The paper introduces and utilizes a few new concepts: “nonstandard Peano arithmetic”, “complementary Peano arithmetic”, “Hilbert arithmetic”. They identify the foundations of both mathematics and physics demonstrating the equivalence of the newly introduced Hilbert arithmetic and the separable complex Hilbert space of quantum mechanics in turn underlying physics and all the world. That new both mathematical and physical ground can be recognized as information complemented and generalized by quantum information. A few fundamental mathematical problems of the present such (...) as Fermat’s last theorem, four-color theorem as well as its new-formulated generalization as “four-letter theorem”, Poincaré’s conjecture, “P vs NP” are considered over again, from and within the new-founding conceptual reference frame of information, as illustrations. Simple or crucially simplifying solutions and proofs are demonstrated. The link between the consistent completeness of the system mathematics-physics on the ground of information and all the great mathematical problems of the present (rather than the enumerated ones) is suggested. (shrink)

In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA (...) under the interpretation. The second yields a strong, finitary, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically computable Tarskian truth values to the formulas of PA under the interpretation. We situate our investigation within a broad analysis of quantification vis a vis: * Hilbert's epsilon-calculus * Goedel's omega-consistency * The Law of the Excluded Middle * Hilbert's omega-Rule * An Algorithmic omega-Rule * Gentzen's Rule of Infinite Induction * Rosser's Rule C * Markov's Principle * The Church-Turing Thesis * Aristotle's particularisation * Wittgenstein's perspective of constructive mathematics * An evidence-based perspective of quantification. By showing how these are formally inter-related, we highlight the fragility of both the persisting, theistic, classical/Platonic interpretation of quantification grounded in Hilbert's epsilon-calculus; and the persisting, atheistic, constructive/Intuitionistic interpretation of quantification rooted in Brouwer's belief that the Law of the Excluded Middle is non-finitary. We then consider some consequences for mathematics, mathematics education, philosophy, and the natural sciences, of an agnostic, evidence-based, finitary interpretation of quantification that challenges classical paradigms in all these disciplines. (shrink)

We consider the argument that Tarski's classic definitions permit an intelligence---whether human or mechanistic---to admit finitary evidence-based definitions of the satisfaction and truth of the atomic formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two, hitherto unsuspected and essentially different, ways: (1) in terms of classical algorithmic verifiabilty; and (2) in terms of finitary algorithmic computability. We then show that the two definitions correspond to two distinctly different assignments of satisfaction and (...) truth to the compound formulas of PA over N---I_PA(N; SV ) and I_PA(N; SC). We further show that the PA axioms are true over N, and that the PA rules of inference preserve truth over N, under both I_PA(N; SV ) and I_PA(N; SC). We then show: (a) that if we assume the satisfaction and truth of the compound formulas of PA are always non-finitarily decidable under I_PA(N; SV ), then this assignment corresponds to the classical non-finitary putative standard interpretation I_PA(N; S) of PA over the domain N; and (b) that the satisfaction and truth of the compound formulas of PA are always finitarily decidable under the assignment I_PA(N; SC), from which we may finitarily conclude that PA is consistent. We further conclude that the appropriate inference to be drawn from Goedel's 1931 paper on undecidable arithmetical propositions is that we can define PA formulas which---under interpretation---are algorithmically verifiable as always true over N, but not algorithmically computable as always true over N. We conclude from this that Lucas' Goedelian argument is validated if the assignment I_PA(N; SV ) can be treated as circumscribing the ambit of human reasoning about `true' arithmetical propositions, and the assignment I_PA(N; SC) as circumscribing the ambit of mechanistic reasoning about `true' arithmetical propositions. (shrink)

The concept of quantum information is introduced as both normed superposition of two orthogonal sub-spaces of the separable complex Hilbert space and in-variance of Hamilton and Lagrange representation of any mechanical system. The base is the isomorphism of the standard introduction and the representation of a qubit to a 3D unit ball, in which two points are chosen. The separable complex Hilbert space is considered as the free variable of quantum information and any point in it (a wave function (...) describing a state of a quantum system) as its value as the bound variable. A qubit is equivalent to the generalization of ‘bit’ from the set of two equally probable alternatives to an infinite set of alternatives. Then, that Hilbert space is considered as a generalization of Peano arithmetic where any unit is substituted by a qubit and thus the set of natural number is mappable within any qubit as the complex internal structure of the unit or a different state of it. Thus, any mathematical structure being reducible to set theory is re-presentable as a set of wave functions and a subspace of the separable complex Hilbert space, and it can be identified as the category of all categories for any functor represents an operator transforming a set (or subspace) of the separable complex Hilbert space into another. Thus, category theory is isomorphic to the Hilbert-space representation of set theory & Peano arithmetic as above. Given any value of quantum information, i.e. a point in the separable complex Hilbert space, it always admits two equally acceptable interpretations: the one is physical, the other is mathematical. The former is a wave function as the exhausted description of a certain state of a certain quantum system. The latter chooses a certain mathematical structure among a certain category. Thus there is no way to be distinguished a mathematical structure from a physical state for both are described exhaustedly as a value of quantum information. This statement in turn can be utilized to be defined quantum information by the identity of any mathematical structure to a physical state, and also vice versa. Further, that definition is equivalent to both standard definition as the normed superposition and in-variance of Hamilton and Lagrange interpretation of mechanical motion introduced in the beginning of the paper. Then, the concept of information symmetry can be involved as the symmetry between three elements or two pairs of elements: Lagrange representation and each counterpart of the pair of Hamilton representation. The sense and meaning of information symmetry may be visualized by a single (quantum) bit and its interpretation as both (privileged) reference frame and the symmetries of the Standard model. (shrink)

The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of equality between two arbitrary observables, since the Born formula gives the probability distribution only for a commuting family of observables. In this paper, quantum set theory developed by Takeuti and the present author is used to systematically extend the standard probabilistic interpretation of quantum theory (...) to define the probability of equality between two arbitrary observables in an arbitrary state. We apply this new interpretation to quantum measurement theory, and establish a logical basis for the difference between simultaneous measurability and simultaneous determinateness. (shrink)

