Predictivism and the periodic table

This is a comment on the paper by Barnes (2005) and the responses from Scerri (2005) and Worrall (2005), debating the thesis (‘predictivism’) that a fact successfully predicted by a theory is stronger evidence than a similar fact known before the prediction was made. Since Barnes and Scerri both use evidence presented in my paper on Mendeleev’s periodic law (Brush, 1996) to support their views, I reiterate my own position on predictivism. I do not argue for or against predictivism in the normative sense that philosophers of science employ, rather I describe how scientists themselves use facts and predictions to support their theories. I find wide variations, and no support for the assumption that scientists use a single ‘Scientific Method’ in deciding whether to accept a proposed new theory.     

Deviant encodings and Turing’s analysis of computability

Turing’s analysis of computability has recently been challenged; it is claimed that it is circular to analyse the intuitive concept of numerical computability in terms of the Turing machine. This claim threatens the view, canonical in mathematics and cognitive science, that the concept of a systematic procedure or algorithm is to be explicated by reference to the capacities of Turing machines. We defend Turing’s analysis against the challenge of ‘deviant encodings’.     

John Venn’s opposition to probability as degree of belief

John Venn is known as one of the clearest expounders of the interpretation of probability as the frequency of a particular outcome in a potentially unlimited series of possible events. This view he held to be incompatible with the alternate interpretation of probability as a measure of the degree of belief that would rationally be held about a certain outcome based upon the reliability of testimony and other prior information. This paper explores the reasons why Venn may have been so opposed to the degree-of-belief interpretation and suggests that it may have been a way for him to resolve a conflict in his own mind between his ideas of proper scientific methods of inference and the religious beliefs that he held as a young man.     

Weyl’s ‘agens theory’ of matter and the Zurich Fichte

This paper investigates Hermann Weyl’s reception of philosophical concepts stemming from the German Idealist Johann Gottlieb Fichte. In particular, Weyl’s ‘agens theory’ of matter, which he held around 1925, will be looked at. In the extant literature, the—admittedly also important—influence of Husserl on Weyl has mainly been addressed. Thus, apart from investigating some detailed Fichtean inheritances in Weyl’s concepts of causality, chance and continuity, the general difference which Weyl saw between the philosophies of Fichte and Husserl will also be discussed. For Weyl this is above all a difference between an active constructivism and a rather passive phenomenological seeing (Schau). Further, the paper shows in some detail the way Weyl was drawn into a certain reading of Fichte by his Zurich colleague, the philosopher Fritz Medicus. The methodological frame of the paper is that of Konstellationsforschung, a historical and systematic approach which proves to be particularly fruitful when investigating a (broadly speaking) German Idealist context and which allows special attention to be given to the acting subjects within the constellation under investigation. Conversely, Weyl’s agens theory suggests amendments to this methodology.     

The third law in Newton’s Waste book (or, the road less taken to the second law)

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.     

From centripetal forces to conic orbits: a path through the early sections of Newton’s Principia

In this study, we test the security of a crucial plank in the Principia’s mathematical foundation, namely Newton’s path leading to his solution of the famous Inverse Kepler Problem: a body attracted toward an immovable center by a centripetal force inversely proportional to the square of the distance from the center must move on a conic having a focus in that center. This path begins with his definitions of centripetal and motive force, moves through the second law of motion, then traverses Propositions I, II, and VI, before coming to an end with Propositions XI, XII, XIII and this trio’s first corollary. To test the security of this path, we answer the following questions. How far is Newton’s path from being truly rigorous? What would it take to clarify his ambiguous definitions and laws, supply missing details, and close logical gaps? In short, what would it take to make Newton’s route to the Inverse Kepler Problem completely convincing? The answer is very surprising: it takes far less than one might have expected, given that Newton carved this path in 1687.     

