Husserl's two notions of "definiteness" enabled him to clarify the problem of imaginary numbers. The exact meaning of these notions is a topic of much controversy. A "definite" axiom system has been interpreted as a syntactically complete theory, and also as a categorical one. I discuss whether and how far these readings manage to capture Husserl's goal of elucidating the problem of imaginary numbers, raising objections to both positions. Then, I suggest an interpretation of "absolute definiteness" as semantic completeness and (...) argue that this notion does not suffice to explain Husserl's solution to the problem of imaginary numbers. (shrink)

In his Doppelvortrag, Edmund Husserl introduced two concepts of “definiteness” which have been interpreted as a vindication of his role in the history of completeness. Some commentators defended that the meaning of these notions should be understood as categoricity, while other scholars believed that it is closer to syntactic completeness. A detailed study of the early twentieth-century axiomatics and Husserl’s Doppelvortrag shows, however, that many concepts of completeness were conflated as equivalent. Although “absolute definiteness” was principally an attempt to characterize (...) non-extendible manifolds and axiom systems, an absolutely definite theory has a unique model and, thus, it is non-forkable and semantically complete. Non-forkability and decidability were formally delimited by Fraenkel and Carnap almost three decades later and, in fact, they mentioned Husserl as precursor of the latter. Therefore, this paper contributes to a reassessment of Husserl’s place in the history of logic. (shrink)

The aim of this paper is to define a partial Propositional Type Theory. Our system is partial in a double sense: the hierarchy of (propositional) types contains partial functions and some expressions of the language, including formulas, may be undefined. The specific interpretation we give to the undefined value is that of Kleene’s strong logic of indeterminacy. We present a semantics for the new system and prove that every element of any domain of the hierarchy has a name in the (...) object language. Finally, we provide a proof system and a (constructive) proof of completeness. (shrink)

The aim of this paper is to clarify why propositional logic is Post complete and its weak completeness was almost unnoticed by Hilbert and Bernays, while first-order logic is Post incomplete and its weak completeness was seen as an open problem by Hilbert and Ackermman. Thus, I will compare propositional and first-order logic in the Prinzipien der Mathematik, Bernays’s second Habilitationsschrift and the Grundzüge der Theoretischen Logik. The so called “arithmetical interpretation”, the conjunctive and disjunctive normal forms and the soundness (...) of the propositional rules of inference deserve special emphasis. (shrink)

The aim of this paper is to clarify why propositional logic is Post complete and its weak completeness was almost unnoticed by Hilbert and Bernays, while first-order logic is Post incomplete and its weak completeness was seen as an open problem by Hilbert and Ackermman. Thus, I will compare propositional and first-order logic in the Prinzipien der Mathematik, Bernays’s second Habilitationsschrift and the Grundzüge der Theoretischen Logik. The so called “arithmetical interpretation”, the conjunctive and disjunctive normal forms and the soundness (...) of the propositional rules of inference deserve special emphasis. (shrink)

In this article we define a logical system called Hybrid Partial Type Theory ( $\mathcal {HPTT}$ ). The system is obtained by combining William Farmer’s partial type theory with a strong form of hybrid logic. William Farmer’s system is a version of Church’s theory of types which allows terms to be non-denoting; hybrid logic is a version of modal logic in which it is possible to name worlds and evaluate expressions with respect to particular worlds. We motivate this combination of (...) ideas in the introduction, and devote the rest of the article to defining, axiomatising, and proving a completeness result for $\mathcal {HPTT}$. (shrink)

En este estudio analizamos dos tendencias claramente distintas y contrapuestas en la forma de impartir cursos elementales de Lógica en la formación superior. Para este propósito, se ha seleccionado una muestra de manuales angloamericanos clásicos, así como otra más pequeña de la tradición iberoamericana para comprobar nuestras hipótesis. Los estilos identificados y analizados en dichos manuales son lo que hemos denominado lógica matemática y lógica para filósofos. En ambos casos se trata de tendencias muy generales reconocibles en las más diversas (...) tradiciones locales. El periodo analizado, 1940-1980, responde al proceso de introducción de la Lógica contemporánea en el ámbito académico occidental. (shrink)