Tarski's Undefinability of Truth Theorem comes in two versions: that no consistent theory which interprets Robinson's Arithmetic (Q) can prove all instances of the T-Scheme and hence define truth; and that no such theory, if sound, can even express truth. In this note, I prove corresponding limitative results for validity. While Peano Arithmetic already has the resources to define a predicate expressing logical validity, as Jeff Ketland has recently pointed out (2012, Validity as a primitive. Analysis 72: 421-30), no (...) theory which interprets Q closed under the standard structural rules can define nor express validity, on pain of triviality. The results put pressure on the widespread view that there is an asymmetry between truth and validity, viz. that while the former cannot be defined within the language, the latter can. I argue that Vann McGee's and Hartry Field's arguments for the asymmetry view are problematic. (shrink)

This essay explores Kaila's interpretation of the special theory of relativity. Although the relevance of his work to logical empiricism is well-known, not much has been written on what Kaila calls the ‘Einstein-Minkowski invariance theory’. Kaila's interpretation focuses on two salient features. First, he emphasizes the importance of the invariance of the spacetime interval. The general point about spacetime invariance has been known at least since Minkowski, yet Kaila applies his overall tripartite theory of invariances to space, time and spacetime (...) in an original way. Second, Kaila provides a non-conventionalist argument for the isotropic speed of electromagnetic signals. The standard Einstein synchrony is not a mere convention but a part of a larger empirical theory. According to Kaila's holistic principle of testability, which stands in contrast to the theses of translatability and verification, different items in the theory cannot be sharply divided into conventional and empirical. Kaila's invariantism/non-conventionalism about relativity reflects an interesting case in the gradual transition from positivism to realism within the philosophy of science. (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 paper investigates the understanding of quantum indistinguishability after quantum information in comparison with the “classical” quantum mechanics based on the separable complex Hilbert space. The two oppositions, correspondingly “distinguishability / indistinguishability” and “classical / quantum”, available implicitly in the concept of quantum indistinguishability can be interpreted as two “missing” bits of classical information, which are to be added after teleportation of quantum information to be restored the initial state unambiguously. That new understanding of quantum indistinguishability is linked to the (...) distinction of classical (Maxwell-Boltzmann) versus quantum (either Fermi-Dirac or Bose-Einstein) statistics. The latter can be generalized to classes of wave functions (“empty” qubits) and represented exhaustively in Hilbert arithmetic therefore connectible to the foundations of mathematics, more precisely, to the interrelations of propositional logic and set theory sharing the structure of Boolean algebra and two anti-isometric copies of Peano arithmetic. (shrink)

This paper develops an interpretation of what is essential to kant's doctrine of the highest good, Which defends it while also explaining why it is often rejected. While it is commonly viewed as a theological ideal in which happiness is proportioned to virtue, The paper gives an account in which neither feature appears. The highest good is best understood as a state of affairs to be achieved through human agency, Containing the moral perfection of all individuals and the satisfaction of (...) their permissible ends-I.E., One in which all act from the moral law and in doing so achieve their intended ends. The paper shows that the texts contain two distinct conceptions not distinguished by kant-Both a theological and a secular (political) notion. The standard objections apply to the theological, But the secular conception is consistent with kant's conception of moral conduct. Moreover, That the highest good is introduced as an end to be constructed out of the moral law indicates that the secular version is the essential notion. (shrink)

The article shows a difference in Aristotle’s ethical theory between the Protrepticus and Eudemian Ethics on the one hand and the Nicomachean Ethics on the other. The difference is explicated by means of the interpretation of the concept of ὅρος (standard) in these writings. The Protrepticus and Eudemian Ethics present ethical theory as an expertise which – together with other sciences – has a standard for decisions and actions taken from nature and the divine. The ethical theory presented (...) in the Nicomachean Ethics does not entail such a strong concept of ὅρος and it treats ethics in contrast to other, more exact, sciences. Finally, the article presents a tentative suggestion as to why it seems that the Nicomachean Ethics VI,1 raises hopes that it will provide a detailed account of ὅρος when in fact there is no discussion of it. (shrink)

According to a standard interpretation of Aristotle, a material substance, like a dog, is a hylomorphic composite of matter and form, its “essential” parts. Is such a composite some thing in addition to its essential parts as united? The moderate reductionist says “no,” whereas the anti-reductionist says “yes.” In this paper, I will clarify and defend Durand of St.-Pourçain’s surprisingly influential version of moderate reductionism, according to which hylomorphic composites are nothing over and above their essential parts and the (...) union of those parts, where this union is explained by the presence of two modes: a mode of inherence on the side of form and a mode of substanding on the side of matter. (shrink)

According to Schopenhauer’s compensation argument for pessimism, the non-existence of the world is preferable to its existence because no goods can ever compensate for the mere existence of evil. Standard interpretations take this argument to be based on Schopenhauer’s thesis that all goods are merely the negation of evils, from which they assume it follows that the apparent goods in life are in fact empty and without value. This article develops a non-standard variant of the standard (...) interpretation, which accepts the relevance of the negativity thesis but rejects that the argument assumes that life’s goods are all empty and valueless. Instead, it argues that whatever value negative goods might possess, they do not have the kind of value to compensate for positive evils. This involves additional development of the negativity thesis and a defence of it against objections from Byron Simmons (2021). (shrink)

This thesis presents an interpretation of David Hume’s essay ‘Of the Standard of Taste’. The most distinguishing feature of this interpretation is the emphasis placed on the significance of Hume’s general philosophical position in a faithful reading of this philosophical classic. The success of this interpretation will show that Hume’s essay should be read as an integral part of his system of philosophy. There are three parts in this thesis. The first part is an overview of some key aspects (...) of Hume’s philosophy which are relevant to my interpretation. Unlike many contemporary philosophers in the analytic tradition, Hume is a systematic thinker. A faithful reading of his works should take his general philosophical framework seriously. Therefore, this overview of his system serves as the general background of the next two parts. The second part is a discussion of Hume’s aesthetic thought. More specifically, it provides an exposition of his view on beauty and judgements of beauty. This part completes the stage-setting for the development of my interpretation, by helping the reader form a more specific conceptual framework for understanding Hume’s essay. The third part develops an interpretation of ‘Of the Standard of Taste’ according to what has been provided in the previous two parts. It starts with an outline of the essay, which indicates Hume’s aim in writing it. After that, a few sections are devoted to some central elements of the essay. The last section of this part discusses four controversies concerning Hume’s essay. These discussions establish the strength of this interpretation, or at least, the fruitful prospect of an interpretative project that integrates Hume’s essay into his whole system. (shrink)

