Moodle@Warwick

This course is a first introduction to philosophy of mathematics, via one of our most fascinating and perplexing concepts: the infinite. We encounter the concept of infinity in myriad ways. In Zeno’s paradoxes of time, space, and motion, the idea of infinite division is used to argue in favour of a radical monism. The ancient atomists Leucippus and Democritus claimed that the universe consisted of an infinity of atoms moving in an infinite void, and contemporary cosmology still considers the issue of whether the universe is infinite to be an open question.

But what does it mean for something to be infinite? It is mathematics that offers us the precise definitions that let us begin to answer this question, and thus in mathematics that many of the most important questions concerning the infinite arise. Do the infinite structures that we talk about in mathematics really exist? If so, how can we have knowledge of them? Is it even coherent to talk about the truly infinite, or does it fall victim to paradox? This course will investigate these and other questions by engaging with the ideas of philosophers and mathematicians from across history, with a focus on the reception of Georg Cantor’s theory of sets, and the crisis in the foundations of mathematics that it precipitated.

Photography is ubiquitous. Advertising, the internet and social media depend upon it. With this come worries about image-manipulation and so-called “fake news.” Prior to the worries provoked by digital imaging, photography was generally taken to be a reliable source of knowledge about the world: assuming that images have not been digitally manipulated or misleadingly staged, we have reason to believe what we see in forensic, scientific and medical photographs, if not advertising or propaganda—certainly by comparison to what we see in hand-made images. We rely on crime scene photographs for a reason. Call this photography’s (relative) “epistemic advantage:” It depends on the intuition that machine-generated images are free from certain kinds of unreliability (selective attention, false beliefs, etc) that human beings suffer from. 

But photography is also taken to be aesthetically rewarding: it is widely collected and exhibited in museums, and we appreciate different photographer’s styles or oeuvres for different reasons—not least because different photographers and different schools of photography depict the world in very different ways, focusing on different subject matters, and stressing some features of the scene while suppressing others. We appreciate art in general for these kinds of reasons, and photography is no different in this regard. Call this photography’s “aesthetic capacity.” But note that such capacities are precisely what photography’s “epistemic advantage” depends on bypassing—by providing an ostensibly objective, or “belief-independent” recording of the world.  

So it looks as if the reasoning, and underlying intuitions, behind attributing epistemic and aesthetic capacities to photography conflict. If so, both cannot be true and one will need to be surrendered. This has generated debate between “orthodox” and “new theorists” of photography over the past decade. Orthodox theorists foreground photography’s epistemic capacities; new theorists stress its aesthetic capacities. Spoiler: I’m a new theorist, of sorts. One reason for being a new theorist is that it enables us to take the intentions, beliefs and other mental states of photographers seriously, and this opens up the possibility of using photography for various artistic, ethical and political purposes—in addition to its well documented scientific, medical and forensic uses—some of which we will look at on this course. The challenge for new theorists will be how to account in turn for photography’s epistemic capacities in manner consistent their claims for its aesthetic capacities.