The mathematical structure of realist quantum theories has given rise to a debate about how our ordinary 3-dimensional space is related to the 3N-dimensional configuration space on which the wave function is defined. Which of the two spaces is our (more) fundamental physical space? I review the debate between 3N-Fundamentalists and 3D-Fundamentalists and evaluate it based on three criteria. I argue that when we consider which view leads to a deeper understanding of the physical world, especially given the deeper topological (...) explanation from the unordered configurations to the Symmetrization Postulate, we have strong reasons in favor of 3D-Fundamentalism. I conclude that our evidence favors the view that our fundamental physical space in a quantum world is 3-dimensional rather than 3N-dimensional. I outline lines of future research where the evidential balance can be restored or reversed. Finally, I draw lessons from this case study to the debate about theoretical equivalence. (shrink)

One of the most difficult problems in the foundations of physics is what gives rise to the arrow of time. Since the fundamental dynamical laws of physics are (essentially) symmetric in time, the explanation for time's arrow must come from elsewhere. A promising explanation introduces a special cosmological initial condition, now called the Past Hypothesis: the universe started in a low-entropy state. Unfortunately, in a universe where there are many copies of us (in the distant ''past'' or the distant ''future''), (...) the Past Hypothesis is not enough; we also need to postulate self-locating (de se) probabilities. However, I show that we can similarly use self-locating probabilities to strengthen its rival---the Fluctuation Hypothesis, leading to in-principle empirical underdetermination and radical epistemological skepticism. The underdetermination is robust in the sense that it is not resolved by the usual appeal to 'empirical coherence' or 'simplicity.' That is a serious problem for the vision of providing a completely scientific explanation of time's arrow. (shrink)

Gravity remains the most elusive field. Its relationship with the electromagnetic field is poorly understood. Relativity and quantum mechanics describe the aforementioned fields, respectively. Bosons and fermions are often credited with responsibility for the interactions of force and matter. It is shown here that fermions factually determine the gravitational structure of the universe, while bosons are responsible for the three established and described forces. Underlying the relationships of the gravitational and electromagnetic fields is a symmetrical probability distribution of fermions and (...) bosons. Werner Heisenberg's assertion that the Schr\'f6dinger wave function and Heisenberg matrices do not describe one thing is confirmed. It is asserted that the conscious observation of Schr\'f6dinger's wave function never causes its collapse, but invariably produces the classical space described by the Heisenberg picture. As a result, the Heisenberg picture can be explained and substantiated only in terms of conscious observation of the Schr\'f6dinger wave function. Schr\'f6dinger\'92s picture is defined as information space, while Heisenberg\'92s picture is defined as classical space. B-theory postulates that although the Schr\'f6dinger picture and the Heisenberg picture are mathematically connected, the former is eternal while the latter is discrete, existing only as the sequence of discrete conscious moments. Inferences related to information-based congruence between physical and mental phenomena have long been discussed in the literature. Moreover, John Wheeler suggested that information is fundamental to the physics of the universe. However, there is a great deal of uncertainty about how the physical and the mental complement each other. Bishop Berkeley and Ernst Mach, to name two who have addressed the subject, simply reject the concept of the material world altogether. Professor Hardy defined physical reality as 'dubious and elusive'. It is proposed in this paper that physical reality, or physical instantiation in the classical space as described by Heisenberg picture is one thing with the consciousness. (shrink)

Interreligious and intercultural dialogue is supposed to be the best way to solve the conflicts arising from rival religious hermeneutics and different modes to conceive the ideal of a good life in contemporary multicultural and pluralistic societies. In regard to communicative or dialogical reason, respectful coexistence can be reached only by argumentative communication between interested people. In this sense, only rational arguments, strong enough to pass the test of the shared rationality can be valid at a discursive level. However, Jewish (...) philosopher Emmanuel Levinas and Catholic theologian Johann Baptist Metz challenge the symmetrical and rational-based dialogue in order to postulate an asymmetrical relation by giving voice to the other. For them, the core of interreligious and intercultural engagement does not start from rational agreements as Habermas, for instance, has proposed; but from prophetic and anamnestic reasons. (shrink)

Metaphysical orthodoxy maintains that the relation of ontological dependence is irreflexive, asymmetric, and transitive. The goal of this paper is to challenge that orthodoxy by arguing that ontological dependence should be understood as non- symmetric, rather than asymmetric. If we give up the asymmetry of dependence, interesting things follow for what we can say about metaphysical explanation— particularly for the prospects of explanatory holism.

It is a metaphysical orthodoxy that interesting non-symmetric relations cannot be reduced to symmetric ones. This orthodoxy is wrong. I show this by exploring the expressive power of symmetric theories, i.e. theories which use only symmetric predicates. Such theories are powerful enough to raise the possibility of Pythagrapheanism, i.e. the possibility that the world is just a vast, unlabelled, undirected graph.