We spend our lives protecting an elusive self - but does the self actually exist? Drawing on literature from Western philosophy, neuroscience and Buddhism (interpreted), the author argues that there is no self. The self - as unified owner and thinker of thoughts - is an illusion created by two tiers. A tier of naturally unified consciousness (notably absent in standard bundle-theory accounts) merges with a tier of desire-driven thoughts and emotions to yield the impression of a self. So (...) while the self, if real, would think up the thoughts, the thoughts, in reality, think up the self. (shrink)

Two families of mathematical methods lie at the heart of investigating the hierarchical structure of genetic variation in Homo sapiens: /diversity partitioning/, which assesses genetic variation within and among pre-determined groups, and /clustering analysis/, which simultaneously produces clusters and assigns individuals to these “unsupervised” cluster classifications. While mathematically consistent, these two methodologies are understood by many to ground diametrically opposed claims about the reality of human races. Moreover, modeling results are sensitive to assumptions such as preexisting theoretical commitments to certain (...) linguistic, anthropological, and geographic human groups. Thus, models can be perniciously reified. That is, they can be conflated and confused with the world. This fact belies standard realist and antirealist interpretations of “race,” and supports a pluralist conventionalist interpretation. (shrink)

On the standard interpretation of Metaphysics IX, Aristotle proceeds from the original sense of δύναμις and ἐνέργεια to an ontological conception of these terms. This should raise the question of what is not ontological about the former and what is ontological about the latter. To address these questions I discuss the commentaries by Heidegger and Menn, which alone come close to addressing these issues. But their readings cannot neatly distinguish between the two senses of δύναμις and ἐνέργεια that we (...) find in the Aristotelian text, thus compelling us to seek a better way of clarifying the standard interpretation, which I argue can be more precisely understood in the following way: δύναμις and ἐνέργεια in their customary meaning cannot be considered ontological in the sense that they have a particular locus among the categories, which is what sets them apart from their newer, ontological meaning. I conclude therefore that the text of Metaphysics IX can be understood as proceeding from an intracategorial conception of δύναμις and ἐνέργεια toward a transcategorial conception of these terms. (shrink)

Standard models of visual perception hold that vision is an inferential or interpretative process. Such models are said to be superior to competing, non-inferential views in explanatory power. In particular, they are said to be capable of explaining a number of otherwise mysterious, visual phenomena such as multi-stable perception. Multi-stable perception paradigmatically occurs in the presence of ambiguous figures, single images that can give rise to two or more distinct percepts. Different interpretations are said to produce the different (...) percepts. In this paper, I argue that a non-inferential account of visual perception is just as capable of explaining multi-stable perception. I propose an embedded understanding of vision, and show how the embedded account can, after properly qualifying them, use the explanatory resources of the inferential view to explain just what such a view explains. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. That theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather a metamathematical axiom about the relation of mathematics and reality. Its investigation needs philosophical (...) means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. A comparison to Mach’s doctrine is used to be revealed the fundamental and philosophical reductionism of Husserl’s phenomenology leading to a kind of Pythagoreanism in the final analysis. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. Thus the problem which of the two mathematics is more relevant to our being is discussed. An information interpretation of the Schrödinger equation is involved to illustrate the above problem. (shrink)

Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-type coordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: these logics are standardly interpreted on structures where agents move (...) simultaneously, opening the possibility that an agent cannot foresee the concurrent choices of other agents. In this paper we introduce a variant of CL we call Two-Player Strategic Coordination Logic (SCL2). The key novelty of this framework is an operator for capturing coalitional ability when the cooperating agents cannot share strategic information. We identify significant differences in the expressive power and validities of SCL2 and CL2, and present a sound and complete axiomatization for SCL2. We briefly address conceptual challenges when shifting attention to games with more than two players and stronger notions of rationality. (shrink)

This paper investigates “A Feminist Interpretation and Reconstruction of John 7:53-8:11 in the light violence Against Women and its Implications Today.” This comes on the heels of the fact that violence against women is not only a fact of the contemporary times but was there in the days of Jesus Christ. The paper using two major theories of Feminist hermeneutics, especially the Hermeneutics of Recounting Tales of Terror in Memoriam and the Hermeneutic of Documenting Cases Against Women in the Bible (...) and social feminism theories of Radical Feminism and Liberal Feminism. This work brought to the fore that in most interpretation of John 7:53-8:11, the emphasis has been on forgiveness of sin and the issue of ὁ ἀναμάρτητος (that is one without sin) without any note about the andriarchal system of which the „adulterous‟ woman was a victim of. This paper which used the New Revised Standard Version (NRSV) as its preferred translation because of its gender sensitivity arrived at the conclusion that, the whole episode was male orchestrated; the Scribes and Pharisees bringing the woman to be judged by Jesus without the man in the alleged “adultery” case tantamount to judging the female fold different from the male fold; and that, there was no actual committing of adultery by the woman who was brought to Jesus, but she was brought to Jesus because of the inferiority, weak and vulnerable place of women in Jesus‟ andriarchal community. Hence, Jesus setting the woman free typified the role of religion as the vanguard in ending violence against women. (shrink)

The way, in which quantum information can unify quantum mechanics (and therefore the standard model) and general relativity, is investigated. Quantum information is defined as the generalization of the concept of information as to the choice among infinite sets of alternatives. Relevantly, the axiom of choice is necessary in general. The unit of quantum information, a qubit is interpreted as a relevant elementary choice among an infinite set of alternatives generalizing that of a bit. The invariance to the axiom (...) of choice shared by quantum mechanics is introduced: It constitutes quantum information as the relation of any state unorderable in principle (e.g. any coherent quantum state before measurement) and the same state already well-ordered (e.g. the well-ordered statistical ensemble of the measurement of the quantum system at issue). This allows of equating the classical and quantum time correspondingly as the well-ordering of any physical quantity or quantities and their coherent superposition. That equating is interpretable as the isomorphism of Minkowski space and Hilbert space. Quantum information is the structure interpretable in both ways and thus underlying their unification. Its deformation is representable correspondingly as gravitation in the deformed pseudo-Riemannian space of general relativity and the entanglement of two or more quantum systems. The standard model studies a single quantum system and thus privileges a single reference frame turning out to be inertial for the generalized symmetry [U(1)]X[SU(2)]X[SU(3)] “gauging” the standard model. As the standard model refers to a single quantum system, it is necessarily linear and thus the corresponding privileged reference frame is necessary inertial. The Higgs mechanism U(1) → [U(1)]X[SU(2)] confirmed enough already experimentally describes exactly the choice of the initial position of a privileged reference frame as the corresponding breaking of the symmetry. The standard model defines ‘mass at rest’ linearly and absolutely, but general relativity non-linearly and relatively. The “Big Bang” hypothesis is additional interpreting that position as that of the “Big Bang”. It serves also in order to reconcile the linear standard model in the singularity of the “Big Bang” with the observed nonlinearity of the further expansion of the universe described very well by general relativity. Quantum information links the standard model and general relativity in another way by mediation of entanglement. The linearity and absoluteness of the former and the nonlinearity and relativeness of the latter can be considered as the relation of a whole and the same whole divided into parts entangled in general. (shrink)

