This chapter contains sections titled: Introduction: Questions of Meaning Theories of Meaning Language, Mind and Metaphysics: Questions of Priority Semantic Theories: Davidson's Programme Analysing the Concept of Meaning: Grice's Programme Pragmatics: Conversational Implicature and Relevance Theory.

Adding higher types to set theory differs from adding inaccessible cardinals, in that higher type arguments apply to all sets rather than just ordinary ones. Levy's reflection axiom is justified, by considering the principle that we can pretend that the universe is a set, together with methods of Gaifman [8]. We reprove some results of Gaifman, and some facts about Levy's reflection axiom, including the fact that adding higher types yields no new theorems about sets. Some remarks on (...) standard models are made. An obvious strengthening of Levy's axiom to higher types is considered, which implies the existence of indescribable cardinals. Other remarks about larger cardinals are made; some questions of Gloede [9] are settled. Finally we argue that the evidence for V = L is strong, and that CH is certainly true. MSC: 03E30, 03E55. (shrink)

This chapter contains section titled: Discussion.

We give a new characterization of the class of completely representable cylindric algebras of dimension 2 #lt; n ≤ w via special neat embeddings. We prove an independence result connecting cylindric algebra to Martin's axiom. Finally we apply our results to finite-variable first order logic showing that Henkin and Orey's omitting types theorem fails for Ln, the first order logic restricted to the first n variables when 2 #lt; n#lt;w. Ln has been recently (and quite extensively) studied as (...) a many-dimensional modal logic. (shrink)

We give a new characterization of the class of completely representable cylindric algebras of dimension 2 #lt; n w via special neat embeddings. We prove an independence result connecting cylindric algebra to Martin''s axiom. Finally we apply our results to finite-variable first order logic showing that Henkin and Orey''s omitting types theorem fails for L n, the first order logic restricted to the first n variables when 2 #lt; n#lt;w. L n has been recently (and quite extensively) studied as (...) a many-dimensional modal logic. (shrink)

We show that it is consistent that Martin's axiom holds, the continuum is large, and yet the dual distributivity number ℌ is κ1. This answers a question of Halbeisen.

There exist two notions of equivalence of behavior between states of a Labelled Markov Process (LMP): state bisimilarity and event bisimilarity. The first one can be considered as an appropriate generalization to continuous spaces of Larsen and Skou’s probabilistic bisimilarity, whereas the second one is characterized by a natural logic. C. Zhou expressed state bisimilarity as the greatest fixed point of an operator that there is such a process with an uncountable Zhou ordinal.

The main result of this paper is a formal argument for the principle of maximizing expected utility that does not rely on the law of large numbers. Unlike the well-known arguments by Savage and von Neumann & Morgenstern, this argument does not presuppose the sure-thing principle or the independence axiom. The principal idea is to use the concept of transformative decision rules for decomposing the principle of maximizing expected utility into a sequence of normatively reasonable subrules. It is shown (...) that this procedure provides a resolution of Allais's paradox that cannot be obtained by Savage-style or von Neumann & Morgenstern-style arguments. (shrink)

This paper presents an axiomatization of the principle of maximizing expected utility that does not rely on the independence axiom or sure-thing principle. Perhaps more importantly the new axiomatization is based on an ex ante approach, instead of the standard ex post approach. An ex post approach utilizes the decision maker's preferences among risky acts for generating a utility and a probability function, whereas in the ex ante approach a set of preferences among potential outcomes are on the input (...) side of the theory and the decision maker's preferences among risky acts on the output side. (shrink)

Martin's axiom is equivalent to the statement that the universe is absolute under ccc forcing extensions for Σ 1 sentences with a subset of $\kappa, \kappa , as a parameter.

Introduction -- The end of history and the Kantian moment -- The progressive mind and the Islamist challenge -- The incoherence of the philosophers -- The language of progress and the closure of the European mind -- The networked global order -- All roads lead to China -- Maxims or axioms? -- The revenge of politics and the search for order -- Conclusion -- Afterword : the study of international relations and the erosion of acdemic integrity.

