Science Influences Philosophy

The claims of the new natural philosophers that their methodical reasoning and newly invented instruments produced knowledge of reality had a profound effect on contemporary mainstream philosophers. Hobbes allied himself with the rationalist pursuers of certainty but rejected the ability of experimental philosophy to reveal certain truths about nature. Gassendi defended a probabilistic theory of knowledge, while Locke’s theory of knowledge accepted “moral,” or near, certainty as a limit to knowledge of reality. Berkeley reinterpreted the materialistic ontology underlying the new science, arguing the metaphysical character played in it by the concept matter. Hume formulated an openly skeptical theory of knowledge of the world, arguing the metaphysical character of the roles played by causality and induction in the new natural philosophy. Kant responded by creating a philosophy that restored certainty to knowledge, but its object was now experience, not a reality independent of the mind.

The Weirdness Theorem and the Origin of Quantum Paradoxes

We argue that there is a simple, unique, reason for all quantum paradoxes, and that such a reason is not uniquely related to quantum theory. It is rather a mathematical question that arises at the intersection of logic, probability, and computation. We give our ‘weirdness theorem’ that characterises the conditions under which the weirdness will show up. It shows that whenever logic has bounds due to the algorithmic nature of its tasks, then weirdness arises in the special form of negative probabilities or non-classical evaluation functionals. Weirdness is not logical inconsistency, however. It is only the expression of the clash between an unbounded and a bounded view of computation in logic. We discuss the implication of these results for quantum mechanics, arguing in particular that its interpretation should ultimately be computational rather than exclusively physical. We develop in addition a probabilistic theory in the real numbers that exhibits the phenomenon of entanglement, thus concretely showing that the latter is not specific to quantum mechanics.

Analysing causal structures in generalised probabilistic theories

Causal structures give us a way to understand the origin of observed correlations. These were developed for classical scenarios, but quantum mechanical experiments necessitate their generalisation. Here we study causal structures in a broad range of theories, which include both quantum and classical theory as special cases. We propose a method for analysing differences between such theories based on the so-called measurement entropy. We apply this method to several causal structures, deriving new relations that separate classical, quantum and more general theories within these causal structures. The constraints we derive for the most general theories are in a sense minimal requirements of any causal explanation in these scenarios. In addition, we make several technical contributions that give insight for the entropic analysis of quantum causal structures. In particular, we prove that for any causal structure and for any generalised probabilistic theory, the set of achievable entropy vectors form a convex cone.

Hume and Ancient Academic Scepticism

Chapter One of Hume’s Scepticism sets out a short history of Academic scepticism, tracing its development from Socrates and Plato’s ‘Old Academy’, through Arcesilaus’ ‘Middle Academy’, into Carneades’ ‘New Academy’, and Philonian scepticism, as well as Cicero and the divergent stream breaking off from the Academy that would become Pyrrhonist thought. Academic scepticism is set off from its stoic competitors. Chapter One crucially describes both the development of sceptical probabilistic thinking and, anticipating Hume, the non-dogmatic doxastic position developed by Clitomachus of Carthage in contrast to the dogmatic doxastic and probabilistic theory of Metrodorus of Stratonikiae, which anticipates Locke.

Experimental Test of Tracking the King Problem

In quantum theory, the retrodiction problem is not as clear as its classical counterpart because of the uncertainty principle of quantum mechanics. In classical physics, the measurement outcomes of the present state can be used directly for predicting the future events and inferring the past events which is known as retrodiction. However, as a probabilistic theory, quantum-mechanical retrodiction is a nontrivial problem that has been investigated for a long time, of which the Mean King Problem is one of the most extensively studied issues. Here, we present the first experimental test of a variant of the Mean King Problem, which has a more stringent regulation and is termed “Tracking the King.” We demonstrate that Alice, by harnessing the shared entanglement and controlled-not gate, can successfully retrodict the choice of King’s measurement without knowing any measurement outcome. Our results also provide a counterintuitive quantum communication to deliver information hidden in the choice of measurement.