We show that many singular cardinals λ above a strongly compact cardinal have regular ultrafilters D that violate the finite square principle $\square _{\lambda ,D}^{\mathit{fin}}$ introduced in [3]. For such ultrafilters D and cardinals λ there are models of size λ for which Mλ / D is not λ⁺⁺-universal and elementarily equivalent models M and N of size λ for which Mλ / D and Nλ / D are non-isomorphic. The question of the existence of such ultrafilters and models (...) was raised in [1]. (shrink)

Classically, any structure for a signature ${\rm{\Sigma }}$ may be completed to a model of a desired regular theory ${T}}$ by means of the chase construction or small object argument. Moreover, this exhibits ${\rm{Mod}}\left$ as weakly reflective in ${\rm{Str}}\left$.We investigate this in the constructive setting. The basic construction is unproblematic; however, it is no longer a weak reflection. Indeed, we show that various reflectivity principles for models of regular theories are equivalent to choice principles in the ambient set theory. However, (...) the embedding of a structure into its chase-completion still satisfies a conservativity property, which suffices for applications such as the completeness of regular logic with respect to Tarski models.Unlike most constructive developments of predicate logic, we do not assume that equality between symbols in the signature is decidable. While in this setting, we also give a version of one classical lemma which is trivial over discrete signatures but more interesting here: the abstraction of constants in a proof to variables. (shrink)

In earlier work by the first and second authors, the equivalence of a finite square principle $\square^{\mathrm{fin}}_{\lambda,D}$ with various model-theoretic properties of structures of size $\lambda $ and regular ultrafilters was established. In this paper we investigate the principle $\square^{\mathrm{fin}}_{\lambda,D}$—and thereby the above model-theoretic properties—at a regular cardinal. By Chang’s two-cardinal theorem, $\square^{\mathrm{fin}}_{\lambda,D}$ holds at regular cardinals for all regular filters $D$ if we assume the generalized continuum hypothesis. In this paper we prove in ZFC that, for certain (...) regular filters that we call $\mathit{doubly}^{+}$ regular, $\square^{\mathrm{fin}}_{\lambda,D}$ holds at regular cardinals, with no assumption about GCH. Thus we get new positive answers in ZFC to Open Problems 18 and 19 in Chang and Keisler’s book Model Theory. (shrink)

Many philosophers have become worried about the use of standard real numbers for the probability function that represents an agent's credences. They point out that real numbers can't capture the distinction between certain extremely unlikely events and genuinely impossible ones—they are both represented by credence 0, which violates a principle known as “regularity.” Following Skyrms 1980 and Lewis 1980, they recommend that we should instead use a much richer set of numbers, called the “hyperreals.” This essay argues that (...) this popular view is the result of two mistakes. The first mistake, which this essay calls the “numerical fallacy,” is to assume that a distinction that isn't represented by different numbers isn't represented at all in a mathematical representation. In this case, the essay claims that although the real numbers do not make all relevant distinctions, the full mathematical structure of a probability function does. The second mistake is that the hyperreals make too many distinctions. They have a much more complex structure than credences in ordinary propositions can have, so they make distinctions that don't exist among credences. While they might be useful for generating certain mathematical models, they will not appear in a faithful mathematical representation of credences of ordinary propositions. (shrink)

In this paper I explore the relationship between the “Humean” regularity view of causation, the view that a cause is a necessary condition of its effect, and the asymmetry of causation—the principle that if an event e1 causes e2, then it is false that e2 causes e1. I argue that the regularity view, in combination with the view that a cause is a necessary condition of its effect, is inconsistent with the asymmetry of causation, and that the (...) inconsistency can be removed by a modification of the view that a cause is a necessary condition of its effect that captures what is plausible in that view. I defend Hume, then, against the objection that he cannot accommodate a cause as being a necessary condition of its effect without absurdly denying the asymmetry of causation. This is only a limited defense, though, for I do not address the issue on which the tenability of the regularity view ultimately depends: viz., whether it can distinguish between causal laws and accidental generalizations without appealing to natural necessity. (shrink)

Prediction of daily rainfall is important for flood forecasting, reservoir operation, and many other hydrological applications. The artificial intelligence algorithm is generally used for stochastic forecasting rainfall which is not capable to simulate unseen extreme rainfall events which become common due to climate change. A new model is developed in this study for prediction of daily rainfall for different lead times based on sea level pressure which is physically related to rainfall on land and thus able to predict unseen rainfall (...) events. Daily rainfall of east coast of Peninsular Malaysia was predicted using SLP data over the climate domain. Five advanced AI algorithms such as extreme learning machine, Bayesian regularized neural networks, Bayesian additive regression trees, extreme gradient boosting, and hybrid neural fuzzy inference system were used considering the complex relationship of rainfall with sea level pressure. Principle components of SLP domain correlated with daily rainfall were used as predictors. The results revealed that the efficacy of AI models is predicting daily rainfall one day before. The relative performance of the models revealed the higher performance of BRNN with normalized root mean square error of 0.678 compared with HNFIS, BART, xgBoost, and ELM. Visual inspection of predicted rainfall during model validation using density-scatter plot and other novel ways of visual comparison revealed the ability of BRNN to predict daily rainfall one day before reliably. (shrink)

