The present paper investigates why logical empiricists remained silent about one of the most philosophy-laden matters of theoretical physics of their day, the principle of least action (PLA). In the two decades around 1900, the PLA enjoyed a remarkable renaissance as a formal unification of mechanics, electrodynamics, thermodynamics, and relativity theory. Taking Ernst Mach's historico-critical stance, it could be liberated from much of its physico-theological dross. Variational calculus, the mathematical discipline on which the PLA was based, obtained (...) a new rigorous basis. These three developments prompted Max Planck to consider the PLA as formal embodiment of his convergent realist methodology. Typically rejecting ontological reductionism, David Hilbert took the PLA as the key concept in his axiomatizations of physical theories. It served one of the main goals of the axiomatic method: ''deepening the foundations.'' Although Moritz Schlick was a student of Planck's, and Hans Hahn and Philipp Frank enjoyed close ties to Gottingen, the PLA became a veritable Shibboleth to them. Rather than being worried by its historical connections with teleology and determinism, they erroneously identified Hilbert's axiomatic method tout court with Planck's metaphysical realism. Logical empiricists' strict containment policy against metaphysics required so strict a separation between physics and mathematics to exclude even those features of the PLA and the axiomatic method not tainted with metaphysics. (shrink)

Despite the importance of the variational principles of physics, there have been relatively few attempts to consider them for a realistic framework. In addition to the old teleological question, this paper continues the recent discussion regarding the modal involvement of the principle of least action and its relations with the Humean view of the laws of nature. The reality of possible paths in the principle of least action is examined from the perspectives of the (...) contemporary metaphysics of modality and Leibniz's concept of essences or possibles striving for existence. I elaborate a modal interpretation of the principle of least action that replaces a classical representation of a system's motion along a single history in the actual modality by simultaneous motions along an infinite set of all possible histories in the possible modality. This model is based on an intuition that deep ontological connections exist between the possible paths in the principle of least action and possible quantum histories in the Feynman path integral. I interpret the action as a physical measure of the essence of every possible history. Therefore only one actual history has the highest degree of the essence and minimal action. To address the issue of necessity, I assume that the principle of least action has a general physical necessity and lies between the laws of motion with a limited physical necessity and certain laws with a metaphysical necessity. (shrink)

The paper delves into the methodological aspects of how foundational mathematical and physical tenets, most notably the principle of least action, are interpreted and assimilated within humanities discourse. The pursuit of the article’s objectives is driven by the necessity for a philosophical and methodological analysis of the current conceptual status of the principle of least action. This analysis is informed by cognitive-axiological and teleological imperatives of a “synthetic” development program for the principle. Any (...) fundamental principle will not have a definitive explanation, as otherwise it would not be fundamental, but in this case, some justification can be given based on deeper grounds discussed in the article. Drawing on the epistemological frameworks of French philosophers P. Hadot, E. Levinas, J. Bouveresse, and J.-T. Desanti, the article weaves together mathematical abstractions with human experience and philosophical doctrines with physical theories. J.-T. Desanti’s perspective on mathematical objects as an outcome of human activity is examined. Also scrutinized is B. Nicolescu’s concept of transdisciplinarity, which challenges the traditional subject-object dualism in science. The author’s methodological stance emerges from a dialectical viewpoint, one that eschews a simplistic dichotomy between materialism and idealism and is grounded in rigorous scientific inquiry and an exhaustive examination of the subject matter itself. The principle of least action, as a paramount principle in physics, is shown to exemplify a legacy of innovation, positioning it as both methodologically insightful and heuristically valuable. The paper also highlights how this principle diverges from the classical principle of economy. The broader goal – within the context of “sustainable development,” transdisciplinary studies, and creative industries – is to establish the principle of least action as a paradigmatic imperative for interaction within social and economic systems. The conclusions drawn from this study contribute to a deeper understanding of the principle’s essence, the nature of transdisciplinarity, and confront the vestiges of scientism in the humanities. (shrink)

Some time ago, Joel Katzav and Brian Ellis debated the compatibility of dispositional essentialism with the principle of least action. Surprisingly, very little has been said on the matter since, even by the most naturalistically inclined metaphysicians. Here, we revisit the Katzav–Ellis arguments of 2004–05. We outline the two problems for the dispositionalist identified Katzav in his 2004 , and claim they are not as problematic for the dispositional essentialist at it first seems – but not for (...) the reasons espoused by Ellis. (shrink)

My aim is to argue for the incompatibility of one of the central principles of physics, namely the principle of least action (PLA), with the increasingly popular view that the world is, ultimately, merely something like a con- glomerate of objects and irreducible dispositions. First, I argue that the essentialist implications many suppose this view has are not compatible with the PLA. Second, I argue that, irrespective of whether this view has any essentialist implications, it is not (...) compatible with the kind of explanation that the PLA affords. (shrink)

