In this paper I address the question of whether the incompleteness theorems imply that “the mind cannot be mechanized,” where this is understood in the specific sense that “the mathematical outputs of the idealized human mind do not coincide with the mathematical outputs of any idealized finite machine.” Gödel argued that his incompleteness theorems implied a weaker, disjunctive conclusion to the effect that either “the mind cannot be mechanized” or “mathematical truth outstrips the idealized human mind.” Others, most notably, Lucas (...) and Penrose, have claimed more—they have claimed that the incompleteness theorems actually imply the first disjunct. I will show that by sharpening the fundamental concepts involved and articulating the background assumptions governing them, one can prove Gödel’s disjunction, one can show that the arguments of Lucas and Penrose fail, and one can see what likely led proponents of the first disjunct astray. (shrink)

Gödel initiated the program of finding and justifying axioms that effect a significant reduction in incompleteness and he drew a fundamental distinction between intrinsic and extrinsic justifications. Reflection principles are the most promising candidates for new axioms that are intrinsically justified. Taking as our starting point Tait’s work on general reflection principles, we prove a series of limitative results concerning this approach. These results collectively show that general reflection principles are either weak ) or inconsistent. The philosophical significance of these (...) results is discussed. (shrink)

The paper begins with an examination of Gödel's views on absolute undecidability and related topics in set theory. These views are sharpened and assessed in light of recent developments. It is argued that a convincing case can be made for axioms that settle many of the questions undecided by the standard axioms and that in a precise sense the program for large cardinals is a complete success “below” CH. It is also argued that there are reasonable scenarios for settling CH (...) and that there is not currently a convincing case to the effect that a given statement is absolutely undecidable. (shrink)

Gödel argued that his incompleteness theorems imply that either “the mind cannot be mechanized” or “there are absolutely undecidable sentences.” In the precursor to this paper I examined the early arguments for the first disjunct. In the present paper I examine the most sophisticated argument for the first disjunct, namely, Penrose’s new argument. It turns out that Penrose’s argument requires a type-free notion of truth and a type-free notion of absolute provability. I show that there is a natural such system, (...) DTK. I prove a series of results which show that Gödel’s disjunction is provable in the system, Penrose’s argument is invalid in the system, there can be no proof or refutation of either disjunct in the system, the independence results are robust in that they persist when one strengthens the principles governing absolute provability, and there are reasons to believe that the situation will not improve under any plausible alteration of the underlying theory of truth. (shrink)

In this paper we investigate strong logics of first and second order that have certain absoluteness properties. We begin with an investigation of first order logic and the strong logics ω-logic and β-logic, isolating two facets of absoluteness, namely, generic invariance and faithfulness. It turns out that absoluteness is relative in the sense that stronger background assumptions secure greater degrees of absoluteness. Our aim is to investigate the hierarchies of strong logics of first and second order that are generically invariant (...) and faithful against the backdrop of the strongest large cardinal hypotheses. We show that there is a close correspondence between the two hierarchies and we characterize the strongest logic in each hierarchy. On the first-order side, this leads to a new presentation of Woodin's Ω-logic. On the second-order side, we compare the strongest logic with full second-order logic and argue that the comparison lends support to Quine's claim that second-order logic is really set theory in sheep's clothing. (shrink)

In this paper I examine Feferman’s reasons for maintaining that while the statements of first-order number theory are “completely clear” and “completely definite,” many of the statements of analysis and set theory are “inherently vague” and “indefinite.” I critique his five main arguments and argue that in the end the entire case rests on the brute intuition that the concept of subsets of natural numbers—along with the richer concepts of set theory—is not “clear enough to secure definiteness.” My response to (...) this final, remaining point will be that the concept of “being clear enough to secure definiteness” is about as clear a case of an inherently vague and indefinite concept as one might find, and as such it can bear little weight in making a case against the definiteness of analysis and set theory. (shrink)

The independence results in set theory invite the search for new and justified axioms. In Chapter 1 I set the stage by examining three approaches to justifying the axioms of standard set theory and argue that the approach via reflection principles is the most successful. In Chapter 2 I analyse the limitations of ZF and use this analysis to set up a mathematically precise minimal hurdle which any set of new axioms must overcome if it is to effect a significant (...) reduction in incompleteness. In Chapter 3 I examine the standard method of justifying new axioms---reflection principles---and prove a result which shows that no reflection principle can overcome the minimal hurdle and yield a significant reduction in incompleteness. In Chapter 4 I introduce a new approach to justifying new axioms---extension principles---and show that such principles can overcome the minimal hurdle and much more, in particular, such principles imply PD and that the theory of second-order arithmetic cannot be altered by set size forcing. I show that in a sense these principles are inevitable. In Chapter 5 I close with a brief discussion of meta-mathematical justifications stemming from the work of Woodin. These touch on the continuum hypothesis and other questions which are beyond the reach of standard large cardinals. (shrink)

