I. Prelude -- About this Book -- II. School Mathematics and Its Consequences -- The Foundations of Mathematical Thinking -- Compression, Connection and Blending of Mathematical Ideas -- Set-befores, Met-befores and Long-term Learning -- Mathematics and the Emotions -- The Three Worlds of Mathematics -- Journeys through Embodiment and Symbolism -- Problem-Solving and Proof -- III. Interlude -- The Historical Evolution of Mathematics -- IV. University Mathematics and Beyond -- The Transition to Formal Knowledge -- Blending Knowledge Structures in the (...) Calculus -- Expert Thinking and Structure Theorems -- Contemplating the Infinitely Large and the Infinitely Small -- Expanding the Frontiers through Mathematical Research -- Reflections -- Appendix: Where the Ideas Came From. (shrink)

The Dirac δ function has solid roots in nineteenth century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac’s discovery by over a century, and illuminating the nature of Cauchy’s infinitesimals and his infinitesimal definition of δ.

The Foundations of Mathematics (Stewart and Tall) is a horse of a different color. The writing is excellent and there is actually some useful mathematics. I definitely like this book."--The Bulletin of Mathematics Books.

Hong Oak Yun is a person who is over three inches tall. And now you know who Hong Oak Yun is. For if someone were to ask you ‘Who is Hong Oak Yun?’, you could answer that Hong Oak Yun is a person who is over three inches tall, and you would know what you were saying. So you know an answer to the question ‘Who is Hong Oak Yun?’, and that is sufficient for knowing who Hong Oak (...) Yun is. Getting to know who a person is may be easier than you think. (shrink)

Take a hypothetical sequence of human beings ordered by height from tallest to shortest. Make sure there is no more than a difference of a millimeter between each person and make sure the tallest person is clearly tall and the shortest person is clearly not tall. Now consider the following argument: P1 A person of height n is tall ; P2 For any height n, if n is tall, then n–1mm is tall ; C Therefore, (...) a person of height n = 1mm is tall. P1 and P2 are intuitively true, C is intuitively false, yet the argument is deductively valid (the conclusion follows... (shrink)