The principle of least action (PLA) has often been cited as a counterexample to the dominant mode of causal explanation in physics. In particular, PLA seems to involve an appeal to final causes or some other teleological ideology. However, Ben-Menahem (Causation in science, Princeton University Press, Princeton, 2018) argues that such implications no longer apply given that PLA can be recovered as limiting case from quantum theory. In this paper, I argue that the metaphysical implications of PLA-based (...) explanations are not undermined by its status as derivative. However, I contend that PLA functions as a diachronic constraint that licenses explanations by constraint (Lange, Because without cause: non-casual explanations in science and mathematics. Oxford University Press, Oxford, 2016). PLA-based explanations, on this account, are non-causal but also differ from familiar cases of teleological explanations in several respects. (shrink)

In the Appendix to the Transcendental Dialectic, Kant formulates teleological principles, or rather ideas, and explicates them referring to concrete examples of natural science such as chemistry, astronomy, biology, empirical psychology, and physical geography. Despite the increasing interest in the systematic relevance of the Appendix to the Transcendental Dialectic and its importance for Kant’s conception of natural science, the numerous historical sources for the regulative use of reason have not yet been investigated. One that is very central is Maupertuis’ (...) class='Hi'>principle of least action. In 1781, Kant transformed teleology into heuristics and methodology, but in doing so, he partially develops a teleology which was disqualified by Maupertuis because its starting point lies in the construction of animals or plants, the structure of the earth, and the immensity of the celestial bodies. Based on Maupertuis’ principle of action, it can be shown that the Appendix forms a systematic interface between Universal Natural History and Theory of the Heavens and Critique of Judgement which allows the reconstruction of Kant’s regulative use of reason and its specific status in the context of natural science and his critical appraisal of Maupertuis. (shrink)

Maupertuis and Euler had an ambivalent and tense relationship to their Leibniz, especially concerning his grounding of physics in metaphysics. Consequently, this paper has two intersecting goals: first, it attempts to flesh out some aspects of the reception of Leibnizian thought in the context of Enlightenment physics, more precisely, in the deduction of the Principle of least action (henceforth PLA). Second, it also highlights a specific approach towards the intersection of physics and metaphysics that was championed by (...) the Berlin Academy, which would not have been well received in Paris or London. To that end, I will briefly examine some aspects of the strategies of argumentation, metaphysical presumptions and self-ascribed methodologies (often quite different from their actual methodology) employed by Maupertuis and Euler in their respective deductions of the PLA. (shrink)

Towards the middle of the 18th century, Pierre-Louis Moreau de Maupertuis proposed the “principle of least action” as a fundamental law of physics and as a proof of the existence of God. Samuel König and other contemporary authors criticized Maupertuis’ work. There ensued a fierce discussion concerning this subject, in which Leonhard Euler, the king Frédéric II of Prussia and Voltaire took part. This paper discusses that debate, emphasizing its extrascientific features and analyzing the interests that motivated (...) the actions of the people involved in that episode. Key words: Pierre-Louis Moreau de Maupertuis, François Marie Arouet Voltaire, Johann Samuel König, Frédéric II – king of Prussia, principle of least action, history of physics, scientific controversies. (shrink)

Without doubt, the principle of least action is a fundamental principle in classical mechanics. Contemporary physicists, however, consider the PLA as a purely mathematical principle – even an axiom which they cannot completely justify. Such an account stands in sharp contrast with the historical meaning of the PLA. When the principle was introduced in the 1740s, by Pierre-Louis Moreau de Maupertuis, its meaning was much more versatile. For Maupertuis the principle of least (...) action signified that nature is thrifty or economical in all its actions, i.e., that nature avoids to do anything unnecessary. Maupertuis understood the principle in teleological terms and even considered the principle as an expression of God’s wisdom. It has been correctly pointed out by historians that Maupertuis in his later years moved towards a more speculative and metaphysical approach, whereas his contemporary Euler and later Lagrange, wanted to avoid such theological and metaphysical implications and frame the PLA in purely mathematical terms. Such readings, however, have had the unintended side-effect that they lose out of sight the question how the mathematical and metaphysical aspect of the principle of least action fit together within Maupertuis’ own work. Investigating if and how the mathematical and metaphysical aspects of the PLA are compatible within Maupertuis’ thought will be the main goal of this paper. (shrink)

The success of a few theories in statistical thermodynamics can be correlated with their selectivity to reality. These are the theories of Boltzmann, Gibbs, end Einstein. The starting point is Carnot’s theory, which defines implicitly the general selection of reality relevant to thermodynamics. The three other theories share this selection, but specify it further in detail. Each of them separates a few main aspects within the scope of the implicit thermodynamic reality. Their success grounds on that selection. Those aspects can (...) be represented by corresponding oppositions. These are: macroscopic – microscopic; elements – states; relational – non-relational; and observable – theoretical. They can be interpreted as axes of independent qualities constituting a common qualitative reference frame shared by those theories. Each of them can be situated in this reference frame occupying a different place. This reference frame can be interpreted as an additional selection of reality within Carnot’s initial selection describable as macroscopic and both observable and theoretical. The deduced reference frame refers implicitly to many scientific theories independent of their subject therefore defining a general and common space or subspace for scientific theories (not for all). The immediate conclusion is: The examples of a few statistical thermodynamic theories demonstrate that the concept of “reality” is changed or generalized, or even exemplified (i.e. “de-generalized”) from a theory to another. Still a few more general suggestions referring the scientific realism debate can be added: One can admit that reality in scientific theories is some partially shared common qualitative space or subspace describable by relevant oppositions and rather independent of their subject quite different in general. Many or maybe all theories can be situated in that space of reality, which should develop adding new dimensions in it for still newer and newer theories. Its division of independent subspaces can represent the many-realities conception. The subject of a theory determines some relevant subspace of reality. This represents a selection within reality, relevant to the theory in question. The success of that theory correlates essentially with the selection within reality, relevant to its subject. (shrink)