Aim: The presence of noise in urban environments is rarely considered a factor that causes damage to the environment. The primary generating source is transportation means, with vehicles being the ones that affect cities the most. Traffic noise has a particular influence on the quality of life of those who are exposed to it and can cause health alterations ranging from annoyance to cardiovascular diseases. This study aims to describe the relationship between the traffic noise level and the perceived annoyance (...) in the inhabitants of a city on the Northern Border of Mexico. The work carried out in a city represents the vulnerability characteristics: economic, social, and migratory of its sizable portion of the inhabitants. Due to that, it is impossible to identify precisely the number of residents as the number of vehicles in circulation.Methods: The streets and avenues with an annual average daily traffic of more than 1,000 vehicles were considered for the measurement of traffic noise. The equipment used was a vehicle gauge with non-invasive speed radar; type I integrating sound level meters, with their respective gauges and tripods. A questionnaire was applied to people living within 250 m of the streets and avenues in which the noise was measured.Results: The noise measurement found a parameter of LAeq estimated for 12 h during the day, exceeding 70 dBA. The data received from the questionnaire were statistically tested by using Pearson's correlation tests. A total number of 2,350 people were participated, of whom 1,378 were women and 972 were men. The age of participants is ranged from 18 to 75 years. The overall perception of traffic noise annoyance identified that 1,131 participants responded “Yes” as they considered the noise annoying. Participants who responded “No” as well as those who responded “Do not know” resulted in a total of 1,219 people.Conclusion: The results show that the population is desensitized to traffic noise and does not perceive it as an annoyance. The flow of vehicles and the type of vehicles are the significant factors for the propagation and increase in the traffic noise levels. Women present a considerable appreciation of traffic noise perception instead of younger people who demonstrate a higher tolerance to high-level exposure. This reflects the lack of information of the population around the noise problem and its effects. (shrink)

In this article I argue that there are two different types of understanding: the understanding we get from explanations, and the understanding we get from unification. This claim is defended by first showing that explanation and unification are not as closely related as has sometimes been thought. A critical appraisal of recent proposals for understanding without explanation leads us to discuss the example of a purely classificatory biology: it turns out that such a science can give us understanding of the (...) world through unification of the phenomena, even though it does not give us any explanations. The two types of understanding identified in this paper, while strictly separate, do have in common that both consist in seeing how the individual phenomena of the universe hang together. Explanations give us connections between the phenomena through the asymmetric, ‘vertical’ relation of determination; unifications give us connections through the symmetric, ‘horizontal’ relation of kinship. We then arrive at a general definition of understanding as knowledge of connections between the phenomena, and indicate that there might be more than two types of understanding. (shrink)

In this paper, I argue that unification is neither necessary nor sufficient for explanation. Focusing on the versions of the unificationist theory of explanation of Kitcher and of Schurz and Lambert, I establish three theses. First, Kitcher’s criterion of unification is vitiated by the fact that it entails that every proposition can be explained by itself, a flaw that it is unable to overcome. Second, because neither Kitcher’s theory nor that of Schurz and Lambert can solve the problems of asymmetry (...) and accidental generalizations, it follows that unification is not sufficient to ground explanation. Third, some good explanations are disunifying, which entails that unification is not necessary for explanation either. (shrink)

Argues that many claims by theists are based on their misunderstanding of science. He looks at the specific parameters and shows that plausible reasons can be found for the values they have within the existing standard models of physics and cosmology.

Scriven’s paradox of predictability arises from the combination of two ideas: first, that everything in a deterministic universe is, in principle, predictable; second, that it is possible to create a system that falsifies any prediction that is made of it. Recently, the paradox has been used by Rummens and Cuypers to argue that there is a fundamental difference between embedded and external predictors; and by Ismael to argue against a governing conception of laws. The present paper defends a new diagnosis (...) of the roots of the paradox. First, it is argued that the unpredictability has to be understood in the light of Turing’s famous results about computability, in particular his proof that there is no solution to the ‘halting problem.’ This allows us to see that previous analyses of the paradox were either mistaken or not fully adequate. Second, the sense of paradox that nevertheless remains is traced to the idea that rational behaviour is not dependent on contingent environmental circumstances: that it is always up to us to engage in activities such as rational prediction or rational belief. The paradox of predictability teaches us that this idea, natural though it may be, is mistaken. (shrink)

In the paper below the authors describe three super-tasks. They show that although the abstract notion of a super-task may be, as Benacerraf suggested, a conceptual mismatch, the completion of the three super-tasks involved can be defined rather naturally, without leading to inconsistency, by means of a particular kinematical interpretation combined with a principle of continuity.

