A λ-theory T is a consistent set of equations between λ-terms closed under derivability. The degree of T is the degree of the set of Godel numbers of its elements. H is the $\lamda$ -theory axiomatized by the set {M = N ∣ M, N unsolvable. A $\lamda$ -theory is sensible $\operatorname{iff} T \supset \mathscr{H}$ , for a motivation see [6] and [4]. In § it is proved that the theory H is ∑ 0 2 -complete. We present Wadsworth's proof (...) that its unique maximal consistent extention $\mathscr{H}^\ast (= \mathrm{T}(D_\infty))$ is Π 0 2 -complete. In $\S2$ it is proved that $\mathscr{H}_\eta(= \lambda_\eta-\text{Calculus} + \mathscr{H})$ is not closed under the ω-rule (see [1]). In $\S3$ arguments are given to conjecture that $\mathscr{H}\omega (= \lambda + \mathscr{H} + omega-rule)$ is Π 1 1 -complete. This is done by representing recursive sets of sequence numbers as λ-terms and by connecting wellfoundedness of trees with provability in Hω. In $\S4$ an infinite set of equations independent over H η will be constructed. From this it follows that there are 2^{ℵ_0 sensible theories T such that $\mathscr{H} \subset T \subset \mathscr{H}^\ast$ and 2 ℵ 0 sensible hard models of arbitrarily high degrees. In $\S5$ some nonprovability results needed in $\S\S1$ and 2 are established. For this purpose one uses the theory H η extended with a reduction relation for which the Church-Rosser theorem holds. The concept of Gross reduction is used in order to show that certain terms have no common reduct. (shrink)
Mijn wetenschappelijke bijdrage sluit aan bij het stuk van Jan WillemKlop in deze zelfde afscheidsbundel, dat ik van Jan Willem onder embargo te lezen heb gekregen. Je zult je herinneren dat Jan Willem in de CWI lezing ter gelegenheid van zijn eredoctoraat kort refereerde aan de Thue Morse reeks. Noem deze reeks M . Jan Willem gaf de versie die start met 1. Noem het resultaat van omwisselen van nullen en enen in de Thue (...) Morse reeks M . De reeks M is wat je krijgt als je het Thue Morse proces start met 0. (shrink)
It frequently concentrates on the subjects in which the honorand has made important discoveries. The volume concludes with a complete bibliography of Jaap Mansfeld's scholarly work so far.
This paper describes the work of the Polish logician Jan Kalicki (1922?1953). After a biographical introduction, his work on logical matrices and equational logic is appraised. A bibliography of his papers and reviews is also included.
In this paper I fix a typical regress argument, locate a typical gap in the argument, and try to supply a number of gap-filling readings of its first premise.
Nelson Goodman defends the seemingly radical view that, in a certain sense, all facts depend on our perspective on the matter. We make the world, rather than merely find it. The aim of this contribution is three-fold: to make sense of Goodman's metaphysical perspectivalism, clearly explain how it differs from other branches of perspectivalism (epistemic and semantic), and put two issues on the agenda that deserve renewed attention.
The general view is that metaphysical explanation is asymmetric. For instance, if resemblance facts can be explained by facts about their relata, then, by the asymmetry of explanation, these latter facts cannot in turn be explained by the former. The question however is: is there any reason to hold on to the asymmetry? If so, what does it consist in? In the paper we approach these questions by comparing them to analogous questions that have been investigated for scientific explanations. Three (...) main asymmetry criteria have been proposed for the latter: (i) causation, (ii) unification, and (iii) explanatory dependence. We argue that the last criterion, but not the former two, can be of help to metaphysical explanation: metaphysical explanations are asymmetric if the explanatory dependence criterion (in modified format) holds of them. (shrink)
What is the Problem of Universals? In this paper we take up the classic question and proceed as follows. In Sect. 1 we consider three problem solving settings and define the notion of problem solving accordingly. Basically I say that to solve problems is to eliminate undesirable, unspecified, or apparently incoherent scenarios. In Sect. 2 we apply the general observations from Sect. 1 to the Problem of Universals. More specifically, we single out two accounts of the problem which are based (...) on the idea of eliminating apparently incoherent scenarios, and then propose modifications of those two accounts which, by contrast, are based on the idea of eliminating unspecified scenarios. In Sect. 3 we spell out two interesting ramifications. (shrink)
Important sceptical arguments by Sextus Empiricus, Hume and Boghossian (concerning disputes, induction, and relativism respectively) are based on circularities and infinite regresses. Yet, philosophers' practice does not keep circularities and infinite regresses clearly apart. In this metaphilosophical paper I show how circularity and infinite regress arguments can be made explicit, and shed light on two powerful tools of the sceptic.
