Infinite Regress Research Articles

The infinitely fractal universe paradigm and consupponibility

The inability of Albert Einstein and quantum physicists to resolve whether the laws of nature operate exactly or probabilistically impacted scientific methodology. Karl Popper further compounded the problem by stressing empirical falsifiability and proposing causes cannot be proven because of infinite regress. For these and other reasons, many investigators either downplayed propositions of cause or even ridiculed them. With causality vilified, metaphysics took a back seat to empirical science. In Earth sciences, however, causality remains a top priority. Thus, a significant interdisciplinary rift developed in established scientific procedures. Yet, some physicists still wanted to know why their equations worked, and some still postulated causality despite its diminished stature. Metaphysics has a rightful place in science and revive a forgotten approach, consupponibility, for testing metaphysical assumptions and theories. A set of fundamental assumptions and theories are consupponible if they exist without contradicting one another. Importantly, a single contradiction among the set falsifies the entire paradigm. To demonstrate the concepts associated with fundamental assumptions and a paradigm, this work analyses a paradigm based on infinitely fractal matter. Just like Popperian falsifiability, a large set of prohibitive fundamental assumptions allows proponents, opponents, and undecided investigators a means for falsifying the infinitely fractal universe model if the paradigm incorrectly describes the universe. That is, the goal is never to prove the paradigm, which is impossible. Instead, the goal is to attempt to disprove the paradigm by finding contradictions. Repeated failures to disprove the paradigm increase the likelihood of its correctness.

Rules all the way down: Consumer behaviour from the standpoint of the ‘ONE behavioural’ research programme

AbstractThis article sets out a unified behavioural research programme that integrates compatible elements of old, new and evolutionary behavioural approaches to economics as an alternative to the dominant unified approach to economics based on rational choice theory and a Walrasian view of market coordination. However, the proposed programme can also be viewed as a general framework for interdisciplinary research on consumer behaviour. It employs the view of scientific research programmes proposed by Lakatos, setting out groups of ‘hard‐core’ propositions and their associated ‘do’ and ‘do not’ rules for the conduct of researchers. The unifying theme is that evolution in the economy (and in human systems more generally) entails the creation, adoption and abandonment of rules for dealing effectively with open‐ended choice problems that are bedevilled by infinite regress problems and cognitive challenges that people seek to address via personal repertoires of hierarchically related rules. To anticipate behaviour, researchers need to develop knowledge of these rules (including heuristics and routines), their functionality and the processes by which they get changed or prove difficult to change even where they cause problems.

A Husserlian Critique of Pannenberg’s Understanding of Subjectivity

Abstract I argue that Wolfhart Pannenberg’s view of human subjectivity presupposes a metaphysics of eternity that both contracts and expands the human subject. For this purpose, Edmund Husserl’s phenomenology is a useful criterion. Pannenberg rejects substantialist theories of subjectivity that give priority to the agency of the ego over the passivity of the self. Following Friedrich Schleiermacher, Pannenberg thinks self-reflection must be grounded on a symbiotic totality of life, and he views essences, even of subjectivity, as determined by that totality. In contrast, Husserl provides both an essentialist theory of subjectivity and a viable model for self-reflection that does not suffer from infinite regress. Husserl does more justice to the mineness of consciousness and the agency of the ego, while not discarding the narrativity of the self.

Monetary policy in a world of radical uncertainty

Monetary policy in a world of radical uncertainty

Kant and the Duty to Act from Duty

Abstract Several interpreters argue that Kant believes we have a duty to act “from duty.” If there is such a duty, however, then Kant's moral theory faces a serious problem, namely that of an allegedly vicious infinite regress of duties. No serious attempt has been made to determine how Kant might respond to this problem and insufficient work has been done to determine whether he even believes we have a duty to act from duty. In this paper I argue that not only does Kant not hold that there is a duty to act from duty, but he also explicitly rejects the idea.

Social Stigma: A Systematic Review of Cognitive Insights from Behavioral Economics (1940-2019).

