Andy Curzon replied (often quoting from the opening sections of Lester 2014, chapter 10) in an ongoing debate with Lee Waaks, which Mr Waaks forwarded (with approval) to the Libertarian Alliance Forum (27 February 2015). This response replies to the criticisms after directly quoting them (the indented text; except where Lester is occasionally quoted, as indicated). A few cuts have been made to avoid some repetition and irrelevance. However, just as Mr Curzon sometimes repeats his main points in slightly different (...) ways and contexts in the hope that some of them might prove cogent, so this reply does the same. The dialogue-like result seems to engage more directly and completely than producing a new stand-alone exposition. And some new arguments are even developed in the process. But the full nature of many of the criticisms and replies often only becomes clear as the “dialogue” proceeds. An addendum then rebuts two further brief critical responses in the same manner. (shrink)

The main purpose of this article is to tackle the problem of living together – as dignified human beings – in a certain territory in the field of social philosophy, on the theoretical grounding ensured by some remarkable exponents of the Austrian School − and by means of the praxeologic method. Because political tools diminish the human nature not only of those who use them, but also of those who undergo their effects, people can live a life worthy of a (...) human being only as members of some autarchic or self-governing communities. As a spontaneous order, every autarchic community is inherently democratic, inasmuch as it makes possible free involvement, peaceful coordination, free expression and the free reproduction of ideas. The members of autarchic communities are moral individuals who avoid aggression, practice self-control, seek a dynamical efficiency and establish a democratic public discourse. (shrink)

Most analysts view the United Nations as a positive stabilising force in international affairs. In this paper, I critically assess this opinion of the UN’s peace enforcement actions using the case studies of the Korean War and the Gulf War while relying on the non-aggression axiom of libertarian philosophy. In the process, I shed light on some of the moral considerations at play when deciding on UN-sanctioned military intervention.

The central thesis of my article is that people live a life worthy of a human being only as self-ruling members of some autarchic (or self-governing) communities. On the one hand, nobody is born as a self-ruling individual, and on the other hand, everybody can become such a person by observing progressively the non-aggression principle and, ipso facto, by behaving as a moral being. A self-ruling person has no interest in controlling her neighbors, but in mastering his own impulses, (...) needs, wishes, desires, behaviors, etc. Inasmuch as he is an imperfect being who lives in an imperfect world, he needs to share certain interests, beliefs, values, customs and other characteristics with other people, i.e. to be involved in some communities. Depending on the following four criteria – the regulatory principle, the essential resources, the specific feedback and the fundamental values –, the countless and manifold human communities can be grouped in three categories: (1) affinity communities, (2) economic communities, and (3) civic communities. In other words, every community or human behavior has an affinity, an economic, and a civic dimension. If a civic community is merely a state shaped society, it can be called a political community. All communities are intrinsically variable. Throughout time, they ceaselessly change their composition, values, interpersonal processes and relations, territory, etc. Interestingly enough, the variability is unanimously recognized and accepted in affinity and communities economic, but is denied or abusively interpreted in the case of state shaped societies. If we confuse two types of order − cosmos and taxis – and two types of rule – nomos and thesis –, as well as we exaggerate the importance of certain type of community we bring some social maladies, namely the traditionalism, the commercialism and the civism, (with the worst form of it – the politicality). Whatever the communities they are involved in, all persons relate (implicitly or explicitly) to the libertarian non-aggression principle, living their life in strict accordance with the logical implications of the position they adopt. People who respect the non-aggression axiom necessarily manifest self-control, consideration for the life and property of the others, commitment to offer value for value, love of freedom and a high level of individual responsibility. By contrast, people who violate this axiom – the villains and the statists – invariably strive to control their neighbors, behave as parasites or predators, prefer forced exchanges, reject the personal responsibility (at most accepting the idea of social responsibility), and apply double moral standards. The first category of people generates a libertarian civic discourse as a spontaneous order, and the second creates a political/ statist civic discourse as a result of the human design and will to power. As a spontaneous order, the libertarian civic discourse implies free involvement, peaceful coordination, free expression, free reproduction of ideas and the power of one. Every communication performance in the frame of the libertarian civic discourse is important and has relevant results. All participants to the libertarian civic discourse are automatically members of some self-governing communities (at least members of the general libertarian community). The most important thing for these communities is to be connected to a communicational infrastructure which would make possible free involvement, free expression and the free reproduction of ideas. Inasmuch as today democracy means the tyranny of majority and participatory democracy the tyranny of majority plus the power of vested (and illegitimate) interests, only the emergence of self-governing communities by libertarian discourse offers us a little hope. It’s high time to fall in love (again) with liberty and to embrace the non-aggression principle. We don’t have to create a perfect world, but we can strive to develop our human nature. (shrink)

This article connects François Laruelle's non-philosophical experiments with the axiomatic method to non-philosophy's anti-hermeneutic stance. Focusing on two texts from 1987 composed using the axiomatic method, "The Truth According to Hermes" and "Theorems on the Good News," I demonstrate how non-philosophy utilizes structural mechanisms to both expand and contract the field of potential models allowed by non-philosophy. This demonstration involves developing a notion of interpretation, which synthesizes Rocco Gangle's work on model theory with respect to non-philosophy with Laruelle's critique of (...) hermeneutics. I use Alexander Galloway's interpretation of "The Truth According to Hermes" as a case study of the limits non-philosophy sets upon its use as a basis for philosophical models, in contrast to arguments by Gangle regarding non-philosophy's greater genericity in comparison to philosophy. (shrink)

In situations where we ignore everything but the space of possibilities, we ought to suspend judgment—that is, remain agnostic—about which of these possibilities is the case. This means that we cannot sum our degrees of belief in different possibilities, something that has been formalized as an axiom of non-additivity. Consistent with this way of representing our ignorance, I defend a doxastic norm that recommends that we should nevertheless follow a certain additivity of possibilities: even if we cannot sum degrees (...) of belief in different possibilities, we should be more confident in larger groups of possibilities. It is thus shown that, in the type of situation considered (in so-called ‘classical ignorance’, i.e. “behind a thin veil of ignorance”), it is epistemically rational for advocates of suspending judgment to endorse this comparative confidence; while on the other hand it is shown that, even in classical ignorance, no stronger belief—such as a precise uniform probability distribution—is warranted. (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)