Twenty extremal principles of the natural sciences are reformulated to the general ontological scheme. The hypothesis is substantiated that the unique role of the principle of least action is based on its probabilistic interpretation. It is shown how most of the variational principles can be reduced to the principle of maximal probability, which is based on a realistic interpretation of Feynman’s path integral method.

The idea of obtaining a pilot-wave quantum theory on a lattice with discrete time is presented. The motion of quantum particles is described by a \-distributed Markov chain. Stochastic matrices of the process are found by the discrete version of the least-action principle. Probability currents are the consequence of Hamilton’s principle and the stochasticity of the Markov process is minimized. As an example, stochastic motion of single particles in a double-slit experiment is examined.

A new variational method, the principle of least radix economy, is formulated. The mathematical and physical relevance of the radix economy, also called digit capacity, is established, showing how physical laws can be derived from this concept in a unified way. The principle reinterprets and generalizes the principle of least action yielding two classes of physical solutions: least action paths and quantum wavefunctions. A new physical foundation of the Hilbert space of quantum (...) mechanics is then accomplished and it is used to derive the Schrödinger and Dirac equations and the breaking of the commutativity of spacetime geometry. The formulation provides an explanation of how determinism and random statistical behavior coexist in spacetime and a framework is developed that allows dynamical processes to be formulated in terms of chains of digits. These methods lead to a new foundation for Lorentz transformations and special relativity. The Parker-Rhodes combinatorial hierarchy is encompassed within our approach and this leads to an estimate of the interaction strength of the electromagnetic and gravitational forces that agrees with the experimental values to an error of less than one thousandth. Finally, it is shown how the principle of least-radix economy naturally gives rise to Boltzmann’s principle of classical statistical thermodynamics. A new expression for a general nonequilibrium entropy is proposed satisfying the Second Law of Thermodynamics. (shrink)

In 1751, LEONHARD EULER established “harmony” between two principles that had been stated by PIERRE-LOUIS-MOREAU DE MAUPERTUIS a few years earlier. These principles are intended to be the foundations of Mechanics; they are the principle of rest and the principle of least action.My claim is that the way in which “harmony” is achieved sets the foundations of so called Analytical Mechanics: it discloses the physical bases of the general ideas, concepts, and motivations of the formalism. My (...) paper intends to show what those physical bases are, and how a picture of the formalism issues from them. This picture is shown to be recast in JOSEPH-LOUIS LAGRANGES justification of the formalism, which strengthens my claim. (shrink)

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

We show that the formulations of non-relativistic quantum mechanics can be derived from an extended least action principle. The principle can be considered as an extension of the least action principle from classical mechanics by factoring in two assumptions. First, the Planck constant defines the minimal amount of action a physical system needs to exhibit during its dynamics in order to be observable. Second, there is constant vacuum fluctuation along a classical trajectory. (...) A novel method is introduced to define the information metrics to measure additional observability due to vacuum fluctuations, which is then converted to an additional action through the first assumption. Applying the variational principle to minimize the total actions allows us to recover the basic quantum formulations including the uncertainty relation and the Schrödinger equation in the position representation. In the momentum representation, the same method can be applied to obtain the Schrödinger equation for a free particle while further investigation is still needed for a particle with an external potential. Furthermore, the principle brings in new results on two fronts. At the conceptual level, we find that the information metrics for vacuum fluctuations are responsible for the origin of the Bohm quantum potential. Even though the Bohm potential for a bipartite system is inseparable, the underlying vacuum fluctuations are local. Thus, inseparability of the Bohm potential does not justify a non-local causal relation between the two subsystems. At the mathematical level, quantifying the information metrics for vacuum fluctuations using more general definitions of relative entropy results in a generalized Schrödinger equation that depends on the order of relative entropy. The extended least action principle is a new mathematical tool. It can be applied to derive other quantum formalisms such as quantum scalar field theory. (shrink)

This work deals with obstacles hindering a metaphysics of laws of nature in terms of dispositions, i.e., of fundamental properties that are causal powers. A recent analysis of the principle of least action has put into question the viability of dispositionalism in the case of classical mechanics, generally seen as the physical theory most easily amenable to a dispositional ontology. Here, a proper consideration of the framework role played by the least action principle within (...) the classical image of the world allows us to build a consistent metaphysics of dispositions as charges of interactions. In doing so we develop a general approach that opens the way towards an ontology of dispositions for fundamental physics also beyond classical mechanics. (shrink)