.There are minority and stigmatized groups who face particular challenges to their full participation in society. This study’s objective was to conduct a systematic review to determine theoretical and methodological underpinnings in behavioral economics that explain how stigmatization emerges within the relationship processes and social structures of individuals. Data from 1940 to 2019 were sourced from 12 relevant electronic databases such as Scopus and Web of Science. Following PRISMA guidelines for systematic reviews, 26 studies out of 3459 met the inclusion criteria. Most of the studies applied experimental economics and were published between 2002 and 2018. Overall, the articles focus their research on the experiences of discrimination based on stereotypes and test their hypotheses through economic games. The data synthesis seems to reveal weak conceptual clarity, circular reasoning, and a hint of the problem of infinite regress. Thus, these issues open new and exciting avenues for future research to explore via an array of experimental applications.

Permissions, Deontic Voids, and the Karamazov Argument

Abstract: This essay criticizes three positions concerning permissions taken by Christoph Kletzer in his book The Idea of a Pure Theory of Law. First, Kletzer argues that Hans Kelsen should have understood X has having a legal obligation to φ if and only if someone else is permitted (rather than empowered) to exercise force upon X for not-φ-ing. Kelsen in fact had good reasons to speak of empowerment rather than only of permission. The second topic concerns the type of strong permission that Joseph Raz calls exclusionary. Kletzer argues that Raz’s definition of an exclusionary permission generates an infinite regress. In what is arguably the most detailed account of the structure of exclusionary permissions in print, this essay defends Raz’s definition. The third and primary topic concerns Kletzer’s understanding of a permission to φ as a deontic void: the absence of duties to φ and of duties to not-φ. Many share Kletzer’s view. Joseph Raz understands weak permissions as absences. And the usual reading of Wesley Newcomb Hohfeld’s related idea of a privilege to φ is that it is the absence of a duty to not-φ. But the absence theory is mistaken. When a normative system does not exist, there is no permission to φ, even though there are no duties to φ or to not-φ either. The same is true when φ-ing is outside the system’s scope and when φ-ing (although within the system’s scope) falls in a gap in the system. Conversely, if a normative system is inconsistent, one can have a permission to φ and a duty to not-φ (or to φ). It follows that a permission, even a weak permission, is a deontic something, not a nothing, and that weak permissions can have an effect on our practical reasoning. The same points apply to Hohfeldian privileges.

On What Ground Do Thin Objects Exist? In Search of the Cognitive Foundation of Number Concepts

AbstractLinnebo in 2018 argues that abstract objects like numbers are “thin” because they are only required to be referents of singular terms in abstraction principles, such as Hume's principle. As the specification of existence claims made by analytic truths (the abstraction principles), their existence does not make any substantial demands of the world; however, as Linnebo notes, there is a potential counter‐argument concerning infinite regress against introducing objects this way. Against this, he argues that vicious regress is avoided in the account of arithmetic based on Hume's principle because we are specifying numbers in terms of the concept of equinumerosity, or its ordinal equivalent. But far from being only a matter for philosophy, this implies a distinct empirical prediction: in cognitive development, the principle of equinumerosity is primary to number concepts. However, by analysing and expanding on the bootstrapping theory of Carey in 2009, I argue in this paper that there are good reasons to think that the development could be the other way around: possessing numerosity concepts may precede grasping the principle of equinumerosity. I propose that this analysis of early numerical cognition can also help us understand what numbers as thin objects are like, moving away from Platonist interpretations.

Başkalık Üzerine: İbn Sînâ’nın Görelilik Teorisi Bağlamında Bir İnceleme

The mode of existence of relatives has been a matter of debate throughout the history of thought. Having evaluated the debate through the contrast between a first intelligible that has individuals in the external world and a second intelligible that has no counterpart at the individual level in the external world, Ibn Sīnā believed the relative to be a categorical accident with individuals that can be pointed at in the external world. In the Metaphysics of al-Shifā, Ibn Sīnā proposed a solution aimed at eliminating the objections based on the infinite regress against his view. The article tests the applicability of the model built in this solution to the meaning of otherness (al-mughāyara), the results of which reveal the incompatibility of otherness with this model as a problem. When examining the source of this problem, the following findings are noted: The categorical relative (al-muḍāf) and pure relation (iḍāfa) are not the same thing. Pure relation is a general concept upon which the categorical relative is based and to which it cannot be reduced, because the predicate of oneness (wahda) becomes valid for multiplicity (kathra) through pure relation. Otherness is a general predicate that is inherent in and coextensive with pure relation; in this way, otherness is included in the most general class of concepts that explain the order in the existence of all existents including the categorical relative. As Ibn Sīnā’s solution model in Metaphysics aims to explain the result of pure relation in essences, it cannot be applied to pure relation phases that prioritize results and transcend categories and thus cannot be applied to otherness.

