logical structure of the infinite regress problem in decision-making generally. Next, parts 2 and 3 explore the problem of infinite regress in legal decision-making, explaining why the regress problem arises in all forms of adjudication requiring research and deliberation (part 2) and providing an illustration of the regress problem from the law of torts (part 3). Part 4 then explores some possible solutions to the regress problem in law. Part 5 concludes.

Supplementing the Supplement: Looking at the Function of Afterwords and Acknowledgements in some Canadian Historical Novels

But the supplement supplements. adds only to replace. Jacques Derrida Of Grammatology IN perhaps the most well-known chapter in Of Grammatology,... That Dangerous Supplement ... Jacques Derrida examines the concept of the supplement. Here, he uses Jean Jacques Rousseau's work to show how writing complements/stands in for the speech act and tries to recapture the presence of the speech and the speaker: It is the addition of a technique, a sort of artificial and artful ruse to make speech present when it is actually absent (144). Rousseau, Derrida goes on to argue, perceives writing as a dangerous means for capturing presence, but a necessary one: Writing is dangerous from the moment that representation there claims to be presence and the sign of the thing itself. And there is a fatal necessity, inscribed in the very functioning of the sign, that the substitute makes one forget the vicariousness of its own function and makes itself pass for the plenitude of a speech whose deficiency and infirmity it nevertheless only supplements. (144) The supplement is dangerous because it fools the reader into perceiving a completeness when, in fact, the supplement only ever points to a lack not only in the absence it is ostensibly rectifying but in itself as well. Derrida's notion of supplement, then, is one that plays with the space between presence and absence. Its very presence highlights its own absence; what is there highlights what is missing. Supplementarity is perhaps a particularly useful lens through which to consider the end notes so often included in historical fiction. These afterwords or acknowledgements, as they are typically titled, potentially occupy the infinite regression of the supplement in that they are themselves supplements to novels which are themselves supplements to previous narratives about capital-H history. Moreover, these paratextual devices simultaneously point to the presence of historical authority and archive as well as its absence in both the novel they proceed and in themselves as ostensible complement to that novel. At the heart of these afterword/ acknowledgements there is an anxiety about the ways in which not just history and not just historical fiction but the paratextual apparatus itself falls short. Using Derrida's discussion of supplementarity as a means of illuminating how the material of the afterword/acknowledgements functions within historical fiction, this paper will examine the ways in which these paratextual devices expand on, conflict with, and further complicate the issues of absence and presence with which a novelistic narrative of history engages. Through a close analysis of the afterword/acknowledgements sections of five contemporary Canadian novels--John Steffler's The Afterlife of George Cartwright, Rudy Wiebe's A Discovery of Strangers, Margaret Atwood's Alias Grace, Daphne Marlatt's Ana Historic, Joseph Boyden's Three Day Road--I will explore how each engages with the problems of representation (problems also explored within the novels themselves) to varying degrees and in different ways. However, before unpacking the novels, let me first draw a more in depth connection between history, afterwords, and supplementarity. Although Derrida discusses the supplement within the context of language, it is a concept that is also applicable to representations of history. That is, when a historian presents a new account of the past, it is a supplement to those accounts that already exist--it both adds to and completes the existing records. However, there is a further complication with the supplement, for in its paradoxical function there also exists a latent sense of continuity. We expect, in other words, that the supplement will be added to or further completed by other supplements. The supplement, therefore, is never enough. The supplement will always already require another supplement. This problem with the historical supplement is particularly apparent within contemporary historical fiction, a genre that exists to supplement history, while bearing within it an awareness of its own supplementarity. …

Een systematische catalogus van argumenten

In this article I develop a systematic catalogue of arguments that is based on a formal ordering principle and can be used as a point of departure for research in artificial intelligence and various kinds of empirical research such as research into argument quality. The catalogue is constructed by combining a formal-linguistic typology of arguments, developed and presented in earlier articles, with a formalized account of the pragma-dialectical classification of standpoints. First, I provide an account of the nature of arguments that avoids infinite regress problems in argument reconstruction. Then, I summarize the formal-linguistic typology of arguments, which consists of two main types – 'predicate arguments' and 'subject arguments' – and combine the typology with a formalized account of the pragma-dialectical classification of standpoints, which consists of three types – 'prescriptive standpoints', 'evaluative standpoints', and 'descriptive standpoints'. Finally, for each of the types of standpoints, I discuss what types of arguments are suitable to support them, describe the relations between the predicates and subjects of the argument and the standpoint involved, and give some examples of argument types distinguished in the literature that match the description.

Finite Reasons Without Foundations

AbstractThis article develops a theory of reasons that has strong similarities to Peter Klein's infinitism. The view it develops, Framework Reasons, upholds Klein's principles of avoiding arbitrariness (PAA) and avoiding circularity (PAC) without requiring an infinite regress of reasons. A view of reasons that holds that the “reason for” relation is constrained by PAA and that PAC can avoid an infinite regress if the “reason for” relation is contextual. Moreover, such a view of reasons can maintain that skepticism is false by the maintaining that there is more to epistemic justification than can be expressed in any reasoning session. One crucial argument for Framework Reasons is that justification depends on a background of plausibility considerations. The final section of the article applies this view of reasons to Michael Bergmann's argument that any nonskeptical epistemology must embrace epistemic circularity.