Two apparently mutually exclusive ideas about the relation between contrastive and non-contrastive explanations can be found in the literature. According to contrastivists, all explanation is contrastive explanation and the supposed existence of non-contrastive explanations can be revealed to be an illusion. According to non-contrastivists, on the other hand, contrastive explanation can be fully analysed in terms of non-contrastive explanation, and is thus not of fundamental importance. In the current article, I discuss the main arguments in favour of and against each (...) of the two positions. This discussion leads to the idea that contrastive explanations are to be understood as parts of a bigger, more complete non-contrastive explanation; but that all actual explanations explain only a limited set of contrasts. I conclude that, once the relation between contrastive and non-contrastive explanations is understood correctly, there remains no substantial issue to divide contrastivism and non-contrastivism. (shrink)

Many theists regard the claim that certain fundamental constants of nature are fine-tuned for life as the best scientific argument for the existence of God since Paley’s watch. Even atheist physicists find these so-called “anthropic coincidences” difficult to explain naturally and many think they need to invoke multiple universes and the so-called “anthropic principle” to do so. Certainly if there are many universes, fine-tuning is simple. Our universe is not fine-tuned for life. Life is fine-tuned to our universe. While multiple (...) universes are expected from modern cosmological theories, theists and some scientists object that invoking the unobservable is not science. Of course, God is unobservable too, so the best theists can claim is a standoff. (shrink)

Woodward’s interventionist theory of causation is beset by a problem of circularity: the analysis of causes is in terms of interventions, and the analysis of interventions is in terms of causes. This is not in itself an argument against the correctness of the analysis. But by requiring us to have causal knowledge prior to making any judgements about causation, Woodward’s theory does make it mysterious how we can ever start acquiring causal knowledge. We present a solution to this problem by (...) showing how the interventionist notion of causation can be rationally generated from a more primitive agency notion of causation. The agency notion is easily and non-circularly applicable, but fails when we attempt to capture causal relations between non-actions. We show that the interventionist notion of causation serves as an appropriate generalisation of the agency notion. Furthermore, the causal judgements based on the latter generally remain true when rephrased in terms of the former, which allows one to use the causal knowledge gained by applying the agency notion as a basis for applying Woodward’s interventionist theory. We then present an overview of relevant empirical evidence from developmental psychology which shows that our proposed rational reconstruction lines up neatly with the actual development of causal reasoning in children. This gives additional plausibility to our proposal. The article thus provides a solution to one of the main problems of interventionism while keeping Woodward’s analysis intact. (shrink)

In an earlier paper the authors discussed some super-tasks by means of a kinematical interpretation. In the present paper we show a semi-formal way that a more abstract treatment is possible. The core idea of our approach is simple: if a super-task can be considered as a union of (finite) tasks, it is natural to define the effect of the super-task as the union of the effects of the finite tasks it consists of. We show that this approach enables us (...) to handle two of the three super-tasks that we discussed earlier. We also argue that recent objections against our original kinematical interpretation do not hold water. One of our arguments is based on the construction of an elegant correspondence between the first of those three super-tasks and Zeno's Achilles and the Tortois. (shrink)

Elizabeth Anscombe’s classic paper Causality and Determination claims that causation can be perceived. It also defends causal singularism, the idea that the causal relation is fundamentally between the particular cause and effect, and does not depend on regularities holding elsewhere in the universe. But does the former furnish an argument for the latter? The present paper analyses a special type of causal experience involving emotional reactions to present stimuli; for instance, being frightened by a spider. It argues that such experiences (...) are strongly local, in the sense that they justify belief in a local causal relation independently of our knowledge about events elsewhere in the universe. If this analysis is correct, Humean regularity theories of causation are false; and all other non-singularist theories of causation face a difficult explanatory challenge. This means that the case for causal singularism comes out considerably strengthened. (shrink)