We deal with the consistency strength of ZFC + variants of MA + suitable sets of reals are measurable (and/or Baire, and/or Ramsey). We improve the theorem of Harrington and Shelah [2] repairing the asymmetry between measure and category, obtaining also the same result for Ramsey. We then prove parallel theorems with weaker versions of Martin's axiom (MA(σ-centered), (MA(σ-linked)), MA(Γ + ℵ 0 ), MA(K)), getting Mahlo, inaccessible and weakly compact cardinals respectively. We prove that if there exists (...) r ∈ R such that ω L[ r] 1 = ω 1 and MA holds, then there exists a ▵ 1 3 -selective filter on ω, and from the consistency of ZFC we build a model for ZFC + MA(I) + every ▵ 1 3 -set of reals is Lebesgue measurable, has the property of Baire and is Ramsey. (shrink)

We strengthen a result of Harrington and Shelah by showing that, unless ω1 is an inaccessible cardinal in L, a relatively weak fragment of Martin's axiom implies that there exists a δ13 set of reals without the property of Baire.

Assuming an inaccessible cardinal $\kappa$ , there is a generic extension in which $MA + 2^{\aleph_0} = \kappa$ holds and the reals have a $\Delta^2_1$ well-ordering.

Kurt Gödel is almost as famous—one might say “notorious”—for his extreme platonist views as he is famous for his mathematical theorems. Moreover his platonism is not a myth; it is well-documented in his writings. Here are two platonist declarations about set theory, the first from his paper about Bertrand Russell and the second from the revised version of his paper on the Continuum Hypotheses.Classes and concepts may, however, also be conceived as real objects, namely classes as “pluralities of things” or (...) as structures consisting of a plurality of things and concepts as the properties and relations of things existing independently of our definitions and constructions.It seems to me that the assumption of such objects is quite as legitimate as the assumption of physical bodies and there is quite as much reason to believe in their existence.But, despite their remoteness from sense experience, we do have something like a perception also of the objects of set theory, as is seen from the fact that the axioms force themselves upon us as being true. I don't see any reason why we should have less confidence in this kind of perception, i.e., in mathematical intuition, than in sense perception.The first statement is a platonist declaration of a fairly standard sort concerning set theory. What is unusual in it is the inclusion of concepts among the objects of mathematics. This I will explain below. The second statement expresses what looks like a rather wild thesis. (shrink)

It is shown that every locally countable upper semi-lattice of cardinality the continuum can be embedded into the Turing degrees, assuming Martin’s Axiom.

We introduce the anti-rectangle refining property for forcing notions and investigate fragments of Martin’s axiom for ℵ1 dense sets related to the anti-rectangle refining property, which is close to some fragment of Martin’s axiom for ℵ1 dense sets related to the rectangle refining property, and prove that they are really weaker fragments.

Why was it that Francis Bacon, trained for high political office, devoted himself to proposing a celebrated and sweeping reform of the natural sciences? Julian Martin's investigative study looks at Bacon's family context, his employment in Queen Elizabeth's security service and his radical critique of the relationship between the Common Law and the Monarchy, to find the key to this important question. Deeply conservative and elitist in his political views, Bacon adapted Tudor strategies of State management and bureaucracy, the (...) social anxieties and prejudices of the late-Elizabethan governing elite, and a principal intellectual resource of the English governing classes - the Common Law - into a novel vision and method for the sciences. Bacon's axiom that 'Knowledge is Power' takes on far-reaching implications in Martin's challenging argument that the reform of natural philosophy was a central part of an audacious plan to strengthen the powers of the Crown in the State. (shrink)

We show that either PFA + or Martin's maximum implies Fleissner's Axiom R, a reflection principle for stationary subsets of P ℵ 1 (λ). In fact, the "plus version" (for one term denoting a stationary set) of Martin's axiom for countably closed partial orders implies Axiom R.

