A number of classical theories are interpreted in analogous theories that are based on intuitionistic logic. The classical theories considered include subsystems of first- and second-order arithmetic, bounded arithmetic, and admissible set theory.

“La théorie, c'est bon, mais ça n'empêche pas d'exister”J. M. CharcotRoughly speaking, references relate what is said to just those things about which it is said. A theory of reference is commonly taken to be a statement or characterization of that relation which references effect — that relation, that is, which holds between something that is said and some object just in case in that which is said reference is made to that object. Such a theory is often (...) further conceived as answering one or both of the questions: For any given object X, what is it for a reference to be made to X, and For any given reference, R, what is it for an object X to be the referent of R. Let us call a theory which correctly answers at least some of these questions a classical theory of reference. (shrink)

Vol 1. Substance truth and person -- vol 2. Perfecting reality -- vol 3. Practical implication -- vol 4. The idealist theory of truth.

In this paper I urge friends of truth-value gaps and truth-value gluts – proponents of paracomplete and paraconsistent logics – to consider theories not merely as sets of sentences, but as pairs of sets of sentences, or what I call ‘bitheories,’ which keep track not only of what holds according to the theory, but also what fails to hold according to the theory. I explain the connection between bitheories, sequents, and the speech acts of assertion and denial. I (...) illustrate the usefulness of bitheories by showing how they make available a technique for characterising different theories while abstracting away from logical vocabulary such as connectives or quanti- fiers, thereby making theoretical commitments independent of the choice of this or that particular non-classical logic. (shrink)

Classical political theorists such as Thucydides, Kant, Rousseau, Smith, Hegel, Grotius, Mill, Locke and Clausewitz are often employed to explain and justify contemporary international politics and are seen to constitute the different schools of thought in the discipline. However, traditional interpretations frequently ignore the intellectual and historical context in which these thinkers were writing as well as the lineages through which they came to be appropriated in International Relations. This collection of essays provides alternative interpretations sensitive to these political (...) and intellectual contexts and to the trajectory of their appropriation. The political, sociological, anthropological, legal, economic, philosophical and normative dimensions are shown to be constitutive, not just of classical theories, but of international thought and practice in the contemporary world. Moreover, they challenge traditional accounts of timeless debates and schools of thought and provide new conceptions of core issues such as sovereignty, morality, law, property, imperialism and agency. (shrink)

There are well-known quasi-formal arguments that identity is a "strict" relation in at least the following three senses: (1) There is a single identity relation and a single distinctness relation; (2) There are no contingent cases of identity or distinctness; and (3) There are no vague or indeterminate cases of identity or distinctness. However, the situation is less clear cut than it at first may appear. There is a natural formal theory of identity that is very close to the (...) standard classical theory but which does not validate the formal analogues of (1)-(3). The core idea is simple: We weaken the Principle of the Indiscernibility of Identicals from a conditional to an entailment and we adopt a weakly classical logic. This paper investigates this weakly classical theory of identity (and related theories) and discusses its philosophical ramifications. It argues that we can accept a reasonable theory of identity without committing ourselves to the uniqueness, necessity, or determinacy of identity. (shrink)

I extract several common assumptions in the Classical Theory of Mind (CTM) - mainly of Locke and Descartes - and work out a partial formalisation of the logic implicit in CTM. I then define the modal (logical) properties and relations of propositions, including the modality of conditional propositions and the validity of argument, according to the principles of CTM: that is, in terms of clear and distinct ideas, and without any reference to either possible worlds, or deducibility in (...) an axiomatic system, or linguistic convention. (shrink)

