It is shown that a fundamental question of revealed preference theory, namely whether the weak axiom of revealed preference (WARP) implies the strong axiom of revealed preference (SARP), can be reduced to a Hamiltonian cycle problem: A set of bundles allows a preference cycle of irreducible length if and only if the convex monotonic hull of these bundles admits a Hamiltonian cycle. This leads to a new proof to show that preference cycles can be (...) of arbitrary length for more than two but not for two commodities. For this, it is shown that a set of bundles satisfying the given condition exists if and only if the dimension of the commodity space is at least three. Preference cycles can be constructed by embedding a cyclic $(L-1)$ -polytope into a facet of a convex monotonic hull in $L$ -space, because cyclic polytopes always admit Hamiltonian cycles. An immediate corollary is that WARP only implies SARP for two commodities. The proof is intuitively appealing as this gives a geometric interpretation of preference cycles. (shrink)

Principlism has been advocated as an approach to resolving concrete cases and issues in bioethics, but critics have pointed out that a main problem for principlism is its lack of a method for assigning priorities to conflicting ethical principles. A version of principlism referred to as 'specified principlism' has been put forward in an attempt to overcome this problem. However, none of the advocates of specified principlism have attempted to demonstrate that the method actually works in resolving detailed clinical cases. (...) This paper shows that when one tries to use it, specified principlism fails to provide practical assistance in deciding how to resolve concrete cases. Proponents of specified principlism have attempted to defend it by arguing that it is superior to casuistry, but it can be shown that their arguments are faulty. Because of these reasons, specified principlism should not be considered a leading contender in the search for methods of making justifiable decisions in clinical cases. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Barrow and Newton E. W. STRONG As E. A. Buxrr HAS ADDUCED,Isaac Barrow (1630-1677) in his philosophy of space, time, and mathematical method strongly influenced the thinking of Newton: The recent publication of an early paper written by Newton (his De gravitatione et aequipondio fluidorum)2 affords evidence not known to Burtt of Newton's indebtedness in philosophy to Barrow, his teacher. Prior to its publication in 1962, this paper (...) was utilized by Alexandre Koyrd in his essay, "Newton and Descartes," 3 a study based on the third Horblit Lecture in the History of Science which he gave at Harvard University, March 8, 1961. Koyr8 maintains that there is a radical opposition in Newton's Principia not only to Descartes' purely scientific theories but also to the Cartesian philosophy. Yet, as he remarks, "we do not find in the Principia an open criticism of the philosophy of Descartes.... " He attributes this fact principally "to the very structure of the Principia: it is essentially a book on rational mechanics, which provides principles for physics and astronomy. In such a book there is a normal place for the discussion of Cartesian optics, but not of the conception of the relations of mind and body, and other such things." Koyrd asserts, nonetheless, that the criticism is not absent. It lurks in Newton's carefully worded definitions of fundamental concepts--those of space, time, motion, and matter--and becomes more apparent in the Optice of 1706 and in the second odition of the Principia. In support of this argument, he makes much of young Newton's unfini.~hed paper. He holds that this essay is of exceptional value "as it enables us to get some insight into the formation of Newton's thought, and to recognize that preoccupation with philosophic problems was not an external additatmentum but an integral dement of his thinking." 4 As concerns "young Newton's conception of space in its being and in its relation to God and time," Koyrd remarks that we learn from this essay The Metaphysical Foundations of Modern Physical Science (New York, 1927), p. 144. A. Rupert Hall and Marie Boas Hall, Unpublished Scientific Papers of Isaac Newton (Cambridge, 1962), Introduction, pp. 75-88; Latin text, pp. 90-121; English translation, pp. 121156. " Newtonian Studies (Harvard University Press, 1965), pp. 53-114. " Newtonian Studies, pp. 82-83. In his De gravitatione et aequipondio fluidorum, Newton is indeed engrossed with philosophic problems. With regard, however, to the announced purpose of his paper, namely, "to treat of the science of gravity and solid bodies in fluids by two methods," does Newton represent kis metaphysical "explanation of the nature of body" as an element of his science essential to its completeness7 He does not do so. At the end of his explanation he remarks: "I have already digressed enough; let us return to the main theme." He proceeds to set forth fifteen more definitions and then turns to the demonstration of two "Propositions on Non-Elastic Fluids." [155] 156 HISTORY OF PHILOSOPHY "that space is necessary, eternal, immutz~ble, and unmovable, that though we can imagine that there is nothing in space we cannot think space is not.., and that if there is no space, God would be nowhere. We learn also that all points of space are simultaneous and that, therefore, the divine omnipresence does not introduce composition in God.... " What we here learn from Newton about space in confutation of Descartes is to be found in Barrow's tenth mathematical lecture, "'Of Space, and Impenetrability." 5 In this lecture, Barrow opposes both Descartes and Hobbes. He objects, as does Newton, to the position taken by Descartes in his Principia Philosophiae, namely, "it is necessary.forMatter to be infinitely extended." He proceeds, as does Newton, to show how "very much Cartesius's great Subtility has failed him in this Case" to conclude that there is space empty of matter and distinct from magnitude from which an infinity of matter cannot be deduced. The correspondence of arguments tendered by Barrow and Newton indicates that the tenth lecture constituted a source from which Newton gleaned principal objections to Descartes' Principia Philosophiae. Although Koyr~ makes reference to Burtt's... (shrink)

