, Rudolf Carnap became a chief proponent of the doctrine that the statements of intuitionism carry nonstandard intuitionistic meanings. This doctrine is linked to Carnap's ‘Principle of Tolerance’ and claims he made on behalf of his notion of pure syntax. From premises independent of intuitionism, we argue that the doctrine, the Principle, and the attendant claims are mistaken, especially Carnap's repeated insistence that, in defining languages, logicians are free of commitment to mathematical statements intuitionists would reject. I am grateful to (...) Nathan Carter, Gary Ebbs, Janet Folina, Luise Prior McCarty, Stewart Shapiro, Neil Tennant, Christopher Tillman, Beth Tropman, Wen-fang Wang, and two anonymous referees for their comments and suggestions. CiteULike Connotea Del.icio.us What's this? (shrink)

This chapter considers in what sense, if any, planning and future thinking is involved both in the sort of behaviour examined by McCarty et al. (1999) and in the sort of behaviour measured by researchers creating versions of Tulving's spoon test. It argues that mature human planning and future thinking involves a particular type of temporal cognition, and that there are reasons to be doubtful as to whether either of those two approaches actually assesses this type of cognition. To (...) anticipate, it argues that there is a commonsense notion of planning according to which planning involves event-independent thought about time. It also argues that thinking about the future involves the ability to think about the potential temporal locations of events within a linear temporal framework in which temporal locations are unique rather than repeated. (shrink)

Although virtually all comparative research about risk perception focuses on which hazards are of concern to people in different culture groups, much can be gained by focusing on predictors of levels of risk perception in various countries and places. In this case, we examine standard and novel predictors of risk perception in seven sites among communities affected by a flood in Mexico (one site) and volcanic eruptions in Mexico (one site) and Ecuador (five sites). We conducted more than 450 interviews (...) with questions about how people feel at the time (after the disaster) regarding what happened in the past, their current concerns, and their expectations for the future. We explore how aspects of the context in which people live have an effect on how strongly people perceive natural hazards in relationship with demographic, well-being, and social network factors. Generally, our research indicates that levels of risk perception for past, present, and future aspects of a specific hazard are similar across these two countries and seven sites. However, these contexts produced different predictors of risk perception—in other words, there was little overlap between sites in the variables that predicted the past, present, or future aspects of risk perception in each site. Generally, current stress was related to perception of past danger of an event in the Mexican sites, but not in Ecuador; network variables were mainly important for perception of past danger (rather than future or present danger), although specific network correlates varied from site to site across the countries. (shrink)

An interview with Charles McCarty by Piotr Urbańczyk concerning mathematical explanation.

The theory of action underlying Immanuel Kant's ethical theory is the subject of this book.

There seems to be a view that intuitionists not only take the Axiom of Choice (AC) to be true, but also believe it a consequence of their fundamental posits. Widespread or not, this view is largely mistaken. This article offers a brief, yet comprehensive, overview of the status of AC in various intuitionistic and constructivist systems. The survey makes it clear that the Axiom of Choice fails to be a theorem in most contexts and is even outright false in some (...) important contexts. Of the systems surveyed, only intensional type theory renders AC a theorem, but the extent of AC in that theory does not include, for instance, real analysis. Only a small amount of extensionality is required in order for the obvious proof an intuitionist might offer for AC to break down. (shrink)

: A standard interpretation of Kantian "maxims" sees them as expressing reasons for action, implying that we cannot act without a maxim. But recent challenges to this interpretation claim that Kant viewed acting on maxims as optional. Kant's understanding of maxims derives from Christian Wolff, who regarded maxims as major premises of the practical syllogism. This supports the standard interpretation. Yet Kant also viewed commitments to maxims as essential for virtue and character development, which supports challenges to the standard interpretation, (...) and raises questions about the coherence of Kant's overall conception of the role of maxims in practical philosophy. (shrink)