Laws of motion given in terms of differential equations can not always be derived from an action principle, at least not without introducing auxiliary variables. By allowing auxiliary variables, e.g. in the form of Lagrange multipliers, an action is immediately obtained. Here, we consider some ways how this can be done, with illustrations from the literature, and apply this to Bohmian mechanics. We also discuss the possible metaphysical status of these auxiliary variables. A particularly interesting approach (...) brings the theory in the form of a gauge theory, with the auxiliary variables as gauge degrees of freedom. (shrink)

The thesis we develop in this essay is that all humans are endowed with a moral faculty. The moral faculty enables us to produce moral judgments on the basis of the causes and consequences of actions. As an empirical research program, we follow the framework of modern linguistics.1 The spirit of the argument dates back at least to the economist Adam Smith (1759/1976) who argued for something akin to a moral grammar, and more recently, to the political philosopher John (...) Rawls (1971). The logic of the argument, however, comes from Noam Chomsky’s thinking on language specifically and the nature of knowledge more generally (Chomsky, 1986, 1988, 2000; Saporta, 1978). If the nature of moral knowledge is comparable in some way to the nature of linguistic knowledge, as defended recently by Harman (1977), Dwyer (1999, 2004), and Mikhail (2000; in press), then what should we expect to find when we look at the anatomy of our moral faculty? Is there a grammar, and if so, how can the moral grammarian uncover its structure? Are we aware of our moral grammar, its method of operation, and its moment-to-moment functioning in our judgments? Is there a universal moral grammar that allows each child to build a particular moral grammar? Once acquired, are different moral grammars mutually incomprehensible in the same way that a native Chinese speaker finds a native Italian speaker incomprehensible? How does the child acquire a particular moral grammar, especially if her experiences are impoverished relative to the moral judgments she makes? Are there certain forms of brain damage that disrupt moral competence but leave other forms of reasoning intact? And how did this machinery evolve, and for what particular adaptive function? We will have more to say about many of these questions later on, and Hauser (2006) develops others. However, in order to flesh out the key ideas and particular empirical research paths, let us turn to some of the central questions in the study of our language faculty.. (shrink)

Our concept of the universe and the material world is foundational for our thinking and our moral lives. In an earlier contribution to the URAM project I presented what I called 'the ultimate organizational principle' of the universe. In that article (Grandpierre 2000, pp. 12-35) I took as an adversary the wide-spread system of thinking which I called 'materialism'. According to those who espouse this way of thinking, the universe consists of inanimate units or sets of material such as (...) atoms or elementary particles. Against this point of view on reality, I argued that it is 'logic', which exists in our inner world as a function of our mind, that is the universal organizing power of the universe. The present contribution builds upon this insight. Then I focussed on rationality; now I am interested in the responsibility that is the driving force behind our effort to find coherence and ultimate perspectives in our cosmos. It is shown that biology fundamentally differs from physics. Biology has its own fundamental principle, which is formulated for the first time in history in a scientific manner by Ervin Bauer. This fundamental principle is the cosmic life principle. I show that if one considers the physical laws as corresponding to reality, as in scientific realism, than physicalism becomes fundamentally spiritual because the physical laws are not material. I point out that the physical laws originate from the fundamental principle of physics which is the least action principle. I show that the fundamental principle of physics can be considered as the "instinct of atoms". Our research has found deep and meaningful connections between the basic principle of physics and the ultimate principles of the universe: matter, life and reason. Therefore, the principle of least action is not necessarily an expression of sterile inanimateness. On the contrary, the principle of physics is related to the life principle of the universe, to the world of instincts behind the atomic world, in which the principles of physics, biology, and psychology arise from the same ultimate principle. Our research sheds new light to the sciences of physics, biology, and psychology in close relation to the basic principles. These ultimate principles have a primary importance in our understanding of the nature of Man and the Universe, together with the relations between Man and Nature, Man and the Universe. The results offer new foundations for our understanding our own role in the Earth, in the Nature and in the Universe. Even the apparently inanimate world of physics shows itself to be animate on long timescales and having a kind of pre- human consciousness in its basic organisation. This hypothesis offers a way to understand when and how the biological laws may direct physical laws, and, moreover, offers a new perspective to study and understand under which conditions can self-consciousness govern the laws of biology and physics. This point of view offers living beings and humans the possibility of strengthening our natural identity, and recognising the wide perspective arising from having access to the deepest ranges of our own human resources and realising the task for which human and individual life has been created. (shrink)

Increasingly, contemporary medical ethicists have become aware of the need to explicate a foundation for their various models of applied ethics. Many of these theories are inspired by the apparent incompatibility of patient autonomy and provider beneficence. The principle of patient autonomy derives its current primacy to a large extent from its legal origins. However, this principle seems at odds with the clinical reality. In the bioethical literature, the notion of authenticity has been proposed as an alternative foundational (...) principle to autonomy. This article examines this proposal in reference to various existentialist philosophers (Heidegger, Sartre, Camus and Marcel). It is concluded that the principle of autonomy fails to do what it is commonly supposed to do: provide a criterion of distinction that can be invoked to settle moral controversies between patients and providers. The existentialist concept of authenticity is more promising in at least one crucial respect: It acknowledges that the essence of human life disappears from sight if life's temporal character is reduced to a series of present decisions and actions. This also implies that the very quest for a criterion that allows physicians to distinguish between sudden, unexpected decisions of their patients to be or not to be respected, without recourse to the patient's past or future, is erroneous. (shrink)