In standard probability theory, probability zero is not the same as impossibility. But many have suggested that only impossible events should have probability zero. This can be arranged if we allow infinitesimal probabilities, but infinitesimals do not solve all of the problems. We will see that regular probabilities are not invariant over rigid transformations, even for simple, bounded, countable, constructive, and disjoint sets. Hence, regular chances cannot be determined by space-time invariant physical laws, and regular credences cannot satisfy seemingly reasonable (...) symmetry principles. Moreover, the examples here are immune to the objections against Williamson’s infinite coin flips. (shrink)

Roger Shepard's proposals and supporting experiments concerning evolutionary internalized regularities have been very influential in the study of vision and in other areas of psychology and cognitive science. This paper examines issues concerning the need, nature, explanatory role, and justification for postulating such internalized constraints. In particular, I seek further clarification from Shepard on how best to understand his claim that principles of kinematic geometry underlie phenomena of motion perception. My primary focus is on the ecological validity of Shepard's kinematic (...) constraint in the context of ordinary motion perception. First, I explore the analogy Shepard draws between internalized circadian rhythms and the supposed internalization of kinematic geometry. Next, questions are raised about how to interpret and justify applying results from his own and others' experimental studies of apparent motion to more everyday cases of motion perception in richer environments. Finally, some difficulties with Shepard's account of the evolutionary development of his kinematic constraint are considered. Key Words: apparent motion; circadian rhythms; constraints; ecological validity; evolution; internalizated regularities; kinematic principle. (shrink)

In reply to certain cosmological arguments for theism, critics regularly argue that the causal principle ex nihilo nihil fit may be false. Various theistic counter-replies to this challenge have emerged. One type of strategy is to double down on ex nihilo nihil fit. Another, very different strategy of counter-reply is to grant for the sake of argument that the principle is false, while maintaining that sound cosmological arguments can be formulated even with this concession in place. Notably, one (...) can employ a weaker opening premise formulated in modal terms, proceeding for instance from the proposition that for any contingent object coming into existence it is at least possible that it have a cause. My aim here is to try out a related strategy for weakening the relevant opening premise. Granting that it is possible for a contingent object to come into existence out of nothing without a cause, I proceed from the extremely modest claim that the obtaining of exceptionless longstanding contingent regularities demands an explanation. As such, the contingent regularity that empirically accessible macro-level contingent objects do not pop into existence causelessly demands explanation. And as it turns out, that explanation will have to be in terms of an object or objects possessed of at least some of the traditional divine attributes. (shrink)

If the laws of nature are as the Humean believes, it is an unexplained cosmic coincidence that the actual Humean mosaic is as extremely regular as it is. This is a strong and well-known objection to the Humean account of laws. Yet, as reasonable as this objection may seem, it is nowadays sometimes dismissed. The reason: its unjustified implicit assignment of equiprobability to each possible Humean mosaic; that is, its assumption of the principle of indifference, which has been attacked (...) on many grounds ever since it was first proposed. In place of equiprobability, recent formal models represent the doxastic state of total ignorance as suspension of judgment. In this paper I revisit the cosmic coincidence objection to Humean laws by assessing which doxastic state we should endorse. By focusing on specific features of our scenario I conclude that suspending judgment results in an unnecessarily weak doxastic state. First, I point out that recent literature in epistemology has provided independent justifications of the principle of indifference. Second, given that the argument is framed within a Humean metaphysics, it turns out that we are warranted to appeal to these justifications and assign a uniform and additive credence distribution among Humean mosaics. This leads us to conclude that, contrary to widespread opinion, we should not dismiss the cosmic coincidence objection to the Humean account of laws. (shrink)

Thomas Brown was one of the tail-enders of the Scottish Enlightenment. He shared with Dugald Stewart the chair of Moral Philosophy at the University of Edinburgh from 1810 until his premature death in 1820. He is sometimes classed with the Scottish common-sense philosophers and, to some extent at least, his basic philosophical principles were akin to those of the common-sense philosophy. He did, for instance, forfeit the issue of the justification of some of our most basic beliefs and rested them, (...) instead, on their being intuitively irresistible; in particular, he thought that some of our most basic beliefs could be seen as permanent principles of human nature—a claim made popular by Thomas Reid. Based on his theory of the workings of the human mind—which was developed in a course of lectures on the philosophy of mind presented at the University of Edinburgh and appeared posthumously as a book titled Lectures on the Philosophy of the Human Mind—some philosophers and psychologists have characterised him as an ‘associationist’.1 Brown ’s main contribution to the philosophy of causation was his book Inquiry into the Relation of Cause and Effect, published in 1818. This is, actually, the third edition of his little book titled Observations on. (shrink)