Sometimes Strauss argues as if he thought it possible to understand man without raising questions about his relations to other things, and hence about his place in the whole. But when they are viewed in their broader context, such arguments are seen not to be his final word. Man's humanity cannot be understood in its own terms alone. The human soul differs from everything else in that it is "... open to the whole and therefore more akin to the whole (...) than anything else is." In ordinary usage, "whole" implies completeness and autonomy. But the openness of the soul--i.e., of a part--to the whole can only mean that the whole is open to itself. The whole is, then, not, in the ordinary sense of the term, whole. Nor is the soul which is "open" to it. Stripped of myths, "... the human soul is... more akin to the whole than anything else is" because neither of them is whole. The same conclusion follows when one tries to understand the definition of the philosopher as the man animated by quest for knowledge of the whole. Qua philosopher he knows neither that there is a whole, nor what it might be if there were one. To define the philosopher as the man who knows that he does not know only paraphrases the difficulty. It does not solve it. For "know" is here used equivocally. The same equivocation is at play in the comment "... one cannot know that one does not know without knowing what one does not know". Admittedly "knowledge of ignorance is not ignorance." The philosopher believes and perhaps divines more than he actually knows. All men do. The essential difference between the philosopher and other men may well consist in the fact that the philosopher distinguishes more conscientiously than do others between what he knows and what he believes, and that he strives more single-mindedly than do they to transform as large a share of his beliefs as possible into knowledge. He may conceivably at some point be said to have reached the stage where his aspirations have become reasoned expectations. But that is as far as he can possibly go as long as he remains a philosopher and has not become a wise man or a god. Until and unless the philosopher knows, in the strong sense of the term, he can no more decide whether his aspirations could be fulfilled than he can swim before getting wet. (shrink)

Recent interest in the idea that there can be scientific understanding without explanation lends new relevance to Duhem's notion of natural classification. According to Duhem, a classification that is natural teaches us something about nature without being explanatory. However, Duhem's conception of naturalness leaves much to be desired. In this paper, I argue that we can measure the naturalness of classification by using an amended version of the notion of unification as defined by Schurz and Lambert. If this thesis is (...) correct, it both leads to a better conceptual understanding of scientific understanding, and also gives the nascent literature on this topic some much-needed precision. (shrink)

On the face of it, On Tyranny is a straightforward commentary on Xenophon's dialogue Hiero or Tyrannicus. As such it is a very model of thoroughness and learning. It amply repays careful study, and it goes a long way toward explaining Strauss's influence in training a generation of scholars. The dialogue proper takes up just under 20 pages. Its analysis runs to 90-odd pages, followed by another 30 pages of tightly packed notes that are largely devoted to parallels between the (...) Hiero, Xenophon's teaching as a whole, and the teachings of Plato, of Aristotle and, to a lesser extent, of Cicero. What at first appears as an exercise in textual analysis soon reveals itself as a much broader undertaking: the delineation of the main features of classical political philosophy. Strauss does not mean to deny that differences in perspective, procedure, and even conclusions separate the major representatives of classical political philosophy. He does want to maintain, however, that their agreements are more fundamental than are their differences. But even this is incidental to his main purpose: to understand classical political philosophy for the guidance it might provide in understanding the great moral and political problems that confront us here and now. He conceives of these problems in large measure as the consequence of modern philosophy, of what he calls "the modern project." But modern philosophy cannot be understood on its own terms alone any more than it can be understood by directly confronting it with the phenomena. For it does not owe its most characteristic features to such a confrontation. It owes them, rather, to the fact that, from its very outset, it defined itself in explicit contrast to classical philosophy. Modern philosophy is essentially derivative. It presupposes the tradition it opposes. Classical philosophy, and in particular classical political philosophy, on the other hand "... belongs to the fertile moment when all political traditions were shaken, and there was not yet in existence a tradition of political philosophy." Hence "only in the light of the quarrel between the ancients and the moderns can modernity be understood. By rediscovering the urgency of this quarrel we return to the origins of modernity." It further follows from this line of reasoning that the quarrel must be re-kindled if we are once again to gain access to the phenomena themselves. To this end historical studies become necessary which do not presuppose that the whole issue has, for all intents and purposes, been settled in favor of the moderns. The most basic and most constant assumption of Strauss's historical studies is, therefore, the assumption that classical philosophy is truer than are any of the teachings that criticize or reject it. The passion and the inventiveness with which he defends this assumption sufficiently prove that he does not put it forward merely for reasons of method or of rhetoric. Yet it seems to fall short of being his settled belief. By stressing his agreements with the ancients and his disagreements with the moderns, by holding the moderns responsible for the great problems that face us while calling for a restoration of classical political philosophy, he fosters the impression that his own views coincide fully with those of classical political philosophy. But even if classical political philosophy spoke with a single clear voice, the fact remains that "no competent man of our age would regard as simply true the complete teaching of any thinker of the past." Presumably only someone who thinks himself competent would issue such a warning. (shrink)

KANT HELD THAT NEWTON AND ROUSSEAU HAD REVEALED the ways of Providence: “After Newton and Rousseau, God is justified, and Pope’s thesis is henceforth true.”.

