The paper addresses Leon Hen.kin's proposition as a " lighthouse", which can elucidate a vast territory of knowledge uniformly: logic, set theory, information theory, and quantum mechanics: Two strategies to infinity are equally relevant for it is as universal and t hus complete as open and thus incomplete. Henkin's, Godel's, Robert Jeroslow's, and Hartley Rogers' proposition are reformulated so that both completeness and incompleteness to be unified and thus reduced as a joint property of infinity and of all infinite sets. (...) However, only Henkin's proposition equivalent to an internal position to infinity is consistent . This can be retraced back to set theory and its axioms, where that of choice is a key. Quantum mechanics is forced to introduce infinity implicitly by Hilbert space, on which is founded its formalism. One can demonstrate that some essential properties of quantum information, entanglement, and quantum computer originate directly from infinity once it is involved in quantum mechanics. Thus, these phenomena can be elucidated as both complete and incomplete, after which choice is the border between them. A special kind of invariance to the axiom of choice shared by quantum mechanics is discussed to be involved that border between the completeness and incompleteness of infinity in a consistent way. The so-called paradox of Albert Einstein, Boris Podolsky, and Nathan Rosen is interpreted entirely in the same terms only of set theory. Quantum computer can demonstrate especially clearly the privilege of the internal position, or " observer'' , or "user" to infinity implied by Henkin's proposition as the only consistent ones as to infinity. An essential area of contemporary knowledge may be synthesized from a single viewpoint. (shrink)

Two strategies to infinity are equally relevant for it is as universal and thus complete as open and thus incomplete. Quantum mechanics is forced to introduce infinity implicitly by Hilbert space, on which is founded its formalism. One can demonstrate that essential properties of quantum information, entanglement, and quantum computer originate directly from infinity once it is involved in quantum mechanics. Thus, thеse phenomena can be elucidated as both complete and incomplete, after which choice is the border between them. A (...) special kind of invariance to the axiom of choice shared by quantum mechanics is discussed to be involved that border between the completeness and incompleteness of infinity in a consistent way. The so-called paradox of Albert Einstein, Boris Podolsky, and Nathan Rosen is interpreted entirely in the same terms only of set theory. Quantum computer can demonstrate especially clearly the privilege of the internal position, or “observer”, or “user” to infinity implied by Henkin’s proposition as the only consistent ones as to infinity. (shrink)

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.

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)

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)

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)

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.

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)

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)

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 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)

From the comparison of time in inertial frames, possible types of transformations between inertial frames are deduced. This elementary deduction directly relates the properties of time with the type of transformations. When all inertial frames measure the same time (time is absolute), the transformations are Galilean. When each inertial frame has its own time, different from the times of other inertial frames (time is not invariant) the transformations are Lorentz-like with the same positive parameter k. The parameter k is the (...) supremum of possible velocities in an inertial frame, the same for all inertial frames. Einstein's postulate about the invariance of the speed of light says more: there is a uniform motion with the supremum k, which is exactly the motion of light. At the end of the article, attempts to reduce the special theory of relativity to the principle of relativity are criticized. (shrink)

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.

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)

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.

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)

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)

Contingentism is the view that it is possible for there to be contingent existents. Timothy Williamson has argued that contingentists cannot provide a satisfactory interpretation of the possible-world semantics for modal logic. This paper aims to provide such an interpretation on behalf of contingentists.

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)

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.

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)

An argument is given that Euclidean geometry is a priori in the same way that numbers are a priori, the result of modeling, not the world, but our activities in the world.

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.

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)

The distinction between teleology and teleonomy that biologists sometimes refer to seems to be helpful in certain contexts, but it is used in several different ways and has rarely been clearly drawn. This paper discusses three prominent uses of the term “teleonomy” and traces its history back to what seems to be its first use. This use is examined in detail and then justified and refined on the basis of elements found in the philosophy of Aristotle, Kant, Anscombe and others. (...) In the course of this explication, it will also be shown how the description of end-directed processes relates to their explanation. (shrink)