According to Husserl, Hume’s empirical method was deeply flawed—like all empiricists, Hume did not, and could not adequately justify his method, much less his findings. Instead, Hume gives us a “circular” and “irrational” “psychological explanation” of “mediate judgments of fact,” i.e. of inductive inferences. Yet Husserl was certain that he could justify both his own method and his own findings with an appeal to the phenomenological, pre-theoretical, pre-naturalistic “epoché”. However, whether or not Husserl’s notion of an epoché is justified, or (...) even viable, is not our focus here. Rather, our issue is with Hume, particularly: How could Hume have responded? In this paper, I show that in Book I of the Treatise, Hume did—however implicitly—appeal to a “pre-theoretical” notion of belief, which meets Husserl’s demands for a pre-theoretical grounding, i.e. a justificatory grounding. And so, his method is, at least in this respect, justified. But this belief is by no means “prenaturalistic.” Rather, it is a function of empirical data. In particular, it is a product of the “constant and coherent” impressions that seem to naturally obtain of experience. As a result, Hume’s method, which, in agreement with Husserl, we may characterize as psychology, does admit of a certain degree of regularity, but an empirical regularity. And according to Hume, contra Husserl’s complaints, this is the best that we can hope for; regularity will have to suffice, not certainty. However, it must be noted up front that this justification is implicit—Hume is not nearly as forthright as he could have been. Thus, making his position more explicit is the task of this paper. I am not presenting my own position, where I offer my own arguments. Instead, I present textual evidence, contextualized with ample explication. It is my hope that by doing so, Hume may more effectively make his case. (shrink)

With only two to five slots of visual working memory (VWM), humans are able to quickly solve complex visual problems to near optimal solutions. To explain the paradox between tightly constrained VWM and impressively complex human visual problem‐solving ability, we propose several principles for dynamic VWM allocation. In particular, we propose that complex visual information is represented in a temporal manner using only a few slots of VWM that include global and local visual chunks. We built a model of human (...) traveling salesman problem solving based on these principles of VWM allocation and tested the model with eye‐movement data. Exactly as the model predicted, human eye movements during traveling salesman problem solving have precise quantitative regularities with regard to both the general statistical pattern of attentional fixations and how they vary across individuals with different VWM capacities. Even though VWM capacity is very limited, eye movements dynamically allocate VWM resources to both local and global information, enabling attention to fine details without loss of the big picture. (shrink)

The Reading Augustine series presents short, engaging books offering personal readings of St. Augustine of Hippo's contributions to western philosophical, literary, and religious life. This two-volume work provides a new understanding of Western subjectivity as theorized in the Augustinian Rule. A theopolitical synthesis of Antiquity, the Rule is a humble, yet extremely influential example of subjectivity production. In these volumes, Jodra argues that the Classical and Late-Ancient communitarian practices along the Mediterranean provide historical proof of a worldview in which the (...) self and the other are not disjunctive components, but mutually inclusive forces. The Augustinian Rule is a culmination of this process and also the beginning of something new: The paradigm of the monastic self as protagonist of the new, medieval worldview. Three main theoretical challenges leading to, and present in the Rule are tackled: What are the sources of our modern understanding of subjectivity? Can Ancient sources provide an alternative genealogy that resists the individualistic turn of Modernity? And can the commons be saved without suppressing individuality? Jodra seeks to prove that the synthesis-which is also an appropriation-of Greek and Judaic sources carried out by the first Christians allowed for two contrasting models of subjectivity, the self-less and the other-less, to 'take turns' to dominate our understanding of human nature. The Greek world provided the political dimension and the Jewish world established the key theological principles of a Mediterranean synthesis which took place in Rome. Coherently and progressively, Jodra emphasizes the theopolitical nature of our worldview even today, and claim that the subject of the primitive Church is its most visible incarnation. These volumes therefore restore the unity of the Hellenistic and Judaic world as found by the first Christians, proving that the self and the other are two essential pieces in the construction of our world. (shrink)

I argue that moral principles involve the same sort of generalization as ordinary yet elusive generic generalizations in natural language such as ‘Tigers are striped’ or ‘Peppers are spicy’. A notable advantage of the generic view is that it simultaneously allows for pessimism and optimism about the role and status of moral principles in our lives. It provides a new perspective on the nature of moral principles on which principles are not apt for determining the moral status of particular actions (...) while they may be apt, and even fundamental, to our acquisition of moral knowledge. A natural consequence of the view is variation among moral principles, with some regularly warranting exceptions and some appearing arguably exceptionless. I will also argue that this generic conception of moral principles has significant advantages, as a normative model of moral reasoning, over the view of moral principles as defaults advanced in recent years. (shrink)

Regular polysemes are sets of ambiguous words that all share the same relationship between their meanings, such as CHICKEN and LOBSTER both referring to an animal or its meat. To probe how a distributional semantic model, here exemplified by bidirectional encoder representations from transformers (BERT), represents regular polysemy, we analyzed whether its embeddings support answering sense analogy questions similar to “is the mapping between CHICKEN (as an animal) and CHICKEN (as a meat) similar to that which maps between LOBSTER (as (...) an animal) to LOBSTER (as a meat)?” We did so using the LRcos model, which combines a logistic regression classifier of different categories (e.g., animal vs. meat) with a measure of cosine similarity. We found that (a) the model was sensitive to the shared structure within a given regular relationship; (b) the shared structure varies across different regular relationships (e.g., animal/meat vs. location/organization), potentially reflective of a “regularity continuum;” (c) some high-order latent structure is shared across different regular relationships, suggestive of a similar latent structure across different types of relationships; and (d) there is a lack of evidence for the aforementioned effects being explained by meaning overlap. Lastly, we found that both components of the LRcos model made important contributions to accurate responding and that a variation of this method could yield an accuracy boost of 10% in answering sense analogy questions. These findings enrich previous theoretical work on regular polysemy with a computationally explicit theory and methods, and provide evidence for an important organizational principle for the mental lexicon and the broader conceptual knowledge system. (shrink)