Conceptual Metaphor Theory makes some strong claims against so-called Classical Theory which spans the accounts of metaphors from Aristotle to Davidson. Most of these theories, because of their traditional literal-metaphorical distinction, fail to take into account the phenomenon of conceptual metaphor. I argue that the underlying mechanism for explaining metaphor bears some striking resemblances among all of these theories. A mapping between two structures is always expressed. Conceptual Metaphor Theory insists, however, that the literal-metaphorical distinction of (...) Classical Theories is empirically wrong. I claim that this criticism is based rather on terminological decisions than on empirical issues. Conceptual Metaphor Theory focusses primarily on conventional metaphors and struggles to extend its mechanism to novel metaphors, whereas Classical Theories focus on novel metaphors and struggle to extend their mechanisms to conventional metaphors. Since all of these theories study metaphors from the synchronic point of view, they are unable to take into account any semantic change. A diachronic perspective is what we need here, one which would allow us to explain the role of metaphor in semantic change and the development of language in general. (shrink)

The classical theory of types in question is essentially the theory of Martin-Löf [1] but with the law of double negation elimination. I am ultimately interested in the theory of types as a framework for the foundations of mathematics and, for this purpose, we need to consider extensions of the theory obtained by adding ‘well-ordered types,’ for example the type N of the finite ordinals; but the unextended theory will suffice to illustrate the treatment (...) of extensional equality. (shrink)

Among the most characteristic effects of the onset of "romanticism" in the eighteenth century was the underinining of the "classical" ethics, based on rational selfdiscipline, by the "romantic" or humanitarian ethics, based on benevolism. A useful indication of the point at which this change in ethics occurred is the moment in which the institution of Negro slavery was attacked by benevolistic theory. As Trevelyan says, the anti-slavery movement was "the first successful propagandist agitation of the modern type" ; (...) years before the eighteenth century there had been sporadic objection against Negro slavery, especially religious objection because Negro slaves were commonly not considered "children of God." But until Francis Hutcheson's System of Moral Philosophy , no writer formulated ethical principles inimical to slavery as an institution. (shrink)

Arnopoulos explains the thoughts and practices of the ancient Greeks with regard to external affairs, or exopolitics, integrating political philosophy with modern international theory. He examines the political ideas of Plato and Aristotle specifically, and evaluates the ancient Greek policy ideals regarding constitutionalism, statesmanship, and foreign policy. In many ways, Arnopoulos would say this is a study not of what people do, but rather how they justify their deeds. He has been writing on the subject for about 30 years, (...) and this monograph is a consolidation of his thinking. His current academic affiliation is not noted. (shrink)

A standard view within psychology is that there have been two important shifts in the study of concepts and that each has led to some improvements. The first shift was from the classical theory of concepts to probabilistic theories, including the prototype theory. The second shift was from probabilistic theories to theory-based theories. In this article, I critically evaluate the view that the first shift was a major advance and argue that the prototype theory suffers (...) some of the same problems that have been thought to challenge the classical theory. (shrink)

A fundamental philosophical question that arises in connection with evolutionary theory is whether the fittest patterns of behavior are always the most rational. Are fitness and rationality fully compatible? When behavioral rationality is characterized formally as in classical decision theory, the question becomes mathematically meaningful and can be explored systematically by investigating whether the optimally fit behavior predicted by evolutionary process models is decision-theoretically coherent. Upon investigation, it appears that in nontrivial evolutionary models the expected behavior is (...) not always in accord with the norms of the standard theory of decision as ordinarily applied. Many classically irrational acts, e.g. betting on the occurrence of one event in the knowledge that the probabilities favor another, can under certain circumstances constitute adaptive behavior.One interesting interpretation of this clash is that the criterion of rationality offered by classical decision theory is simply incorrect (or at least incomplete) as it stands, and that evolutionary theory should be called upon to provide a more generally applicable theory of rationality. Such a program, should it prove feasible, would amount to the logical reduction of the theory of rational choice to evolutionary theory. (shrink)

