The Denjoy integral is an integral that extends the Lebesgue integral and can integrate any derivative. In this paper, it is shown that the graph of the indefinite Denjoy integral f↦∫xaf is a coanalytic non-Borel relation on the product space M[a,b]×C[a,b], where M[a,b] is the Polish space of real-valued measurable functions on [a,b] and where C[a,b] is the Polish space of real-valued continuous functions on [a,b]. Using the same methods, it is also shown that the class of indefinite Denjoy integrals, (...) called ACG∗[a,b], is a coanalytic but not Borel subclass of the space C[a,b], thus answering a question posed by Dougherty and Kechris. Some basic model theory of the associated spaces of integrable functions is also studied. Here the main result is that, when viewed as an ℝ[X]-module with the indeterminate X being interpreted as the indefinite integral, the space of continuous functions on the interval [a,b] is elementarily equivalent to the Lebesgue-integrable and Denjoy-integrable functions on this interval, and each is stable but not superstable, and that they all have a common decidable theory when viewed as ℚ[X]-modules. (shrink)

This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church’s intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also model other axioms (...) of Church’s intensional logic that have been criticized by Parsons and Klement: this, it turns out, is due to resources which also permit an interpretation of a fragment of Gallin’s intensional logic. Finally, the relation between the predicative response to the Russell-Myhill paradox of propositions and the Russell paradox of sets is discussed, and it is shown that the predicative conception of set induced by this predicative intensional logic allows one to respond to the Wehmeier problem of many non-extensions. (shrink)

This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent ‘internal’ renditions of the famous categoricity arguments for arithmetic and set theory.

A crucial part of the contemporary interest in logicism in the philosophy of mathematics resides in its idea that arithmetical knowledge may be based on logical knowledge. Here an implementation of this idea is considered that holds that knowledge of arithmetical principles may be based on two things: (i) knowledge of logical principles and (ii) knowledge that the arithmetical principles are representable in the logical principles. The notions of representation considered here are related to theory-based and structure-based notions of representation (...) from contemporary mathematical logic. It is argued that the theory-based versions of such logicism are either too liberal (the plethora problem) or are committed to intuitively incorrect closure conditions (the consistency problem). Structure-based versions must on the other hand respond to a charge of begging the question (the circularity problem) or explain how one may have a knowledge of structure in advance of a knowledge of axioms (the signature problem). This discussion is significant because it gives us a better idea of what a notion of representation must look like if it is to aid in realizing some of the traditional epistemic aims of logicism in the philosophy of mathematics. (shrink)

A semantics for quantified modal logic is presented that is based on Kleene's notion of realizability. This semantics generalizes Flagg's 1985 construction of a model of a modal version of Church's Thesis and first-order arithmetic. While the bulk of the paper is devoted to developing the details of the semantics, to illustrate the scope of this approach, we show that the construction produces (i) a model of a modal version of Church's Thesis and a variant of a modal set theory (...) due to Goodman and Scedrov, (ii) a model of a modal version of Troelstra's generalized continuity principle together with a fragment of second-order arithmetic, and (iii) a model based on Scott's graph model (for the untyped lambda calculus) which witnesses the failure of the stability of non-identity. (shrink)

This paper presents new constructions of models of Hume's Principle and Basic Law V with restricted amounts of comprehension. The techniques used in these constructions are drawn from hyperarithmetic theory and the model theory of fields, and formalizing these techniques within various subsystems of second-order Peano arithmetic allows one to put upper and lower bounds on the interpretability strength of these theories and hence to compare these theories to the canonical subsystems of second-order arithmetic. The main results of this paper (...) are: (i) there is a consistent extension of the hyperarithmetic fragment of Basic Law V which interprets the hyperarithmetic fragment of second-order Peano arithmetic, and (ii) the hyperarithmetic fragment of Hume's Principle does not interpret the hyperarithmetic fragment of second-order Peano arithmetic, so that in this specific sense there is no predicative version of Frege's Theorem. (shrink)

