At the centenary of Frank H. Knight’s Risk, Uncertainty, and Profit (1921), we explore the continuing relevance of Knightian uncertainty to the theory and practice of entrepreneurship. There are three challenges facing such assessment. First, RUP is complex and difficult to interpret. The key but neglected element of RUP is that Knight’s account is not solely about risk and uncertainty as states of nature, but about how an agent’s beliefs about uncertain outcomes and confidence in those beliefs guide their choices. (...) Second, RUP is Knight’s only effort in this area. His subsequent career led elsewhere, so he did not engage with subsequent interpretations of this work. Third, much of the current literature emphasizes that decisions must be different under the two states of nature with a consequent misunderstanding of entrepreneurial agency. This paper addresses each challenge in sequence. First, we explicate Knight’s (1921) approach and explain why that approach is murky. Second, as a complement to Knight’s interpretation, we examine Frank P. Ramsey’s approach to subjective probabilities to help clarify Knight’s murky approach. What links Knight and Ramsey is a shared pragmatism about entrepreneurial agency under uncertainty that depends upon the beliefs about, and confidence in, their judgments of possible outcomes. This Knight-Ramsey approach does not require actor’s behaviors to be determined by the class of uncertain environment (whether risk, uncertainty, or ambiguity) they face. We focus on the response by the entrepreneur to the existence of uncertainty in all its forms. We argue that this reductive account provides a foundation to examine common problems in management, including managerial hubris, the interaction between entrepreneurs and venture capitalists, and the need for experimentation (such as prototyping and market research) in advance of new product and venture launches. Third, we critique current literature that favors epistemic purism about the ontology of risk and uncertainty and ignores Knight-Ramsey pragmatism in meeting uncertainty, such as using formal and informal institutions for uncertainty mitigation. Our account locates Frank Knight’s subtleties in entrepreneurial behavior firmly in the literature on entrepreneurial agency a century later. (shrink)

This paper presents an exposition of subsystems and of Quine's , originally defined and shown to be consistent by Crabbé, along with related systems and of type theory. A proof that (and so ) interpret the ramified theory of types is presented (this is a simplified exposition of a result of Crabbé). The new result that the consistency strength of is the same as that of is demonstrated. It will also be shown that cannot be finitely axiomatized (as can and (...) ). (shrink)

At the centenary of Frank H. Knight’s Risk, Uncertainty, and Profit, we explore the continuing relevance of Knightian uncertainty to the theory and practice of entrepreneurship. There are three challenges facing such assessment. First, RUP is complex and difficult to interpret. The key but neglected element of RUP is that Knight’s account is not solely about risk and uncertainty as states of nature, but about how an agent’s beliefs about uncertain outcomes and confidence in those beliefs guide their choices. Second, (...) RUP is Knight’s only effort in this area. His subsequent career led elsewhere, so he did not engage with subsequent interpretations of this work. Third, much of the current literature emphasizes that decisions must be different under the two states of nature with a consequent misunderstanding of entrepreneurial agency. This paper addresses each challenge in sequence. First, we explicate Knight’s approach and explain why that approach is murky. Second, as a complement to Knight’s interpretation, we examine Frank P. Ramsey’s approach to subjective probabilities to help clarify Knight’s murky approach. What links Knight and Ramsey is a shared pragmatism about entrepreneurial agency under uncertainty that depends upon the beliefs about, and confidence in, their judgments of possible outcomes. This Knight-Ramsey approach does not require actor’s behaviors to be determined by the class of uncertain environment they face. We focus on the response by the entrepreneur to the existence of uncertainty in all its forms. We argue that this reductive account provides a foundation to examine common problems in management, including managerial hubris, the interaction between entrepreneurs and venture capitalists, and the need for experimentation in advance of new product and venture launches. Third, we critique current literature that favors epistemic purism about the ontology of risk and uncertainty and ignores Knight-Ramsey pragmatism in meeting uncertainty, such as using formal and informal institutions for uncertainty mitigation. Our account locates Frank Knight’s subtleties in entrepreneurial behavior firmly in the literature on entrepreneurial agency a century later. (shrink)

This paper offers a qualified defence of physician non-compliance with antiabortion legislation in the wake of the Supreme Court’s decision in Dobbs v. Jackson Women’s Health Organization. The paper examines two ethically troubling trends of post-Dobbs legislation: narrow and vague maternal health exemption clauses and mandatory reporting of miscarriages in jurisdictions where patients may criminal prosecution for medically induced abortions. It then examines and defends a professional obligation on the part of physicians to comply with the law. This obligation, however, (...) is defeasible. The paper then argues that physicians’ obligations to comply with the law is defeated when the law is illegitimate and following the law would constitute bad medical practice. Finally, it argues that the ethically troubling trends in post-Dobbs antiabortion legislation may meet these criteria. (shrink)

