Provided here is a characterisation of absolute probability functions for intuitionistic (propositional) logic L, i.e. a set of constraints on the unary functions P from the statements of L to the reals, which insures that (i) if a statement A of L is provable in L, then P(A) = 1 for every P, L's axiomatisation being thus sound in the probabilistic sense, and (ii) if P(A) = 1 for every P, then A is provable in L, L's axiomatisation being thus (...) complete in the probabilistic sense. As there are theorems of classical (propositional) logic that are not intuitionistic ones, there are unary probability functions for intuitionistic logic that are not classical ones. Provided here because of this is a means of singling out the classical probability functions from among the intuitionistic ones. (shrink)

ABSTRACT We show that some PRO-sentences appear to receive de re interpretations when they occur in suitable discourse contexts or linguistic environments. This finding is surprising given the received view that such sentences are unambiguously de se [Morgan. 1970. “On the Criterion of Identity for Noun Phrase Deletion.” Papers from the Sixth Regional Meeting of the Chicago Linguistics Society, Chicago, IL, 380–389; Chierchia. 1990. “Anaphora and Attitudes de se.” In Semantics and Contextual Expression, edited by R. Bartsch, J. van Benthem, (...) and P. van Emde Boas, 1–32. Dordrecht: Foris]. We argue that these apparent de re readings are not genuine readings assigned by the grammar, but rather arise via a pragmatic process that results in what we call ‘excluded entailments’. The interpretation of PRO-sentences thus shows a certain amount of pragmatic latitude that is reminiscent of other cases of non-literal language, such as examples of ‘pragmatic slack’ first discussed in Lasersohn [1999. “Pragmatic Halos.” Language 75: 522–551]. However, we show that there are crucial differences between the puzzling data at hand and more familiar cases of pragmatic slack, and argue that they constitute a different class of non-literal meaning that has received less attention in the literature. This class of meanings is akin to that introduced by the modifier ‘in effect’. Our view has consequences for semantic methodology, understanding the limits of non-literal language use and interpretation, and the division of labour between semantics and pragmatics in the analysis of attitude reports. (shrink)

While the classical account of the linear continuum takes it to be a totality of points, which are its ultimate parts, Aristotle conceives of it as continuous and infinitely divisible, without ultimate parts. A formal account of this conception can be given employing a theory of quantification for nonatomic domains and a theory of region-based topology.

Reflection Principles are commonly thought to produce only strong axioms of infinity consistent with V = L. It would be desirable to have some notion of strong reflection to remedy this, and we have proposed Global Reflection Principles based on a somewhat Cantorian view of the universe. Such principles justify the kind of cardinals needed for, inter alia , Woodin’s Ω-Logic.

Gentzen's account of logical consequence is extended so as to become a matter of degree. We characterize and study two kinds of function G, where G(X,Y) takes values between 0 and 1, which represent the degree to which the set X of statements (understood conjunctively) logically implies the set Y of statements (understood disjunctively). It is then shown that these functions are essentially the same as the absolute and the relative probability functions described by Carnap.

Evolutionary fitness threats and rewards are associated with subjectively unpleasant and pleasant sensations, respectively. Initially, these correlations appear explainable via adaptation by natural selection. But here I analyse the major metaphysical perspectives on consciousness – physicalism, dualism, and panpsychism – and conclude that none help to understand the adaptive-seeming correlations via adaptation. I also argue that a recently proposed explanation, the phenomenal powers view, has major problems that mean it cannot explain the adaptive-seeming correlations via adaptation either. So the mystery (...) – call it the evolutionary paradox of consciousness – remains. Some have used this mystery to argue for non-naturalistic (e.g. theistic) explanations. But I propose a naturalistic, non-adaptive explanation of the adaptive-seeming correlations: namely, ‘sensational associative learning’ during development. In this perspective, pairing of particular sensations with unconditioned stimuli – fitness rewards or threats – cause the sensations themselves to come to be interpreted as good or bad, respectively. Sensations, like colours, that are not reliably paired with either fitness rewards or threats remain largely unvalenced. Sensational associative learning also provides explanations for adaptive-seeming structural aspects of sensations, such as the observation that sounds of different pitch are experienced as ordinal in correspondence to their wavelengths while the same is not true of colours of different hue. The sensational associative learning perspective appears compatible with physicalism, panpsychism, and dualism (though not epiphenomenalism). (shrink)

A topological description of space is given, based on the relation of connection among regions and the property of being limited. A minimal set of 10 constraints is shown to permit definitions of points and of open and closed sets of points and to be characteristic of locally compact T2 spaces. The effect of adding further constraints is investigated, especially those that characterise continua. Finally, the properties of mappings in region-based topology are studied. Not all such mappings correspond to point (...) functions and those that do correspond to continuous functions. (shrink)