Infinite regress arguments play an important role in many distinct philosophical debates. Yet, exactly how they are to be used to demonstrate anything is a matter of serious controversy. In this paper I take up this metaphilosophical debate, and demonstrate how infinite regress arguments can be used for two different purposes: either they can refute a universally quantified proposition (as the Paradox Theory says), or they can demonstrate that a solution never solves a given problem (as the Failure Theory says). (...) In the meantime, I show that Black’s view on infinite regress arguments (1996, this journal) is incomplete, and how his criticism of Passmore can be countered. (shrink)
This paper is about the Problem of Order, which is basically the problem how to account for both the distinctness of facts like a’s preceding b and b’s preceding a, and the identity of facts like a’s preceding b and b’s succeeding a. It has been shown that the Standard View fails to account for the second part and is therefore to be replaced. One of the contenders is Anti-Positionalism. As has recently been pointed out, however, Anti-Positionalism falls prey to (...) a regress argument which is to prove its failure. In the paper we spell out this worry, show that the worry is a serious one, and distinguish four possible strategies for Anti-Positionalism to deal with it. (shrink)
This dissertation is on infinite regress arguments in philosophy. Its main goals are to explain what such arguments from many distinct philosophical debates have in common, and to provide guidelines for using and evaluating them. Two theories are reviewed: the Paradox Theory and the Failure Theory. According to the Paradox Theory, infinite regress arguments can be used to refute an existentially or universally quantified statement (e.g. to refute the statement that at least one discussion is settled, or the statement that (...) discussions are settled only if there is an agreed-upon criterion to settle them). According to the Failure Theory, infinite regress arguments can be used to demonstrate that a certain solution fails to solve an existentially or universally quantified problem (e.g. to demonstrate that a certain solution fails to settle all discussions, or that it fails to settle even one discussion). In the literature, the Paradox Theory is fairly well-developed, and this dissertation provides the Failure Theory with the same tools. (shrink)
If an argument can be reconstructed in at least two different ways, then which reconstruction is to be preferred? In this paper I address this problem of argument reconstruction in terms of Ryle’s infinite regress argument against the view that knowledge-how requires knowledge-that. First, I demonstrate that Ryle’s initial statement of the argument does not fix its reconstruction as it admits two, structurally different reconstructions. On the basis of this case and infinite regress arguments generally, I defend a revisionary take (...) on argument reconstruction: argument reconstruction is mainly to be ruled by charity (viz. by general criteria which arguments have to fulfil in order to be good arguments) rather than interpretation. (shrink)
Until now, antirealists have offered sketches of a theory of truth, at best. In this paper, we present a probabilist account of antirealist truth in some formal detail, and we assess its ability to deal with the problems that are standardly taken to beset antirealism.
Much of present-day epistemology is divided between internalists and externalists. Different as these views are, they have in common that they strip justification from its dialectical component in order to block the skeptic’s argument from disagreement. That is, they allow that one may have justified beliefs even if one is not able to defend it against challenges and resolve the disagreements about them. Lammenranta (2008, 2011a) recently argued that neither internalism nor externalism convinces if we consider the argument in its (...) most interesting format. In this paper I zoom in on this debate, and fix further details of Lammenranta’s lead. Specifically, I will side with skepticism that justification is dialectical, yet only if certain conditions are in place. (shrink)
This paper investigates the viability of the Bayesian model of belief change. Van Benthem (2003) has shown that a particular kind of information change typical for dynamic epistemic logic cannot be modelled by Bayesian conditioning. I argue that the problems described by van Benthem come about because the information change alters the semantics in which the change is supposed to be modelled by conditioning: it induces a shift in meanings. I then show that meaning shifts can be modelled in terms (...) of conditioning by employing a semantics that makes these changes in meaning explicit, and that the appropriate probability kinematics can be described by Dempster’s rule. The new model thereby facilitates a better understanding between probabilistic epistemology and dynamic epistemic logic. (shrink)
According to Vallicella's 'Relations, Monism, and the Vindication of Bradley's Regress' (2002), if relations are to relate their relata, some special operator must do the relating. No other options will do. In this paper we reject Vallicella's conclusion by considering an important option that becomes visible only if we hold onto a precise distinction between the following three feature-pairs of relations: internality/externality, universality/particularity, relata-specificity/relata-unspecificity. The conclusion we reach is that if external relations are to relate their relata, they must be (...) relata-specific (and no special operator is needed). As it eschews unmereological complexes, this outcome is of relevance to defenders of the extensionality of composition. (shrink)
Rationality requires us to have certain propositional attitudes (beliefs, intentions, etc.) given certain other attitudes that we have. Carroll's Tortoise repeatedly shows up in this discussion. Following up on Brunero (2005, this journal), I ask what Carroll-style considerations actually prove. This paper rejects two existing suggestions, and defends a third.
