Boris Kment takes a new approach to the study of modality that emphasises the origin of modal notions in everyday thought. He argues that the concepts of necessity and possibility originate in counterfactual reasoning, which allows us to investigate explanatory connections. Contrary to accepted views, explanation is more fundamental than modality.

The Repugnant Conclusion served an important purpose in catalyzing and inspiring the pioneering stage of population ethics research. We believe, however, that the Repugnant Conclusion now receives too much focus. Avoiding the Repugnant Conclusion should no longer be the central goal driving population ethics research, despite its importance to the fundamental accomplishments of the existing literature.

This paper analyzes the historical context and systematic importance of Kant's hypothetical use of reason. It does so by investigating the role of hypotheses in Kant's philosophy of science. We first situate Kant’s account of hypotheses in the context of eighteenth-century German philosophy of science, focusing on the works of Wolff, Meier, and Crusius. We contrast different conceptions of hypotheses of these authors and elucidate the different theories of probability informing them. We then adopt a more systematic perspective to discuss (...) Kant's idea that scientific hypotheses must articulate real possibilities. We argue that Kant's views on the intelligibility of scientific hypotheses constitute a valuable perspective on scientific understanding and the constraints it imposes on scientific rationality. (shrink)

In this handbook, I put into practice my philosophical views on children's mathematics. The handbook contains brief instructions and examples of mathematical activities. In the INSTRUCTIONS section, instructions are given on how, and in part why that way, to help preschool children in their mathematical development. In the ACTIVITIES section, there are examples of activities through which the child develops her mathematical abilities.

Evidential decision theory (EDT) says that the choiceworthiness of an option depends on its evidential connections to possible outcomes. Causal decision theory (CDT) holds that it depends on your beliefs about its causal connections. While Newcomb cases support CDT, Arif Ahmed has described examples that support EDT. A new account is needed to get all cases right. I argue that an option A's choiceworthiness is determined by the probability that a good outcome ensues at possible A‐worlds that match actuality in (...) the facts causally unaffected by your decision (the “unaffected facts”). Moreover, you should evaluate A on the assumption that A is compossible with the unaffected facts. This view entails that you should use EDT when evaluating A on the assumption that the unaffected facts determine your action, but use CDT when assessing A on the opposite assumption. A's choiceworthiness equals a weighted average of these conditional assessments. The weights are determined by your beliefs about whether the unaffected fact determine your action. This account gets both Newcomb and Ahmed cases right. According to an influential view, whether you take the unaffected facts to determine your action can make a difference to whether you can regard yourself as free and the action as being under your control. While my account is neutral on this issue, it entails that whether you take the unaffected facts to determine your action is important in a different way: it matters to whether you should follow EDT or CDT. (shrink)

It is often claimed that the greatest value of the Bayesian framework in cognitive science consists in its unifying power. Several Bayesian cognitive scientists assume that unification is obviously linked to explanatory power. But this link is not obvious, as unification in science is a heterogeneous notion, which may have little to do with explanation. While a crucial feature of most adequate explanations in cognitive science is that they reveal aspects of the causal mechanism that produces the phenomenon to be (...) explained, the kind of unification afforded by the Bayesian framework to cognitive science does not necessarily reveal aspects of a mechanism. Bayesian unification, nonetheless, can place fruitful constraints on causal–mechanical explanation. 1 Introduction2 What a Great Many Phenomena Bayesian Decision Theory Can Model3 The Case of Information Integration4 How Do Bayesian Models Unify?5 Bayesian Unification: What Constraints Are There on Mechanistic Explanation?5.1 Unification constrains mechanism discovery5.2 Unification constrains the identification of relevant mechanistic factors5.3 Unification constrains confirmation of competitive mechanistic models6 ConclusionAppendix. (shrink)

In this article, logical concepts are defined using the internal syntactic and semantic structure of language. For a first-order language, it has been shown that its logical constants are connectives and a certain type of quantifiers for which the universal and existential quantifiers form a functionally complete set of quantifiers. Neither equality nor cardinal quantifiers belong to the logical constants of a first-order language.

