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 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.

Historians of seventeenth-century science have frequently asserted that Kepler's laws of planetary motion were largely ignored between the time of their first publication and the publication of Newton's Principia . In fact, however, they were more widely known and accepted than has been generally recognized.Kepler's ideas were, indeed, rather slow in establishing themselves, and until about 1630 there are few references to them in the literature of the time. But from then onwards, interest in them increased fairly rapidly. In (...) particular, the principle of elliptical orbits had been accepted by most of the leading astronomers in France before 1645 and in England by about 1655. It also received quite strong support in Holland.The second law had a more chequered history. It was enunciated in its exact form by a few writers and was used in practice by some others without being explicitly formulated, but the majority, especially after 1645, preferred one or another of several variant forms which were easier to use but only approximately correct. The third law attracted less interest than the others, chiefly perhaps because it had no satisfactory theoretical basis, but it was correctly stated by at least six writers during the period under review.Between about 1630 and 1650 Kepler's Epitome Astronomiae Copernicanae was probably the most widely read work on theoretical astronomy in northern and western Europe, while his Rudolphine Tables, which were based upon the first two laws, were regarded by the majority of astronomers as the most accurate planetary tables available.Kepler's work certainly did not receive all the recognition it deserved, but the extent to which it was neglected has been much exaggerated. (shrink)

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)

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)

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)

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)

There is considerable evidence that listeners’ understanding of a spoken sentence need not always follow from a full analysis of the words and syntax of the utterance. Rather, listeners may instead conduct a superficial analysis, sampling some words and using presumed plausibility to arrive at an understanding of the sentence meaning. Because this latter strategy occurs more often for sentences with complex syntax that place a heavier processing burden on the listener than sentences with simpler syntax, shallow processing may represent (...) a resource conserving strategy reflected in reduced processing effort. This factor may be even more important for older adults who as a group are known to have more limited working memory resources. In the present experiment, 40 older adults and 20 younger adults were tested for comprehension of plausible and implausible sentences with a simpler subject-relative embedded clause structure or a more complex object-relative embedded clause structure. Dilation of the pupil of the eye was recorded as an index of processing effort. Results confirmed greater comprehension accuracy for plausible than implausible sentences, and for sentences with simpler than more complex syntax, with both effects amplified for the older adults. Analysis of peak pupil dilations for implausible sentences revealed a complex three-way interaction between age, syntactic complexity, and plausibility. Results are discussed in terms of models of sentence comprehension, and pupillometry as an index of intentional task engagement. (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)

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 (...) class='Hi'>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)

Contact between culturally distinct human groups in the contemporary ‘glocal’ -global and local- world is much greater than at any point in history. The challenge we face is the identification of the most convenient ways to organise the coexistence of different human language groups in order that we might promote their solidarity as members of the same culturally developed biological species. Processes of economic and political integration currently in motion are seeing increasing numbers of people seeking to become polyglots. (...) Thus, English is establishing itself as the usual world supra-language, although it coexists with other lingua francas that are widely used in certain parts of the globe. All this communicative reorganization of the human species may very well pose new problems and aggravate existing tensions as regards language and identity. It would seem that these processes comprise at least four major conceptual dimensions which must be taken into account above all else, as they are both widespread and, left unaddressed, may lead to significant social instability. These dimensions concern linguistic recognition, communicability, sustainability and integration. While accepting the utility of having an inter-national language, the keystone of the system is clearly that it must ensure the linguistic sustainability of each group. The basic principle is likely to be functional subsidiarity, i.e., whatever can be done by the local language should not be done by another one which is more global. As in the quote from Paracelsus --“the dose alone makes the poison”-- contact between languages is not ‘poisonous’ per se, but when the correct dose is exceeded it can prove harmful to the language whose position is weaker. A multilingual and communicated humanity is possible. (shrink)

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)

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)

Thomas Hobbes based his natural philosophy on definitions and general principles of matter in motion, which he refrained from calling “laws of nature.” Across the channel, René Descartes had presented his own account of matter in motion in such a way that laws of nature play a central causal-explanatory role. Despite some notable differences in the two systems of natural philosophy, the content of the three Cartesian laws of nature is shared by Hobbesian principles of motion. Why (...) is it the case that Hobbes never ‘transferred’ the concept of law of nature from the sphere of civil society to the realm of nature? What is the status of the Hobbesian principles of motion if they are not laws? Answering these questions is the main aim of this article. It is shown that Hobbes made available an importantly different and genuinely original way to do natural philosophy, which renders it free of metaphysics and eschews the need to ground it in anything other than ‘natural reason’. Briefly put, Hobbes took the category of ‘laws of nature’ to involve commitments that cannot be met in the natural world, unless natural philosophy loses its autonomy from theology and metaphysics. (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)

