To investigate mechanisms of rational representation, I consider construction of an ordered continuum of psychophysical scale of magnitude of sensation; counting mechanism leading to an approximate numerosity scale for integers; and conjoint measurement structure pitting the denominator against the numerator in tradeoff positions. Number sense of resulting rationals is neither intuitive nor expedient in their manipulation.

This article examines the politicization processes of male students of a technical secondary school from the Ciudad Autónoma de Buenos Aires (CABA) referenced in the extreme right-wing party La Libertad Avanza, whose main figure is the economist Javier Milei. The study investigates how these boys polemicize with peers and teachers referenced in feminisms, appealing to typical attributes of liberal masculinity. We focus on three instances of their political socialization: i) their adherence to meritocratic tenets; ii) the use of irony in (...) their daily combat against feminist "fashion"; and iii) their resistance to the impositions of Comprehensive Sexual Education (ESI, for its acronym in Spanish). The results are part of an ethnographic research conducted in a technical school in the south of CABA between 2019 and 2023. (shrink)

This article aims to show that unless we consider Zeno’s paradoxes in the original metaphysical perspective in which they were generated, any attempt at understanding, let alone solving them, is destined to fail. This perspective, I argue, is the dichotomy of One and change. These latter were defined at the outset of Western philosophical thought by Parmenides as the two paths of the rational, i.e. accountable by a self-identical thought and thus real , and the non-identical change, irrational and unreal. (...) In this perspective, the irrational, is by definition unnameable and thus uncountable. I claim that we have inherited this dichotomic thought and if we become aware of this legacy, many deadlocked paradoxes or logical aporias in Western epistemology will acquire the status of logical necessities that follow directly from this dichotomy. (shrink)

We prove that the additive group of the rationals does not have an automatic presentation. The proof also applies to certain other abelian groups, for example, torsion-free groups that are p-divisible for infinitely many primes p, or groups of the form ⊕ p∈I Z(p ∞ ), where I is an infinite set of primes.

We show how to reconstruct the topology on the monoid of endomorphisms of the rational numbers under the strict or reflexive order relation, and the polymorphism clone of the rational numbers under the reflexive relation. In addition we show how automatic homeomorphicity results can be lifted to polymorphism clones generated by monoids.

Meyer and Mortensen’s Alien Intruder Theorem includes the extraor- dinary observation that the rationals can be extended to a model of the relevant arithmetic R♯, thereby serving as integers themselves. Al- though the mysteriousness of this observation is acknowledged, little is done to explain why such rationals-as-integers exist or how they operate. In this paper, we show that Meyer and Mortensen’s models can be identified with a class of ultraproducts of finite models of R♯, providing insights into some (...) of the more mysterious phenomena of the rational models. (shrink)

We investigate cardinal invariants related to the structure of dense sets of rationals modulo the nowhere dense sets. We prove that, thus dualizing the already known [B. Balcar, F. Hernández-Hernández, M. Hrušák, Combinatorics of dense subsets of the rationals, Fund. Math. 183 59–80, Theorem 3.6]. We also show the consistency of each of and. Our results answer four questions of Balcar, Hernández and Hrušák [B. Balcar, F. Hernández-Hernández, M. Hrušák, Combinatorics of dense subsets of the rationals, Fund. (...) Math. 183 59–80, Questions 3.11]. (shrink)

Let K be an infinite Galois extension of the rationals such that every finite subextension has odd degree over the rationals and its prime ideals dividing 2 are unramified. We show that its ring of integers is first-order definable in K. As an application we prove that equation image together with all its Galois subextensions are undecidable, where Δ is the set of all the prime integers which are congruent to −1 modulo 4.

Rational numbers are ratios _ p q of two natural numbers (with q_ ≠ 0). Their ordering is dense. Rational numbers are also special cases of ratios of dimensional magnitudes—the latter, typically, being lengths of line segments. It is now known that collectively these di mensional magnitudes form the ordering of the reals. And this ordering is not just dense, but is also continuous. This chapter begins with a brief survey of how the rationals have figured, or been treated, (...) from the time of Eudoxus through to present-day double-barreled abstractionism. Then it turns to a more detailed study of Euclid’s account of ratios, and their method of abstraction. Euclid’s method proves to be a precursor of double-barreled abstractionism. But this kind of abstractionism fails to ensure that any natural number is ‘itself again’, _qua_ rational number. And the Euclidean method of abstraction has the drawback that it does not _create_ (or explain our entitlement to be committed to the exis tence of) rational numbers on the basis of our prior grasp of natural numbers. The method employed in Natural Logicism that will ‘get’ the rationals from the naturals and recognize the naturals as themselves again _qua_ rationals will be explained in Chapter 16. (shrink)

In 1995 we gave a new simple principle of combinatorial set theory and showed that it implies the existence of a nontrivial elementary embedding from a rank into itself, and follows from the existence of a nontrivial elementary embedding from V into M, where M contains the rank at the first fixed point above the critical point. We then gave a “diamondization” of this principle, and proved its relative consistency by means of a standard forcing argument.

