This paper reports on an exploration of Boolos’ Curious Inference, using higher-order automated theorem provers (ATPs). Surprisingly, only suitable shorthand notations had to be provided by hand for ATPs to find a short proof. The higher-order lemmas required for constructing a short proof are automatically discovered by the ATPs. Given the observations and suggestions in this paper, full proof automation of Boolos’ and related examples now seems to be within reach of higher-order ATPs.

This book presents a comprehensive treatment of basic mathematical logic. The author's aim is to make exact the vague, intuitive notions of natural number, preciseness, and correctness, and to invent a method whereby these notions can be communicated to others and stored in the memory. He adopts a symbolic language in which ideas about natural numbers can be stated precisely and meaningfully, and then investigates the properties and limitations of this language. The treatment of mathematical concepts in the main body (...) of the text is rigorous, but, a section of 'historical remarks' traces the evolution of the ideas presented in each chapter. Sources of the original accounts of these developments are listed in the bibliography. (shrink)

A supplemental document for "Metalinguistic Gradability".

Summary Influenced by the account of K. Popper and, moreover, of C. G. Hempel and P. Oppenheim, it is generally assumed, that a prediction can be logically deduced from hypotheses, i. e. lawlike propositions, and initial conditions. It is not clear, in which respect a prediction can correctly be supposed to be a proposition which is either true or false. From a logical point of view, serious difficulties arise in assuming that the deductive-nomological model consists of a valid argument. Further (...) objections to this account are developed with regard to lawlike propositions. Since a lawlike proposition is — by definition — not true or definitely true, but only supposed to be true, it cannot function as a true premise among other true premises for the purpose of deduction. Special difficulties arise with regard to predictions: A predictive argument does not give any reason for the truth of the predictionK, but only — if at all — for the prediction of the truth ofK. In the latter case, the conclusion K clearly does not consist of a proposition (which could be either true or false) but rather of a predicting proposition. (shrink)

Multiple states are at risk of becoming uninhabitable due to climate change, forcing their populations to flee. While the 1951 Refugee Convention provides the gold standard of international protection, it is only applied to a limited subset of people fleeing their countries, those who suffer persecution, which most people fleeing climate change cannot establish. While many journalists and non-lawyers freely use the term “climate refugees,” governments, and courts, as well as UNHCR and many refugee experts, have excluded most climate refugees (...) from the Convention as a matter of legal interpretation. In our 2015 paper, “Unable to Return in the 1951 Refugee Convention: Stateless Refugees and Climate Change”, we sought to reopen the debate on “climate refugees” by arguing that some climate refugees qualify under the 1951 Convention as it is currently written (even if they are not persecuted): those who are stateless and are unable to return to their country of origin because climate change has rendered it uninhabitable. Our interpretation, however, has been rejected by Goodwin-Gill and McAdam (2021) and by Foster and Lambert (2019), which explicitly responds to our paper. Here, we address and respond to their arguments, and develop a new supplementary one, drawing on the principle of systemic integration, as enshrined in Article 31(3)(c) of the Vienna Convention on the Law of Treaties. (shrink)

When is a belief or judgment justified? One might be forgiven for thinking the search for single answer to this question to be hopeless. The concept of justification is required to fulfil several tasks: to evaluate beliefs epistemically, to fill in the gap between truth and knowledge, to describe the virtuous organization of one’s beliefs, to describe the relationship between evidence and theory (and thus relate to confirmation and probabilification). While some of these may be held to overlap, the prospects (...) for fulfilling all may well seem poor. Furthermore the internalist requires that justification be an introspectible property of beliefs and a fundamental epistemic concept, while the externalist is often happy to ignore the concept altogether or at best regard it as an embarrassing add-on to their epistemology. In the light of this one might reasonably give up on justification altogether or adopt pluralist approach, denying that justification is any single property of beliefs of judgments. (shrink)

In this paper we discuss how Causal Decision Theory should be modified to handle a class of problematic cases involving deterministic laws. Causal Decision Theory, as it stands, is problematically biased against your endorsing deterministic propositions (for example it tells you to deny Newtonian physics, regardless of how confident you are of its truth). Our response is that this is not a problem for Causal Decision Theory per se, but arises because of the standard method for assessing the truth of (...) certain counterfactuals. The truth of deterministic laws is `modally fragile' on the standard semantics for counterfactuals: if determinism is true and you were to do otherwise, the laws would be different. We provide two ways of avoiding this problem: 1) supplement the standard semantics for counterfactuals with impossible worlds, or 2) introduce rigid designators into the description of problematic decision situations. We argue that both of these approaches are well-motivated and can be readily incorporated into Lewisian Causal Decision Theory. (shrink)

This book explores the relationship between people living relatively simple lives and the cultural complexity of their live worlds by rethinking culture in terms of complexity theory.

