Church's simple theory of types is a system of higher-order logic in which functions are assumed to be total. We present in this paper a version of Church's system called PF in which functions may be partial. The semantics of PF, which is based on Henkin's general-models semantics, allows terms to be nondenoting but requires formulas to always denote a standard truth value. We prove that PF is complete with respect to its semantics. The reasoning mechanism in PF for partial (...) functions corresponds closely to mathematical practice, and the formulation of PF adheres tightly to the framework of Church's system. (shrink)

The k-provability for an axiomatic system A is to determine, given an integer k 1 and a formula in the language of A, whether or not there is a proof of in A containing at most k lines. In this paper we develop a unification-theoretic method for investigating the k-provability problem for Parikh systems, which are first-order axiomatic systems that contain a finite number of axiom schemata and a finite number of rules of inference. We show that the k-provability problem (...) for a Parikh system reduces to a unification problem that is essentially the unification problem for second-order terms. By solving various subproblems of this unification problem , we solve the k- probability problem for a variety of Parikh systems, including several formulations of Peano arithmetic. Our method for investigating the k-provability problem employs algorithms that compute and characterize unifiers. We give some examples of how these algorithms can be used to solve complexity problems other than the k-provability problem. (shrink)

This paper presents an algorithm that, given a finite set E of pairs of second-order monadic terms, returns a finite set U of ‘substitution schemata’ such that a substitution unifies E iff it is an instance of some member of U . Moreover, E is unifiable precisely if U is not empty. The algorithm terminates on all inputs, unlike the unification algorithms for second-order monadic terms developed by G. Huet and G. Winterstein. The substitution schemata in U use expressions which (...) represent sets of terms that differ only in how many times designated strings of function constants follow themselves. The substitution schemata may contain unresolved ‘identity restrictions’; consequently, the members of U generally do not characterize all the unifiers of E in a completely explicit way. The algorithm is particularly useful for investigating the complexity of formal proofs. (shrink)

Partial functions are ubiquitous in both mathematics and computer science. Therefore, it is imperative that the underlying logical formalism for a general-purpose mechanized mathematics system provide strong support for reasoning about partial functions. Unfortunately, the common logical formalisms — first-order logic, type theory, and set theory — are usually only adequate for reasoning about partial functionsin theory. However, the approach to partial functions traditionally employed by mathematicians is quite adequatein practice. This paper shows how the traditional approach to partial functions (...) can be formalized in a range of formalisms that includes first-order logic, simple type theory, and Von-Neumann—Bernays—Gödel set theory. It argues that these new formalisms allow one to directly reason about partial functions; are based on natural, well-understood, familiar principles; and can be effectively implemented in mechanized mathematics systems. (shrink)

Simple type theory is a higher-order predicate logic for reasoning about truth values, individuals, and simply typed total functions. We present in this paper a version of simple type theory, called PF*, in which functions may be partial and types may have subtypes. We define both a Henkin-style general models semantics and an axiomatic system for PF*, and we prove that the axiomatic system is complete with respect to the general models semantics. We also define a notion of an interpretation (...) of one PF* theory in another. PF* is intended as a foundation for mechanized mathematics. It is the basis for the logic of, an Interactive Mathematical Proof System developed at The MITRE Corporation. (shrink)

Partial functions can be easily represented in set theory as certain sets of ordered pairs. However, classical set theory provides no special machinery for reasoning about partial functions. For instance, there is no direct way of handling the application of a function to an argument outside its domain as in partial logic. There is also no utilization of lambda-notation and sorts or types as in type theory. This paper introduces a version of von-Neumann-Bernays-Gödel set theory for reasoning about sets, proper (...) classes, and partial functions represented as classes of ordered pairs. The underlying logic of the system is a partial first-order logic, so class-valued terms may be nondenoting. Functions can be specified using lambda-notation, and reasoning about the application of functions to arguments is facilitated using sorts similar to those employed in the logic of the IMPS Interactive Mathematical Proof System. The set theory is intended to serve as a foundation for mechanized mathematics systems. (shrink)