This essay examines the interconnected nature of salvation and health, and it does so by engaging both recent qualitative research and three scriptural accounts from the life, death, and resurrection of Jesus. In doing so, the essay argues that salvation and health—and their conceptual pairings, sin and disease—are never individualistic. These realities are always cosmic, communal, and interpersonal, even as sin and disease are fundamentally disintegrating and isolating. The salvation and health of people suffering with substance use issues are bound (...) up with the transformations of governing principalities and powers, social realities, and relationships. Health care practitioners and clergy should be wise, communal guides offering care and accompaniment in the pursuit of salvation and health. (shrink)

McCarty, Douglas Morality and ethics would be recognised by virtually everyone as a necessity in human society. In fact morality and ethics are the very foundations on which human society is built. Humans are complex individuals, with personal needs, desires, inclinations, dispositions and preferences, but are also naturally predisposed to live in social groups large and small with similarly complex individuals.

We call a logic regular for a semantics when the satisfaction predicate for at least one of its nontheorems is closed under double negation. Such intuitionistic theories as second-order Heyting arithmetic HAS and the intuitionistic set theory IZF prove completeness for no regular logics, no matter how simple or complicated. Any extensions of those theories proving completeness for regular logics are classical, i.e., they derive the tertium non datur. When an intuitionistic metatheory features anticlassical principles or recognizes that a logic (...) regular for a semantics is nonclassical, it proves explicitly that the logic is incomplete with respect to that semantics. Logics regular relative to Tarski. Beth and Kripke semantics form a large collection that includes propositional and predicate intuitionistic, intermediate and classical logics. These results are corollaries of a single theorem. A variant of its proof yields a generalization of the Gödel-Kreisel Theorem linking weak completeness for intuitionistic predicate logic to Markov's Principle. (shrink)

This chapter presents and illustrates fundamental principles of the intuitionistic mathematics devised by L.E.J. Brouwer and then describes in largely nontechnical terms metamathematical results that shed light on the logical character of that mathematics. The fundamental principles, such as Uniformity and Brouwer’s Theorem, are drawn from the intuitionistic studies of logic and topology. The metamathematical results include Gödel’s negative and modal translations and Kleene’s realizability interpretation. The chapter closes with an assessment of anti-realism as a philosophy of intuitionism.

In The Anticipatory Corpse, Jeffrey Bishop claims that modern medicine has lost formal and final causality as the dead body has become epistemologically normative, and that a singular focus on efficient and material causality has thoroughly distorted modern medical practice. Bishop implies that the renewal of medicine will require its housing in alternate social spaces. This essay critiques both Bishop’s diagnosis and therapy by arguing, first, that alternate social imaginaries, though perhaps marginalized, are already present within the practice of medicine. (...) And second, the essay argues that alternate social imaginaries in medicine can be reclaimed not through separatist communities but in the re-narration of conceptually underdetermined practices. Given Bishop’s invitation for theology to engage medicine, this essay then draws from theologian Dietrich Bonhoeffer for the kind of diagnosis and therapy currently needed, concluding with a contemporary example of how an alternate social imaginary is being instantiated in modern medicine. (shrink)