Blood supplies have become indexes of national security and the public good. While blood shortages can provoke anxiety, controversies continue to erupt in many countries over proper donor screening, especially with reference to HIV. This article sketches these dynamics in several global settings, focusing especially on activist efforts by gay men to reform exclusionary blood donor guidelines. The contours of the debate recall familiar conflicts between the putative demands of public health and the rights of individuals in the era (...) of AIDS. However, if gay activists marshal a discourse of individual rights vis-a-vis forms of institutional exclusion, they also seek a broader shift in social and cultural understandings of gay identity. To capture this complex interplay of citizenship and sociality, risk and responsibility, the article introduces the notion of `vital publics' to refer to the peculiar associational form represented by blood supplies. Vital publics are kinds of embodied association elicited through the generalized exchange of body — in this case, blood. Hailed to `give life' by the jargon of the pervasive social marketing of varied blood service systems, activists seek to contribute to the life of the `vital public' that transfusion medicine calls into being. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 273 Verene, Donald Phillip. Vico's Science of Imagination. Ithaca, New York: Cornell University Press, 1981, Pp. 227. $19.5o. In Chapter 1 (Introduction: Vico's Originality), Verene announces two principal concerns, a two-fold approach, and the predominant contention of his study.. 1. Principal concerns: "to consider the philosophical truth of Vico's ideas themselves, rather than to examine their historical character" (p. 19); to consider "the importance of Vico's conception (...) of barbarism for understanding present society" (p. 28). 2. Two-fold approach: "to interpret the central theses of Vico's thought" from the inside in the spirit of the whole and, at the same time, "to develop the problems of Vico's philosophy themselves" (pp. 19--21 ). 3. Predominant contention: "that Vico's ideas constitute a philosophy of recollective universals which generates philosophical understanding fronl the image, not the rational category. This approach regards imagination as a method of pfiilosophical thought" (p. 19) and the imaginative universal as "a key to his conception of knowledge" (p. 67). Vico's philosophy is depicted and characterized by Verene as fi)llows. Beginning with the imagination (fantasia) as an original and independent power of mind, Vico builds his philosophy on the image, the imaginative universal, thereby creating a position outside Western philosophy as traditionally understood. His New Science is a process of recollective fantasia, a kind of memory, and the system built constitutes a system of memory for all of human reality. By means of his concept of memory, Vico works his way back to the world of original thought, the mythicopoeticfantasia of the first men. His discovery of the imaginative universal as their way of thinking and their kind of knowledge establishes a new genetic origin for philosophical thought. Recollective fantasia constitutes the subject-matter and form of Vico's science itself', i.e., the term designates a type of nlemory through which the New Science is acconlplished as well as the type of thought from which it must be understood. "The New Science is a metaphysical fable, h creates a vera narratio of the recollectire imagination. The storia ideale eterna is an ideal trnth, but not an a priori or fictional one. As the master image of the recollective mind, it precisely contains all of the human event. Metaphysical truth, achieved through the exercise of.[antasia.., is generated out of the mind itself.., as images that actually contain the providential structure of reality" (p. 125). Vico's per|ornlative science "is man's true production of a knowledge of" his own nature" (p. 133). "The proof of the science is found through the reader making it for himself" (p. 156). What is the "recollective imaginative universal"? (a term coined by Verene) as distinguished from the universale fantastico? Vico identifies the latter quite simply. Poetic imagination, he tells us, was active in the first men who, "not being able to form intelligible class concepts of things, had a natural need to create poetic characters ; that is, imaginative class concepts or universals, to which, as to certain models or ideal portraits, to reduce all the particular species that resembled them." (The New Science of Giambattista Vico, trans. Thomas Goddard Bergin and Max Harold Fisch. Cornell University Press, 1968; orig. pub. 1948, w ) Thus in the theological age, 274 HISTORY OF PHILOSOPHY "Jove was born naturally in poetry as a divine character or imaginative universal, to which everything having to do with the auspices was referred by all the ancient gentile nations, which must therefore all have been poetic by nature" (9 381). In the age of heroes, Achilles embodies the idea of valor common to all strong men and Ulysses the idea of prudence common to all wise men (9 403). The myths, fables, and allegories brought to birth by poetic imagination were true stories for their makers. Imaginative universals or genera, "as the human mind later learned to abstract forms and properties from subjects, passed over into intelligible genera, which prepared the way for philosophers.... " (9 934)- Abstracting, categorizing, and predicating on the basis of properties in common, the philosophers in their intelligible class concepts no hmger think in the same manner as the first men did... (shrink)