Infinite Epistemic Regresses and Internalism

AbstractThis article seeks to state, first, what traditionally has been assumed must be the case in order for an infinite epistemic regress to arise. It identifies three assumptions. Next it discusses Jeanne Peijnenburg's and David Atkinson's setting up of their argument for the claim that some infinite epistemic regresses can actually be completed and hence that, in addition to foundationalism, coherentism, and infinitism, there is yet another solution (if only a partial one) to the traditional epistemic regress problem. The article argues that Peijnenburg and Atkinson fail to address the traditional regress problem, as they don't adopt all of the three assumptions that underlie the traditional regress problem. It also points to a problem in the notion of making probable that Peijnenburg and Atkinson use in their account of justification.

No successful infinite regress

We model infinite regress structures — not arguments — by means of ungrounded recursively defined functions in order to show that no such structure can perform the task of providing determination to the items composing it, that is, that no determination process containing an infinite regress structure is successful.

Bourgeois versus anti-Bourgeois: a model of infinite regress

One of the first applications of game theory in the field of animal behaviour was to show that respect for ownership (Bourgeois behaviour) can arise as an arbitrary convention to avoid costly disputes. However, this same theory indicated that a mirror-image dispute-avoiding convention in which owners concede their property to intruders (anti-Bourgeois) is also stable under the same conditions. It has since been shown repeatedly that the first individuals to find resources are frequently left unchallenged, while evidence for the alternative convention, according to which owners relinquish property to intruders without conflict, is rare at best. By far the most commonly invoked explanation for the rarity of anti-Bourgeois is that two individuals employing such behaviour over repeated rounds would be swapping roles continually, a potentially inefficient outcome known as ‘infinite regress.’ Here we set out to test the validity of this verbal reasoning by analysing a Hawk–Dove model with ownership asymmetry but introducing a fixed probability w that two individuals meet again. While assuming that the resource has value to the winner (realized either at the end of the interaction, or after each round) and losers of fights pay costs, we also assume that individuals incur costs in taking ownership and relinquishing it. Contrary to expectation and despite the inefficiency of the anti-Bourgeois equilibrium, ‘infinite regress’ does not always render anti-Bourgeois unviable. Indeed if fighting is cheap, then repeated interactions can generate an anti-Bourgeois equilibrium where previously only obligate Hawk was a stable population strategy. Nevertheless, when probability w exceeds thresholds determined by the costs of taking and relinquishing ownership, Bourgeois can become the only stable convention. Collectively, our model demonstrates that although infinite regress can facilitate the evolution of Bourgeois-like conventions, it is no panacea.

Feeling Another's Pain: Sympathy and Psychology Saga Style

Progress is hardly a given in the humanities or the suspect sciences. In many ways we are not quite as astute as our grandparents, and they not as much as theirs, and so forth in an infinite entropic regress. Would I trade Montaigne or Stendhal's psychological acumen for even the best work that comes from social psychology departments? In this short essay I want to show just how good some medieval people, medieval Icelanders to be exact, were at understanding the mental and emotional states of others, and if of others then presumably, though not necessarily, also of themselves. And I hope to show in some ways they were rather more sophisticated than we are.

Tropes with a Kantian Flavor

This paper discusses one of the major problems for resemblance nominalism, posed by Bertrand Russell in 1911–12, and often referred to as Russell’s regress. It is the problem that resemblance must either be a universal, thus refuting a thorough nominalism, or must itself resemble other resemblances to count as a resemblance, which ultimately leads to an infinite regress of resemblances. I am going to discuss two solutions that have been proposed to this problem. I will then attempt to show in how far these are unsatisfactory, and propose my own solution which treats resemblance as a subject-relative phenomenon. My aim is to show that, on my account, there is no infinite regress and therefore no problem.

Infinite regress in decision theory, philosophy of science, and formal epistemology

Infinite regresses have had a mixed reception in philosophy. On the one hand, they are often quickly brushed aside as being unreasonable and even preposterous. If a position or a theory is shown to engender an infinite regress, that pretty well means the end of it: an argumentum ad infinitum is as good as a reductio ad absurdum. On the other hand, the alleged absurdity of infinite regresses has been a source of inspiration and the ground for far-reaching conclusions. It led to the requirement that a regress should come to a stop and thence to the verdict that there exist such things as a Prime Mover, a First Cause, a Highest Good, or a Causa Sui. Infinite regresses have been discussed in practically all branches of philosophy, not only in metaphysics and epistemology, but also in ethics, philosophy of mind, logic, and argumentation theory. In recent years, they have spurred a lively debate in traditional epistemology, where ‘infinitism’ (the idea that an infinite chain of epistemic justification is not prima facie absurd) is on its way to becoming a mature alternative to the traditional positions, foundationalism and coherentism. The papers in the present volume are about infinite regress in decision theory, philosophy of science, and formal epistemology. We are fortunate to have brought together a number of renowned philosophers and promising young scholars: John Barker is associate professor of Philosophy at the University of Illinois at Springfield, and chair of the Philosophy Department. His Ph.D. dissertation, defended in 1998 at Princeton University, is entitled ‘The Inconsistency Theory of Truth’. His areas of interest are philosophical logic and philosophy of language (especially paradoxes and inconsistencies) with side-interests in philosophy of mind and philosophy of science.

Hohfeldian Infinities: Why Not to Worry

Hillel Steiner has recently attacked the notion of inalienable rights, basing some of his arguments on the Hohfeldian analysis to show that infinite arrays of legal positions would not be associated with any inalienable rights. This discussion addresses the nature of the Hohfeldian infinity: the main argument is that what Steiner claims to be an infinite regress is actually a wholly unproblematic form of infinite recursion. First, the nature of the Hohfeldian recursion is demonstrated. Second, the alleged problems that this might pose for the analysis are discussed. Finally, the point is made that infinite recursions of legal positions ensue regardless of whether inalienable rights exist or not.