In 1985 the second author showed that if there is a proper class of measurable Woodin cardinals and $V^{B1} $ and $V^{B2} $ are generic extensions of V satisfying CH then $V^{B1} $ and $V^{B2} $ agree on all $\Sigma _1^2 $ -statements. In terms of the strong logic Ω-logic this can be reformulated by saying that under the above large cardinal assumption ZFC + CH is Ω-complete for $\Sigma _1^2 $ Moreover. CH is the unique $\Sigma _1^2 $ -statement (...) with this feature in the sense that any other $\Sigma _1^2 $ -statement with this feature is Ω-equivalent to CH over ZFC. It is natural to look for other strengthenings of ZFC that have an even greater degree of Ω-completeness. For example, one can ask for recursively enumerable axioms A such that relative to large cardinal axioms ZFC + A is Ω-complete for all of third-order arithmetic. Going further, for each specifiable segment $V_\lambda $ of the universe of sets (for example, one might take $V_\lambda $ to be the least level that satisfies there is a proper class of huge cardinals), one can ask for recursively enumerable axioms A such that relative to large cardinal axioms ZFC + A is Ω-complete for the theory of $V_\lambda $ . If such theories exist, extend one another, and are unique in the sense that any other such theory B with the same level of Ω-completeness as A is actually Ω-equivalent to A over ZFC, then this would show that there is a unique Ω-complete picture of the successive fragments of the universe of sets and it would make for a very strong case for axioms complementing large cardinal axioms. In this paper we show that uniqueness must fail. In particular, we show that if there is one such theory that Ω-implies CH then there is another that Ω-implies¬CH. (shrink)

Religion research is gaining prominence in family firms due to its strong connection to family traditions, values, and culture. This expanding literature highlights the need for systematic, bibliometric, and meta-studies to comprehensively understand religion's role in family businesses. Addressing this gap, we conducted a bibliometric analysis of 131 documents (1992–2024) from Scopus. Alongside descriptive analyses, we rigorously reviewed these documents, identifying major theories, methods, and frameworks in the field. Co-citation analysis revealed three intellectual foundations: ethics and values, family dynamics, and (...) decision-making with financial performance. Bibliographic coupling identified four emerging research areas: spirituality and decision-making, ethics and values, family unity and traditions, and entrepreneurial activities. The thematic analysis highlighted the most and least explored topics about the role of religion in family businesses. Based on these insights, we developed a conceptual model and a framework outlining antecedents, moderators, mediators, and outcomes in the study of religion in family firms. Consequently, this study identifies research gaps and proposes future directions to advance scholarship in this field. (shrink)

In this paper I examine Feferman’s reasons for maintaining that while the statements of first-order number theory are “completely clear'” and “completely definite,”' many of the statements of analysis and set theory are “inherently vague'” and “indefinite.”' I critique his four central arguments and argue that in the end the entire case rests on the brute intuition that the concept of subsets of natural numbers—along with the richer concepts of set theory—is not “clear enough to secure definiteness.” My response to (...) this final, remaining point will be that the concept of “being clear enough to secure definiteness” is about as clear a case of an inherently vague and indefinite concept as one might find, and as such it can bear little weight in making a case against the definiteness of analysis and set theory. (shrink)

This chapter discusses the predicative conception of the continuum. It has three parts. The first part gives a historical account of the origins of the concept of predicativity, from its birth in the general logical setting of Russell’s work on the paradoxes, to its relocation to a more specific mathematical setting in Weyl’s work on his limitative conception of analysis. The second part traces the development of the subsequent analysis of the concept of predicativity, and culminates in Feferman’s celebrated analysis. (...) The third part addresses—in the light of these developments —the question of what the continuum looks like from the predicative point of view. Three predicative conceptions of the continuum are distinguished—one associated with Weyl, and two associated with Feferman—and it is argued that each predicative conception involves, in one way or another, a radical departure from our default conception of the continuum. (shrink)