This paper explores the topic of meaning and its relation to symbolism through a contrastive reading of Whitehead’s 1927 Barbour-Page Lectures alongside the contemporary anthropologist Roy Wagner’s Symbols that Stand for Themselves. Despite their adoption of different registers of inquiry, a complementary relation may be posited between the two approaches. In particular, Whitehead’s emphasis on the foundational nature of symbolic reference within experience and its extendedness beyond merely human contexts may be grafted productively onto Wagner’s discussion of the “orders (...) of trope’”and “figure-ground reversal” within the formation of meaning in language. The argument is exemplified through reference to two contexts within Western culture where the play of symbol and meaning is strikingly evident—the Christian Eucharist and the contemporary sociological pervasiveness of motifs of screens and screening. (shrink)

This paper explores the topic of meaning and its relation to symbolism through a contrastive reading of Whitehead’s 1927 Barbour-Page Lectures alongside the contemporary anthropologist Roy Wagner’s Symbols that Stand for Themselves. Despite their adoption of different registers of inquiry, a complementary relation may be posited between the two approaches. In particular, Whitehead’s emphasis on the foundational nature of symbolic reference within experience and its extendedness beyond merely human contexts may be grafted productively onto Wagner’s discussion of the “orders (...) of trope’”and “figure-ground reversal” within the formation of meaning in language. The argument is exemplified through reference to two contexts within Western culture where the play of symbol and meaning is strikingly evident—the Christian Eucharist and the contemporary sociological pervasiveness of motifs of screens and screening. (shrink)

Recent studies suggest that trust is culturally determined and that differentials in trust exist globally between cultures. The trusting culture may be an artifact given that there is little empirical support for such a notion. The results of an international survey of 122 business leaders failed to reveal significant differences in trust between cultures.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Knee proprioception deficits and neuroplasticity have been indicated following injury to the anterior cruciate ligament. Evidence is, however, scarce regarding brain response to knee proprioception tasks and the impact of ACL injury. This study aimed to identify brain regions associated with the proprioceptive sense of joint position at the knee and whether the related brain response of individuals with ACL reconstruction differed from that of asymptomatic controls. Twenty-one persons with unilateral ACL reconstruction of either the right or left knee, as (...) well as 19 controls matched for sex, age, height, weight and current activity level, performed a knee joint position sense test during simultaneous functional magnetic resonance imaging. Integrated motion capture provided real-time knee kinematics to activate test instructions, as well as accurate knee angles for JPS outcomes. Recruited brain regions during knee angle reproduction included somatosensory cortices, prefrontal cortex and insula. Neither brain response nor JPS errors differed between groups, but across groups significant correlations revealed that greater errors were associated with greater ipsilateral response in the anterior cingulate, supramarginal gyrus and insula. This is the first study to capture brain response using fMRI in relation to quantifiable knee JPS. Activated brain regions have previously been associated with sensorimotor processes, body schema and interoception. Our innovative paradigm can help to guide future research investigating brain response to lower limb proprioception. (shrink)

In education, we are concerned with the teaching and learning of subjects, but the word “subject” can refer to the discipline being studied as well as the individual who is studying. In this essay, Teresa Strong-Wilson explores this “double entendre” of curriculum studies through the analogy afforded by German author-in-exile W. G. Sebald's working through of difficult subjects by way of semi-autobiographical writing that takes the form of an “invisible subject”: a preoccupation with an unnamed injustice entangled with his (...) own upbringing. Curriculum theory, as currere, has foregrounded the autobiographical. While the place of autobiography in curriculum studies has often been taken to mean writing, currere is more an allegorical method of study, of intellectual engagement, of learning through reading and writing, and of teaching so as to open spaces for agency. Strong-Wilson suggests that Sebald can provide a strong example for us in curriculum studies of how to ethically bring into being an allegorical, autobiographical practice focused on “invisible” subjects of deep concern. (shrink)

: Bernard Gert's theory of morality has received much critical attention, but there has been relatively little commentary on its practical value for bioethics. An important test of an ethical theory is its ability to yield results that are helpful and plausible when applied to real cases. An examination of Gert's theory and his own attempts to apply it to bioethics cases reveals that there are serious difficulties with regard to its application. These problems are sufficiently severe to support the (...) conclusion that Gert's theory is unacceptable as an approach for resolving bioethics cases, even relatively noncontroversial cases. (shrink)