We analyze the representation of binary relations in general, and in particular of functions and of total antisymmetric relations, in monadic third order logic, that is, the simple typed theory of sets with three types. We show that there is no general representation of functions or of total antisymmetric relations in this theory. We present partial representations of functions and of total antisymmetric relations which work for large classes of these relations, and show that there is an adequate representation of (...) cardinality in this theory. The relation of our work to similar work by Henrard and Allen Hazen is discussed. This work can be understood as part of a program of assessing the capabilities of weak logical frameworks: our results are applicable for example, to the framework in David Lewis’s Parts of Classes. (shrink)

This paper discusses a sequence of extensions ofNFU, Jensen's improvement of Quine's set theory “New Foundations” (NF) of [16].The original theoryNFof Quine continues to present difficulties. After 60 years of intermittent investigation, it is still not known to be consistent relative to any set theory in which we have confidence. Specker showed in [20] thatNFdisproves Choice (and so proves Infinity). Even if one assumes the consistency ofNF, one is hampered by the lack of powerful methods for proofs of consistency and (...) independence such as are available for use withZFC; very clever work has been done with permutation methods, starting with [18] and [5], and exemplified more recently by [14], but permutation methods can only be applied to show the consistency or independence of unstratified sentences (see the definition ofNFUbelow for a definition of stratification). For example, there is no method available to determine whether the assertion “the continuum can be well-ordered” is consistent with or independent ofNF. There is one substantial independence result for an assertion with nontrivial stratified consequences, using metamathematical methods: this is Orey's proof of the independence of the Axiom of Counting fromNF(see below for a statement of this axiom).We mention these difficulties only to reassure the reader of their irrelevance to the present work. Jensen's modification of “New Foundations” (in [13]), which was to restrict extensionality to sets, allowing many non-sets (urelements) with no elements, has almost magical effects. (shrink)

An ω-model (a model in which all natural numbers are standard) of the predicative fragment of Quine's set theory "New Foundations" (NF) is constructed. Marcel Crabbe has shown that a theory NFI extending predicative NF is consistent, and the model constructed is actually a model of NFI as well. The construction follows the construction of ω-models of NFU (NF with urelements) by R. B. Jensen, and, like the construction of Jensen for NFU, it can be used to construct α-models for (...) any ordinal α. The construction proceeds via a model of a type theory of a peculiar kind; we first discuss such "tangled type theories" in general, exhibiting a "tangled type theory" (and also an extension of Zermelo set theory with Δ 0 comprehension) which is equiconsistent with NF (for which the consistency problem seems no easier than the corresponding problem for NF (still open)), and pointing out that "tangled type theory with urelements" has a quite natural interpretation, which seems to provide an explanation for the more natural behaviour of NFU relative to the other set theories of this kind, and can be seen anachronistically as underlying Jensen's consistency proof for NFU. (shrink)

This paper discusses a sequence of extensions ofNFU, Jensen's improvement of Quine's set theory “New Foundations” (NF) of [16].The original theoryNFof Quine continues to present difficulties. After 60 years of intermittent investigation, it is still not known to be consistent relative to any set theory in which we have confidence. Specker showed in [20] thatNFdisproves Choice (and so proves Infinity). Even if one assumes the consistency ofNF, one is hampered by the lack of powerful methods for proofs of consistency and (...) independence such as are available for use withZFC; very clever work has been done with permutation methods, starting with [18] and [5], and exemplified more recently by [14], but permutation methods can only be applied to show the consistency or independence of unstratified sentences (see the definition ofNFUbelow for a definition of stratification). For example, there is no method available to determine whether the assertion “the continuum can be well-ordered” is consistent with or independent ofNF. There is one substantial independence result for an assertion with nontrivial stratified consequences, using metamathematical methods: this is Orey's proof of the independence of the Axiom of Counting fromNF(see below for a statement of this axiom).We mention these difficulties only to reassure the reader of their irrelevance to the present work. Jensen's modification of “New Foundations” (in [13]), which was to restrict extensionality to sets, allowing many non-sets (urelements) with no elements, has almost magical effects. (shrink)

Systems TRC and TRCU of illative combinatory logic are introduced and shown to be equivalent in consistency strength and expressive power to Quine's set theory ‘New Foundations’ and the fragment NFU + Infinity of NF described by Jensen, respectively. Jensen demonstrated the consistency of NFU + Infinity relative to ZFC; the question of the consistency of NF remains open. TRC and TRCU are presented here as classical first-order theories, although they can be presented as equational theories; they are not constructive.

