Ioannis G. Ntagkas

. Philosophers and scientists often cite ontic factors when explaining the methods and success of scientific inquiry. That is, the adoption of a method or approach is explained in reference to the kind of system in which the scientist is interested: these are explanations of why scientists do what they do, that appeal to properties of their target systems. We present a framework for understanding such “Opticks to his Principia. Newton’s optical work is largely experiment-driven, while the Principia is primarily mathematical, so usually, each work is taken to exemplify a different kind of science. However, Newton himself often presented them in terms of a largely consistent method. We use our framework to articulate an original and plausible position: that the differences between the Opticks and the Principia are due to the kinds of systems targeted. That is, we provide an ontic-driven explanation of methodological differences. We suspect that ontic factors should have a more prominent role in historical explanations of scientific method and development.

In this paper, I attempt to argue for a different kind of philosophical discourse. Namely, I delineate a philosophical approach that can be defined in opposition to traditional philosophy, conceived as a more or less ahistorical and transcendental inquiry. According to this approach, exemplified in the thought of Richard Rorty, the different ontological and epistemological claims of philosophy are nothing but variations of the same metaphysical themes, constitutive of its very tradition. In order to present and argue for this point, I show how Rorty’s nominalist, conceptualist, and particularistic stance can be better understood in light of Raymond Geuss’ and Ian Hacking’s two metaphilosophical schemas. I also attempt to show how certain conceptual tensions that seem to emerge from the use of these schemas for understanding Rorty’s stance, can contribute to the critique of philosophy traditionally conceived.

In this paper I address some of the problems that the historical development of science poses for a realist and discuss whether a realist construal of scientific activity is conducive to historiographical practice. First, I discuss, by means of historical examples, Ian Hacking's defense of entity realism. Second, I try to show, drawing on Kuhn's recent work on incommensurability, that the realism problem is relevant to historiography and that a realist position entails a particular historiographical strategy, which faces problems. Finally, I suggest that for historiographical purposes an agnostic attitude with respect to scientific theories and unobservable entities is the most appropriate.

In this paper we offer a critical account of Aristotelian theory of time. After a brief presentation of the main views of Aristotle on the infinite, we focus the attention to the status of points with respect to the potentiality-actuality distinction. Then we address Aristotle’s views on time on the basis of the Aristotelian notion of continuity. We construe the “nows” as potentialities awaiting to be actualized. We show that it is the intervention of an agent, who, through finitely many unitary mental acts of noticing or perceiving, guarantees the actualization of particular “nows”, constructs or brings into existence time intervals and through their comparison measures them, so producing what Aristotle calls time.

In this paper we attempt to clear out the ground concerning the Aristotelian notion of density. Aristotle himself appears to confuse mathematical density with that of mathematical continuity. In order to enlighten the situation we discuss the Aristotelian notions of infinity and continuity. At the beginning, we deal with Aristotle’s views on the infinite with respect to addition as well as to division. In the sequel, we focus our attention to points and discuss their status with respect to the actuality–potentiality distinction. Then we focus our attention to the nature of continuity, which Aristotle tends to consider as leading to infinite divisibility and potential density of the extended.

We may define words or concepts, and we may also, as Aristotle and others have thought, define the things for which words stand and of which concepts are concepts. Definitions of words or concepts may be explicit or implicit, and may seek to report preexisting synonymies, as Quine put it, but they may instead be wholly or partly stipulative. Definition by abstraction, of which Hume’s principle is a much discussed example, seek to define a term-forming operator, such as the number operator, by fixing the truth-conditions of identity-statements featuring terms formed by means of that operator. Such definitions are a species of implicit definition. They are typically at least partly stipulative. Definitions of things, or real definitions, are, by contrast, typically conceived as true or false statements about the nature or essence of their definienda, and so not stipulative. There thus appears to be an obvious and head-on clash between taking Hume’s principle as an implicit and at least partly stipultative definition of the number operator and taking it as a real definition, stating the nature or essence of cardinal numbers. This paper argues that this apparent tension can be resolved, and that resolving it sheds light on part of the epistemology or essence and necessity, showing how some of our knowledge of essence and necessity can be a priori.