Frege's Grundgesetze was one of the 19th century forerunners to contemporary set theory which was plagued by the Russell paradox. In recent years, it has been shown that subsystems of the Grundgesetze formed by restricting the comprehension schema are consistent. One aim of this paper is to ascertain how much set theory can be developed within these consistent fragments of the Grundgesetze, and our main theorem shows that there is a model of a fragment of the Grundgesetze which defines a (...) model of all the axioms of Zermelo-Fraenkel set theory with the exception of the power set axiom. The proof of this result appeals to G\"odel's constructible universe of sets, which G\"odel famously used to show the relative consistency of the continuum hypothesis. More specifically, our proofs appeal to Kripke and Platek's idea of the projectum within the constructible universe as well as to a weak version of uniformization (which does not involve knowledge of Jensen's fine structure theory). The axioms of the Grundgesetze are examples of abstraction principles, and the other primary aim of this paper is to articulate a sufficient condition for the consistency of abstraction principles with limited amounts of comprehension. As an application, we resolve an analogue of the joint consistency problem in the predicative setting. (shrink)

Many recent writers in the philosophy of mathematics have put great weight on the relative categoricity of the traditional axiomatizations of our foundational theories of arithmetic and set theory. Another great enterprise in contemporary philosophy of mathematics has been Wright's and Hale's project of founding mathematics on abstraction principles. In earlier work, it was noted that one traditional abstraction principle, namely Hume's Principle, had a certain relative categoricity property, which here we term natural relative categoricity. In this paper, we show (...) that most other abstraction principles are not naturally relatively categorical, so that there is in fact a large amount of incompatibility between these two recent trends in contemporary philosophy of mathematics. To better understand the precise demands of relative categoricity in the context of abstraction principles, we compare and contrast these constraints to stability-like acceptability criteria on abstraction principles, the Tarski-Sher logicality requirements on abstraction principles studied by Antonelli and Fine, and supervaluational ideas coming out of Hodes' work. (shrink)

This paper presents a systematic study of the prehistory of the traditional subsystems of second-order arithmetic that feature prominently in the reverse mathematics program of Friedman and Simpson. We look in particular at: (i) the long arc from Poincar\'e to Feferman as concerns arithmetic definability and provability, (ii) the interplay between finitism and the formalization of analysis in the lecture notes and publications of Hilbert and Bernays, (iii) the uncertainty as to the constructive status of principles equivalent to Weak K\"onig's (...) Lemma, and (iv) the large-scale intellectual backdrop to arithmetical transfinite recursion in descriptive set theory and its effectivization by Borel, Lusin, Addison, and others. (shrink)

Frege's theorem says that second-order Peano arithmetic is interpretable in Hume's Principle and full impredicative comprehension. Hume's Principle is one example of an abstraction principle, while another paradigmatic example is Basic Law V from Frege's Grundgesetze. In this paper we study the strength of abstraction principles in the presence of predicative restrictions on the comprehension schema, and in particular we study a predicative Fregean theory which contains all the abstraction principles whose underlying equivalence relations can be proven to be equivalence (...) relations in a weak background second-order logic. We show that this predicative Fregean theory interprets second-order Peano arithmetic. (shrink)

Philosophy and model theory frequently meet one another. Philosophy and Model Theory aims to understand their interactions -/- Model theory is used in every ‘theoretical’ branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics. But these wide-ranging appeals to model theory have created a highly fragmented literature. On the one hand, many philosophically significant mathematical results are found only in mathematics textbooks: these are aimed squarely at mathematicians; (...) they typically presuppose that the reader has a significant background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are then scattered across disconnected pockets of papers, separated by decades or more. -/- The first aim of Philosophy and Model Theory, then, is to consider the philosophical uses of model theory. On a technical level, we try to show how philosophically significant results connect to one another, and also to state the best version of a result for philosophical purposes. On a philosophical level, we show how similar dialectical situations arise repeatedly, across fragmented debates in varied philosophical areas. -/- The second aim of Philosophy and Model Theory, though, is to consider the philosophy of model theory. Model theory itself is rarely taken as the subject matter of philosophising (contrast this, say, with the philosophy of biology, or the philosophy of set theory). But model theory is a beautiful part of pure mathematics, and worthy of philosophical study in its own right. (shrink)