Die vorliegende Arbeit geht zunächst der Frage der Möglichkeit einer spezifischen, methodisch von den Naturwissenschaften unterschiedenen „Phänomenologie der Natur“ nach. Das Paradigma einer solchen Phänomenologie der Natur ist Goethes Farbenlehre, deren Methode über die Farberscheinungen hinaus Anwendungsmöglichkeiten auf neue Gegenstände eröffnet. Im Zusammenhang damit werden in der vorliegenden Arbeit die Ergebnisse eines philosophischen Versuchs vorgestellt, das Paradigma der Farbenlehre auf die Erscheinung Kraft zu übertragen. Die Anwendung des Paradigmas der Farbenlehre auf den Kraftbegriff ist möglich; das Ergebnis stellt bis in (...) die verwendete Terminologie hinein einen ähnlich deutlichen Kontrapunkt zur Physik dar wie die Inhalte der goetheschen Farbenlehre. Dadurch wird eine Lesart der Farbenlehre gestützt, nach welcher deren Anliegen methodisch und inhaltlich deutlich vom Anliegen der modernen Physik unterschieden werden muss; die Farbenlehre erschließt sich somit viel deutlicher durch Herausarbeiten und Rekonstruieren der Differenzen zwischen Phänomenologie und Physik als durch Postulieren vermeintlicher Schnittmengen. Als Ausblick ergibt sich ein über das philosophische Experiment hinausgehender und noch zu begründender Geltungsanspruch einer in der Tradition der Farbenlehre arbeitenden Naturphänomenologie, indem sie die allgemeinen Bedingungen eines erfahrbaren und vermittelbaren Wissenskorpus von Natur aufzeigen und damit einen grundlegenden Beitrag zur Erkenntniskritik liefern könnte; diese Reflexion ist jedoch zunächst noch ein Desideratum. (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)

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)

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.

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)

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)

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)

Descartes claims that God is a substance, and that mind and body are two different and separable substances. This paper provides some background that renders these claims intelligible. For Descartes, that something is real means it can exist in separation, and something is a substance if it does not depend on other substances for its existence. Further, separable objects are correlates of distinct ideas, for an idea is distinct (in an objective sense) if its object may be easily and clearly (...) separated from everything that is not its object. It follows that if our idea of God is our most distinct idea, as Descartes claims, then God must be a substance in the Cartesian sense of the term. Also, if we can have an idea of a thinking subject which does not in any sense refer to bodily things, and if bodily things are substances, then mind and body must be two different substances. (shrink)

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)

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)

Complex logic is a novel logical framework, which formalizes the semantics of the categories of matter, space, and time in a system of logic that operates with complex logical objects. A complex logical object represents a superposition of a logical statement and its logical negation positioning any statement co-relatively to its logical negation. In the system of logical notations, where S is a logical statement and Not S is its logical negation, complex logic includes co-relative logical positions of S and (...) Not S with the probabilities of their truth within the scale 0... 1, excluding the boundary values of 0 and 1, into a single logical superposition. Thus, the logical superposition, summing up the probabilistic positions of S and Not S, has an invariant truth value equal to 1. In this context, complex logic proves to be invariant to reality, offering a unified logical interpretation of reality, spanning from quantum to cosmological scales. By defining the nature of matter and reality as a complex two-format processual essence with corresponding logical consequences, complex logic enhances our concept and understanding of reality. (shrink)

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)

The sciences may be able to describe living beings, but this is not to account for their life. Life is not a describable property of things. There is also no philosophical a priori argument by which one could prove the existence of life – except perhaps our own. In order to understand what life is, we must start with our conception of that life that we know, human life, and reduce the notion of this life to a notion of mere (...) life. We may do this by introducing the following distinctions. Intentional movements may succeed, be interrupted, or be mistaken. In contrast, merely teleological movements can only succeed or be interrupted, but not mistaken. Further, intentional movements are executed as more or less suitable means for achieving an end. Merely teleological movements are not performed as means to ends in this sense, but that does not render them less goal-directed. (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)

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)

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)

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)