This inclusive cross-cultural study rethinks the nexus between engineering education and context. In so doing the book offers a reflection on contextual boundaries with an overall boundary crossing ambition and juxtaposes important cases of critical participation within engineering education with sophisticated scholarly reflection on both opportunities and discontents. Whether, and in what way engineering education is or ought to be contextualized or de-contextualized is an object of heated debate among engineering educators. The uniqueness of this study is that this debate (...) is given comprehensive coverage - presenting both instrumentally inclined as well as radical positions on transforming engineering education. In contextualizing engineering education, this book offers diverse commentary from a range of disciplinary, meta- and interdisciplinary perspectives on how cultural, professional, institutional, and educational systems contexts shape histories, structural dynamics, ideologies and challenges as well as new pathways in engineering education. Topics addressed include examining engineering education in countries ranging from India to America, to racial and gender equity in engineering education and incorporating social awareness into the area. Using context as "bridge" this book confronts engineering education head on. Contending engineering ideologies and corresponding views on context are juxtaposed with contending discourses of reform. The uniqueness of the book is that it brings together scholars from the humanities, the social sciences and engineering from Europe - both East and West - with the United States, China, Brazil, India and Australia. (shrink)

Two sources of possible disagreement in bioethics may be associated with pessimism about what bioethics can achieve. First, pluralism implies that bioethics engages with interlocutors who hold divergent moral beliefs. Pessimists might believe that these disagreements significantly limit the extent to which bioethics can provide normatively robust guidance in relevant areas. Second, the interdisciplinary nature of bioethics suggests that interlocutors may hold divergent views on the nature of bioethics itself—particularly its practicality. Pessimists may suppose that interdisciplinary disagreements could frustrate the (...) goals of bioethics. In this article, I explore how wonder may alleviate the concerns of the first group of pessimists regarding problems associated with pluralism, provided that we are willing to accept some interdisciplinary frustrations. Then, I invite readers of this issue of The Journal of Medicine & Philosophy to test these intuitions by considering the role of wonder in these articles. (shrink)

I develop an expressivist account of verbal disagreements as practical disagreements over how to use words rather than factual disagreements over what words actually mean. This account enjoys several advantages over others in the literature: it can be implemented in a neo-Stalnakerian possible worlds framework; it accounts for cases where speakers are undecided on how exactly to interpret an expression; it avoids appeals to fraught notions like subject matter, charitable interpretation, and joint-carving; and it naturally extends to an analysis of (...) metalinguistic negotiations. (shrink)

Steen Brock paints a cross-disciplinary picture of the philosophical and scientific background for the rise of the quantum theory. He accounts for the unity of Kantian metaphysics of Nature, the Helmholtzian principles, and the Hamiltonian methods of modern pre-quantum physics. Brock shows how Planck's vision of a generalization of classical physics implies that the original quantum mechanics of Heisenberg can be regarded as a successful attempt to maintain this modern unity of physics.However, for Niels Bohr, the unity of science (...) and metaphysics did not end in the world of physics. The development of quantum physics had general implications both for other sciences and for various philosophical issues. Brock discusses these matters with respect to recent topics within the philosophy of science and major interpretations of Bohr's ideas. The author invites the reader to follow a long andwinding route of thought which, in the end, culminates in Bohr's ideas of complementarity, culture and Spirit. (shrink)

A common objection to the very idea of conceptual engineering is the topic continuity problem: whenever one tries to “reengineer” a concept, one only shifts attention away from one concept to another. Put differently, there is no such thing as conceptual revision: there’s only conceptual replacement. Here, I show that topic continuity is compatible with conceptual replacement. Whether the topic is preserved in an act of conceptual replacement simply depends on what is being replaced (a conceptual tool or a conceptual (...) role) and what the topic under discussion is. Thus, the topic continuity problem only arises from a failure to specify these two things. (shrink)

The correspondence view of memory is not a metaphor. However, correspondence is the essential feature of the archaeology metaphor, which harks back to Freud and Neisser. A modern version of this metaphor and some of its implications are briefly described. The archaeology metaphor integrates the idea of stored traces in a nonmechanistic framework.

