What is it to know more? By what metric should the quantity of one's knowledge be measured? I start by examining and arguing against a very natural approach to the measure of knowledge, one on which how much is a matter of how many. I then turn to the quasi-spatial notion of counterfactual distance and show how a model that appeals to distance avoids the problems that plague appeals to cardinality. But such a model faces fatal problems of its (...) own. Reflection on what the distance model gets right and where it goes wrong motivates a third approach, which appeals not to cardinality, nor to counterfactual distance, but to similarity. I close the paper by advocating this model and briefly discussing some of its significance for epistemic normativity. In particular, I argue that the 'trivial truths' objection to the view that truth is the goal of inquiry rests on an unstated, but false, assumption about the measure of knowledge, and suggest that a similarity model preserves truth as the aim of belief in an intuitively satisfying way. (shrink)

Drawing on the latest work in cognitive neuroscience, a philosopher proposes that delusions are narrative models that accommodate anomalous experiences.

The current literature standardly conceives of voting power in terms of decisiveness: the ability to change the voting outcome by unilaterally changing one’s vote. I argue that this classic conception of voting power, which fails to account for partial decisiveness or efficacy, produces erroneous results because it saddles the concept of voting power with implausible microfoundations. This failure in the measure of voting power in turn reflects a philosophical mistake about the concept of social power in general: a failure (...) to recognize that an agent can exercise individual social power with others’ assistance, in virtue of the group’s collective power, sometimes even when she could not unilaterally scuttle the group’s collective power. I therefore develop a conception of efficacy that admits of degrees and defend a Recursive Measure of voting power that takes partial efficacy into account. (shrink)

Fitelson (1999) demonstrates that the validity of various arguments within Bayesian confirmation theory depends on which confirmation measure is adopted. The present paper adds to the results set out in Fitelson (1999), expanding on them in two principal respects. First, it considers more confirmation measures. Second, it shows that there are important arguments within Bayesian confirmation theory and that there is no confirmation measure that renders them all valid. Finally, the paper reviews the ramifications that this "strengthened problem (...) of measure sensitivity" has for Bayesian confirmation theory and discusses whether it points at pluralism about notions of confirmation. (shrink)

Magnanimity is a virtue that has led many lives. Foregrounded early on by Plato as a philosophical virtue par excellence, it became one of the crown jewels in Aristotle's account of human excellence and was accorded equally salient place by other ancient thinkers. It is one of the mostdistinctive elements of the ancient tradition to filter into the medieval Islamic and Christian worlds. It sparked important intellectual engagements and went on to carve deep tracks through several of the later philosophies (...) to inherit from this tradition. Under changing names and reworked forms, itwould continue to breathe in the thought of Descartes and Hume, Kant, and Nietzsche. Its many lives have been joined by important continuities, yet they have also been fragmented by discontinuities - discontinuities reflecting larger shifts in ethical perspectives and competing answers to questionsabout the nature of the good life, the moral nature of human beings, and their relationship to the social and natural world they inhabit. They have also been punctuated by moments of intense controversy in which the vision of human greatness has itself been called into doubt.The aim of this volume is to provide an insight into the complex trajectory of a virtue whose glitter has at times been as dazzling as it has been divisive. By exploring the many lives it has lived, we will be in a better position to evaluate whether this is a virtue we still want to make central toour own ethical lives, and why. (shrink)

I argue that prioritarianism cannot be assessed in abstraction from an account of the measure of utility. Rather, the soundness of this view crucially depends on what counts as a greater, lesser, or equal increase in a person’s utility. In particular, prioritarianism cannot accommodate a normatively compelling measure of utility that is captured by the axioms of John von Neumann and Oskar Morgenstern’s expected utility theory. Nor can it accommodate a plausible and elegant generalization of this theory that (...) has been offered in response to challenges to von Neumann and Morgenstern. This is, I think, a theoretically interesting and unexpected source of difficulty for prioritarianism, which I explore in this article. (shrink)

Hallucinatory states are experienced not only in connection with drugs and psychopathologies but occur naturally and spontaneously across the human circadian cycle: Our nightly dreams bring multimodal experiences in the absence of adequate external stimuli. The current study proposes a new, tighter measure of these hallucinatory states: Sleep onset, REM sleep, and non-REM sleep are shown to differ with regard to motor imagery indicating interactions with a rich imaginative world, and cognitive agency that could enable sleepers to recognize their (...) hallucinatory state. Mentation reports from the different states were analysed quantitatively with regard to two grammatical–semantic constructs, motor agency and cognitive agency. The present results support earlier physiological and psychological evidence in revealing a decline in cognitive functions and an increase in simulated interactions with a hallucinatory world, en route to normal REM sleep. This leads us to introduce the hypothesis that REM sleep, which exhibits remarkably high levels of sensorimotor processes, may have evolved to serve as a virtual laboratory for the development and rehearsal of embodied cognition. The new measure of hallucinatory states presented here may also hold implications for the study of executive functions and cognitions, which might be interesting, for example, for the investigation of lucid dreaming. (shrink)