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)

In lieu of an abstract, here is a brief excerpt of the content:Plato's Doctrine of the Psyche as a Self-Moving Motion RAPHAEL DEMOS I WILLXSXTHEREADERto ignore for the time being what he has gleaned about the soul from the reading of the Phaedo and the Republic. In these dialogues Plato speaks of the soul sometimes as wholly rational, as having three parts, and so forth. But in these dialogues he is t~lklng of the human soul, which is a special (...) case, whereas in this essay I am de~Hng with the wider role and the concept of the soul as the efficient cause of motion, change, and all becoming everywhere in the cosmos. My cardinal texts in this exposition are the Sophist (246a-249d), the Phaedrus (245c, d), and a considerable portion of Laws, X. Consider the Phaedo, a dialogue with at least four motifs: it is a dramatic evocation of the last day in the life of Socrates, it is an argument for the immortality of the soul and for the reality of the world of ideas, it is a myth of the nether world, and finally, it is a theory of the cosmos as ruled by purpose--all in all, one of the great pieces of literature of the Western world. For the reader, it is an evocation of an attitude to life, based on Plato's conception of the soul--an attitude expressed in the famous phrase that the wise man spends his life meditating on death. As contrasted with what may be called his existential concern with the soul, in the other dialogues on which I will comment, Plato approaches the topic of the soul as part of his explanation of the cosmos. In these his attitude is objective and quasi-scientific. It is to this side of Plato's thought that I wish to call attention in this essay, where the establishment of the immortality of the soul is incidental to the more basic doctrine that the soul is an arche, a primary factor and an ontological principle. In the,Sophist, we find Plato playing the music of his philosophy in a new key. He refers to the "friends of the forms" as though he, himself, were an outsider looking in; then, too, he asserts that motion is really real in contrast to his derogatory references to motion in the Cratylus, the Phaedo, and the Republic.I In these (and other) dialogues, Plato contrasts change and changing things with the timeless forms in respect of reality: the former are said, at best, to be semi-real; only the latter are really real. But in the Sophist he changes his tune, arguing that total reality (~o ~v, to' ~a~rE~ By) includes both motion and rest (248e 8; 249d 3-4). What does he mean by these two words? That by 'rest' he means the realm of ideas is indicated (if not proved) by his references to the forms in the same context (247b 1But in the Theaeteius,he classifiesmotions in a semi-scientific fashion, leaving the impression on the reader that he regards motion as a reality. [133] 134 HISTORY OF PHILOSOPHY 1-2; 249b, 10, c 1).2 As for motion, Plato makes it clear that the term covers not only (a) physical motion but also (b) life, (c) psyche, and (d) phronesis or naus (249b 5). All these are said to be forms of kinesis; how this is so--how life, soul, mason may be described as motions or changes--is a matter for later comment. What is more to the point is Plato's insistence that motion and what is moved are onta (beings, 249b 2, d 3). Plato uses change (metabol$) interchangeably with kinesis; anticipating the Phaedrus, I will include activity under change. And anticipating the Laws, I will characterize some of this activity as mental; indeed the Sophist, includes within change nous, phronesis, and episteme; that is to say, understanding (in the sense of an activity, 249a, b, c).s Plato offers various reasons in support of his contention that change is real. He may also be offering a special demonstration as follows. The philosopher who denies that change is real is engaged in a mental activity, in short... (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.

In this work we review the derivation of Dirac and Weinberg equations based on a “principle of indistinguishability” for the (j,0) and (0,j) irreducible representations (irreps) of the homogeneous Lorentz group (HLG). We generalize this principle and explore its consequences for other irreps containing j≥1. We rederive Ahluwalia–Kirchbach equation using this principle and conclude that it yields $\mathcal{O}(p^{2j} )$ equations of motion for any representation containing spin j and lower spins. We also use the obtained generators (...) of the HLG for a given representation to explore the possibility of the existence of first order equations for that representation. We show that, except for j= $ - \frac{1}{2}$ , there exists no Dirac-like equation for the (j,0)⊕(0,j) representation nor for the ( $ - \frac{1}{2}$ , $ - \frac{1}{2}$ ) representation. We rederive Kemmer–Duffin–Petieau (KDP) equation for the (1,0)⊕( $ - \frac{1}{2}$ , $ - \frac{1}{2}$ )⊕(0,1) representation by this method and show that the (1, $ - \frac{1}{2}$ )⊕( $ - \frac{1}{2}$ ,1) representation satisfies a Dirac-like equation which describes a multiplet of $j = \frac{3}{2}{\text{ and }}j = \frac{1}{2}$ with masses m and m/2, respectively. (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)