In this paper, I first consider a famous objection that the standard interpretation of the Lockean account of diachronicity (i.e., one’s sense of personal identity over time) via psychological connectedness falls prey to breaks in one’s personal narrative. I argue that recent case studies show that while this critique may hold with regard to some long-term autobiographical self-knowledge (e.g., episodic memory), it carries less warrant with respect to accounts based on trait-relevant, semantic self-knowledge. The second issue I address concerns (...) the question of diachronicity from the vantage point that there are (at least) two aspects of self—the self of psychophysical instantiation (what I term the epistemological self) and the self of first person subjectivity (what I term the ontological self; for discussion, see Klein SB, The self and its brain, Social Cognition, 30, 474–518, 2012). Each is held to be a necessary component of selfhood, and, in interaction, they are appear jointly sufficient for a synchronic sense of self (Klein SB, The self and its brain, Social Cognition, 30, 474–518, 2012). As pertains to diachronicity, by contrast, I contend that while the epistemological self, by itself, is precariously situated to do the work required by a coherent theory of personal identity across time, the ontological self may be better positioned to take up the challenge. (shrink)

The paper deals with the "deuteros plous", literally ‘the second voyage’, proverbially ‘the next best way’, discussed in Plato’s "Phaedo", the key passage being Phd. 99e4–100a3. The second voyage refers to what Plato’s Socrates calls his “flight into the logoi”. Elaborating on the subject, the author first (I) provides a non-standard interpretation of the passage in question, and then (II) outlines the philosophical problem that it seems to imply, and, finally, (III) tries to apply this philosophical problem to the (...) "ultimate final proof" of immortality and to draw an analogy with the ontological argument for the existence of God, as proposed by Descartes in his 5th "Meditation". The main points are as follows: (a) the “flight into the logoi” can have two different interpretations, a common one and an astonishing one, and (b) there is a structural analogy between Descartes’s ontological argument for the existence of God in his 5th "Meditation" and the "ultimate final proof" for the immortality of the soul in the "Phaedo". (shrink)

I consider the field of aesthetics to be at its most productive and engaging when adopting a broadly philosophically informative approach to its core issues (e.g., shaping and testing putative art theoretic commitments against the relevant standard models employed in philosophy of language, metaphysics, and philosophy of mind) and to be at its most impotent and bewildering when cultivating a philosophically insular character (e.g., selecting interpretative, ontological, or conceptual models solely for fit with pre-fixed art theoretic commitments). For example, (...) when philosophical aesthetics tends toward insularity, we shouldn’t be surprised to find standard art-ontological categories incongruous with those standardly employed in contemporary metaphysics. Of course, when contemporary metaphysics tends to ignore aesthetic and art theoretic concerns, perhaps we likewise shouldn’t be surprised to find the climate of contemporary metaphysics inhospitable for a theory of art. While this may seem to suggest at least a prima facie tension between our basic art theoretic commitments considered from within philosophical aesthetics and our standard ontological commitments considered from without, I think any perceived tension or antagonism largely due to metaphysicians and aestheticians (at least implicitly) assuming there to be but two available methodological positions with respect to the relationship between contemporary metaphysics and philosophical aesthetics (in the relevant overlap areas). I call these two opposing views the Deference View and the Independence View. I argue that either view looks to lead to what I call the Paradox of Standards. (shrink)

How should addictive behavior be explained? In terms of neurobiological illness and compulsion, or as a choice made freely, even rationally, in the face of harmful social or psychological circumstances? Some of the disagreement between proponents of the prevailing medical models and choice models in the science of addiction centres on the notion of “loss of control” as a normative characterization of addiction. In this article I examine two of the standard interpretations of loss of control in addiction, (...) one according to which addicts have lost free will, the other according to which their will is weak. I argue that both interpretations are mistaken and propose therefore an alternative based on a dual-process approach. This alternative neither rules out a capacity in addicts to rationally choose to engage in drug-oriented behavior, nor the possibility that addictive behavior can be compulsive and depend upon harmful changes in their brains caused by the regular use of drugs. (shrink)

Chilling Effects occur when the risks surrounding a speech restriction inadvertently deter speech that lies outside the restriction’s official scope. Contrary to the standard interpretation of this phenomenon I show how speech deterrence for individuals can sometimes, instead of suppressing discourse at the group level, intensify it – with results that are still unwelcome, but crucially unlike a ‘chill’. Inadvertent deterrence of speech may, counterintuitively, create a Heating Effect. This proposal gives us a promising explanation of the intensity of (...) public debate on topics for which there is, simultaneously, evidence of people self-censoring, for fear of breaching speech restrictions. It also helps to pinpoint two problems with existing theoretical analyses of the Chilling Effect: (i) in how they construe the relation between individual- and group-level discursive phenomena; and (ii) how they characterize the distinctively wrongful nature of inadvertent speech deterrence. (shrink)

Classical interpretations of Goedels formal reasoning, and of his conclusions, implicitly imply that mathematical languages are essentially incomplete, in the sense that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is, both, non-algorithmic, and essentially unverifiable. However, a language of general, scientific, discourse, which intends to mathematically express, and unambiguously communicate, intuitive concepts that correspond to scientific investigations, cannot allow its mathematical propositions to be interpreted ambiguously. Such a language must, therefore, define mathematical (...) truth verifiably. We consider a constructive interpretation of classical, Tarskian, truth, and of Goedel's reasoning, under which any formal system of Peano Arithmetic---classically accepted as the foundation of all our mathematical Languages---is verifiably complete in the above sense. We show how some paradoxical concepts of Quantum mechanics can, then, be expressed, and interpreted, naturally under a constructive definition of mathematical truth. (shrink)