In this essay, I will argue for the actuality of principles. Principles are normative in that they regulate the relation of actuality and potentiality as well as operate across time, from the past and present to the future. They may also apply across space, that is, that the same principle operates in different places in the same way, for example the laws of motion. Principles mean that change follows certain regularities. I will examine the modality of principles, the relation (...) to pluralism. I will argue negatively for the principle of principles, that is, that the world actually exhibits or contains principles. I will then argue that principles as origins cannot be accounted for by ontology. Principles are neither material nor substantial beings but both of the latter presume, as generals or “universals,” the actuality of principles. Thus principles could be considered in the category of “thirds” in Peirce. I will argue that principles also support James’s model of a “pluralistic universe” of change. (shrink)

This paper investigates the principles □λ,δta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square^{{{\rm ta}}}_{\lambda,\delta}}$$\end{document}, weakenings of □λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_\lambda}$$\end{document} which allow δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\delta}$$\end{document} many clubs at each level but require them to agree on a tail-end. First, we prove that □λ,<ωta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square^{{\rm {ta}}}_{\lambda,< \omega}}$$\end{document} implies □λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_\lambda}$$\end{document}. Then, (...) by forcing from a model with a measurable cardinal, we show that □λ,2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_{\lambda,2}}$$\end{document} does not imply □λ,δta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square^{{\rm{ta}}}_{\lambda,\delta}}$$\end{document} for regular λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\lambda}$$\end{document}, and □δ+,δta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square^{{\rm{ta}}}_{\delta^+,\delta}}$$\end{document} does not imply □δ+,<δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_{\delta^+,< \delta}}$$\end{document}. With a supercompact cardinal the former result can be extended to singular λ, and the latter can be improved to show that □λ,δta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square^{{\rm {ta}}}_{\lambda,\delta}}$$\end{document} does not imply □λ,<δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_{\lambda,< \delta}}$$\end{document} for δ<λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\delta < \lambda}$$\end{document}. (shrink)

A regularity theory of causation analyses type-level causation in terms of Boolean difference-making. The essential ingredient that helps this theoretical framework overcome the problems of Hume’s and Mill’s classical accounts is a principle of non-redundancy: only Boolean dependency structures from which no elements can be eliminated track causation. The first part of this article argues that the recent regularity-theoretic literature has not consistently implemented this principle, for it disregarded an important type of redundancies: structural redundancies. Moreover, (...) it is shown that a regularity theory needs to be underwritten by a hitherto neglected metaphysical background assumption stipulating that the world’s causal makeup is not ambiguous. Against that background, the second part then develops a new regularity theory that does justice to all types of redundancies and, thereby, provides the first all-inclusive notion of Boolean difference-making. (shrink)

Eugene Wigner's several general discussions of symmetry and invariance principles are among the canonical texts of contemporary philosophy of physics. Wigner spoke from a position of authority, having pioneered for recognition of the importance of symmetry principles from nuclear to molecular physics. But perhaps recent commentators have not sufficiently stressed that Wigner always took care to situate the notion of invariance principles with respect to two others, initial conditions and laws of nature. Wigner's first such general consideration of invariance principles, (...) an address presented at Einstein's 70th birthday celebration, held in Princeton on 19 March 1949, began by laying out just this distinction, and in a way that seems to suggest that the three notions arise through abstraction in an analysis of the general problem of cognition in the natural sciences: The world is very complicated and it is clearly impossible for the human mind to understand it completely. Man has therefore devised an artifice which permits the complicated nature of the world to be blamed on something which is called accidental and thus permits him to abstract a domain in which simple laws can be found. The complications are called initial conditions; the domain of regularities, laws of nature. the underlying abstraction is probably one of the most fruitful the human mind has made. It has made the natural sciences possible. (shrink)

The authors show, by means of a finitary version □finλ, D of the combinatorial principle □b*λ of [7], the consistency of the failure, relative to the consistency of supercompact cardinals, of the following: for all regular filters D on a cardinal λ, if Mi and Ni are elementarily equivalent models of a language of size ≤ λ, then the second player has a winning strategy in the Ehrenfeucht-Fraïssé game of length λ+ on ∏i Mi/D and ∏i Ni/D. If in (...) addition 2λ=λ+ and i <λ implies |Mi|+|Ni|≤ λ+ this means that the ultrapowers are isomorphic. This settles negatively conjecture 18 in [2]. (shrink)