According to history texts, philosophers searched for a unifying natural law whereby natural phenomena and numbers are related. More than 2300 years ago, Aristotle postulated that nature requires minimum energy. More than 220 years ago, Euler applied the minimum energy postulate. More than 200 years ago, Lagrange provided a mathematical “proof” of the postulate for conservative systems. The resulting Principle of Least Action served only to derive the differential equations of motion of a conservative system. Then, 170 (...) years ago, Hamilton presented what he claimed to be a “general method in dynamics.” Hamilton's resulting “Law of Varying Action” was supposed to apply to both conservative and non-conservative systems and was supposed to yield either the differential equations of motion or the integrals of those differential equations. However, no direct evaluation of the integrals of motion ever resulted from Hamilton's law of varying action. In 1975, a scant 29 years ago, following five years of controversy with engineer mechanicians, Dr. Wolfgang Yourgrau, Editor, Foundations of Physics, published my first paper based on Aristotle's postulate, without mathematical proof. That and subsequent papers present, through applications, a true “general method in dynamics.” In this essay, I present the mathematical proof that is missing from my 1975 and subsequent papers. Six fundamental integrals of analytical mechanics are derived from Aristotle's postulate. First, however, Hamilton must be revisited to show why his H function and his “force function” prevents the law of varying action from being the general method in dynamics that he claimed it to be. I have found that Hamilton’s Law of Varying Action (HLVA), as Hamilton presented it, cannot be applied to systems for which the force function is non-integrable. In 1972, Dr. B.E. Gatewood and Dr. D.P. Beres (then a graduate student) discovered that the end-point term associated with the principle of least action does not vanish. I named the new equation, “the general energy equation.” In 1973, because I was doing with it what Hamilton claimed could be done with HLVA, I simply assumed that this new equation was HLVA. I gave the new equation the misnomer HLVA. In 2001, I learned that I had made a grave mistake. I found that HLVA is at most a special case of the general energy equation. My interpretation of Aristotle's postulate permits one to by-pass the differential equations of motion completely for both conservative and non-conservative systems (no calculus of variations). (shrink)

The topic of this paper may be introduced by fast zooming in and out of the philosophy of information. In recent years, philosophical interest in the nature of information has been increasing steadily. This has led to a focus on semantic information, and then on the logic of being informed, which has attracted analyses concentrating both on the statal sense in which S holds the information that p (this is what I mean by logic of being informed in the rest (...) of this article) and on the actional sense in which S becomes informed that p. One of the consequences of the logic debate has been a renewed epistemological interest in the principle of information closure (henceforth PIC), which finally has motivated a revival of a skeptical objection against its tenability first made popular by Dretske. This is the topic of the paper, in which I seek to defend PIC against the skeptical objection. If I am successful, this means – and we are now zooming out – that the plausibility of PIC is not undermined by the skeptical objection, and therefore that a major epistemological argument against the formalization of the logic of being informed based on the axiom of distribution in modal logic is removed. But since the axiom of distribution discriminates between normal and non-normal modal logics, this means that a potentially good reason to look for a formalization of the logic of being informed among the non-normal modal logics, which reject the axiom, is also removed. And this in turn means that a formalization of the logic of being informed in terms of the normal modal logic B (also known as KTB) is still very plausible, at least insofar as this specific obstacle is concerned. In short, I shall argue that the skeptical objection against PIC fails, so it is not a good reason to abandon the normal modal logic B as a good formalization of the logic of being informed. (shrink)