The usual construction of models of NFU (New Foundations with urelements, introduced by Jensen) is due to Maurice Boffa. A Boffa model is obtained from a model of (a fragment of) Zermelo–Fraenkel with Choice (ZFC) with an automorphism which moves a rank: the domain of the Boffa model is a rank that is moved. “Most” elements of the domain of the Boffa model are urelements in terms of the interpreted NFU. The main result of this paper is that the restriction (...) of the membership relation of the original model of set theory with automorphism to the domain of the Boffa model is first-order definable in the language of NFU. In particular, all information about the extensions in the original model of the urelements of the model of NFU is definable in terms of NFU. A corollary (answering a question of Thomas Forster) is that the urelements in a Boffa model are not homogeneous. (shrink)

Related Works: Original Paper: M. Randall Holmes. Strong Axioms of Infinity in NFU. J. Symbolic Logic, Volume 66, Issue 1 , 87--116. Project Euclid: euclid.jsl/1183746361.

Background:Psychiatric nurses are regularly confronted with the uses and effects of control interventions such as mechanical restraints. Although there are evident tensions in the literature regarding the use of mechanical restraints, very little research has focused on the lived and embodied experience of their use, whether from the patient’s perspective or the perspective of nursing staff responsible for their application.Research aims: to gain access to the bodily phenomenon of being placed in mechanical restraints; to give voice to the intimate experiential (...) understanding of this experience; and through phenomenological interpretation, to understand the subjective processes and meaning-making of this experience.Research design:For this research, we adopted a distinctly ethics-oriented application of the methodology known as interpretative phenomenological analysis, that is, the interpretive dimension of the research focused on ethical practice in mental healthcare – one that is informed by experiential accounts of the lived body.Participants and research context:A total of 40 in-depth semi-structured, nondirected interviews with both nurses and patients we conducted to meet the aims of this article. Participants were recruited from an inpatient psychiatric unit of a Canadian general hospital.Ethical considerations:The research received research ethics board clearance from both the hospital where the study took place and the University of Ottawa.Findings:The comparative analysis is presented under the following headings: context of care, meaning of quality of care, emotional reactions and nurse–patient relationship, meeting the needs and need for alternatives.Discussion/conclusions:The research findings are discussed in light of current literature and implications for practice. (shrink)

Humanism in forensic psychiatry: the use of the tidal nursing model The humanist school of thought, which finds resonance in many conceptual models and theories designed to guide nursing practice, needs to be understood in the context of the total institution, where the individual is subjected to a mortification of the self, and denied autonomy. This article will engage in a critical reflection on how humanism has influenced nursing theorists and the subsequent production of conceptual models and theories, especially as (...) they relate to the field of forensic psychiatric nursing. Although humanism provides optimism for nurse–patient relations, this article explores the incapability of such a philosophy to acknowledge the power relationships between individuals and its inability to explain the day‐to‐day realities experienced in forensic nursing, where the possibility of interpersonal violence reshapes nursing care. The tidal model will be discussed in detail as an example of a recently developed humanistic nursing model. Viewed from this perspective, it is clear that humanistic philosophy and its subsequent models of care are in discordance with the highly specialized field of forensic nursing. (shrink)

We show in (the usual set theory without Choice) that for any set X, the collection of sets Y such that each element of the transitive closure of is strictly smaller in size than X (the collection of sets hereditarily smaller than X) is a set. This result has been shown by Jech in the case (where the collection under consideration is the set of hereditarily countable sets).

Three systems of double extension set theory have been proposed by Andrzej Kisielewicz in two papers. In this paper, it is shown that the two stronger systems are inconsistent, and that the third, weakest system does not admit extensionality for general sets or the use of general sets as parameters in its comprehension scheme. The parameter-free version of the comprehension principle of double extension set theory is also shown to be inconsistent with extensionality. The definitions of the systems and a (...) self-contained exposition of their properties is given, sufficient to develop the inconsistency proofs. (shrink)

This paper extends the results of an earlier paper by the author . New subsystems of the combinatory logic TRC shown in that paper to be equivalent to NF are introduced; these systems are analogous to subsystems of NF with predicativity restrictions on set comprehension introduced and shown to be consistent by Crabbé. For one of these systems, an exact equivalence in consistency strength and expressive power with the analogous subsystem of NF is established.