Simple type theory is a higher-order predicate logic for reasoning about truth values, individuals, and simply typed total functions. We present in this paper a version of simple type theory, called PF*, in which functions may be partial and types may have subtypes. We define both a Henkin-style general models semantics and an axiomatic system for PF*, and we prove that the axiomatic system is complete with respect to the general models semantics. We also define a notion of an interpretation (...) of one PF* theory in another. PF* is intended as a foundation for mechanized mathematics. It is the basis for the logic of , an Interactive Mathematical Proof System developed at The MITRE Corporation. (shrink)

At the beginning of 2020, COVID-19 became a global problem. Despite all the efforts to emphasize the relevance of preventive measures, not everyone adhered to them. Thus, learning more about the characteristics determining attitudinal and behavioral responses to the pandemic is crucial to improving future interventions. In this study, we applied machine learning on the multi-national data collected by the International Collaboration on the Social and Moral Psychology of COVID-19 (N = 51,404) to test the predictive efficacy of constructs from (...) social, moral, cognitive, and personality psychology, as well as socio-demographic factors, in the attitudinal and behavioral responses to the pandemic. The results point to several valuable insights. Internalized moral identity provided the most consistent predictive contribution—individuals perceiving moral traits as central to their self-concept reported higher adherence to preventive measures. Similar was found for morality as cooperation, symbolized moral identity, self-control, open-mindedness, collective narcissism, while the inverse relationship was evident for the endorsement of conspiracy theories. However, we also found a non-negligible variability in the explained variance and predictive contributions with respect to macro-level factors such as the pandemic stage or cultural region. Overall, the results underscore the importance of morality-related and contextual factors in understanding adherence to public health recommendations during the pandemic. (shrink)

Genetically modified cassava is currently being developed to address problems of diseases that threaten the food security of farmers in developing countries. The technologies are aimed at smallholder farmers, in hopes of reducing the vulnerability of cassava production to these diseases. In this paper we examine barriers to farmers’ voice in the development of GM cassava. We also examine the role of a translational research process to enhance farmers’ voice, to understand the sources of vulnerability farmers in a group in (...) Kenya’s Coast face, and to determine if their concerns are consistent with those of the scientists in agriculture addressing farmers’ needs. A two-way communication participatory process provided insights into the complex vulnerability context of farmers, their primary concerns with processing and markets of cassava in order to improve livelihoods, the lack of networks with two way communication flows, and the lack of information on GM technologies. The translational research engaged farmers and scientists in an iterative process where scientists are learning what farmers need, and farmers are learning about the potential benefits and risks from GM technologies, while at the same time expressing their concerns. (shrink)

Critics of modern agriculture decry the dominance of monocultural landscapes and look to multifunctionality as a desirable alternative that facilitates the production of public goods. In this study, we explored opportunities for multifunctional Midwestern agriculture through participatory research led by farmers, landowners, and other local actors. We suggest that agriculture typically fosters some degree of multifunctionality that arises from the divergent intentions of actors. The result is a scattered arrangement of what we term patchwork multifunctionality, a ubiquitous status quo in (...) which individuals provide public goods without coordination. In contrast, interwoven multifunctionality describes deliberate collaboration to provide public goods, especially those cases where landowners work across fence lines to weave a synergistic landscape. Using examples from two case studies, we demonstrate the spectrum of patchwork and interwoven multifunctionality that currently exists in the Corn Belt, and present underutilized opportunities for public good creation. (shrink)

In response to the chronic overuse and misuse of pesticides in agriculture, governments in Southeast Asia have sought to improve food safety by introducing public standards of good agricultural practices (GAP). Using quantitative farm-level data from an intensive horticultural production system in northern Thailand, we test if fruit and vegetable producers who follow the public GAP standard use fewer and less hazardous pesticides than producers who do not adhere to the standard. The results show that this is not the case. (...) By drawing on qualitative data from expert interviews and an action research project with local litchi (“lychee”) producers we explain the underlying reasons for the absence of significant differences. The qualitative evidence points at poor implementation of farm auditing related to a program expansion that was too rapid, at a lack of understanding among farmers about the logic of the control points in the standard, and at a lack of alternatives given to farmers to manage their pest problems. We argue that by focusing on the testing of farm produce for pesticide residues, the public GAP program is paying too much attention to the consequences rather than the root cause of the pesticide problem; it needs to balance this by making a greater effort to change on-farm practices. (shrink)