According to the standard interpretation of Einstein’s field equations, gravity consists of mass-energy curving spacetime, and an additional physical force or entity—denoted by Λ (the ‘cosmological constant’)—is responsible for the Universe’s metric-expansion. Although General Relativity’s direct predictions have been systematically confirmed, the dominant cosmological model thought to follow from it—the ΛCDM (Lambda cold dark matter) model of the Universe’s history and composition—faces considerable challenges, including various observational anomalies and experimental failures to detect dark matter, dark energy, or inflation-field candidates. (...) This paper shows that Einstein’s Equivalence Principle entails two possible physical interpretations of General Relativity’s field equations. Although the field equations facially appear to support the standard interpretation—that gravity consists of mass-energy curving spacetime—the field equations can be equivalently understood as holding that gravitational effects instead result from mass-energy accelerating the metric-expansion of a second-order spacetime fabric superimposed upon an absolute, first-order Euclidean space, resulting in the observational appearance of spacetime curvature. This alternative interpretation of relativity is shown to be empirically equivalent to the standard interpretation of relativity, albeit with a changing value for Λ (which is similar to how Λ is understood in the conception of Λ as ‘quintessence’, but in this case takes Λ to be gravity). The reconceptualization is then shown to potentially resolve major observational anomalies for the ΛCDM model, including recent observations conflicting with ΛCDM predictions, as well as failures to directly detect dark matter, dark energy, and inflation field/particle candidates. (shrink)

The notions of inference and default are used in pragmatics with different meanings, resulting in theoretical disputes that emphasize the differences between the various pragmatic approaches. This paper is aimed at showing how the terminological and theoretical differences concerning the two aforementioned terms result from taking into account inference and default from different points of view and levels of analysis. Such differences risk making a dialogue between the theories extremely difficult. However, at a functional level of analysis the different theories, (...) definitions, and approaches to interpretation can be compared and integrated. At this level, the standardization of pragmatic inferences can be regarded as the development of a specific type of presumptions, used to draw prima-facie interpretations. (shrink)

Virginia Held argues that terrorism can be justified in some instances. But unlike standard, consequentialist justifications, hers is deontological. This paper critically examines her argument. It explores how the values of fairness, responsibility, and desert can serve to justify acts of terrorism. In doing so, two interpretations of her account are considered: a responsibility-insensitive and a responsibility-sensitive interpretation. On the first, her argument collapses into a consequentialist justification. On the second, it relies on an implausible conception of responsibility. (...) Either way, her argument fails as a distinctly deontological defense of terrorism. (shrink)

In this article, we analyse the ontological import of adding classes to set theories. We assume that this increment is well represented by going from ZF system to NBG. We thus consider the standard techniques of reducing one system to the other. Novak proved that from a model of ZF we can build a model of NBG (and vice versa), while Shoenfield have shown that from a proof in NBG of a set-sentence we can generate a proof in ZF (...) of the same formula. We argue that the first makes use of a too strong metatheory. Although meaningful, this symmetrical reduction does not equate the ontological content of the theories. The strong metatheory levels the two theories. Moreover, we will modernize Shoenfields proof, emphasizing its relation to Herbrands theorem and that it can only be seen as a partial type of reduction. In contrast with symmetrical reductions, we believe that asymmetrical relations are powerful tools for comparing ontological content. In virtue of this, we prove that there is no interpretation of NBG in ZF, while NBG trivially interprets ZF. This challenges the standard view that the two systems have the same ontological content. (shrink)

The paper proposes (1.) a non-standard interpretation of the proverbial expression “deuteros plous” by giving a fresh look to Phaedo, 99c9-d1. Then (2.) it proceeds to the philosophical problem raised in this passage according to this interpretation, that is, the problem of the “hypothesis” or the “unproved principle”. It indicates finally (3.) the kernel of truth contained in the standard Interpretation and it concludes with some remarks on the “weakness of the logoi”.

Animals are an important part of our social, economic and corporate world. Their wellbeing is significantly affected by the ways in which humans treat them. However, animals have long remained (and, indeed, continue to remain) effectively invisible in the business ethics and corporate responsibility discourse. This article argues in favor of the moral necessity of according animal welfare a higher priority in business. In line with most streams in both recent and traditional animal ethics, this article derives the avoidance of (...) unnecessary animal suffering as the moral minimum standard for responsible management in the livestock industry. Based on a broad range of different interpretations of what animal suffering may be necessary, the article discusses three distinct ways in which humans working in the animal industry could meet their moral responsibility to avoid unnecessary suffering, and, with this, increase animal welfare: by ameliorating circumstances for animals, by aiming at a two-pronged transformation, or by transforming into a “zero-suffering” business. Considering animal welfare as a legitimate ethical value in and of itself is a first step towards overcoming the anthropocentric bias in today's sustainability and corporate responsibility debate. (shrink)

The concept of formal transcendentalism is utilized. The fundamental and definitive property of the totality suggests for “the totality to be all”, thus, its externality (unlike any other entity) is contained within it. This generates a fundamental (or philosophical) “doubling” of anything being referred to the totality, i.e. considered philosophically. Thus, that doubling as well as transcendentalism underlying it can be interpreted formally as an elementary choice such as a bit of information and a quantity corresponding to the number of (...) elementary choices to be defined. This is the quantity of information defined both transcendentally and formally and thus, philosophically and mathematically. If one defines information specifically, as an elementary choice between finiteness (or mathematically, as any natural number of Peano arithmetic) and infinity (i.e. an actually infinite set in the meaning of set theory), the quantity of quantum information is defined. One can demonstrate that the so-defined quantum information and quantum information standardly defined by quantum mechanics are equivalent to each other. The equivalence of the axiom of choice and the well-ordering “theorem” is involved. It can be justified transcendentally as well, in virtue of transcendental equivalence implied by the totality. Thus, all can be considered as temporal as far anything possesses such a temporal counterpart necessarily. Formally defined, the frontier of time is the current choice now, a bit of information, furthermore interpretable as a qubit of quantum information. (shrink)