Concentrating upon applications that are most relevant to modern physics, this valuable book surveys variational principles and examines their relationship to dynamics and quantum theory. Stressing the history and theory of these mathematical concepts rather than the mechanics, the authors provide many insights into the development of quantum mechanics and present much hard-to-find material in a remarkably lucid, compact form. After summarizing the historical background from Pythagoras to Francis Bacon, Professors Yourgrau and Mandelstram cover Fermat's principle of least (...) time, the principle of least action of Maupertuis, development of this principle by Euler and Lagrange, and the equations of Lagrange and Hamilton. Equipped by this thorough preparation to treat variational principles in general, they proceed to derive Hamilton's principle, the Hamilton-Jacobi equation, and Hamilton's canonical equations. An investigation of electrodynamics in Hamiltonian form covers next, followed by a resume of variational principles in classical dynamics. The authors then launch into an analysis of their most significant topics: the relation between variational principles and wave mechanics, and the principles of Feynman and Schwinger in quantum mechanics. Two concluding chapters extend the discussion to hydrodynamics and natural philosophy. Professional physicists, mathematicians, and advanced students with a strong mathematical background will find this stimulating volume invaluable reading. Extremely popular in its hardcover edition, this volume will find even wider appreciation in its first fine inexpensive paperbound edition. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:CHARITY LOST: TBE SECtJLA'.RIZATfON OF THE PRINCIPLE OF DOUBLE EFFECT IN THE JUST-WAR TRADITION TIMOTHY M. RENICK Georgia State University Atlanta, Georgia 0 N AUGUST 12, 1945, the city of Hiroshima still smoldered, and President Harry Truman addressed the American people : We have used [the atomic bomb] against those who have attacked us without warning at Pearl Harbor, against those who have starved and beaten and executed (...) American prisoners of war, against those who have abandoned all pretense of obeying international laws of warfare. We have used it in order to shorten the agony of war.1 Truman and his military advisers had made a calculation. Japan was preparing for a last-ditch defense of the Japanese Islands. The prospect was ominous, to say the least. The United States had suffered eighty thousand casualties in the taking of the smaller and less protected Okinawa just two months earlier; 120,000 Japanese soldiers had been killed (and only ten-thousand taken prisoner). Strategists estimated that losses, both military and civilian, from a full scale battle for Japan itself would exceed one million. Surely the tens of thousands killed by exploding a bomb over Hiroshima was the lesser evil. Surely this was a proportionate act : fifty thousand lives traded for a million. As Winston Churchill wrote in support of Truman's decision: "To avert a vast, indefinite butchery... at the cost of a few explosions seemed, after all our toils and perils, a miracle of deliverance." 2 1 Michael Walzer, lust and Unjust Wars (New York: Basic Books, 1979), p.164. 2 Ibid., pp. 266-267. 441 442 TIMOTHY M. RENICK From an ethical perspective, however, the act was anything but a deliverance. I am not alone in this assessment. Advocates of the just-war tradition including Elizabeth Anscombe, Paul Ramsey, George Kennan, John Langan, and Michael Walzer have condemned the bombing of Hiroshima by means of a shared just-war argument.8 The argument goes as follows, and it is a good one. In times of war, many actions are likely to have both good and evil effects. One destroys an enemy's munitions factory (good effect) but kills an innocent child in the process (evil effect). The jus in bello of the just-war tradition, however, stipulates that an action which has a " double effect " is permissible if and only if: ( 1) it is discriminate (i.e., the actor aims only at the good effect and does not intend the evil effect, nor is the evil effect a means to the end, however good); and (2) it is proportionate (i.e., the good created by the act outweighs the bad).4 Now, the argument continues, Truman's decision to bomb Hiroshima failed the first criterion. It was not a discriminate act because the evil effect (the killing of tens of thousands of Japanese civilians) was not unintended. In fact, the evil was the very means to the good end. Although Truman himself claimed to have selected Hiroshima as a target because it was "a war s See, for example, G. E. M. Anscombe, "Mr. Truman's Decision," in Ethics, Religion and Politics (Minneapolis, Minn.: University of Minnesota, 1981); M. Walzer "Supreme Emergency," in Just and Unjust Wars; and John Langan, "The American Hierarchy and Nuclear Weapons," Theological Studies 43 (1982) : 447-467. ' I utilize here a helpful shorthand version of the principle of double effect introduced by Paul Ramsey in War and the Christian Conscience (Durham, North Carolina: Duke, 1961). More frequently, the principle is rendered by means of four criteria: It is permissible to perform an act likely to have evil consequences if and only if (I) the act is good in itself or at least indifferent; (2) the direct effect is morally justified; (3) the actor aims only at the acceptable effect and does not intend the evil effect, nor is the evil effect a means to the end, however good ; and (4) there is in the good effect a proportionately grave reason for permitting the evil effect. The shortened version of the theory captures all components essential to my discussion and enhances clarity. I thus will make use of it throughout this essay. CHARITY AND... (shrink)

Reconstructing Popper's research programme for the Human Sciences, Noretta Koertge (Inquiry, Vol. 18 [1975]) has given a deductive?nomological account of explanations of actions by means of a Rationality Principle. It is argued here that such a Rationality Principle is fundamentally redundant. Neither is it logically necessary in order to deduce a cognitive action?explanandum, nor can it be given a semantic non?empty interpretation, at least not within Koertge's own syllogism. Any attempt to save the Rationality Principle (...) as unfalsifiablc but nevertheless indispensable for action explanations is rejected in the light of possible alternative action explanations by empirical and therefore in principle falsifiable psychological laws. (shrink)

Planck’s pioneering contributions to special relativity have received less consideration than one might expect in the historiography and philosophy of physics. Although they are celebrated in isolation, they are mostly not understood as integral to an overarching project. This paper aims (a) to provide a historically accurate overview of Planck’s contributions to the early history of relativity that is reasonably accessible to today’s reader, (b) to demonstrate how these contributions can be presented against the background of Planck’s ‘Helmholtzian’ vision of (...) relativistic general dynamics based on the principle of relativity and principle of least action, and (c) to argue that Planck’s general dynamics serves as an illuminating example of the use of ‘principles’ in physics. (shrink)