As a survey of many technical results in probability theory and probability logic, this monograph by two widely respected scholars offers a valuable compendium of the principal aspects of the formal study of probability. Hugues Leblanc and Peter Roeper explore probability functions appropriate for propositional, quantificational, intuitionistic, and infinitary logic and investigate the connections among probability functions, semantics, and logical consequence. They offer a systematic justification of constraints for various types of probability functions, in particular, an exhaustive account of (...) probability functions adequate for first-order quantificational logic. The relationship between absolute and relative probability functions is fully explored and the book offers a complete account of the representation of relative functions by absolute ones. The volume is designed to review familiar results, to place these results within a broad context, and to extend the discussions in new and interesting ways. Authoritative, articulate, and accessible, it will interest mathematicians and philosophers at both professional and post-graduate levels. (shrink)

인간의 이성적 의식과 법의 관계를 밝히고 법의 해석 과 판단에 인간의 의식이 어떻게 작용하는가를 고찰 한 저술. 제1부에서는 법의 형이상학적인 측면에서 법의 실체, 그리스의 법, 데카르트의 법, 로크와 법, 칸트와 법, 헤겔과 법, 아담스미스의 법의 경제, 중국의 도덕과 법사상을 다루었다. 제2부에서는 심리학적 분석으로 헌법의 심리학적 해석, 법의 판결절차, 증거법, 형법과 죄, 청소년과 가족법, 조세법, 플라톤의 법, 칸트의 도덕론의 경험적 확인, 헤겔의 자아와 노동법, 법의 4차원에 대해 다뤘다.

Inleidend overzicht van de wijsgerige ethiek.

It is argued that the usual proposals for dealing with mass-Quantification--All x is f--Are inadequate with the predicate is complex or when multiple quantification is considered. Mass-Quantification is seen as a generalisation of ordinary (thing) quantification in that the specialising assumption that the domain of quantification is atomic is not made. It is suggested that the semantic values of predicates are complete ideals of the boolean algebra consisting of the quantity which is the domain of quantification and all its sub-Quantities, (...) While logical connectives are represented by operations on complete ideals. (shrink)

We analyze expressive small clauses like you fool (and their counterparts in other languages) as contributors of expressive content. Independently known restrictions on expressive content in turn allow us to derive their limited distribution. The theory has ramifications for child language. It correctly predicts which root-level small clauses will survive into adult grammar and which will be blocked by the acquisition of higher functional projections. It also opens the way to an analysis of children’s one- and two-word utterances as denoting (...) expressive, rather than straightforwardly propositional, content. (shrink)

Frege regarded Hume's Principle as insufficient for a logicist account of arithmetic, as it does not identify the numbers; it does not tell us which objects the numbers are. His solution, generally regarded as a failure, was to propose certain sets as the referents of numerical terms. I suggest instead that numbers are properties of pluralities, where these properties are treated as objects. Given this identification, the truth-conditions of the statements of arithmetic can be obtained from logical principles with the (...) help of definitions, just as the logicist thesis maintains. (shrink)

Together again for the first time, Marx and Durkheim join forces in the pages of Disintegration: Bad Love, Collective Suicide, and the Idols of Imperial Twilight for a dialectical exploration of the moral economy of neoliberalism, animated, as it is not only by the capitalist chase for surplus value, but also by an immortal vortex of sacred powers. Classical sociology and psychoanalysis are reconstituted within Hegelian social ontology and dialectical method that differentiates between the ephemeral and free and the eternal (...) and fixed aspects of modern life. (shrink)

t. 1. Dialog s V. V. Davydovym -- t. 2. Nereshennye problemy razvivai︠u︡shchego obrazovanii︠a︡.

George Berkeley is one of the greatest and most influential modern philosophers. In defending the immaterialism for which he is most famous, he redirected modern thinking about the nature of objectivity and the mind's capacity to come to terms with it. Along the way, he made striking and influential proposals concerning the psychology of the senses, the workings of language, the aims of science, and the scope of mathematics. In this Companion volume a team of distinguished authors not only examines (...) Berkeley's achievements but also his neglected contributions to moral and political philosophy, his writings on economics and development, and his defense of religious commitment and religious life. The volume places Berkeley's achievements in the context of the many social and intellectual traditions - philosophical, scientific, ethical, and religious - to which he fashioned a distinctive response. (shrink)