Colorado’s Amendment 36 proposed to switch Colorado’s representation in the Electoral College from winner-takes-all to proportionality. We evaluate unilateral and uniform switches to proportionality both from Colorado’s perspective and from an impartial perspective on the basis of a priori and a posteriori voting power measures. The present system is to be preferred to a unilateral switch from any perspective on any measure. A uniform switch is to be preferred to the present system from Colorado’s perspective on an a priori (...) measure, and from an impartial perspective on an a posteriori measure. The present system is to be preferred to a uniform switch from Colorado’s perspective on an a posteriori measure (with some qualifications), and from an impartial perspective on an a priori measure. We conclude with a discussion of the appropriateness of these measures. (shrink)

I argue that it may well be the case that space and time do not consist of points, indeed that they have no smallest parts. I examine two different approaches to such pointless spaces : a topological approach and a measure theoretic approach. I argue in favor of the measure theoretic approach.

In the Theaetetus Socrates provides an elaboration and discussion of Protagoras’ measure doctrine, grounding it in a “secret doctrine” of flux. This paper argues that the anthropology of the myth in the Protagoras provides an earlier, very different way to explain the measure doctrine, focusing on its application to civic values, such as “just,” “fine,” and “pious.” The paper shows that Protagoras’ explanation of the dual etiology of virtue – that it is acquired both by nature and by (...) nurture – tracks the two meanings of “anthropos” in his formulation of the measure doctrine, as “humankind” and “individual human.” On Protagoras’ account, humankind’s survival can be explained by the fact that humans share shame and justice, which enables them to live together in cities. (shrink)

The statistical technique of analysis of variance is often used by biologists as a measure of causal factors’ relative strength or importance. I argue that it is a tool ill suited to this purpose, on several grounds. I suggest a superior alternative, and outline some implications. I finish with a diagnosis of the source of error – an unwitting inheritance of bad philosophy that now requires the remedy of better philosophy.

This article is about the analogy between inclusive fitness and utility. In behavioral ecology, it is often assumed that individual organisms behave as if they were “striving” to maximize their inclusive fitness—a measure analogue to the kind of utility function that is used to represent the preferences of rational agents. Here, I explore some conceptual puzzles related to this view and question whether the kind of biological utility posited by the advocates of the “maximizing agent analogy” can be adequately (...) interpreted in inclusive fitness terms. (shrink)

We identify several ongoing debates related to implicit measures, surveying prominent views and considerations in each debate. First, we summarize the debate regarding whether performance on implicit measures is explained by conscious or unconscious representations. Second, we discuss the cognitive structure of the operative constructs: are they associatively or propositionally structured? Third, we review debates whether performance on implicit measures reflects traits or states. Fourth, we discuss the question of whether a person’s performance on an implicit measure reflects characteristics (...) of the person who is taking the test or characteristics of the situation in which the person is taking the test. Finally, we survey the debate about the relationship between implicit measures and (other kinds of) behavior. (shrink)

This paper investigates the semantics of measure phrases in Japanese. Based on new data, we argue that the interpretation of measure phrases in Japanese is sensitive to scale structure such that (i) measure phrases are introduced by a degree morpheme that selects only for gradable predicates whose scale contains a minimal element (i.e., a lower closed scale) and (ii) violations to this restriction are repaired via coercion, which forces a comparative interpretation with a contextually determined standard and (...) hence a minimal element. We compare the Japanese facts to data in other languages and argue that the requirement of having a minimal element is not specific to Japanese, but universal. We show that languages may vary in how they deal with potential violations of this universal constraint, including coercion of a contextually recoverable derived minimal element (Japanese), ungrammaticality (e.g., Spanish, Korean, Russian), and a hybrid system of ungrammaticality for some adjectives and allowed constraint violation for others (e.g., English, German, Italian). (shrink)

(2014). ‘Heidegger and the Measure of Truth’, by McManus, Denis. Australasian Journal of Philosophy: Vol. 92, No. 3, pp. 602-605. doi: 10.1080/00048402.2013.834953.

In this paper, the cosine similarity measure of neutrosophic refined (multi-) sets is proposed and its properties are studied. The concept of this cosine similarity measure of neutrosophic refined sets is the extension of improved cosine similarity measure of single valued neutrosophic. Finally, using this cosine similarity measure of neutrosophic refined set, the application of medical diagnosis is presented.