Cognitive load theory has been widely used to help understand the process of learning and to design teaching interventions. The Cognitive Load Scale developed by Leppink and colleagues has emerged as one of the most validated and widely used self-report measures of intrinsic load, extraneous load, and germane load. In this paper we investigated an expansion of the CLS by using a multidimensional conceptualization of the EL construct that is relevant for physical and online teaching environments. The Multidimensional Cognitive Load (...) Scale for Physical and Online Lectures goes beyond the CLS's operationalization of EL by expanding the EL component which originally included factors related to instructions/explanations with sub-dimensions including EL stemming from noises, and EL stemming from both media and devices within the environment. Through three studies, we investigated the reliability, and internal and external validity of the MCLS-POL using the Partial Credit Model, Confirmatory Factor Analysis, and differences between students either attending a lecture physically or online. The results of Study 1 provide initial evidence for the validity and reliability of the MCLS-POL within a higher education sample, but also highlighted several potential improvements which could be made to the measure. These changes were made before re-evaluating the validity and reliability of the measure in a new sample of higher education psychology students, and psychological testing students. Together the studies provide evidence for a multidimensional conceptualization cognitive load and provide evidence of the validity, reliability, and sensitivity of the MCLS-POL and provide suggestions for future research directions. (shrink)

We present a number of results involving almost disjoint sets and Martin's axiom. Included is an example, due to K. Kunen, of a c.c.c. partial order without property K whose product with every c.c.c. partial order is c.c.c.

This article surveys western business ethics' recent history to show how this ethic has neglected recently its religious traditions and become construed more narrowly as an applied philosophy and social science. It argues that this narrowness has confused business ethics' role in business education and helped to weaken the distinctiveness of certain institutions of higher education. It then suggests ways that western business ethics might become more integrated, interesting, and autonomous as an academic discipline by incorporating its key religious traditions.

This book is a collection of papers presented at an interdisciplinary workshop at the Calgary Institute for the Humanities in May 1980. The three broad issues covered are: the physician-patient relationship, the allocation of responsibility among doctors and nurses, and the political and social framework of the health care system. The first set of essays is concerned with the moral and legal aspects of the physician-patient relationship. The link between knowledge and power is examined as well as the moral dilemmas (...) posed by medical technology. These initial essays would alone justify this publ. (shrink)

We introduce a variant of Martin's axiom, called the grounded Martin's axiom, or math formula, which asserts that the universe is a c.c.c. forcing extension in which Martin's axiom holds for posets in the ground model. This principle already implies several of the combinatorial consequences of math formula. The new axiom is shown to be consistent with the failure of math formula and a singular continuum. We prove that math formula is preserved in (...) a strong way when adding a Cohen real and that adding a random real to a model of math formula preserves math formula. We also consider the analogous variant of the proper forcing axiom. (shrink)

A psychoanalyst looks at the portrayal of love in poems from Homer to Shakespeare, discusses Freud's writings on love, and examines the relationship between narcissism and love.

We discuss the criteria for deriving new information from coordinate transformations, focusing on the property of implementability, or measurability in practice. We contrast the role of coordinate transformations in classical and quantum physics, and demonstrate that many well-known applications fail to meet the criteria for new information. Finally, we discuss some mathematical properties of the coordinate transformations, and then relate these properties to a practical measurement scheme.