There are two ways to characterize symmetric relations. One is intensional: necessarily, _Rxy_ iff _Ryx_. In some discussions of relations, however, what is important is whether or not a relation gives rise to the same completion of a given type (fact, state of affairs, or proposition) for each of its possible applications to some fixed relata. Kit Fine calls relations that do ‘strictly symmetric’. Is there is a difference between the notions of necessary and strict symmetry that would prevent them (...) from being used interchangeably in such discussions? I show that there is. While the notions coincide assuming an intensional account of relations and their completions, according to which relations/completions are identical if they are necessarily coinstantiated/equivalent, they come apart assuming a hyperintensional account, which individuates relations and completions more finely on the basis of relations’ real definitions. I establish this by identifying two definable relations, each of which is necessarily symmetric but nonetheless results in distinct facts when it applies to the same objects in opposite orders. In each case, I argue that these facts are distinct because they have different grounds. (shrink)

McMahan’s own example of a symmetrical defense case, namely his tactical bomber example, opens the door wide open for soldiers to defend their fellow-citizens (on grounds of their special obligations towards them) even if as part of this defense they target non-liable soldiers. So the soldiers on both sides would be permitted to kill each other and, given how McMahan defines “justification,” they would also be justified in doing so and hence not be liable. Thus, we arrive, against McMahan’s intentions, (...) at a moral equality of combatants. In addition, his own account of liability cannot deal adequately with symmetrical defense cases in the first place. This undermines his presupposition that justification defeats liability, which is central to his defense of the moral inequality of combatants. I shall argue that McMahan’s attempts to counter these objections fail and that therefore his general claim of the moral inequality of combatants remains unpersuasive. (shrink)

Why must incompatibility be symmetric? An odd question, but recent work in the semantics of non-classical logic, which appeals to the notion of incompatibility as a primitive and defines negation in terms of it, has brought this question to the fore. Francesco Berto proposes such a semantics for negation argues that, since incompatibility must be symmetric, double negation introduction must be a law of negation. However, he offers no argument for the claim that incompatibility really must be symmetric. Here, I (...) provide such an argument, showing that, insofar as we think of incompatibility in normative pragmatic terms, it can play its basic pragmatic function only if it is symmetric. The upshot is that we can vindicate Berto’s claim about the symmetry of incompatibility but only if we, pace Berto, think about incompatibility, in the first instance, as a pragmatic relation between acts rather than a semantic relation between contents. (shrink)

Can an agent's intelligence level be negative? We extend the Legg-Hutter agent-environment framework to include punishments and argue for an affirmative answer to that question. We show that if the background encodings and Universal Turing Machine (UTM) admit certain Kolmogorov complexity symmetries, then the resulting Legg-Hutter intelligence measure is symmetric about the origin. In particular, this implies reward-ignoring agents have Legg-Hutter intelligence 0 according to such UTMs.

We extend Barbanera and Berardi's symmetric lambda calculus [2] to second-order classical propositional logic and prove its strong normalization.

Although convinced by Frankfurt-style cases that moral responsibility does not require the ability to do otherwise, semicompatibilists have not wanted to accept a parallel claim about moral responsibility for omissions, and so they have accepted asymmetrical requirements on moral responsibility for actions and omissions. In previous work, I have presented a challenge to various attempts at defending this asymmetry. My view is that semicompatibilists should give up these defenses and instead adopt symmetrical requirements on moral responsibility for actions and omissions, (...) and in this paper I highlight three advantages of doing so: first, it avoids a strange implication of the truth of determinism; second, it allows for a principled reply to Philip Swenson’s recent ‘No Principled Difference Argument’; third, it provides a reason to reject a crucial inference rule invoked by Peter van Inwagen’s ‘Direct Argument’ for the incompatibility of moral responsibility and determinism. (shrink)

In this paper I argue that Kant would have endorsed Clifford’s principle. The paper is divided into four sections. In the first, I review Kant’s argument for the practical postulates. In the second, I discuss a traditional objection to the style of argument Kant employs. In the third, I explain how Kant would respond to this objection and how this renders the practical postulates consistent with Clifford’s principle. In the fourth, I introduce positive grounds for thinking that Kant would have (...) endorsed this principle. (shrink)

This essay is titled "Critique the Postulation of the Historical Law Theory and relate it to African Law. The postulation of the historical law school that law emanates from customs through an ordered pattern of systematized progress into a codified system in relation to African law forms the crust of this essay. To achieve this task, this essay adopts a critical method in exposing c postulation of the historical law school and the African Law (keeping in mind the Ukelle communal (...) Law System). This essay questions whether there can be an independent law made or promulgated without targeting a given people or that there can be a people-free law? This essay claims that like the historical law school, laws emanate from their ground norms but insists that unlike the historical law school, laws in Ukelle Traditional System do not necessarily have to submit to through the rigor of systematic and strict evolutionary pattern of progress. Like Herder, this essay avers that there is a unique character with each culture, and as such Ukelle Traditional Law does not have to submit to any universal character of law. (shrink)