In 'Yeogi (禮記)', the Chinese scriptures of Confucianism, they recoded the solar calendar of modern viewpoints. According to the ancient document, the 24 solar terms was one of seasonal divisions in a year. The regularly change of the four seasons play an important part in the national economic project. For a national economy depended on agriculture in East Asia of ancient times, the administration to pay no regard to the change of the season was directly connected to the fall of (...) the nation. And then the legislator must enact laws to reflect the change of the season. According to the 'Wolryeong (月令)' in 'Yeogi (禮記)', there is recoded national regulations to suit with the each twelve momth. The first month of spring is the prime of the year (February). The month shows sign of new livingthings. The ruler take order to protect the first breath of spring and ought to put a ban on the military training and labor mobilization. The reasons are to safeguard the new life and not to interrupt the preparation for farming. Confucian attach value to the nature within a human’s way of life. Therefore the norm of human do correlate closely with the principle of nature. The rule of Wuju (宇宙) was not a simple concept of the natural phenomenon and Cheon (天) was not the Almighty for himself. Cheon was just the existence of virtue and moral influence in the confidence of man. And Ji (地) was the Mother of all things. In this space man had to manage the world in sympathy with the process of cheonJi (天地); Cheonsi (天時), JIri (地利), Inhwa (人和). (shrink)

The authors show. by means of a finitary version $\square_{\lambda D}^{fin}$ of the combinatorial principle $\square_\lambda^{h*}$ of [7]. the consistency of the failure, relative to the consistency of supercompact cardinals, of the following: for all regular filters D on a cardinal A. if Mi and Ni are elementarily equivalent models of a language of size $\leq \lambda$ , then the second player has a winning strategy in the Ehrenfeucht- $Fra\uml{i}ss\acute{e}$ game of length $\lambda^{+}$ on $\pi_{i} M_{i}/D$ and $\pi_{i} N_{i}/D$ (...) . If in addition $2^{\lambda} = \labda^{+}$ and i < $\lambda$ implies | $M_{i}$ | +| $N_{i}$ | $\leq$ \lambda^{+} this means that the ultrapowers are isomorphic. This settles negatively conjecture 18 in [2]. (shrink)

This chapter focuses on the “America” part of Captain America's name and explores the more political aspects of his life and character. It looks at patriotism in general and how to characterize Captain America's brand of it; Cap's uneasy relationship with politics and the United States government; and how Cap puts principles above politics, even if it means defying his own government and giving up the shield and the title. The chapter explains that Cap's devotion to his country is based (...) on the principles and ideals upon which it was founded, and he regularly holds his government accountable to those same standards, which he interprets as inclusive and cosmopolitan, applying to the world outside America as well as everybody within it. It dispels any illusions that Captain America is a jingoist flag‐waver, and explains instead that he embodies an inclusive and cosmopolitan patriotism that balances idealism with clear‐eyed pragmatism. (shrink)

This paper develops the model theory of ordered structures that satisfy Keisler’s regularity scheme and its strengthening REF ${(\mathcal{L})}$ (the reflection scheme) which is an analogue of the reflection principle of Zermelo-Fraenkel set theory. Here ${\mathcal{L}}$ is a language with a distinguished linear order <, and REF ${(\mathcal {L})}$ consists of formulas of the form $$\exists x \forall y_{1} < x \ldots \forall y_{n} < x \varphi (y_{1},\ldots ,y_{n})\leftrightarrow \varphi^{ < x}(y_1, \ldots ,y_n),$$ where φ is an ${\mathcal{L}}$ (...) -formula, φ shrink)

We extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship to the first order principles of Regularity and Super Regularity.

This doctoral dissertation investigates the notion of physical necessity. Specifically, it studies whether it is possible to account for non-accidental regularities without the standard assumption of a pre-existent set of governing laws. Thus, it takes side with the so called deflationist accounts of laws of nature, like the humean or the antirealist. The specific aim is to complement such accounts by providing a missing explanation of the appearance of physical necessity. In order to provide an explanation, I recur to fields (...) that have not been appealed to so far in discussions about the metaphysics of laws. Namely, I recur to complex systems’ theory, and to the foundations of statistical mechanics. The explanation proposed is inspired by how complex systems’ theory has elucidated the way patterns emerge, and by the probabilistic explanations of the 2nd law of thermodynamics. More specifically, this thesis studies how some constraints that make no direct reference to the dynamics can be a sufficient condition for obtaining in the long run, with high probability, stable regular behavior. I hope to show how certain metaphysical accounts of laws might benefit from the insights achieved in these other fields. According to the proposal studied in this thesis, some regularities are not accidental not in virtue of an underlying physical necessity. The non-accidental character of certain regular behavior is only due to its overwhelming stability. Thus, from this point of view the goal becomes to explain the stability of temporal patterns without assuming a set of pre-existent guiding laws. It is argued that the stability can be the result of a process of convergence to simpler and stable regularities from a more complex lower level. According to this project, if successful, there would be no need to postulate a (mysterious) intermediate category between logical necessity and pure contingency. Similarly, there would be no need to postulate a (mysterious) set of pre-existent governing laws. Part I of the thesis motivates part II, mostly by arguing why further explanation of the notions of physical necessity and governing laws should be welcomed (chapter 1), and by studying the plausibility of a lawless fundamental level (chapters 2 and 3). Given so, part II develops the explanation of formation of simpler and stable behavior from a more complex underlying level. (shrink)

The possibility of using private military and security companies to bolster the capacity to undertake intervention for human rights purposes has been increasingly debated. The focus of such discussions has, however, largely been on practical issues and the contingent problems posed by private force. By contrast, this article considers the principled case for privatising humanitarian intervention. It focuses on two central issues. First, does outsourcing humanitarian intervention to private military and security companies pose some fundamental, deeper problems in this context, (...) such as an abdication of a state's duties? Second, on the other hand, is there a case for preferring these firms to other, state-based agents of humanitarian intervention? For instance, given a state's duties to their own military personnel, should the use of private military and security contractors be preferred to regular soldiers for humanitarian intervention? (shrink)