The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. (...) that of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) “discrete reference frame” to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the “ether” from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or “quantum mechanics and information”). The identification of entanglement and gravity can be considered also as a ‘byproduct” implied by the transition from the smooth “ether of special and general relativity’ to the “flat” ether of quantum mechanics and information. The qubit ether is out of the “temporal screen” in general and is depicted on it as both matter and energy, both dark and visible. (shrink)

The semeiotic of Charles Sanders Peirce is irreducibly triadic, positing that a sign mediates between the object that determines it and the interpretant that it determines. He eventually holds that each sign has two objects and three interpretants, standardizing quickly on immediate and dynamical for the objects but experimenting with a variety of names for the interpretants. The two most prominent terminologies are immediate/dynamical/final and emotional/energetic/logical, and scholars have long debated how they are related to each other. This paper seeks (...) to shed new light on the matter by reviewing the numerous manuscript drafts where Peirce develops the latter nomenclature while attempting to introduce his pragmatism to a general audience. It then goes on to examine an additional set of interpretants, intentional/effectual/communicational, and shows that the three different trichotomies can be understood as complementary, rather than redundant or conflicting. (shrink)

Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex Hilbert space of quantum mechanics), on the other hand, allows for an arithmetic version of Gentzen’s cut elimination and quantum measurement to be described uniformy as two processes occurring accordingly in those two branches. A philosophical reflection also justifying that unity by quantum (...) neo-Pythagoreanism links it to the opposition of propositional logic, to which Gentzen’s cut rule refers immediately, on the one hand, and the linguistic and mathematical theory of metaphor therefore sharing the same structure borrowed from Hilbert arithmetic in a wide sense. An example by hermeneutical circle modeled as a dual pair of a syllogism (accomplishable also by a Turing machine) and a relevant metaphor (being a formal and logical mistake and thus fundamentally inaccessible to any Turing machine) visualizes human understanding corresponding also to Gentzen’s cut elimination and the Gödel dichotomy about the relation of arithmetic to set theory: either incompleteness or contradiction. The metaphor as the complementing “half” of any understanding of hermeneutical circle is what allows for that Gödel-like incompleteness to be overcome in human thought. (shrink)

This chapter provides an interpretation of the early Heidegger’s underdeveloped conception of the undistinguishedness of everyday human existence in Being and Time. After explaining why certain translation choices of some key terms in this text are interpretively and philosophically important, I first provide a concise argument for why the social constitution interpretation of the relation between ownedness and unownedness makes better overall sense of Heidegger’s ambivalent attitude toward the social constitution of the human being than the standard existentialist interpretation (...) of this relation. I then proceed to the heart of this chapter, which develops his inchoate conception of the undistinguishedness of everydayness by arguing that it specifies the third distinctive mode of concrete human existence in addition to ownedness and unownedness. Accordingly, I show how unownedness is actually a generic phenomenon with two distinct species, namely, undistinguishedness and disownedness, which are at once closely related to, but also differ in significant respects from, each other. Consequently, instead of taking for granted a one-dimensional and mutually exclusive opposition between ‘authenticity’ and ‘inauthenticity’, I argue that we should adopt a two-dimensional and more nuanced understanding of the relations among undistinguishedness, disownedness, and ownedness that intersects with Heidegger’s underappreciated distinction between genuineness and ungenuineness. After raising and replying to some objections to this interpretation of undistinguishedness, I conclude this chapter by briefly sketching three of its philosophical consequences and pointing out its potential as an important resource for contemporary social theories. (shrink)

The previous two parts of the paper demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a subspace (...) of Hilbert space and especially its uniqueness can be unambiguously linked to that of partial algebra or incommensurability, or interpreted as a relation of the two dual branches of Hilbert arithmetic in a wide sense. The investigation of the last relation allows for FLT and Gleason’s theorem to be equated in a sense, as two dual counterparts, and the former to be inferred from the latter, as well as vice versa under an additional condition relevant to the Gödel incompleteness of arithmetic to set theory. The qubit Hilbert space itself in turn can be interpreted by the unity of FLT and Gleason’s theorem. The proof of such a fundamental result in number theory as FLT by means of Hilbert arithmetic in a wide sense can be generalized to an idea about “quantum number theory”. It is able to research mathematically the origin of Peano arithmetic from Hilbert arithmetic by mediation of the “nonstandard bijection” and its two dual branches inherently linking it to information theory. Then, infinitesimal analysis and its revolutionary application to physics can be also re-realized in that wider context, for example, as an exploration of the way for physical quantity of time (respectively, for time derivative in any temporal process considered in physics) to appear at all. Finally, the result admits a philosophical reflection of how any hierarchy arises or changes itself only thanks to its dual and idempotent counterpart. (shrink)

We intoduce a novel extension of Description Logics (DLs) of typicality by means of probabilities able to represent and reason about typical properties and defeasible inheritance in DLs.

The general topic of this paper is the ontological commitment to so-called "fictitious objects", that is, things and characters of fictional stories, like Sherlock Holmes and Pegasus. Discourse about fiction seems to entail an ontological commitment to fictitious entities, a commitment that is often deemed inconsistent with empirical facts. For instance, "Pegasus is a flying horse" seems to entail "There are flying horses" as well as "Pegasus exists" (according to some widely accepted logical principles). I discuss two solutions that have (...) been proposed in the literature. The first one amounts to rejecting sentences like "Pegasus is a flying horse" as false, at least if they are taken at face value. This solution is called the "story operator strategy". It consists in paraphrasing sentences like "Pegasus is a flying horse" by means of the expression "according to a story" such that they are interpreted as an elliptic formulation of, e.g., "According to a story, Pegasus is a flying horse". I spell out the difficulties of the story operator strategy and opt for a realist ontology of fiction. A novel interpretation of the story operator "according to a story" is given, which is not only consistent with but even sheds new light on such a realist ontology. In particular, it is shown how the story operator can be used as a tool to introduce the so-called "modes of predication distinction" (which is an essential ingredient of many realist ontologies of fiction) in a commonsensical way. (shrink)

