Confirmation and justification. A commentary on Shogenji’s measure

So far no known measure of confirmation of a hypothesis by evidence has satisfied a minimal requirement concerning thresholds of acceptance. In contrast, Shogenji’s new measure of justification (Shogenji, Synthese, this number 2009) does the trick. As we show, it is ordinally equivalent to the most general measure which satisfies this requirement. We further demonstrate that this general measure resolves the problem of the irrelevant conjunction. Finally, we spell out some implications of the general measure for the Conjunction Effect; in particular we give an example in which the effect occurs in a larger domain, according to Shogenji justification, than Carnap’s measure of confirmation would have led one to expect.     

Confusion and dependence in uses of history

Many people argue that history makes a special difference to the subjects of biology and psychology, and that history does not make this special difference to other parts of the world. This paper will show that historical properties make no more or less of a difference to biology or psychology than to chemistry, physics, or other sciences. Although historical properties indeed make a certain kind of difference to biology and psychology, this paper will show that historical properties make the same kind of difference to geology, sociology, astronomy, and other sciences. Similarly, many people argue that nonhistorical properties make a special difference to the nonbiological and the nonpsychological world. This paper will show that nonhistorical properties make the same difference to all things in the world when it comes to their causal behavior and that historical properties make the same difference to all things in the world when it comes to their distributions. Although history is special, it is special in the same way to all parts of the world.     

Is knowledge justified true belief?

Is knowledge justified true belief? Most philosophers believe that the answer is clearly ‘no’, as demonstrated by Gettier cases. But Gettier cases don’t obviously refute the traditional view that knowledge is justified true belief (JTB). There are ways of resisting Gettier cases, at least one of which is partly successful. Nevertheless, when properly understood, Gettier cases point to a flaw in JTB, though it takes some work to appreciate just what it is. The nature of the flaw helps us better understand the nature of knowledge and epistemic justification. I propose a crucial improvement to the traditional view, relying on an intuitive and independently plausible metaphysical distinction pertaining to the manifestation of intellectual powers, which supplements the traditional components of justification, truth and belief.     

A case of confusing probability and confirmation

Tom Stoneham put forward an argument purporting to show that coherentists are, under certain conditions, committed to the conjunction fallacy. Stoneham considers this argument a reductio ad absurdum of any coherence theory of justification. I argue that Stoneham neglects the distinction between degrees of confirmation and degrees of probability. Once the distinction is in place, it becomes clear that no conjunction fallacy has been committed.     

Physico-mathematics and the search for causes in Descartes’ optics—1619–1637

One of the chief concerns of the young Descartes was with what he, and others, termed “physico-mathematics”. This signalled a questioning of the Scholastic Aristotelian view of the mixed mathematical sciences as subordinate to natural philosophy, non explanatory, and merely instrumental. Somehow, the mixed mathematical disciplines were now to become intimately related to natural philosophical issues of matter and cause. That is, they were to become more ’physicalised’, more closely intertwined with natural philosophising, regardless of which species of natural philosophy one advocated. A curious, short-lived yet portentous epistemological conceit lay at the core of Descartes’ physico-mathematics—the belief that solid geometrical results in the mixed mathematical sciences literally offered windows into the realm of natural philosophical causation—that in such cases one could literally “see the causes”. Optics took pride of place within Descartes’ physico-mathematics project, because he believed it offered unique possibilities for the successful vision of causes. This paper traces Descartes’ early physico-mathematical program in optics, its origins, pitfalls and its successes, which were crucial in providing Descartes resources for his later work in systematic natural philosophy. It explores how Descartes exploited his discovery of the law of refraction of light—an achievement well within the bounds of traditional mixed mathematical optics—in order to derive—in the manner of physico-mathematics—causal knowledge about light, and indeed insight about the principles of a “dynamics” that would provide the laws of corpuscular motion and tendency to motion in his natural philosophical system.     

Kepler’s optics without hypotheses

This paper argues that Kepler considered his work in optics as part of natural philosophy and that, consequently, he aimed at change within natural philosophy. Back-to-back with John Schuster’s claim that Descartes’ optics should be considered as a natural philosophical appropriation of innovative results in the tradition of practical and mixed mathematics the central claim of my paper is that Kepler’s theory of optical imagery, developed in his Paralipomena ad Vitellionem (1604), was the result of a move similar to Descartes’ by Kepler. My argument consists of three parts. First, Kepler borrowed a geometrical model and experiment of optical imagery from the mélange of mixed and practical mathematics provided in the works of the sixteenth-century mathematicians Ettore Ausonio and Giovanni Battista Della Porta. Second, Kepler criticized the Aristotelian theory of light and he developed his own alternative metaphysics. Third, Kepler used his natural philosophical assumptions about the nature of light to re-interpret the model of image formation taken from Della Porta’s work. Taken together, I portray Kepler’s theory of optical imagery as a natural philosophical appropriation of an innovative model of image formation developed in a sixteenth-century practical and mixed mathematical tradition which was not interested in questioning philosophical assumptions on the nature of light.     

