We prove that compactness is equivalent to the amalgamation property, provided the occurrence number of the logic is smaller than the first uncountable measurable cardinal. We also relate compactness to the existence of certain regular ultrafilters related to the logic and develop a general theory of compactness and its consequences. We also prove some combinatorial results of independent interest.

The classical Feferman–Vaught Theorem for First Order Logic explains how to compute the truth value of a first order sentence in a generalized product of first order structures by reducing this computation to the computation of truth values of other first order sentences in the factors and evaluation of a monadic second order sentence in the index structure. This technique was later extended by Läuchli, Shelah and Gurevich to monadic second order logic. The technique has wide applications in decidability and (...) definability theory. Here we give a unified presentation, including some new results, of how to use the Feferman–Vaught Theorem, and some new variations thereof, algorithmically in the case of Monadic Second Order Logic MSOL . We then extend the technique to graph polynomials where the range of the summation of the monomials is definable in MSOL . Here the Feferman–Vaught Theorem for these polynomials generalizes well known splitting theorems for graph polynomials. Again, these can be used algorithmically. Finally, we discuss extensions of MSOL for which the Feferman–Vaught Theorem holds as well. (shrink)

We investigate the expressive power of second-order logic over finite structures, when two limitations are imposed. Let SAA ) be the set of second-order formulas such that the arity of the relation variables is bounded by k and the number of alternations of second-order quantification is bounded by n . We show that this imposes a proper hierarchy on second-order logic, i.e. for every k , n there are problems not definable in AA but definable in AA for some c (...) 1 , d 1 . The method to show this is to introduce the set AUTOSAT of formulas in F which satisfy themselves. We study the complexity of this set for various fragments of second-order loeic. For first-order logic FOL with unbounded alternation of quantifiers AUTOSAT is PSpace complete. For first-order logic FOL n with alternation of quantifiers bounded by n , AUTOSAT is definable in AA . AUTOSAT) is definable in AA for some c 1 , d 1. (shrink)

Graph polynomials are graph parameters invariant under graph isomorphisms which take values in a polynomial ring with a fixed finite number of indeterminates. We study graph polynomials from a model theoretic point of view. In this paper we distinguish between the graph theoretic (semantic) and the algebraic (syntactic) meaning of graph polynomials. Graph polynomials appear in the literature either as generating functions, as generalized chromatic polynomials, or as polynomials derived via determinants of adjacency or Laplacian matrices. We show that these (...) forms are mutually incomparable, and propose a unified framework based on definability in Second Order Logic. We show that this comprises virtually all examples of graph polynomials with a fixed finite set of indeterminates. Finally we show that the location of zeros and stability of graph polynomials is not a semantic property. The paper emphasizes a model theoretic view. It gives a unified exposition of classical results in algebraic combinatorics together with new and some of our previously obtained results scattered in the graph theoretic literature. (shrink)

We show that the spectrum of a sentence ϕ in Counting Monadic Second Order Logic (CMSOL) using one binary relation symbol and finitely many unary relation symbols, is ultimately periodic, provided all the models of ϕ are of clique width at most k, for some fixed k. We prove a similar statement for arbitrary finite relational vocabularies τ and a variant of clique width for τ-structures. This includes the cases where the models of ϕ are of tree width at most (...) k. For the case of bounded tree-width, the ultimate periodicity is even proved for Guarded Second Order Logic GSOL. We also generalize this result to many-sorted spectra, which can be viewed as an analogue of Parikh's Theorem on context-free languages, and its analogues for context-free graph grammars due to Habel and Courcelle. Our work was inspired by Gurevich and Shelah (2003), who showed ultimate periodicity of the spectrum for sentences of Monadic Second Order Logic where only finitely many unary predicates and one unary function are allowed. This restriction implies that the models are all of tree width at most 2, and hence it follows from our result. (shrink)

We study the effects of Vopěnka's principle on properties of model theoretic logics. We show that Vopěnka's principle is equivalent to the assumption that every finitely generated logic has a compact cardinal. We show also that it is equivalent to the assumption that every such logic has a global Hanf number.

Finitary sketches, i.e., sketches with finite-limit and finite-colimit specifications, are proved to be as strong as geometric sketches, i.e., sketches with finite-limit and arbitrary colimit specifications. Categories sketchable by such sketches are fully characterized in the infinitary first-order logic: they are axiomatizable by σ-coherent theories, i.e., basic theories using finite conjunctions, countable disjunctions, and finite quantifications. The latter result is absolute; the equivalence of geometric and finitary sketches requires (in fact, is equivalent to) the non-existence of measurable cardinals.

A dictionary definition of Bioethics is, 'the ethics, or moral principles and rules of conduct, of medical and biological research'. This book is an introductory text of just biological and not medical bioethics. It covers the ethics of experimentation, including genetic manipulation, in plants and animals; ethics and biodiversity, ethics and the environment. There is increasing interest in bioethics - both in academia and by the media and the general public. Awareness of bioethics is incorporated into Biological / Environmental Science (...) courses, plus the first dedicated modular courses on bioethics are starting up. * Includes case studies * Has questions for students * Chapters include environmental, animal, agricultural and reproductive ethics as well as a wide range of issues regarding genetic manipulation. (shrink)

Recent accounts of the life of Protagoras differ widely from one another in their treatment of the ancient sources, and in the conclusions which they draw from them. A re-examination of the evidence, undertaken in 1949–50 as part of a study of the Prometheus trilogy, has convinced me that a new discussion is urgently needed if we are to place the earlier stages of the sophistic movement in the right context historically; and the purpose of this paper is to lay (...) at least a part of the foundation for such a discussion. Since the evidence for the life of Protagoras includes some allusions to his relations with Democritus, and there are some obvious affinities between the careers of Protagoras and Anaxagoras, I have added a short account of the relevant points in the biography of Democritus and a more detailed study of the evidence for the life of Anaxagoras. (shrink)

v. 1. Nicomachean ethics. Politics. The Athenian Constitution. Rhetoric. On Poetics.--v. 2. Logic.--v. 3. Physics. Metaphysics. On the soul. Short physical treaties.--v. 4. On the heavens. On generation and corruption. Meteorology. Biological treatises.

