Several very exciting philosophical events are lined-up for this new academic year at Keele, and the organisation of a few others is under way! The excellent Royal Institute of Philosophy Invited Lecture Series has already started (details of the first event are pasted below and the programme can be accessed by clicking here).
In exactly one month, the “Jean-Jacques Rousseau” Annual Lecture and Conference will take place in the Conference Room of the Claus Moser Research Centre at Keele. The Annual Lecturer is at the same time one of the world’s best contemporary philosophers and best contemporary artists. In addition, several top speakers and participants will be present at the Annual Conference. Both Annual Lecture and Conference will discuss the value of playing by the rules. Registration is now open and you can register here.
Our reading group on A. W. Moore’s latest book (The Evolution of Modern Metaphysics: Making Sense of Things. CUP 2012) continues. During the next few weeks, participants will discuss the last few chapters of this big (not only significant, but also of over 650 pages!) volume.
First Royal Institute of Philosophy Lecture for this academic year:
Are There Unanswerable Mathematical Questions?
By: Marianna Antonutti Marfori (Keele)
Tuesday 22nd October, 6-7.30 pm
CBA0.060, Chancellor’s Building
Mathematical knowledge is held as a paradigm of certainty. The idea—from a broadly realist point of view—is that axioms capture the properties of a mathematical structure (e.g. the axioms of arithmetic capture the properties of the natural number structure), and truth-preserving rules allow us to derive theorems that are absolutely certain. Some have even argued that it follows from this view that there are no unanswerable mathematical questions.
However, there are reasons to doubt this picture of mathematical knowledge. Gödel’s famous incompleteness theorems show that no formal system (meeting certain minimal conditions) can capture the totality of true mathematical statements. In other words, there are meaningful mathematical questions that our axioms do not answer. To answer them, we need to go beyond the axioms. But what is the right way to extend them? And even if we answer certain questions relative to a certain way of extending the axioms, are there absolutely unanswerable mathematical questions? In this lecture, I will consider some famous examples of such questions and draw conclusions for any purported account of mathematical knowledge.
About the Speaker:
Marianna studied in Rome before moving to Cambridge for her master’s and then to Bristol for her PhD, which she recently defended. Her main area of research is the philosophy of mathematics, and in particular on theories of mathematical provability and computability. She has published on informal proofs in mathematics and on the possibility of accounting for mathematical knowledge and methodology in a scientific-naturalist framework. She joined Keele in September as a temporary lecturer.