The book is a collection of papers and aims to unify the questions of syntax and semantics of language, which are included in logic, philosophy and ontology of language. The leading motif of the presented selection of works is the differentiation between linguistic tokens (material, concrete objects) and linguistic types (ideal, abstract objects) following two philosophical trends: nominalism (concretism) and Platonizing version of realism. The opening article under the title “The Dual Ontological Nature of Language Signs and the Problem of (...) Their Mutual Relations” provides a broad introduction into the problem area connected with this differentiation, while the logic-formal characteristics of the distinction are framed in the work entitled “On the Type-Token Relationships” (Chapter 1). The basic part of the book deals with issues relating to syntax (Chapters 2-4) and semantics of language (Chapters 5-6), as well as pertaining to syntactic-semantic pragmatic questions (Chapters 7-13). Throughout the book, language, categorial language, is characterized syntactically as generated by classical categorial grammar (Chapter 2) and formalized on two opposing levels: as language of expression-tokens (level of tokens) and language of expression-types (level of types). The author’s considerations contained in Chapters 2 and 4 lead to the important philosophical conclusion that in formal-logical syntactic studies on language the assumption that expression-types constitute the primary language layer while expression-tokens make the secondary one, can be neglected; thus, this speaks in favour of the opposing standpoint—the concretistic one—in the ontology of language syntax. In the works “Meaning and Interpretations”, Parts I and II (Chapters 5 and 6), it is underlined, however, that such semantic concepts as: meaning, denotation and interpretation are defined on the types level, yet their formal definitions require making use of notions of the tokens level. The semantic notions introduced in the above-mentioned articles are also used in the following works of the present selection, under the titles: “Three Principles of Compositionality” and “On Metaknowledge and Truth” (Chapters 7 and 8). They formalize two principles of compositionality that are well known in the literature on the subject, deriving from Frege, i.e. those of meaning and of denotation; they are related to the syntactic principle of compositionality which was introduced by the author. All the three principles are, at the same time, three conditions of homomorphism of categorial language algebra into three kinds of non-standard models of language (one syntactic and two semantic ones: intensional and extensional), which allows introducing three definitions of truthfulness into these models. The next two works in the collection, entitled: “On Language Adequacy” and “What is the Sense in Logic and Philosophy of Language” (Chapters 9 and 10) concern adequacy of categorial language syntax along with its dual semantics: intensional and extensional, and categorial compatibility of any of its syntactic categories with two corresponding semantic categories: intensional and extensional, based on the compatibility the syntactic category of each language expression with the ontological category assigned to its denotatum. The well-known problem of categorial compatibility for first-order quantifiers finds its solution in the paper “Categories of First-Order Quantifiers” (Chapter 11). In the work “Logic and Ontology of Language” (Chapter 12), being in a sense a summary of the considerations presented in the preceding chapters of the book, language is treated as an ontological being, characterized in compliance with the logical conception of language proposed by Ajdukiewicz. Application—like throughout the book—of tools of classical logic and set theory has resulted in emergence of a general formal logical theory of syntax, semantics and pragmatics of language, which takes into account duality in the understanding of linguistic expressions as tokens (concretes) and types (abstract objects). In terms that take into account a functional approach to language itself, there comes out an ontological neutrality of logic with respect to existential assumptions relating to the ontological nature of linguistic expressions and their extra-linguistic ontological counterparts. The issues connected with applying logic while explaining the manner of using linguistic tokens and linguistic types to determine notions of language communication are raised and illustrated in the last chapter of the work, bearing the title “A Logical Conceptualization of Knowledge on the Notion of Language Communication”. (shrink)

The paper follows the track of a previous paper “Natural cybernetics of time” in relation to history in a research of the ways to be mathematized regardless of being a descriptive humanitarian science withal investigating unique events and thus rejecting any repeatability. The pathway of classical experimental science to be mathematized gradually and smoothly by more and more relevant mathematical models seems to be inapplicable. Anyway quantum mechanics suggests another pathway for mathematization; considering the historical reality as dual or “ (...) class='Hi'>complimentary” to its model. The historical reality by itself can be seen as mathematical if one considers it in Hegel’s manner as a specific interpretation of the totality being in a permanent self-movement due to being just the totality, i.e. by means of the “speculative dialectics” of history, however realized as a theory both mathematical and empirical and thus falsifiable as by logical contradictions within itself as emprical discrepancies to facts. Not less, a Husserlian kind of “historical phenomenology” is possible along with Hegel’s historical dialectics sharing the postulate of the totality (and thus, that of transcendentalism). One would be to suggest the transcendental counterpart: an “eternal”, i.e. atemporal and aspatial history to the usual, descriptive temporal history, and equating the real course of history as with its alternative, actually happened branches of the regions of the world as with only imaginable, counterfactual histories. That universal and transcendental history is properly mathematical by itself, even in a neo-Pythagorean model. It is only represented on the temporal screen of the standard historiography as a discrete series of unique events. An analogy to the readings of the apparatus in quantum mechanics can be useful. Even more, that analogy is considered rigorously and logically as implied by the mathematical transcendental history and sharing with it the same quantity of information as an invariant to all possible alternative or counterfactual histories. One can involve the hypothetical external viewpoint to history (as if outside of history or from “God’s viewpoint to it), to which all alternative or counterfactual histories can be granted as a class of equivalence sharing the same information (i.e. the number choices, but realized in different sequence or adding redundant ones in each branch) being similar and even mathematically isomorphic to Feynman trajectories in quantum mechanics. Particularly, a fundamental law of mathematical history, the law of least choice of the real historical pathway is deducible from the same approach. Its counterpart in physics is the well-known and confirmed law of least action as far as the quantity of action corresponds equivocally to the quantity of information or that of number elementary historical choices. (shrink)