On the received view, counterfactuals are analysed using the concept of closeness between possible worlds: the counterfactual 'If it had been the case that p, then it would have been the case that q' is true at a world w just in case q is true at all the possible p-worlds closest to w. The degree of closeness between two worlds is usually thought to be determined by weighting different respects of similarity between them. The question I consider in the (...) paper is which weights attach to different respects of similarity. I start by considering Lewis's answer to the question and argue against it by presenting several counterexamples. I use the same examples to motivate a general principle about closeness: if a fact obtains in both of two worlds, then this similarity is relevant to the closeness between them if and only if the fact has the same explanation in the two worlds. I use this principle and some ideas of Lewis's to formulate a general account of counterfactuals, and I argue that this account can explain the asymmetry of counterfactual dependence. The paper concludes with a discussion of some examples that cannot be accommodated by the present version of the account and therefore necessitate further work on the details. (shrink)

During the last quarter of a century, a number of philosophers have become attracted to the idea that necessity can be analyzed in terms of a hyperintensional notion of essence. One challenge for proponents of this view is to give a plausible explanation of our modal knowledge. The goal of this paper is to develop a strategy for meeting this challenge. My approach rests on an account of modality that I developed in previous work, and which analyzes modal properties in (...) terms of the notion of a metaphysical law. I discuss what information about the metaphysical laws is required for modal knowledge. Moreover, I describe two ways in which we might be able to acquire this information. The first way employs inference to the best explanation. The metaphysical laws, including the essential truths, play a crucial role in causal and grounding explanations and we can gain knowledge of these laws by abductive inferences from facts of which we have perceptual or a priori knowledge. The second way of gaining information about the metaphysical laws rests on knowledge that is partly constitutive of competence with the concepts that are needed to express the relevant information. Finally, I consider how knowledge of the metaphysical laws can be used to establish modal claims, paying special attention to the much-discussed connection between conceiving and possibility. (shrink)

Many philosophers have argued that statistical evidence regarding group characteristics (particularly stereotypical ones) can create normative conflicts between the requirements of epistemic rationality and our moral obligations to each other. In a recent article, Johnson-King and Babic argue that such conflicts can usually be avoided: what ordinary morality requires, they argue, epistemic rationality permits. In this article, we show that as data get large, Johnson-King and Babic’s approach becomes less plausible. More constructively, we build on their project and develop a (...) generalized model of reasoning about stereotypes under which one can indeed avoid normative conflicts, even in a big data world, when data contain some noise. In doing so, we also articulate a general approach to rational belief updating for noisy data. (shrink)

Approximate coherentism suggests that imperfectly rational agents should hold approximately coherent credences. This norm is intended as a generalization of ordinary coherence. I argue that it may be unable to play this role by considering its application under learning experiences. While it is unclear how imperfect agents should revise their beliefs, I suggest a plausible route is through Bayesian updating. However, Bayesian updating can take an incoherent agent from relatively more coherent credences to relatively less coherent credences, depending on the (...) data observed. Thus, comparative rationality judgments among incoherent agents are unduly sensitive to luck. (shrink)

This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counterarguments for various proposed solutions (“the revenge of the Liar”). This solution complements the classical procedure of determining the truth values of sentences by its own failure and, when the procedure fails, through an appropriate semantic shift allows us to express the failure in a classical two-valued language. (...) Formally speaking, the solution is a language with one meaning of symbols and two valuations of the truth values of sentences. The primary valuation is a classical valuation that is partial in the presence of the truth predicate. It enables us to determine the classical truth value of a sentence or leads to the failure of that determination. The language with the primary valuation is precisely the largest intrinsic fixed point of the strong Kleene three-valued semantics (LIFPSK3). The semantic shift that allows us to express the failure of the primary valuation is precisely the classical closure of LIFPSK3: it extends LIFPSK3 to a classical language in parts where LIFPSK3 is undetermined. Thus, this article provides an argumentation, which has not been present in contemporary debates so far, for the choice of LIFPSK3 and its classical closure as the right model for the truth predicate. In the end, an erroneous critique of Kripke-Feferman axiomatic theory of truth, which is present in contemporary literature, is pointed out. (shrink)

While there are satisfactory answers to the question “How should we teach children mathematics?”, there are no satisfactory answers to the question “What mathematics should we teach children?”. This paper provides an answer to the last question for preschool children (early childhood), although the answer is also applicable to older children. This answer, together with an appropriate methodology on how to teach mathematics, gives a clear conception of the place of mathematics in the children’s world and our role in helping (...) children develop their mathematical abilities. Briefly, children’s mathematics consists of the world of children’s internal activities that they eventually purposefully organize in order to understand and control the outside world and organize their overall activities in it. We need to support a child in mathematical activities that she does spontaneously and in which she shows interest, and we need to teach her mathematics that she is interested in developing through these activities. In doing so, we must be fully aware that the child’s mathematics is part of the child’s world of internal activities and is not outside of it. We help the child develop mathematical abilities by developing them in the context of her world and not outside of it. From the point of view of this conception, the standards established today are limiting and too focused on numbers and geometric figures: these topics are too prominent and elaborated, and other mathematical contents are subordinated to them. Adhering to the standards, we drastically limit the mathematics of the child’s world, hamper the correct mathematical development of a child, and we can turn her away from mathematics. (shrink)

Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial interpretation of the corresponding language. It follows from the analysis that (i) mathematical objects do not exist in the external world: they are our internally imagined objects, some of which, at least approximately, we can realize or represent; (ii) mathematical truths are not (...) truths about the external world but specifications (formulations) of mathematical conceptions; (iii) mathematics is first and foremost our imagined tool by which, with certain assumptions about its applicability, we explore nature and synthesize our rational cognition of it. (shrink)

Aristotle’s aitiai are middle terms in Aristotelian syllogisms. I argue that stating the aitia of a thing therefore amounts to re-describing this same thing in an alternative and illuminating way. This, in turn, means that a thing and its aitiai really are one and the same thing under different descriptions. The purpose of this paper is to show that this view is implied by Aristotle’s account of explanation, and that it makes more sense than one might expect.

The Russell-Myhill paradox puts pressure on the Russellian structured view of propositions by showing that it conflicts with certain prima facie attractive ontological and logical principles. I describe several versions of RMP and argue that structurists can appeal to natural assumptions about metaphysical grounding to provide independent reasons for rejecting the ontological principles used in these paradoxes. It remains a task for future work to extend this grounding-based approach to all variants of RMP.

In this article, modern standards of early years mathematics education are criticized and a proposal for change is presented. Today's early years mathematics education standards rest on a view of mathematics that became obsolete already at the end of the 19th century while the spirit of children's mathematics is precisely the spirit of modern mathematics. The proposal for change is not a return to the “new mathematics” movement, but something different.

In this essay I defend the claim that the life of a living being is not one of its properties but something different: a mode of being. It follows from this that living beings should not be taken to be things that possess the property of being alive. Second, I argue that living beings are essentially involved in ongoing activities as long as they exist. Life cannot only be a disposition to be active, but must itself be an ongoing activity. (...) Third, I suggest that for something to be a living being is to engage in activities whose success is determined by criteria that emerge exclusively from a proper account of the nature of the living being in question. To identify something as a living being is not to attribute a particular property to it, but to say what criteria apply to what it actually is or does. (shrink)

Will it rain tomorrow? Will there be a sea battle tomorrow? Will my death be painful? Wondering about the future plays a central role in our cognitive lives. It is integral to our inquiries, our planning, our hopes, and our fears. The aim of this paper is to consider various accounts of future contingents and the implications that they have for wondering about the future. I argue that reflecting on the nature of wondering about the future supports an Ockhamist account (...) of future contingents according to which many of them are true. Alternative accounts which maintain that no future contingents are true, either by claiming that they are all false or by claiming that they are neither true nor false, face difficulties concerning why it is appropriate to wonder about them. Reflecting on wondering in general, and wondering about the future in particular, suggests that in wondering how the future will go, we implicitly assume that there is a determinate fact of the matter. After presenting an attractive account of interrogative attitudes that has been recently proposed by Jane Friedman and outlining some norms governing wondering, I argue that all accounts of future contingents except Ockhamism face difficulties concerning why it is appropriate to wonder about them. (shrink)

This chapter argues that the distinction between ambitious and modest transcendental arguments, developed and deployed by various authors in the wake of Stroud’s influential critique of transcendental reasoning, may be pointless when applied to transcendental arguments from performative inconsistency that have moral statements as their conclusions. If moral truth is assertorically constrained, then any modest moral transcendental argument from performative inconsistency can be converted into an ambitious moral transcendental argument. The chapter provides an account of performative inconsistency and suggests an (...) alternative to the widespread reading of transcendental conditionals in terms of an ‘if-then’-sentences whose antecedents express a proposition to the effect that some x is possible and whose consequents express a statement to the effect that some y is actual. (shrink)