We show that the weak monadic second order theory of the structure is first order interpretable in its automorphism group.

We study some properties of the quotient forcing notions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{tr(I)} = \wp(2^{< \omega})/tr(i)}$$\end{document} and PI = B(2ω)/I in two special cases: when I is the σ-ideal of meager sets or the σ-ideal of null sets on 2ω. We show that the remainder forcing RI = Qtr(I)/PI is σ-closed in these cases. We also study the cardinal invariant of the continuum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{h}_{\mathbb{Q}}}$$\end{document}, the distributivity (...) number of the quotient \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Dense(\mathbb{Q})/nwd}$$\end{document}, in order to show that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\wp(\mathbb{Q})/nwd}$$\end{document} collapses \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{c}}$$\end{document} to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{h}_{\mathbb{Q}}}$$\end{document}, thus answering a question addressed in Balcar et al. (Fundamenta Mathematicae 183:59–80, 2004). (shrink)

Extended Rationality: A Hinge Epistemology provides a novel account of the structure of epistemic justification. Its central claim builds upon Wittgenstein's idea in On Certainty that epistemic justifications hinge on some basic assumptions and that epistemic rationality extends to these very hinges. It exploits these ideas to address major problems in epistemology, such as the nature of perceptual justifications, external world skepticism, epistemic relativism, the epistemic status of basic logical laws, of the Principle of the Uniformity of Nature, of our (...) belief in the existence of the past and of other minds, and the nature of testimonial justification. Along the way, further technical issues, such as the scope of the Principle of Closure of epistemic operators under known entailment, the notion of transmission failure, and the existence of entitlements are addressed in new and illuminating ways. (shrink)

Believing rationally is epistemically valuable, or so we tend to think. It’s something we strive for in our own beliefs, and we criticize others for falling short of it. We theorize about rationality, in part, because we want to be rational. But why? I argue that how we answer this question depends on how permissive our theory of rationality is. Impermissive and extremely permissive views can give good answers; moderately permissive views cannot.

The study of rationality and practical reason, or rationality in action, has been central to Western intellectual culture. In this invigorating book, John Searle lays out six claims of what he calls the Classical Model of rationality and shows why they are false. He then presents an alternative theory of the role of rationality in thought and action. A central point of Searle's theory is that only irrational actions are directly caused by beliefs and desires—for example, the actions of a (...) person in the grip of an obsession or addiction. In most cases of rational action, there is a gap between the motivating desire and the actual decision making. The traditional name for this gap is "freedom of the will." According to Searle, all rational activity presupposes free will. For rationality is possible only where one has a choice among various rational as well as irrational options. Unlike many philosophical tracts, Rationality in Action invites the reader to apply the author's ideas to everyday life. Searle shows, for example, that contrary to the traditional philosophical view, weakness of will is very common. He also points out the absurdity of the claim that rational decision making always starts from a consistent set of desires. Rational decision making, he argues, is often about choosing between conflicting reasons for action. In fact, humans are distinguished by their ability to be rationally motivated by desire-independent reasons for action. Extending his theory of rationality to the self, Searle shows how rational deliberation presupposes an irreducible notion of the self. He also reveals the idea of free will to be essentially a thesis of how the brain works. (shrink)

This paper proposes a new account of bounded or minimal doxastic rationality (in the sense of Cherniak 1986), based on the notion that beliefs are answers to questions (à la Yalcin 2018). The core idea is that minimally rational beliefs are linked through thematic connections, rather than entailment relations. Consequently, such beliefs are not deductively closed, but they are closed under parthood (where a part is an entailment that answers a smaller question). And instead of avoiding all inconsistency, minimally rational (...) believers only avoid blatant inconsistencies (where some beliefs are blatantly inconsistent when they contradict one another on a particular question). Rather than cohering into a single overall world view, beliefs are more loosely connected in what is best described as a web of questions. This view of minimally rational belief naturally gives rise to an account of deductive inquiry on which deductive reasoning is a matter of posing new questions. (shrink)

In Minimal Rationality, Christopher Cherniak boldly challenges the myth of Man the the Rational Animal and the central role that the "perfectly rational...