In the Critique of Practical Reason, Kant grounds his postulate for the immortality of the soul on the presupposed practical necessity of the will’s endless progress toward complete conformity with the moral law. Given the important role that this postulate plays in Kant’s ethical and political philosophy, it is hard to understand why it has received relatively little attention. It is even more surprising considering the attention given to his other postulates of practical reason: the existence of God (...) and freedom. The project of this paper is to examine Kant’s postulate of the immortality of the soul, examine critiques of this argument, and show why the argument succeeds in showing that belief in the moral law also obligates one to believe in the soul’s immortality. (shrink)

I summarize, in this informal interview, the main approaches to the ‘Past Hypothesis’, the postulation of a low-entropy initial state of the universe. I’ve chosen this as an open problem in the philosophical foundations of physics. I hope that this brief overview helps readers in gaining perspective and in appreciating the diverse range of approaches in this fascinating unresolved debate.

In this paper I trace the arc of Kant’s critical stance on the belief in God, beginning with the Critique of Pure Reason (1781) and culminating in the final chapter of the Metaphysics of Morals (1797). I argue that toward the end of his life, Kant changed his views on two important topics. First, despite his stinging criticism of it in the Critique of Pure Reason, by the time of the Metaphysics of Morals, Kant seems to endorse the physico-theological argument. (...) Second, some time around the publication of the Metaphysics of Morals, Kant seems to move away from the argument for the practical postulates. (shrink)

Moritz Geiger (1880–1937) in Phänomenologische Ästhetik paper postulates aesthetics to become an autonomous science. The new science is intended to analyze aesthetic values and to discover the rules of their regulations. It tends to be separated from aesthetics as the sub-discipline of philosophy (especially under the influence of metaphysics) and aesthetics as a field of applying other sciences (mainly psychology). It may be achieved by the usage of a phenomenological method.

I argue that, in the currently gender-unjust societies a basic income would not advance feminist goals. To assess the impact of a social policy on gender justice I propose the following criterion: a society is gender-just when the costs of engaging in a lifestyle characterized by gender-symmetry (in both the domestic and public spheres) are, for both men and women, smaller or equal to the costs of engaging in a gender-asymmetrical lifestyle. For a significant number of women, a basic income (...) would increase the costs of leading gender-symmetrical lifestyles because it would make it easier for both women and men to pursue gender-unjust preferences. I argue that preference satisfaction is distinct from justice. I conclude by showing why a basic income would lead to further privatisation of caregiving, and I outline the negative effects this would have on women. (shrink)

In the article, I consider seven metaphysical postulates that lie in the foundations of modern physics. These are postulates: about the nature of space-time, about the existence, about the direction of time, about the causality, about the elementary event, about the nature of information and about the immutability of laws. The directions of critical analysis and possible radical revision of these postulates are briefly presented. It is supposed that this revision can indirectly contribute to the development of a theory that (...) will be able to generalize quantum phenomena, gravity and the evolution of the universe. (shrink)

In this paper, we provide a detailed review of previous classifications of 2 × 2 games and suggest a mathematically simple way to classify the symmetric 2 × 2 games based on a decomposition of the payoff matrix into a cooperative and a zero-sum part. We argue that differences in the interaction between the parts is what makes games interesting in different ways. Our claim is supported by evolutionary computer experiments and findings in previous literature. In addition, we provide a (...) method for using a stereographic projection to create a compact 2-d representation of the game space. (shrink)

I present new counterexamples to the asymmetry of grounding: we have prima facie reason to think that some conditional probabilities partially ground their inverse conditional probabilities, and vice versa. These new counterexamples may require that we reject the asymmetry of grounding, or alternatively may require that we reject one or more of the assumptions which enable the counterexamples. Either way, by reflecting on these purported counterexamples to grounding asymmetry we learn something important, either about the formal properties of grounding, or (...) about the nature of probability. (shrink)

Electrical and electronic devices are constantly present in human lives, as providing communication, entertainment or transportation. Ever increasing use of power electronics equipment and communication equipment in everyday life is increasing electromagnetic pollution day by day. This pollution may degrade the performance of electronic and electrical equipment. Any RF radiation emitting devices emit Electro Magnetic (EM) radiation and without proper shielding, the radiation could be harmful to humans and other biological elements. Modernization in new generation of mobile telecommunication system, with (...) enhanced bandwidth and power, the biological effects of electromagnetic radiation from these gadgets is a real concern to many It is necessary that all electronics equipment or systems must be constructed to ensure that any electromagnetic disturbance it generates must be constructed with inherent level of immunity to externally generated Electromagnetic disturbances. These needs to design the equipment known as TEM cell with symmetric open structure geometry to limit the amount of unwanted radiation, the shielding of critical parts, making equipment less immune to external interference. (shrink)