Many competent speakers initially judge that (i) is true and (ii) isfalse, though they know that (iii) is true. (i) Superman leaps more tallbuildings than Clark Kent. (ii) Superman leaps more tall buildings thanSuperman. (iii) Superman is identical with Clark Kent. Semanticexplanations of these intuitions say that (i) and (ii) really can differin truth-value. Pragmatic explanations deny this, and say that theintuitions are due to misleading implicatures. This paper argues thatboth explanations are incorrect. (i) and (ii) cannot differ intruth-value, (...) yet the intuitions are not due to implicatures, but ratherto mistakes in evaluating (i) and (ii). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:76 Reviews PROPOSITIONAL ANALYSIS David Blitz Philosophy Dept. and Peace Studies / Central Connecticut State U. New Britain, ct 06050, usa [email protected] Graham Stevens. The Russellian Origins of Analytical Philosophy: Bertrand Russell and the Unity of the Proposition. London and New York: Routledge, 2005. Pp. xii, 185. isbn: 978-0-415-36044-9 (hb). £80.00. us$155.95. Graham Stevens has written a short book on a diUcult subject: the unity of the proposition. (...) While the title of the volume is The Russellian Origins of Analytic Philosophy, the underlying theme is the comparatively little discussed problem of how the elements of a proposition come together to form a unity, as indicated in the book’s subtitle: “Bertrand Russell and the Unity of the Prop­ osition”. Stevens traces this concept, as a unifying thread or “central concern”, throughout Russell’s many philosophies which constitute for Stevens a “consis­ tent and constantly evolving philosophy” (p. 2) stretching from the earliest log­ ical writings to the later works of the 1930s and 1940s. This is an important and well written volume, which Russellians should have in their personal and uni­ versity libraries. That the “unity of the proposition” is a problem at all requires the reader to return to the neo-Hegelian idealism which Russell encountered as a student at Cambridge.1 Russell, inXuenced by Peano and Frege, broke with the doctrine of internal relations, defended by Bradley and others, according to which external relations are unreal and false appearance. However, an important element of idealism remains even during the Principia period, due to Russell’s continued belief that a proposition is a non-linguistic, non-mental, abstract entity; these elements are all of the same ontological kind, which can be identiWed through analysis and recombined so that their synthesis reconstitutes the original “unity of the proposition”. This turns out to be a very tall order which will occupy Russell for nearly half a century. Consider the standard example Russell gives: “Desdemona loves Cassio”. According to Russell, this proposition (independently of its truth or falsity) actually contains its “simple constituents”z—zwith “Desdemona” and “Cassio” being things and “loves” a concept. Russell, as a founder of analytic philosophy, has to defend the legitimacy of this analysis from the claim that it has reduced 1 Chapter 1: “Russell, Frege and the Analysis of Unities”. December 2, 2009 (5:28 pm) E:\CPBR\RUSSJOUR\TYPE2901\russell 29,1 060 red.wpd E:\CPBR\RUSSJOUR\TYPE2901\russell 29,1 060 red.wpd Reviews 77 the structured unity of the proposition into an unstructured set of parts (or heap) where the original order of combination has been lost. The problem of is that merely listing “Desdemona”, “Cassio” and “loves” does not indicate the way in which the terms were originally combined or re­ lated. For reasons to be made clear later, this is referred to in the literature as the “narrow order problem”. In particular, the question arises as to how analysis enables us to assert that it is Desdemona who loves Cassio (supposing this to be the case), rather than the other way around (since love may not be requited). Stevens deals with logical form in a later chapter devoted to the problem of belief statements, but the notion applies here as well: analysis seems to have skip­ ped the logical form, the way in which the constituents are combined. But if the logical form is included, then there seems to be an extra constituent in the prop­ osition not given by direct inspection, and analysis would appear to have added something above and beyond what was there before the analysis. Adding linking relations to indicate how the components were originally combined does not help either. If there is some relation Lz which relates “Desdemona” and “loves” and another relation Rz which relates “loves” and “Cassio”, then there are Wve constituents, not three. Moreover, there is now room for inWnite regress, with a relation L2 linking “Desdemona” and L, R2 linking “loves” and “Cassio”, and so on. But without adding these additional items, there is an apparent failure of an­ alysis to fully provide the order of the elements present in the original... (shrink)

Phaedo. As I recall. when these points had been granted him, and it was agreed that each of the forms was something, and that the other things, partaking in them. took the name of the forms themselves, he next asked: ‘If you say that that is so, then whenever you say that Simmias is taller than Socrates but shorter than Phaedo, you mean the, don't you, that both things are in Simmias, tallness and shortness?’.

In this survey paper we collect several known results on destroying tall ideals on countable sets and maximal almost disjoint families with forcing. In most cases we provide streamlined proofs of the presented results. The paper contains results of many authors as well as a preview of results of a forthcoming paper of Brendle, Guzmán, Hrušák, and Raghavan.

Transhumanists are ambitious. We want unlimited lifespan, unlimited intelligence, unlimited computer power. But this doesn't mean that we're ambitious about everything, for example height. Perhaps we want to be a bit taller, and we want to ensure that e.g. midgets have the opportunity to reach "normal" stature. Yet even in Second Life, or in tomorrow's immersive virtual realities, we don't for the most part want to be 1000 metres tall - despite freedom from the constraints of gravity. Of course, (...) there are some very exotic creatures in Second Life: they might say the rest of us have stunted imaginations. But intuitively, there is quite a narrow optimum for body height. Moreover, height may be regarded as what economists call a "positional good". It's socially advantageous to be slightly taller than average; but if everyone were to become taller, then no one would be better off. (shrink)