Doctors’ strikes are legally permissible in the UK, with the situation differing in other countries. But are they morally permissible? Doug McConnell and Darren Mann have systematically attempted to dismiss the arguments for the moral impermissibility of doctors’ strikes and creatively attempted to provide further moral justification for them. Unfortunately for striking doctors, they fail to achieve this. Meanwhile, junior doctors’ strikes have continued in the UK through 2023 and have now extended into 2024. In this response, which focuses on (...) the UK situation and specifically junior doctors’ strikes in the National Health Service (NHS) in England, I will demonstrate a central problem with their arguments—namely that they underplay the harms caused by prolonged doctors’ strikes by ignoring the harms to patients with cancer. This weakens their conclusion that strikes are morally permissible in terms of the conditions and thresholds they set. I then provide a psychological critique of their justification for strikes in terms of the interests of the public. It follows that invoking the controversial concept of supererogatory action is ungrounded but also absurd when you consider time-critical cancer care. If those representing striking doctors wish to maintain a modicum of moral respectability, they should mitigate for patients with cancer and negotiate reasonably and with urgency. (shrink)

Shown here is that a constraint used by Popper in The Logic of Scientific Discovery (1959) for calculating the absolute probability of a universal quantification, and one introduced by Stalnaker in "Probability and Conditionals" (1970, 70) for calculating the relative probability of a negation, are too weak for the job. The constraint wanted in the first case is in Bendall (1979) and that wanted in the second case is in Popper (1959).

Pensons aux divers énoncés qui peuvent être composés à partir d'un ensemble fini ou dénombrable d'énoncés atomiques à l'aide de, disons, ‘˜’ et ‘&’; soit A n'importe lequel de ces énoncés; et soit l'ensemble SA des composantes atomiques de A. La valeur de vérité de A dépend évidemment des valeurs de vérité de certains membres de SA. En effet, si aux valeurs de vérité Vrai et Faux sont substitués les entiers 1 et 0, respectivement; la valeur de vérité VVV d'une (...) négation ˜A est 1–VV; et la valeur de vérité VV d'une conjonction A & B est min, VV), alors la valeur de vérité de A s'avère être une fonction numérique des valeurs de vérité de certains membres de SA. Et les fonctions de valeurs de vérité sont dites, à titre de résultat, récursivement définissables. (shrink)

This paper studies the extent to which probability functions are recursively definable. It proves, in particular, that the (absolute) probability of a statement A is recursively definable from a certain point on, to wit: from the (absolute) probabilities of certain atomic components and conjunctions of atomic components of A on, but to no further extent. And it proves that, generally, the probability of a statement A relative to a statement B is recursively definable from a certain point on, to wit: (...) from the probabilities relative to that very B of certain atomic components and conjunctions of atomic components of A, but again to no further extent. These and other results are extended to the less studied case where A and B are compounded from atomic statements by means of `` ∀ '' as well as `` ∼ '' and "&". The absolute probability functions considered are those of Kolmogorov and Carnap, and the relative ones are those of Kolmogorov, Carnap, Renyi, and Popper. (shrink)

This paper offers a justification of the ‘Hilbert-Bernays Derivability Conditions’ by considering what is required of a theory which gives an account of provability in itself.

Provided here is an account, both syntactic and semantic, of first-order and monadic second-order quantification theory for domains that may be non-atomic. Although the rules of inference largely parallel those of classical logic, there are important differences in connection with the identification of argument places and the significance of the identity relation.

The introduction of novel diagnostic techniques in clinical domains such as genomics and radiology has led to a rich ethical debate on how to handle unsolicited findings that result from these innovations. Yet while unsolicited findings arise in both genomics and radiology, most of the relevant literature to date has tended to focus on only one of these domains. In this article, we synthesize and critically assess similarities and differences between “scanning the body” and “sequencing the genome” from an ethical (...) perspective. After briefly describing the novel diagnostic contexts leading to unsolicited findings, we synthesize and reflect on six core ethical issues that relate to both specialties: terminology; benefits and risks; autonomy; disclosure of unsolicited findings to children; uncertainty; and filters and routine screening. We identify ethical rationales that pertain to both fields and may contribute to more ethically sound policies. Considerations of preserving public trust and ensuring that people perceive healthcare policies as fair also support the need for a combined debate. (shrink)

ABSTRACT Although Frege’s theory of real numbers in Grundgesetze der Arithmetik, Vol. II, is incomplete, it is possible to provide a logicist justification for the approach he is taking and to construct a plausible completion of his account by an extrapolation which parallels his theory of cardinal numbers.

The aim of the paper is to formulate rules of inference for the predicate 'is true' applied to sentences. A distinction is recognised between (ordinary) truth and definite truth and consequently between two notions of validity, depending on whether truth or definite truth is the property preserved in valid arguments. Appropriate sets of rules of inference governing the two predicates are devised. In each case the consequence relation is in harmony with the respective predicate. Particularly appealing is a set of (...) ND rules for ordinary truth in which premises and assumptions play different roles, premises being taken to assert definite truth, assumptions to suppose truth. This set of rules can be said to capture everyday reasoning with truth. Also presented are formal characterisations, in the meta-language and in the object language, of paradoxical and 'truth teller'-like sentences. (shrink)