We describe in some detail how to build an infinite computing machine within a continuous Newtonian universe. The relevance of our construction to the Church-Turing thesis and the Platonist-Intuitionist debate about the nature of mathematics is also discussed.

We approach the philosophy of mathematics via a discussion of the differences between classical mathematics and constructive mathematics, arguing that each is a valid activity within its own context.

This book discusses deep problems about our place in the world with a minimum of jargon. It argues that 'absolutist' ideas dating back to Plato continue to mislead generations of mathematicians, physicists and theologians, and reveals the underlying reasons for the current conflicts between science and religion.

We discuss the philosophical status of the statement that (9n – 1) is divisible by 8 for various sizes of the number n. We argue that even this simple problem reveals deep tensions between truth and verification. Using Gillies's empiricist classification of theories into levels, we propose that statements in arithmetic should be classified into three different levels depending on the sizes of the numbers involved. We conclude by discussing the relationship between the real number system and the physical continuum.

I examine Popper’s claims about Newton’s use of induction in Principia with the actual contents of Principia and draw two conclusions. Firstly, in common with most other philosophers of his generation, it appears that Popper had very little acquaintance with the contents and methodological complexities of Principia beyond what was in the famous General Scholium. Secondly Popper’s ideas about induction were less sophisticated than those of Newton, who recognised that it did not provide logical proofs of the results obtained using (...) it, because of the possibilities of later, contrary evidence. I also trace the historical background to commonplace misconceptions about Newton’s method.Author Keywords: Newton; Popper; Induction; Principia; Kepler’s laws. (shrink)

BackgroundThough sobriety in young people is on the rise, students who drink little or no alcohol may experience social exclusion at University, impacting well-being. We aim to understand the social experiences of United Kingdom undergraduate students who drink little or no alcohol.MethodsA mixed-methods study using semi-structured, one-to-one interviews and the 24-Item Social Provisions Scale and Flourishing Scale with 15 undergraduate students who drink little or no alcohol. Descriptive statistics are presented for quantitative data and thematic analysis for qualitative.ResultsEight main themes (...) and four subthemes were generated from thematic analysis summarised in two sections ‘views of drinkers from non-drinkers’ and ‘how peer pressure feels and how people deal with it.’ The initial transition to University represented a challenge, where participants struggled to find their ‘true’ friends. However, students generally had high levels of social provision, well-being and enjoyed close friendships with fewer casual acquaintances. All students experienced some kind of peer pressure and developed coping strategies when in social situations involving alcohol. Fear of missing out on the ‘typical’ University experience heightened self-imposed expectations to drink. Despite participants acknowledging their counter-normative behaviour, some felt they were subject to stigmatisation by drinkers, doubting their non-drinker status, causing feelings of exclusion or being ‘boring.’ Their desire to ‘be like everyone else’ exposed some insight into the negative stereotypes of sobriety, including frustration behind alcohol’s status elevation.ConclusionStudents adopt strategies to minimise peer pressure and to fit in. Future research should interrogate drinkers’ perceptions of their sober peers to deepen understanding, better break down ‘us and them,’ and mitigate future expectations within the University drinking culture. (shrink)

A number of those actively involved in the physical sciences anticipate the creation of a unified approach to all human knowledge based on reductionism in physics and Platonism in mathematics. We argue that it is implausible that this goal will ever be achieved, and argue instead for a pluralistic approach to human understanding, in which mathematically expressed laws of nature are merely one way among several of describing a world that is too complex for our minds to be able to (...) grasp in its entirety. (shrink)

Although many physicists have little interest in philosophical arguments about their subject, an analysis of debates about the paradoxes of quantum mechanics shows that their disagreements often depend upon assumptions about the relationship between theories and the real world. Some consider that physics is about building mathematical models which necessarily have limited domains of applicability, while others are searching for a final theory of everything, to which their favourite theory is supposed to be an approximation. We discuss some particular recent (...) debates about quantum theory in which the underlying assumptions are not fully articulated. Introduction Setting the scene The Ghirardi, Rimini and Weber theory Quantum marbles Radioactive decay and isomerism The limits of quantum theory. (shrink)

This article examines the text of Principia Mathematica to discover the extent to which Newton's claims about his own contribution to it were justified. It is argued that for polemical reasons the General Scholium, written twenty-six years after the first edition, substantially misrepresented the methodology of the main body of the text. The article discusses papers of Wallis, Wren and Huygens that use the third law of motion as set out by Newton in Book 1. It also argues that Newton's (...) use of induction is quite different from and subtler than the ‘logical’ and ‘probabilistic’ notions of induction discussed and then rejected by a number of twentieth-century philosophers. (shrink)

Many of those actively involved in the physical sciences adopt a reductionist point of view, in which all aspects of the world are ultimately controlled by physical laws that are expressed in terms of mathematical equations. In this article we adopt a pluralistic approach to human understanding in which mathematically expressed laws of nature are merely one way among several of describing a world that is too vast and complex for our minds to be able to grasp in its entirety.

We study the state of mechanics and astronomy between 1660 and 1675 in order to understand the extent of the commitment to the mechanical philosophy of Kepler prior to the writing of Principia.

We discuss the extent to which the visibility of the heavens was a necessary condition for the development of science, with particular reference to the measurement of time. Our conclusion is that while astronomy had significant importance, the growth of most areas of science was more heavily influenced by the accuracy of scientific instruments, and hence by current technology.