A regularity theory of causation analyses type-level causation in terms of Boolean difference-making. The essential ingredient that helps this theoretical framework overcome the problems of Hume’s and Mill’s classical accounts is a principle of non-redundancy: only Boolean dependency structures from which no elements can be eliminated track causation. The first part of this paper argues that the recent regularity theoretic literature has not consistently implemented this principle, for it disregarded an important type of redundancies: structural redundancies. (...) Moreover, it is shown that a regularity theory needs to be underwritten by a hitherto neglected metaphysical background assumption stipulating that the world's causal makeup is not ambiguous. Against that background, the second part then develops a new regularity theory that does justice to all types of redundancies and, thereby, provides the first all-inclusive notion of Boolean difference-making. (shrink)

I argue for the claim that if Lewis’s regularity theory of laws were true, we could not know any positive law statement to be true. Premise 1: According to that theory, for any law statement true of the actual world, there is always a nearby world where the law statement is false (a world that differs with respect to one matter of particular fact). Premise 2: One cannot know a proposition to be true if it is false in a (...) nearby world (the epistemological safety principle). The conclusion that no law statement can be known to be true follows immediately from the two premises. (shrink)

We examine the necessary physical underpinnings for setting up the cosmological standard model with a global cosmic time parameter. In particular, we discuss the role of Weyl's principle which asserts that cosmic matter moves according to certain regularity requirements. After a brief historical introduction to Weyl's principle we argue that although the principle is often not explicitly mentioned in modern standard texts on cosmology, it is implicitly assumed and is, in fact, necessary for a physically well-defined (...) notion of cosmic time. We finally point out that Weyl's principle might be in conflict with the wide-spread idea that the universe at some very early stage can be described exclusively in terms of quantum theory. (shrink)

Berkeley's Principles: Expanded and Explained includes the entire classical text of the Treatise Concerning the Principles of Human Knowledge in bold font, a running commentary blended seamlessly into the text in regular font and analytic summaries of each section. The commentary is like a professor on hand to guide the reader through every line of the daunting prose and every move in the intricate argumentation. The unique design helps students learn how to read and engage with one of modern philosophy's (...) most important and exciting classics. (shrink)

A Scientific Integrity Consortium developed a set of recommended principles and best practices that can be used broadly across scientific disciplines as a mechanism for consensus on scientific integrity standards and to better equip scientists to operate in a rapidly changing research environment. The two principles that represent the umbrella under which scientific processes should operate are as follows: Foster a culture of integrity in the scientific process. Evidence-based policy interests may have legitimate roles to play in influencing aspects of (...) the research process, but those roles should not interfere with scientific integrity. The nine best practices for instilling scientific integrity in the implementation of these two overarching principles are Require universal training in robust scientific methods, in the use of appropriate experimental design and statistics, and in responsible research practices for scientists at all levels, with the training content regularly updated and presented by qualified scientists. Strengthen scientific integrity oversight and processes throughout the research continuum with a focus on training in ethics and conduct. Encourage reproducibility of research through transparency. Strive to establish open science as the standard operating procedure throughout the scientific enterprise. Develop and implement educational tools to teach communication skills that uphold scientific integrity. Strive to identify ways to further strengthen the peer review process. Encourage scientific journals to publish unanticipated findings that meet standards of quality and scientific integrity. Seek harmonization and implementation among journals of rapid, consistent, and transparent processes for correction and/or retraction of published papers. Design rigorous and comprehensive evaluation criteria that recognize and reward the highest standards of integrity in scientific research. (shrink)

Given an uncountable regular cardinal κ, we study the structural properties of the class of all sets of functions from κ to κ that are definable over the structure 〈H,∈〉 by a Σ1-formula with parameters. It is well known that many important statements about these classes are not decided by the axioms of ZFC together with large cardinal axioms. In this paper, we present other canonical extensions of ZFC that provide a strong structure theory for these classes. These axioms are (...) variations of the Maximality Principle introduced by Stavi and Väänänen and later rediscovered by Hamkins. (shrink)

The weakly compact reflection principle\\) states that \ is a weakly compact cardinal and every weakly compact subset of \ has a weakly compact proper initial segment. The weakly compact reflection principle at \ implies that \ is an \-weakly compact cardinal. In this article we show that the weakly compact reflection principle does not imply that \ is \\)-weakly compact. Moreover, we show that if the weakly compact reflection principle holds at \ then there is (...) a forcing extension preserving this in which \ is the least \-weakly compact cardinal. Along the way we generalize the well-known result which states that if \ is a regular cardinal then in any forcing extension by \-c.c. forcing the nonstationary ideal equals the ideal generated by the ground model nonstationary ideal; our generalization states that if \ is a weakly compact cardinal then after forcing with a ‘typical’ Easton-support iteration of length \ the weakly compact ideal equals the ideal generated by the ground model weakly compact ideal. (shrink)