The HOD Dichotomy Theorem states that if there is an extendible cardinal, δ, then either HOD is “close” to V or HOD is “far” from V. The question is whether the future will lead to the first or the second side of the dichotomy. Is HOD “close” to V, or “far” from V? There is a program aimed at establishing the first alternative—the “close” side of the HOD Dichotomy. This is the program of inner model theory. In recent years the (...) third author has provided evidence that there is an ultimate inner model—Ultimate-L—and he has isolated a natural conjecture associated with the model—the Ultimate-L Conjecture. This conjecture implies that that the first alternative holds—HOD is “close” to V. This is the future in which pattern prevails. In this paper we introduce a very different program, one aimed at establishing the second alternative—the “far” side of the HOD Dichotomy. This is the program of large cardinals beyond choice. Kunen famously showed that if AC holds then there cannot be a Reinhardt cardinal. It has remained open whether Reinhardt cardinals are consistent in ZF alone. It turns out that there is an entire hierarchy of choiceless large cardinals of which Reinhardt cardinals are only the beginning, and, surprisingly, this hierarchy appears to be highly ordered and amenable to systematic investigation, as we shall show in this paper. The point is that if these choiceless large cardinals are consistent then the Ultimate-L Conjecture must fail. This is the future where chaos prevails. (shrink)

This volume contains the proceedings of the Logic at Harvard conference in honor of W. Hugh Woodin's 60th birthday, held March 27–29, 2015, at Harvard University. It presents a collection of papers related to the work of Woodin, who has been one of the leading figures in set theory since the early 1980s. The topics cover many of the areas central to Woodin's work, including large cardinals, determinacy, descriptive set theory and the continuum problem, as well as connections between set (...) theory and Banach spaces, recursion theory, and philosophy, each reflecting a period of Woodin's career. Other topics covered are forcing axioms, inner model theory, the partition calculus, and the theory of ultrafilters. This volume should make a suitable introduction to Woodin's work and the concerns which motivate it. The papers should be of interest to graduate students and researchers in both mathematics and philosophy of mathematics, particularly in set theory, foundations and related areas. (shrink)

To get to grips with what Shapiro does and can say about higher-order vagueness, it is first necessary to thoroughly review and evaluate his conception of (first-order) vagueness, a conception which is both rich and suggestive but, as it turns out, not so easy to stabilise. In Sections I–IV, his basic position on vagueness (see Shapiro [2003]) is outlined and assessed. As we go along, I offer some suggestions for improvement. In Sections V–VI, I review two key paradoxes of higher-order (...) vagueness, while in Section VII, I explore a possible line of response to such paradoxes given by Keefe [2000]. In Section VIII, I assess whether which Shapiro might adapt Keefe's response to combat both paradoxes. (shrink)

This richly textured book bridges analytic and hermeneutic and phenomenological philosophy of science. It features unique resources for students of the philosophy and history of quantum mechanics and the Copenhagen Interpretation, cognitive theory and the psychology of perception, the history and philosophy of art, and the pragmatic and historical relationships between religion and science.

_Has liberalism failed because it has succeeded?__ “___Why Liberalism Failed___ offers cogent insights into the loss of meaning and community that many in the West feel, issues that liberal democracies ignore at their own peril.’—President Barack Obama__ “Deneen’s book is valuable because it focuses on today’s central issue. The important debates now are not about policy. They are about the basic values and structures of our social order.”—David Brooks, ___New York Times__ Of the three dominant ideologies of the twentieth century—fascism, (...) communism, and liberalism—only the last remains. This has created a peculiar situation in which liberalism’s proponents tend to forget that it _is _an ideology and not the natural end-state of human political evolution. As Patrick Deneen argues in this provocative book, liberalism is built on a foundation of contradictions: it trumpets equal rights while fostering incomparable material inequality; its legitimacy rests on consent, yet it discourages civic commitments in favor of privatism; and in its pursuit of individual autonomy, it has given rise to the most far-reaching, comprehensive state system in human history. Here, Deneen offers an astringent warning that the centripetal forces now at work on our political culture are not superficial flaws but inherent features of a system whose success is generating its own failure. (shrink)

This book launches a sustained defense of a radical interpretation of the doctrine of the open future. Patrick Todd argues that all claims about undetermined aspects of the future are simply false.

Throughout his life, Kant was concerned with questions about empirical psychology. He aimed to develop an empirical account of human beings, and his lectures and writings on the topic are recognizable today as properly 'psychological' treatments of human thought and behavior. In this book Patrick R. Frierson uses close analysis of relevant texts, including unpublished lectures and notes, to study Kant's account. He shows in detail how Kant explains human action, choice, and thought in empirical terms, and how a (...) better understanding of Kant's psychology can shed light on major concepts in his philosophy, including the moral law, moral responsibility, weakness of will, and cognitive error. Frierson also applies Kant's accounts of mental illness to contemporary philosophical issues. His book will interest students and scholars of Kant, the history of psychology, philosophy of psychology, and philosophy of action. (shrink)

Tens of thousands of students have learned to be more discerning at constructing and evaluating arguments with the help of Patrick J. Hurley. Hurley’s lucid, friendly, yet thorough presentation has made A CONCISE INTRODUCTION TO LOGIC the most widely used logic text in North America. In addition, the book’s accompanying technological resources, such as CengageNOW and Learning Logic, include interactive exercises as well as video and audio clips to reinforce what you read in the book and hear in class. (...) In short, you’ll have all the assistance you need to become a more logical thinker and communicator. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. (shrink)

00 Drawing on the phenomenological tradition in the philosophy of science and philosophy of nature, Patrick Heelan concludes that perception is a cognitive, ...