In this paper, I develop an argument for the thesis that ‘maximality is extrinsic’, on which a whole physical object is not a whole of its kind in virtue of its intrinsic properties. Theodore Sider has a number of arguments that depend on his own simple argument that maximality is extrinsic. However, Peter van Inwagen has an argument in defence of his Duplication Principle that, I will argue, can be extended to show that Sider's simple argument fails. However, van Inwagen's (...) argument fails against a more complex, sophisticated argument that maximality is extrinsic. I use van Inwagen's own commitments to various forms of causation and metaphysical possibility to argue that maximality is indeed extrinsic, although not for the mundane reasons that Sider suggests. I then argue that moral properties are extrinsic properties. Two physically identical things can have different moral properties in a physical world. This argument is a counterexample to a classical ethical supervenience idea (often attributed to G.E. Moore) that if there is identity of physical properties in a physical world, then there is identity in moral properties as well. I argue moral value is ‘border sensitive’ and extrinsic for Kantians, utilitarians, and Aristotelians. (shrink)

The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgements of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to say that the thesis defended here is heterodox from the vantage point of traditional philosophy (...) of mathematics. So this paper focuses on providing a preliminary defense of this thesis, in that it focuses on responding to several objections. Some of these objections are from the classical literature, such as Frege's concern about indiscernibility and circularity, while other are more recent, such as Baker's concern about the unreliability of small samplings in the setting of arithmetic. Another family of objections suggests that we simply do not have access to probability assignments in the setting of arithmetic, either due to issues related to the~$\omega$-rule or to the non-computability and non-continuity of probability assignments. Articulating these objections and the responses to them involves developing some non-trivial results on probability assignments, such as a forcing argument to establish the existence of continuous probability assignments that may be computably approximated. In the concluding section, two problems for future work are discussed: developing the source of arithmetical confirmation and responding to the probabilistic liar. (shrink)

Theorists interested in learning more about any given interpretive approach are often required to navigate a dizzying array of sources, with no clear sense of where to begin. The prose of many primary sources is often steeped in dense and technical argot that novices find intimidating or even impenetrable. Interpretation in Political Theory provide students of political theory a single introductory reference guide to major approaches to interpretation available in the field today. Comprehensive and clearly written, the book includes: A (...) historical and theoretical overview that situates the practice of interpretation within the development of political theory in the twentieth century. Chapters on Straussian esotericism, historical approaches within the Cambridge School of interpretation, materialist approaches associated with Marxism, the critical approaches associated with varieties of feminism, Greimassian semiotics, Foucaultian genealogy, the negative dialectics of Theodor Adorno, deconstruction as exemplified by Jacques Derrida and Paul de Man, and Lacanian psychoanalysis. An exposition of the theoretical and disciplinary background of each approach, the tools and techniques of interpretation it uses, its assumptions about what counts as a relevant text in political theory, and what it considers to be the purpose or objective of reading in political theory. A reading of Thomas Hobbes s Leviathan to illustrate how each approach can be applied in practice. A list of suggestions for further reading that will guide those interested in pursuing more advanced study. An invaluable textbook for advanced undergraduates, graduate students, and even seasoned scholars of political theory interested in learning more about different interpretive approaches. ". (shrink)

In this book, Sean Noah Walsh applies Herbert Marcuse’s observations on counterrevolution to recent developments in education politics. Seemingly disparate issues such as the exercise of state power to reorganize curricula, the derision of intellectuals, the permeation of consumerism into the collegiate experience, and the expansion of online teaching belong to the same strategy in which the faculties of dissent are neutralized before they can develop and dissent is established as the paramount political obscenity.

David Lewis insists that restrictivist composition must be motivated by and occur due to some intuitive desiderata for a relation R among parts that compose wholes, and insists that a restrictivist’s relation R must be vague. Peter van Inwagen agrees. In this paper, I argue that restrictivists need not use such examples of relation R as a criterion for composition, and any restrictivist should reject a number of related mereological theses. This paper critiques Lewis and van Inwagen (and others) on (...) their respective mereological metaphysics, and offers a Golden Mean between their two opposite extremes. I argue for a novel account of mereology I call Modal Mereology that is an alternative to Classical Mereology. A modal mereologist can be a universalist about the possible composition of wholes from parts and a restrictivist about the actual composition of wholes from parts. I argue that puzzles facing Modal Mereology (e.g., puzzles concerning Cambridge changes and the Problem of the Many, and how to demarcate the actual from the possible) are also faced in similar forms by classical universalists. On my account, restricted composition is rather motivated by and occurs due to a possible whole’s instantiating an actual type. Universalists commonly believe in such types and defend their existence from objections and puzzles. The Modal Mereological restrictivist can similarly defend the existence of such types (adding that such types are the only wholes) from similar objections and puzzles. (shrink)