l investigate versions of the Maximality Principles for the classes of forcings which are <κ-closed. <κ-directed-closed, or of the form Col (κ. <Λ). These principles come in many variants, depending on the parameters which are allowed. I shall write MPΓ(A) for the maximality principle for forcings in Γ, with parameters from A. The main results of this paper are: • The principles have many consequences, such as <κ-closed-generic $\Sigma _{2}^{1}(H_{\kappa})$ absoluteness, and imply. e.g., that ◇κ holds. I give an (...) application to the automorphism tower problem, showing that there are Souslin trees which are able to realize any equivalence relation, and hence that there are groups whose automorphism tower is highly sensitive to forcing. • The principles can be separated into a hierarchy which is strict, for many κ. • Some of the principles can be combined, in the sense that they can hold at many different κ simultaneously. The possibilities of combining the principles are limited, though: While it is consistent that MP<κ-closed(HκT) holds at all regular κ below any fixed α. the "global" maximality principle, stating that MP<κ-closed(Hκ ∪ {κ}) holds at every regular κ. is inconsistent. In contrast to this, it is equiconsistent with ZFC that the maximality principle for directed-closed forcings without any parameters holds at every regular cardinal. It is also consistent that every local statement with parameters from HκT that's provably <κ-closed-forceably necessary is true, for all regular κ. (shrink)

��This paper investigates how an evolutionary al- gorithm with an indirect encoding exploits the property of phenotypic regularity, an important design principle found in natural organisms and engineered designs. We present the first comprehensive study showing that such phenotypic regularity enables an indirect encoding to outperform direct encoding con- trols as problem regularity increases. Such an ability to produce regular solutions that can exploit the regularity of problems is an important prerequisite if evolutionary algorithms are (...) to scale to high-dimensional real-world problems, which typically contain many regularities, both known and unrecognized. The indirect encoding in this case study is HyperNEAT, which evolves artificial neural networks (ANNs) in a manner inspired by concepts from biological development. We demonstrate that, in contrast to two direct encoding controls, HyperNEAT produces both regular behaviors and regular ANNs, which enables HyperNEAT to significantly outperform the direct encodings as regularity increases in three problem domains. We also show that the types of regularities HyperNEAT produces can be biased, allowing domain knowledge and preferences to be injected into the search. Finally, we examine the downside of a bias toward regularity. Even when a solution is mainly regular, some irregularity may be needed to perfect its functionality. This insight is illustrated by a new algorithm called HybrID that hybridizes indirect and direct encodings, which matched HyperNEAT’s performance on regular problems yet outperformed it on problems with some irregularity. HybrID’s ability to improve upon the performance of HyperNEAT raises the question of whether indirect encodings may ultimately excel not as stand-alone algorithms, but by being hybridized with a further process of refinement, wherein the indirect encoding produces patterns that exploit problem regu-. (shrink)

A controversy in political philosophy and applied ethics concerns the validity of duty‐imposing powers, that is, rights entitling one person to impose new duties on others without their consent. Many philosophers have criticized as unplausible any such moral right, in particular that of appropriating private property unilaterally. Some, finding duty‐imposing powers weird, unfamiliar or baseless, have argued that principles of justified acquisition should be rejected; others have required them to satisfy exacting criteria. I investigate the many ways in which we (...) regularly impose duties on one another without prior consent. I show that doing so is not weird, and I offer criteria which demarcate the reasonable from the worrisome aspects of duty‐imposing powers. (shrink)

Abstract: In Vacco v. Quill, 521 U.S. 793 (1997), the Supreme Court for the first time in American case law explicitly applied the principle of double effect to reject an equal protection claim to physician-assisted suicide. Double effect, traced historically to Thomas Aquinas, proposes that under certain circumstances it is permissible unintentionally to cause foreseen evil effects that would not be permissible to cause intentionally. The court rejected the constitutional claim on the basis of a distinction marked out by (...) the principle, i.e., between directly intending the death of a terminally ill patient as opposed to merely foreseeing that death as a consequence of medical treatment. The Court held that the distinction comports with fundamental legal principles of causation and intent. Id. at 802. -/- Critics allege that the principle itself is intrinsically flawed and that, in any event, its employment in Vacco is without legal precedent. I argue in response to contemporary objections that double effect is a valid principle of ethical reflection (Part II); claims to the contrary notwithstanding, double effect analysis is a pervasive, albeit generally unacknowledged principle employed regularly in American case law (Part III); and drawing on the preceding two sections, Vacco's application of the principle of double effect is appropriate (Part IV). -/- My conclusion is that [o]peration of some form of the principle, by whatever name, is inevitable. In an imperfect world where duties and interests collide, the possibility of choices of action foreseen to have both good and evil consequences cannot be avoided. In rare circumstances, ethics and the law require that a person refrain from acting altogether. More often, however, they provide that a determination of whether an actor may pursue a good effect although knowing it will or may unintentionally cause an harmful effect requires a more complex analysis - a double effect analysis. -/- Keywords: Equal protection, double effect, intention, physician-assisted suicide, Constitutional Law, Bioethics. (shrink)

