The Skylla group in Constantinople's hippodrome

The Skylla group was among the most famous bronze sculptures installed in the hippodrome at Constantinople. This paper suggests that the Skylla was a feature of Constantinople at its re-foundation, but perhaps originally stood facing the Bosphorus. In around AD 400 it was moved to the hippodrome where it stood until its destruction in 1204, and where it may for some time have served as a fountain

How to solve the knowability paradox with transcendental epistemology

A novel solution to the knowability paradox is proposed based on Kant’s transcendental epistemology. The ‘paradox’ refers to a simple argument from the moderate claim that all truths are knowable to the extreme claim that all truths are known. It is significant because anti-realists have wanted to maintain knowability but reject omniscience. The core of the proposed solution is to concede realism about epistemic statements while maintaining anti-realism about non-epistemic statements. Transcendental epistemology supports such a view by providing for a sharp distinction between how we come to understand and apply epistemic versus non-epistemic concepts, the former through our capacity for a special kind of reflective self-knowledge Kant calls ‘transcendental apperception’. The proposal is a version of restriction strategy: it solves the paradox by restricting the anti-realist’s knowability principle. Restriction strategies have been a common response to the paradox but previous versions face serious difficulties: either they result in a knowability principle too weak to do the work anti-realists want it to, or they succumb to modified forms of the paradox, or they are ad hoc. It is argued that restricting knowability to non-epistemic statements by conceding realism about epistemic statements avoids all versions of the paradox, leaves enough for the anti-realist attack on classical logic, and, with the help of transcendental epistemology, is principled in a way that remains compatible with a thoroughly anti-realist outlook

Logicism, Possibilism, and the Logic of Kantian Actualism

In this extended critical discussion of 'Kant's Modal Metaphysics' by Nicholas Stang (OUP 2016), I focus on one central issue from the first chapter of the book: Stang’s account of Kant’s doctrine that existence is not a real predicate. In §2 I outline some background. In §§3-4 I present and then elaborate on Stang’s interpretation of Kant’s view that existence is not a real predicate. For Stang, the question of whether existence is a real predicate amounts to the question: ‘could there be non-actual possibilia?’ (p.35). Kant’s view, according to Stang, is that there could not, and that the very notion of non-actual or ‘mere’ possibilia is incoherent. In §5 I take a close look at Stang’s master argument that Kant’s Leibnizian predecessors are committed to the claim that existence is a real predicate, and thus to mere possibilia. I argue that it involves substantial logical commitments that the Leibnizian could reject. I also suggest that it is danger of proving too much. In §6 I explore two closely related logical commitments that Stang’s reading implicitly imposes on Kant, namely a negative universal free logic and a quantified modal logic that invalidates the Converse Barcan Formula. I suggest that each can seem to involve Kant himself in commitment to mere possibilia

General Fragmentation Trees

We show that the genealogy of any self-similar fragmentation process can be encoded in a compact measured real tree. Under some Malthusian hypotheses, we compute the fractal Hausdorff dimension of this tree through the use of a natural measure on the set of its leaves. This generalizes previous work of Haas and Miermont which was restricted to conservative fragmentation processes

Binary synthesis: Goethe's aesthetic intuition in literature and science

Argument This essay seeks to identify the cultural significance of Goethe's scientific writings. He reformulates, in the light of his own concrete experience, “crucial turning-points” (Hauptmomente) in the history of science – key ideas, the historical understanding of which is vital to present understanding – thus situating his own scientific work at the bi-polar center of the Western scientific tradition, conceived as the dramatic interplay over centuries of two opposing modes of thought. For in his experimentation he recaptures the glimpse of living form gained in aesthetic perception (Anschauung), from which such inherited theoretical positions are ultimately derived. At each stage of this process, imagination, in its aesthetic modality, is essential, for it alone reveals the world as it truly is. The literary quality of his writings on nature, as on culture, reveals Goethe's stylistic achievement in devising a medium in which the insights gained in contemplation may be so transmitted as to make a similar, imaginative, appeal to his reader – re-enacting the abstract-concrete equilibrium characterizing all aesthetic experience. Matching his style to the subtle, delicate, connectedness of Nature, Goethe recreates the delights of participating in natural creativity. His Janus-faced, scientific-literary, style illustrates “binary synthesis,” the principle that unites Goethe's science with his art

Review of Nicholas Boyle, Goethe: the poet and the age, vol. 2: Revolution and renunciation (1790-1803)

No abstract available

On the exponential functional of Markov Additive Processes, and applications to multi-type self-similar fragmentation processes and trees

A Markov Additive Process is a bi-variate Markov process $(\xi,J)=\big((\xi_t,J_t),t\geq0\big)$ which should be thought of as a multi-type L\'evy process: the second component $J$ is a Markov chain on a finite space $\{1,\ldots,K\}$, and the first component $\xi$ behaves locally as a L\'evy process, with local dynamics depending on $J$. In the subordinator-like case where $\xi$ is nondecreasing, we establish several results concerning the moments of $\xi$ and of its exponential functional $I_{\xi}=\int_{0}^{\infty} e^{-\xi_t}\mathrm dt,$ extending the work of Carmona et al., and Bertoin and Yor. We then apply these results to the study of multi-type self-similar fragmentation processes: these are self-similar analogues of Bertoin's homogeneous multi-type fragmentation processes Notably, we encode the genealogy of the process in a tree, and under some Malthusian hypotheses, compute its Hausdorff dimension in a generalisation of our previous work.Comment: Minor corrections and typo

Simulating Film Grain using the Noise Power Spectrum

Adding grain to simulated images makes them look more exciting. While its relativly easy to add some noise, here we use the principles developed by imaging scientists to produce grain which is theoretically "correct". While the results are usefull, they also illustrate the limitations of current photographic theories of grain