A system of logic usually comprises a language for which a model-theory and a proof-theory are defined. The model-theory defines the semantic notion of model-theoretic logical consequence (⊨), while the proof-theory defines the proof- theoretic notion of logical consequence (or logical derivability, ⊢). If the system in question is sound and complete, then the two notions of logical consequence are extensionally equivalent. The concept of full formalization is a more restrictive one and requires in addition the preservation of the standard (...) meanings of the logical terms in all the admissible interpretations of the logical calculus, as it is proof-theoretically defined. Although classical first-order logic is sound and complete, its standard formalizations fall short to be full formalizations since they allow non-intended interpretations. This fact poses a challenge for the logical inferentialism program, whose main tenet is that the meanings of the logical terms are uniquely determined by the formal axioms or rules of inference that govern their use in a logical calculus, i.e., logical inferentialism requires a categorical calculus. This paper is the first part of a more elaborated study which will analyze the categoricity problem from its beginning until the most recent approaches. I will first start by describing the problem of a full formalization in the general framework in which Carnap (1934/1937, 1943) formulated it for classical logic. Then, in sections IV and V, I shall discuss the way in which the mathematicians B.A. Bernstein (1932) and E.V. Huntington (1933) have previously formulated and analyzed it in algebraic terms for propositional logic and, finally, I shall discuss some critical reactions Nagel (1943), Hempel (1943), Fitch (1944), and Church (1944) formulated to these approaches. (shrink)

We prove a representation theorem for preference relations over countably infinite lotteries that satisfy a generalized form of the Independence axiom, without assuming Continuity. The representing space consists of lexicographically ordered transfinite sequences of bounded real numbers. This result is generalized to preference orders on abstract superconvex spaces.

In this paper, I consider the use of mathematical results in philosophical arguments arriving at conclusions with non-mathematical content, with the view that in general such usage requires additional justification. As a cautionary example, I examine Kreisel’s arguments that the Continuum Hypothesis is determined by the axioms of Zermelo-Fraenkel set theory, and interpret Weston’s 1976 reply as showing that Kreisel fails to provide sufficient justification for the use of his main technical result. If we take the perspective that mathematical results (...) are used in the context of a modelling of something not necessarily mathematical, then the situation is clarified somewhat, and the procedure for arriving at justification for the use of such results becomes clear. I give an example of a particularly strong form this justification might take, using the idea of formalism independence due to Gödel and Kennedy. (shrink)

It might be that the phrase ‘local holism’ covers a range of explanatory possibilities spreading to consistencies of theories generally, that we can take something from Peacocke’s caution about delimiting and differentiating modes of support for abstracts to sort something in the varieties of tensions at work in settling contents of theories self-determined to be consistent (facing a barrage of neo-consistencies). The subject-matter becomes then a holism in its entirety in self-consistent self-representation underpinned by that recognition operating over items formulated (...) in a vocabulary supporting consistent representations and operations. In A Study of Concepts scenarios—described by me as ‘containers’— associate a type of primitive to a grammar worked on transitions paralleling a proposed familiar egocentric type of orientation’s handling of objects in a vicinity. The value of scenarios though is distanced from origination, it lies in the depiction of support for and delineation and record of separable coordinate valuations and conceptual transcribing. (shrink)

Suppose one has a system, the infinite set of positive integers, P, and one wants to study the characteristics of a subset (or subsystem) of that system, the infinite subset of odd positives, O, relative to the overall system. In mathematics, this is done by pairing off each odd with a positive, using a function such as O=2P+1. This puts the odds in a one-to-one correspondence with the positives, thereby, showing that the subset of odds and the original set of (...) positives are the same size, or have the same cardinality. This counter-intuitive result ignores the “natural” relationship of one odd for every two positives in the sequence of positive integers, which would suggest that O is one-half the size of P. However, in the set of axioms that constitute mathematics, it is considered valid. Fair enough. In the physical universe (i.e., the starting system), though, relationships between entities matter. In biochemistry, if you start with an organism, say a rat, and you want to study its heart, you can do this by removing some heart cells and studying them in isolation in a cell culture system. But, the results often differ compared to what occurs in the intact animal because studying the isolated cultured cells ignores the relationships in the intact body between the cells, the rest of the heart tissue and the rest of the rat. In chemistry, if a copper atom were studied in isolation, it would never be known that copper atoms in bulk can conduct electricity because the atoms share their electrons. In physics, the relationships between inertial reference frames in relativity, and observer and observed in quantum physics can't be ignored. Relationships matter in the physical world, but the mathematics of infinite sets is still used to describe it. Does this matter? It seems to, at least in physics. Infinities cause numerous problems in theoretical physics such as non-renormalizability and problems in unifying quantum mehanics and general relativity . This suggests that the pairing off method and the mathematics of infinite sets based on it are analogous to a cell culture system or studying a copper atom in isolation if they are used in studying the physical universe because they ignore the inherent relationships between entities. In the real, physical world, the natural, inherent, relationships between entities can't be ignored. Said another way, the set of axioms that constitute abstract mathematics may be similar but not identical to the set of physical axioms by which the real, physical universe runs. This suggests that the results from abstract mathematics about infinities may not apply to or should be modified for use in physics. (shrink)

A nation commits mitigated aggression by threatening to kill the citizens of a victim nation if and only if they do not submit to being ruled in a non-egregiously oppressive way. Such aggression primarily threatens a nation’s common way of life . According to David Rodin, a war against mitigated aggression is automatically disproportionate, as the right of lethal self-defense only extends to protecting against being killed or enslaved. Two strategies have been adopted in response to Rodin. (...) The first strategy grants that CWL is insufficiently valuable to lethally defend, however, other considerations can satisfy the proportionality requirement. I argue that this strategy is not persuasive. The second strategy argues for the sufficient value of CWL. This, however, fails to answer the forceful ‘benign dictator’ objection. I respond to this objection by grounding the proportionality of a defensive war in the value of what Phillip Pettit calls ‘anti-power’. (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 objects to an explanation I extract from Jeanette Edwards, concerning a pattern she observes of questions asked and not asked. There are propositions accepted as axioms which apparently lead to that pattern. I present an axiomatization but it leads to different questions.