In this paper I argue that metalinguistic negotiations are not as common as David Plunkett and Timothy Sundell assume. They make two related controversial claims: the claim that speakers don’t know what they say and the claim that they directly communicate metalinguistic contents. These two claims generate two challenges that the metalinguistic-negotiation view should meet. Firstly, it should clarify why speakers are oblivious to what they are saying and communicating, and secondly, it should explain the mechanism that transforms what (...) seems like a typical object-language disagreement into a metalinguistic dispute. I argue that the way in which Plunkett and Sundell meet these challenges is unsatisfactory. Regarding their answer to the first challenge, I’ll argue that the theoretical cost of postulating massive semantic and pragmatic blindness in otherwise competent speakers is too high. Regarding what they say in relation to the second challenge, I’ll claim that metalinguistic contents can only be conveyed when speakers uttering apparently contradicting claims know that they are using terms with different meanings. If my arguments are correct, then metalinguistic negotiations are certainly not ubiquitous. (shrink)

Part of the appeal of the biological approach to personal identity is that it does not have to countenance spatially coincident entities. But if the termination thesis is correct and the organism ceases to exist at death, then it appears that the corpse is a dead body that earlier was a living body and distinct from but spatially coincident with the organism. If the organism is identified with the body, then the unwelcome spatial coincidence could perhaps be avoided. It is (...) argued that such an identification would be a mistake. A living organism has a different part/whole relationship and persistence conditions than the alleged body. A case will be made that the concept ‘human body’ is a conceptual mess, vague in an unprincipled manner, and that an eliminativist stance towards dead bodies is the appropriate response. CiteULike Connotea Del.icio.us What's this? (shrink)

When Carol Gilligan (1982) first introduced the ethic of care she did so from the discipline of psychology using empirical data that questioned Kohlberg's (1981) negative assumptions about the mora...

Children with developmental disorders, such as attention-deficit/hyperactivity disorder, are at high risk of school-refusal behavior compared with their peers. One of the most used scales to assess SRB is the school refusal behavior scale – revised. The SRAS-R has demonstrated good psychometric properties when used with the general population of children, but, recently, its validity has been questioned when used with children with developmental disorders. We tested the psychometric properties of the SRAS-R parental reports in 96 children with ADHD. Results (...) showed good model fit and internal consistency for the original four-factor structure. Three of the factors were strongly correlated, suggesting that SRB among children with ADHD is caused by several factors. (shrink)

As a continuation of the work of the third author in [5], we make further observations on the features of Galois cohomology in the general model theoretic context. We make explicit the connection between forms of definable groups and first cohomology sets with coefficients in a suitable automorphism group. We then use a method of twisting cohomology (inspired by Serre’s algebraic twisting) to describe arbitrary fibres in cohomology sequences—yielding a useful “finiteness” result on cohomology sets. Applied to the special case (...) of differential fields and Kolchin’s constrained cohomology, we complete results from [3] by proving that the first constrained cohomology set of a differential algebraic group over a bounded, differentially large, field is countable. (shrink)

The consistency of a second-order version of Morley’s Theorem on the number of countable models was proved in [EHMT23] with the aid of large cardinals. We here dispense with them.

In this classic work David Bohm, writing clearly and without technical jargon, develops a theory of quantum physics which treats the totality of existence as an unbroken whole.

In this innovative study, Lea David critically investigates the relationship between human rights and memory, suggesting that, instead of understanding human rights in a normative fashion, human rights should be treated as an ideology. Conceptualizing human rights as an ideology gives us useful theoretical and methodological tools to recognize the real impact human rights has on the ground. David traces the rise of the global phenomenon that is the human rights memorialization agenda, termed 'Moral Remembrance', and explores what (...) happens once this agenda becomes implemented. Based on evidence from the Western Balkans and Israel/Palestine, she argues that the human rights memorialization agenda does not lead to a better appreciation of human rights but, contrary to what would be expected, it merely serves to strengthen national sentiments, divisions and animosities along ethnic lines, and leads to the new forms of societal inequalities that are closely connected to different forms of corruptions. (shrink)