The focus in this essay will be upon the paradoxes, and foremostly in set theory. A central result is that the librationist set theory £ extension \Pfund $\mathscr{HR}(\mathbf{D})$ of \pounds \ accounts for \textbf{Neumann-Bernays-Gödel} set theory with the \textbf{Axiom of Choice} and \textbf{Tarski's Axiom}. Moreover, \Pfund \ succeeds with defining an impredicative manifestation set $\mathbf{W}$, \emph{die Welt}, so that \Pfund$\mathscr{H}(\mathbf{W})$ %is a model accounts for Quine's \textbf{New Foundations}. Nevertheless, the points of view developed support the view that (...) the truth-paradoxes and the set-paradoxes have common origins, so that the librationist resolutions of the set theoretic paradoxes are at the same time resolutions of the truth theoretic paradoxes. Both the librationist resolutions of the set theoretic paradoxes and the truth theoretic paradoxes have non-trivial philosophical implications: librationist set theories have the consequence that there are no absolutely uncountable sets, and librationist truth theories allow the use of syntactical modalities in ways which circumvent limitations as those of \parencite{Montague1963}, and a truth predicate which is useful for more precise philosophical discourse. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:32. HUME'S CLASSICAL THEORY OF JUSTICE1 Let me begin by formulating a broad distinction between two sorts of theories of justice. I shall stipulate that a modern theory of justice is one which treats justice as a moral quality, in fact as one moral quality among a multitude of moral virtues, and which accordingly takes the obligation tö' be just as pre-eminently a moral obligation. On (...) this approach the philosophical appreciation of justice requires that we interpret it in terms of a moral theory, and correspondingly any viable moral theory is expected to afford a framework within which the virtue of justice is to be understood. The important philosophical question to be asked about justice concerns the moral obligation to abide by the conventions and rules of justice. By a classical theory of justice I mean one which treats this quality not as one moral virtue among many others but as fundamental to morality itself. Here justice would have to be explained before one could develop a satisfactory account of morality. Questions about the moral obligation of justice are on this approach not as important philosophically as questions about the basis of justice itself. The modern and the classical theories are distinguished by the relationship each posits between justice and morality. In the modern approach, the account one offers of morality conditions the account one can offer of justice, while in the classical theory the account one offers of justice conditions the account one can offer of morality. As exemplifying a classical theory of justice one might cite Plato's Republic or, closer to the present topic, Hobbes' De Homi ne. While there seems to be no definitive interpretation of Hobbes ' overall moral and political theories, in this work he maintains that the development of a settled morality is subsequent to the establishment of civil society and therein, of course, also of the order of justice. The following passage from the De Homine shows how the order 33. of civil justice plays a foundational role relative to the moral order. Eut whatsoever is the object of any man's appetite or desire, that is it which he for his part calleth good: and the object of his hate and aversion, evil; and of his contempt, vile and inconsiderable. For these words of good, evil, and contemptible, are ever used with relation to the person that useth them: there being nothing simply and absolutely so; nor any common rule of good and evil, to be taken from the nature of the objects themselves; but from the person of the man, where there is no commonwealth; or, in a commonwealth, from the person that representeth it; or from an arbitrator or judge, whom men disagreeing shall by consent set up, and make his sentence the rule thereof. 2 Attributing to Hobbes the view that the account one gives of justice and the civil order conditions and serves as a necessary presupposition to the account one can give of a settled morality permits us to count Hobbes among those thinkers who have offered a classical theory of justice. Because Hume seems in so many ways to deserve the appellation of thoroughly modern philosopher, it is not surprising that he is naturally construed as sharing in the modern conception of justice. I want to argue that this way of interpreting Hume is mistaken and that he is in fact a classical theorist of justice. I shall contend, furthermore, that getting clear about the kind of theory of justice Hume offers allows us to resolve a problem in his moral theory—specifically a problem relating to the correction of the moral judgment. In view of these aims, the paper has three parts: (1) investigation as to what kind of theory of justice Hume offers; (2) exploration of a quandary inherent in the modernist interpretation which serves as an objection to the thesis of this paper; and (3) resolution of this objection and conclusion as to the character of Hume's theory of morality. At the end I shall explore a few corollaries 34. of the thesis that Hume is a classical theorist of justice. 1. Hume: A Classical Theorist of Justice There are... (shrink)