Kant's arguments for the synthetic a priori status of geometry are generally taken to have been refuted by the development of non-Euclidean geometries. Recently, however, some philosophers have argued that, on the contrary, the development of non-Euclidean geometry has confirmed Kant's views, for since a demonstration of the consistency of non-Euclidean geometry depends on a demonstration of its equi-consistency with Euclidean geometry, one need only show that the axioms of Euclidean geometry have 'intuitive content' in order to show that both (...) Euclidean and non-Euclidean geometry are bodies of synthetic a priori truths. Michael Friedman has argued that this defence presumes a polyadic conception of logic that was foreign to Kant. According to Friedman, Kant held that geometrical reasoning itself relies essentially on intuition, and that this precludes the very possibility of non-Euclidean geometry. While Friedman's characterization of Kant's views on geometrical reasoning is correct, I argue that Friedman's conclusion that non-Euclidean geometries are logically impossible for Kant is not. I argue that Kant is best understood as a proto-constructivist and that modern constructive axiomatizations (unlike Hilbert-style axiomatizations) of both Euclidean and non-Euclidean geometry capture Kant's views on the essentially constructive nature of geometrical reasoning well. (shrink)

Katerina Kolozova is a Macedonian philosopher whose publications from last two decades aim to analyze various topics using François Laruelle’s “non-philosophy” or “non-standard philosophy.” Non-philosophy could be roughly described as radicalized deconstruction: Laruelle claims that not everything can be grasped by a philosophy: for Laruelle, “philosophy is too serious an affair to be left to the philosophers alone.”1 Non-philosophy opposes the “principle of sufficient philosophy” through which philosophy determines and decides what is real. According to Laruelle, the ultimate limit of (...) philosophical thought and its self-proclaimed sufficiency lies in its inherent tendency to close itself in a transcendental system of autofetishist conceptions, which presume that one can grasp the Real (“The Real is neither capable of being known or even ‘thought,’ but can be described in axioms. [...] Even ‘immanence’ only serves to name the Real which tolerates nothing but axiomatic descriptions or formulations.”) by a philosophical thought, or that the Real could be mediated only through human thought. Laruelle criticizes this tendency of philosophy, which is usually expressing itself through the structure of “philosophical Decision.” (“To philosophize is to decide Reality and the thoughts that result from this, i.e. to believe to be able to order them in the universal order of the Principle of Reason [Logos].”) Katerina Kolozova use Laruelle’s non-philosophy to explore more explicitly political topics. In the Cut Of Th e Real (2014), she criticized certain dogmatism of poststructuralist philosophy and feminist theory, namely their symptomatic rejection of the Real and the One. In Toward a Radical Metaphysics of Socialism (2015) and The Lived Revolution (2016) Kolozova presented a rereading of Marx, whose work she found relevant for the critique of speculative philosophical dimension of the capitalist economy, embodied in the 2008 global finance crisis, and in the latter book, she explored the possibility of a new political solidarity, based on “bodies in pain.” Kolozova doesn’t call to philosophically reconstruct Marx’s thought for the current situation, but she goes back to Marx with the help of Laruelle’s non-Marxism, contrary to the usual approach of Marxist philosophers, who often try to create certain philosophical system of Marx’s work. Together with Eileen A. Joy, Kolozova edited the anthology After the “Speculative Turn” (2016), which addressed recent realist and materialist tendencies in feminist philosophy. In her most recent book, Capitalism’s Holocaust of Animals (2019), Kolozova aimed to explore broader philosophical foundations of neoliberal capitalism, and its dealing with nonhuman animals and their suffering. According to Kolozova, “We have to start by coming to terms with what we did to the animals in the constitutive act of philosophy and via proxy to all those dehumanised that belong to the species of man ‘by courtesy’ only.” . (shrink)

Dugundji proved in 1940 that most parts of standard modal systems cannot be characterized by a single finite deterministic matrix. In the eighties, Ivlev proposed a semantics of four-valued non-deterministic matrices (which he called quasi-matrices), in order to characterize a hierarchy of weak modal logics without the necessitation rule. In a previous paper, we extended some systems of Ivlev’s hierarchy, also proposing weaker six-valued systems in which the (T) axiom was replaced by the deontic (D) axiom. In this (...) paper, we propose even weaker systems, by eliminating both axioms, which are characterized by eight-valued non-deterministic matrices. In addition, we prove completeness for those new systems. It is natural to ask if a characterization by finite ordinary (deterministic) logical matrices would be possible for all those Ivlev-like systems. We will show that finite deterministic matrices do not characterize any of them. (shrink)

Propensities are presented as a generalization of classical determinism. They describe a physical reality intermediary between Laplacian determinism and pure randomness, such as in quantum mechanics. They are characterized by the fact that their values are determined by the collection of all actual properties. It is argued that they do not satisfy Kolmogorov axioms; other axioms are proposed.