In 1957, Gödel proved that completeness for intuitionistic predicate logic HPL implies forms of Markov's Principle, MP. The result first appeared, with Kreisel's refinements and elaborations, in Kreisel. Featuring large in the Gödel-Kreisel proofs are applications of the axiom of dependent choice, DC. Also in play is a form of Herbrand's Theorem, one allowing a reduction of HPL derivations for negated prenex formulae to derivations of negations of conjunctions of suitable instances. First, we here show how to deduce Gödel's results (...) by alternative means, ones arguably more elementary than those of Kreisel. We avoid DC and Herbrand's Theorem by marshalling simple facts about negative translations and Markov's Rule. Second, the theorems of Gödel and Kreisel are commonly interpreted as demonstrating the unprovability of completeness for HPL, if means of proof are confined within strictly intuitionistic metamathematics. In the closing section, we assay some doubts about such interpretations. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Peacebuilding: Catholic Theology, Ethics, and Praxis ed. by Robert J. Schreiter, R. Scott Appleby, Gerard F. PowersJames W. McCarty IIIPeacebuilding: Catholic Theology, Ethics, and Praxis Edited by Robert J. Schreiter, R. Scott Appleby, and Gerard F. Powers Maryknoll, NY: Orbis Books, 2010. 480pp. $27.00Peacebuilding results from a four-year research project sponsored by the Catholic Peacebuilding Network. A wide-ranging and interdisciplinary set of fifteen essays, Peacebuilding not only (...) brings to the fore the unique ways that Roman Catholic theology and practice has contributed to the global work of peacebuilding, but it also makes the case that the Catholic Church needs to develop a more robust theology of peacebuilding to complement and strengthen traditional Catholic approaches to the ethics of war and peace. The two most bold proposals along these lines are Daniel Philpott’s call for a papal encyclical on peacebuilding (92, 120) and Maryann Cusimano Love’s proposal of “just peace” criteria for guiding peacebuilding work in a fashion similar to the way “just war” criteria have guided the conduct of war (82, 425–27).Peacebuilding is organized into two main sections. The first documents and theorizes the work of Catholic actors and organizations in peacebuilding work. In one of the most helpful essays in this section, John Paul Lederach describes how the “ubiquitous presence” of the Catholic Church in a society is, in fact, one of the most unique contributions the Church has to make to global peacebuilding. Lederach uses the phrase “ubiquitous presence” to describe the unique role Catholic “actors” play within the “pyramid approach” to peacebuilding that he develops elsewhere (see Lederach, The Moral Imagination: The Art and Soul of Peacebuilding [New York: Oxford University Press, 2005], 79). Because of its hierarchical structure, the Catholic Church—especially in Catholic-majority countries—has the potential to cultivate peacebuilding allies among different sectors of a society: the elite, “midlevel” actors, and at the grassroots level. Many other peacebuilding actors—politicians, civil society activists, and the historic peace churches, for instance—do not have such a ubiquitous presence. While Lederach has previously emphasized the importance of midlevel actors in peacebuilding, in this essay he argues that the “ubiquitous presence” of the Catholic Church [End Page 213] in a society provides a basis for making connections for peacebuilding work among a range of sectors within a society. Several of the other contributors to this book draw on this observation and demonstrate its usefulness to a variety of settings. In my estimation, this is the most important contribution of the volume.The second section consists of six essays that both expand upon existing Catholic moral theology and make the case that Catholic theology needs to develop a more robust theology of peacebuilding. Here we find a range of arguments—from Robert Schreiter’s proposal for a practical theology of reconciliation and Peter Phan’s outline of a fourfold Catholic understanding of interreligious dialogue to Kenneth Himes’s discussion of the ways peacebuilding theory challenges and complements contemporary Catholic social teaching. Himes, in particular, claims that the current acceptance of a Catholic “presumption against war” requires a more robust Catholic approach to conflict transformation; in making his case, he draws on resonances between contemporary peacebuilding theory and recent reflections on jus post bellum (justice after war) as a new category of just war thinking.As in nearly every edited collection, the quality of the essays in Peacebuilding varies. I found the essays in the first section to be the most stimulating. Not only do they highlight the peacebuilding work the Catholic Church is currently doing around the world, they also ground their proposals for how we should understand and do peacebuilding from a Catholic perspective in relevant historical examples.Indeed, the varied nature of the essays in Peacebuilding is precisely what makes it a valuable resource for both researchers and teachers of peacebuilding. On the one hand, it includes essays that break new ground and move forward our understanding of the unique nature of Catholic peacebuilding. On the other, it includes essays that introduce the topic of peacebuilding to students of religion and ethics. This book, then, serves as an excellent resource for a range... (shrink)

The categorical imperative can be construed as a universalization test for moral permissibility. False negatives of the categorical imperative would be maxims failing this test, despite the permissibility of their actions; maxims like: ‘I’ll withdraw all my savings on April 15th’. Examples of purported false negatives familiar from the literature can be grouped into three general categories, and dispatched by applying category-specific methods for proper formulation of their maxims, or for proper testing. Methods for reformulating failing maxims, such as the (...) addition of appropriate conditional clauses, do not generate false-positive counterexamples in other instances. (shrink)