We describe a novel Internet-based method for building consensus and clarifying con icts in large stakeholder groups facing complex issues, and we use the method to survey and map the scienti c and organizational perspectives of the arti cial life community during the Seventh International Conference on Arti cial Life (summer 2000). The issues addressed in this survey included arti cial life’s main successes, main failures, main open scienti c questions, and main strategies for the future, as well as the (...) bene ts and pitfalls of creating a professional society for arti cial life. By illuminating the arti cial life community’s collective perspective on these issues, this survey illustrates the value of such methods of harnessing the collective intelligence of large stakeholder groups. (shrink)

What makes a cell? How are cells able to replicate themselves in a stable manner? How did cellular life emerge on our planet? The answer to these fundamental questions lies at the base of biology. Cellular life is the basic unit of living organization and defines the presence of a stable information reservoir connected through the external world by a well-defined boundary. Inside the cell, chains of computations and chemical reactions take place, sustained by self-assembled molecular machines. At the cell (...) membrane, the environment and the cell communicate with each other through proteins that are able to detect small concentration changes and send the appropriate signals. But modern cells are very sophisticated entities and extracting the logic of cell organization from them is a gigantic effort. In order to answer these questions, we need to look at cells in a more basic level: a reduction of complexity is needed. Protocells, roughly defined as the simplest instances of autonomous cell-like structures, have been a matter of exploration for decades. Although most of the original work in this area was largely theoretical, the end of the twentieth century was marked by very active experimental research on minimal cells. One approach has been the top-down strategy, where living organisms (the simplest life forms) are being selectively modified to reduce their genome complexity. Such a minimal genome would be the smallest one able to sustain reproduction and growth under a given set of external constraints (mainly available molecules). The second approach is the bottom-up one, very much in the tradition of research into the origins of life. Under this approach, extremely simple life forms are built from basic chemical components, including lipids and a basic.. (shrink)

This paper commences by making a case for a naturalized approach to knowledge‐first epistemology. On this basis it then goes on to describe and defend a naturalized, functionalist account of group knowledge. It then contrasts this with Jennifer Lackey's (2021) account of the epistemological status of groups.

In the paper, a detailed analysis of some new logical aspects of Cantor’s diagonal proof of the uncountability of continuum is presented. For the first time, strict formal, axiomatic, and algorithmic definitions of the notions of potential and actual infinities are presented. It is shown that the actualization of infinite sets and sequences used in Cantor’s proof is a necessary, but hidden, condition of the proof. The explication of the necessary condition and its factual usage within the framework of Cantor’s (...) proof makes, Cantor’s proof invalid. It’s shown that traditional Cantor’s proof has a second necessary, but hidden as well, condition which is teleological by its nature, i.e., is not mathematical. The explication of the second necessary condition makes Cantor’s statement on the uncountability of continuum unprovable from the point of view of classical logic.One of the most dramatic facts in history of science is connected just with the notion of actual infinity and consists in the following. On the one hand, Aristotle, Berkeley, Locke, Descartes, Spinoza, Gauss, Kant, Cauchy, Kronecker, Hermite, Poincaré, Bair, Borel, Brouwer, Quine, Wittgenstein, Weyl, Luzin, and a lot of other outstanding creators of classical logic and classical mathematics, during millenniums, stated categorically and insistently warned about that the actual infinity is a self-contradictory notion and its usage in mathematics is inadmissible (e.g., according to Poincare, “There is no actual infinity. - Cantorians forgot that and fell into contradictions. Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered”). On the other hand, a lot of outstanding scientists of the XX c.c., such as Hilbert, Church, Turing, Gödel, etc., and modern axiomatic set theory as a whole ignored this (intuitive though) opinion of genii and accepted Cantor’s “transfinite paradise”, based on the actual infinity. In the paper some logical, philosophical, and psychological aspects of this historical “favorable opposition” are analyzed, and the fact that the scientific intuition of genii has won the historical battle against the mytho-’logic’ of Cantor’s transfinite ‘paradise’ is explained and logically justified. (shrink)

