AbstractIntegrity is considered an important corporate value. Yet recent global events have highlighted the challenges firms face at living up to their stated values, especially when extended supply chain partners are involved. The concept of Supply Chain Integrity (SCI) can help firms shift focus beyond internal corporate integrity, toward supply chain integrity. Researchers and managers will benefit from an understanding of the SCI concept toward implementing SCI to better align supply chain partners with stated corporate values. This research fully develops (...) and empirically grounds the firm-level, inter-firm-oriented SCI concept. The thematic analysis of six firms’ archival and website content elaborated empirical descriptions of SCI themes and enabled the development of a process model for SCI, presenting a novel view of the underlying process by which firms can assess, develop, and maintain SCI across their supply chains. We propose the SCI model as an evolutionary process to improve a firm’s supply chain sustainability, rather than a dichotomous end state where firms either “have” integrity or they don’t. The SCI model could be used as a tool to help leaders create necessary change to better align values and supporting statements with culture, while influencing and affecting stakeholders across the supply chain. This is particularly important in today’s world, where business leaders must consider all stakeholders and address important stakeholder-driven issues such as supply chain sustainability, resilience, and security, which are now at the forefront in the ever-changing environment. (shrink)

Previous research has demonstrated electroencephalogram (EEG) changes in response to low-odor concentrations, resulting in near-chance detection. Such findings have been taken as evidence for olfaction without awareness. We replicated and extended previous work by examining EEG responses to water-water control, 0.0001, 0.001, 0.01, and 1 ppm isoamyl acetate (IAA) in water paired with water only. Detection was above chance (>50%) for .001 and above, and alpha decreased only to those concentrations, suggesting that EEG changes corresponded to IAA awareness. However, when (...) correct trial EEGs were compared to incorrect trial EEGs during .001 ppm, right posterior/central alpha decreased during incorrect trials and alpha decreased more globally (including frontal sites) during correct trials. These data may not reflect awareness or unawareness per se. Instead, results are discussed regarding activation of perceptual systems in the posterior region during incorrect trials and the activation of frontal action systems during a subset of correct trials. (shrink)

Full proofs of the Gödel incompleteness theorems are highly intricate affairs. Much of the intricacy lies in the details of setting up and checking the properties of a coding system representing the syntax of an object language (typically, that of arithmetic) within that same language. These details are seldom illuminating and tend to obscure the core of the argument. For this reason a number of efforts have been made to present the essentials of the proofs of Gödel’s theorems without getting (...) mired in syntactic or computational details. One of the most important of these efforts was made by Löb [8] in connection with his analysis of sentences asserting their own provability. Löb formulated three conditions (now known as the Hilbert-Bernays-Löb derivability conditions), on the provability predicate in a formal system which are jointly sufficient to yield the Gödel’s second incompleteness theorem for it. A key role in Löb’s analysis is played by (a special case of) what later became known as the diagonalization or fixed point property of formal systems, a property which had already, in essence, been exploited by Gödel in his original proofs of the incompleteness theorems. The fixed point property plays a central role in Lawvere’s [7] category-theoretic account of incompleteness phenomena (see also [10]). Incompleteness theorems have also been subjected to intensive investigation within the framework of modal logic (see, e.g.[4], [5]). In this formulation the modal operator takes up the role previously played by the provability predicate, and the derivability conditions on the latter are translated into algebraic conditions (the so-called GL, i.e., Gödel–Löb, conditions) on the former. My purpose here is to present a framework for incompleteness phenomena, fully compatible with intuitionistic or constructive principles, in which the idea of a coding system is retained, only in a 2 simple, but very general form, a form wholly free of syntactical notions. As codes we shall take the elements of an arbitrary given nonempty set, possibly, but not necessarily, the set of natural numbers.. (shrink)

A structure is a triple A = (A, {Ri: i ∈ I}, {ej: j ∈ J}), where A, the domain or universe of A, is a nonempty set, {Ri: i ∈ I} is an indexed family of relations on A and {ej: j ∈ J}) is an indexed set of elements —the designated elements of A. For each i ∈ I there is then a natural number λ(i) —the degree of Ri —such that Ri is a λ(i)-place relation on A, (...) i.e., Ri ⊆ Aλ(i). This λ may be regarded as a function from I to the set ω of natural numbers; the pair (λ, J) is called the type of A. Structures of the same type are said to be similar. Note that since an n-place operation f: An → A can be regarded as an (n+1)-place relation on A, algebraic structures containing operations such as groups, rings, vector spaces, etc. may be construed as structures in the above sense. (shrink)