Liberal thinkers of the eighteenth and nineteenth centuries were alert to the political costs and human cruelties involved in European colonialism, but they also thought that European expansion held out progressive possibilities. In Progress, Pluralism, and Politics David Williams examines the colonial and anti-colonial arguments of Adam Smith, Immanuel Kant, Jeremy Bentham, and L.T. Hobhouse. Williams locates their ambivalent attitude towards European conquest and colonial rule in a set of tensions between the impact of colonialism on European states, the (...) possibilities of progress in distant and diverse places, and the relationship between universalism and cultural pluralism. In so doing he reveals some of the central ambiguities that characterize the ways that liberal thought has dealt with the reality of an illiberal world. Of particular importance are appeals to various forms of universal history, attempts to mediate between the claims of identity and the reality of difference, and the different ways of thinking about the achievement of liberal goods in other places. Pointing to key elements in still ongoing debates within liberal states about how they should relate to illiberal places, Progress, Pluralism, and Politics enriches the discussion on political thought and the relationship between liberalism and colonialism. (shrink)

Thus, Meyers provides a valuable account, not only of current medical attitudes, but also of relevant case and statute law as it stands at present.

David Charles presents a major new study of Aristotle's views on meaning, essence, necessity, and related topics. These interconnected views are central to Aristotle's metaphysics, philosophy of language, and philosophy of science, and are also highly relevant to current philosophical debates. Charles aims to reach a clear understanding of Aristotle's claims and arguments, to assess their truth, and to evaluate their importance to ancient and modern philosophy.

Beneath the stylized violence and thrilling car crashes, the Mad Max films consider universal questions about the nature of human life, order and anarchy, justice and moral responsibility, society and technology, and ultimately, human redemption. In Mad Max and Philosophy, a diverse team of political scientists, historians, and philosophers investigates the underlying themes of the blockbuster movie franchise, following Max as he attempts to rebuild himself and the world. -/- This book guides you through the barren wastelands of a post-apocalyptic (...) future as you explore ethics and politics in The Wasteland, the importance of costumes and music, humankind's relationship with nature, commerce, gender, religion, madness, and more. (shrink)

Here the philosopher and physicist David Z Albert argues, among other things, that the difference between past and future can be understood as a mechanical phenomenon of nature and that quantum mechanics makes it impossible to present the entirety of what can be said about the world as a narrative of “befores” and “afters.”.

David Cooper explores and defends the view that a reality independent of human perspectives is necessarily indescribable, a "mystery." Other views are shown to be hubristic. Humanists, for whom "man is the measure" of reality, exaggerate our capacity to live without the sense of an independent measure. Absolutists, who proclaim our capacity to know an independent reality, exaggerate our cognitive powers. In this highly original book Cooper restores to philosophy a proper appreciation of mystery-that is what provides a measure (...) of our beliefs and conduct. (shrink)

David Lewis (1941-2001) was Class of 1943 University Professor of Philosophy at Princeton University. His contributions spanned philosophical logic, philosophy of language, philosophy of mind, philosophy of science, metaphysics, and epistemology. In On the Plurality of Worlds, he defended his challenging metaphysical position, "modal realism." He was also the author of the books Convention, Counterfactuals, Parts of Classes, and several volumes of collected papers.

The critical concern of the present volume is contemporary naturalism, both in its scientific version and as represented by newly emerging hopes for another, philosophically more liberal, naturalism.1 The papers collected here are state-of-the-art discussions that question the appeal, rational motivations, and presuppositions of scientific naturalism across a broad range of philosophical topics. As an alternative to scientific naturalism, we offer the outlines of a new non- reductive form of naturalism and a more inclusive conception of nature than any provided (...) by the natural sciences. Our authors collectively believe that holding scientific naturalism up for philosophical scrutiny and challenging its misconceptions is of the first importance both for understanding ourselves and our place in the world; and, also, for the future direction of philosophy itself. (shrink)