Cognitive representation is the single most important explanatory notion in the sciences of the mind and has served as the cornerstone for the so-called 'cognitive revolution'. This book critically examines the ways in which philosophers and cognitive scientists appeal to representations in their theories, and argues that there is considerable confusion about the nature of representational states. This has led to an excessive over-application of the notion - especially in many of the fresher theories in computational neuroscience. Representation Reconsidered shows (...) how psychological research is actually moving in a non-representational direction, revealing a radical, though largely unnoticed, shift in our basic understanding of how the mind works. (shrink)

Socrates (469-399 BC) is one of history's most enigmatic figures. Our knowledge of him comes to us second-hand, primarily from the philosopher Plato, who was Socrates' most gifted student, and from the historian and sometime-philosopher Xenophon, who counted himself as a member of Socrates' inner circle of friends. We also hear of Socrates in one comic play produced during his lifetime (Aristophanes' Clouds) and in passing from the philosopher Aristotle, a student of Plato. Socrates is a figure of enduring interest. (...) He is often considered the father of Western Philosophy, yet the four most famous accounts we have of him present a contradictory, confusing picture. Just who was Socrates? A brilliant philosopher, at times confounding and infuriating, morally serious and yet ironic; the ever-worldly man, sometime mystic, and uncommon martyr depicted by Plato? Or did Plato conflate Socrates' views with his own startling genius, as Aristotle suggests? Was So rates instead the less impressive, more mundane man whose commonsense impressed the laconic Xenophon? Or was Socrates the charlatan, the long-winded phony of Aristophanes' play? The Socratic works of Diogenes Laertius (3rd century AD), Libanius (AD 314 -- c. 393), Maximus of 'Tyre (2nd century AD), and Apuleius (born c. AD 125) add important dimensions to the portrait of Socrates: Diogenes Laertius' Life of Socrates emphasizes Socrates' deep ethical nature and his extraordinary personality; Libanius' Apology of Socrates is based on sources now lost to us; Maximus of Tyre's Whether Socrates Did the Right Thing When He Did Not Defend Himself makes the star ling claim (against testimony of Plato and Xenophon) that Socrates never spoke athis own trial; from Apuleius' On the God of Socrates we hear at length of Socrates' infamous daimonion: the "divine sign" only mentioned elsewhere, the sign that warned Socrates against certain courses of action. In short, from these four texts we are reintroduced to Socrates, and new wrinkles are added to an already intriguing historical figure. (shrink)

The last two decades have seen two significant trends emerging within the philosophy of science: the rapid development and focus on the philosophy of the specialised sciences, and a resurgence of Aristotelian metaphysics, much of which is concerned with the possibility of emergence, as well as the ontological status and indispensability of dispositions and powers in science. Despite these recent trends, few Aristotelian metaphysicians have engaged directly with the philosophy of the specialised sciences. Additionally, the relationship between fundamental Aristotelian concepts—such (...) as "hylomorphism", "substance", and "faculties"—and contemporary science has yet to receive a critical and systematic treatment. _Neo-Aristotelian Perspectives on Contemporary Science _aims to fill this gap in the literature by bringing together essays on the relationship between Aristotelianism and science that cut across interdisciplinary boundaries. The chapters in this volume are divided into two main sections covering the philosophy of physics and the philosophy of the life sciences. Featuring original contributions from distinguished and early-career scholars, this book will be of interest to specialists in analytical metaphysics and the philosophy of science. (shrink)

The movement called Experimental Philosophy (‘x-Phi’) has now passed its tenth anniversary. Its central insight is compelling: When an argument hinges on accepting certain ‘facts’ about human perception, knowledge, or judging, the evoking of relevant intuitions by thought experiments is intended to make those facts seem obvious. But these intuitions may not be shared universally. Experimentalists propose testing claims that traditionally were intuition-based using real experiments, with real samples. Demanding that empirical claims be empirically supported is certainly reasonable; though experiments (...) are not necessarily the only means available. When experiments are conducted, adequately interpreting their results requires understanding the study’s design (and possibly flaws) that produced them. Experiment-based reports should document the design clearly. If Plato, writing his Meno, replaced accounts of Socrates demonstrating geometry to a slave-boy, with a survey of 100 real boys—some grasping his demonstrations, others not—what conclusions could be reached? Before answering, the reader needs details on key design questions, including (among others): (a) What population are these samples intended to represent? (E.g., ‘all slave boys’?; ‘math-ignorant people’?; ‘everyone’?) (b) What statistical tests were conducted, on what assumptions? (c) How was ‘significance’ of results determined? (d) Was the test instrument’s validity established? For readers wishing to explore x-Phi’s potentials, as contributors or as interpreters of their findings, this paper offers some cautionary considerations. Throughout their literature, examples can be found casting doubt on some experimentalists’ findings, due to design-related issues. Increased awareness of methodological questions would tighten the x-phi literature, going forward . (shrink)