Some propositions add more information to bodies of propositions than do others. We start with intuitive considerations on qualitative comparisons of information added . Central to these are considerations bearing on conjunctions and on negations. We find that we can discern two distinct, incompatible, notions of information added. From the comparative notions we pass to quantitative measurement of information added. In this we borrow heavily from the literature on quantitative representations of qualitative, comparative conditional probability. We look at two ways (...) to obtain a quantitative conception of information added. One, the most direct, mirrors Bernard Koopman’s construction of conditional probability: by making a strong structural assumption, it leads to a measure that is, transparently, some function of a function P which is, formally, an assignment of conditional probability (in fact, a Popper function). P reverses the information added order and mislocates the natural zero of the scale so some transformation of this scale is needed but the derivation of P falls out so readily that no particular transformation suggests itself. The Cox–Good–Aczél method assumes the existence of a quantitative measure matching the qualitative relation, and builds on the structural constraints to obtain a measure of information that can be rescaled as, formally, an assignment of conditional probability. A classical result of Cantor’s, subsequently strengthened by Debreu, goes some way towards justifying the assumption of the existence of a quantitative scale. What the two approaches give us is a pointer towards a novel interpretation of probability as a rescaling of a measure of information added. (shrink)

According to the colored-brain thesis, sense data or qualia are real physical-chemical qualities, located inside the brain, possibly at a specific locus. Our hypothesis is that the seats of phenomenal consciousness have a structure and a materiality. According to the proposed view, a chromatic quale emerges when a certain pixel of the visual sensorium is fed with a certain pattern Σ of spikes; a change in this pattern quickly changes the color that is subjectively generated. How could one manage to (...) measure chromatic qualia? In principle, with nanoscopical techniques, one could capture all the patterns that fall on the sensorium, and transmit the information to other media. But this does not capture the qualia. However, if the patterns are made to fall on a tissue of the same kind, typically inside another person’s brain, this other person will have roughly the same subjective experience as the first person. The model is used to explore two different situations involving qualia inversion. The paper also explores Cartesian materialism, and the claim that phenomenal time and space are identical to a region of physical time and space. (shrink)

Recent interest in the idea that there can be scientific understanding without explanation lends new relevance to Duhem's notion of natural classification. According to Duhem, a classification that is natural teaches us something about nature without being explanatory. However, Duhem's conception of naturalness leaves much to be desired. In this paper, I argue that we can measure the naturalness of classification by using an amended version of the notion of unification as defined by Schurz and Lambert. If this thesis (...) is correct, it both leads to a better conceptual understanding of scientific understanding, and also gives the nascent literature on this topic some much-needed precision. (shrink)

Relative to a hyperstrong cardinal, it is consistent that measure one covering fails relative to HOD. In fact it is consistent that there is a superstrong cardinal and for every regular cardinal κ, κ + is greater than κ + of HOD. The proof uses a very general lemma showing that homogeneity is preserved through certain reverse Easton iterations.

The search for an ethics rooted in human experience is the crux of this deeply compassionate work, here translated from the 1983 German edition. Distinguished philosopher Werner Marx provides a close reading, critique, and _Weiterdenken_, or "further thinking," of Martin Heidegger's later work on death, language, and poetry, which has often been dismissed as both obscure and obscurantist. In it Marx seeks, and perhaps finds, both a measure for distinguishing between good and evil and a motive for preferring the (...) former. The poet Hölderlin posed the question, "Is there a measure on earth?" His own answer was emphatic, "There is none," for he was convinced that the measure for man was to be found only in the domain of the heavenly beings. Such metaphysical assumptions, as well as the attempt to found ethical conduct in the nature of man as a rational being, have been rejected by many contemporary thinkers, particularly Heidegger. Yet these thinkers have not been able to provide a satisfactory alternative to metaphysical foundations of the standards for responsible human conduct. Marx, therefore, goes beyond Heidegger in demonstrating how several of his most basic notions could be relevant to a secular morality in our age. It is death, Marx claims, that unsettles man and transforms his conduct toward his fellow man. the common experience of mortality nourishes ethical life—and leads to the measures of compassion, love, and recognition of one's fellow human beings. "It is only on the basis of these 'traditional virtues,'" Marx writes, "that we can find a motive for averting the impending dangers which have often enough been described so vividly and convincingly.". (shrink)

Reasons for seeking an index of social well‐being are identified in this chapter. Four are given prominence: to compare well‐being across countries ; to compare well‐being across time and generations for the same country ; to check if well‐being is sustainable; and to derive a criterion for judging if a policy is worth undertaking. There is no a priori reason why the same index would be appropriate for the four sets of exercises.

This volume examines a selection of late medieval works devoted to the intensive infinite in order to draw a comprehensive picture of the context, character and ...