The classical theory of probability has long been abandoned and is seen by most philosophers as a non-contender—a mere precursor to newer and better theories. In this paper I argue that this is a mistake. The main reasons for its rejection—all related to the notorious principle of indifference—are that it is circular, of limited applicability, inconsistent, and dependent upon unjustified empirical assumptions. I argue that none of these claims is true and that the classical theory remains (...) to be refuted. (shrink)

""Why theories of religion?" After raising and answering this question the author begins his examination of theories of religion by first looking at the explanations given by religious believers (Revelation and Religious Experience). He then considers the view of thinkers who have sought to transform religion into philosophy (Plato, Kant and Hegel), before reviewing the theories of those who have seen religion as arising out of errors in primitive thinking (Tyler, Frazer and Levy-Bruhl) and those 'masters of suspicion', as Paul (...) Ricoeur has called them, (Feuerbach, Nietzsche, Marx and Freud) who offered what they believed to be exhaustive psychological and sociological theories of the origin and nature of religion. In the course of his discussion the author also engages with many contemporary thinkers whose discussions of religion have been based on these classical accounts."--BOOK JACKET. (shrink)

The article is about one of the vital problem for analytic philosophy which is how to define truth value for sentences which include their own truth predicate. The aim of the article is to determine Saul Kripke’s approach to widen epistemological truth to create a systemic model of truth. Despite a lot of work on the subject, the theme of truth is no less relevant to modern philosophy. With the help of S. Kripke’s article “Outline of the Theory of (...) Truth” and R. L. Kirkham’s work “Theories of Truth: A Critical Introduction” the author tried to represent a non-classical approach which is now known as Saul Kripke’s truth value gaps theory. Considering his solving of the Liar Paradox, as well as the Strenghened Liar, it is obvious that there could be the circumstances (or facts) that make sentences have no truth value. In that case the solving of the paradox attracts Kleene’s non-classical three-valued logic which contains the third way and the solution falls into the gap between truth and falsity. Hence there are no relevant and full satisfactory ways to solve the Liar’s Paradox by the language-levels ap- proach. The task consists in an extension of the approach to natural languages and elimination of an ad hoc element as well. Besides that, the language-levels approach refers to the speaker that means that only the last one is allowed to define the hierarchy of the levels and truth value of sentence, but often he does not know what level he is speaking of. As Kripke stated, contingent facts can lead to a paradox which isn’t allowed for a logical point of view. However usage of mathematical apparatus allows the theory in question to be universalized and moreover paves the way to futher epistemological develop- ment of the problem in question. As Kripke’s theory is formalized and presented as a functional series, it gives access to a system model of truth whose elements would be epistemological theories (concepts) of truth. Such a model, for instance, confirms the validity of the deflationary concept of truth. Refs 7. (shrink)

We formulate from first principles a theory of stochastic processes in configuration space. The fundamental equations of the theory are an equation of motion which generalizes Newton's second law and an equation which expresses the condition of conservation of matter. Two types of stochastic motion are possible, both described by the same general equations, but leading in one case to classical Brownian motion behavior and in the other to quantum mechanical behavior. The Schrödinger equation, which is derived (...) here with no further assumption, is thus shown to describe a specific stochastic process. It is explicitly shown that only in the quantum mechanical process does the superposition of probability amplitudes give rise to interference phenomena; moreover, the presence of dissipative forces in the Brownian motion equations invalidates the superposition principle. At no point are any special assumptions made concerning the physical nature of the underlying stochastic medium, although some suggestions are discussed in the last section. (shrink)