Some forms of defining PNC in Aristotle’s works are as follows: a) Everything must be either affirmed or denied (φάναι ἢ ἀποφάναι). (Met., B, 996b28-29) or: it will not be possible to assert and deny the same thing truly at the same time. (Met., Γ, 1008a36-b1) In other words, ‘contradictory statements (ἀντικειμένας φάσεις) are not at the same time true. (Met., Γ, 1011b13-14) Also, ‘It is impossible that contradictories (ἀντίφασιν) should be at the same time true of the same thing.’ (...) (Met., Γ, 1011b15-16) Also, ‘Opposite statements (ἀντικειμένας φάσεις) can never be true of the same subjects.’ (Met., K, 1062a33-34; 1063b15-17) Also, ‘Of all affirmation or negation one is impossible. (PsA., A, 11, 77a22) b) A thing cannot at the same time be and not be. (Met., B, 996b30-31; Γ, 1006a3-5) This can also be extended to many other similar pairs of opposites: ‘The same thing cannot at the same time be and not be, or admit any other similar pair of opposites.’ (Met., K, 1061b34-1062a2) Also, ‘It will be possible for the same thing to be and not to be, except in virtue of an ambiguity.’ (Met., Γ, 1006b18-19) This is also asserted in another similar way: it is impossible that it should be at the same time true to say the same thing is a thing and is not a thing.’ (Met., Γ, 1006b33-34) c) ‘The same attribute cannot at the same time belong (ὑπάρχειν) and not belong to the same object in the same respect.’ (Met., Γ, 1005b19-21) d) Those positive and negative propositions are said to be contradictory which have the same subject and predicate. (OI, I, 7, 17a33-35) The opposition between an affirmation and a denial makes contradictories (ἀντίφασεως). (PsA., A, 2, 72a11-14) Based on Aristotle’s definition, ‘An affirmation is opposed to a denial in the sense which I denote by the term ‘contradictory’ (ἀντίφατικως), when, while the subject remains the same, the affirmation is of universal character and the denial is not.’ (OI., I, 7, 17b16-19) 1) Characteristics of PNC a) It is the most certain (Met., Γ, 1005b22-23 and b11) and the most indisputable (Met., Γ, 1006a5-6) of all principles. b) It is impossible: to believe its contrary (Met., Γ, 1005b24-30); to be really in that position (Met., Γ, 1008b11-13); and to defend it. (OI, I, 9, 18b17-19) Nonetheless, Aristotle thinks that many of the writers about nature assert the contrary of PNC and use a language opposite to it. (Met., Γ, 1005b35-1006a3) c) It is the starting point of all the other axioms. (Met., Γ, 1005b32-34) d) It is not hypothetical. (Met., Γ, 1005b13-17) e) Contradictories are extremely opposed to each other. (Met., Γ, 1007a1-4) f) Believing in PNC saves substance and essence and not believing in it makes all attributes accidents and there will be nothing as being essentially something. The reason is that something which essentially is a being cannot avoid being that thing. (Met., Γ, 1007a20-29 and b16-18) g) PNC supports plurality of things because otherwise all things will be one: ‘If all contradictories are true of the same subject at the same time, evidently all things will be one. For the same thing will be a trireme, a wall, and a man, if it is equally possible to affirm and deny anything of anything.’ (Met., Γ, 1007b18-22) In fact, PNC supports difference: ‘For if contradictories can be predicated alike of each subject, one thing will in no wise differ from another; for if it differs, this difference will be something true and peculiar to it.’ (Met., Γ, 1008a25-27) h) To accept truth and falsity, whether in an absolute sense (e.g. A is more true than B; or C is less true than D) entails PNC. (Met., Γ, 1008b2-7 and b31-35; 1009a2-5) In fact, PNC is entailed by accepting true affirmation. (Met., K, 1062b7-11) i) Judging and choosing between at least two things entails PNC: you cannot choose one as better than another without a previous judging that one is A and the other not A. (Met., Γ, 1008b18-24) The same is true about avoiding. (Met., Γ, 1008b24-29) j) PNC guarantees speaking and saying anything intelligible because otherwise e.g. saying ‘yes’ means both yes and no. (Met., Γ, 1008b7-13) k) Contradictories do not accept intermediates that means we must either affirm or deny a predicate on a subject and there is no third option. (Met., Γ, 1011b23-24; Met., I, 1055b1-2; PsA., A, 2, 72a11-14; Met., I, 1057a33-36) l) PNC is applicable also to the future time. (OI., I, 9, 19a28-29) m) PNC is presupposed by the least semantic of words. If we accept that each word has a meaning and, thus, signifies something definite, we cannot accept that it has the contradictory meaning and signies contradictory things and this approves PNC. Thus, Aristotle asks the opponent of PNC to say just one word, a significant word and takes this as the demonstration of PNC because by saying the word e.g. ‘man’ you have already signified man and not-man. (Met., Γ, 1005a11-13 and a18-22; 1006a28-31 and b13-15) Therefore, signification entails PNC: ‘He, then, who says this is and is not denies what he affirms, so that what the word signifies, he says it does not signify; and this is impossible. Therefore, if ‘This is’ signifies something, one cannot truly assert the contradictory.’ (Met., K, 1062a16-20) He says again: ‘If the word signifies something and this can be truly asserted of it, it necessarily is this; and it is not possible that that which is necessary should ever not be: it is not possible therefore to make the opposed assertions truly of the same subject.’ (Met., K, 1062a20-23; cf. Met., K, 1062a24-31) n) At Met., 4, 3, 1005b9-10 (check???) PNC is called as principle of things (ἀρχὰς τοῦ πράγματος). (quoted from B215, 517) . (shrink)

Michael Walzer argues that except in cases involving genocide or mass slaughter, humanitarian intervention is unjustifiable because “citizens get the government they deserve, or, at least, the government for which they are ‘fit.’”Yet, if people are autonomous and deserve the government that rules over them, then it would seem that they are responsible for the government’s actions, including their nation’s wars of aggression.That line of thought undermines the doctrine of noncombatant immunity, which is perhaps the most important of Walzer’s (...) jus in bello principles. In this way, the concept of self-determination frustrates Walzer’s attempts to keep jus ad bellum and jus in bello considerations separate. (shrink)

In this paper we extend the NeutroAlgebra & AntiAlgebra to the geometric spaces, by founding the NeutroGeometry & AntiGeometry. While the Non-Euclidean Geometries resulted from the total negation of one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom or even of more axioms from any geometric axiomatic system (Euclid’s, Hilbert’s, etc.) and from any type of geometry such as (Euclidean, Projective, Finite, Affine, Differential, Algebraic, Complex, Discrete, Computational, Molecular, Convex, etc.) Geometry, (...) and the NeutroGeometry results from the partial negation of one or more axioms [and no total negation of no axiom] from any geometric axiomatic system and from any type of geometry. Generally, instead of a classical geometric Axiom, one may take any classical geometric Theorem from any axiomatic system and from any type of geometry, and transform it by NeutroSophication or AntiSophication into a NeutroTheorem or AntiTheorem respectively in order to construct a NeutroGeometry or AntiGeometry. Therefore, the NeutroGeometry and AntiGeometry are respectively alternatives and generalizations of the Non-Euclidean Geometries. In the second part, we recall the evolution from Paradoxism to Neutrosophy, then to NeutroAlgebra & AntiAlgebra, afterwards to NeutroGeometry & AntiGeometry, and in general to NeutroStructure & AntiStructure that naturally arise in any field of knowledge. At the end, we present applications of many NeutroStructures in our real world. (shrink)