I suggest a way of extending Stalnaker’s account of assertion to allow for centered content. In formulating his account, Stalnaker takes the content of assertion to be uncentered propositions: entities that are evaluated for truth at a possible world. I argue that the content of assertion is sometimes centered: the content is evaluated for truth at something within a possible world. I consider Andy Egan’s proposal for extending Stalnaker’s account to allow for assertions with centered content. I argue that Egan’s (...) account does not succeed. Instead, I propose an account on which the contents of assertion are identified with sets of multi-centered worlds. I argue that such a view not only provides a plausible account of how assertions can have centered content, but also preserves Stalnaker’s original insight that successful assertion involves the reduction of shared possibilities. (shrink)

A commonly held idea regarding the nature of time is that the future is open and the past is fixed or closed. This article investigates the notion that there is an asymmetry in openness between the past and the future. The following questions are considered: How exactly is this asymmetry in openness to be understood? What is the relation between an open future and various ontological views about the future? Is an open future a branching future? What is the relation (...) between an open future and the question of whether contingent statements about the future are true or false? Is an open future compatible with a single determinate future? (shrink)

Eric Watkins argues that according to Kant, causation is not a relation between two events, but a relation between the “causality” of a substance and an event. It is shown that his arguments are partly based on a confusion between causation and interaction. Further, Watkins claims that for Kant, causes cannot be temporally determined. If this were true, it would follow that there can be no causal chains, and that all factors that determine the time when an effect occurs do (...) not belong to its cause. However, it is not true. In order to understand Kant, one must distinguish between causation, action, and interaction. When two substances interact, each of them does something (an event), which causes something to happen to the other one. (shrink)

The essential role of language in rational cognition is analysed. The approach is functional: only the results of the connection between language, reality, and thinking are considered. Scientific language is analysed as an extension and improvement of everyday language. The analysis gives a uniform view of language and rational cognition. The consequences for the nature of ontology, truth, logic, thinking, scientific theories, and mathematics are derived.

Much of the modern philosophy of causation has been governed by two ideas: (i) causes make their effects inevitable; (ii) a cause is something that makes a difference to whether its effect occurs. I focus on explaining the origin of idea (ii) and its connection to (i). On my view, the frequent attempts to turn (ii) into an analysis of causation are wrongheaded. Patterns of difference-making aren't what makes causal claims true. They merely provide a useful test for causal claims. (...) Moreover, what justifies us in using them as a test is idea (i). That's how (i) and (ii) are connected. (shrink)

There is currently disagreement about whether the phenomenon of first-person, or de se, thought motivates a move towards special kinds of contents. Some take the conclusion that traditional propositions are unable to serve as the content of de se belief to be old news, successfully argued for in a number of influential works several decades ago.1 Recently, some philosophers have challenged the view that there exist uniquely de se contents, claiming that most of the philosophical community has been under the (...) grip of an attractive but unmotivated myth.2 At the very least, this latter group has brought into question the arguments in favor of positing special kinds of content for de se belief; I think they have successfully shown that these arguments are not as conclusive, or fully articulated, as many have taken them to be. In this paper I will address these challenges directly and I will present and defend an argument for the conclusion that the phenomenon of de se thought does indeed motivate the move to a special kind of content, content that is uniquely de se. First, I characterize a notion of de se belief that is neutral with respect to friends and foes of uniquely de se content. I then argue for a determination thesis relating de se belief to belief content: that there is no difference in de se belief without a difference in belief content. I argue that various proposals for rejecting this determination thesis are unsuccessful. In the last part of the paper, I employ this determination thesis to argue for the existence of a type of belief content that is uniquely de se. (shrink)

In this article I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us, all directions are the same to us and all units of length we use to create geometric figures are the same to us. On the other hand, through the process of algebraic simplification, this system of axioms directly provides the Weyl’s (...) system of axioms for Euclidean geometry. The system of axioms, together with its a priori interpretation, offers new views to philosophy and pedagogy of mathematics: it supports the thesis that Euclidean geometry is a priori, it supports the thesis that in modern mathematics the Weyl’s system of axioms is dominant to the Euclid’s system because it reflects the a priori underlying symmetries, it gives a new and promising approach to learn geometry which, through the Weyl’s system of axioms, leads from the essential geometric symmetry principles of the mathematical nature directly to modern mathematics. (shrink)

Loss of self is widely regarded to be a consequence of dementia, and this perceived loss presents a variety of problems - not least because a clear understanding of the concept of self is elusive. This paper suggests a way to cut through problems that arise because we rely on conceptions of self in our understanding of the effects of dementia. It is proposed that we can avoid reliance on the concept of self through an approach based in in bio-phenomenology. (...) Such an approach would help us better understand the inner life of those with dementia and assist us to recognize that even in late stage dementia they are semiotic subjects with unique value. (shrink)