Aristotle’s best human life is attained through theoretical contemplation, and Confucius’ is attained through practical cultivation of the social self. However, I argue that in the best human life for both Confucius and Aristotle, a form of theoretical contemplation must occur and can only occur with an ethical commitment to community life. Confucius, like Aristotle, sees that the best contemplation comes after later-life, greater-learning and is central to ethical and community life. Aristotle, like Confucius, sees the best contemplation as presupposing (...) full ethical commitment to community life. So, I argue for the theses that: on Aristotle’s view, the best human contemplation requires one be fully morally good; on Confucius’ view, to be fully morally good requires the best human contemplation; being fully morally good for both requires commitment to the good of others and the community. (shrink)

The aim of this article is to address the recently renewed debate pertaining to esotericism, secret messages encoded within writings from antiquity, especially in the writings of Plato. The question of esotericism has assumed a prominent role within debates concerning the history of political thought. Ever since Leo Strauss offered his suspicion that there were secrets ‘buried in the writings of the rhetoricians of antiquity’, the idea that philosophers deliberately concealed their true beliefs in a way that few could detect (...) has been fiercely debated. More recently, the research of J.B. Kennedy has made international headlines for discovering a musical pattern embedded within Platonic writings, a pattern that Kennedy insists is evidence of Plato’s Pythagorean allegiance. The theses proffered by Strauss and Kennedy are empty doctrines of esotericism, or empty esotericisms. These doctrines insinuate the presence of secret or coded writing within Platonic dialogues but reveal no actual secret. These theses of esotericism falsely represent Plato as hyper-cryptic.Without actually providing substantive content, these notions of esotericism compel the reader to merely negate the exoteric writings of Plato, which actually render his already heterodox writings as commonplace and orthodox. (shrink)

Two puzzles with regard to the Kritik der reinen Vernunft are incongruent counterparts and causality. In De mundi sensibilis atque intelligibilis forma et principiis, Kant indicates that the experience of things like left and right hands, so-called incongruent counterparts, involve certain pure intuitions, and hence constitute one line of evidence for the claim that the concept of space itself is a pure intuition. In KrV, Kant again argues that the concept of space itself is a pure intuition, but does not (...) cite the experience of incongruent counterparts as evidence for this claim. Since there is ostensibly nothing in KrV which tells against the existence of the experiences of incongruent counterparts, the natural question is: “Why, in KrV, does Kant not cite the experience of incongruent counterparts as evidence for the claim that the concept of space is a pure intuition?” The problem with causality is as follows. One of the most primary and basic claims of KrV is that empirical experience is structured by non-empirical concepts, such as substantiality and causality. In a portion of KrV entitled the Transcendental Deduction, Kant gives section 20 the heading “All sensible intuitions stand under the categories, as conditions under which alone their the manifold can come together in one consciousness”. Since categories are those concepts which structure empirical experience, section 20 has demonstrated that all sensible intuitions are subject to substantiality and causality. However, there is a later portion of KrV entitled the Second Analogy with the heading “Principle of temporal sequence according to the law of causality: All alterations occur in accordance with the law of the connection of cause and effect”. Thus, the natural question is: “What does the Second Analogy demonstrate about causality which the Transcendental Deduction did not already demonstrate about causality?”. (shrink)

Many philosophers believe that a moral theory, given all the relevant facts, should be able to determine what is morally right and wrong. It is commonly argued that Aristotle’s ethical theory suffers from a fatal flaw: it places responsibility for determining right and wrong with the virtuous agent who has phronesis rather than with the theory itself. It is also commonly argued that Immanuel Kant’s ethical theory does provide a concept of right that is capable of determining right and wrong (...) in specific cases. I argue, however, that Kant never gives a determinate moral theory of right. Rather, I argue that Kant’s moral theory is similar in many ways to that of Aristotle, in that it still holds that a moral agent with phronesis, rather than the theory, determines what is right. Kant’s practical philosophy was not so much meant to tell us right and wrong as to prevent bad moral theory from corrupting our moral common sense, and it is our moral common sense that determines right and wrong naturally. (shrink)