The Problem with Impure Infinitism

It is generally believed that pure versions of infinitism face two problems, namely: 1) they are unable to distinguish between potential and actual series of justified reasons because they are defined strictly in terms of relations between beliefs in the series so that every succeeding belief is justified by the belief before it and so on ad infinitum and, 2) they are unable to mark the difference between a set of justified reasons that are connected to truth and one that is not because they are defined strictly in terms of a relation between beliefs in the series of reasons. However, Aikin argues that impure infinitism could surmount these problems without undermining the infinite regress condition because impure infinitism can solve the Modus Ponens Reductio, MPR, argument that threatens pure versions of infinitism. I argue that Aikin does not succeed because his impure infinitism faces some fatal consequences and any attempt to salvage it will undermine the infinite regress of justification

Thomas Hobbes’s substantially constrained absolutism: the fundamental law of the commonwealth as a substantial constraint on the sovereign’s power

ABSTRACT In this essay, I contend that the usually neglected Fundamental Law of the Commonwealth, which commands that the essential rights of the sovereign be retained by the sovereign, imposes substantial limitations on the sovereign’s power, where substantial limitations mean limitations that render some options strictly closed for the sovereign. The option that the Fundamental Law strictly closes for the sovereign, I argue, is the transferral or renouncement of any of his essential rights. Therefore, I follow David Dyzenhaus and Thomas Poole in arguing that Hobbes’s absolutism is constrained; but, by focusing on The Fundamental Law overlooked by them, I suggest that Hobbes recognises substantial – and not just formal – limitations on the sovereign’s power. Secondly, I claim that the Fundamental Law, given that it arises from the ‘the Essence of Sovereignty’, is to be understood as a constitutive principle of sovereignty and so that, as such, it needs no external enforcement. This means that the Fundamental Law can constrain the sovereign without the need of a ‘Judge above [the sovereign with the capacity] to punish him’ – which, as Hobbes points out, ‘[would imply] making a new Sovereign’ and, thus, trigger an infinite regress.

The Parmenidean Ascent

<i>The Parmenidean Ascent</i>

Averroes’s Unity Argument Against Multiple Intellects

Abstract Averroes (Ibn Rushd) is well-known for his controversial thesis that there is only one separate intellect for all humankind. This article provides a detailed analysis of Averroes’s Unity Argument from his Long Commentary on De Anima, which argues from unified intelligible concepts to a single transcendent intellect. I set out the Unity Argument in its textual and philosophical context, explain exactly how the argument works on a new interpretation of its infinite regress (based on Averroes’s other assumptions about the mind-dependence of universals), and offer some brief suggestions as to how it might be further evaluated in light of alternative ancient and medieval theories. Ultimately, I demonstrate that the Unity Argument is Averroes’s most important philosophical argument for his distinctive view of intellect.

Learning 2D Gabor filters by infinite kernel learning regression

Gabor functions have wide-spread applications both in analyzing the visual cortex of mammalians and in designing machine vision algorithms. It is known that the receptive field of neurons of V1 layer in the visual cortex can be accurately modeled by Gabor functions. In addition, Gabor functions are extensively used for feature extraction in machine vision tasks. In this paper, we prove that Gabor functions are translation-invariant positive-definite kernels and show that the problem of image representation with Gabor functions can be formulated as infinite kernel learning regression. Specifically, we use the stabilized infinite kernel learning regression algorithm that has already been introduced for learning translation-invariant positive-definite kernels and has enough flexibility and generality to embrace the class of Gabor kernels. The algorithm yields a representation of the image as a support vector expansion with a compound kernel that is a finite mixture of Gabor functions. The problem with this representation is that all Gabor functions are present at all support vector pixels. Using LASSO, we propose a method for sparse representation of an image with Gabor functions in which each Gabor function is positioned at a very sparse set of pixels. As a practical application, we introduce a novel method for learning a dataset-specific set of Gabor filters that can be used subsequently for feature extraction. Our experiments on CMU-PIE and Extended Yale B datasets show that use of the learned Gabor filters significantly improves the recognition accuracy of a recently introduced face recognition algorithm.