Van Fraassen's Judy Benjamin problem has generally been taken to show that not all rational changes of belief can be modelled in a probabilistic framework if the available update rules are restricted to Bayes's rule and Jeffrey's generalization thereof. But alternative rules based on distance functions between probability assignments that allegedly can handle the problem seem to have counterintuitive consequences. Taking our cue from a recent proposal by Bradley, we argue that Jeffrey's rule can solve the Judy Benjamin problem after (...) all. Moreover, we show that the specific instance of Jeffrey's rule that solves the Judy Benjamin problem can be underpinned by a particular distance function. Finally, we extend the set of distance functions to ones that take into account the varying degrees to which propositions may be epistemically entrenched. (shrink)
Pyrrhonism is the view that we should suspend all our beliefs in order to be rational and reach peace of mind. One of the main objections against this view is that it makes action impossible. One cannot suspend all beliefs and act normally at once. Yet, the question is: What is it about actions that they require beliefs? This issue has hardly been clarified in the literature. This is a bad situation, for if the objection fails and it turns out (...) that the Pyrrhonists found a way to secure peace of mind, we better know the details. In the following, I take up this systematic query and show how the objection can be made precise. Despite Sextus Empiricus? ingenious appearance/reality distinction, which is to ensure Pyrrhonism in this, I eventually argue that a life by appearances is quite unlike a normal life. (shrink)
List and Pettit have stated an impossibility theorem about the aggregation of individual opinion states. Building on recent work on the lottery paradox, this paper offers a variation on that result. The present result places different constraints on the voting agenda and the domain of profiles, but it covers a larger class of voting rules, which need not satisfy the proposition-wise independence of votes.
Coercion is by its very nature hostile to the individual subjected to it. At the same time, it often is a necessary evil: political life cannot function without at least some instances of coercion. Hence, it is not surprising that coercion has been the topic of heated philosophical debate for many decades. Though numerous accounts have been put forth in the literature, relatively little attention has been paid to the question what exactly being subjected to coercion does to an individual (...) that makes it so hostile to his person. This paper develops an analysis of the subjective aspect of coercion whereby this hostility is explained. It is argued that coercion is not just a matter of interference with one’s agency, but also affects one’s morality. Because coercion is a form of subjugation it does more than merely limit one’s freedom, it constitutes an affront to one’s dignity as well. A new account of coercion is developed that pays particular attention to the subjectivity inherent in coercion. This account takes a middle ground in the ongoing debate between advocates of moralised and non-moralised conceptualisations of coercion. The paper closes by applying this account to two prominent issues in the literature on coercion: the use of coercion claims in attempts to avoid being held responsible for one’s actions, and the coerciveness of the law. (shrink)
This article argues that time?asymmetric processes in spacetime are enantiomorphs. Subsequently, the Kantian puzzle concerning enantiomorphs in space is reviewed to introduce a number of positions concerning enantiomorphy, and to arrive at a dilemma: one must either reject that orientations of enantiomorphs are determinate, or furnish space or objects with orientation. The discussion on space is then used to derive two problems in the debate on the direction of time. First, it is shown that certain kinds of reductionism about the (...) direction of time are at variance with the claim that orientation of enantiomorphic objects is intrinsic. Second, it is argued that reductive explanations of time?asymmetric processes presuppose that enantiomorphic processes do not have determinate orientation. (shrink)
This article presents a generalization of the Condorcet Jury Theorem. All results to date assume a fixed value for the competence of jurors, or alternatively, a fixed probability distribution over the possible competences of jurors. In this article, we develop the idea that we can learn the competence of the jurors by the jury vote. We assume a uniform prior probability assignment over the competence parameter, and we adapt this assignment in the light of the jury vote. We then compute (...) the posterior probability, conditional on the jury vote, of the hypothesis voted over. We thereby retain the central results of Condorcet, but we also show that the posterior probability depends on the size of the jury as well as on the absolute margin of the majority. (shrink)