Downward causation without foundations

Emergence is interpreted in a non-dualist framework of thought. No metaphysical distinction between the higher and basic levels of organization is supposed, but only a duality of modes of access. Moreover, these modes of access are not construed as mere ways of revealing intrinsic patterns of organization: They are supposed to be constitutive of them, in Kant’s sense. The emergent levels of organization, and the inter-level causations as well, are therefore neither illusory nor ontologically real: They are objective in the sense of transcendental epistemology. This neo-Kantian approach defuses several paradoxes associated with the concept of downward causation, and enables one to make good sense of it independently of any prejudice about the existence (or inexistence) of a hierarchy of levels of being.     

Nature’s drawing: problems and resolutions in the mathematization of motion

The mathematical nature of modern science is an outcome of a contingent historical process, whose most critical stages occurred in the seventeenth century. ‘The mathematization of nature’ (Koyré 1957, From the closed world to the infinite universe, 5) is commonly hailed as the great achievement of the ‘scientific revolution’, but for the agents affecting this development it was not a clear insight into the structure of the universe or into the proper way of studying it. Rather, it was a deliberate project of great intellectual promise, but fraught with excruciating technical challenges and unsettling epistemological conundrums. These required a radical change in the relations between mathematics, order and physical phenomena and the development of new practices of tracing and analyzing motion. This essay presents a series of discrete moments in this process. For mediaeval and Renaissance philosophers, mathematicians and painters, physical motion was the paradigm of change, hence of disorder, and ipso facto available to mathematical analysis only as idealized abstraction. Kepler and Galileo boldly reverted the traditional presumptions: for them, mathematical harmonies were embedded in creation; motion was the carrier of order; and the objects of mathematics were mathematical curves drawn by nature itself. Mathematics could thus be assigned an explanatory role in natural philosophy, capturing a new metaphysical entity: pure motion. Successive generations of natural philosophers from Descartes to Huygens and Hooke gradually relegated the need to legitimize the application of mathematics to natural phenomena and the blurring of natural and artificial this application relied on. Newton finally erased the distinction between nature’s and artificial mathematics altogether, equating all of geometry with mechanical practice.     

Reassessing logical hylomorphism and the demarcation of logical constants

The paper investigates the propriety of applying the form versus matter distinction to arguments and to logic in general. Its main point is that many of the currently pervasive views on form and matter with respect to logic rest on several substantive and even contentious assumptions which are nevertheless uncritically accepted. Indeed, many of the issues raised by the application of this distinction to arguments seem to be related to a questionable combination of different presuppositions and expectations; this holds in particular of the vexed issue of demarcating the class of logical constants. I begin with a characterization of currently widespread views on form and matter in logic, which I refer to as ‘logical hylomorphism as we know it’—LHAWKI, for short—and argue that the hylomorphism underlying LHAWKI is mereological. Next, I sketch an overview of the historical developments leading from Aristotelian, non-mereological metaphysical hylomorphism to mereological logical hylomorphism (LHAWKI). I conclude with a reassessment of the prospects for the combination of hylomorphism and logic, arguing in particular that LHAWKI is not the only and certainly not the most suitable version of logical hylomorphism. In particular, this implies that the project of demarcating the class of logical constants as a means to define the scope and nature of logic rests on highly problematic assumptions.     

Individual differences in the mixture ratio of rotation and nonrotation trials during rotated mirror/normal letter discriminations

Mental rotation is thought to underlie the increase in response times (RTs) for deciding whether rotated letters are normal or mirrored versions. However, mental rotation predicts a linear increase in RTs, whereas the mirror/normal letter discrimination task typically produces a curved function. Recently, Kung and Hamm suggested that this curved function results from a mixture of trials in which mental rotation is employed and trials in which it is not. The mixture ratio may vary between individuals, with some individuals relying more on mental rotation than others. There is no factor in the Kung and Hamm model that reflects such individual differences. In the present study, we suggest that a possible exponent parameter could be added to the Kung and Hamm model to capture individual differences in the mixture ratio. This exponent parameter appears to capture an individual characteristic since the value obtained correlates between the mirror/normal letter task and a left/right object facing task. The development of a quantity that represents the mixture ratio will aid further testing of processes involved in the visual imagery system.