This paper described a formal theory of type judgments for propositional logic notations of PM; I felt the need of my own automated type checker to check their examples. The type checker I wrote did indeed serve to help me referee the paper, but also took a rather different approach to notation and typing for propositional functions of PM, which proved worth writing up independently in our own paper: Holmes, M. Randall, “Polymorphic type– checking for the ramified theory (...) of types of Principia Mathematica”, in Fairouz Kamareddine, ed., Thirty–five Years of Automating Mathematics, Kluwer, 2003, pp. 173-215. (shrink)

This is a brief report on results reported at length in our paper [2], made for the purpose of a presentation at the workshop to be held in November 2011 in Cambridge on the Principia Mathematica of Russell and Whitehead ([?], hereinafter referred to briefly as PM ). That paper grew out of a reading of the paper [3] of Kamareddine, Nederpelt, and Laan. We refereed this paper and found it useful for checking their examples to write our own independent (...) computer type-checker for the type system of PM ([1]), which led us to think carefully about formalization of the language and the type system of PM A modern mathematical logician reading PM finds that it is not completely formalized in a modern sense. The type theory in particular is inarguably not formalized, as no notation for types is given at all! In PM itself, the only type annotations which appear are occasional numerical indices indicating order; the type notation we use here extends one introduced later by Ramsey. The authors of PM regard the absence of explicit indications of type as a virtue of their system: they call it “systematic ambiguity”; modern computer scientists refer to this as “polymorphism”. The language of PM is also not completely formalized, and it is typographically inconvenient for computer software to which ASCII input is to be given. The notation of PM for abstractions (propositional functions) does not use head binders; the order of the arguments of a complex expression is determined by the alphabetical order of the bound variables. For example ˆa < ˆb is the “less than” relation while ˆb < ˆa is the “greater than” relation (this is indicated by the alphabetical order of the variables). In PM , the fact that a variable is bound in a propositional function is indicated by circumflexing it. Variables bound by quantifiers are not circumflexed. A feature of the notation of [3], carried over into ours, is that no circumflexes are used: notations for propositions and the corresponding propositional functions are identical.. (shrink)

A common objection to Quine’s set theory “New Foundations” is that it is inadequately motivated because the restriction on comprehension which appears to avert paradox is a syntactical trick. We present a semantic criterion for determining whether a class is a set (a kind of symmetry) which motivates NF.

A common objection to Quine's set theory "New Foundations" is that it is inadequately motivated because the restriction on comprehension which appears to avert paradox is a syntactical trick. We present a semantic criterion for determining whether a class is a set which motivates NF.

Andrzej Kisielewicz has proposed three systems of double extension set theory of which we have shown two to be inconsistent in an earlier paper. Kisielewicz presented an argument that the remaining system interprets ZF, which is defective: it actually shows that the surviving possibly consistent system of double extension set theory interprets ZF with Separation and Comprehension restricted to 0 formulas. We show that this system does interpret ZF, using an analysis of the structure of the ordinals.

How do educators better reach their students, better capture their attention and imagination without sacrificing scholarship? Teachable Moments: Essays on Experiential Education examines the pedagogy of Prescott College, a school that has embraced experiential education and been finding success with it for over thirty years. These essays—from scholars in fields as wide ranging as religious studies, environmental science, psychology, dance, literature, adventure education, and peace studies—examine the challenges and, ultimately, the rewards of student-centered education.

George Holmes Howison’s 1895 essay entitled “The Limits of Evolution,” argued that there are four things evolutionary theory does not explain. In examining whether 11 decades have made a difference in these four, I argue that the arrogance of scientists over the past century in refusing to distinguish between full explanations and explanatory hypotheses is in some ways responsible for the fundamentalist backlash against evolutionary science. A scientific community that is honest and forthcoming about its limitations is to be (...) sought. The best response to Intelligent Design, Creation Science, and other current trends in pseudoscience is to be very clear about the limits of evolutionary theory and the scope of scientific explanation. (shrink)

Technical criticism of Jacob Ross's "Sleeping Beauty, Countable Additivity and Rational Dilemmas" and Double Halfing.

Diauxie is at the origin of research that led Jacques Monod, François Jacob, and André Lwoff to win the Nobel Prize in Physiology or Medicine in 1965 for their description of the first genetic regulatory model. Diauxie is a term coined by Jacques Monod in 1941 in his doctoral dissertation that refers to microbial growth in two phases. In this article, we first examine Monod’s thesis to demonstrate how and why Monod interpreted diauxie as a phenomenon of enzyme inhibition (...) or suppression of adaptive enzymes. We also briefly investigate prior enzyme suppression studies, before Monod’s work, which indicate that he is the first person to observe diauxic growth. Second, we analyse Monod’s post-thesis publications throughout his scientific career, revealing that diauxic inhibition was a significant part of Monod’s scientific activities and greatly fascinated Monod until the end of his life. Paradoxically, Monod’s work and interest on diauxic inhibition are still neglected in historical recounts, focused mostly on Monod’s enzymatic adaptation studies. Indeed, we uncovered a statement by Monod’s colleague, Lwoff, who transformed a quotation from Monod by replacing the word phenomenon with enzymatic adaptation, which we believe has influenced historians. Finally, we offer hypotheses to explain why Lwoff altered Monod’s statement. (shrink)

