The neural realization of number in abstract form is implausible, but from this it doesn't follow that numbers are not abstract. Clear definitions of abstraction are needed so they can be applied homogenously to numerical and non-numerical cognition. To achieve a better understanding of the neural substrate of abstraction, productive cognition must be investigated.

Clarke and Beck's defense of the theoretical construct “approximate number system” is flawed in serious ways – from biological misconceptions to mathematical naïveté. The authors misunderstand behavioral/psychological technical concepts, such as numerosity and quantical cognition, which they disdain as “exotic.” Additionally, their characterization of rational numbers is blind to the essential role of symbolic reference in the emergence of number.

This article examines the primacy of real-world bodily experience for understanding the human mind. I defend the idea that the peculiarities of the living human brain and body, and the bodily experiences they sustain, are essential ingredients of human sense-making and conceptual systems. Conceptual systems are created, brought forth, understood and sustained, through very specific cognitive mechanisms ultimately grounded in bodily experience. They don't have a transcendental abstract logic independent of the species-specific bodily features. To defend this position, I focus (...) on a case study: the fundamental concept of time flow. Using tools of cognitive linguistics, I analyse the foundations of this concept, as it is manifested naturally in everyday language. I show that there is a precise conceptual metaphor whose inferential structure gives an account of a huge variety of linguistic expressions, semantic contents, and unconscious spontaneous gestures: Time Events Are Things In Space. I discuss various special cases of this conceptual metaphor. This mapping grounds its source domain in specific spatial bodily experiences and projects its inferential structure onto a target domain making inferences in that domain possible. This mechanism allows us to unconsciously, effortlessly, and precisely understand expressions such as ‘the year 2000 is approaching’ or ‘the days ahead of us’. The general form of the mapping seems to be universal. The analysis raises important issues which demand a deeper and richer understanding of cognition and the mind: a view that sees the mind as fully embodied. In order to avoid misunderstandings with a general notion of ‘embodiment’ which has become fashionable in contemporary cognitive science, I describe what I mean by ‘full embodiment’: an embodied-oriented approach that has an explicit commitment to all of cognition, not just to low-level aspects of cognition such as sensory-motor activity or locomotion . I take embodiment to be a living phenomenon in which the primacy of bodily grounded experience is inherently part of the very subject matter of the study of the mind. (shrink)

Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo , is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides the three usual (...) operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations. (shrink)

We establish, for the quantum system made up of a single free particle, the formula ΔE Δt≳(v/c) ħ, where ΔE is the precision to whichE can be ascertained in time Δt. The measurement can be carried out with zero disturbance inE itself.

In the longstanding foundational debate whether to require that probability is countably additive, in addition to being finitely additive, those who resist the added condition raise two concerns that we take up in this paper. (1) _Existence_: Settings where no countably additive probability exists though finitely additive probabilities do. (2) _Complete Additivity_: Where reasons for countable additivity don’t stop there. Those reasons entail complete additivity—the (measurable) union of probability 0 sets has probability 0, regardless the cardinality of that union. Then (...) probability distributions are discrete, not continuous. We use Easwaran’s (Easwaran, Thought 2:53–61, 2013) advocacy of the _Comparative_ principle to illustrate these two concerns. Easwaran supports countable additivity, both for numerical probabilities and for finer, qualitative probabilities, by defending a condition he calls the _Comparative_ principle [ \({\mathcal{C}}\) ]. For numerical probabilities, principle \({\mathcal{C}}\) contrasts pairs, P 1 and P 2, defined over a common partition \(\prod\) = {a _i_ : _i_ ∈ I} of measurable events. \({\mathcal{C}}\) requires that no P 1 may be pointwise dominated, i.e., no (finitely additive) probability P 2 exists such that for each _i_ ∈ I, P 2 (a _i_ ) > P 1 (a _i_ ). By design, the cardinality of \(\prod\) is not limited in \({\mathcal{C}}\), which Easwaran asserts is important when arguing that the principle does not require more, or less, than that probability is countably additive. We agree that a numerical probability P satisfies principle \({\mathcal{C}}\) in all partitions just in case P is countably additive. However, we show that for numerical probabilities, by considering the size of the algebra of events to which probability is applied, principle \({\mathcal{C}}\) is subject to each of the above concerns, (1) and (2). Also, Easwaran considers principle \({\mathcal{C}}\) with non-numerical, qualitative probabilities, where a qualitative probability may be finer than an almost agreeing numerical probability P. A qualitative probability is regular if possible events are strictly more likely than impossible events. Easwaran motivates and illustrates regular qualitative probabilities using a continuous, almost agreeing quantitative probability that is uniform on the unit interval. We make explicit the conditions for applying principle \({\mathcal{C}}\) with qualitative probabilities and show that \({\mathcal{C}}\) restricts regular qualitative probabilities to those whose almost agreeing quantitative probabilities are completely additive. For instance, Easwaran’s motivating example of a regular qualitative probability is precluded by principle \({\mathcal{C}}\). (shrink)