In the paper, a detailed analysis of some new logical aspects of Cantor’s diagonal proof of the uncountability of continuum is presented. For the first time, strict formal, axiomatic, and algorithmic definitions of the notions of potential and actual infinities are presented. It is shown that the actualization of infinite sets and sequences used in Cantor’s proof is a necessary, but hidden, condition of the proof. The explication of the necessary condition and its factual usage within the framework of Cantor’s (...) proof makes, Cantor’s proof invalid. It’s shown that traditional Cantor’s proof has a second necessary, but hidden as well, condition which is teleological by its nature, i.e., is not mathematical. The explication of the second necessary condition makes Cantor’s statement on the uncountability of continuum unprovable from the point of view of classical logic.One of the most dramatic facts in history of science is connected just with the notion of actual infinity and consists in the following. On the one hand, Aristotle, Berkeley, Locke, Descartes, Spinoza, Gauss, Kant, Cauchy, Kronecker, Hermite, Poincaré, Bair, Borel, Brouwer, Quine, Wittgenstein, Weyl, Luzin, and a lot of other outstanding creators of classical logic and classical mathematics, during millenniums, stated categorically and insistently warned about that the actual infinity is a self-contradictory notion and its usage in mathematics is inadmissible (e.g., according to Poincare, “There is no actual infinity. - Cantorians forgot that and fell into contradictions. Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered”). On the other hand, a lot of outstanding scientists of the XX c.c., such as Hilbert, Church, Turing, Gödel, etc., and modern axiomatic set theory as a whole ignored this (intuitive though) opinion of genii and accepted Cantor’s “transfinite paradise”, based on the actual infinity. In the paper some logical, philosophical, and psychological aspects of this historical “favorable opposition” are analyzed, and the fact that the scientific intuition of genii has won the historical battle against the mytho-’logic’ of Cantor’s transfinite ‘paradise’ is explained and logically justified. (shrink)

Current research findings on metaphor in language and thought may be interpreted as producing a paradox of metaphor; that is, most metaphor is not processed metaphorically by a cross-domain mapping involving some form of comparison. This paradox can be resolved by attending to one crucial aspect of metaphor in communication: the question whether metaphor is used as deliberately metaphorical or not. It is likely that most deliberate metaphor is processed metaphorically (by comparison), as opposed to most nondeliberate metaphor, which may (...) be assumed to be typically not processed metaphorically (that is, by categorization). This resolves the paradox of metaphor because it suggests that all “metaphor in communication” (all deliberate metaphor) is processed metaphorically. Detailed comments are offered on the notion of metaphor deliberateness and on the nature of a three-dimensional model of metaphor in discourse involving metaphor in language, thought, and communication. (shrink)

A new speculative ontology of aesthetics. In Aesthesis and Perceptronium, Alexander Wilson presents a theory of materialist and posthumanist aesthetics founded on an original speculative ontology that addresses the interconnections of experience, cognition, organism, and matter. Entering the active fields of contemporary thought known as the new materialisms and realisms, Wilson argues for a rigorous redefining of the criteria that allow us to discriminate between those materials and objects where aesthesis (perception, cognition) takes place and those where it doesn't. (...) Aesthesis and Perceptronium negotiates between indiscriminately pluralist views that attribute mentation to all things and eliminative views that deny the existence of mentation even in humans. By recasting aesthetic questions within the framework of "epistemaesthetics," which considers cognition and aesthetics as belonging to a single category that can neither be fully disentangled nor fully reduced to either of its terms, Wilson forges a theory of nonhuman experience that avoids this untenable dilemma. Through a novel consideration of the evolutionary origins of cognition and its extension in technological developments, the investigation culminates in a rigorous reevaluation of the status of matter, information, computation, causality, and time in terms of their logical and causal engagement with the activities of human and nonhuman agents. (shrink)

That any filled location of spacetime contains a persisting thing has been defended based on the ‘argument from vagueness.’ It is often assumed that since the epistemicist account of vagueness blocks the argument from vagueness it facilitates a conservative ontology without gerrymandered objects. It doesn't. The epistemic vagueness of ordinary object predicates such as ‘bicycle’ requires that objects that can be described asalmost‐but‐not‐quite‐bicycleexist even though they fall outside the predicate's sharp extension. Since the predicates that begin with ‘almost’ are vague (...) as well, epistemicism's ontological backdrop is far from the conservative picture it is thought to enable. (shrink)