Wenn überhaupt in einem Gebiet Wahrheit und Existenz unabhängig von unseren Erkenntnisfähigkeiten sind, dann in der Metaphysik – etwa bei der Frage, ob es Gott gibt oder eine Seele, die unseren Tod überdauert. Die metaphysica specialis schreit geradezu nach metaphysischem Realismus und dem zugehörigen Wahrheitsbegriff. Von diesem Ausgangspunkt gerät man allerdings schnell in Verlegenheit, wenn man fragt: Nach welchen Kriterien sollen wir uns richten, wenn wir uns über Gott oder Unsterblichkeit ein Urteil bilden wollen? Mit den Mitteln der Naturwissenschaft und (...) deren rationaler Methodologie (in der es um Empirie, Einfachheit, Sparsamkeit usw. geht) kommen wir bei Themen wie Gott oder Unsterblichkeit immer nur bis zum Patt. Genauso steht es bei der Frage, ob wir in unseren Entscheidungen frei sind. Urteilsenthaltung können wir uns nicht erlauben, dafür sind die metaphysischen Fragen zu wichtig; Auslosen kommt auch nicht infrage. Statt erkenntnistheoretisch zu kapitulieren, schlage ich programmatisch vor, die Erkenntnislehre auf weichere Weise weiterzubetreiben. Emotion, Intuition, Moral – das sind einige der zusätzlichen außerrationalen Hilfsmittel, mit deren Hilfe wir weiterkommen können. Ich zeige, dass diese Hilfsmittel respektabler und gewichtiger sind, als kühle, rationale Erkenntnistheoretiker zugeben wollen. Diese Hilfsmittel führen zu guten Postulaten aus Unvernunft (und zwar nicht nur in der Metaphysik). Wie schlimm es für den Realismus ist, dass diese Postulate immer noch falsch sein könnten, diese Frage werde ich im vorliegenden Aufsatz nicht mehr klären. (shrink)

This paper will annoy modern logicians who follow Bertrand Russell in taking pleasure in denigrating Aristotle for [allegedly] being ignorant of relational propositions. To be sure this paper does not clear Aristotle of the charge. On the contrary, it shows that such ignorance, which seems unforgivable in the current century, still dominated the thinking of one of the greatest modern logicians as late as 1831. Today it is difficult to accept the proposition that Aristotle was blind to the fact that, (...) for example, incommensurability is a relation and not a property: that the proposition “In every square, the diagonals are incommensurable with the sides” is relational and not categorical. This paper asks the reader to do something more difficult: to accept the proposition that as late as 1831 De Morgan was blind to the same fact. This paper shows conclusively that in 1831, De Morgan was still in the grips of the allegedly Aristotelian paradigm. (shrink)

The famous EPR article of 1935 challenged the completeness of quantum mechanics and spurred decades of theoretical and experimental research into the foundations of quantum theory. A crowning achievement of this research is the demonstration that nature cannot in general consist in noncontextual pre-measurement properties that uniquely determine possible measurement outcomes, through experimental violations of Bell inequalities and Kochen-Specker theorems. In this article, I reconstruct an argument from Niels Bohr’s writings that the reality of the Einstein-Planck-de Broglie relations alone implies (...) that no such properties can exist for momentum and position measurements, show how this argument responds to the challenge of EPR on general physical grounds, and advance that this reconstruction shows that and how Bohr’s “complementarity” is a view of the objective content and logic of quantum theory. (shrink)

Is vision merely a state of the beholder’s sensory organ which can be explained as an immediate effect caused by external sensible objects? Or is it rather a successive process in which the observer actively scanning the surrounding environment plays a major part? These two general attitudes towards visual perception were both developed already by ancient thinkers. The former is embraced by natural philosophers (e.g., atomists and Aristotelians) and is often labelled “intromissionist”, based on their assumption that vision is an (...) outcome of the causal influence exerted by an external object upon a sensory organ receiving an entity from the object. The latter attitude to vision as a successive process is rather linked to the “extramissionist” theories of the proponents of geometrical optics (such as Euclid or Ptolemy) who suggest that an entity – a visual ray – is sent forth from the eyes to the object. The present paper focuses on the contributions to this ancient controversy proposed by some 13th-century Latin thinkers. [...]. (shrink)

Russell's a priori postulates of empirist theories of knowledge. Kurze Darstellung von Russells Postulaten als Ermöglichung einer empiristischen Erkenntnistheorie.

In the pure powers ontology (PPO), basic physical properties have wholly dispositional essences. PPO has clear advantages over categoricalist ontologies, which suffer from familiar epistemological and metaphysical problems. However, opponents argue that because it contains no qualitative properties, PPO lacks the resources to individuate powers, and generates a regress. The challenge for those who take such arguments seriously is to introduce qualitative properties without reintroducing the problems that PPO was meant to solve. In this paper, I distinguish the core claim (...) of PPO: (i) basic physical properties have dispositional essences, from a hitherto unnoticed assumption: (ii) the dispositional essences of basic physical properties exclusively involve type-causal relations to other basic physical properties. I reject (ii), making room for a structuralist ontology in which all basic physical properties are pure powers, individuated by their places in a causal structure that includes not only other powers, but also physically realized qualitative properties such as shapes, patterns and structures. Such qualities individuate pure powers in the way that non-mental input and output properties individuate realized mental properties in functionalist theories of mind, except that here it is basic physical powers that are individuated by relations to realized non-powers. I distinguish one Platonic and two Aristotelian version of this theory, and argue that the Aristotelian versions require that grounding is not always a relative fundamentality relation, because the powers ground the qualities that individuate them. By considering ontic structural realism, I argue that symmetric grounding is the best way to make sense of relational individuation in structuralist ontologies, and is therefore no additional commitment of the one proposed here. (shrink)