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)

We present an approach to understanding the origin of inertia involving the electromagnetic component of the quantum vacuum and propose this as a step toward an alternative to Mach's principle. Preliminary analysis of the momentum flux of the classical electromagnetic zero-point radiation impinging on accelerated objects as viewed by an inertial observer suggests that the resistance to acceleration attributed to inertia may be at least in part a force of opposition originating in the vacuum. This analysis avoids the (...) ad hoc modeling of particle-field interaction dynamics used previously by Haisch, Rueda, and Puthoff (Phys. Rev. A 49, 678, (1994)) to derive a similar result. This present approach is not dependent upon what happens at the particle point, but on how an external observer assesses the kinematical characteristics of the zero-point radiation impinging on the accelerated object. A relativistic form of the equation of motion results from the present analysis. Its manifestly covariant form yields a simple result that may be interpreted as a contribution to inertial mass. We note that our approach is related by the principle of equivalence to Sakharov's conjecture (Sov. Phys. Dokl. 12, 1040, (1968)) of a connection between Einstein action and the vacuum. The argument presented may thus be construed as a descendant of Sakharov's conjecture by which we attempt to attribute a mass-giving property to the electromagnetic component—and possibly other components—of the vacuum. In this view the physical momentum of an object is related to the radiative momentum flux of the vacuum instantaneously contained in the characteristic proper volume of the object. The interaction process between the accelerated object and the vacuum (akin to absorption or scattering of electromagnetic radiation) appears to generate a physical resistance (reaction force) to acceleration suggestive of what has been historically known as inertia. (shrink)

I argue that the Aristotelian definition of motion,“the act of what exists potentially insofar as it exists potentially,” and the mover causality principle,“whatever is moved is moved by another,” are compatible with Newton’s First Law of Motion, which treats inertialmotion as a state equivalent to rest and which requires no sustaining mover for such motion. Both traditions treat motion as such as requiring an initial, generating mover but not necessarily a sustaining motor. Through examining examples (...) of motion as treated by Newtonian physics, and through arguing that potential energy is Aristotelian potentiality, I argue that the First Law is understandable according to the Aristotelian definition as an incomplete act with a twofold ordination of the same potentiality. I then propose that, through the notion of spacetime, Special and General Relativity instantiate motion as a unity of differentiated prior and posterior parts that do not coexist in reality. (shrink)

Open peer commentary on the target article “How and Why the Brain Lays the Foundations for a Conscious Self” by Martin V. Butz. Excerpt: Butz proposes an anticipatory drive that is postulated to be responsible for brain function and the development of brain structure. It is especially interesting because Butz suggests that the anticipatory drive guides brain development, in addition to function. This is an ambitious and provocative proposal, and bears close examination. I focus on just one aspect here: in (...) the spirit of constructivism, I ask, where is it? (shrink)

A conservation principles tell us that some quantity, quality, or aspect remains constant through change. Such principles appear already in ancient and medieval natural philosophy. In one important strand of Greek cosmology, the rotatory motion of the celestial orbs is eternal and immutable. In optics, from at least the time of Euclid, the angle of reflection is equal to the angle of incidence when a ray of light is reflected. According to some versions of the medieval impetus theory (...) of motion, impetus remains in a projected body (and the associated motion persists) permanently unless the body is subject to outside interference. These examples could be multiplied. But it was in the seventeenth century that conservation principles began to play an absolutely central role in scientific theories. Each of Galileo Galilei, René Descartes, Christiaan Huygens, Gottfried Leibniz, and Isaac Newton founded his approach to physics upon the principle of inertia—that unless interfered with a body will undergo uniform rectilinear motion. A multitude of other conservation principles gained currency during the seventeenth century—some still with us, some long ago left behind. Descartes provides an interesting example of an author who attempted to derive all of his physical principles from conservation laws (Principles of Philosophy, see especially articles 36 to 42 of Part II). Descartes believed that the principles of his physics could be derived from the immutability of God, supplemented only by very weak assumptions about the existence of change in the world. He claims, in fact, that we ought to postulate the strongest conservation laws consistent with such change. These include. (shrink)

Lycan (1985, 1988) defended a “Principle of Credulity”: “Accept at the outset each of those things that seem to be true” (1988, p. 165). Though that takes the form of a rule rather than a thesis, it does not seem very different from Huemer’s (2001, 2006, 2007) doctrine of phenomenal conservatism (PC): “If it seems to S that p , then, in the absence of defeaters, S thereby has at least some degree of justification for believing that p (...) ” (2007, p. 30). My Principle was differently motivated and put to uses different from Huemer’s. In this paper I shall explore some of the differences. (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)