The paper surveys different notions of implicit definition. In particular, we offer an examination of a kind of definition commonly used in formal axiomatics, which in general terms is understood as providing a definition of the primitive terminology of an axiomatic theory. We argue that such “structural definitions” can be semantically understood in two different ways, namely as specifications of the meaning of the primitive terms of a theory and as definitions of higher-order mathematical concepts or structures. We analyze these two conceptions of structural definition both in the history of modern axiomatics and in contemporary philosophical debates. Based on that, we give a systematic assessment of the underlying semantics of these two ways of understanding the definiens of such definitions, by considering alternative model-theoretic and inferential accounts of meaning.

The difference between Carnap and Quine over analyticity is usually thought to turn on a disagreement as to whether there is a notion of meaning, or rules of language, which enable us to define that idea. This paper argues that the more important disagreement is epistemological. Quine came to accept a notion of analyticity. That leaves him in a position somewhat like Putnam's in ‘The Analytic and the Synthetic’: that there is a notion of analyticity, but that it is of no philosophical importance. But their reasons for thinking analyticity unimportant are quite different: for Putnam it is because all analytic truths are trivial; for Quine, the notion of analyticity itself is unimportant. I contrast Putnam's position with that of Carnap, and also contrast Carnap and Quine. Analyticity only has the force that it has for Carnap because he accepts the Principle of Tolerance, the idea that changes within a language and changes of language are subject to justification in different senses. Quine rejects that idea. That is why he does not take analyticity to be philosophically important or useful.

If the force on a particle fails to satisfy a Lipschitz condition at a point, it relaxes one of the conditions necessary for a locally unique solution to the particle’s equation of motion. I examine the most discussed example of this failure of determinism in classical mechanics—that of Norton’s dome—and the range of current objections against it. Finding there are many different conceptions of classical mechanics appropriate and useful for different purposes, I argue that no single conception is preferred. Instead of arguing for or against determinism, I stress the wide variety of pragmatic considerations that, in a specific context, may lead one usefully and legitimately to adopt one conception over another in which determinism may or may not hold

This paper consists in an exposition of a proof Newton gave in 1666 of the parallelogram law for compounding velocities, and an examination of its implications for understanding his treatment of motion resulting from a continuously acting force in the Principia. I argue that the “moments” invoked in the fluxional proof of the vector resolution and composition of velocities are “virtual times”, a device allowing Newton to represent motions by the linear displacements produced in such a time; the ratio of velocities at an instant can then be represented by assuming the velocities continue for such a virtual time. By the Method of First and Ultimate Ratios, the first ratio of the velocities is then given by the ratio of such lines, under the presupposition that in the limit they will shrink to zero magnitude. I then argue that the same device is implicit in Newton’s appeal to “moments” or “particles of time” in his proof of Kepler’s Area Law in the “Locke Paper” and in Proposition 1 of Book 1 of the Principia, and that the limiting process involved there is therefore the same as that implicit in the Method of First and Ultimate Ratios.

Einstein regarded as one of the triumphs of his 1915 theory of gravity - the general theory of relativity - that it vindicated the action-reaction principle, while Newtonian mechanics as well as his 1905 special theory of relativity supposedly violated it. In this paper we examine why Einstein came to emphasise this position several years after the development of general relativity. Several key considerations are relevant to the story: the connection Einstein originally saw between Mach's analysis of inertia and both the equivalence principle and the principle of general covariance, the waning of Mach's influence owing to de Sitter's 1917 results, and Einstein's detailed correspondence with Moritz Schlick in 1920

If the laws of nature are metaphysically necessary, then it appears that miracles are metaphysically impossible. Yet Locke accepts both Essentialism, which takes the laws to be metaphysically necessary, and the possibility of miracles. I argue that the apparent conflict here can be resolved if the laws are by themselves insufficient for guaranteeing the outcome of a particular event. This suggests that, on Locke’s view, the laws of nature entail how an object would behave absent divine intervention. While other views of laws also make miracles counterfactually dependent on God’s will, I show how this view is consistent with the Essentialist commitment to the view that the laws are metaphysically necessary. Further, I argue Locke’s view is a relatively attractive version of Essentialism, in part, because it allows for the possibility of miracles.