If we imagine a chess-board with alternate blue and red squares, then this is something in which the individual red and blue areas allow themselves to be distinguished from each other in juxtaposition, and something similar holds also if we imagine each of the squares divided into four smaller squares also alternating between these two colours. If, however, we were to continue with such divisions until we had exceeded the boundary of noticeability for the individual small squares which result, then (...) it would no longer be possible to apprehend the individual red and blue areas in their respective positions. But would we then see nothing at all? Not in the least; rather we would see the whole chessboard as violet, i.e. apprehend it as something that participates simultaneously in red and blue. (shrink)

In this paper I reflect on the nature of mathematical beauty, and examine the connections between mathematics and the arts. I employ Plutarch’s distinction between the intelligible and the sensible, to compare the beauty of mathematics with the beauties of music, poetry and painting. While the beauty of mathematics is almost exclusively intelligible, and the beauties of these arts primarily sensible, it is pointed out that the latter share with mathematics a certain kind of intelligible beauty. The paper also contains (...) reflections on the formal beauty and timelessness of mathematics, beauty as richness flowing from simplicity, form and content in mathematics, and mathematics and fiction. It concludes with some remarks on the question of why mathematical beauty is so little appreciated by non-mathematicians. (shrink)

This paper treats some of the issues raised by Putnam's discussion of, and claims for, quantum logic, specifically: that its proposal is a response to experimental difficulties; that it is a reasonable replacement for classical logic because its connectives retain their classical meanings, and because it can be derived as a logic of tests. We argue that the first claim is wrong (1), and that while conjunction and disjunction can be considered to retain their classical meanings, negation crucially does not. (...) The argument is conducted via a thorough analysis of how the meet, join and complementation operations are defined in the relevant logical structures, respectively Boolean- and ortholattices (3). Since Putnam wishes to reinstate a realist interpretation of quantum mechanics, we ask how quantum logic can be a logic of realism. We show that it certainly cannot be a logic of bivalence realism (i.e., of truth and falsity), although it is consistent with some form of ontological realism (4). Finally, we show that while a reasonable explication of the idealized notion of test yields interesting mathematical structure, it by no means yields the rich ortholattice structure which Putnam (following Finkelstein) seeks. (shrink)

then E has a subset which is the domain of a model of Peano's axioms for the natural numbers. (This result is proved explicitly, using classical reasoning, in section 3 of [1].) My purpose in this note is to strengthen this result in two directions: first, the premise will be weakened so as to require only that the map ν be defined on the family of (Kuratowski) finite subsets of the set E, and secondly, the argument will be constructive, i.e., (...) will involve no use of the law of excluded middle. To be precise, we will prove, in constructive (or intuitionistic) set theory3, the following.. (shrink)

ABSTRACT Notwithstanding recent controversies involving echo chambers and social media, “post-truth” has always been central to philosophical investigations of what is knowable and good. The internal tension of the term offers a choice: to gasp in feigned astonishment at the hell-in-a-handbasket state of public discourse, or to reflect critically on what is beyond, after, or other than the truth. In this essay, we approach post-truth via elements of narrative, biography, and myth, portraying Friedrich Nietzsche's polytropic figure, Zarathustra, as he might (...) have spoken to the contemporary moment. We demonstrate how Zarathustra affords access to the idea that truth and life are inextricable in the human condition. To temper this tension, we depict a character whose disposition toward post-truth spans from certainty and doubt to exuberance and despair. Our hope is to indicate how, for the humans of Motley Cow, post-truth is ubiquitous, institutional, and infrastructural. (shrink)