The article shows that three antirealistic theories of classical analysis and synthesis are logically possible: presentationistic, solipsistic and Kantian, but only the latter is actually being developed. Revealed its specific features and features shared with other, logically possible antirealistic theories. The correlation of the Kantian theory of analysis and synthesis of knowledge with his theory of analysis and synthesis of subjects of knowledge is analyzed. Gnoseological problems that forced Kant to assert that new knowledge is provided only (...) by the synthesis of knowledge, and analysis only clarifies the results of synthesis, are characterized. The Kantian solution to these problems is correlated with their realistic solution. The role that the Kantian "Copernican revolution in philosophy" plays in his interpretation of the analysis and synthesis of subjects of knowledge is investigated. The Kantian theory of analytical and synthetic judgments is considered. It is shown that the Kantian question "how are synthetic judgments a priori possible?" is essentially a question about the nature of theoretical knowledge, which was historically formed in ancient geometry precisely as the unity of analysis and synthesis. A qualitative difference is shown between classical and geometric (by origin) analysis and synthesis. Three historical stages of their formation are described. The assertion of I. Newton that the natural science experiment arose as a result of the extension of the method of geometric analysis and synthesis to the natural sciences is investigated. (shrink)

Gregory Reichberg’s argument against my reading of the classical just war theorists falsely assumes that if just cause is unilateral, then there is no moral equality of combatants. This assumption is plausible if we assume an individualist framework. However, the classical theorists accepted quasi-Aristotelian, communitarian social ontologies and theories of justice. For them, the political community is ontologically and morally prior to the private individual. The classical just war theorists build their theories within this framework. They argue (...) that just war is only waged by supra-individual political communities for irreducibly social ends. War by private individuals for private ends is always unjust. The ends sought in just war presuppose the justice of a hierarchy of authority over war such that the soldier is obligated to serve in war upon the command of his legitimate authority. In this way, the classical theorists accept a unilateral theory of just cause and a division of authority over war that entails the possibility of the moral equality of combatants. (shrink)

We discuss the solution proposed by Fermi to the so called “4/3 problem” in the classical theory of the electron, a problem which puzzled the physics community for many decades before and after his contribution. Unfortunately his early resolution of the problem in 1922–1923 published in three versions in Italian and German journals (after three preliminary articles on the topic) went largely unnoticed. Even more recent texts devoted to classical electron theory still do not present his (...) argument or acknowledge the actual content of those articles. The calculations initiated by Fermi at the time are completed here by formulating and discussing the conservation of the total 4-momentum of the accelerated electron as seen from the instantaneous rest frame in which it is momentarily at rest. (shrink)

Any "classical" theory of truth will satisfy tarski's criterion ("p" is true if and only if p), And the principle of bivalence (every proposition is either true or false). A non-Classical theory may be obtained by rejecting these principles: - in fact it is shown that rejection of the second entails rejection of the first. If the resulting non-Classical theory is formalized, A system structurally isomorphic to either s4 or s5 is obtained. An attempt (...) is made to show that the essential insights of intuitionist logic may be preserved if we replace their complex and in many respects "unintuitive" propositional logic by a theory of truth which is non-Classical in the sense described above. (shrink)

The article examines main competing conceptions of the cor­respondence theory of truth. First, the author investigates pos­sible candidates for the role of truth-bearers. Among those he examines following entities: instances of sentences as concrete sequences of symbols (sounds or letters), which should satisfy wide scope of requirements, such as to be grammatical, mean­ingful, affirmative and so on; abstract propositions, which are ex­pressed by concrete sentences; utterances (either explicit or in lingua mentalis); beliefs of agents as their special mental states. (...) Then he turns to the study of possible candidates for the role of truth-makers, i.e. of those entities to which truth-bearers should correspond to be true. He observes states of affairs, situations, facts and mereological sums of individuals. Then he shows that a notion of correspondence is a functional relationship of interpre­tation of linguistic expressions, where certain fragment of real­ity is taken as a model, i.e. as a finite set of elements on which some functions and relations can be operationally defined. He shows how in some simple cases such interpretation function can be built in operationalist’s manner. After that, he considers some natural objections to this approach, which point that he has no direct cognitive access to the actual world, so it is not possible to take its fragments as a model for any theory. Such objections lead us to the coherentist’s approach, but he shows that the question about origin and status of so-called “specified set” implicitly either leads to infinite regress or requires certain correspondence on some level of investigation and reasoning. Finally, the authore presents some reflections on the meaning of correspondence approach for scientific realism and all other versions of realistic philosophy and metaphysics. (shrink)