The notion of so-called "postulated ontology" appears in the context of a well- -known thesis of the underdetermination of scientific theories by empirical data. It is argued in the paper, that the conviction of the existence of some kind of relation between a given theory and ontological ideas can be derived from this thesis, regardless of its particular form. Therefore, certain solutions to classical philosophical questions can be obtained, in principle, by careful inspection of scientific achievements. However, if the thesis (...) of underdetermination holds, such philosophical solutions are not imposed by science itself. In order to arrive at some kind of ontology based on science, it seems necessary to accept certain philosophical presuppositions in the first place. This, and the fact that scientific theories change in time show that although such a kind of ontology is possible, and perhaps desirable, it can never be ultimate. (shrink)

In the paper, certain rational postulates for protocols describing real communicating are introduced.These rational postulates, on the one hand, allow assigning a certain typology of real systems of interactions, which is consistent with the reality of epistemic argumentation in systems of communicating, and on the other one – defining rules of using argumentation in real situations. Moreover, the presented postulates for protocols characterize information networks and administering knowledge in real interactivity systems. Due to the epistemic character of the considerations, the (...) problem undertaken in the paper concerns working out fundamental assumptions that refer to building of epistemic logics. They allow establishing the correctness of the discourse defined by rational postulates of protocols of real communication. In the context of the presented problem there are the following two research questions distinguished: 1) How do we determine the rule of building of real dynamic epistemic logics? and 2) How should we define semantics for these logics? Within the framework of considerations relating to the research questions asked, certain epistemic operators, relativized to types of communicating, are introduced. Basic logical relations between using these operators are established for these operators. The relations are presented by a diagram called the square of epis temic operators. On the basis of these logical relations some axioms for real dynamic epistemic logics are presented. The semantics of real dynamic epistem ic logics is extended by the methods of lower and upper approximation of formula evaluating. This allows defining ‘approximation Kripke models’. The results of conceptualization of knowledge on real premises of epistemic argum entation presented in this paper can be applied to rhetoric in real systems of interaction. (shrink)

Exemption from blameworthiness is often bound to implicit or explicit claims of diminished agency, or even non-agency. This poses a dilemma in navigating moral relationships affected by mental illness. While it is crucial for assessments of responsibility to be responsive to the significance of mental illness, must this responsiveness come at a cost to symmetrical moral relations? In this paper we argue, contra recent critiques, that Strawsonian accounts of responsibility are able to navigate this dilemma, and can accommodate significant exculpation (...) on the basis of mental illness while maintaining symmetrical relations. We understand this to be part of the larger recognition that while we have certain fundamental entitlements within our moral relationships, it is also possible to be over-entitled, and to expect too much of others. Our account draws, in particular, on the moral significance of difficulty. Difficulty is inherently scalar, and in drawing on this explanatory framework we explicate a theory of both excuse and exemption by degree. We argue for a significant realm of excuse on the basis of mental illness that is fully compatible with symmetrical relations. However, we also acknowledge the limits of this accommodation on Strawsonian grounds, and argue that these limits are justified and appropriate. (shrink)

In his classic book “the Foundations of Statistics” Savage developed a formal system of rational decision making. The system is based on (i) a set of possible states of the world, (ii) a set of consequences, (iii) a set of acts, which are functions from states to consequences, and (iv) a preference relation over the acts, which represents the preferences of an idealized rational agent. The goal and the culmination of the enterprise is a representation theorem: Any preference relation that (...) satisfies certain arguably acceptable postulates determines a (finitely additive) probability distribution over the states and a utility assignment to the consequences, such that the preferences among acts are determined by their expected utilities. Additional problematic assumptions are however required in Savage's proofs. First, there is a Boolean algebra of events (sets of states) which determines the richness of the set of acts. The probabilities are assigned to members of this algebra. Savage's proof requires that this be a σ-algebra (i.e., closed under infinite countable unions and intersections), which makes for an extremely rich preference relation. On Savage's view we should not require subjective probabilities to be σ-additive. He therefore finds the insistence on a σ-algebra peculiar and is unhappy with it. But he sees no way of avoiding it. Second, the assignment of utilities requires the constant act assumption: for every consequence there is a constant act, which produces that consequence in every state. This assumption is known to be highly counterintuitive. The present work contains two mathematical results. The first, and the more difficult one, shows that the σ-algebra assumption can be dropped. The second states that, as long as utilities are assigned to finite gambles only, the constant act assumption can be replaced by the more plausible and much weaker assumption that there are at least two non-equivalent constant acts. The second result also employs a novel way of deriving utilities in Savage-style systems -- without appealing to von Neumann-Morgenstern lotteries. The paper discusses the notion of “idealized agent" that underlies Savage's approach, and argues that the simplified system, which is adequate for all the actual purposes for which the system is designed, involves a more realistic notion of an idealized agent. (shrink)