We begin with the following quotation from Karp [1964]: My interest in infinitary logic dates back to a February day in 1956 when I remarked to my thesis supervisor, Professor Leon Henkin, that a particularly vexing problem would be so simple if only I could write a formula which would say x = 0 or x = 1 or x = 2 etc. To my surprise, he replied, "Well, go ahead." Traditionally, expressions in formal systems have been regarded as signifying (...) finite inscriptions which are—at least in principle—capable of actually being written out in primitive notation. However, the fact that (first-order) formulas may be identified with natural numbers (via "Gödel numbering") and hence with finite sets makes it no longer necessary to regard formulas as inscriptions, and suggests the possibility of fashioning "languages" some of whose formulas— such as that in the above quotation—would be naturally identified as infinite sets. A "language" of this kind is called an infinitary language: in this article we discuss those infinitary languages which can be obtained in a straightforward manner from first-order languages by allowing conjunctions, disjunctions and, possibly, quantifier sequences, to be of infinite length. In the course of the discussion we shall see that, while the expressive power of such languages far exceeds that of their finitary (first-order) counterparts, very few of them possess the "attractive" features (e.g., compactness and completeness) of the latter. Accordingly, the infinitary languages that do in fact possess these features merit special attention. In §1 we lay down the basic syntax and semantics of infinitary languages and demonstrate their expressive power by means of examples. §2 is devoted to those infinitary languages which permit only finite quantifier sequences: these languages turn out to be relatively well-behaved. In §3 we discuss the compactness problem for infinitary languages and its.. (shrink)

Traditionally, expressions in formal systems have been regarded as signifying finite inscriptions which are—at least in principle—capable of actually being written out in primitive notation. However, the fact that (first-order) formulas may be identified with natural numbers (via "Gödel numbering") and hence with finite sets makes it no longer necessary to regard formulas as inscriptions, and suggests the possibility of fashioning "languages" some of whose formulas would be naturally identified as infinite sets . A "language" of this kind is called (...) an infinitary language : in this article I discuss those infinitary languages which can be obtained in a straightforward manner from first-order languages by allowing conjunctions, disjunctions and, possibly, quantifier sequences, to be of infinite length. In the course of the discussion it will be seen that, while the expressive power of such languages far exceeds that of their finitary (first-order) counterparts, very few of them possess the "attractive" features (e.g., compactness and completeness) of the latter. Accordingly, the infinitary languages that do in fact possess these features merit special attention. (shrink)

Theorem 3.1. can be strengthened. Let S be a (well-termed) local set theory and (E, ≤) a partially ordered S-set. An element m of E is internally maximal if it satisfies S ∀x∈E [m ≤ x → m = x]. We can then prove the..

One of the most familiar uses of the Russell paradox, or, at least, of the idea underlying it, is in proving Cantor's theorem that the cardinality of any set is strictly less than that of its power set. The other method of proving Cantor's theorem — employed by Cantor himself in showing that the set of real numbers is uncountable — is that of diagonalization. Typically, diagonalization arguments are used to show that function spaces are "large" in a suitable sense. (...) Classically, these two methods are equivalent. But constructively they are not: while the argument for Russell's paradox is perfectly constructive, (i.e., employs intuitionistically acceptable principles of logic) the method of diagonalization fails to be so. I describe the ways in which these two methods.. (shrink)

Axioms for the continuum, or smooth real line R. These include the usual axioms for a commutative ring with unit expressed in terms of two operations + and i , and two distinguished elements 0 ≠ 1. In addition we stipulate that R is a local ring, i.e., the following axiom: ∃y x i y = 1 ∨ ∃y (1 – x) i y = 1. Axioms for the strict order relation < on R. These are: 1. a < b (...) and b < c implies a < c. 2. ¬(a < a) 3. a < b implies a + c < b + c for any c. ≤ 4. a < b and 0 < c implies acbc.. (shrink)

Call a family F of subsets of a set E inductive if ∅ ∈ F and F is closed under unions with disjoint singletons, that is, if ∀X∈F ∀x∈E–X(X ∪ {x} ∈ F]. A Frege structure is a pair (E.

By a lattice we shall always mean a distributive lattice which is bounded, i.e. has both a bottom element 0 and a top element 1. Lattice homomorphisms will always be assumed to preserve 0 and 1.

Born in 1945, John Lane Bell is not only one of the greatest logicians of our time, but he is also one the most gifted in the art of writing, as witnessed by the success of his introductory texts, many of which were originally written as lecture notes: their essential clarity is an exemplar of the Attic style. More generally, Bell’s works are a rare example of how rigour and sophisticated elegance can coexist.

