Uncertainty is a part of everyday life. We live with a range of situations that inherently have an element of uncertainty in them – for example, crossing the road, going on holiday, or making a major purchase – but we often ignore the embedded chance in these activities. Risk is acknowledged in many activities, and much effort is expended in identifying these risks and minimising any potential negative outcomes. In schools, for example, a risk assessment is required prior to any excursion with children. Probability is the strand of mathematics that addresses uncertainty. This chapter explores ideas relating to probability in the mathematics classroom.

This chapter reconstructs Heidegger’s 1955–56 interpretation of the principle of reason as a principle that resonates or sounds variously in the history of philosophy. The principle is first fully formulated by Leibniz as the principle of sufficient reason, which states that there is no true fact or proposition without sufficient reason for it being so and not otherwise. Heidegger takes Leibniz’s principle of sufficient reason to be a historically specific version of the principle of reason, which is a fundamental ontological principle holding that nothing is without a reason or ground, and so that being is ground/reason. Heidegger hears this association between being and ground resonating in the ancient Greek concept of logos, which is taken up but distorted by the Romans in the concept of ratio. From there, the ontological principle develops into the principle articulated by Leibniz and comes to express the distinctive commitments of modern philosophy and technology. While Heidegger’s historical story is not entirely plausible and contains significant omissions, attempting to reconstruct it reveals why this purported history of the principle of reason is relevant to Heidegger’s broader ontological project.

In this chapter, I examine the dynamics of contemporary so-called leisure, which is largely how we attempt to ameliorate boredom. With contemporary leisure what appears to offer self-renewal and self-actualization actually advances a form of blissful self-obliteration that enables the despair that Kierkegaard alerts us to. I then turn to an alternative conception of leisure, which draws inspiration from classical sources. This tradition, which has evolved and developed in several cultural eras, traces a line from Aristotle to St. Benedict of Nursia to Thomas Aquinas up to more recent leisure visionaries, including Simone Weil and Josef Pieper. Rather than enhancing self-restoration, these writers contend, the vacancy and inaction of free time are prey to acedia – a spiritual and mental sloth. The classical leisure tradition takes direct aim at this tendency, cultivating practices of leisure which protect the self from falling into despair. The argument here is that contemporary leisure, as it is often understood and practiced, offers a temporary anesthetic that in the end intensifies existential boredom and despair. True leisure, by contrast, restores and renews the self, offering a powerful antidote to existential boredom and the despair that afflicts the self.

As a preliminary to discussing the idea that, for Aristotle, sensibility and intelligence are “measures” of their respective objects, in this chapter I discuss Aristotle’s conception of “measure.” Though the devil is in the details, the fundamental point is tolerably clear. It is that measures for knowing the objects of some genus are prior to – enter into the very idea of – certain particular forms of that genus. The inch, for example, is a measure of length, and it enters into the very idea of certain particular lengths, e.g. one inch, two inches, three inches, and so on. Similarly, if straight is the measure of linear shape, it enters into the very idea of certain particular shapes, e.g. straight and curved. In this way and in this sense, measures are “forms of forms”: that is, what it is to be certain particular quantities or qualities of a genus is to stand in some relation to the “measure” of that genus.

This chapter is focused on Aristotle’s account of sensibility in De Anima II 12. My thesis is that the account defines sensibility as the standard in relation to which perceptible qualities are the sorts of quality they are. To illustrate, Aristotle holds that some colors are dark, others light; this implies that the spectrum of dark and light is “divided” into two “sides,” one dark, the other light. In the previous chapter I suggested that what it is for a quality to lie on one side of a spectrum – e.g. to be one of the dark colors – is a matter of its relation to the “middle” of the associated spectrum. In this chapter I argue that the claim that sensibility just is “as it were a kind of mean of the contrariety in perceptible qualities” implies that these “middles” are defined by sensibility itself, the form or essence of the primary sense organ. The upshot is that the senses are “forms” or “standards” of perceptible qualities, in that the particular qualities known by their means are the sorts of quality they are (e.g. dark colors or light ones) thanks to their relationship to the form of the primary sense organ.

Prescribers need to perform calculations regularly, even with the advent of electronic systems. This is true for every ward, but more so for high-risk specialties such as paediatrics, ICU and anaesthetics. The reader is provided with several rules to manage this, including being clear about units, performing calculations in two directions and avoiding confusion with percentages and ratios.