There are two traditional ways to read Kant's claim that every event necessarily has a cause: the weaker every-event some-cause and the stronger same-cause same-effect causal principles. The focus of the debate about whether and where he subscribes to the SCP has been in the Analogies in the Critique of Pure Reason and in the Metaphysical Foundations of Natural Science. By analysing the arguments and conclusions of both the Analogies and the Postulates as well as the two Latin principles non (...) datur casus and non datur fatum that summarise their results, I will argue for the novel thesis that the SCP is actually demonstrated in the Postulates of the First Critique. (shrink)

This paper discusses knowledge of opposites. In particular, attention is given to the linguistic notion of antonymy and how it represents oppositional relations that are commonly found in perception. The paper draws upon the long history of work on the formalisation of antonymy in linguistics and formal semantics, and also upon work on the perception of opposites in psychology, and an assessment is made of the main approaches. Treatments of these phenomena in linguistics and psychology posit that the principles of (...) minimal difference and invariance are centrally important. It will be suggested that the standard approach employing meaning postulates fails to capture the relevant notion of antonymy, in part because it is not informed by these principles, and in part due to a number of other problems with this kind of approach, many of which may be overcome by building in the central principles from the beginning. The paper also discusses the issue of whether we can know that opposites necessarily exclude each other and, if so, how. This issue is intertwined with what is known as the colour incompatibility problem that Wittgenstein wrangled with at various times during his life. The paper assesses various solutions to these problems including an approach that was first put forward by Jerrold J. Katz. The relation between this approach and the theory of determinables and determinates is also examined. A further development upon this approach is proposed and then applied to the case of the formalisation of antonymy. It is argued that this approach avoids the problems suffered by the main approaches discussed earlier in the paper. (shrink)

The measurement problem concerns an apparent conflict between the two fundamental principles of quantum mechanics, namely the Schrödinger equation and the measurement postulate. These principles describe inconsistent behavior for quantum systems in so-called "measurement contexts." Many theorists have thought that the measurement problem can only be resolved by proposing a mechanistic explanation of (genuine or apparent) wavefunction collapse that avoids explicit reference to "measurement." However, I argue here that the measurement problem dissolves if we accept Humeanism about laws of (...) nature. On a Humean metaphysics, there is no conflict between the two principles, nor is there any inherent problem with the concept of "measurement" figuring into the account of collapse. (shrink)

Science is founded on a method based on critical thinking. A prerequisite for this is not only a sufficient command of language but also the comprehension of the basic concepts underlying our understanding of reality. This constraint implies an awareness of the fact that the truth of the World is not directly accessible to us, but can only be glimpsed through the construction of mod- els designed to anticipate its behaviour. Because the relationship between models and reality rests on the (...) interpretation of founding postulates and in- stantiations of their predictions (and is therefore deeply rooted in language and culture), there can be no demarcation between science and non-science. However, critical thinking is essential to ensure that the link between models and reality is gradually made more adequate to reality, based on what has already been established, thus guaranteeing that science progresses on this basis and excluding any form of relativism. (shrink)

As timely renovation of artificial ideology about authenticity of nature in proportion to contemporaneous historical background of remarkable highlight of microcosmic configuration of matter, “Homogenous Cosmos Originated from Unique Genesis” is innovative cosmos redefinition and thoroughly coherent PNT dynamics about universal existence & motion as spontaneous occurrence in the nature of essence of matter in a class by itself, which is radically extended from newly highlighted factuality that “discretionary particles in cosmos are mutually convertible” as lineal logic system based on (...) unique assumable precondition of Homogenous cosmos originated from unique genesis postulate. (shrink)

Savage's framework of subjective preference among acts provides a paradigmatic derivation of rational subjective probabilities within a more general theory of rational decisions. The system is based on a set of possible states of the world, and on acts, which are functions that assign to each state a consequence€. The representation theorem states that the given preference between acts is determined by their expected utilities, based on uniquely determined probabilities (assigned to sets of states), and numeric utilities assigned to consequences. (...) Savage's derivation, however, is based on a highly problematic well-known assumption not included among his postulates: for any consequence of an act in some state, there is a "constant act" which has that consequence in all states. This ability to transfer consequences from state to state is, in many cases, miraculous -- including simple scenarios suggested by Savage as natural cases for applying his theory. We propose a simplification of the system, which yields the representation theorem without the constant act assumption. We need only postulates P1-P6. This is done at the cost of reducing the set of acts included in the setup. The reduction excludes certain theoretical infinitary scenarios, but includes the scenarios that should be handled by a system that models human decisions. (shrink)