This short personal essay considers the principles behind housing reform in New York at the turn of the last century in light of the controversies around the ghetto law in contemporary Denmark. I take the example of documentary journalist and reformer Jacob Riis, who photographed housing conditions in immigrant neighbor-hoods on the Lower East Side in New York at the turn of the twentieth century, as a case study for considering the ways that race informed—and continues to inform—ideals around (...) urban planning. Conversely, I also consider contemporary controversies around the ghetto law, and activism by community members as a way of re-thinking a research approach to historical urban reforms. (shrink)

George Holmes Howison’s 1895 essay entitled “The Limits of Evolution,” argued that there are four things evolutionary theory does not explain. In examining whether 11 decades have made a difference in these four, I argue that the arrogance of scientists over the past century in refusing to distinguish between full explanations and explanatory hypotheses is in some ways responsible for the fundamentalist backlash against evolutionary science. A scientific community that is honest and forthcoming about its limitations is to be (...) sought. The best response to Intelligent Design, Creation Science, and other current trends in pseudoscience is to be very clear about the limits of evolutionary theory and the scope of scientific explanation. (shrink)

Related Works: Original Paper: M. Randall Holmes. Strong Axioms of Infinity in NFU. J. Symbolic Logic, Volume 66, Issue 1, 87--116. Project Euclid: euclid.jsl/1183746361.

Deals with Vaughan's connection with the "Occult" philosophy which his brother Thomas embraced & practiced & discusses Henry's indebtedness to the philosophies of Jacob Boehme, Cornelius Agrippa, Paracelsus, & others.

Through network diagrams and sustained narrative, sociologist Randall Collins traces the development of philosophical thought from ancient Greece to modern ...

A student's future as a knowledge worker (one who "thinks for a living" with the task of problem solving) is the starting point of this book. With this in mind, the book combines a review of philosophical positions and problems with practical examples and perspectives gained from everyday challenges faced by knowledge workers in their businesses and organizations. Through the use of summative chapters, highlighted key concepts, questions for reflection, and illustrative examples on how to work with the theories presented, (...) the book provides a clear and accessible introduction to this challenging subject. Philosophy of Science primarily addresses students studying language, communication, marketing, economics, and management. However, the survey of the theoretical schools of thought - as well as the discussions on research ethics and the role of research in society - will be equally relevant for other students in the humanities and the natural and social sciences. (shrink)

In the popular misconception fostered by blockbuster action movies and best-selling thrillers--not to mention conventional explanations by social scientists--violence is easy under certain conditions, like poverty, racial or ideological hatreds, or family pathologies. Randall Collins challenges this view in Violence, arguing that violent confrontation goes against human physiological hardwiring. It is the exception, not the rule--regardless of the underlying conditions or motivations. -/- Collins gives a comprehensive explanation of violence and its dynamics, drawing upon video footage, cutting-edge forensics, and (...) ethnography to examine violent situations up close as they actually happen--and his conclusions will surprise you. Violence comes neither easily nor automatically. Antagonists are by nature tense and fearful, and their confrontational anxieties put up a powerful emotional barrier against violence. Collins guides readers into the very real and disturbing worlds of human discord--from domestic abuse and schoolyard bullying to muggings, violent sports, and armed conflicts. He reveals how the fog of war pervades all violent encounters, limiting people mostly to bluster and bluff, and making violence, when it does occur, largely incompetent, often injuring someone other than its intended target. Collins shows how violence can be triggered only when pathways around this emotional barrier are presented. He explains why violence typically comes in the form of atrocities against the weak, ritualized exhibitions before audiences, or clandestine acts of terrorism and murder--and why a small number of individuals are competent at violence. (shrink)

According to the Generality Constraint, mental states with conceptual content must be capable of recombining in certain systematic ways. Drawing on empirical evidence from cognitive science, I argue that so-called analogue magnitude states violate this recombinability condition and thus have nonconceptual content. I further argue that this result has two significant consequences: it demonstrates that nonconceptual content seeps beyond perception and infiltrates cognition; and it shows that whether mental states have nonconceptual content is largely an empirical matter determined by the (...) structure of the neural representations underlying them. (shrink)