The Great Divide in metaphysical debates about laws of nature is between Humeans, who think that laws merely describe the distribution of matter, and non-Humeans, who think that laws govern it. The metaphysics can place demands on the proper formulations of physical theories. It is sometimes assumed that the governing view requires a fundamental / intrinsic direction of time: to govern, laws must be dynamical, producing later states of the world from earlier ones, in accord with the fundamental direction of (...) time in the universe. In this paper, we propose a minimal primitivism about laws of nature (MinP) according to which there is no such requirement. On our view, laws govern by constraining the physical possibilities. Our view captures the essence of the governing view without taking on extraneous commitments about the direction of time or dynamic production. Moreover, as a version of primitivism, our view requires no reduction / analysis of laws in terms of universals, powers, or dispositions. Our view accommodates several potential candidates for fundamental laws, including the principle of least action, the Past Hypothesis, the Einstein equation of general relativity, and even controversial examples found in the Wheeler-Feynman theory of electrodynamics and retrocausal theories of quantum mechanics. By understanding governing as constraining, non-Humeans who accept MinP have the same freedom to contemplate a wide variety of candidate fundamental laws as Humeans do. (shrink)

The principle of the lesser evil--the acceptability of pursuing one exceptional course of action in order to prevent a greater injustice--has long been a cornerstone of Western ethical philosophy. From its roots in classical ethics and Christian theology, to Hannah Arendt's exploration of the work of the Jewish Councils during the Nazi regime, the author explores its development in three key transformations of the problem: the defining intervention of Medecins Sans Frontisres in mid-1980s in Ethiopia; the separation wall (...) in Israel-Palestine; and international and human rights law in Bosnia, Gaza and Iraq. Drawing on a wealth of new research, the author charts the latest manifestation of this age-old idea. In doing so he shows how military and political intervention acquired a new humanitarian acceptability and legality in the late twentieth and early twenty-first centuries.--Publisher description. (shrink)

In his Zur Einstein’schen Relativitätstheorie, Ernst Cassirer presents relativity theory as the last manifestation of the tradition of the “physics of principles” that, starting from the nineteenth century, has progressively prevailed over that of the “physics of models.” In particular, according to Cassirer, the relativity principle plays a role similar to the energy principle in previous physics. In this article, I argue that this comparison represents the core of Cassirer’s neo-Kantian interpretation of relativity. Cassirer pointed out that before (...) and after Kant, the history of physics presents significant instances in which the search for formal conditions that the laws of nature must satisfy preceded and made possible the direct search for such laws. In his earlier years, Cassirer seems to have regarded principles like the energy principle, the relativity principle, and the principle of least action as a constitutive but provisional form of a priori, imposing specific limitations on the form of the allowable laws of nature. Only in his later years, by attributing an autonomous status to these statements of principle, did Cassirer attribute a definitive but merely regulative meaning to the a priori. This does not impose specific requirements on natural laws but only a motivation to search for them. (shrink)

This collection sheds new light on the nature, role and practice of philosophy and science in the renewed Berlin Academy from the mid-1740s to the 1790s, and in so doing provides a robust new instalment of materials for the broader task of constructing a historiography of philosophy at this important Enlightenment institution. The collection ranges from discussions of the roles of philosophy and natural philosophy in the formation of the reinvigorated Academy in the mid-1740s, to conceptions of the correct philosophical (...) methodology to be deployed by the Academy. It provides the first ever study of the nature and arrangement of the new classes of the Academy, and a fresh appraisal of the Academy's methodological eclecticism. One recurring theme is the status of metaphysics: there are studies of both special metaphysics, including the study of the soul; general metaphysics, that is, the study of being in general; and foundational metaphysical principles and concepts, such as Maupertuis's Principle of least action, Euler's concept of space and Lambert's notion of an experimental metaphysics. The collection also takes the study of the Academy in new directions through focused studies of important figures whose writings deserve to be better understood, such as Jean Bernard Merian, Louis de Beausobre, Jean Henri Samuel Formey and Johann Georg Sulzer. (shrink)

It has been recognized in the literature of the calculus of variations that the classical statement of the principle of least action (Hamilton's principle for conservative systems) is not strictly correct. Recently, mathematical proofs have been offered for what is claimed to be a more precise statement of Hamilton's principle for conservative systems. According to a widely publicized version of this more precise statement, the action integral for conservative systems is a minimum for discrete (...) systems for small time intervals only and is never minimum for continuous systems. In this paper, two contradictions to this “more precise” statement are demonstrated, one for a discrete system and one for a continuous system. (shrink)

We begin by presenting William of Ockham's various formulations of his principle of parsimony, Ockham's Razor. We then define a reaction mechanism and tell a personal story of how Ockham's Razor entered the study of one such mechanism. A small history of methodologies related to Ockham's Razor, least action and least motion, follows. This is all done in the context of the chemical (and scientific) community's almost unthinking acceptance of the principle as heuristically valuable. Which (...) is not matched, to put it mildly, by current philosophical attitudes toward Ockham's Razor. What ensues is a dialogue, pro and con. We first present a context for questioning, within chemistry, the fundamental assumption that underlies Ockham's Razor, namely that the world is simple. Then we argue that in more than one pragmatic way the Razor proves useful, without at all assuming a simple world. Ockham's Razor is an instruction in an operating manual, not a world view. Continuing the argument, we look at the multiplicity and continuity of concerted reaction mechanisms, and at principal component and Bayesian analysis (two ways in which Ockham's Razor is embedded into modern statistics). The dangers to the chemical imagination from a rigid adherence to an Ockham's Razor perspective, and the benefits of the use of this venerable and practical principle are given, we hope, their due. (shrink)

