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)

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)

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)

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)

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)

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.

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)

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)

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)

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..

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.

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)

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)

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)

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)

As a work of a scholarship it seems to me to compare favourably with the best books on the subject, including those by Marcus Singer and Onora Nell.' Prof.

In response to Charles Taylor's book "Sources of the Self: The Making of the Modern Identity," Becker defends the Western view of ethical conceptions based on our unique identity, reasoning, and historical heritage.

Examines Arthur Schopenhauer's (1788-1860) conception of human agency and responsibility, his unique ethics of the morally virtuous character, and his assessment of life as fundamentally suffering. This title focuses on his contention that the human will and the human body cannot have a cause and effect relationship with each other.

This book presents a detailed fieldwork-based study of the ancient Indian religion of Jainism. Drawing on field research in northern Gujarat and on the study of both ancient Sanskrit and Prakrit and modern vernacular Jain religious literature, John Cort provides a rounded portrait of the religion as it is practiced today.

A mutual relation between God and the world provides a crucial distinction between panentheism and both classical theism and pantheism. Several proposals responding to Analytical Theology's challenge to distinguish panentheism from other forms of theism are considered and found inadequate. After defining mutual relation, conceptual evidence and the frequency of descriptions of panentheism that affirm a mutual relation between God and the world provide evidence that a mutual relation is crucial to distinguishing panentheism. Finally, benefits of recognizing a mutual relation (...) between God and the world as crucial to panentheism are described. (shrink)