In industrial societies where civil law and state institutions have become well established secular vehicles for governing the populace, it is widely assumed that the state no longer has an interest in fortifying the religious sector as a complementary source of social control. Thus, a distinction is drawn between the Islamic state that is ruled by religious law and the secular state of Western industrial societies in which religion is deemed to have lost its influence in the public sphere. This (...) dissertation argues that civil law is not religiously neutral and thus challenges a central premise of secularization theory. Introducing a new theoretical model that classifies civil law on the basis of its purpose-to protect religious liberty, engage or fortify the religious sector, or to advance universal norms-the author examines the impact of the three different types of legislation upon religious freedom and the individual autonomy of religious minorities in Sweden, an aggressively secularized industrial society. The author concludes that, viewed from the standpoint of a religious nonconformist, there is no discernible difference between living in a society that is overtly ruled by religious law (e.g., an Islamic state) and living in a "secular” society that is ruled by civil law either embedded with religious norms or designed to facilitate state appropriation of the religious sector as a complementary means of social control. In either environment, the author argues, the religious nonconformist will be forced to conform to the religious norms of the predominant religious group. (shrink)

The scope of libertarian law is normally limited to the application of the non-aggression principle (NAP), nothing more and nothing less. However, judging when the NAP has been violated requires not only a conception of praxeological notions such as aggression, but also interpretive understanding of what synthetic events count as the relevant praxeological types. Interpretive understanding—or verstehen—can be extremely heterogeneous between agents. The particular verständnis taken by a judge has considerable moral and political implications. Since selecting a verständnis (...) is pre-requisite to applying the NAP, the NAP itself cannot tell us which one we ought morally to choose. Therefore the application of the NAP calls on moral and political considerations outside of the NAP itself. Since some of these are more consistent with an endorsement of the NAP than others, libertarianism is not a “thin” commitment to the NAP alone, but a “thick” commitment to the NAP and other supporting moral and political considerations. (shrink)

There are many factors that may affect the analysis of ethical problems: the physical acts that occur, the relevant history, verbal communication, contracts, etc. One factor that can be difficult to incorporate is the role that socials norms play. This is because norms can vary widely between societies, and even within societies individuals are not usually consciously aware of the norms that they act upon. This paper examines how norms can effect ethical problems and gives one approach for investigating their (...) effect. (shrink)

In the United States, police use of force experts often maintain that controversial police shootings where an unarmed person’s hand gesture was interpreted as their “going for a gun” are justifiable. If an officer waits to confirm that a weapon is indeed being pulled from a jacket pocket or waistband, it may be too late to defend against a lethal attack. This article examines police policy norms for self-defense against “uncertain threats” in three contexts: (1) known in-progress violent crimes, (2) (...) interactions with civilians behaving non-aggressively, and (3) interactions with civilians behaving aggressively. It is argued that the context of a known in-progress violent crime gives rise to threat probability-, fairness-, and lesser evil-based reasons for a norm permitting police officers to use lethal force. However, in the contexts of civilians behaving non-aggressively and civilians behaving aggressively, such a norm is not justifiable. In the former case, I introduce two conditions, the Justification condition and the Valuing Civilian Lives condition, which I argue are not presently met. In the latter case, these two conditions again are not met; aggression may moreover be excused or justified due to background injustices around race and the criminal justice system. (shrink)

This paper aims to show issues raised by lacanian psychoanalyses concerning the reasons of the phenomenon of aggressiveness, mainly due to the frequency of this phenomenon in education. In this paper, it was intended to highlight the philosophical dimension of the problem, since we are using basically the dissertative method. Lacan takes Hegelian and Marxist legacy to develop the thesis of aggressiveness as realization of a dynamic introduced from the gaze and that has its modus operandi in the movements of (...) alienation and non-alienation. The aggressiveness illustrated, for example, by the injuries suffered by teachers shows itself as a tentative to cause the fall of the Other, this fall is considered as the object a of which its appearance is regulated by the Oedipus Complex. Namely, both the way how the parental authority figures are inscribed in the significant chains that compose the individual and how this inscription shapes the existential possibilities of interaction with the opposite sex would be the key to foresee the extent the individual makes use of aggressiveness. In this way, the Oedipus complex, reinvested by the event of puberty would be responsible for the displacement of the libido one time to the ´Other´ and other time to the own subject. The Other, in the theoretical development of Lacan that follows the decade of 1960, comprehends the identifier choices and also what escapes from any identification. The Other, as a teacher, has the role of positioning itself to generate intuitively one process of identification and has the delicate function of sustain the dialectic that emerges in the moment where the Other falls, moment which usually comes after the identification and that happens with a joy capable of unveiling the object a. Although the role of education is not to maintain an auscultation to this object, the education can influence its nonexclusion and make this object be contoured with the advent of singularities. In this moment, the explicitness of the rules which education constitutes itself as well as the empathy from the educator can be a fundamental instrument in education like the subject to be taught. From the text, we can conclude that: we need to put the aggressiveness in our speech as via of achievement of the non-alienation process conjugated with the possibility to support the desire. (shrink)

Inchoate crime consists of acts that are regarded as crimes despite the fact that they are only partial or incomplete in some respect. This includes acts that do not succeed in physically harming the victim or are only indirectly related to such a result. Examples include attempts (as in attempted murder that does not eventuate in the killing of anyone), conspiracy (in which case the crime has only been planned, not yet acted out) and incitement (where the inciter does not (...) himself commit the crime he is urging others to undertake). The present paper attempts to analyze these inchoate crimes from a libertarian perspective, based on the non-aggression principle. (shrink)

This essay details wolves’ sense of their surround in terms of how wolves’ perceptual acuities, motor abilities, daily habits, overriding concerns, network of intimate social bonds and relationship to prey gives them a unique sense of space, time, belonging with other wolves, memorial sense, imaginative capacities, dominant emotions (of affection, play, loyalty, hunger, etc.), communicative avenues, partnership with other creatures, and key role in ecological thriving. Wolves are seen to live within a vast sense of aroundness and closeness to aspects (...) of their surround (compared to humans), a highly charged intimacy and cooperation with other wolves, and a caring and non-aggressive attitude that goes beyond the pack, despite their loyalty and defense of territory. The cultural myths and history that absurdly demonize the wolf are explored in their self-righteous attempts to exterminate wolves, which I call “speciocide” and probe for projections of human viciousness. The supposed rapaciousness of wolves is re-examined by expanding Barry Lopez’s sense of the silent dialogue of death with other creatures to be reconsidered as a kind of respect, assertion of vitality, recognition or mortality and cooperation. (shrink)