In an earlier essay in this journal I critiqued Don Marquis's well-known argument against abortion. I distinguished two versions of Marquis's argument, which I refer to as ‘the essence argument’ and ‘the sufficient condition argument’. I presented two counterexamples showing that the essence argument was mistaken, and I argued that the sufficient condition argument should be rejected because Marquis had not adequately responded to an important objection to it. In response to my critique, Marquis put forward in this journal a (...) revised version of his argument. In his modified approach he no longer advocates the essence argument and he offers a new version of the sufficient condition argument. In the current essay, I discuss how Marquis's revised argument deals with my original objections, and I argue that his new sufficient condition argument is unsuccessful. (shrink)

What is encoded in working memory may be a content-addressable pointer, but a critical portion of the information that is addressed includes the motor information to achieve deictic reference in the environment. Additionally, the same strategy that is used to access environment information just in time for its use may also be used to access long-term memory via the pre-frontal cortex.

One of the most distinctive and intriguing developments of modern set theory has been the realization that, despite widely divergent incentives for strengthening the standard axioms, there is essentially only one way of ascending the higher reaches of infinity. To the mathematical realist the unexpected convergence suggests that all these axiomatic extensions describe different aspects of the same underlying reality.

This paper discusses a sequence of extensions ofNFU, Jensen's improvement of Quine's set theory “New Foundations” (NF) of [16].The original theoryNFof Quine continues to present difficulties. After 60 years of intermittent investigation, it is still not known to be consistent relative to any set theory in which we have confidence. Specker showed in [20] thatNFdisproves Choice (and so proves Infinity). Even if one assumes the consistency ofNF, one is hampered by the lack of powerful methods for proofs of consistency and (...) independence such as are available for use withZFC; very clever work has been done with permutation methods, starting with [18] and [5], and exemplified more recently by [14], but permutation methods can only be applied to show the consistency or independence of unstratified sentences (see the definition ofNFUbelow for a definition of stratification). For example, there is no method available to determine whether the assertion “the continuum can be well-ordered” is consistent with or independent ofNF. There is one substantial independence result for an assertion with nontrivial stratified consequences, using metamathematical methods: this is Orey's proof of the independence of the Axiom of Counting fromNF(see below for a statement of this axiom).We mention these difficulties only to reassure the reader of their irrelevance to the present work. Jensen's modification of “New Foundations” (in [13]), which was to restrict extensionality to sets, allowing many non-sets (urelements) with no elements, has almost magical effects. (shrink)

This paper discusses a sequence of extensions ofNFU, Jensen's improvement of Quine's set theory “New Foundations” (NF) of [16].The original theoryNFof Quine continues to present difficulties. After 60 years of intermittent investigation, it is still not known to be consistent relative to any set theory in which we have confidence. Specker showed in [20] thatNFdisproves Choice (and so proves Infinity). Even if one assumes the consistency ofNF, one is hampered by the lack of powerful methods for proofs of consistency and (...) independence such as are available for use withZFC; very clever work has been done with permutation methods, starting with [18] and [5], and exemplified more recently by [14], but permutation methods can only be applied to show the consistency or independence of unstratified sentences (see the definition ofNFUbelow for a definition of stratification). For example, there is no method available to determine whether the assertion “the continuum can be well-ordered” is consistent with or independent ofNF. There is one substantial independence result for an assertion with nontrivial stratified consequences, using metamathematical methods: this is Orey's proof of the independence of the Axiom of Counting fromNF(see below for a statement of this axiom).We mention these difficulties only to reassure the reader of their irrelevance to the present work. Jensen's modification of “New Foundations” (in [13]), which was to restrict extensionality to sets, allowing many non-sets (urelements) with no elements, has almost magical effects. (shrink)

We consider choice correspondences that assign a subset to every choice set of alternatives, where the total set of alternatives is an arbitrary finite or infinite set. We focus on the relations between several extensions of the condition of independence of irrelevant alternatives on one hand, and conditions on the revealed preference relation on sets, notably the weak axiom of revealed preference, on the other hand. We also establish the connection between the condition of independence of irrelevant (...) alternatives and so-called strong sets; the latter characterize a social choice correspondence satisfying independence of irrelevant alternatives. (shrink)