Provides comprehensive, yet concise coverage of the broad field of bioethics, dealing with the scientific, medical, social, religious, political and international concerns.

“Spinoza's Extended Substance: Cartesian and Leibnizian Reflections” This essay examines Woolhouse's interpretation of Spinoza's extended substance. According to that interpretation, the extended substance is a quasi‐Platonic form, and Spinoza's substance is not actually extended. This essay argues that the burden of defending such an interpretation is very great indeed, and requires that we read Spinoza's understanding of Descartes and Leibniz's understanding of Spinoza in unusual and awkward ways.

Establishment holds that thc psychological mechanism of inference is the ment psychological thcorizing. Moreover, given this conciliatory reading, transformation of mental representations, it follows that perception is in.

Extant semantic theories for languages containing vague expressions violate intuition by delivering the same verdict on two principles of classical propositional logic: the law of noncontradiction and the law of excluded middle. Supervaluational treatments render both valid; many-Valued treatments, Neither. The core of this paper presents a natural deduction system, Sound and complete with respect to a 'mixed' semantics which validates the law of noncontradiction but not the law of excluded middle.

The selection of wanted from unwanted messages requires discriminatory mechanisms of as great a complexity as those in normal perception, as is indicated by behavioral evidence. The results of neurophysiology experiments on selective attention are compatible with this supposition. This presents a difficulty for Filter theory. Another mechanism is proposed, which assumes the existence of a shifting reference standard, which takes up the level of the most important arriving signal. The way such importance is determined in the system is further (...) described. Neurophysiological evidence relative to this postulation is discussed. (shrink)

Whenever some form of beneficent killing--for example, voluntary euthanasia--is advocated, the proposal is greeted with a flood of slippery-slope arguments warning of the dangers of a Nazi-style slide into genocide. This paper is an attempt systematically to evaluate arguments of this kind. Although there are slippery-slope arguments that are sound and convincing, typical formulations of the Nazi-invoking argument are found to be seriously deficient both in logical rigour and in the social history and psychology required as a scholarly underpinning. As (...) an antidote, an attempt is made both to identify some of the likely causes of genocide and to isolate some of the more modest but legitimate fears that lie behind slippery-slope arguments of this kind. (shrink)

At least since the seminal work of the (US) National Commission for the Protection of Human Subjects of Biomedical and Behavioral Research in the 1970s, a fundamental distinction between research and practice has underwritten both conceptual work in research ethics and regulations governing research involving human subjects. Notwithstanding its undoubted historical importance, I believe the distinction is problematic because it misrepresents clinical inquiry. In this essay, I aim to clarify the character of clinical inquiry by identifying crucial contextual constraints on (...) justification constitutive of clinical science. This analysis shows that, from an epistemological point of view, clinical research and clinical practice are not sharply distinct but intimately intertwined. This result is important in its own right—an enriched understanding of the epistemology of clinical research is valuable in and of itself. But this result is also important because it has profound implications for the ethics of human subjects research. (shrink)

I aim to show how and why some definitions can be benignly circular. According to Lloyd Humberstone, a definition that is analytically circular need not be inferentially circular and so might serve to illuminate the application-conditions for a concept. I begin by tidying up some problems with Humberstone's account. I then show that circular definitions of a kind commonly thought to be benign have inferentially circular truth-conditions and so are malign by Humberstone's test. But his test is too demanding. The (...) inferences we actually use to establish the applicability of, e.g., colour concepts are designed to establish warranted assertability and not truth. Understood thus, dispositional analyses are not inferentially circular. (shrink)

Although this note is prompted by the recent exchange between Gellner [2], [3] and Needham [4], I shall ignore the issues raised by Gellner's specification for an ideal language. I am concerned here only with Needham's statement that ‘biology is one matter and descent is quite another, of a different order’ which, it will be remembered, Gellner treats as Needham's first error. I write under a sense of obligation, for I discussed this matter with Gellner in 1955 while he was (...) preparing his first article and my arguments then were phrased similarly to those advanced by Needham. It appears that I did not make myself clear to Gellner and I shall try again. I do not wish to attack or defend either protagonist; each is quite able to look after himself. Therefore I propose neither to examine where they have misunderstood each other, nor to discuss the difference between kinship and descent, but simply to state the connexion, as I see it, between physical and social kinship. (shrink)

In The Face of Emotions, which was Carroll Izard’s first major attempt at elaborating his differential emotions theory, he stated that the book “presents a theoretical framework for the study of emotions and their role in personality and interpersonal processes.” Yet, over the years, his contribution to personality theory has generally been overshadowed by the attention focused on his views on facial expressions and the structure of emotions. This article will begin with a brief overview of the DET perspective on (...) personality development. Then, it will examine how the DET framework can be used to organize recent findings from three lines of research on adult personality. It will conclude with suggestions for future research as well as some personal recollections. (shrink)