It is common in the literature on classical electrodynamics and relativity theory that the transformation rules for the basic electrodynamical quantities are derived from the hypothesis that the relativity principle applies to Maxwell's electrodynamics. As it will turn out from our analysis, these derivations raise several problems, and certain steps are logically questionable. This is, however, not our main concern in this paper. Even if these derivations were completely correct, they leave open the following questions: Is the RP a (...) true law of nature for electrodynamical phenomena? Are, at least, the transformation rules of the fundamental electrodynamical quantities, derived from the RP, true? Is the RP consistent with the laws of ED in a single inertial frame of reference? Are, at least, the derived transformation rules consistent with the laws of ED in a single frame of reference? Obviously, and are empirical questions. In this paper, we will investigate problems and. Abstract First we will give a general mathematical formulation of the RP. In the second part, we will deal with the operational definitions of the fundamental electrodynamical quantities. As we will see, these semantic issues are not as trivial as one might think. In the third part of the paper, applying what J. S. Bell calls “Lorentzian pedagogy”---according to which the laws of physics in any one reference frame account for all physical phenomena---we will show that the transformation rules of the electrodynamical quantities are identical with the ones obtained by presuming the covariance of the equations of ED, and that the covariance is indeed satisfied. Abstract As to problem, the situation is much more complex. As we will see, the RP is actually not a matter of the covariance of the physical equations, but it is a matter of the details of the solutions of the equations, which describe the behavior of moving objects. This raises conceptual problems concerning the meaning of the notion “the same system in a collective motion”. In case of ED, there seems no satisfactory solution to this conceptual problem; thus, contrary to the widespread views, the question we asked in the title has no obvious answer. (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)

Peter van Inwagen presented a powerful argument against the Principle of Sufficient Reason, which I henceforth abbreviate as ‘PSR’. For decades, the consensus was that this argument successfully refuted PSR. However, now a growing consensus holds that van Inwagen’s argument is fatally flawed, at least when ‘sufficient reason’ is understood in terms of ground, for on this understanding, an ineliminable premiss of van Inwagen’s argument is demonstrably false and cannot be repaired. I will argue that this growing consensus (...) is mistaken and that a powerful argument relevantly similar to van Inwagen’s should still concern us, even when we understand ‘sufficient reason’ in terms of ground. (shrink)

Research on human infants has begun to shed light on early-developing processes for segmenting perceptual arrays into objects. Infants appear to perceive objects by analyzing three-dimensional surface arrangements and motions. Their perception does not accord with a general tendency to maximize figural goodness or to attend to nonaccidental geometric relations in visual arrays. Object perception does accord with principles governing the motions of material bodies: Infants divide perceptual arrays into units that move as connected wholes, that move separately from one (...) another, that tend to maintain their size and shape over motion, and that tend to act upon each other only on contact. These findings suggest that o general representation of object unity and boundaries is interposed between representations of surfaces and representations of objects of familiar kinds. The processes that construct this representation may be related to processes of physical reasoning. (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)

Aberrations -- Absorption -- Accuracy and precision -- Alpha radiation -- Amplitude -- Angular forces -- Angular momentum -- Antenna -- Arago dot -- Aperture -- Archimedes's principle -- Band theory of solids -- Bernoulli's principle -- Beta radiation -- Blackbody radiation -- Bohr atom -- Bose condensation -- Bra-ket notation -- British thermal unit (BTU) -- Calculating system efficiency -- Circular motion -- Closed systems and isolated systems -- Concave and convex -- Conservation of charge -- (...) Conservation of energy -- Convection and conduction -- Cosmic radiation -- Crest and trough -- Density and specific gravity -- Diode -- Distance and area -- Distortion -- Doppler effect -- Dynamic systems theory -- Edison effect -- Eigenvectors -- Elastic and inelastic collisions -- Electric circuits: Parallel vs series, diagrams and components -- Electric potential -- Energy and power -- Enthalpy -- Entropy -- Euler's laws of motion -- Falling bodies and physics -- Faraday's law -- Feynman diagrams -- Flywheel -- Focal point -- Free body diagram -- Frequency -- Gamma radiation -- Gauss's law -- Gluon -- Gravitational potential energy -- Harmonic oscillator -- Harmonics -- Heisenberg uncertainty principle -- Higgs boson -- Horsepower -- Ideal gas law -- Joule --. (shrink)