This chapter sharpens the book’s criticism of exclusivist responsible to religious multiplicity, firstly through close critical attention to arguments which religious exclusivists provide, and secondly through the introduction of several new, formal arguments / dilemmas. Self-described ‘post-liberals’ like Paul Griffiths bid philosophers to accept exclusivist attitudes and beliefs as just one among other aspects of religious identity. They bid us to normalize the discourse Griffiths refers to as “polemical apologetics,” and to view its acceptance as the only viable form of (...) pluralism. This reasoning may seem initially plausible, but on closer examination his and other’s defence of the reasonableness of exclusivist responses to religious multiplicity fall apart. Informed by our study of luck-leaning theological explanations of religious difference and the counter-inductive thinking they exemplify, I argue that exclusivist responses to religious multiplicity are best explained by personal and group bias, and that a discourse between exclusivist authors or sects is beyond the pale of reasonable disagreement. Our study of descriptive (psychological) and prescriptive (religious) fideism in the first sections of Chapter Five suggests that we turn back to formal features of doxastic methods (i.e., of how people process), features that may be straightforwardly tested for in studies utilizing scales of religious orientation. These formal features allow us to better recognize not only the multiplicity of models of faith that religious adherents adhere to, but also that the relationship between forms of fideism is scalar: there is a spectrum of views running from rationalism to fideism, and at the fideistic end from moderate to strong forms of religious fideism. I further explain why developing tests and markers for a high degree of fideistic orientation is important to all those who study religion. The second half of the chapter turns to criticism or censure of exclusivist attitudes to religious multiplicity, in contrast to apologetic defenses of exclusivism. While we have examined the close connections between fideism and fundamentalism, and again between fundamentalism and exclusivism in earlier chapters, a sharper focus reveals an important but little-recognized distinction reflected in the literature: the distinction between religion-specific (or particularist) and mutualist exclusivism. The mutualist doesn’t talk just about the right of adherents of one specific religion to assert exclusivism, but the adherents of any and all “home” religions. I argue that some previously unrecognized problems for the reasonableness of exclusivist responses to religious multiplicity are brought to light when we make the distinction between the two basic ways to understand the claim that exclusivists are making. I put particularist (Barth, Lindbeck, Plantinga) and mutualist (Griffiths, Gellman, Margalit, D’Costa) defenses of exclusivism on the horns of a dilemma, and argue that despite the popularity it presently enjoys among post-liberal theologians, a close examination reveals that the very conceptual coherence of mutualist exclusivism is in serious doubt. (shrink)

We interpret solution rules on a class of simple allocation problems as data on the choices of a policy maker. We analyze conditions under which the policy maker’s choices are (i) rational (ii) transitive-rational, and (iii) representable; that is, they coincide with maximization of a (i) binary relation, (ii) transitive binary relation, and (iii) numerical function on the allocation space. Our main results are as follows: (i) a well-known property, contraction independence (a.k.a. IIA) is equivalent to rationality; (ii) every contraction (...) independent and other-c monotonic rule is transitive-rational; and (iii) every contraction independent and other-c monotonic rule, if additionally continuous, can be represented by a numerical function. (shrink)

Related Works: Original Paper: M. Randall Holmes. Strong Axioms of Infinity in NFU. J. Symbolic Logic, Volume 66, Issue 1 , 87--116. Project Euclid: euclid.jsl/1183746361.

Related Works: Original Paper: M. Randall Holmes. Strong Axioms of Infinity in NFU. J. Symbolic Logic, Volume 66, Issue 1, 87--116. Project Euclid: euclid.jsl/1183746361.

We show that either PFA + or Martin's maximum implies Fleissner's Axiom R, a reflection principle for stationary subsets of P ℵ 1 (λ). In fact, the "plus version" (for one term denoting a stationary set) of Martin's axiom for countably closed partial orders implies Axiom R.

This study aims to determine the paradigm shift of scientists who use inner reason to external reason (mind), a concept initiated by Aristotle. The change allegedly occurred because of the strict laws of science. Philosophers basically talk about a topic broadly and deeply about inner reason, while scientists are more focused and narrower (outer reason). Data are obtained from six articles closely related to reason, mind, and brain, then explored and presented by six expert panels for data analysis using the (...) N Vivo 12 QSR tool. The study shows a very strong correlation between the philosophical factor and reason. The results of the cluster analysis describe various comprehensive topics discussed by philosophers regarding reason which are correlated with inner reason and God, while the scientific discussion shows a very strong correlation between the brain and the alpha band. The alpha band is a condition that exists in brain waves. The cluster analysis results illustrate that scientists' discussions are focused and narrow on the brain. Thus, there has been a paradigm shift, where scientists now use outer reason to solve problems in life rather than applying inner reason. An interesting finding from this paper is that philosophers refer to reason as a noun, which means that reason is matter. This information is helpful because until now, based on a literature search, there have been no articles from scientists explaining that reason is a matter. (shrink)

In a recent paper, Andy Clark (2008) has argued that the literature on embodied cognition reveals a tension between two prominent strands within this movement. On the one hand, there are those who endorse what Clark refers to as body-centrism, a view which emphasizes the special contribution made by the body to a creature’s mental life. Among other things, body centrism implies that significant differences in embodiment translate into significant differences in cognition and consciousness. On the other hand, there are (...) those who endorse what Clark calls extended functionalism, a view which sees the mind as the joint product of the computational resources presented by (i) intracranial processing, (ii) bodily input, and (iii) environmental scaffolding. As such, extended functionalism allows for the possibility that any contribution of the body to cognition and consciousness can be compensated for by the other two contributing factors. While Clark’s sympathies lie with the latter approach, we argue in favour of the former. In particular, we focus on consciousness and argue that the unique contribution the body makes to a creature’s manifold of phenomenal experience cannot be compensated for, in the manner, and on the scale, that Clark envisages. (shrink)