Straightforwardly and strictly intuitionistic inferences show that the Brouwer– Heyting–Kolmogorov interpretation, in the presence of a formulation of the recognition principle, entails the validity of the Law of Testability: that the form ¬ f V ¬¬ f is valid. Therefore, the BHK and recognition, as described here, are inconsistent with the axioms both of intuitionistic mathematics and of Markovian constructivism. This finding also implies that, if the BHK and recognition are suitably formulated, then Brouwer’s original weak counterexample reasoning was fallacious. (...) The results of the present article extend and refine those of McCarty, C.. Antirealism and Constructivism: Brouwer’s Weak Counterexamples. The Review of Symbolic Logic. First View. Cambridge University Press. (shrink)

In Religion within the Boundaries of Mere Reason Kant wrote that ‘freedom of the power of choice has the characteristic, entirely peculiar to it, that it cannot be determined to action through any incentive except insofar as the human being has incorporated it into his maxim.’ This is an obscure statement, in both meaning and provenance. Yet almost all recent interpreters of Kant's practical philosophy find it crucial for understanding his theories of freedom and motivation, since it seems to indicate (...) what we are required to do in order to act by our own free choice. Here I refer to Kant's statement expressing the requirement that incentives be incorporated into maxims as his ‘incorporation requirement.’ How that requirement is best understood will be the leading question in what follows: a question I shall answer by showing why the incorporation requirement, and Kant's theories of freedom and motivation, should be understood differently from the way they are now usually understood. (shrink)

“Pierre Teilhard de Chardin is one of those unusual men who fit no mold and cannot be easily labeled. A complex and brilliant thinker, he had a simple and mystical faith. A Frenchman who loved his homeland, he spent most of his life in China because he was not allowed by his superiors to teach in French. As a Jesuit priest he held views on creation and evolution considered highly suspect and unorthodox, yet he submitted humbly to his order’s prohibition (...) against teaching or publishing during his lifetime. His profession-palaeontology-called on him to study the past, but the greater portion of his thinking and writing has to do with the future-the future of man and society. Teilhard de Chardin is one of the few modern thinkers who have tried to integrate all phenomena into one system. His first book, The Phenomenon of Man, published after his death, took the reading public by storm because of its vast sweep and bold attempt to create a complex and cosmic system from both a scientific and a Christian point of view. Doran McCarty’s treatment of Teilhard covers all the important aspects of his life and thought. Here you will find discussions of Teilhard’s views on the nature of God, the nature of man, the structure of reality, creation and evolution, democracy and totalitarianism. Here too are explanations of his unique terminology, including centreism, withinness, Christogenesis, Christophere,noosphere, the Omega Point. Dr. McCarty presents Teilhard’s ideas in more traditional terms, while still remaining faithful to the original complexity and terminology. This is especially important since Teilhard never had a chance to refine his thought against the reaction and criticism of the scholarly world. Dr. McCarty’s treatment is an excellent introduction for the person who wants to know more about Teilhard, as well as being a useful and important study of this unique and influential thinker.”- Publisher. (shrink)

Recent first-person memoirs of Christians living with mental health challenges helpfully confront stigma and encourage care-seeking, while also reinforcing the individualistic and technical logics of modern medicine. This clinical framework, however, is inadequate to the realities indicated by rising rates of depression, anxiety, substance use issues, and deaths from overdose and suicide. Because mental health challenges are bound up with political realities, a more politically-attuned framework for Christian engagement with mental health is necessary. By attending to the witness of Jesus (...) as revealed in the Gospel of Mark (3:20–35, 5:1–20, and 5:21–43), we can better receive the stories of people deemed by our society as mentally ill and so better perceive the interconnected personal, communal, and cosmic dimensions of illness and healing. (shrink)