The Naked Self is a great book. It is good Kierkegaard scholarship and an excellent model of bringing history of philosophy to bear on contemporary metaphysics. After a stage-setting introduction, the book has eight main chapters and a conclusion including questions and answers from an imagined interlocutor. Stokes takes the reader from how “Kierkegaard’s phenomenology of self-experience may… be a useful resource for neo-Lockean metaphysics” to a sustained defense that “Kierkegaard himself is playing a different, and altogether more interesting, game”.Stokes’s (...) boldness is evident in his title, which remains mysterious until late in the book. Stokes draws on two key passages... (shrink)

As J. Baird Callicott has argued, Adam Smith’s moral theory is a philosophical ancestor of recent work in environmental ethics. However, Smith’s “all important emotion of sympathy” (Callicott 2001: 209) seems incapable of extension to entities that lack emotions with which one can sympathize. Drawing on the distinctive account of sympathy developed in Smith’s Theory of Moral Sentiments , as well as his account of anthropomorphizing nature in “History of Astronomy and Physics,” I show that sympathy with non-sentient nature is (...) possible within a Smithian ethics. This provides the possibility of extending sympathy, and thereby benevolence and justice, to nature. (shrink)

This volume reveals the wisdom we can learn from sailing, a sport that pits human skills against the elements, tests the mettle and is a rich source of valuable lessons in life. Unravels the philosophical mysteries behind one of the oldest organized human activities Features contributions from philosophers and academics as well as from sailors themselves Enriches appreciation of the sport by probing its meaning and value Brings to life the many applications of philosophy to sailing and the profound lessons (...) it can teach us A thought-provoking read for sailors and philosophers alike. (shrink)

Hugh Connelly, An authentic Celtic voice : the Irish penitential and contemporary discourse on reconciliation -- Padraig Corkery, Bio-ethics and contemporary Irish moral discourse -- Amelia Fleming, The silent voice of creation and moral discourse. -- Raphael Gallagher, CSsR., A church silence in sexual moral discourse? -- Donal Harrington, Moral discourse and journalism. -- Linda Hogan, Contemporary humanitarianism: neutral or impartial? -- Vincent MacNamara, On having a religious morality. -- Enda McDonagh, A discourse on the centrality of justice in moral (...) theology. -- Suzanne Mulligan, Moral discourse in a time of AIDS. (shrink)

Patrick Riley traces the forgotten roots of Rousseau's concept to seventeenth-century questions about the justice of God. If He wills that all men be saved, does He have a general will that produces universal salvation? And, if He does not, why does He will particularly" that some men be damned? The theological origin of the "general will" was important to Rousseau himself. He uses the language of divinity bequeathed to him by Pascal, Malebranche, Fenelon, and others to dignify, to (...) elevate, and to "save" politics. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

Patrick Aidan Heelan’s The Observable offers the reader a completely articulated development of his 1965 philosophy of quantum physics, Quantum Mechanics and Objectivity. In this previously unpublished study dating back more than a half a century, Heelan brings his background as both a physicist and a philosopher to his reflections on Werner Heisenberg’s physical philosophy. Including considerably broader connections to the contributions of Niels Bohr, Wolfgang Pauli, and Albert Einstein, this study also reflects Heelan’s experience in Eugene Wigner’s laboratory (...) at Princeton along with his reflections on working with Erwin Schrödinger dating from Heelan’s years at the Institute for Advanced Cosmology in Dublin. A contribution to continental philosophy of science, the phenomenological and hermeneutic resources applied in this book to the physical and ontological paradoxes of quantum physics, especially in connection with laboratory science and measurement, theory and model making, will enrich students of the history of science as well as those interested in different approaches to the historiography of science. University courses in the philosophy of physics will find this book indispensable as a resource and invaluable for courses in the history of science. (shrink)

Patrick Shade makes a strong argument for the necessity of hope in a cynical world that too often rejects it as foolish. While most accounts of hope situate it in a theological context, Shade presents a theory rooted in the pragmatic thought of such American philosophers as C. S. Peirce, William James, and John Dewey.