The sample space of the chance distribution at a given time is a class of possible worlds. Thanks to this connection between chance and modality, one’s views about modal space can have significant consequences in the theory of chance and can be evaluated in part by how plausible these implications are. I apply this methodology to evaluate certain forms of modal contingentism, the thesis that some facts about what is possible are contingent. Any modal contingentist view that meets certain conditions (...) that I specify generates difficulties in the philosophy of chance, including a problem usually associated with Humeanism that is known as ‘the problem of undermining futures’. I consider two well-known versions of modal contingentism that face this difficulty. The first version, proposed by Hugh Chandler and Nathan Salmon, rests on an argument for the claim that many individuals have their modal features contingently. The second version is motivated by the thesis that the existence of a possible world depends on the existence of the contingent individuals inhabiting it, and that many worlds are therefore contingent existents. (shrink)

Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical concepts -- logical constants, logical truths, and logical consequence -- are defined using the internal syntactic and semantic structure of language. For a first-order language, it has been shown that its logical constants are connectives and a certain type of quantifiers for which the universal and existential quantifiers form (...) a functionally complete set of quantifiers. Neither equality nor cardinal quantifiers belong to the logical constants of a first-order language. (shrink)

Many philosophers and non-philosophers who reflect on the causal antecedents of human action get the impression that no agent can have morally relevant freedom. Call this the ‘non-existence impression.’ The paper aims to understand the (often implicit) reasoning underlying this impression. On the most popular reconstructions, the reasoning relies on the assumption that either an action is the outcome of a chance process, or it is determined by factors that are beyond the agent’s control or which she did not bring (...) about. I argue that arguments based on this premise fail to apply to some possible agents for whom the non-existence impression arises. On the alternative reconstruction I offer, the impression rests on the assumption that free will requires being involved in the ultimate explanation of one’s actions in a novel sense in which nothing can be involved in the ultimate explanation of anything. (shrink)

This entry sketches the theory of personal identity that has come to be known as animalism. Animalism’s hallmark claim is that each of us is identical with a human animal. Moreover, animalists typically claim that we could not exist except as animals, and that the (biological) conditions of our persistence derive from our status as animals. Prominent advocates of this view include Michael Ayers, Eric Olson, Paul Snowdon, Peter van Inwagen, and David Wiggins.

Non è un caso che l’enhancement umano, cioè il potenziamento di capacità fisiche, cognitive ed emotive degli esseri umani con l’ausilio di tecnologie, sia diventato un tema centrale nei dibattiti etico-applicativi e nei tentativi contemporanei di arrivare a una comprensione più adeguata della natura umana. In esso si incontrano quesiti decisamente ricchi e complessi, sia dal punto di vista tecnoscientifico e medico sia da quello filosofico – e lo fanno in un modo che ci permette di vedere questi quesiti sotto (...) una nuova luce. Il numero raccoglie alcune voci italiane, tedesche, inglesi e statunitensi su diversi aspetti della problematica dell’enhancement umano. Tra le tematiche discusse troviamo il potenziamento genetico, le dimensioni etiche dell’enhancement, la relazione uomo-tecnologia, il cosiddetto enhancement morale, la relazione tra enhancement ed eugenetica, la distinzione tra potenziamento e terapia e la rilevanza delle neuroscienze per lo sviluppo futuro delle bio-tecnologie, della medicina e dell’etica. (shrink)

Since the 1860s, petroleum companies, through their influence on local governments, port authorities, international actors and the general public gradually became more dominant in shaping the urban form of ports and cities. Under their development and pressure, the relationships between industrial and urban areas in port cities hosting oil facilities evolved in time. The borders limiting industrial and housing territories have continuously changed with industrial places moving progressively away from urban areas. Such a changing dynamic influenced the permeability of these (...) borders. Port cities are nodes and logistic points where various flows of commodities, wealth, and knowledge gathered before further re‐distribution. These flows affected port cities by changing their spatial organization and the availabiity of space between borders. The main question here is: How did industrial and urban borders evolve through time in port cities? Through a historical analysis, the article explores the settlements of oil facilities and the influence of oil companies over local, regional, and national governments in creating borders and how it influenced the porosity of port cities. This article, through the petroleum narrative, illustrates the impacts of past borders on the contemporary urban form through the evolution of the French port city of Dunkirk, in the North of France. As a historical study, the article analyzes the changing relationships between petroleum industrial sites and housing areas in the city of Dunkirk, using aerial pictures, archival sources, and regulations of different periods. The importance of this analysis lies in knowing that former oil sites previously located on the periphery of Dunkirk, that were forgotten by the authorities are now located within the current urban tissue. This process demonstrates the importance of historical developments to understand current challenges in the urban planning of industrial port cities. (shrink)