Does rationality require logical omniscience? Our best formal theories of rationality imply that it does, but our ordinary evaluations of rationality seem to suggest otherwise. This paper aims to resolve the tension by arguing that our ordinary evaluations of rationality are not only consistent with the thesis that rationality requires logical omniscience, but also provide a compelling rationale for accepting this thesis in the first place. This paper also defends an account of apriori justification for logical beliefs that is designed (...) to explain the rational requirement of logical omniscience. On this account, apriori justification for beliefs about logic has its source in logical facts, rather than psychological facts about experience, reasoning, or understanding. This account has important consequences for the epistemic role of experience in the logical domain. In a slogan, the epistemic role of experience in the apriori domain is not a justifying role, but rather an enabling and disabling role. (shrink)

Rational Powers in Action presents a conception of instrumental rationality as governing actions that are extended in time with indeterminate ends. Tenenbaum argues that previous philosophical theories in this area, in focusing on momentary snapshots of the mind of idealized agents, miss central aspects of human rationality.

There are at least two threads in our thought and talk about rationality, both practical and theoretical. In one sense, to be rational is to respond correctly to the reasons one has. Call this substantive rationality. In another sense, to be rational is to be coherent, or to have the right structural relations hold between one’s mental states, independently of whether those attitudes are justified. Call this structural rationality. According to the standard view, structural rationality is associated with a distinctive (...) set of requirements that mandate or prohibit certain combinations of attitudes, and it’s in virtue of violating these requirements that incoherent agents are irrational. I think the standard view is mistaken. The goal of this paper is to explain why, and to motivate an alternative account: rather than corresponding to a set of law-like requirements, structural rationality should be seen as corresponding to a distinctive kind of pro tanto rational pressure—i.e. something that comes in degrees, having both magnitude and direction. Something similar is standardly assumed to be true of substantive rationality. On the resulting picture, each dimension of rational evaluation is associated with a distinct kind of rational pressure—substantive rationality with (what I call) justificatory pressure and structural rationality with attitudinal pressure. The former is generated by one’s reasons while the latter is generated by one’s attitudes. Requirements turn out to be at best a footnote in the theory of rationality. (shrink)

Axiomatic rationality is defined in terms of conformity to abstract axioms. Savage limited axiomatic rationality to small worlds, that is, situations in which the exhaustive and mutually exclusive set of future states S and their consequences C are known. Others have interpreted axiomatic rationality as a categorical norm for how human beings should reason, arguing in addition that violations would lead to real costs such as money pumps. Yet a review of the literature shows little evidence that violations are actually (...) associated with any measurable costs. Limiting axiomatic rationality to small worlds, I propose a naturalized version of rationality for situations of intractability and uncertainty, all of which are not in. In these situations, humans can achieve their goals by relying on heuristics that may violate axiomatic rationality. The study of ecological rationality requires formal models of heuristics and an analysis of the structures of environments these can exploit. It lays the foundation of a moderate naturalism in epistemology, providing statements about heuristics we should use in a given situation. Unlike axiomatic rationality, ecological rationality can explain less-is-more effects, formalize when one should move from ‘is’ to ‘ought,’ and be evaluated by goals beyond coherence, such as predictive accuracy, frugality, and efficiency. Ecological rationality can be seen as a formalization of means–end instrumentalist rationality, based on Herbert Simon’s insight that rational behavior is a function of the mind and its environment. (shrink)

Rational Rules argues that moral learning can be understood in terms of general-purpose rational learning procedures. Nichols provides statistical learning accounts of some fundamental aspects of moral development, combining aspects of traditional empiricist and rationalist approaches.

"Rationalism in Politics, " first published in 1962, has established the late Michael Oakeshott as the leading conservative political theorist in modern Britain. This expanded collection of essays astutely points out the limits of "reason" in rationalist politics.Oakeshott criticizes ideological schemes to reform society according to supposedly "scientific" or rationalistic principles that ignore the wealth and variety of human experience. "Rationalism in politics," says Oakeshott, "involves a misconception with regard to the nature of human knowledge." History has shown that it (...) produces unexpected, often disastrous results. "Having cut himself off from the traditional knowledge of his society, and denied the value of any education more extensive than a training in a technique of analysis," the Rationalist succeeds only in undermining the institutions that hold civilized society together. In this regard, rationalism in politics is "a corruption of the mind."Timothy Fuller is Professor of Political Science and Dean of the College at Colorado College. (shrink)