The purpose of this communication is to present some recent advances on the consequences that forcing axioms and large cardinals have on the combinatorics of singular cardinals. I will introduce a few examples of problems in singular cardinal combinatorics which can be fruitfully attacked using ideas and techniques coming from the theory of forcing axioms and then translate the results so obtained in suitable large cardinals properties.The first example I will treat is the proof that the proper forcing axiom (...) PFA implies the singular cardinal hypothesis SCH, this will easily lead to a new proof of Solovay's theorem that SCH holds above a strongly compact cardinal. I will also outline how some of the ideas involved in these proofs can be used as means to evaluate the “saturation” properties of models of strong forcing axioms like MM or PFA.The second example aims to show that the transfer principle ↠ fails assuming Martin's Maximum MM. Also in this case the result can be translated in a large cardinal property, however this requires a familiarity with a rather large fragment of Shelah's pcf-theory.Only sketchy arguments will be given, the reader is referred to the forthcoming [25] and [38] for a thorough analysis of these problems and for detailed proofs. (shrink)

We suggest a new approach for addressing the problem of establishing an axiomatic foundation for large cardinals. An axiom asserting the existence of a large cardinal can naturally be viewed as a strong Axiom of Infinity. However, it has not been clear on the basis of our knowledge of ω itself, or of generally agreed upon intuitions about the true nature of the mathematical universe, what the right strengthening of the Axiom of Infinity is—which large cardinals (...) ought to be derivable? It was shown in the 1960s by Lawvere that the existence of an infinite set is equivalent to the existence of a certain kind of structure-preserving transformation from V to itself, not isomorphic to the identity. We use Lawvere's transformation, rather than ω, as a starting point for a reasonably natural sequence of strengthenings and refinements, leading to a proposed strong Axiom of Infinity. A first refinement was discussed in later work by Trnková—Blass, showing that if the preservation properties of Lawvere's tranformation are strengthened to the point of requiring it to be an exact functor , such a transformation is provably equivalent to the existence of a measurable cardinal. We propose to push the preservation properties as far as possible, short of inconsistency. The resulting transformation V→V is strong enough to account for virtually all large cardinals, but is at the same time a natural generalization of an assertion about transformations V→V known to be equivalent to the Axiom of Infinity. (shrink)

The method of morphisms is a well-known application of Dialectica categories to set theory. In a previous work, Valeria de Paiva and the author have asked how much of the Axiom of Choice is needed in order to carry out the referred applications of such method. In this paper, we show that, when considered in their full generality, those applications of Dialectica categories give rise to equivalents of either the Axiom of Choice or Partition Principle —which is a (...) consequence of $\textbf{AC}$ whose precise status of its relationship with$\textbf{AC}$ itself is an open problem for more than a hundred years. (shrink)

An online survey of 654 Australians found that the NP seniors is associated with positive personal characteristics of health and well-being such as ‘like to travel’, ‘lead an involved and active life’, ‘are vibrant and full of purpose’. Older people is also associated with positive characteristics, but somewhat less so than seniors and more socially oriented. Older people are seen to ‘benefit the workforce through their experience’, ‘have wisdom and can always be turned to for advice’, ‘play an important role (...) in their extended family’s life’. By contrast, the characteristics of those typically referred to by the elderly are negative in that the referents are incompetent or impose a burden on society, cf. ‘are frail and fall more often’, ‘are often victims of mental and physical abuse’, ‘are unable to look after themselves and depend on others for help’. The referents of old people and oldies have no particular set of characteristics assigned to them; perhaps that is why they only figure in the one characteristic ‘are tight-fisted with money’ that itself is not strongly associated with any one of the five NPs. (shrink)

We construct creature forcings with strong Axiom A that specialize a given Aronszajn tree. We work with tree creature forcing. The creatures that live on the Aronszajn tree are normed and have the halving property. We show that our models fulfill ℵ1=d

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In economics, it has often been claimed that testing choice data for violation of certain axioms-particularly if the choice data is observed under laboratory conditions-allows conclusions about the validity of certain preference axioms and the neoclassical maximization hypothesis. In this paper I argue that these conclusions are unfounded. In particular, it is unclear what exactly is tested, and the interpretation of the test results are ambiguous. Further, there are plausible reasons why the postulated choice axioms should not hold. Last, these (...) tests make implicit assumptions about beliefs that further blur the interpretations of the results. The tests therefore say little if anything about the validity of certain preference axioms or the maximization hypothesis. (shrink)