In recent years the term ‘recognition’ has been used in ever more variegated theoretical contexts. This article contributes to the discussion of how the concept(s) expressed by this term in different debates should be explicated and understood. For the most part it takes the concept itself as its topic rather than making theoretical use of it. Drawing on important work by Ikäheimo and Laitinen and taking Honneth’s tripartite distinction of recognition into love, respect, and esteem as a starting point it (...) introduces the conceptual distinction between recognitive attitudes, recognitive relations, and recognitive acts, discusses Brandom’s attempt at explaining self-consciousness in terms of reflexive recognition mediated by intersubjective recognitive relations and suggests some critical points on how Butler puts the concept of recognition to work in her conception of ethics. (shrink)

Wenn Tugenden Praxisformen sind, dann kann man einiges über Praxisformen lernen, indem man nachsieht, was Tugenden sind. Ich werde dies im Folgenden partiell und indirekt tun, indem ich die sprachliche Form untersuche, in der Aristoteles die ethischen Tugenden beschreibt. Er tut dies im Wesentlichen dadurch, dass er den derart Tugendhaften in der dritten Person Singular beschreibt. Dann werde ich kurz auf die Grenzen von Aristoteles’ Verfahren zu sprechen kommen, indem ich auf eine den Tugenden und anderen Praxisformen inhärente Pluralität hinweise. (...) Eine vergleichbare Untersuchung der sprachlichen Form in der Nikomachischen Ethik ist mir nicht bekannt; die Hinweise auf die Pluralität der Tugend dagegen beanspruchen keine besondere Originalität. (shrink)

The concept of inertial frame of reference in classical physics and special theory of relativity is analysed. It has been shown that this fundamental concept of physics is not clear enough. A definition of inertial frame of reference is proposed which expresses its key inherent property. The definition is operational and powerful. Many other properties of inertial frames follow from the definition, or it makes them plausible. In particular, the definition shows why physical laws obey space and time symmetries and (...) the principle of relativity, it resolves the problem of clock synchronization and the role of light in it, as well as the problem of the geometry of inertial frames. (shrink)

De se attitudes seem to play a special role in action and cognition. This raises a challenge to the traditional way in which mental attitudes have been understood. In this chapter, we review the case for thinking that de se attitudes require special theoretical treatment and discuss various ways in which the traditional theory can be modified to accommodate de se attitudes.

According to Cantor (Mathematische Annalen 21:545–586, 1883 ; Cantor’s letter to Dedekind, 1899 ) a set is any multitude which can be thought of as one (“jedes Viele, welches sich als Eines denken läßt”) without contradiction—a consistent multitude. Other multitudes are inconsistent or paradoxical. Set theoretical paradoxes have common root—lack of understanding why some multitudes are not sets. Why some multitudes of objects of thought cannot themselves be objects of thought? Moreover, it is a logical truth that such multitudes do (...) exist. However we do not understand this logical truth so well as we understand, for example, the logical truth $${\forall x \, x = x}$$ . In this paper we formulate a logical truth which we call the productivity principle. Rusell (Proc Lond Math Soc 4(2):29–53, 1906 ) was the first one to formulate this principle, but in a restricted form and with a different purpose. The principle explicates a logical mechanism that lies behind paradoxical multitudes, and is understandable as well as any simple logical truth. However, it does not explain the concept of set. It only sets logical bounds of the concept within the framework of the classical two valued $${\in}$$ -language. The principle behaves as a logical regulator of any theory we formulate to explain and describe sets. It provides tools to identify paradoxical classes inside the theory. We show how the known paradoxical classes follow from the productivity principle and how the principle gives us a uniform way to generate new paradoxical classes. In the case of ZFC set theory the productivity principle shows that the limitation of size principles are of a restrictive nature and that they do not explain which classes are sets. The productivity principle, as a logical regulator, can have a definite heuristic role in the development of a consistent set theory. We sketch such a theory—the cumulative cardinal theory of sets. The theory is based on the idea of cardinality of collecting objects into sets. Its development is guided by means of the productivity principle in such a way that its consistency seems plausible. Moreover, the theory inherits good properties from cardinal conception and from cumulative conception of sets. Because of the cardinality principle it can easily justify the replacement axiom, and because of the cumulative property it can easily justify the power set axiom and the union axiom. It would be possible to prove that the cumulative cardinal theory of sets is equivalent to the Morse–Kelley set theory. In this way we provide a natural and plausibly consistent axiomatization for the Morse–Kelley set theory. (shrink)