Arthur Clark and Michael Kube–McDowell (“The Triger”, 2000) suggested the sci-fi idea about the direct transformation from a chemical substance to another by the action of a newly physical, “Trigger” field. Karl Brohier, a Nobel Prize winner, who is a dramatic persona in the novel, elaborates a new theory, re-reading and re-writing Pauling’s “The Nature of the Chemical Bond”; according to Brohier: “Information organizes and differentiates energy. It regularizes and stabilizes matter. Information propagates through matter-energy and mediates the interactions of (...) matter-energy.” Dr Horton, his collaborator in the novel replies: “If the universe consists of energy and information, then the Trigger somehow alters the information envelope of certain substances –“. “Alters it, scrambles it, overwhelms it, destabilizes it” Brohier adds. There is a scientific debate whether or how far chemistry is fundamentally reducible to quantum mechanics. Nevertheless, the fact that many essential chemical properties and reactions are at least partly representable in terms of quantum mechanics is doubtless. For the quantum mechanics itself has been reformulated as a theory of a special kind of information, quantum information, chemistry might be in turn interpreted in the same terms. Wave function, the fundamental concept of quantum mechanics, can be equivalently defined as a series of qubits, eventually infinite. A qubit, being defined as the normed superposition of the two orthogonal subspaces of the complex Hilbert space, can be interpreted as a generalization of the standard bit of information as to infinite sets or series. All “forces” in the Standard model, which are furthermore essential for chemical transformations, are groups [U(1),SU(2),SU(3)] of the transformations of the complex Hilbert space and thus, of series of qubits. One can suggest that any chemical substances and changes are fundamentally representable as quantum information and its transformations. If entanglement is interpreted as a physical field, though any group above seems to be unattachable to it, it might be identified as the “Triger field”. It might cause a direct transformation of any chemical substance by from a remote distance. Is this possible in principle? (shrink)

This paper discusses how the general and abstract concept of legitimacy applies to international institutions, using the United Nations Security Council as an example. We argue that the evaluation of the Security Council’s legitimacy requires considering three significant and interrelated aspects: its purpose, competences, and procedural standards. We consider two possible interpretations of the Security Council’s purpose: on the one hand, maintaining peace and security, and, on the other, ensuring broader respect for human rights. Both of these purposes are (...) minimally morally acceptable for legitimacy. Second, we distinguish between three different competences of the UNSC: 1) the decision-making competence, 2) the quasi-legislative competence, and 3) the referral competence. On this basis, we argue that different procedural standards are required to legitimise these competences, which leads to a more differentiated understanding of the Security Council’s legitimacy. While maintaining that the membership structure of the Council is a severe problem for its legitimacy, we suggest other procedural standards that can help to improve its overall legitimacy, which include broad transparency, deliberation, and the revisability of the very terms of accountability themselves. (shrink)

My goal in this paper is, to tentatively sketch and try defend some observations regarding the ontological dignity of object references, as they may be used from within in a formalized language. -/- Hence I try to explore, what properties objects are presupposed to have, in order to enter the universe of discourse of an interpreted formalized language. -/- First I review Frege′s analysis of the logical structure of truth value definite sentences of scientific colloquial language, to draw suggestions from (...) his saturated vs. unsaturated sentence components paradigm. -/- Next try investigate, in how far reference to non pure math objects might allow for a role as argument of a truth value function. Object kinds to be considered are: common sense objects, technical objects, humanities object kinds (social, psychical, ...), objects of art, ... , be they abstract, concrete, or in this respect mixed objects. -/- Then have a comment on the just referenced label abstract objects. -/- Next try to get an idea wrt the ontological significance of the fact, that pure math objects and functions in some important classical cases can be uniquely defined by means of categorical theories. Here, in the course of my argument, I have a little corollary wrt the standard model of first order Peano arithmetic, reducing the epistemological significance of the existence of the non standard models. -/- Next, wrt a special concept of a formalized empirical theory, I care for whether the impure math objects and mixed objects described here, and complying best with truth value function mapping, are also reliable candidates for the ontological commitment of such theories: and discuss an alternative, which reduces the ontological significance of the universe of discourse of the theories intended models. -/- In the end I sum up what is - from my point of view - the status quo, according to my respective findings. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather (...) a metamathematical axiom about the relation of mathematics and reality. The main statement is formulated as follows: Any scientific theory admits isomorphism to some mathematical structure in a way constructive. Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. The sketch of the proof is organized in five steps: a generalization of epoché; involving transfinite induction in the transition between Peano arithmetic and set theory; discussing the finiteness of Peano arithmetic; applying transfinite induction to Peano arithmetic; discussing an arithmetical model of reality. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. The present paper follows a pathway grounded on Husserl’s phenomenology and “bracketing reality” to achieve the generalized arithmetic necessary for the principle to be founded in alternative ontology, in which there is no reality external to mathematics: reality is included within mathematics. That latter mathematics is able to self-found itself and can be called Hilbert mathematics in honour of Hilbert’s program for self-founding mathematics on the base of arithmetic. The principle of universal mathematizability is consistent to Hilbert mathematics, but not to Gödel mathematics. Consequently, its validity or rejection would resolve the problem which mathematics refers to our being; and vice versa: the choice between them for different reasons would confirm or refuse the principle as to the being. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. The Schrödinger equation in quantum mechanics is involved to illustrate that ontology. Thus the problem which of the two mathematics is more relevant to our being is discussed again in a new way A few directions for future work can be: a rigorous formal proof of the principle as an independent axiom; the further development of information ontology consistent to both kinds of mathematics, but much more natural for Hilbert mathematics; the development of the information interpretation of quantum mechanics as a mathematical one for information ontology and thus Hilbert mathematics; the description of consciousness in terms of information ontology. (shrink)

Kant’s most prominent formulation of the Categorical Imperative, known as the Formula of Universal Law (FUL), is generally thought to demand that one act only on maxims that one can will as universal laws without this generating a contradiction. Kant's view is standardly summarized as requiring the 'universalizability' of one's maxims and described in terms of the distinction between 'contradictions in conception' and 'contradictions in the will'. Focusing on the underappreciated significance of the simultaneity condition included in the FUL, I (...) argue, by contrast, that the principle is better read as requiring that one be able to will two things simultaneously without self-contradiction, namely, that a maxim be one's own and that it be a universal law. This amounts to a new interpretation of the FUL with significant interpretive and philosophical advantages. (shrink)

Everyone has heard of "the invisible hand," the famous metaphor used by Adam Smith (1723-1790) in The Wealth of Nations. Although he uses the expression only once in the book, it has given rise to controversy that has lasted for over two centuries. -/- The famous expression has been understood, in (at least) two very different ways. In one way by most of academia, and in a very different way by Keynes, Noah Chomsky and more lately by Mark Blaug (in (...) the second edition of The New Palgrave, 2008). -/- In the standard textbook interpretation, it is considered a poetical name for "the price mechanism" and presented as an argument in favor of laisser-faire and free trade. In this paper we recall the less well-known interpretation (of Keynes, Blaug and Chomsky), showing that Smith was more reserved towards laisser-faire than is commonly believed and that by "invisible hand" he did not mean the price mechanism. (shrink)