La educación cívica se encuentra en la misma base de la democracia . T odo sistema democrático que prescinda de esta necesidad acabará haciendo de s v anecerse la racionalidad democrática de sus instituciones. La democracia liberal es un buen ejemplo de este debilitamiento pr o g res i v o de las estructuras democráticas. Benjamin R. Barber no tarda en referirse a ella como "democracia débil". La democracia carece de plenitud sin ciudadanos fo r mados cívicamente. Educación y democracia (...) están indisol u b lemente unidas. P or eso, para este autor la r e generación de la democracia, con sus contenidos reales de pa r ticipación política, pasa necesariamente por la educación. Enseñar democracia es se r vir a la comuni dad. (shrink)

Throughout the Old Testament, the stories, laws, and songs not only teach a way of life that requires individuals to be moral, but they demonstrate how. In biblical studies, character ethics has been one of the fastest-growing areas of interest. Whereas ethics usually studies rules of behavior, character ethics focuses on how people are formed to be moral agents in the world. This book presents the most up-to-date academic work in Old Testament character ethics, covering topics throughout the Torah, the (...) Prophets, and the Writings, in addition to the use of the Bible in the modern world. In addition to Carroll and Lapsley, contributors are Denise M. Ackermann, Cheryl B. Anderson, Samuel E. Balentine, William P. Brown, Walter Brueggemann, Thomas B. Dozeman, Bob Ekblad, Jose Rafael Escobar R., Theodore Hiebert, Kathleen O'Connor, Dennis T. Olson, J. David Pleins, Luis R. Rivera Rodriguez, J. J. M. Roberts, and Daniel L. Smith-Christopher. (shrink)

In four experiments, we offer evidence that virtues are often judged as uniquely important for some business practices (e.g., hospital management and medical error investigation). Overall, actions done only from virtue (either by organizations or individuals) were judged to feel better, to be more praiseworthy, to be more morally right, and to be associated with more trustworthy leadership and greater personal life satisfaction compared to actions done only to produce the best consequences or to follow the correct moral rule. These (...) results accord with claims made by some virtue ethicists. The current data contribute to a small but growing body of literature emphasizing both empirical soundness and philosophical rigor in the scientific study of virtue. Results also offer some guidance concerning how businesses, employees, and executives are evaluated and perceived. Implications for theory and practice are discussed. (shrink)

Accepted quantum description is stochastic, yet history is nonstochastic, i.e., not representable by a probability distribution. Therefore ordinary quantum mechanics is unsuited to describe history. This is a limitation of the accepted quantum theory, rather than a failing of mechanics in general. To remove the limitation, it would be desirable to find a form of quantum mechanics that describes the future stochastically and the past nonstochastically. For this purpose it proves sufficient to introduce into quantum mechanics, by means of a (...) perfected formal correspondence, certain analogs of the classical initial-condition constants. Through the restoration of such parameters at the quantum level one accomplishes a natural accommodation of time anisotropy, wave-function reduction, and “event” description by quantum mechanical equations of motion alone, without the need for extra postulates (e.g., a projection postulate). This requires a complete restructuring of quantum measurement theory. (shrink)

Vitruvius has something interesting to say at De architectura 2.8.8: Non enim quae sunt e molli caemento subtili facie venustatis, non eae possunt esse in vetustate non ruinosae. itaque cum arbitrio communium parietum sumuntur, non aestimant eos quanti facti fuerint, sed cum ex tabulis inveniunt eorum locationes, pretia praeteritorum annorum singulorum deducunt octogesimas et ita – ex reliqua summa parte reddi pro his parietibus – sententiam pronuntiant eos non posse plus quam annos LXXX durare.Those structures made of soft rubble, for (...) all their subtle attractiveness, are not the ones that will resist ruin as time passes. And thus when assessors are appointed to evaluate party walls, they never assess soft rubble walls according to their initial cost, but rather, when they look at the price recorded in the original contracts, they deduct 1/80th of that sum for each subsequent year, and the remaining amount is fixed as the current value of the walls. They have rendered judgement, in effect, that such walls cannot last more than 80 years.By contrast, mud-brick walls were not depreciated at all if they were standing when assessed. The calculation performed for concrete walls demonstrates clear understanding of what we call ‘depreciation’ or ‘amortization’ in ancient Roman thought. It appears to have been overlooked to date. (shrink)