Called the “greatest philosophical essayist of his time,” Rorty is both famous and notorious in academic philosophy for his uniquely engaging writing style. While his fellow analytic philosophers look askance at his flamboyant prose, suspicious that it lacks the care and precision that their discipline demands, literary intellectuals who champion the essay genre can have their qualms about Rorty as well: his work is too professional and specialized to be properly called essays. I argue not only that Rorty's work fits (...) into the essay genre, but also that his use of the essay form is integral to his rhetorical project of advancing his ideal of pragmatic liberalism. Rorty writes essays because the essay is a pragmatic literary genre: it is anti‐essentialist, conversational, and experimentalist and provocatively aims at “breaking the crust of convention,” in Dewey's phrase. Using the essay, Rorty “joshes” us to becoming more pragmatic and, therefore, better liberals. (shrink)

Experiments may contribute to understanding the basic processes of cultural evolution. We drew features from previous laboratory research with small groups in which traditions arose during several generations. Groups of four participants chose by consensus between solving anagrams printed on red cards and on blue cards. Payoffs for the choices differed. After 12 min, the participant who had been in the experiment the longest was removed and replaced with a naı¨ve person. These replacements, each of which marked the end of (...) a generation, continued for 10 – 15 generations, at which time the day’s session ended. Time-out duration, which determined whether the group earned more by choosing red or blue, and which was fixed for a day’s session, was varied across three conditions to equal 1, 2, or 3 min. The groups developed choice traditions that tended toward maximizing earnings. The stronger the dependence between choice and earnings, the stronger was the tradition. Once a choice tradition evolved, groups passed it on by instructing newcomers, using some combination of accurate information, mythology, and coercion. Among verbal traditions, frequency of mythology varied directly with strength of the choice tradition. These methods may be applied to a variety of research questions. D 2004 Elsevier Inc. All rights reserved. (shrink)

Rosa Calcaterra has written an extremely learned and thoughtful book about Richard Rorty’s controversial neopragmatism. It is a worthy addition to the growing number of works that offer a more generous and balanced assessment of Rorty’s thought, in contrast to the scores of highly critical treatments it received during his career. But, as Calcaterra insists, her book is “not an apology for Rorty” (Calcaterra 2019: ix); she critically approaches what she calls Rorty’s philosophical “provocatio...

Virtue liberalism holds that the success of liberal politics and society depends on the citizenry possessing a set of liberal virtues, including traits like open-mindedness, toleration, and individual autonomy. Virtue liberalism is thus an ethically demanding conception of liberalism that is at odds with conceptions, like Rawlsian political liberalism andmodus vivendiliberalism, that attempt to minimize liberalism’s ethical impact in order to accommodate a greater range of ethical pluralism. Although he claims to be a Rawlsian political liberal, Richard Rorty’s pragmatic liberalism (...) is best understood as a version of virtue liberalism that, in particular, recommends a controversial civic virtue of irony for good liberal citizenship. Indeed, Rorty ultimately joins Dewey in conceiving of liberal democracy as a “way of life,” rather than merely a set of political relations that have a minimal effect on our characters or on the shape of our private commitments and projects. (shrink)

In this paper my aim is to get clearer on what eliminative materialism actually does and does not entail. I look closely at one cluster of views that is often described as a form of eliminativism in contemporary philosophy and cognitive science and try to show that this characterization is a mistake. More specifically, I look at conceptions of eliminativism recently endorsed by writers such as Edouard Machery, Paul Griffiths, Valerie Hardcastle and others, and argue that although these views do (...) endorse the elimination of something, they offer only what I will call a sort of category dissolution, and should be treated as something altogether different from traditional eliminativism. Spelling out the main contrast between eliminative materialism proper and this alternative view, and defending the need to keep them distinct, is my primary objective. As I show, a central irony is that proponents of the problematic outlook often insist that divergent things should not be classified together under a single label. By characterizing their own views as a form of eliminativism, they commit a fundamental error that they themselves argue should not be made. While my focus here is on eliminative materialism, the error I intend to highlight appears across various discussions about alleged eliminativism of all sorts of things. (shrink)