The present first part about the eventual completeness of mathematics (called “Hilbert mathematics”) is concentrated on the Gödel incompleteness (1931) statement: if it is an axiom rather than a theorem inferable from the axioms of (Peano) arithmetic, (ZFC) set theory, and propositional logic, this would pioneer the pathway to Hilbert mathematics. One of the main arguments that it is an axiom consists in the direct contradiction of the axiom of induction in arithmetic and the axiom of infinity in set theory. (...) Thus, the pair of arithmetic and set are to be similar to Euclidean and non-Euclidean geometries distinguishably only by the Fifth postulate now, i.e. after replacing it and its negation correspondingly by the axiom of finiteness (induction) versus that of finiteness being idempotent negations to each other. Indeed, the axiom of choice, as far as it is equivalent to the well-ordering “theorem”, transforms any set in a well-ordering either necessarily finite according to the axiom of induction or also optionally infinite according to the axiom of infinity. So, the Gödel incompleteness statement relies on the logical contradiction of the axiom of induction and the axiom of infinity in the final analysis. Nonetheless, both can be considered as two idempotent versions of the same axiom (analogically to the Fifth postulate) and then unified after logicism and its inherent intensionality since the opposition of finiteness and infinity can be only extensional (i.e., relevant to the elements of any set rather than to the set by itself or its characteristic property being a proposition). So, the pathway for interpreting the Gödel incompleteness statement as an axiom and the originating from that assumption for “Hilbert mathematics” accepting its negation is pioneered. A much wider context relevant to realizing the Gödel incompleteness statement as a metamathematical axiom is consistently built step by step. The horizon of Hilbert mathematics is the proper subject in the third part of the paper, and a reinterpretation of Gödel’s papers (1930; 1931) as an apology of logicism as the only consistent foundations of mathematics is the topic of the next second part. (shrink)

This paper argues that (1) Richard Swinburne’s general account of the simplicity of empirical hypotheses fails because it involves a deeply problematic notion of postulating a property, while there is a wide range of hypotheses where the assessment of simplicity rests entirely on the number and kinds of postulated properties, (2) Swinburne’s main argument in ’The Christian God’ for the simplicity of theism, the one based on considerations about pure limitless intentional power, is significantly weaker than he seems to believe. (...) The paper does not draw a conclusion about whether theism is simple. (shrink)

What is a number? Answering this will answer questions about its philosophical foundations - rational numbers, the complex numbers, imaginary numbers. If we are to write or talk about something, it is helpful to know whether it exists, how it exists, and why it exists, just from a common-sense point of view [Quine, 1948, p. 6]. Generally, there does not seem to be any disagreement among mathematicians, scientists, and logicians about numbers existing in some way, but currently, in the mainstream (...) arena only definitions, descriptions of properties, and effects are presented as evidence. Enough historical description of numbers in history provides an empirical basis of number, although a case can be made that numbers do not exist by themselves empirically. Correspondingly, numbers exist as abstractions. All the while, though, these "descriptions" beg the question of what numbers are ontologically. Advocates for numbers being the ultimate reality have the problem of wrestling with the nature of reality. I start on the road to discovering the ontology of number by looking at where people have talked about numbers as already existing: history. Of course, we need to know not only what ontology is but the problems of identifying one, leading to the selection between metaphysics and provisional approaches. While we seem to be dimensionally limited, at least we can identify a more suitable bootstrapping ontology than mere definitions, leading us to the unity of opposites. The rest of the paper details how this is done and modifies Peano's Postulates. (shrink)

Formalizing Euclid’s first axiom. Bulletin of Symbolic Logic. 20 (2014) 404–5. (Coauthor: Daniel Novotný) -/- Euclid [fl. 300 BCE] divides his basic principles into what came to be called ‘postulates’ and ‘axioms’—two words that are synonyms today but which are commonly used to translate Greek words meant by Euclid as contrasting terms. -/- Euclid’s postulates are specifically geometric: they concern geometric magnitudes, shapes, figures, etc.—nothing else. The first: “to draw a line from any point to any point”; the last: the (...) parallel postulate. -/- Euclid’s axioms are general principles of magnitude: they concern geometric magnitudes and magnitudes of other kinds as well even numbers. The first is often translated “Things that equal the same thing equal one another”. -/- There are other differences that are or might become important. -/- Aristotle [fl. 350 BCE] meticulously separated his basic principles [archai, singular archê] according to subject matter: geometrical, arithmetic, astronomical, etc. However, he made no distinction that can be assimilated to Euclid’s postulate/axiom distinction. -/- Today we divide basic principles into non-logical [topic-specific] and logical [topic-neutral] but this too is not the same as Euclid’s. In this regard it is important to be cognizant of the difference between equality and identity—a distinction often crudely ignored by modern logicians. Tarski is a rare exception. The four angles of a rectangle are equal to—not identical to—one another; the size of one angle of a rectangle is identical to the size of any other of its angles. No two angles are identical to each other. -/- The sentence ‘Things that equal the same thing equal one another’ contains no occurrence of the word ‘magnitude’. This paper considers the problem of formalizing the proposition Euclid intended as a principle of magnitudes while being faithful to the logical form and to its information content. (shrink)