Traditionally, miracles have been defined as supernaturally caused events which are outside the scope of scientific explicability. In this paper I will criticize the argument that, when we lack a scientific explanation for an event but it has an adequate explanation in theistic terms, then the most reasonable conclusion is to claim that the event is a miracle. I will defend that this argument would not work unless we had prior independent evidence for God’s existence. Furthermore, I will argue that even within a theistic worldview in which the reality of God were unquestioned, we would not be justified in claiming that an event is a miracle because we would not have sufficient knowledge of God’s intentions and purposes.

On the basis of evidence drawn from the Waste book, Westfall and Nicholas have argued that Newton arrived at his second law of motion by reflecting on the implications of the first law. I analyze another argument in the Waste book which reveals that Newton also arrived at the second law by another very different route. On this route, it is the consideration of the third law and the principle of conservation of motion—and not the first law—that prompts Newton to formulate the second law. The existence of these two routes is significant because each employs a distinct kind of reasoning about forces. Whereas the Nicholas–Westfall route via the principle of inertia bears the mark of Descartes’s influence, the alternative route proceeds from the action–reaction principle, which is widely regarded as an original Newtonian contribution to mechanics. In the course of exploring this alternate route to the second law, the origins and justification of the third law are examined.Keywords: Issac Newton; Waste book; Third law of motion; Second law of motion; Richard Westfall; John Nicholas

A four dimensional approach to Newtonian physics is used to distinguish between a number of different structures for Newtonian space-time and a number of different formulations of Newtonian gravitational theory. This in turn makes possible an in-depth study of the meaning and status of Newton's Law of Inertia and a detailed comparison of the Newtonian and Einsteinian versions of the Law of Inertia and the Newtonian and Einsteinian treatments of gravitational forces. Various claims about the status of Newton's Law of Inertia are critically examined including these: the Law of Inertia is not an empirical law but a definition; it is not a law simpliciter but a family of schemata; it is a convention and gravitational forces exist only by convention; it is (or is not) redundant; the concepts it embodies can be dispensed with in favor of operationally defined entities; it is unique for a given theory. More generally, the paper demonstrates the importance of space-time structure for the philosophy of space and time and provides support for a realist interpretation of space-time theories

The measurement of force is based on a formal law of additivity, which characterizes the effects of two or more configurations on the equilibrium of a material point. The representing vectors (resultant forces) are additive over configurations. The existence of a tight interrelation between the force vector and the geometric space, in which motion is described, depends on observations of partial (directional) equilibria; an axiomatization of this interrelation yields a proof of part two of Newton's second law of motion. The present results (which were derived from a curious and deep isomorphism between force measurement and trichromatic color measurement) yield a kind of subunit, which needs to be incorporated into more complete axiomatizations of mechanics that would fulfill the Mach-Kirchhoff program

Eternalism is the view that all times are equally real. The relativity of simultaneity in special relativity backs this up. There is no cosmically extended, self-existing ‘now.’ This leads to a tricky problem. What makes statements about the present true? I shall approach the problem along the lines of perspectival realism and argue that the choice of the perspective does. To corroborate this point, the Lorentz transformations of special relativity are compared to the structurally similar equations of the Doppler effect. The ‘now’ is perspectivally real in the same way as a particular electromagnetic spectrum frequency. I also argue that the ontology of time licensed by perspectival realism is more credible in this context than its current alternative, the fragmentalist interpretation of special relativity.