Few challenges facing Kantian ethics are more famous and formidable than the so-called "case of the inquiring murderer." It appears in some form today in most introductory ethics texts, but it is not a new objection. Even Kant himself was compelled to respond to it, though by most accounts his response was embarrassingly unpersuasive. A more satisfactory reply can be offered to this old objection, however. It will be shown here that Kantian ethics permits lying to inquirers asking wrong questions, (...) and that, therefore, it can be right to lie to a murderer inquiring whether his intended victim is hiding in your house. We begin by reviewing a now popular and plausible-sounding defense of the right to lie. Finding it unsuccessful, we turn next to scrutinize the type of question asked. The case of the inquiring murderer cannot be presented without supposing that the murderer's inquiry is unevadable. As we shall then see, in Kantian ethics it is usually wrong to ask such questions. (shrink)

We show that, if a suitable intuitionistic metatheory proves that consistency implies satisfiability for subfinite sets of propositional formulas relative either to standard structures or to Kripke models, then that metatheory also proves every negative instance of every classical propositional tautology. Since reasonable intuitionistic set theories such as HAS or IZF do not demonstrate all such negative instances, these theories cannot prove completeness for intuitionistic propositional logic in the present sense.

The present paper is one installment in a lengthy task, the replacement of atomistic interpretations of Wittgenstein's Tractatus by a wholistic interpretation on which the world-in-logical-space is not constructed out of objects but objects are abstracted from out of that space. Here, general arguments against atomism are directed toward a specific target, the four aspects of the atomistic reading of Tractatus given in the Hintikkas' Investigating Wittgenstein (Hintikka & Hintikka 1986). The aspects in question are called the semantical, metaphysical, epistemological (...) and formal.What follows a précis of the Hintikkas' rendering of Wittgenstein's perspective is a characterization of the wholistic interpretation, comparing Wittgenstein's world and the transcendental conditions it sets upon possible notation to a blank page and the conditions it sets upon what is about to be written there. There will not be occasion to bring arguments against each plank in the atomist's platform or in support of each facet of wholism. But there is an extended treatment of the first two aspects — the semantical and metaphysical — which takes off from Wittgenstein's determination that, in his hands, logic must take care of itself. (shrink)

. This paper offers a survey of the current state of Artificial Intelligence and Law, and makes recommendations for future research. Two main areas of investigation are discussed: the practical work on intelligent legal information systems, and the theoretical work on computational models of legal reasoning. In both areas, the knowledge representation problem is identified as the most important issue facing this field.

This article is an exercise in computational jurisprudence. It seems clear thatthe field of AI and Law should draw upon the insights of legal philosophers,whenever possible. But can the computational perspective offer anything inreturn? I will explore this question by focusing on the concept of OWNERSHIP,which has been debated in the jurisprudential literature for centuries. Althoughthe intellectual currents here flow mostly in one direction – from legal philosophy to AI – I will show that there are also some insights to (...) be gained from a computational analysis of the OWNERSHIP relation. In particular, the article suggests a computational explanation for the emergence of abstract property rights, divorced from concrete material objects. (shrink)

After distinguishing three criteria of adequacy for any acceptable moral theory's treatment of moral conflict, or conflicts of duties, I explain how Kant's ethics can satisfy all three. Although Kant denies the possibility of conflicting duties, he does allow conflicting "grounds of obligation." I develop a new interpretation of such conflicts, rejecting one proposed earlier by Onora O'Neill.