An analysis is presented of the significance and consequent limitations on the applicability of the von Neumann measurement postulate in quantum mechanics. Directly observable quantities, such as the expectation value of the velocity operator, are distinguished from mathematical constructs, such as the expectation value of the canonical momentum, which are not directly observable. A simple criterion to distinguish between the two types of operators is derived. The non-observability of the electromagnetic four-potentials is shown to imply the non-measurability of the canonical (...) momentum. The concept of a mechanical gauge is introduced and discussed. Classically the Lagrangian is nonunique within a total time derivative. This may be interpreted as the freedom of choosing a “mechanical” (M) gauge function. In quantum mechanics it is often implicitly assumed that the M-gauge vanishes. However, the requirement that directly observable quantities be independent of the arbitrary mechanical gauge is shown to lead to results analogous to those derived from the requirement of electromagnetic gauge independence of observables. The significance of the above to the observability of transition amplitudes between field-free energy eigenstates in the presence (and absence) of electromagnetic fields is discussed. E- and M-gauge independent transition amplitudes between field-free energy eigenstates in the absence of electromagnetic fields are defined. It is shown that, in general, such measurable amplitudes cannot be defined in the presence of externally applied time-dependent fields. Transition amplitudes in the presence of time-independent fields are discussed. The path dependence of previous derivations of E-gauge independent Hamiltonians and/or transition amplitudes in the presence of electromagnetic fields are related to the inherent M-gauge dependence of these quantities in the presence of such fields. (shrink)

. Ill BERGSONS THEORY OF ART . . .141 THE PHILOSOPHY OF INTENSIVE MANIFOLDS I I CINDERS ..... 215 APPENDICES A. REFLECTIONS ON VIOLENCE . . 249 B. PLAN FOR A ...

In preceding parts of this paper the possibility was examined of accomplishing the entirety of physical description by means of mechanics, without help from field-theoretical ideas. Apart from some easily obtained qualitative agreements with general descriptive features of nuclei and elementary particles, we were balked in this program by an inability to handle in purely mechanical terms the relativistic many-body problem. The present paper is addressed directly to the latter problem. No quantitative calculations are attempted, but three suggestions are made (...) — each of a quite radical nature — concerning the reformulation that will be necessary to restore mechanics to the mainstream of physics. (shrink)

We consider the relation between versions of Ramsey’s Theorem and König’s Infinity Lemma, in the absence of the axiom of choice.

Deep brain stimulation — a novel surgical procedure — is emerging as a treatment of last resort for people diagnosed with neuropsychiatric disorders such as severe obsessive-compulsive disorder. The US Food and Drug Administration granted a so-called humanitarian device exemption to allow patients to access this intervention, thereby removing the requirement for a clinical trial of the appropriate size and statistical power. Bypassing the rigors of such trials puts patients at risk, limits opportunities for scientific discovery, and gives device manufacturers (...) unique marketing opportunities. We argue that Congress and federal regulators should revisit the humanitarian device exemption to ensure that it is not used to sidestep careful research that can offer valuable data with appropriate patient safeguards. (shrink)

Catalepton 10 is a unique survival from antiquity: it is the only parody of an entire poem to reach us, and is written in pure iambic trimeters, a near intractable metre. Addressed to Sabinus, an upstart muleteer, the poem launches a stinging attack at him, and draws attention to his status as a parvenu. It remains incredibly close to its charming model—Catullus 4 —in structural, lexical, stylistic and metrical terms, but rather different in purport. In attempting to reassess a number (...) of problems in the text of the poem, the textual critic ought largely to be guided by the relationship of Sabinus ille to its model, as it is clear that the author of Catalepton 10 was an incredibly close reader of the Catullan text and sought not only to imitate through parody but also to subvert and deflate his predecessor's poem. (shrink)