The central thesis of this article is that populism is a side effect of liberal democracy and a reliable indicator of the relationship between liberal democracy and its polar opposite ‒ illiberal majoritarianism. As long as liberal democracy prevails over illiberal majoritarianism, populism remains dormant. Populism rises and becomes conspicuous only if certain manifestations of illiberal majoritarianism or illiberal elitism reach a critical point in terms of number and impact. More exactly, populism becomes active when there are too few reasonable (...) and effective responses to the growth of illiberal majoritarianism. Illustrating the defense mechanism of compensation, the rise of populism correlates with a cluster of exaggerated or overdone reactions to actions inspired by illiberal majoritarianism. These reactions vary sharply from one society to another according to (a) the specific challenges of illiberal majoritarianism, (b) the reactivity of people who bear the liberal democratic values, and (c) the credibility enjoyed by the mainstream liberal democratic forces in that society. In brief, although illiberal majoritarianism sets off a cluster of populist reactions in any society, the rise of populism always takes distinct forms. Thus, it is confirmed the status of populism as a chameleonistic phenomenon. The argumentative thread has four main parts. Firstly, it is developed a constitutive model of liberal democracy as an ideal political system that is underpinned by the following organizing principles or attractors: inclusiveness, political equality, political participation, predominance of concurrent majority, the containment and predictability of the government power, and the enforcement of the non-aggression principle. Secondly, the attractors of liberal democracy are contrasted against the recent state of affairs in the Euro-Atlantic space to illustrate the assertion presented here that today illiberal majoritarianism tends to prevail over liberal democracy. In the third step, it is argued that the countless definitions of populism only emphasize different symptoms of the rise of populism, depending on the particular circumstances in which society evolves. Finally, it is substantiated the claim that populism and populists can and should be integrated into the democratic political system, in particular into the democratic public sphere. (shrink)

In this paper Kant's "perpetual peace" is being interpreted as a realistic utopia. Kant's "perpetual peace" remains an utopia even today in the sense that the described perpetual world peace is still a long way to go from today's state of world politics. But Kant also tried to show that the utopian scenario is possible under realistic assumptions. Therefore this essay examines the question, if Kant's basic assumptions - such as for example the assumption that democracies are generally non aggressive (...) - are still valid in the light of the political experiences of the two centuries that have elapsed since the publication of the "perpetual peace" and how the realisation of Kant's utopia can best be promoted in today's situation. (shrink)

This replies to Block 2019 (B19), which responds to Lester 2014 (L14). The main issues in the, varyingly sized, sections are as follows. 1 Further explanations of critical rationalism, the theory of liberty, and problems with the non-aggression principle. 2.1 The relationships among law, morality, and libertarianism. 2.2 The objective invasiveness of low-level radiation and that it is therefore an initiated imposition (albeit trivial) if someone inflicts it on non-consenting people. 2.3 The objective and subjective aspects of initiated impositions; (...) and how clashes can be resolved. 2.4 How liberty relates to risk and self-ownership. 2.5 Libertarian initial acquisition versus absolute property rights by labour-mixing. 2.6 Organisational note. 2.7 Libertarianism and mens rea. 2.8 Libertarian rectification versus lex-talionis doubling. 2.9 Indirectly clashing rights, self-preservation, trespasser-hiker, flagpole-grasper, and landmine-layer. 2.10 A logical point is not a moral point. 2.11 Pacifism and libertarianism. 3.1 A weak criticism of utilitarianism. 3.2 Hedonometers; approximate interpersonal comparisons of utility imply libertarianism; what a libertarian is; libertarian rankings. 4. Libertarian philosophy versus propertarian dogma. Coda: the need to take seriously the philosophical problems with propertarian-justificationist libertarianism. (shrink)

The Zwolinski 2013 "libertarianism and liberty" essays on libertarianism_org are argued to have the following problems: taking libertarianism to be a "commitment" to the view that "liberty is the highest political value" ; examining and rejecting the maximization of liberty without a libertarian theory of liberty; accepting a persuasive sense of "coercion" ; misunderstandingliberty in the work place; conflating, to varying degrees, freedom of action and freedom from aggression and justice/rights/morals; focusing on logically possible clashes instead of practically possible (...) congruence among utility, liberty, and justice – in particular, that "rule (preference-)utilitarianism" fits "rule libertarianism" ; failing to distinguish liberty from license (and power) concerning slavery, and so-called "civil and democratic liberties" (and everything else); the idea that any coherent reference to a quantity of liberty requires precise cardinality; failing to see that the quantity of liberty has an inherently qualitative aspect; misunderstanding property as about limiting freedom; mistaking clashing Hobbesian freedom for non-clashing Lockean liberty; adopting G. A. Cohen's confusion about freedom as the libertarian conception of freedom; assuming the – illogical – epistemology of justification" ; not realizing that both allowing and prohibiting pollution "aggresses" and so "aggressions" need to be minimized; the failure of all six of its reasons for rejecting the non-aggression principle. (shrink)

We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...) Lebesgue measurable, suggesting that Connes views a theory as being “virtual” if it is not definable in a suitable model of ZFC. If so, Connes’ claim that a theory of the hyperreals is “virtual” is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren’t definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes’ criticism of virtuality. We analyze the philosophical underpinnings of Connes’ argument based on Gödel’s incompleteness theorem, and detect an apparent circularity in Connes’ logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace −∫ (featured on the front cover of Connes’ magnum opus) and the Hahn–Banach theorem, in Connes’ own framework. We also note an inaccuracy in Machover’s critique of infinitesimal-based pedagogy. (shrink)

The paper sheds fresh light on what Adam Smith was doing in writing the Wealth of Nations by looking at its place in his unaccomplished oeuvre. The Wealth of Nations is just a partial implementation of a part of his project: the history and theory of law and government. In this work, the ‘Socratic method” of persuasion and the “Newtonian method” of didactical discourse coexist with moral discourse. Such coexistence allows a smooth transition from (i) an argument aimed at persuading (...) the public opinion of the advantage carried by non-aggressive commercial policies, high wages and provision of public goods by the public authority to (ii) a simplified reconstruction of economic mechanisms and tendencies through either conjectural history or ‘systems”, and (iii) an argument showing how all the oppressive inequality existent in modern societies is, besides deplorable on whatever moral standard, contrary to everybody’s interest. (shrink)