Philosophers debate the death of philosophy as much as they debate the death of God. Kant claimed responsibility for both philosophy's beginning and end, while Heidegger argued it concluded with Nietzsche. In the twentieth century, figures as diverse as John Austin and Richard Rorty have proclaimed philosophy's end, with some even calling for the advent of "postphilosophy." In an effort to make sense of these conflicting positions—which often say as much about the philosopher as his subject—Isabelle Thomas-Fogiel undertakes the first (...) systematic treatment of "the end of philosophy," while also recasting the history of western thought itself. Thomas-Fogiel begins with postphilosophical claims such as scientism, which she reveals to be self-refuting, for they subsume philosophy into the branches of the natural sciences. She discovers similar issues in Rorty's skepticism and strands of continental thought. Revisiting the work of late-nineteenth and early-twentieth-century philosophers, when the split between analytical and continental philosophy began, Thomas-Fogiel finds both traditions followed the same path—the road of reference—which ultimately led to self-contradiction. This phenomenon, whether valorized or condemned, has been understood as the death of philosophy. Tracing this pattern from Quine to Rorty, from Heidegger to Levinas and Habermas, Thomas-Fogiel reveals the self-contradiction at the core of their claims while also carving an alternative path through self-reference. Trained under the French philosopher Bernard Bourgeois, she remakes philosophy in exciting new ways for the twenty-first century. (shrink)

We propose an extension of Aczel's constructive set theory CZF by an axiom for inductive types and a choice principle, and show that this extension has the following properties: it is interpretable in Martin-Löf's type theory. In addition, it is strong enough to prove the Set Compactness theorem and the results in formal topology which make use of this theorem. Moreover, it is stable under the standard constructions from algebraic set theory, namely exact completion, realizability models, forcing as (...) well as more general sheaf extensions. As a result, methods from our earlier work can be applied to show that this extension satisfies various derived rules, such as a derived compactness rule for Cantor space and a derived continuity rule for Baire space. Finally, we show that this extension is robust in the sense that it is also reflected by the model constructions from algebraic set theory just mentioned. (shrink)

This paper is about pairing relation algebras as well as fork algebras and related subjects. In the 1991-92 fork algebra papers it was conjectured that fork algebras admit a strong representation theorem . Then, this conjecture was disproved in the following sense: a strong representation theorem for all abstract fork algebras was proved to be impossible in most set theories including the usual one as well as most non-well-founded set theories. Here we show that the above quoted conjecture (...) can still be made true by choosing an appropriate set theory as our foundation of mathematics. Namely, we show that there are non-well-founded set theories in which every abstract fork algebra is representable in the strong sense, i.e. it is isomorphic to a set relation algebra having a fork operation which is obtained with the help of the real pairing function. Further, these non-well-founded set theories are consistent if usual set theory is consistent. Finally, we will discuss related developments in propositional multi-modal logics of quantification and substitution, in algebraic logic e.g. cylindric algebras, the so called finitization problem, and applications to a logic introduced and studied in Tarski-Givant [42]. In particular, representable, weakly higher order cylindric algebras are finitely axiomatizable in a set theory which admits the axiom of foundation for finite sets. (shrink)

Located at the intersection of philosophy of cognitive science and philosophy of biology, this thesis aims to provide a novel approach to understanding the strong continuity between life and mind. This thesis applies the Free Energy Framework, predictive processing and the conceptual apparatus from ecological psychology to reveal different manners in which the organizational processes and principles underlying life have been enriched so as to result in cognitive processes. By using these anticipatory cognitive frameworks this thesis unveils different forms (...) of cognition at work in surprising places and considers how such expressions of cognition are ultimately driven by various forms of environmental complexity. Importing the concepts of affordances, environmental information and perceptual medium from ecological psychology into predictive processing and the Free Energy Framework, an empirically grounded account of cognition as an anticipatory process that allows living systems to adapt to various degrees of uncertainty in their environments at distinct and yet overlapping timescales is argued for. In doing so, this thesis attempts to identify both the explanatory limits of ecological coupling accounts of perception and action, and the possible environmental conditions under which the predictive brain evolved from its decentralized non-neural predecessors as a solution to uncertainty. In contributing to a novel approach to constraining the mind, the various concepts deployed in both philosophy and cognitive science are sharpened, furthering the current debate on what cognition is and how it is related to life. (shrink)

Proponents of two axioms of biological evolutionary theory have attempted to find justification by reference to nonequilibrium thermodynamics. One states that biological systems and their evolutionary diversification are physically improbable states and transitions, resulting from a selective process; the other asserts that there is an historically constrained inherent directionality in evolutionary dynamics, independent of natural selection, which exerts a self-organizing influence. The first, the Axiom of Improbability, is shown to be nonhistorical and thus, for a theory of change (...) through time, acausal. Its perception of the improbability of living states is at least partially an artifact of closed system thinking. The second, the Axiom of Historically Determined Inherent Directionality, is supported evidentially and has an explicit historical component. Historically constrained dynamic populations are inherently nonequilibrium systems. It is argued that living, evolving systems, when considered to be historically constrained nonequilibrium systems, do not appear improbable at all. Thus, the two axioms are not compatible. Instead, the Axiom of Improbability is considered to result from an unjustified attempt to extend the contingent proximal actions of natural selection into the area of historical, causal explanations. It is thus denied axiomatic status, and the effects of natural selection are subsumed as an additional level of constraint in an evolutionary theory derived from the Axiom of Historically Determined Inherent Directionality. (shrink)