Coherence is a measure of how much our beliefs hang together. Understanding is achieved when we see that something is not just a brute, isolated fact. This suggests that it might be possible to use the extant probabilistic measures of coherence to formulate a measure of understanding. We attempt to do so, but it turns out that a coherence theory runs into trouble with the asymmetry of understanding. We identify four difficulties and show how they have been solved by a (...) unification approach to explanation. We also identify four advantages of the coherence approach, and assess the possibilities of reconciling the strengths of the two approaches.La coherencia es una medida sobre cuanta interdependencia hay entre nuestras creencias. La comprension se obtiene cuando vemos que algo no es un hecho bruto, aislado. Esto sugiere la posibilidad de usar las medidas probabilisticas de coherencia al uso para elaborar una medida de la comprension. Explorare esta posibilidad, a pesar de que una teoria de la coherencia tropieza con problemas aqui dado el caracter asimetrico de la comprension. Identifico cuatro dificultades al respecto y muestro como han sido resueltas mediante un enfoque de la explicacion basado en la nocion de unificacion. Tambien identifico cuatro ventajas en la aproximacion desde la coherencia y examino que perspectivas hay de reconciliar los puntos fuertes de ambos planteamientos. (shrink)

What are the laws of physics? -- The stuff that kicks back -- Point-of-view invariance -- Gauging the laws of physics -- Forces and broken symmetries -- Playing dice -- After the bang -- Out of the void -- The comprehensible cosmos -- Models of reality.

This article discusses Husserl’s “epoche” and “phenomenological reduction” and early Heidegger’s “fear” and “anxiety” from a conceptual and terminological point of view. The basis for comparing “epoche” and “fear” is their main function of neutralizing the world. The author also considers the way of correlating the epoche and anxiety as philosophical concepts with three types of realizable experience that served as their source. The main points and stages of the introduction of the term “epoche” are highlighted; the main functional differences (...) between the terms “epoche” and “phenomenological reduction” in various works of Husserl are indicated. A number of Husserl’s attempts to transform the methodological principles put forward by him into a description of a special experience of detachment, accessible through moral efforts, courage and honesty, are considered. In this regard, the transformation of Cartesian doubt into the procedure of “epoche” through the artificial procedure of “attempt at doubt” is analyzed. Three types of restrictions on the universality of the epoche are distinguished. Terminological and meaningful relationships between neutralization as a mode of consciousness and the epoche are considered. Two main differences are revealed, with the help of which Husserl tries to transform principles into experience: the difference between positional and neutral consciousness and the difference between an epoche and a quasi-epoche. Husserl’s interpretation of the epoche and reduction as a special experience has two main sources: first, the experience of the imagination, or fantasy, and in this sense the source of the epoche is the quasi-epoche, and not vice versa. Secondly, the postulate of the identity of sensation from the real and illusory object. Heidegger’s distinction between fear and anxiety is critically analyzed. The author comes to the conclusion that a common source of the phenomena of anxiety, fear, horror, fright, and so on consists in the collision and mutual penetration of various human worlds. It is impossible to distance oneself from this diversity; further, it is the true source of philosophical reflection. (shrink)

This article offers an appraisal of the social ministry of Pentecostal churches through fellowship, healing and livelihood creation in the township communities of the city of Tshwane. In meeting this aim the discussion advances a thesis of these churches as agents of social support and survival of the downcast. In particular, the article attempts to show how these churches exert themselves towards establishing not only moral responsibility, but also a context where the weakest and the least privileged can learn how (...) to survive. The squatter camp people are unique with the special challenges requiring distinctive consideration. Pentecostal churches believe that the lost people matter to God and are of importance to their congregations as well. The backyard Bible study ministries and mutual cooperation strategies are employed for mutual support. Making use of the existing empirical research data and available literature will show how Pentecostal churches in the townships support the laity and community in times of need. (shrink)