Is the content of our thoughts determined by norms such as ‘if I know that p, then I ought to believe that p’? Glüer & Wikforss (2009a) set forth a regress argument for a negative answer. The aim of this paper is to clarify and evaluate this argument. In the first part I show how it (just like an argument from Wittgenstein 1953) can be taken as an instance of an argument schema. In the second part, I evaluate the relevant (...) premises in some detail, and argue that the dialectical situation is slightly more complicated than a ‘dilemma of regress and idleness’, as Glüer & Wikforss have dubbed it. (shrink)
This paper studies the use of hypotheses schemes in generatinginductive predictions. After discussing Carnap–Hintikka inductive logic,hypotheses schemes are defined and illustrated with two partitions. Onepartition results in the Carnapian continuum of inductive methods, the otherresults in predictions typical for hasty generalization. Following theseexamples I argue that choosing a partition comes down to making inductiveassumptions on patterns in the data, and that by choosing appropriately anyinductive assumption can be made. Further considerations on partitions makeclear that they do not suggest any solution (...) to the problem of induction.Hypotheses schemes provide the tools for making inductive assumptions, but theyalso reveal the need for such assumptions. (shrink)
An inductive logic is a system of inference that describes the relation between propositions on data, and propositions that extend beyond the data, such as predictions over future data, and general conclusions on all possible data. Statistics, on the other hand, is a mathematical discipline that describes procedures for deriving results about a population from sample data. These results include predictions on future samples, decisions on rejecting or accepting a hypothesis about the population, the determination of probability assignments over such (...) hypotheses, the selection of a statistical model for studying the population, and so on. Both inductive logic and statistics are calculi for getting from the given data to propositions or results that transcend the data. (shrink)
This article argues that time-asymmetric processes in spacetime are enantiomorphs. Subsequently, the Kantian puzzle concerning enantiomorphs in space is reviewed to introduce a number of positions concerning enantiomorphy, and to arrive at a dilemma: one must either reject that orientations of enantiomorphs are determinate, or furnish space or objects with orientation. The discussion on space is then used to derive two problems in the debate on the direction of time. First, it is shown that certain kinds of reductionism about the (...) direction of time are at variance with the claim that orientation of enantiomorphic objects is intrinsic. Second, it is argued that reductive explanations of time-asymmetric processes presuppose that enantiomorphic processes do not have determinate orientation. (shrink)
In this paper I discuss probabilistic models of experimental intervention, and I show that such models elucidate the intuition that observations during intervention are more informative than observations per se. Because of this success, it seems attractive to also cast other problems addressed by the philosophy of experimentation in terms of such probabilistic models. However, a critical examination of the models reveals that some of the aspects of experimentation are covered up rather than resolved by probabilistic modelling. I end by (...) drawing a number of general lessons on the use of formal methods in the philosophy of science. (shrink)
In V. N. Huynh (ed.): Interval / Probabilistic Uncertainty and Non-Classical Logics, Advances in Soft Computing Series, Springer 2008, pp. 268-279. This paper proposes a common framework for various probabilistic logics. It consists of a set of uncertain premises with probabilities attached to them. This raises the question of the strength of a conclusion, but without imposing a particular semantics, no general solution is possible. The paper discusses several possible semantics by looking at it from the perspective of probabilistic argumentation.
Summary. This paper proposes a common framework for various probabilistic logics. It consists of a set of uncertain premises with probabilities attached to them. This raises the question of the strength of a conclusion, but without imposing a particular semantics, no general solution is possible. The paper discusses several possible semantics by looking at it from the perspective of probabilistic argumentation.