The kind of self-reference which Perlis characterizes as strong, as opposed to formal self-reference which he characterizes as weak, is actually already present in standard forms of formal self-reference. Even if formal self-reference is weak because it is delegated, there is no specific delegation of reference for self-referential sentences, and their ‘self’ part is strong enough. In particular, the structure of self-reference in Godel's sentence, with its application of a self-referential process to (...) itself, provides a model of Perlis’ characterization of a self. This structure can also be interpreted visually, in a way relevant to self and consciousness, namely as self-recognition in a mirror. (shrink)

Kant’s ‘Refutation of Idealism’ plainly has an anti-Cartesian conclusion: ‘inner experience in general is only possible through outer experience in general’ (B278). Due to wide-spread preoccupation with Cartesian skepticism, and to the anti-naturalism of early analytic philosophy, most of Kant’s recent commentators have sought to find a purely conceptual, ‘analytic’ argument in Kant’s Refutation of Idealism – and then have dismissed Kant when no such plausible argument can be reconstructed from his text. Kant’s argument supposedly cannot eliminate all relevant alternatives, (...) and so cannot justify its strong modal claims. Kant based his arguments on an inventory of our basic cognitive capacities to employ our forms of intuition and our forms of judgment. Kant provides a variety of considerations and arguments to determine what our cognitive capacities are. This involves ‘transcendental reflection’, which Kant held is absolutely crucial for judging matters a priori (A263/B319). I argue that there is a level of philosophical reflection on our own cognitive capabilities and their preconditions that is significantly richer than has been noticed by recent commentators, and that is a precondition of Kant’s transcendental reflection proper. I explicate certain thought experiments Kant proposes in order for us to recognize some our basic, characteristic cognitive capabilities, and the limits and requirements they entail for the nature and objects of human knowledge. These thought experiments involve a kind of reflection on who we as cognizant subjects are, on what our basic cognitive capabilities are. Engaging in this kind of reflection reveals that Kant’s transcendental arguments are significantly stronger and more persuasive than has been recognized in recent commentary. (shrink)

Saunders Mac Lane has drawn attention many times, particularly in his book Mathematics: Form and Function, to the system of set theory of which the axioms are Extensionality, Null Set, Pairing, Union, Infinity, Power Set, Restricted Separation, Foundation, and Choice, to which system, afforced by the principle, , of Transitive Containment, we shall refer as . His system is naturally related to systems derived from topos-theoretic notions concerning the category of sets, and is, as Mac Lane emphasises, one that is (...) adequate for much of mathematics. In this paper we show that the consistency strength of Mac Lane's system is not increased by adding the axioms of Kripke–Platek set theory and even the Axiom of Constructibility to Mac Lane's axioms; our method requires a close study of Axiom H, which was proposed by Mitchell; we digress to apply these methods to subsystems of Zermelo set theory , and obtain an apparently new proof that is not finitely axiomatisable; we study Friedman's strengthening of , and the Forster–Kaye subsystem of , and use forcing over ill-founded models and forcing to establish independence results concerning and ; we show, again using ill-founded models, that proves the consistency of ; turning to systems that are type-theoretic in spirit or in fact, we show by arguments of Coret and Boffa that proves a weak form of Stratified Collection, and that is a conservative extension of for stratified sentences, from which we deduce that proves a strong stratified version of ; we analyse the known equiconsistency of with the simple theory of types and give Lake's proof that an instance of Mathematical Induction is unprovable in Mac Lane's system; we study a simple set theoretic assertion—namely that there exists an infinite set of infinite sets, no two of which have the same cardinal—and use it to establish the failure of the full schema of Stratified Collection in ; and we determine the point of failure of various other schemata in . The paper closes with some philosophical remarks. (shrink)

We initiate the study of model theory in the absence of the Axiom of Choice, using the Axiom of Determinateness as a powerful substitute. We first show that, in this context, L ω 1 ω is no more powerful than first-order logic. The emphasis then turns to upward Lowenhein-Skolem theorems; ℵ 1 is the Hanf number of first-order logic, of L ω 1 ω , and of a strong fragment of L ω 1 ω . The main (...) technical innovation is the development of iterated ultrapowers using infinite supports; this requires an application of infinite-exponent partition relations. All our theorems can be proven from hypotheses weaker than AD. (shrink)