Philosophical pragmatism takes human experience as the touchstone of any theorizing. Authors like William James and F.C.S. Schiller suggested to transform philosophy into a critical and emancipatory project, turning the quest for truth into a project of creative and responsible world-making. Their basic insight that man is the measure of all things demands for being actively engaged in building a better world. As pragmatism denies objective criteria for critique, listening to a plurality of voices and their experiences becomes crucial. (...) This chapter offers a humanist re-reading of philosophical pragmatism and explores its challenges and prospects. With pointing out problematic assumptions in the work of James and Schiller, the unfinished agenda of their pragmatic humanism becomes visible. (shrink)

For given Boolean algebras$\mathbb {A}$and$\mathbb {B}$we endow the space$\mathcal {H}(\mathbb {A},\mathbb {B})$of all Boolean homomorphisms from$\mathbb {A}$to$\mathbb {B}$with various topologies and study convergence properties of sequences in$\mathcal {H}(\mathbb {A},\mathbb {B})$. We are in particular interested in the situation when$\mathbb {B}$is a measure algebra as in this case we obtain a natural tool for studying topological convergence properties of sequences of ultrafilters on$\mathbb {A}$in random extensions of the set-theoretical universe. This appears to have strong connections with Dow and Fremlin’s result (...) stating that there are Efimov spaces in the random model. We also investigate relations between topologies on$\mathcal {H}(\mathbb {A},\mathbb {B})$for a Boolean algebra$\mathbb {B}$carrying a strictly positive measure and convergence properties of sequences of measures on$\mathbb {A}$. (shrink)

Purpose of the article is the reconstruction of ancient Greek and ancient Roman models of religiosity as anthropological invariants that determine the patterns of thinking and being of subsequent eras. Theoretical basis. The author applied the statement of Protagoras that "Man is the measure of all things" to the reconstruction of the religious sphere of culture. I proceed from the fact that each historical community has a set of inherent ideas about the principles of reality, which found unique "universes (...) of meanings". The historical space acquires anthropological properties that determine the specific mythology of the respective societies, as well as their spiritual successors. In particular, the religious models of ancient Greece and ancient Rome had a huge influence on formation of the worldview of the Christian civilization of the West. Originality. Multiplicity of the Olympic mythology contributed to the diversity of the expression forms of the Greek genius, which manifested itself in different fields of cultural activity, not reducible to political, philosophical or religious unity. The poverty of Roman mythology was compensated by a clear awareness of the unity of the community, which for all historical vicissitudes had always remained an unchanging ideal, and which was conceived as a reflection of the unity of the heavens. These two approaches to the divine predetermined the formation of two interacting, but conceptually different anthropological paradigms of Antiquity. Conclusions. Western concepts of divinity are invariants of two basic theological concepts – "Greek" and "Roman". These are ideal types, so these two tendencies can co-exist in one society. The Roman trend continued to be realized by the anti-Roman religion, which took Roman forms and Roman name. Iconoclasm was a Byzantine version of the Reformation, promoted by the Isaurian emperors and failed due to the strong Hellenistic naturalistic lobby. Modern "Romans" are trying to get rid of the last elements of religious naturalism, and modern "Greeks" are trying to preserve the Hellenic elements in Christianity. Patterns can be transformed, but the observational view will still be able to identify their lineage. The developed model allows a deeper understanding of the culture of both ancient societies, as well as the outlook of Western man. (shrink)

This article provides a political reading of Martin Heidegger's Beiträge zur Philosophie. One of the central themes of the Beiträge is crucial to understanding why Heidegger moved into a position of critical distance from the Nazi regime, because it is an attempt to comprehend what lies behind the events of the time. This is the notion of the politics of calculation, the issue of measure, which relates closely to Heidegger's late concerns with technology. Through readings of Heidegger on Protagoras (...) and Descartes, the role of calculation in the forgetting of being, and the notions of machination, race, and worldview, I show how the Beiträge, and particularly its explicit political context, is valuable in evaluating Heidegger's own career, his political position and politics more generally. (shrink)

A textbook for the undergraduate who is meeting the Lebesgue integral for the first time, relating it to the calculus and exploring its properties before deducing the consequent notions of measurable functions and measure.

Quantum theory is one the most important and successful theories of modern physical science. It has been estimated that its principles form the basis for about 30 per cent of the world's manufacturing economy. This is all the more remarkable because quantum theory is a theory that nobody understands. The meaning of Quantum Theory introduces science students to the theory's fundamental conceptual and philosophical problems, and the basis of its non-understandability. It does this with the barest minimum of jargon and (...) very little mathematics in the main text. Readers wishing to delve more deeply into the theory's mathematical subtleties can do so in an extended series of appendices. The book brings the reader up to date with the results of new experimental tests of quantum weirdness and reviews the latest thinking on alternative interpretations, the frontiers of quantum cosmology, quantum gravity and potential application of this weirdness in computing, cryptography and teleportation. (shrink)