Buddhist karma as infinite regress: vicious or benign?

Buddhist karma as infinite regress: vicious or benign?

Aristotle, Thomas Aquinas, and The Third Man Argument

AbstractThe Third Man argument, as it originated in Plato's Parmenides, is unjustly read into Aristotle. The Parmenides argument is briefly examined, followed by an analysis of the relevant Aristotelian texts, with a special emphasis on the commentary of Thomas Aquinas. Three different versions of Aristotle's Third Man argument are identified, of which none contain the essential infinite regress that characterizes the Parmenides argument. Finally, current scholarship on the Third Man argument, especially as it pertains to Aristotle, is reviewed. In this respect, I note that the overwhelming tendency has been to identify Aristotle's Third Man argument with that of the Parmenides, in spite of the fact that Aristotle only once articulates his version of the Third Man argument, and that this articulation is vastly different from its Parmenides counterpart. I conclude that contemporary Third Man scholarship must take this into account.

The Necessary Existence of Inference-Claims

In (2018) Gilbert Plumer argues against the existence of inference-claims on the grounds that they lead to the kind of vicious infinite regress illustrated in Carroll’s famous Achilles and the Tortoise paper (Carroll 1895). In Plumer’s view, it is not simply that neither arguments nor arguers do make inference-claims, but that they can’t do so, on pain of this regress. In further unpublished work Plumer has generalized from this result: it is a mistake to include reference to standards of argument assessment within the content of the argument. Inference-claims (i.e., sufficiency-claims) do not exist, and neither do relevance-claims or acceptability-claims, and all for much the same reason. I will argue that his arguments fail to show that inference-claims do not exist, because the regresses they lead to either are not vicious, not infinite, or can be avoided. Then I hope to show, on the grounds of what I call the ‘completeness’ of the argument, that inference-claims not only do exist but that they must exist. This is not to say that inference-claims are necessarily asserted in an act of arguing, but asserting them would not lead to the kind of harmful consequences Plumer supposes, any more than their mere existence would.

A biochemically-realisable relational model of the self-manufacturing cell

As shown by Hofmeyr, the processes in the living cell can be divided into three classes of efficient causes that produce each other, so making the cell closed to efficient causation, the hallmark of an organism. They are the enzyme catalysts of covalent metabolic chemistry, the intracellular milieu that drives the supramolecular processes of chaperone-assisted folding and self-assembly of polypeptides and nucleic acids into functional catalysts and transporters, and the membrane transporters that maintain the intracellular milieu, in particular its electrolyte composition. Each class of efficient cause can be modelled as a relational diagram in the form of a mapping in graph-theoretic form, and a minimal model of a self-manufacturing system that is closed to efficient causation can be constructed from these three mappings using the formalism of relational biology. This fabrication-assembly or (F,A)-system serves as an alternative to Robert Rosen’s replicative metabolism-repair or (M,R)-system, which has been notoriously problematic to realise in terms of real biochemical processes. A key feature of the model is the explicit incorporation of formal cause, which arrests the infinite regress that plagues all relational models of the cell. The (F,A)-system is extended into a detailed relational model of the self-manufacturing cell that has a clear biochemical realisation. This (F,A) cell model allows the interpretation and visualisation of concepts such as the metabolism and repair components of Rosen’s (M,R)-system, John von Neumann’s universal constructor, Howard Pattee’s symbol-function split via the symbol-folding transformation, Marcello Barbieri’s genotype–ribotype–phenotype ontology, and Tibor Gánti’s chemoton.

Infinite Regress: Wolff’s Cosmology and the Background of Kant’s Antinomies

Abstract 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.

Frege's Choice

I develop a new reading of Frege’s argument for the indefinability of truth. I concentrate on what Frege literally says in the passage that contains the argument. This literal reading of the passage establishes that the indefinability argument is an arguably sound argument to the following conclusion: provided that the Fregean conception of judgment—which has recently been countered by Hanks—is correct and that truth is a property of truth-bearers, a vicious infinite regress is produced. Given this vicious regress, Frege chooses to reject that truth is a property of truth-bearers. Frege’s choice leads to a unique version of the Fregean conception of judgment. His unique conception of judgment can cope with Hanks’s recent criticisms against the Fregean conception.