Belnap–Dunn’s relevance logic, \(\textsf{BD}\), was designed seeking a suitable logical device for dealing with multiple information sources which sometimes may provide inconsistent and/or incomplete pieces of information. \(\textsf{BD}\) is a four-valued logic which is both paraconsistent and paracomplete. On the other hand, De and Omori, while investigating what classical negation amounts to in a paracomplete and paraconsistent four-valued setting, proposed the expansion \(\textsf{BD2}\) of the four valued Belnap–Dunn logic by a classical negation. In this paper, we introduce a four-valued expansion (...) of BD called \({\textsf{BD}^\copyright }\), obtained by adding an unary connective \({\copyright }\,\ \) which is a consistency operator (in the sense of the Logics of Formal Inconsistency, _LFI_s). In addition, this operator is the unique one with the following features: it extends to \(\textsf{BD}\) the consistency operator of LFI1, a well-known three-valued _LFI_, still satisfying axiom _ciw_ (which states that any sentence is either consistent or contradictory), and allowing to define an undeterminedness operator (in the sense of Logic of Formal Undeterminedness, _LFU_s). Moreover, \({\textsf{BD}^\copyright }\) is maximal w.r.t. LFI1, and it is proved to be equivalent to BD2, up to signature. After presenting a natural Hilbert-style characterization of \({\textsf{BD}^\copyright }\) obtained by means of twist-structures semantics, we propose a first-order version of \({\textsf{BD}^\copyright }\) called \({\textsf{QBD}^\copyright }\), with semantics based on an appropriate notion of four-valued Tarskian-like structures called \(\textbf{4}\) -structures. We show that in \({\textsf{QBD}^\copyright }\), the existential and universal quantifiers are interdefinable in terms of the paracomplete and paraconsistent negation, and not by means of the classical negation. Finally, a Hilbert-style calculus for \({\textsf{QBD}^\copyright }\) is presented, proving the corresponding soundness and completeness theorems. (shrink)

A physician and spokesman for the French Ideologues, Pierre-JeanGeorges Cabanis (1757-1808) stands at the crossroads of several influential developments in modern culture--Enlightenment optimism about human perfectibility, the clinical method in medicine, and the formation and adaptation of liberal social ideals in the French Revolution. This first major study of Cabanis in English traces the influences of these developments on his thought and career. Originally published in 1980. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously (...) out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

These new essays on J. L. Austin's philosophy constitute the first major study of his thought in decades.

In the paper A non-implication between fragments of Martin’s Axiom related to a property which comes from Aronszajn trees , Proposition 2.7 is not true. To avoid this error and correct Proposition 2.7, the definition of the property is changed. In Yorioka [1], all proofs of lemmas and theorems but Lemma 6.9 are valid about this definition without changing the proofs. We give a new statement and a new proof of Lemma 6.9.

Physiognomic properties refer to the nonliteral sensory, perceptual, and affective connotations evoked by an object: a mountain, for example, is big as well as “quiet, looming, and threatening.” In this study (N = 58), the three types of meanings carried by meaningless stimuli were examined. Four equally unfamiliar stimuli, which were either physiognomically evocative (maluma and taketa) or neutral, were rated on 15 perceptual, affective, and sensory scales. Taketa and maluma were distinguished on 21 of the 30 endpoints of the (...) scales, whereas the neutral stimuli were distinguished on only 8. Subjects’ physiognomy and sex did not play a role. The implications of these findings are discussed. (shrink)

The Conferences of John Cassian constitute one of the more noteworthy contributions to early monastic literature. While it reveals decidedly Eastern influences, particularly Evagrius, it is a western contribution completed by the early decades of the fifth century. Among these recollections of what the Eastern fathers taught about the monastic life, Conferences Nine and Ten figure among the most important.4For in these two Conferences Cassian gives both his teaching on the nature and mystery of contemplative prayer and the method or (...) practice by which the monk is disposed unceasingly to this grace; moreover, it is also where one finds Cassian's commentary on the Our Father. This is a very interesting coincidence: the former is characterized by silence, the later by words. The question as to the possible relationship between the two suggests itself for further consideration. (shrink)

The most recent work dealing expressly with adoption in Greece is Wentzel's article in Hermes lxv , 167–76, ‘Studien über die Adoption in Griechen-land’. Her article ranges widely over the whole subject and includes a list of all the inscriptions known to her which refer to adoptions, as well as a list of the adoptive formulae found in these inscriptions. In the present article I shall deal more fully with these formulae.

The most recent work dealing expressly with adoption in Greece is Wentzel's article in Hermes lxv, 167–76, ‘Studien über die Adoption in Griechen-land’. Her article ranges widely over the whole subject and includes a list of all the inscriptions known to her which refer to adoptions, as well as a list of the adoptive formulae found in these inscriptions. In the present article I shall deal more fully with these formulae.