Does postulating skeptical theism undermine the claim that evil strongly confirms atheism over theism? According to Perrine and Wykstra, it does undermine the claim, because evil is no more likely on atheism than on skeptical theism. According to Draper, it does not undermine the claim, because evil is much more likely on atheism than on theism in general. I show that the probability facts alone do not resolve their disagreement, which ultimately rests on which updating procedure – conditionalizing or updating (...) on a conditional – fits both the evidence and how we ought to take that evidence into account. (shrink)

This paper decomposes the Liar Paradox into its semantic atoms using Meaning Postulates (1952) provided by Rudolf Carnap. Formalizing truth values of propositions as Boolean properties of these propositions is a key new insight. This new insight divides the translation of a declarative sentence into its equivalent mathematical proposition into three separate steps. When each of these steps are separately examined the logical error of the Liar Paradox is unequivocally shown.

We review our approach to quantum mechanics adding also some new interesting results. We start by giving proof of two important theorems on the existence of the A(Si) and i,±1 N Clifford algebras. This last algebra gives proof of the von Neumann basic postulates on the quantum measurement explaining thus in an algebraic manner the wave function collapse postulated in standard quantum theory. In this manner we reach the objective to expose a self-consistent version of quantum mechanics. In detail we (...) realize a bare bone skeleton of quantum mechanics recovering all the basic foundations of this theory on an algebraic framework. We give proof of the quantum like Heisenberg uncertainty relations using only the basic support of the Clifford algebra. In addition we demonstrate the well known phenomenon of quantum Mach Zender interference using the same algebraic framework, as well as we give algebraic proof of quantum collapse in some cases of physical interest by direct application of the theorem that we derive to elaborate the i,±1 N algebra. We also discuss the problem of time evolution of quantum systems as well as the changes in space location, in momentum and the linked invariance principles. We are also able to re-derive the basic wave function of standard quantum mechanics by using only the Clifford algebraic approach. In this manner we obtain a full exposition of standard quantum mechanics using only the basic axioms of Clifford algebra. We also discuss more advanced features of quantum mechanics. In detail, we give demonstration of the Kocken-Specher theorem, and also we give an algebraic formulation and explanation of the EPR paradox only using the Clifford algebra. By using the same approach we also derive Bell inequalities. Our formulation is strongly based on the use of idempotents that are contained in Clifford algebra. Their counterpart in quantum mechanics is represented by the projection operators that, as it is well known, are interpreted as logical statements, following the basic von Neumann results. Von Neumann realized a matrix logic on the basis of quantum mechanics. Using the Clifford algebra we are able to invert such result. According to the results previously obtained by Orlov in 1994, we are able to give proof that quantum mechanics derives from logic. We show that indeterminism and quantum interference have their origin in the logic. Therefore, it seems that we may conclude that quantum mechanics, as it appears when investigated by the Clifford algebra, is a two-faced theory in the sense that it looks from one side to “matter per se”, thus to objects but simultaneously also to conceptual entities. We advance the basic conclusion of the paper: There are stages of our reality in which we no more can separate the logic ( and thus cognition and thus conceptual entity) from the features of “matter per se”. In quantum mechanics the logic, and thus the cognition and thus the conceptual entity-cognitive performance, assume the same importance as the features of what is being described. We are at levels of reality in which the truths of logical statements about dynamic variables become dynamic variables themselves so that a profound link is established from its starting in this theory between physics and conceptual entities. Finally, in this approach there is not an absolute definition of logical truths. Transformations , and thus … “redefinitions”…. of truth values are permitted in such scheme as well as the well established invariance principles, clearly indicate . (shrink)

As timely renovation of artificial ideology about authenticity of nature in proportion to contemporaneous historical background of remarkable highlight of microcosmic configuration of matter, “Homogenous Cosmos Originated from Unique Genesis” is innovative cosmos redefinition and thoroughly coherent PNT dynamics about universal existence & motion as spontaneous occurrence in the nature of essence of matter in a class by itself, which is radically extended from newly highlighted factuality that “discretionary particles in cosmos are mutually convertible” as lineal logic system based on (...) unique assumable precondition of Homogenous cosmos originated from unique genesis postulate. (shrink)

Hobbes postulates a social contract to formalize our collective transition from the state of nature to civil society. The prisoner’s dilemma challenges both the mechanics and the outcome of that thought experiment. The incentives for reneging are supposedly strong enough to keep rational persons from cooperating. This paper argues that the prisoner’s dilemma undermines a position Hobbes does not hold. The context and parameters of the social contract steer it safely between the horns of the dilemma. Specifically, in a setting (...) as hostile as the state of nature, Hobbes’s emphasis on self-interest places a premium on survival, and thereby on adaptability, which then promotes progressive concessions toward peaceful coexistence. This transforms the relevant model of rationality from utility maximization to utility satisficing, thus favoring the pursuit of a mutually satisfactory outcome over that of the best personal outcome. The difference not only obviates the prisoner’s dilemma but also better approximates the state of nature while leaving a viable way out. (shrink)