Normal 0 false false false EN-US X-NONE X-NONE Normal 0 false false false EN-US ZH-TW X-NONE It is commonly believed that impartial utilitarian moral theories have significant demands that we help the global poor, and that the partial virtue ethics of Mencius and Aristotle do not. This ethical partiality found in these virtue ethicists has been criticized, and some have suggested that the partialistic virtue ethics of Mencius and Aristotle are parochial (i.e., overly narrow in their scope of concern). I (...) believe, however, that the ethics of Mencius and Aristotle are both more cosmopolitan than many presume and also are very demanding. In this paper, I argue that the ethical requirements to help the poor and starving are very demanding for the quintessentially virtuous person in Mencius and Aristotle. The ethical demands to help even the global poor are demanding for Mencius’ jun-zi ( 君子 chün-tzu / junzi ) and Aristotle’s megalopsuchos . I argue that both the jun-zi and megalopsuchos have a wide scope of concern for the suffering of poor people. I argue that the relevant virtues of the jun-zi and megalopsuchos are also achievable for many people. The moral views of Mencius and Aristotle come with strong demands for many of us to work harder to alleviate global poverty. . (shrink)

This book critically examines Leo Strauss s claim that the philosophers of antiquity, especially Plato, wrote esoterically, hiding the highest truths exclusively between the lines.

This article improves two existing theorems of interest to neologicist philosophers of mathematics. The first is a classification theorem due to Fine for equivalence relations between concepts definable in a well-behaved second-order logic. The improved theorem states that if an equivalence relation E is defined without nonlogical vocabulary, then the bicardinal slice of any equivalence class—those equinumerous elements of the equivalence class with equinumerous complements—can have one of only three profiles. The improvements to Fine’s theorem allow for an analysis of (...) the well-behaved models had by an abstraction principle, and this in turn leads to an improvement of Walsh and Ebels-Duggan’s relative categoricity theorem. (shrink)

Objects appear to fall into different sorts, each with their own criteria for identity. This raises the question of whether sorts overlap. Abstractionists about numbers—those who think natural numbers are objects characterized by abstraction principles—face an acute version of this problem. Many abstraction principles appear to characterize the natural numbers. If each abstraction principle determines its own sort, then there is no single subject-matter of arithmetic—there are too many numbers. That is, unless objects can belong to more than one sort. (...) But if there are multi-sorted objects, there should be cross-sortal identity principles for identifying objects across sorts. The going cross-sortal identity principle, ECIA2 of Cook and Ebert (2005), solves the problem of too many numbers. But, I argue, it does so at a high cost. I therefore propose a novel cross-sortal identity principle, based on embeddings of the induced models of abstracts developed by Walsh (2012). The new criterion matches ECIA2’s success, but offers interestingly different answers to the more controversial identifications made by ECIA2. (shrink)

This paper argues for a Husserlian account of phenomenal intentionality. Experience is intentional insofar as it presents a mind-independent, objective world. Its doing so is a matter of the way it hangs together, its having a certain structure. But in order for the intentionality in question to be properly understood as phenomenal intentionality, this structure must inhere in experience as a phenomenal feature. Husserl’s concept of horizon designates this intentionality-bestowing experiential structure, while his concept of motivation designates the unique phenomenal (...) character of this structure as it is experientially lived through. The way experience hangs together is itself a phenomenal feature of experience. (shrink)

How do people understand questions about cause and prevent? Some theories propose that people affirm that A causes B if A's occurrence makes a difference to B's occurrence in one way or another. Other theories propose that A causes B if some quantity or symbol gets passed in some way from A to B. The aim of our studies is to compare these theories' ability to explain judgements of causation and prevention. We describe six experiments that compare judgements for causal (...) paths that involve a mechanism, i.e. a continuous process of transmission or exchange from cause to effect, against paths that involve no mechanism yet a change in the cause nevertheless brings about a change in the effect. Our results show that people prefer to attribute cause when a mechanism links cause to effect. In contrast, prevention is sensitive both to the presence of an interruption to a causal mechanism and to a change in the outcome in the absence of a mechanism. In this sense, ‘prevent’ means something different than ‘cause not'. We discuss the implications of our results for existing theories of causation. (shrink)