A simple interpretation of quantity calculus is given. Quantities are described as two-place functions from objects, states or processes (or some combination of them) into numbers that satisfy the mutual measurability property. Quantity calculus is based on a notational simplification of the concept of quantity. A key element of the simplification is that we consider units to be intentionally unspecified numbers that are measures of exactly specified objects, states or processes. This interpretation of quantity calculus combines all the advantages of (...) calculating with numerical values (since the values of quantities are numbers, we can do with them everything we do with numbers) and all the advantages of calculating with standardly conceived quantities (calculus is invariant to the choice of units and has built-in dimensional analysis). This also shows that the standard metaphysics and mathematics of quantities and their magnitudes is not needed for quantity calculus. At the end of the article, arguments are given that the concept of quantity as defined here is a pivotal concept in understanding the quantitative approach to nature. As an application of this interpretation of quantity calculus, an easy proof of dimensional homogeneity of physical laws is given. (shrink)

This paper examines two contemporary answers to the question of whether moral values and norms are apt for rational criticism and justification: Richard Rorty’s radically contextualist approach—which is centered around the notion of contingency and is characterized by a dismissal of all claims to philosophical justification—and Karl-Otto Apel’s transcendental-pragmatic version of discourse ethics—which encompasses highly ambitious claims to justification and universal validity. Contrasting the key theses of Rorty’s contextualism with those of Apel’s universalist discourse ethics and reconstructing their respective conceptions (...) of moral progress we argue that neither Rorty’s nor Apel’s position is convincing. (shrink)

According to a standard interpretation of the term, ‘gender’ denotes sets of social roles and expectations conventionally associated with the sexual physiology of human beings. Originally introduced in psychology, the term is now widely used in the social sciences and humanities, as well as in the biological sciences. In this article we introduce and discuss the central themes of contemporary philosophical debates on gender. Particular attention is paid to recent feminist arguments concerning the distinction between sex and gender, and to (...) how feminist debates today intersect with neuroscience research on sex-related differences between human brains. (shrink)

In the article, an argument is given that Euclidean geometry is a priori in the same way that numbers are a priori, the result of modelling, not the world, but our activities in the world.

This paper reviews four leading strategies for addressing the problem of material constitution, along with some of the prominent objections faced by each approach. Sections include (1) "The Orthodox View: Coincident Objects," (2) "Dominant Kinds," (3) "Nihilism," (4) "Revising the Logic of Identity," and (5) "Future Research." Also included is an annotated bibliography.

On the basis of elementary thinking about language functioning, a solution of truth paradoxes is given and a corresponding semantics of a truth predicate is founded. It is shown that it is precisely the two-valued description of the maximal intrinsic fixed point of the strong Kleene three-valued semantics.

The concept of truth has many aims but only one source. The article describes the primary concept of truth, here called the synthetic concept of truth, according to which truth is the objective result of the synthesis of us and nature in the process of rational cognition. It is shown how various aspects of the concept of truth -- logical, scientific, and mathematical aspect -- arise from the synthetic concept of truth. Also, it is shown how the paradoxes of truth (...) arise. (shrink)

Alongside science and law, argumentation is also of central importance in everyday life. But what characterizes a good argument? This question has occupied philosophers and psychologists for centuries. The theory of Bayesian argumentation is particularly suitable for clarifying it, because it allows us to take into account in a natural way the role of uncertainty, which is central to much argumentation. Moreover, it offers the possibility of measuring the strength of an argument in probabilistic terms. One way to do this, (...) implicit in much work, is to identify the strength of an argument with the degree to which the premises of the argument confirm the conclusion. We criticize this prima facie plausible proposal and suggest instead that the strength of an argument has something to do with how much the premises and the conclusion of the argument cohere with each other. This leads to a new probabilistic measure whose properties we examine in more detail. (shrink)