Focusing on a particular facet of entitlement theory, I criticize the view that Nozick’s version of the theory provides an adequate description of procedural justice. I agree with Nozick that justice is procedural; however, I believe his entitlement theory as it currently stands is incomplete. I show that Nozick is committed to believing that the implied content of his entitlement theory is unjust, and therefore that a certain set of market transactions ought to be judged as legally wrong according to (...) Nozick’s own political foundations. Furthermore, I demonstrate that the Non-Aggression Principle is inconsistent with what a procedurally just entitlement theory would require, and therefore diminishes the degree to which a full-fledged account of distributive justice can properly be called libertarian. Finally, I offer a principle intended as a starting point for a discussion of what constitutes just transfer, and briefly speculate as to the legal results of implementing such a principle. (shrink)

Nowhere in the works of what is called Aristotle is there a discussion of anything named Natural Law. Everywhere in the works of what is called Aristotle there are discussions of principles and there are discussion of laws; separately. And for this reason: Nature abides by principles. Humans make laws. By nature, aggression is the principle. Since aggression impedes each particular person in the same way, a universal manner, this universal offense is the impetus for a prescription of (...) any law at all. Law was first prescribed to prohibit that natural aggression. Hence, there is no non-aggression principle. Aggression is the principle, non-aggression is the law. The purpose of good law is to protect and maintain this natural justice of equality before any law. Unjust laws are an attempt to establish some other sort of equality that is not universal. Seeing this distinction of principles and laws as separate makes clear what is right by nature and wrong by law. However, at some places in the works of what is called Aristotle there is a discussion of what may be named natural rights, political rights, and natural justice. The preceding paragraph is the application of Aristotle’s CATEGORIES, INTERPRETATION, ANALYTICS, TOPICS, and RHETORIC as the means of separating the true from the false. (shrink)

The cognition of quantum processes raises a series of questions about ordering and information connecting the states of one and the same system before and after measurement: Quantum measurement, quantum in-variance and the non-locality of quantum information are considered in the paper from an epistemological viewpoint. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as a statistical ensemble after measurement. Quantum in-variance designates (...) the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. A set-theory corollary is the curious in-variance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. However the above equivalence requires it to be equated to a well-ordered set after measurement and thus requires the axiom of choice for it to be able to be obtained. Quantum in-variance underlies quantum information and reveals it as the relation of an unordered quantum “much” (i.e. a coherent state) and a well-ordered “many” of the measured results (i.e. a statistical ensemble). It opens up to a new horizon, in which all physical processes and phenomena can be interpreted as quantum computations realizing relevant operations and algorithms on quantum information. All phenomena of entanglement can be described in terms of the so defined quantum information. Quantum in-variance elucidates the link between general relativity and quantum mechanics and thus, the problem of quantum gravity. The non-locality of quantum information unifies the exact position of any space-time point of a smooth trajectory and the common possibility of all space-time points due to a quantum leap. This is deduced from quantum in-variance. Epistemology involves the relation of ordering and thus a generalized kind of information, quantum one, to explain the special features of the cognition in quantum mechanics. (shrink)

We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are (...) also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preorders. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity. (shrink)

Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general.

Rawls saw need for non-ideal theory also within society but never developed that project. In this chapter, Card suggests that the non-ideal part of Rawls’ Law of Peoples can be a resource for thinking about responding to evils when the subject is not state-centered. It is plausible that defense against great evils other than those of aggressive states should be governed by analogues of scruples that Rawlsian well-ordered societies observe in defending themselves against outlaw states. This essay explores those hypotheses (...) in relation to women’s self-defense and mutual defense against evils of misogyny, the term feminists apply to the most deeply hostile environments of and attitudes toward women and girls and to the cruelest wrongs to them/us, regardless whether perpetrators harbor feelings of hatred. It extrapolates and adapts to this case values, concepts, and methods from Rawls’s life’s work, especially his writing on war. (shrink)

A new non-Archimedean approach to interacted quantum fields is presented. In proposed approach, a field operator φ(x,t) no longer a standard tempered operator-valued distribution, but a non-classical operator-valued function. We prove using this novel approach that the quantum field theory with Hamiltonian P(φ)_4 exists and that the corresponding C^*­ algebra of bounded observables satisfies all the Haag-Kastler axioms except Lorentz covariance. We prove that the λ(φ^4 )_4 quantum field theory model is Lorentz covariant.

Many philosophers in the field of meta-ethics believe that rational degrees of confidence in moral judgments should have a probabilistic structure, in the same way as do rational degrees of belief. The current paper examines this position, termed “moral Bayesianism,” from an empirical point of view. To this end, we assessed the extent to which degrees of moral judgments obey the third axiom of the probability calculus, ifP(A∩B)=0thenP(A∪B)=P(A)+P(B), known as finite additivity, as compared to degrees of beliefs on the (...) one hand and degrees of desires on the other. Results generally converged to show that degrees of moral judgment are more similar to degrees of belief than to degrees of desire in this respect. This supports the adoption of a Bayesian approach to the study of moral judgments. To further support moral Bayesianism, we also demonstrated its predictive power. Finally, we discuss the relevancy of our results to the meta-ethical debate between moral cognitivists and moral non-cognitivists. (shrink)

For the classical Geometry, in a geometrical space, all items (concepts, axioms, theorems, etc.) are totally (100%) true. But, in the real world, many items are not totally true. The NeutroGeometry is a geometrical space that has some items that are only partially true (and partially indeterminate, and partially false), and no item that is totally false. The AntiGeometry is a geometrical space that has some item that are totally (100%) false. While the Non-Euclidean Geometries [hyperbolic and elliptic geometries] resulted (...) from the total negation of only one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom [and in general: theorem, concept, idea etc.] and even of more axioms [theorem, concept, idea, etc.] and in general from any geometric axiomatic system (Euclid’s five postulates, Hilbert’s 20 axioms, etc.), and the NeutroAxiom results from the partial negation of any axiom (or concept, theorem, idea, etc.). Clearly, the AntiGeometry is a generalization of Non-Euclidean Geometries. (shrink)