The thesis deals with the concept of truth and the paradoxes of truth. Philosophical theories usually consider the concept of truth from a wider perspective. They are concerned with questions such as - Is there any connection between the truth and the world? And, if there is - What is the nature of the connection? Contrary to these theories, this analysis is of a logical nature. It deals with the internal semantic structure of language, the mutual semantic connection of sentences, (...) above all the connection of sentences that speak about the truth of other sentences and sentences whose truth they speak about. Truth paradoxes show that there is a problem in our basic understanding of the language meaning and they are a test for any proposed solution. It is important to make a distinction between the normative and analytical aspect of the solution. The former tries to ensure that paradoxes will not emerge. The latter tries to explain paradoxes. Of course, the practical aspect of the solution is also important. It tries to ensure a good framework for logical foundations of knowledge, for related problems in Artificial Intelligence and for the analysis of the natural language. Tarski’s analysis emphasized the T-scheme as the basic intuitive principle for the concept of truth, but it also showed its inconsistency with the classical logic. Tarski’s solution is to preserve the classical logic and to restrict the scheme: we can talk about the truth of sentences of a language only inside another essentially richer metalanguage. This solution is in harmony with the idea of reflexivity of thinking and it has become very fertile for mathematics and science in general. But it has normative nature | truth paradoxes are avoided in a way that in such frame we cannot even express paradoxical sentences. It is also too restrictive because, for the same reason we cannot express a situation in which there is a circular reference of some sentences to other sentences, no matter how common and harmless such a situation may be. Kripke showed that there is no natural restriction to the T-scheme and we have to accept it. But then we must also accept the riskiness of sentences | the possibility that under some circumstances a sentence does not have the classical truth value but it is undetermined. This leads to languages with three-valued semantics. Kripke did not give any definite model, but he gave a theoretical frame for investigations of various models | each fixed point in each three-valued semantics can be a model for the concept of truth. The solutions also have normative nature | we can express the paradoxical sentences, but we escape a contradiction by declaring them undetermined. Such a solution could become an analytical solution only if we provide the analysis that would show in a substantial way that it is the solution that models the concept of truth. Kripke took some steps in the direction of finding an analytical solution. He preferred the strong Kleene three-valued semantics for which he wrote it was "appropriate" but did not explain why it was appropriate. One reason for such a choice is probably that Kripke finds paradoxical sentences meaningful. This eliminates the weak Kleene three valued semantics which corresponds to the idea that paradoxical sentences are meaningless, and thus indeterminate. Another reason could be that the strong Kleene three valued semantics has the so-called investigative interpretation. According to this interpretation, this semantics corresponds to the classical determination of truth, whereby all sentences that do not have an already determined value are temporarily considered indeterminate. When we determine the truth value of these sentences, then we can also determine the truth value of the sentences that are composed of them. Kripke supplemented this investigative interpretation with an intuition about learning the concept of truth. That intuition deals with how we can teach someone who is a competent user of an initial language (without the predicate of truth T) to use sentences that contain the predicate T. That person knows which sentences of the initial language are true and which are not. We give her the rule to assign the T attribute to the former and deny that attribute to the latter. In that way, some new sentences that contain the predicate of truth, and which were indeterminate until then, become determinate. So the person gets a new set of true and false sentences with which he continues the procedure. This intuition leads directly to the smallest fixed point of strong Kleene semantics as an analytically acceptable model for the logical notion of truth. However, since this process is usually saturated only on some transfinite ordinal, this intuition, by climbing on ordinals, increasingly becomes a metaphor. This thesis is an attempt to give an analytical solution to truth paradoxes. It gives an analysis of why and how some sentences lack the classical truth value. The starting point is basic intuition according to which paradoxical sentences are meaningful (because we understand what they are talking about well, moreover we use it for determining their truth values), but they witness the failure of the classical procedure of determining their truth value in some "extreme" circumstances. Paradoxes emerge because the classical procedure of the truth value determination does not always give a classically supposed (and expected) answer. The analysis shows that such an assumption is an unjustified generalization from common situations to all situations. We can accept the classical procedure of the truth value determination and consequently the internal semantic structure of the language, but we must reject the universality of the exterior assumption of a successful ending of the procedure. The consciousness of this transforms paradoxes to normal situations inherent to the classical procedure. Some sentences, although meaningful, when we evaluate them according to the classical truth conditions, the classical conditions do not assign them a unique value. We can assign to them the third value, \undetermined", as a sign of definitive failure of the classical procedure. An analysis of the propagation of the failure in the structure of sentences gives exactly the strong Kleene three-valued semantics, not as an investigative procedure, as it occurs in Kripke, but as the classical truth determination procedure accompanied by the propagation of its own failure. An analysis of the circularities in the determination of the classical truth value gives the criterion of when the classical procedure succeeds and when it fails, when the sentences will have the classical truth value and when they will not. It turns out that the truth values of sentences thus obtained give exactly the largest intrinsic fixed point of the strong Kleene three-valued semantics. In that way, the argumentation is given for that choice among all fixed points of all monotone three-valued semantics for the model of the logical concept of truth. An immediate mathematical description of the fixed point is given, too. It has also been shown how this language can be semantically completed to the classical language which in many respects appears a natural completion of the process of thinking about the truth values of the sentences of a given language. Thus the final model is a language that has one interpretation and two systems of sentence truth evaluation, primary and final evaluation. The language through the symbol T speaks of its primary truth valuation, which is precisely the largest intrinsic fixed point of the strong Kleene three valued semantics. Its final truth valuation is the semantic completion of the first in such a way that all sentences that are not true in the primary valuation are false in the final valuation. (shrink)

In this chapter, we assess the current state-of-the-art of the Hungarian sharing economy sector relying on statistics, previous surveys, and expert interviews around case examples. Although we record a fast emergence of an increasing number and a widening variety of multinational and home-grown initiatives, we also contend that in Hungary, the innovation ecosystem of the collaborative economy is still relatively feeble. The linkages that are created through these initiatives are controversial sociologically. The main end-users are highly educated young urbanites. In (...) contrast, on the service provider front, the non-formal workforce is quite vulnerable as the current regulations hardly provide any protection to platform workers. The motivations of the key players in the sector are varied, as only a few locally based initiatives are transformative. In contrast, most examples are solely linked to finding new business opportunities in a shrinking economy. (shrink)