The author has recently proposed a “quasi-classical” theory of particles and interactions in which particles are pictured as extended periodic disturbances in a universal field χ(x, t), interacting with each other via nonlinearity in the equation of motion for χ. The present paper explores the relationship of this theory to nonrelativistic quantum mechanics; as a first step, it is shown how it is possible to construct from χ a configuration-space wave function Ψ(x 1,x 2,t), and that the (...) theory requires that Ψ satisfy the two-particle Schrödinger equation in the case where the two particles are well separated from each other. This suggests that the multiparticle Schrödinger equation can be obtained as a direct consequence of the quasi-classical theory without any use of the usual formalism (Hilbert space, quantization rules, etc.) of conventional quantum theory and in particular without using the classical canonical treatment of a system as a “crutch” theory which has subsequently to be “quantized.” The quasi-classical theory also suggests the existence of a preferred “absolute” gauge for the electromagnetic potentials. (shrink)

In this work, a neo-classical relativistic mechanics theory is presented where the spin of an electron is an inherent part of its world space-time path as a point particle. The fourth-order equation of motion corresponds to the same covariant Lagrangian function in proper time as in special relativity except for an additional spin energy term. The theory provides a hidden-variable model of the electron where the dynamic variables give a complete description of its motion, giving a (...) class='Hi'>classical mechanics explanation of the electron’s spin, its dipole moments, and Schrödinger’s zitterbewegung, These features are also described mathematically by quantum mechanics theory, of course, but without any physical picture of an underlying reality. The total motion of the electron can be decomposed into a sum of a local spin motion about a point and a global motion of this point, called here the spin center. The global motion is sub-luminal and described by Newton’s Second Law in proper time, the time for a clock fixed at the spin center, while the total motion occurs at the speed of light c, consistent with the eigenvalues of Dirac’s velocity operators having magnitude c. The local spin motion is an inherent perpetual motion, which for a free electron is periodic at the ultra-high zitterbewegung frequency and its path is circular in a spin-center reference frame. In an electro-magnetic field, this spin motion generates magnetic and electric dipole energies through the Lorentz force on the electron’s point charge. The electric dipole energy corresponds to the spin-orbit coupling term involving the electric field that appears in the corrected Pauli non-relativistic Hamiltonian, which has long been used to explain the doublet structure of the spectral lines of the excited hydrogen atom. Pauli’s spin-orbit term is usually derived, however, from his magnetic dipole energy term, including also the effect of Thomas precession, which halves this energy. The magnetic dipole energy from Pauli’s and Dirac’s theory is twice that in the neo-classical theory, a discrepancy that has not been resolved. By defining a spin tensor as the angular momentum of the electron’s total motion about its spin center, the fundamental equations of motion can be re-written in an identical form to those of the Barut–Zanghi electron theory. This allows the equations of motion to be expressed in an equivalent form involving operators applied to a state function of proper time satisfying a neo-classical Dirac–Schrödinger spinor equation. This state function produces the dynamic variables from the same operators as in Dirac’s theory for the electron but without any probability implications. It leads to a neo-classical wave function that satisfies Dirac’s relativistic wave equation for the free electron by applying the Lorentz transformation to express proper time in the state function in terms of an observer’s space-time coordinates, showing that there is a close connection between the neo-classical theory and quantum mechanics theory for the electron’s dynamics. (shrink)

We present the case of a six-year-old child with a fatal brainstem tumour, who was left in a ‘locked-in state’ post-decompressive biopsy. A discussion of the ethical dilemma this situation presents, together with the deliberations of the ethics service when consulted about the optimal course of action, follow. The issues raised highlight an important conflict between the parental view of what is in the child's best interests and what may appear, prima facie, to clinical staff, to be in that child's (...) best interests. We discuss how creative ethical thinking may facilitate resolution of seemingly insoluble situations. (shrink)