In "Omniprescient Agency" (Religious Studies 28, 1992) David P. Hunt challenges an argument against the possibility of an omniscient agent. The argument—my own in "Agency and Omniscience" (Religious Studies 27, 1991)—assumes that an agent is a being capable of intentional action, where, minimally, an action is intentional only if it is caused, in part, by the agent's intending. The latter, I claimed, is governed by a psychological principle of "least effort," viz., that no one intends without (...) antecedently feeling that (i) deliberate effort is needed to achieve desired goals, (ii) such effort has a chance of success, and (iii) it is yet contingent whether the effort will be expended and the goals realized. The goals can be anything from immediate intentional doings, tryings or basic actions, to remote and perhaps unlikely consequences of actions, e.g., global justice. The thrust of the principle is that it would be impossible for a wholly rational self-aware agent to intend without a background presumption of an open future as concerns the desired state and the means to it. But this presumption embodies a sense of contingency which, in turn, requires an acknowledged ignorance about what the future holds, otherwise the future would appear closed relative to present knowledge with the desired state presented as either guaranteed (necessary) or ruled out (impossible). Regardless whether this self-directed attitude is accurate, it follows that intentional action precludes complete knowledge of one's present and future. Consequently, no omniscient or omniprescient being can be an agent. (shrink)

Affirmative action as a state policy is one of the powerful ways of empowering the underprivileged in the society. While such a policy is aimed at lifting the economic and social condition of the underprivileged, this comes with acts that are discriminatory and exclusionary. Yet these acts are termed as positive discrimination. Certain sections of the society are excluded from having access to economic resources and opportunities, while these privileges are earmarked for another section of the society considered marginalized (...) and underprivileged. This is being done guided by the principle of distributive justice. While the principle carries sound moral basis, conceptualizing the deprived and mode of empowerment varies with states and society, thus throws up several challenges. Indian experience draws challenges of negotiating the dual presence of individual and collective in the theorizing—idea of empowerment is directed to an individual, but the identity of the individual is based on his/her social identity. The dual challenge of uplifting a caste/community through empowering an individual belonging to the group has raised several questions in terms of achieving the goal of distributive justice. While the principle of distributive justice aims at empowering the least privileged within an underprivileged group/community, this has not been an easy task. After seventy years of reservation policy a lot more initiative is still called for. There is perhaps need for deeper philosophical deliberation on the nature of empowerment, distributive justice, and the underlying moral foundations. Meaningful policy intervention must be built on well thought out theoretical deliberations. (shrink)

The concept of time is examined using the second law of thermodynamics that was recently formulated as an equation of motion. According to the statistical notion of increasing entropy, flows of energy diminish differences between energy densities that form space. The flow of energy is identified with the flow of time. The non-Euclidean energy landscape, i.e. the curved space–time, is in evolution when energy is flowing down along gradients and levelling the density differences. The flows along the steepest descents, i.e. (...) geodesics are obtained from the principle of least action for mechanics, electrodynamics and quantum mechanics. The arrow of time, associated with the expansion of the Universe, identifies with grand dispersal of energy when high-energy densities transform by various mechanisms to lower densities in energy and eventually to ever-diluting electromagnetic radiation. Likewise, time in a quantum system takes an increment forwards in the detection-associated dissipative transformation when the stationary-state system begins to evolve pictured as the wave function collapse. The energy dispersal is understood to underlie causality so that an energy gradient is a cause and the resulting energy flow is an effect. The account on causality by the concepts of physics does not imply determinism; on the contrary, evolution of space–time as a causal chain of events is non-deterministic. (shrink)

There is a problem about the punishment of potential or future consequences under the principles of the invisible hand and of utility. In the free market, a social pattern and institution, in which the wicked merchants have harmed others and been punished, is obviously evolved at least for protecting individual freedom and security. In the views of Smith and Mill, it is related to the sentiment of justice from sympathy extended by morality of our internal sentiment and sanctions to (...) social lives. In a society or poor country, however, which has never experienced a case such as that of the wicked merchants, a baker, who makes bread with less harmful poison and intends only to satisfy self-interest, can be evaluated as a case of exemplary self-interest by both principles, for example, because he gives the greatest help to solve social hunger. At that moment, we cannot expect any possible evolution of social pattern and institution; and, if another result of his own self-interest is the concentration of poison after a generation, and if the baker is punished, this feature is to reveal a contradiction of the principles of the invisible hand and, in particular, of utility. At the moment, this essay will examine two possible resolutions: the responsibility for the actual and potential consequences, and desert or merit by socially useful behaviour. The former is to regulate certain actions or to examine its propriety and moral rules in the free market and the latter is to have a limit that to calculate future values for returns or merits now is improper as well as injust. By exploring the two alternatives, it might be persuasive that the principle of moral action in the free market be modified in terms of potentially wrong consequences. (shrink)