Let S be a deductive system such that S-derivability (⊦s) is arithmetic and sound with respect to structures of class K. From simple conditions on K and ⊦s, it follows constructively that the K-completeness of ⊦s implies MP(S), a form of Markov's Principle. If ⊦s is undecidable then MP(S) is independent of first-order Heyting arithmetic. Also, if ⊦s is undecidable and the S proof relation is decidable, then MP(S) is independent of second-order Heyting arithmetic, HAS. Lastly, when ⊦s is many-one (...) complete, MP(S) implies the usual Markov's Principle MP. An immediate corollary is that the Tarski, Beth and Kripke weak completeness theorems for the negative fragment of intuitionistic predicate logic are unobtainable in HAS. Second, each of these: weak completeness for classical predicate logic, weak completeness for the negative fragment of intuitionistic predicate logic and strong completeness for sentential logic implies MP. Beth and Kripke completeness for intuitionistic predicate or sentential logic also entail MP. These results give extensions of the theorem of Gödel and Kreisel (in [4]) that completeness for pure intuitionistic predicate logic requires MP. The assumptions of Godel and Kreisel's original proof included the Axiom of Dependent Choice and Herbrand's Theorem, no use of which is explicit in the present article. (shrink)

An examination of and plea for a time-honored answer to the title question, that answer being, “A number is one principal result among others of a process of converting magnitudes drawn from a continuum, via a scheme of measurement, into arithmetic quantities.” Ideas on this subject of Paul du Bois-Reymond, Richard Dedekind, and Otto Hölder are subjected to detailed statement and close analysis. At the very center lies du Bois-Reymond’s demonstration that the Cantor-Dedekind Axiom–that an intuition into the nature of (...) continuous magnitude shows that the geometric line is isomorphic to the array of Dedekind real numbers–is not merely unprovable but wholly false. (shrink)

Anselm described god as “something than which nothing greater can be thought” [1, p. 93], and Descartes viewed him as “a supreme being” [7, p. 122]. I first capture those characterizations formally in a simple language for monadic predicate logic. Next, I construct a model class inspired by Stoic and medieval doctrines of grades of being [8, 20]. Third, I prove the models sufficient for recovering, as internal mathematics, the famous ontological argument of Anselm, and show that argument to be, (...) on this formalization, valid. Fourth, I extend the models to incorporate a modality fit for proving that any item than which necessarily no greater can be thought is also necessarily real. Lastly, with the present approach, I blunt the sharp edges of notable objections to ontological arguments by Gaunilo and by Grant. A trigger warning: every page of this writing flouts the old saw “Existence is not a predicate” and flagrantly. (shrink)

This essay engages Miguel De La Torre’s proposal to “embrace hopelessness” and argues that Christians should hold on to hope. The author places De La Torre’s argument in conversation with others who have written on hope and hopelessness and excavates two main weaknesses in his argument: first, a definition of hope that does not stand up to a review of the literature on the topic, especially as advocated by scholars from oppressed communities, and, second, a proposal for hopelessness that does (...) not address how it can contribute to sustainable social transformation. The author then defends hope by drawing on the theological labor and lived experience of oppressed people who utilize hope to empower transformative social action. (shrink)

The chapter features, first, a critical presentation of Brouwer’s intuitionistic doctrines concerning logic, the real numbers, and continuity in the real number system, including his Principle for Numbers and Continuity Theorem. This is followed by a parallel examination of Hermann Weyl’s quasi-intuitionistic views on logic, continuity, and the real number system, views inspired by (but grossly misrepresenting) ideas of Brouwer. The whole business wraps up with an attempt to place Brouwer’s and Weyl’s efforts within the trajectory of informed thinking, during (...) the late 19th and early 20th centuries, on the subjects of continua, magnitudes, and quantities. (shrink)

Rather than “embracing hopelessness,” many marginalized communities understand their practices of political resistance as exercises in hope. One space of contemporary activism where this is evident is in transformative justice movements. Utilizing the idea of moral imagination as articulated in peacebuilding and conflict transformation literature, and the idea of hope as a social practice as articulated by Keri Day, I argue that a close examination of transformative justice organizing reveals hope as a social practice of embodied moral imagination practiced by (...) communities on the margins. (shrink)

We describe a variety of sets internal to models of intuitionistic set theory that (1) manifest some of the crucial behaviors of potentially infinite sets as described in the foundational literature going back to Aristotle, and (2) provide models for systems of predicative arithmetic. We close with a brief discussion of Church’s Thesis for predicative arithmetic.