This is the second part of a two-part series on the logic of hyperlogic, a formal system for regimenting metalogical claims in the object language (even within embedded environments). Part A provided a minimal logic for hyperlogic that is sound and complete over the class of all models. In this part, we extend these completeness results to stronger logics that are sound and complete over restricted classes of models. We also investigate the logic of hyperlogic when the language is enriched (...) with hyperintensional operators such as counterfactual conditionals and belief operators. (shrink)

It has recently been argued that the following Rule should be part of any characterization of science: Claims concerning specific disputed facts should be endorsed only if they are sufficiently supported by the application of validated methods of research or discovery, and moreover that acceptance of this Rule should lead one to reject religious belief. This paper argues, first, that the Rule, as stated, should not be accepted as it suffers from a number of problems. And second, that even if (...) the Rule were to be acceptable, it should not lead one to reject religious belief. (shrink)

Corporate social responsibility was historically a business-oriented idea that companies should voluntarily improve their social and environmental practices. More recently, CSR has increasingly attracted governments’ attention, and is now promoted in public policy, especially in the European Union. Conflicts can arise, however, when advanced welfare states introduce CSR into public policy. The reason for such conflict is that CSR leaves key public welfare issues to the discretion of private business. This voluntary issue assignment contrasts starkly with advanced welfare states’ traditions (...) favoring negotiated agreements and strong regulation to control corporate conduct. This article analyzes the conflicts and compatibilities arising when advanced welfare states introduce CSR, focusing on how the two traditions diverge and on how conflicts are reconciled. Empirically the study focuses on four Nordic countries—Denmark, Finland, Norway, and Sweden—widely recognized as the most advanced welfare states, and increasingly as leaders in CSR public policy. From interviews of 55 officials of government ministries, nongovernmental organizations, labor unions, and employer associations, the authors conclude that tension indeed exists between CSR public policies and advanced welfare state traditions in all four countries. Whereas CSR’s aims are compatible with Nordic institutional traditions, the means promoted in CSR is in conflict with such Nordic traditions as corporatist agreements and rights-based welfare state regulation of social and environmental issues. There is harmony of goals, but conflict in means between the four Nordic countries studied. (shrink)

This paper investigates the roles that Danish government has played in the development of corporate social responsibility (CSR). Denmark has emerged as a first mover among the Scandinavian countries when it comes to CSR. We argue that government has played a pivotal role in making this happen, and that this reflects strong traditions of regulation, corporatism and active state involvement. However, there is no unitary “Danish model of CSR” being promoted by government. Although Danish society is often associated with a (...) model of consensus, our claim is that Danish government policy on CSR is characterized by a lack of common direction and that we need to approach it on such terms. In order to provide a critical account of ‘the Danish model’ we apply a governmentality perspective that allows us to stress political difference. We argue that Danish government policy consists of three distinct regimes of practice and show how they subject CSR to different modes of rationalization and action. We conclude that the problem with public policy being split into three is not different as such, but the failure of each regime to recognize the value of the others. As a result, government tends to add to the confusion and opaqueness of CSR. (shrink)

Methodological analysis shows that the concepts of fitness and adaptation are more complex than the literature suggests. Various arguments against adaptationism are inadequate since they are couched in terms of unduly simplistic notions.

Ontology and epistemology will never be reconciled, this article argues. There is widespread opinion among scientists and laymen alike that we are standing at the threshold of a fusion and reconciliation of ontology and epistemology. But my thesis is that this will never happen – and my argument can be read as a credo for non-identity. The tensions between being and thinking are here to stay, and this philosophical ‘position’ has a wide range of implications for politics, education, Bildung and (...) thinking. Strongly rooted in Theodor Wiesengrund Adorno’s philosophy, it is claimed that he was right in emphasizing that the non-identical must be honored, defended and emancipated. The vivid dream is that conceptual work opens and ‘dignifies’ the non-identical, while the non-identical ‘longs for’ conceptual assistance so it can come to exist among us. (shrink)