How to tell causes from effects: Kant’s causal theory of time and modern approaches

I attempt a reconstruction of Kant’s version of the causal theory of time that makes it appear coherent. Two problems are at issue. The first concerns Kant’s reference to reciprocal causal influence for characterizing simultaneity. This approach is criticized by pointing out that Kant’s procedure involves simultaneous counterdirected processes—which seems to run into circularity. The problem can be defused by drawing on instantaneous processes such as the propagation of gravitation in Newtonian mechanics. Another charge of circularity against Kant’s causal theory was leveled by Schopenhauer. His objection was that Kant’s approach is invalidated by the failure to deliver non-temporal criteria for distinguishing between causes and effects. I try to show that the modern causal account has made important progress toward a successful resolution of this difficulty. The fork asymmetry, as based on Reichenbach’s principle of the common cause, provides a means for the distinction between cause and effect that is not based on temporal order (if some preconditions are realized).     

Popper’s response to Dingle on special relativity and the problem of the observer

Dingle contended that Einstein’s special theory of relativity was physically impossible for the simple reason that it required clocks to be simultaneously faster and slower than each other. McCrea refuted Dingle using an operationalist argument. An operational response did not satisfy Popper, who wrote an unpublished essay to counter Dingle’s claim. Popper developed an analysis that avoided operationalism by using a system of coinciding clocks, contending that this system showed that special relativity withstood Dingle’s criticism that it was not a symmetrical and consistent physical theory. However, Popper mistakenly included an asymmetric calculation in his analysis. Once this is corrected, the amended result supports Dingle’s position. Popper went on to argue that to avoid determinism, special relativity had to be reconciled with absolute time; this too supports Dingle. Popper’s failure to refute Dingle calls into question his claim that ‘the observer’ is superfluous to special relativity.     

Duhem’s theory of mixture in the light of the Stoic challenge to the Aristotelian conception

The bulk of Duhem’s writing which bears on the understanding of mixtures suggests he adopted an Aristotelian position which he opposed only to the atomic view. A third view from antiquity—that of the Stoics—seems not to be taken into account. But his lines of thought are not always as explicit as could be wished. The Stoic view is considered here from a perspective which Duhem might well have adopted. This provides a background against which his somewhat unorthodox Aristotelianism might be understood.     

Pierre Duhem’s epistemic aims and the intellectual virtue of humility: a reply to Ivanova

David Stump (2007) has recently argued that Pierre Duhem can be interpreted as a virtue epistemologist. Stump’s claims have been challenged by Milena Ivanova (2010) on the grounds that Duhem’s ‘epistemic aims’ are more modest than those of virtue epistemologists. I challenge Ivanova’s criticism of Stump by arguing that she not distinguish between ‘reliabilist’ and ‘responsibilist’ virtue epistemologies. Once this distinction is drawn, Duhem clearly emerges as a ‘virtue-responsibilist’ in a way that complements Ivanova’s positive proposal that Duhem’s ‘good sense’ reflects a conception of the ‘ideal scientist’. I support my proposal that Duhem is a ‘virtue-responsibilist’ by arguing that his rejection of the possibility of our producing a ‘perfect theory’ reflects the key responsibilist virtue of ‘intellectual humility’.     

Plotinus’s conception of unity and multiplicity as the root to the medieval distinction between lux and lumen

Plotinus resolved the paradox of the immanent transcendence, characterizing the relation between the One and the universe, through his theory of the two energeiai. According to this doctrine, all existents have an internal activity and an external activity: the internal activity comprises the true essence and substance of each being; the external activity is emitted outwards as its image. The source of the emission is thus present in the lower layer of being by virtue of its manifold images. The prominence given to light in elucidating this solution led to a distinction between two types of lights: an original light, corresponding to the internal energeia of every existent, and a secondary light, which is the outflow and image of the first light, existing outside of the luminous body.This paper demonstrates the striking similarity between these two Plotinian lights and the concepts of lux and lumen developed by two thirteenth-century philosophers: Robert Grosseteste and Albertus Magnus. Moreover, the paper contends that the purpose of these two medieval concepts of light was identical to what Plotinus had in mind when he first made the distinction: to account for the relation between the one and the many.