Philosophers, anthropologists and biologists have long puzzled over the question of human nature. It is also a question that Kant thought about deeply and returned to in many of his writings. In this lucid and wide-ranging introduction to Kant’s philosophy of human nature - which is essential for understanding his thought as a whole - Patrick R. Frierson assesses Kant’s theories and examines his critics. He begins by explaining how Kant articulates three ways of addressing the question ‘what is (...) the human being?’: the transcendental, the empirical, and the pragmatic. He then considers some of the great theorists of human nature who wrestle with Kant’s views, such as Hegel, Marx, Darwin, Nietzsche, and Freud; contemporary thinkers such as E.O.Wilson and Daniel Dennett, who have sought biological explanations of human nature; Thomas Kuhn, Michel Foucault, and Clifford Geertz, who emphasize the diversity of human beings in different times and places; and existentialist philosophers such as Sartre and Heidegger. He argues that whilst these approaches challenge and enrich Kant’s views in significant ways, all suffer from serious weaknesses that Kant’s anthropology can address. Taking a core insight of Kant’s - that human beings are fundamentally free but finite - he argues that it is the existentialists, particularly Sartre, who are the most direct heirs of his transcendental anthropology. The final part of the book is an extremely helpful overview of the work of contemporary philosophers, particularly Christine Korsgaard and Jürgen Habermas. Patrick R. Frierson explains how these philosophers engage with questions of naturalism, historicism, and existentialism while developing Kantian conceptions of the human being. Including chapter summaries and annotated further reading, What is the Human Being? is an outstanding introduction to some fundamental aspects of Kant’s thought and a judicious assessment of leading theories of human nature. It is essential reading for all students of Kant and the philosophy of human nature, as well as those in related disciplines such as anthropology, politics and sociology. (shrink)

This book steers a middle course between two opposing conceptions that currently dominate the field of semantics, the logical and cognitive approaches. Patrick Duffley brings to light the inadequacies of both of these frameworks, arguing that linguistic semantics must be based on the linguistic sign itself and on the meaning that it conveys across the full range of its uses. The book offers 12 case studies that demonstrate the explanatory power of a sign-based semantics, dealing with topics such as (...) complementation with aspectual and causative verbs, control and raising, wh- words, full-verb inversion, and existential-there constructions. It calls for a radical revision of the semantics/pragmatics interface, proposing that the dividing line be drawn between content that is linguistically encoded and content that is not encoded but still communicated. While traditional linguistic analysis often places meaning at the level of the sentence or construction, this volume argues that meaning belongs at the lower level of linguistic items, where the linguistic sign is stored in a stable, permanent, and direct relation with its meaning outside of any particular context. Building linguistic analysis from the ground up in this way provides it with a more0solid foundation and increases its explanatory power. (shrink)

In The Ethics of Discernment, Patrick H. Byrne presents an approach to ethics that builds upon the cognitional theory and the philosophical method of self-appropriation that Bernard Lonergan introduced in his book Insight, as well as upon Lonergan's later writing on ethics and values. Extending Lonergan's method into the realm of ethics, Byrne argues that we can use self-appropriation to come to objective judgements of value. The Ethics of Discernment is an introspective analysis of that process, in which sustained (...) ethical inquiry and attentiveness to feelings as "intentions of value" leads to a rich conception of the good. Written both for those with an interest in Lonergan's philosophy and for those interested in theories of ethics who have only a limited knowledge of Lonergan's work, Byrne's book is the first detailed exposition of an ethical theory based on Lonergan's philosophical method. (shrink)

Patrick Frierson - Learning to Love: From Egoism to Generosity in Descartes - Journal of the History of Philosophy 40:3 Journal of the History of Philosophy 40.3 313-338 Learning to Love: From Egoism to Generosity in Descartes Patrick R. Frierson The whole of philosophy is like a tree. The roots are metaphysics, the trunk is physics, and the branches emerging from the trunk are all the other sciences, which may be reduced to three principal ones, namely medicine, mechanics, (...) and morals. Descartes is well known for his metaphysics and physics, the roots and trunk of his philosophical project. But Descartes's morals are generally neglected, partly because they are so difficult to find. He does not dedicate a major published work to morality. His most direct comments on it are in letters to Princess Elizabeth and Pierre Chanut. The published work that most touches on moral issues is The Passions of the Soul, which is primarily a treatise on the relationship between mind and body. As a result of this lack of primary sources , there have been only a few significant studies of Descartes's moral philosophy in French, and only two major works devoted to it in English. This neglect of Descartes's ethics is unfortunate, not least since ethical concerns sometimes influence his work in other areas. This.. (shrink)