Most historical accounts of "the West" take it for granted that the guiding principles of the Western tradition—reason, progress, and freedom—have been passed down directly from ancient Greece to modern Europe, evolving in isolation from all non-Western cultures. Today, many political analysts and cultural critics maintain that the Western tradition is fast approaching its end, for better or worse, as it becomes more and more integrated with non-Western cultures in an increasingly globalized world. But what if we are witnessing something (...) else entirely—not the "end" of the West but rather another historical mutation of the idea of the West itself? This groundbreaking work shows that whether the West is hailed as the source of all historical progress or scorned as the root of all cultural imperialism, it remains a deeply problematic concept that is intrinsically connected to an ethnocentric view of the world. In a critical reading of the continental philosophers Husserl, Heidegger, Levinas, and Derrida as well as the postcolonial thinkers Said, Mohanty, Bhabha, and Trinh, Sean Meighoo strikes at the intellectual foundations of Western exceptionalism until its ideological supports show through. Deconstructing the concept of the West in his provocative interpretations of Martin Bernal's controversial publication Black Athena and the Beatles' second film Help!, Meighoo poses a formidable question to philosophers, writers, political analysts, and cultural critics alike: Can we mount an effective critique of Western ethnocentrism without reinforcing the very idea of the West? (shrink)

Graduate-level textbook in general relativity.

Surveying spiritual and philosophical traditions, revives the search for wisdom for modern times"--Provided by publisher.

RésuméJe me demande ici si les conceptions pragmatiques de la vérité peuvent être réconciliées avec les intuitions ordinaires quant à la portée de la bivalence. Je soutiens que les pragmatistes sont conduits à accepter une distinction du genre «type / occurrence» entre les formes d'une investigation et ses instanciations particulières, sous peine de banaliser leur vérificationnisme. Néanmoins, même la conception révisée que j'examine échoue à sauver les approches épistémiques de la vérité de certaines conséquences peu plausibles.

Moritz Schlick, Rudolf Carnap and Herbert Feig are the most prominent of the positivists to formulate views on the mind-body problem (aside from Hempel’s one-off treatment in 1935). While their views differed from each other and changed over time they were all committed to some form of scientific physicalism, though a linguistic or conceptual rather than ontological form of it. In focus here are their views during the heyday of logical positivism and its immediate aftermath, though some initial scene-setting of (...) Schlick’s and Carnap’s pre-positivist views will help to understand the final opposing positions of Carnap and Feigl. (shrink)

An overview and descriptions of the auditory commitments of ancient Greek song, drama, and acoustic theory from the time of Homer to the death of Euripides, this is the first complete study of the cultural system of sound in Greece.

It is commonplace in discussions of modern cosmology to assert that the early universe began in a special state. Conventionally, cosmologists characterize this fine-tuning in terms of the horizon and flatness problems. I argue that the fine-tuning is real, but these problems aren't the best way to think about it: causal disconnection of separated regions isn't the real problem, and flatness isn't a problem at all. Fine-tuning is better understood in terms of a measure on the space of trajectories: given (...) reasonable conditions in the late universe, the fraction of cosmological histories that were smooth at early times is incredibly tiny. This discussion helps clarify what is required by a complete theory of cosmological initial conditions. (shrink)

This book explores the emergence of the modern higher education sector in the independent Irish state. The author traces its origins from the traditional universities, technical schools and teacher training colleges at the start of the twentieth century, cataloguing its development into the complex, multi-layered and diverse system of the early twenty-first century. Focusing on the socio-political and cultural contexts which shaped the evolution of higher education, the author analyses the interplay between the state, academic institutions and other key institutional (...) actors - notably churches, cultural organizations, employers, trade unions and supranational bodies. This study explores policy, structural and institutional change in Irish higher education, suggesting that the emergence of the modern higher education system in Ireland was influenced by ideologies and trends which owed much to a wider European and international context. The book considers how the exercise of power at local, national and international level impinged on the mission, purpose and values of higher education and on the creation and expansion of a distinctive higher education system. The author also explores a transformation in public and political understandings of the role of higher education, charting the gradual evolution from traditionalist conceptions of the academy as a repository for cultural and religious value formation, to the re-positioning of higher education as a vital factor in the knowledge based economy. This comprehensive volume will appeal to students and scholars of the Irish education system, educators and practitioners in the field, and those interested in higher education in Ireland more generally. (shrink)