Emily Carroll and Parker Crutchfield propose a new inconsistency argument against abortion restrictivism. In response, I raised several objections to their argument. Recently Carroll and Crutchfield have replied and seem to be under the impression that I’m a restrictivist. This is puzzling, since my criticism of their view included a very thinly veiled, but purposely more charitable, anti-restrictivist inconsistency argument. In this response, I explain how Carroll and Crutchfield mischaracterize my position and that of the restrictivist.

ABSTRACT Internalization is an important yet puzzling and undertheorized element in Nietzsche's moral psychology. The aim of this article is to resolve some textual puzzles by way of shedding light on Nietzsche's views on the general nature of internalization, and how it relates to other significant concepts deployed in his thought such as bad conscience, the pathos of distance, the will to power, and the ascetic ideal. I begin by providing a brief interpretation of internalization that is somewhat more perspicuous (...) than exists in the literature. I then make a case for the claim that the consequences of internalization are dependent upon the nature of the attitudes that get redirected inward. This insight allows us to explain why Nietzsche does not give a uniform account of all instances of internalization, and provides resources to give a richer and more satisfying interpretation of his moral psychological and ethical thought. (shrink)

Eschewing conventional candidates, like Plato's Republic or Machiavelli's Prince, Richard Rorty praises Aldous Huxley's Brave New World as "the best introduction to political philosophy," because it shows us "what sort of human future would be produced by a naturalism untempered by historicist Romanticism, and by a politics aimed merely at alleviating mammalian pain."1 Huxley's celebrated dystopia is thus a poignant warning to our modern utilitarian political projects. Yet Rorty also suggests that utopian literature can play a positive and inspirational role (...) for liberal politics, and even dubs his own political ideal, "liberal utopia." Rorty's liberal utopia is not an impossible society bereft of political .. (shrink)

Ancients and moderns alike have constructed arguments and assessed theories on the basis of common sense and intuitive judgments. Yet, despite the important role intuitions play in philosophy, there has been little reflection on fundamental questions concerning the sort of data intuitions provide, how they are supposed to lead us to the truth, and why we should treat them as important. In addition, recent psychological research seems to pose serious challenges to traditional intuition-driven philosophical inquiry. Rethinking Intuition brings together a (...) distinguished group of philosophers and psychologists to discuss these important issues. Students and scholars in both fields will find this book to be of great value. (shrink)

When one takes the evolution of operant behavior as prototype, one sees that the term replication is too tied to the peculiarities of genetic evolution. A more general term is recurrence. The important problem raised by recurrence is not “information” but relationship: deciding when two occurrences belong to the same lineage. That is solved by looking at common environmental effects.

The question, “Does the chimpanzee have a theory of mind?” is logically identical to the question, “Does the chimpanzee have a soul?” It is a peculiarity of our culture that we talk about anyone having a mind, and such talk is unhelpful for a science of behavior. The label “killjoy hypothesis” is an ad hominem attack.

Bona fide historians who prefer secondary sources, especially deceptive ones, to primary sources do not come readily to mind. In modern accounts Charlemagne prospers without the archangel Gabriel as a strategic guide. Anglo-Saxon and Norman tall stories about William the Conqueror have given way to writs, Domesday Book, and the Bayeux Tapestry. Columbus no longer astounds his contemporaries by standing eggs on their heads, and further down the road of time, George Washington's shoulders have flexed free of the burden (...) of Mason Weems's pieties. Yet many twentieth-century historians continue to reprocess as gospel sixth-century legends and didactic fiction that portray the first Prankish king of Gaul as a thoroughgoing barbarian. (shrink)

Research on culture would be enriched by studying the connection between gender and peer relations. Cultures vary in the roles, privileges, opportunities and rights that are ascribed to females and males. They are known to differ also in the degree to which females and males interact with each other. Although the preference for same-gender peers has been observed across multiple cultural contexts, the degree of this segregation between females and males varies. We argue that variability in the interactional divide between (...) females and males is an important cultural construct that is likely to account for diversity in developmental processes and outcomes. (shrink)