The epistemology of dialectical materialism emphasizes two characteristic features of the picture of the world existing in our minds. First, it presents itself as reflection, i.e., as an image of an objective reality that exists independent of our consciousness. Secondly, this picture provides a reflection of the real world and the regularities of its development that is only approximately complete. The following comment by Lenin is of fundamental significance in this connection: "Cognition is man's reflection of nature, but it is (...) not a simple, not a direct, not a complete reflection, but a process involving a series of abstractions, the shaping and formation of concepts, laws, and the like, various concepts, laws, etc. and embraces, conditionally and approximately, the universal regularity of nature which is eternally moving and developing". (shrink)

The epistemology of dialectical materialism emphasizes two characteristic features of the picture of the world existing in our minds. First, it presents itself as reflection, i.e., as an image of an objective reality that exists independent of our consciousness. Secondly, this picture provides a reflection of the real world and the regularities of its development that is only approximately complete. The following comment by Lenin is of fundamental significance in this connection: "Cognition is man's reflection of nature, but it is (...) not a simple, not a direct, not a complete reflection, but a process involving a series of abstractions, the shaping and formation of concepts, laws, and the like, various concepts, laws, etc. and embraces, conditionally and approximately, the universal regularity of nature which is eternally moving and developing". (shrink)

My purpose in what follows is not so much to defend the basic principle of utilitarianism as to indicate the form of it which seems most promising as a basic moral and political position. I shall take the principle of utility as offering a criterion for two different sorts of evaluation: first, the merits of acts of government, social policies, and social institutions, and secondly, the ultimate moral evaluation of the actions of individuals. I do not take it (...) as implying that the individual should live his life on the basis of constant evaluations of this sort. For there are different levels of decision making each with its appropriate criteria. For example, we each inevitably make many of our decisions from the point of view of our own personal self-fulfilment and this cannot regularly take a directly utilitarian form, nor should the utilitarian want it to do so. His claim is at most that we should sometimes review our life from the point of view of a kind of impersonal moral truth of a universalistic utilitarian character. (shrink)

König, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of a higher Souslin tree from the strong guessing principle.Complementary to the author’s work on the validity of diamond and non-saturation at the successor of singulars, we deal here with a successor of regulars. It is established that even the non-strong guessing principle entails non-saturation, and that, assuming the necessary cardinal arithmetic configuration, entails a diamond-type principle which suffices for the (...) construction of a higher Souslin tree.We also establish the consistency of GCH with the failure of the weakest form of generalized club guessing. This, in particular, settles a question from the original paper. (shrink)

The article reviews the regular international scientific conference on science fiction – Stanisław Lem Readings. The conference is held since 2007 by the Department of Philosophy in collaboration with the Department of Russian and Foreign Literature and Public Relations of the Samara National Research University. The summary shows the history of the conference, formulates the main definitions of the category of science fiction, proposed by its participants, demonstrates the topics, genres, and key approaches that make up the problem field, lists (...) its most eminent speakers. Lem Readings are currently an international platform for a regular interdisciplinary dialogue between philosophers of technology and futurologists, active engineers and scientists, anthropologists and sociologists. The basic principles of the conference – freedom of expression, professionalism, striving for the synthesis of heterogeneous systems – remain unchanged during the years, and they correspond to the idea of the science fictional as a possibility that can be realized. (shrink)

It seems that hope springs eternal for the cherished idea that norms (or normativeprinciples) explain actions or regularities in actions. But it also seems thatthere are many ways of going wrong when taking norms and normative principlesas explanatory. The author argues that neither norms nor normative principles—insofar as they are the sort of things with normative force—is explanatoryof what is done. He considers the matter using both erotetic and ontic models ofexplanation. He further considers various understandings of norms. Key Words: (...) explanation • norms • social science • rationality. (shrink)

Contemporary arguments for scientific realism are typically based on some form of inference to the best explanation. Sometimes such arguments concern the methods of science: given the success of scientific methodology, realism offers the best explanation of this success. Sometimes such arguments concern the content of scientific theories: given observed regularities in nature, explanations must be given of those regularities; the best such explanations will be realist. One forceful explanationist argument about the content of science can be based on Hans (...) Reichenbach’s Principle of the Common Cause. Roughly, CC says that whenever an enduring correlation between two events is observed, there must be some preceding event which is the common cause of the two, and is the explanation for the correlation. Rigid adherence to this demand for a common cause, however, supposedly goes beyond the instrumentalist explanatory resources available to the antirealist, and hence CC is taken to be a sufficient condition for realism. Further, one might claim that any argument that realism has greater explanatory power than antirealism depends either explicitly or implicitly on CC, and hence CC is also a necessary condition for realism. (shrink)

Scientific knowledge is often categorized as experimental or theoretical. There is, however, a third layer where philosophy of science and science proper overlap, the realm of metatheoretic shaping principles. For example, we assume that the causal regularities observed today will also hold tomorrow. Researchers are thereby relying on two metaphysical doctrines: the uniformity of nature and mechanistic causation. There are also the “explanatory virtues” of simplicity, testability, internal and external coherence, fruitfulness, and wide scope. My first goal is to categorize (...) these principles and show how they’ve operated in the history of science. Particular attention will be paid to their suspension and rejection, even of widely held principles. My second goal is to consider how certain shaping principles impinge on open theology. Of particular interest will be naturalism (both metaphysical and methodological), reductionism, and realism. Surprisingly, differences within the open theology camp are more relevant to these issues than open theism itself. (shrink)