This paper presents the progicnet programme. It proposes a general framework for probabilistic logic that can guide inference based on both logical and probabilistic input. After an introduction to the framework as such, it is illustrated by means of a toy example from psychometrics. It is shown that the framework can accommodate a number of approaches to probabilistic reasoning: Bayesian statistical inference, evidential probability, probabilistic argumentation, and objective Bayesianism. The framework thus provides insight into the relations between these approaches, it (...) illustrates how the results of different approaches can be combined, and it provides a basis for doing efficient inference in each of the approaches. (shrink)
This paper concerns exchangeable analogical predictions based on similarity relations between predicates, and deals with a restricted class of such relations. It describes a system of Carnapian λγ rules on underlying predicate families to model the analogical predictions for this restricted class. Instead of the usual axiomatic definition, the system is characterized with a Bayesian model that employs certain statistical hypotheses. Finally the paper argues that the Bayesian model can be generalized to cover cases outside the restricted class of similarity (...) relations. (shrink)
Susan Okin read Robert Nozick as taking it to be fundamental to his Libertarianism that people own themselves, and that they can acquire entitlement to other things by making them. But she thinks that, since mothers make people, all people must then be owned by their mothers, a consequence Okin finds absurd. She sees no way for Nozick to make a principled exception to the idea that people own what they make when what they make is people, concluding that Nozick’s (...) theory of entitlement must be false, and that entitlement must instead be rooted in people’s needs. I say Okin misreads Nozick’s Libertarianism. In fact, its fundamental principle is that, simply by being persons, people are entitled to the maximum negative liberty compatible with a like liberty for all persons. Further, Nozick, and Jan Narveson, who has taken on the advocacy of Libertarian ideas, analyze liberty as freedom to interact with things, and analyze being entitled to or having property in something, as freedom to interact with it, to determine what may be done with it. People therefore have such freedom to do what they want with themselves, and such freedom to do what they want with other things, as is compatible with all persons having similar freedom. The former is what self-ownership amounts to, the latter, ownership of other things. Libertarianism’s fundamental principle therefore both grounds and delimits entitlements in ways entailing that mothers don’t own persons by dint of making them. Otherwise, since it would then be the prerogative of mothers to determine what shall be done with the persons they made, the persons made would lack equal liberty, this violating the fundamental principle. (shrink)
This is a review of Quantifiers, Logic, and Language, edited by Jaap van der Does and Jan van Eijk, published by CSLI (Center for the Study of Language and Information) Publications in 1996.
By his critical reflections on the crisis of modern civilization, Jan Patočka, phenomenologist of the Other Europe, incarnates the critical consciousness of the phenomenological movement. He was in fact one of the first European philosophers to have emphasized the necessity of abandoning the hitherto Eurocentric propositions of solution to the crisis when he explicitly raised the problems of a “Post-European humanity”. In advocating an understanding of the history of European humanity different from those of Husserl and Heidegger, Patočka directs his (...) philosophical reflections back to sketch a more profound phenomenology of the natural world insufficiently thematized in Husserl and absent in Heidegger’s Sein und Zeit. By virtue of its emphasis on the structural characteristics of movement, of praxis, and of the disclosure of the abyssal nature of human existence and of the original nothingness as the (non-)foundation of the phenomenal world, Patočka’s phenomenology of the natural world constitutes an opening towards the reception of Others and other cultures, in particular that of Chinese Taoist philosophy. (shrink)
Organized around the central concept of struggle, this paper is an introduction to the later thought of the Czech phenomenologist Jan Patočka (1907–1977), with attention to the circumstances of his life. The first section of the paper presents Patočka’s description of the “three movements” of human existence, with emphasis upon the second, the movement of defense, work, and survival. The second section examines his later conception of philosophy, where he reprised elements of classical Greek thought (the Heraclitean notion of polemos (...) and the Socratic notion of “care of the soul”) for their relevance in the modern world. (shrink)
As regular readers of The Pluralist are aware, there appeared in 2008 an issue devoted to Jan Olof Bengtsson's The Worldview of Personalism.1 The issue included five articles, each concerned with a different aspect of the book; and after each article, there was a "Reply" by Bengtsson. In what follows, I shall say something about Bengtsson's reply to my own contribution, "Absolute and Personal Idealism." However, first let me briefly describe that article's argument.In "Absolute and Personal Idealism," I examined the (...) personalist attack on absolutism as formulated by Andrew Seth Pringle-Pattison in two works: Hegelianism and Personality and The Idea of God in the Light of Recent Philosophy. In the first section of .. (shrink)