Curriculum 2000 has meant significant change for the post-16 sector. New qualifications have been introduced (e.g. the new Advanced Subsidiary examination) and the number of students involved in education and training post-16 has increased. In this scenario how can the standards of new qualifications, particularly the new Advanced Subsidiary examinations, be compared with those of previous qualifications? One method is to use the prior achievement of candidates (i.e. GCSE results) as a basis for comparison of their results on subsequent qualifications (...) (i.e. A levels and AS). This method of comparability and its limitations will be explored using examples with actual data. (shrink)

The dissertation's primary task is to discern to what extent the investigations contained in Aristotle's Metaphysics conform to the model of science developed in the Posterior Analytics. It concludes that the Metaphysics substantially follows the model of the Analytics in studying the causes and attributes of a specific nature, although it makes significant departures especially in its conception of the principles of being and substance. ;Two introductory chapters discuss respectively Aristotle's conception of science in the Analytics and the problems one (...) is likely to face in attempting to apply this conception to the Metaphysics . Chapter 3 clarifies the meaning of the phrase "science of being qua being" by reference to the Posterior Analytics, and introduces the concept of pro&d13;v 3&d3;n equivocity. Chapter 4 considers the role of dialectic in metaphysics with particular reference to the principle of noncontradiction. Chapter 5 argues that the second part of Meta. 4.2 introduces a demonstrative science of the per se attributes of being and unity. ;Chapter 6 introduces the investigation into the principles and causes of being and reviews the aporias about the principles . Chapter 7 offers a hypothesis to explain Aristotle's identification of the science of being with first philosophy. The last two chapters argue that Aristotle is pursuing this investigation in the central books of Melaphysics, but his pursuit of the investigation there is incomplete. ;This interpretation provides an alternative to those of T. H. Irwin and Walter Leszl, who argue that metaphysics is a second-order discipline and not a science after the model of the Analytics. It finds explicit support in recent work by Robert Bolton and Alan Code, while widening the range of issues to include the attributes of being and the importance of first philosophy for understanding the nature of being. It supports many of the conclusions of Joseph Owens's, Urbain Dhondt's, and Frede and Patzig's work on the object of metaphysics. There are also substantial discussions of the contributions of G. E. L. Owen, J. G. Stevenson, Theodore Scaltsas, and John Thorp. (shrink)

Feminist Theory: A Philosophical Anthology addresses seven philosophically significant questions regarding feminism, its central concepts of sex and gender, and the project of centering women’s experience. Topics include the nature of sexist oppression, the sex/gender distinction, how gender-based norms influence conceptions of rationality, knowledge, and scientific objectivity, feminist ethics, feminst perspectives on self and autonomy, whether there exist distinct feminine moral perspectives, and what would comprise true liberation. Features an introductory overview illustrating the development of feminism as a philosophical movement (...) Contains both classic and contemporary sources of feminist thought, including selections by Mary Wollstonecraft, John Stuart Mill, Simone de Beauvior, Kate Millett, bell hooks, Marilyn Frye, Martha Nussbaum, Louise Antony, Sally Haslanger, Helen Longino, Marilyn Friedman, Catharine MacKinnon, and Drucilla Cornell. (shrink)

We investigate Hilbert’s varepsilon -calculus in the context of intuitionistic type theories, that is, within certain systems of intuitionistic higher-order logic. We determine the additional deductive strength conferred on an intuitionistic type theory by the adjunction of closed varepsilon -terms. We extend the usual topos semantics for type theories to the varepsilon -operator and prove a completeness theorem. The paper also contains a discussion of the concept of “partially defined‘ varepsilon -term. MSC: 03B15, 03B20, 03G30.

_A new theory of how and why we cooperate, drawing from economics, political theory, and philosophy to challenge the conventional wisdom of game theory_ Game theory explains competitive behavior by working from the premise that people are self-interested. People don’t just compete, however; they also cooperate. John Roemer argues that attempts by orthodox game theorists to account for cooperation leave much to be desired. Unlike competing players, cooperating players take those actions that they would like others to take—which Roemer (...) calls “Kantian optimization.” Through rigorous reasoning and modeling, Roemer demonstrates a simpler theory of cooperative behavior than the standard model provides. (shrink)

Let κ be an infinite cardinal. A κ-complete nonprincipal ultrafilter, or, for short, a κ- ultrafilter on a set A is a (nonempty) family U of subsets of A satisfying (i) S ⊆ U & |S|1 < κ ⇒ ∩S ∈ U (κ-completeness) (ii) X ∈ U & X ⊆ Y ⊆ A ⇒ Y ∈ U, (iii) ∀X ⊆ A [X ∈ U or A – X ∈ U] (iv) {a} ∉ U for any a..