For the last forty years, Hume's Newtonianism has been a debated topic in Hume scholarship. The crux of the matter can be formulated by the following question: Is Hume a Newtonian philosopher? Debates concerning this question have produced two lines of interpretation. I shall call them ‘traditional’ and ‘critical’ interpretations. The traditional interpretation asserts that there are many Newtonian elements in Hume, whereas the critical interpretation seriously questions this. In this article, I consider the main points made by both lines of interpretations and offer further arguments that contribute to this debate. I shall first argue, in favor of the traditional interpretation, that Hume is sympathetic to many prominently Newtonian themes in natural philosophy such as experimentalism, criticality of hypotheses, inductive proof, and criticality of Leibnizian principles of sufficient reason and intelligibility. Second, I shall argue, in accordance with the critical interpretation, that in many cases Hume...

: Newton's critics argued that his treatment of gravity in the Principia saddles him with a substantial dilemma. If he insists that gravity is a real force, he must invoke action at a distance because of his explicit failure to characterize the mechanism underlying gravity. To avoid distant action, however, he must admit that gravity is not a real force, and that he has therefore failed to discover the actual cause of the phenomena associated with it. A reinterpretation of Newton's distinction between the "mathematical" and the "physical" treatment of force indicates how he can reject each horn of this dilemma

Newton described his Principia as a work of ‘experimental philosophy’, where theories were deduced from phenomena. He introduced six ‘phenomena’: propositions describing patterns of motion, generalised from astronomical observations. However, these don’t fit Newton’s contemporaries’ definitions of ‘phenomenon’. Drawing on Bogen and Woodward’s distinction between data, phenomena and theories, I argue that Newton’s ‘phenomena’ were explanatory targets drawn from raw data. Viewed in this way, the phenomena of the Principia and the experiments from the Opticks were different routes to the same end: isolating explananda.

Newton’s earliest publications contained scandalous epistemological claims: not only did he aim for certainty; he also claimed success. Some commentators argue that Newton ultimately gave up claims of certainty in favor of a high degree of probability. I argue that no such shift occurred. I examine the evidence of a probabilistic shift: a passage from query 23/31 of the Opticks and rule 4 of the Principia. Neither passage supports a probabilistic approach to natural philosophy. The aim of certainty, then, was an enduring feature of Newton’s methodology.

In the Discours de la méthode, Descartes presents himself as a heroic figure, standing up against the current Aristotelian orthodoxy in philosophy, and offering something new, a mechanist physics and the metaphysics to go along with it. But Descartes was by no means the only challenger to Aristotelian natural philosophy: by Descartes’s day, there were many. Descartes was read as one of this group, generally called the novatores (innovators) in Latin, and often severely criticized for their advocacy of the new. Descartes himself wanted to separate his philosophy from that of the novatores, who were thought to seek novelty rather than truth. But it was not so easy to distance himself. Many contemporary commentators, like Charles Sorel, put Descartes squarely in their camp, but at exactly the moment when novelty and innovation in natural philosophy was changing from being worthy of scorn to being praiseworthy.

In science and everyday life, we often infer that something is true because it would explain some set of facts better than any other hypothesis we can think of. But what if we have reason to believe that there is a better way to explain these facts that we just haven't thought of? Wouldn't that undermine our warrant for believing the best available explanation? Many philosophers have assumed that we can solve such underconsideration problems by stipulating that a hypothesis should not only be 'the best' explanation available; rather, it should also be 'good enough'. Unfortunately, however, the only current suggestion for what it might mean to say that an explanation is 'good enough' is, well, not good enough. This paper aims to provide a better account of what is required for an explanatory hypothesis to be considered 'good enough'. In brief, the account holds that a `good enough' hypothesis is one that has gone through a process that I call explanatory consolidation, in which accumulating evidence and failed attempts to formulate better alternatives gradually make it more plausible that the explanation we currently have is better than any other that could be formulated.