This paper presents a short biography of Jan Patočka, as well as biographical data of the author in connection to the life and work of Jan Patočka. The paper describes Patočka’s academic activity at Charles University between 1968 and 1972, how he continued by giving private underground seminars in the dark years of 1972 to 1976, and how his engagement culminated in the dissident movement Charter 77. The author explains how the unofficial underground Patočka Archive was established on the very (...) day of Patočka’s death, even before the terrible events around his funeral. Before the official Patočka Archive was founded on the 1st of January, 1990, many volumes of his works were edited secretly during the period of 1977 to 1989. This made it possible to continue successfully publishing the series of the Complete Works of Jan Patočka after 1990. (shrink)
The aim of the present study is (1) to show, on the basis of a number of unpublished documents, how Heinrich Scholz supported his Warsaw colleague Jan ?ukasiewicz, the Polish logician, during World War II, and (2) to discuss the efforts he made in order to enable Jan ?ukasiewicz and his wife Regina to move from Warsaw to Münster under life-threatening circumstances. In the first section, we explain how Scholz provided financial help to ?ukasiewicz, and we also adduce evidence of (...) the risks incurred by German scholars who offered assistance to their Polish colleagues. In the second section, we discuss the dramatic circumstances surrounding the ?ukasiewiczes' move to Münster in the summer of 1944. (shrink)
Common Sense and Logic in Jan Smedslund's 'Psycho-logic'. This paper is about the efforts the norwegian psychologist Jan Smedslund made in analyzing and checking philosophically his theory called 'Psycho-logic'. I am going to reconstruct and discuss the debates between Smedslund and several critics, which have been going on since about 1978, mainly in the "Scandinavian Journal of Psychology". A result will be that the kind of modal logics Smedslund uses - a type with realistic semantics and epistemology - is not (...) the proper one for the analysis of 'Psycho-logic'. (shrink)
In this article the author attempts to establish whether we can find a “theory of appearance” in the philosophy of Jan Patočka. The “appearance” for Patočka is basically composed of two elements. First there is a “primeval movement” which accounts for an infinite possibility of phenomena. The second element is the relation of this movement with an “addressee”, the subjectivity. If we begin to analyse the unity of these two elements we fundamentally come across three problems: what is it that (...) appears, when appearance presupposes a certain totality of appearance; how does this total appearance come forth; and, finally, is this whole “structure of appearance” taken as a free movement, kept once and for all within the boundaries of phenomenology, which is founded on a precise and positive term of “appearance” — or do we have to stipulate a special “experience” as the starting point of a phenomenology, which accepts the abyssal impossibility to control its frame? (shrink)
Terminal kidney patients are faced with lower quality of life, restricted diets and higher morbidity and mortality rates while waiting for deceased donor kidney transplantation. Fortunately, living kidney donation has proven to be a better treatment alternative (e.g. in terms of waiting time and graft survival rates). We observed an inequality in the number of living kidney transplantations performed between the non-European and the European patients in our center. Such inequality has been also observed elsewhere in this field and it (...) has been suggested that this inequality relates to, among other things, attitude differences towards donation based on religious beliefs. In this qualitative research we investigated whether religion might indeed (partly) be the explanation of the inequalities in living donor kidney transplants (LDKT) among non-European patients. Fifty patients participated in focus group discussions and in-depth interviews. The interviews were conducted following the focus group method and analyzed in line with Grounded Theory. The qualitative data analyses were performed in Atlas.ti. We found that religion is not perceived as an obstacle to living donation and that religion actually promotes helping and saving the life of a person. Issues such as integrity of the body were not seen as barriers to LDKT. We observed also that there are still uncertainties and a lack of awareness about the position of religion regarding living organ donation within communities, confusion due to varying interpretations of Holy Scriptures and misconceptions regarding the process of donation. Faith leaders play an important educational role and their opinion is influential. This study has identified modifiable factors which may contribute to the ethnic disparity in our living donation program. We argue that we need to strive for more clarity and awareness regarding the stance of religion on the issue of living donation in the local community. Faith leaders could be key figures in increasing awareness and alleviating uncertainty regarding living donation and transplantation. (shrink)