A formal, logical, theory of events is developed and used as the basis for a definition of causation and to provide a pragmatics for causal counterfactuals. The theory begins with with a logical formalization of events as represented in the planner strips. The resulting inertial theories include a common sense law of inertia and their pragmatics is based on the principle of chronological minimization. The theory of events is then developed by removing some of the simplifying assumptions of the strips (...) representation. To begin with the assumption that events always succeed, given that their preconditions are true when they occur, is dropped. Instead a common sense law of change is introduced with the effect that events normally succeed but may fail if some qualification (some unusual or unexpected condition) arises. The pragmatics of the resulting causal theories is provided by refining the pragmatics of inertial theories. In particular, where there is a conflict between change and inertia, preference is given to change. The resulting defeasibility of events makes it possible to remove the strips assumption that only one event occurs at any given time; as conflicting events now result in failure rather than inconsistency. However it is desirable to provide a means for adjudicating between conflicting events. Consequently the theory is extended so that qualification preferences can be specified and the pragmatics are refined accordingly. A further strips assumption is that the effects of an event are invariant. In order to remove this assumption a distinction is drawn between primary events, events of the kind described above, and secondary events. Secondary events are invoked by primary events in appropriate contexts, they are causally dependent on primary events and when successful produce the additional, variant, effects of the primary events which invoke them. As a result, both the context-dependent effects of events (their ramifications) and non-deterministic events (events whose outcome is uncertain) can be represented. The theory of primary and secondary events is then used as the basis for a definition of causation which can be seen as providing a formal account of Mackie's definition of a cause as an inus condition. A major theme of this paper is the conflict between the opposite but complementary principles of change and inertia. For much of the paper the emphasis is on restricting the effects of inertia and favouring change. The resulting imbalance becomes unnatural when considering the combined effects of several events. However the definition of causation makes it possible to state a law of change and inertia, which is used to regulate change and inertia and thus ensure a proper balance between them: while caused change is preferred to inertia, inertia is preferred to uncaused change. The theory is then used to provide a pragmatics for causal counterfactuals, thereby extending the representation of actual causal reasoning to counterfactual causal reasoning. This is illustrated by the use of causal counterfactuals in order to obtain explanations. (shrink)

John E Olford; The Concept of Creativity, Journal of Philosophy of Education, Volume 5, Issue 1, 30 May 2006, Pages 77–95, https://doi.org/10.1111/j.1467-9752.1.

The topic of the present article is a conceptualization of the notion of contemplation and will develop its reflection around three principal questions: What is the role of desire in contemplation? Is it we who contemplate, or the god who contemplates in us? What is the relation between contemplation and the rest of human life?

Full proofs of the Gödel incompleteness theorems are highly intricate affairs. Much of the intricacy lies in the details of setting up and checking the properties of a coding system representing the syntax of an object language within that same language. These details are seldom illuminating and tend to obscure the core of the argument. For this reason a number of efforts have been made to present the essentials of the proofs of Gödel's theorems without getting mired in syntactic or (...) computational details. One of the most important of these efforts was made by Löb [8] in connection with his analysis of sentences asserting their own provability. Löb formulated three conditions, on the provability predicate in a formal system which are jointly sufficient to yield the Gödel's second incompleteness theorem for it. A key role in Löb's analysis is played by what later became known as the diagonalization or fixed point property of formal systems, a property which had already, in essence, been exploited by Gödel in his original proofs of the incompleteness theorems. The fixed point property plays a central role in Lawvere's [7] category-theoretic account of incompleteness phenomena. (shrink)

Henry at Work invites readers to rethink how we work today by exploring an aspect of Henry David Thoreau that has often been overlooked: Thoreau the worker. John Kaag and Jonathan van Belle overturn the popular misconception of Thoreau as a navel-gazing recluse who was scornful of work and other mundanities. In fact, Thoreau worked hard—surveying land, running his family’s pencil-making business, writing, lecturing, and building his cabin at Walden Pond—and thought intensely about work in its many dimensions. And (...) his ideas about work have much to teach us in an age of remote work and automation, when many people are reconsidering what kind of working lives they want to have. -/- Through Thoreau, readers will discover a philosophy of work in the office, factory, lumber mill, and grocery store, and reflect on the rhythms of the workday, the joys and risks of resigning oneself to work, the dubious promises of labor-saving technology, and that most vital and eternal of philosophical questions, “How much do I get paid?” In ten chapters, including “Manual Work,” “Machine Work,” and “Meaningless Work,” this personal, urgent, practical, and compassionate book introduces readers to their new favorite coworker: Henry David Thoreau. (shrink)