We present an analogue of Gödel’s second incompleteness theorem for systems of second-order arithmetic. Whereas Gödel showed that sufficiently strong theories that are $\Pi ^0_1$ -sound and $\Sigma ^0_1$ -definable do not prove their own $\Pi ^0_1$ -soundness, we prove that sufficiently strong theories that are $\Pi ^1_1$ -sound and $\Sigma ^1_1$ -definable do not prove their own $\Pi ^1_1$ -soundness. Our proof does not involve the construction of a self-referential sentence but rather relies on ordinal analysis.

Few issues cause academics to disagree more than gender and race, especially when topics are addressed in terms of biological differences. To conduct research in these areas or comment favorably on research can subject one to scorn. When these topics are addressed, they generally take the form of philosophical debates. Anthony Walsh focuses upon such debates and supporting research. He divides parties into biologists and social constructionists, arguing that biologists remain focused on laboratory work, while constructionists are acutely aware (...) of the impact of biologists in contested territories. "Science Wars" introduces the ideas motivating the parties and examines social constructionism and its issues with science. He explores arguments over conceptual tools scientists love and constructionists abhor, and he provides a solid discussion of the co-evolution of genes and culture. Walsh then focuses his attention on gender, how constructionists view it, and the neuroscience explanation of gender differences. Moving to race, Walsh looks at how some have tried to bury the concept of race, while others emphasize it. He considers definitions of race--essentialist, taxonomic, population, and lineage--as they have evolved from the time of the Enlightenment to the present. And finally, he attempts to bring the opposing sides together by pointing out what each can bring to a meaningful discussion. (shrink)

Abstract According to Russellianism, the content of a Russellian thought, in which a person ascribes a monadic property to an object, can be represented as an ordered couple of the object and the property. A consequence of this is that it is not possible for a person to believe that a is F and not to believe b is F, when a=b. Many critics of Russellianism suppose that this is possible and thus that Russellianism is false. Several arguments for this (...) claim are criticized and it is argued that Russellians need not appeal to representational notions in order to defeat them. Contrary to popular opinion, the prospects for a pure Russellianism, a Russellianism without representations, are in fact very good. (shrink)

A personalist account of persons -- Persons as beyond good and evil -- Reality transcends itself in persons -- God as the seal of the personal -- Art as the radiance of persons in reality -- History as the memory of persons -- Politics of the person.

In The Priority of the Person, world-class philosopher David Walsh advances the argument set forth in his highly original philosophic meditation Politics of the Person as the Politics of Being (2015), that "person" is the central category of modern political thought and philosophy. This book is divided into three main parts. Beginning with the political discovery of the inexhaustibility of persons, it then explores the philosophic differentiation of the idea of the "person," and finally traces its historical emergence through (...) art, science, and faith. Walsh argues that, although the roots of the idea of "person" are found in the Greek concept of the mind and in the Christian conception of the soul, this notion is ultimately a distinctly modern achievement, because it is only the modern turn toward interiority that illuminated the unique nature of persons as each being a world unto him or herself. As Walsh shows, it is precisely this feature of persons that makes it possible for us to know and communicate with others, for we can only give and receive one another as persons. In this way alone can we became friends and, in friendship, build community. In showing how the person is modernity's central preoccupation, and in demonstrating how it is only as persons that we can truly give ourselves to others and thus develop real community, David Walsh's The Priority of the Person makes an important contribution to current discussions in both political theory and philosophy. It will also appeal to students and scholars of theology and literature, and any groups interested in the person and personalism. (shrink)

Everything you need to know about Learning Theories in Early Childhood practice. This book explores the key theorists and theories that form the foundation of learning and development in early childhood. Building your own understanding and knowledge of children's learning, it then helps you develop the skills of translating theory into practice. How does this book support you? · The structure of the book mirrors your student learning journey, to compliment your course and seminar reading. · Parts 1 and 2 (...) help you develop your reflective and analytical skills through critical questions, photographs and discussion points. · Part 3 gives real life case studies to help you understand how the theories can be practically applied in settings to improve your own practice. (shrink)