Distributive justice deals with allocations of goods and bads within a group. Different principles and results of distributions are seen as possible ideals. Often those normative approaches are solely framed verbally, which complicates the application to different concrete distribution situations that are supposed to be evaluated in regard to justice. One possibility in order to frame this precisely and to allow for a fine-grained evaluation of justice lies in formal modelling of these ideals by metrics. Choosing a metric that is (...) supposed to map a certain ideal has to be justified. Such justification might be given by demanding specific substantiated axioms, which have to be met by a metric. This paper introduces such axioms for metrics of distributive justice shown by the example of needs-based justice. Furthermore, some exemplary metrics of needs-based justice and a three dimensional method for visualisation of non-comparative justice axioms or evaluations are presented. Therewith, a base worth discussing for the evaluation and modelling of metrics of distributive justice is given. (shrink)

In this paper we extend Neutro-Algebra and Anti-Algebra to geometric spaces, founding Neutro/Geometry and AntiGeometry. While Non-Euclidean Geometries resulted from the total negation of a specific axiom (Euclid's Fifth Postulate), AntiGeometry results from the total negation of any axiom or even more axioms of any geometric axiomatic system (Euclidean, Hilbert, etc. ) and of any type of geometry such as Geometry (Euclidean, Projective, Finite, Differential, Algebraic, Complex, Discrete, Computational, Molecular, Convex, etc.), and Neutro-Geometry results from the partial negation (...) of one or more axioms [and without total negation of any axiom] of any geometric axiomatic system and of any type of geometry. Generally, instead of a classical geometric Axiom, one can take any classical geometric Theorem of any axiomatic system and of any type of geometry, and transform it by Neutrosophication or Antisofication into a Neutro-Theorem or Anti-Theorem respectively to construct a Neutro-Geometry or Anti-Geometry. Therefore, Neutro-Geometry and Anti-Geometry are respectively alternatives and generalizations of Non-Euclidean Geometries. In the second part, the evolution from Paradoxism to Neutrosophy, then to NeutroAlgebra and Anti-Algebra, then to Neutro-Geometry and Anti-Geometry, and in general to Neutro-Structure and Anti-Structure that arise naturally in any field of knowledge is recalled. At the end, applications of many Neutro-Structures in our real world are presented. (shrink)

The discussion of the Principle of Non-Contradiction (PNC) in Aristotle’s Metaphysics Γ is usually taken to include three ‘versions’ of the principle: an ontological, psychological, and logical one. In this article I develop an interpretation of Metaphysics Γ3 and a parallel text, De interpretatione 14, in order to show that these texts are concerned with two related but different principles: a version of the Principle of Identity, and a corollary to this, which concerns the ability to accept two ‘opposite’ items (...) at the same time. I argue that these principles must be considered separately in order to properly understand Aristotle’s remarks about PNC in Metaphysics Γ, and in order to defend his approach in these remarks against certain objections raised against the discussion in Metaphysics Γ by Jan Łukasiewicz in his "Über den Satz des Widerspruchs bei Aristoteles". The main result of my interpretation is to distinguish in the discussion of PNC in Metaphysics Γ three principles: one concerning linguistic items (words and statements), one concerning thoughts (δόξαι), and one concerning objects or states of affairs. (shrink)

When people combine concepts these are often characterised as “hybrid”, “impossible”, or “humorous”. However, when simply considering them in terms of extensional logic, the novel concepts understood as a conjunctive concept will often lack meaning having an empty extension (consider “a tooth that is a chair”, “a pet flower”, etc.). Still, people use different strategies to produce new non-empty concepts: additive or integrative combination of features, alignment of features, instantiation, etc. All these strategies involve the ability to deal with conflicting (...) attributes and the creation of new (combinations of) properties. We here consider in particular the case where a Head concept has superior ‘asymmetric’ control over steering the resulting concept combination (or hybridisation) with a Modifier concept. Specifically, we propose a dialogical approach to concept combination and discuss an implementation based on axiom weakening, which models the cognitive and logical mechanics of this asymmetric form of hybridisation. (shrink)

The systems of arithmetic discussed in this work are non-elementary theories. In this paper, natural numbers are characterized axiomatically in two di erent ways. We begin by recalling the classical set P of axioms of Peano’s arithmetic of natural numbers proposed in 1889 (including such primitive notions as: set of natural numbers, zero, successor of natural number) and compare it with the set W of axioms of this arithmetic (including the primitive notions like: set of natural numbers and relation of (...) inequality) proposed by Witold Wilkosz, a Polish logician, philosopher and mathematician, in 1932. The axioms W are those of ordered sets without largest element, in which every non-empty set has a least element, and every set bounded from above has a greatest element. We show that P and W are equivalent and also that the systems of arithmetic based on W or on P, are categorical and consistent. There follows a set of intuitive axioms PI of integers arithmetic, modelled on P and proposed by B. Iwanuś, as well as a set of axioms WI of this arithmetic, modelled on the W axioms, PI and WI being also equivalent, categorical and consistent. We also discuss the problem of independence of sets of axioms, which were dealt with earlier. (shrink)

The text is a continuation of the article of the same name published in the previous issue of Philosophical Alternatives. The philosophical interpretations of the Kochen- Specker theorem (1967) are considered. Einstein's principle regarding the,consubstantiality of inertia and gravity" (1918) allows of a parallel between descriptions of a physical micro-entity in relation to the macro-apparatus on the one hand, and of physical macro-entities in relation to the astronomical mega-entities on the other. The Bohmian interpretation ( 1952) of quantum mechanics proposes (...) that all quantum systems be interpreted as dissipative ones and that the theorem be thus derstood. The conclusion is that the continual representation, by force or (gravitational) field between parts interacting by means of it, of a system is equivalent to their mutual entanglement if representation is discrete. Gravity (force field) and entanglement are two different, correspondingly continual and discrete, images of a single common essence. General relativity can be interpreted as a superluminal generalization of special relativity. The postulate exists of an alleged obligatory difference between a model and reality in science and philosophy. It can also be deduced by interpreting a corollary of the heorem. On the other hand, quantum mechanics, on the basis of this theorem and of V on Neumann's (1932), introduces the option that a model be entirely identified as the modeled reality and, therefore, that absolutely reality be recognized: this is a non-standard hypothesis in the epistemology of science. Thus, the true reality begins to be understood mathematically, i.e. in a Pythagorean manner, for its identification with its mathematical model. A few linked problems are highlighted: the role of the axiom of choice forcorrectly interpreting the theorem; whether the theorem can be considered an axiom; whether the theorem can be considered equivalent to the negation of the axiom. (shrink)