Some personal thoughts and opinions on what “good quality mathematics” is and whether one should try to define this term rigorously. As a case study, the story of Szemer´edi’s theorem is presented.
Mathematics, Morally
A source of tension between Philosophers of Mathematics and Mathematicians is the fact that each group feels ignored by the other; daily mathematical practice seems barely affected by the questions the Philosophers are considering. In this talk I will describe an issue that does have an impact on mathematical practice, and a philosophical stance on mathematics that is detectable in the work of practising mathematicians. No doubt controversially, I will call this issue ‘morality’, but the term is not of my coining: there are mathematicians across the world who use the word ‘morally’ to great effect in private, and I propose that there should be a public theory of what they mean by this. The issue arises because proofs, despite being revered as the backbone of mathematical truth, often contribute very little to a mathematician’s understanding. ‘Moral’ considerations, however, contribute a great deal. I will first describe what these ‘moral’ considerations might be, and why mathematicians have appropriated the word ‘morality’ for this notion. However, not all mathematicians are concerned with such notions, and I will give a characterisation of ‘moralist’ mathematics and ‘moralist’ mathematicians, and discuss the development of ‘morality’ in individuals and in mathematics as a whole. Finally, I will propose a theory for standardising or universalising a system of mathematical morality, and discuss how this might help in the development of good mathematics.
Is it Wrong to Topple Statues and Rename Schools?
In recent years, campaigns across the globe have called for the removal of objects symbolic of white supremacy. This paper examines the ethics of altering or removing such objects. Do these strategies sanitize history, destroy heritage and suppress freedom of speech? Or are they important steps towards justice? Does removing monuments and renaming schools reflect a lack of parity and unfairly erase local identities? Or can it sometimes be morally required, as an expression of respect for the memories of people who endured past injustices; a recognition of this history’s ongoing legacies; and a repudiation of unjust social hierarchies?
Philosophy En Route to Reality: A Bumpy Ride
My intellectual journey in philosophy proceeded along two mountainous paths that coincided at their base, but forked less than halfway up the incline. The first is that of my philosophical development, a steep but steady and continuous ascent. It began in my family, and accelerated in high school, art school, college, and graduate school. Those foundations propelled my philosophical research into the nature of rationality and its relation to the structure of the self, a long-term project focused on the Kantian and Humean metaethical traditions in Anglo-American analytic philosophy. It would have been impossible to bring this project to completion without the anchor, compass, and conceptual mapping provided by my prior, longstanding involvement in the practice and theory of Vedic philosophy. The second path is that of my professional route through the field of academic philosophy, which branched onto a rocky detour in graduate school, followed by a short but steep ascent, followed next by a much steeper, sustained descent off that road, into the ravine, down in flames, and out of the profession. In order to reach the summit of the first path, I had to reach the nadir of the second. It was the right decision. My yoga practice cushioned my landing.
Hatata [II] (~1692)
Translating to ‘an investigation’, this is the second of two 17th century ethical and rational treatises from present-day Ethiopia. Walda Heywat (Wäldä Hewat) continued the work of his mentor, Zera Yacob (Zär’a Ya’eqob, Wärqe), and expanded on it, turning it into more of a practical guide. Hatata (II) is considered to be more in line with more traditional views in its approach to topics such as marriage and abortion. However, where as Zara Yacob’s ideas were relatively individualistic, Walda Heywat was particularly known for his social ethics. In his writing, he states, “God did not create me only for myself, but placed me in the midst of other created [men] who are equal to me.” He also adds, “Man cannot come to existence, grow and serve by himself without the help of other men.”
The Racism of Philosophy’s Fear of Cultural Relativism
By looking at a canonical article representing academic philosophy’s orthodox view against cultural relativism, James Rachels’ “The Challenge of Cultural Relativism,” this paper argues that current mainstream western academic philosophy’s fear of cultural relativism is premised on a fear of the racial Other. The examples that Rachels marshals against cultural relativism default to the persistent, ubiquitous, and age-old stereotypes about the savage/barbarian Other that have dominated the history of western engagement with the non-western world. What academic philosophy fears about cultural relativism, it is argued, is the barbarians of the western imagination and not fellow human beings. The same structure that informs fears of cultural relativism, whereby people with different customs are reduced to the barbarian/savage of the western imagination, can be seen in the genesis of international law which arose as a justification for the domination of the Amerindian (parsed as “barbarians”). It is argued that implicit in arguments against cultural relativism is the preservation of the same right to dominate the Other. Finally, it is argued that the appeal of the fear of cultural relativism is that, in directing moral outrage at others, one can avoid reflecting on the failures of one’s own cultural tradition.
The Ink of the Scholars: Reflections on Philosophy in Africa
What are the issues discussed today by African philosophers? Four important topics are identified here as important objects of philosophical reflection on the African continent. One is the question of ontology in relation to African religions and aesthetics. Another is the question of time and, in particular, of prospective thinking and development. A third issue is the task of reconstructing the intellectual history of the continent through the examination of the question of orality but also by taking into account the often neglected tradition of written erudition in Islamic centres of learning. Timbuktu is certainly the most important and most famous of such intellectual centres. The fourth question concerns political philosophy: the concept of African socialisms is revisited and the march that led to the adoption of the African Charter of Human and Peoples Rights is examined. All these important issues are also fundamental to understanding the question of African languages and translation.
Hatata [I] (1667)
Translating to ‘an investigation’, this is the first of two 17th century ethical and rational treatises from present-day Ethiopia. Zera Yacob (Zär’a Ya’eqob, Wärqe) is most noted for his philosophy surrounding the principle of harmony. He asserted that an action’s morality is decided by whether it advances or degrades overall harmony in the world. While he did believe in a deity, whom he referred to as God, he criticised several sets of religious beliefs. Rather than deriving beliefs from any organized religion, Yacob sought the truth in observing the natural world. In Hatata, Zera Yacob applied the idea of a first cause to produce a proof for the existence of God, thus proposing a cosmological argument. “If I say that my father and my mother created me, then I must search for the creator of my parents and of the parents of my parents until they arrive at the first who were not created as we [are] but who came into this world in some other way without being generated.” However, the knowability of God does not depend on human intellect, but “Our soul has the power of having the concept of God and of seeing him mentally. God did not give this power purposelessly; as he gave the power, so did he give the reality.” Yacob’s work was continued in a second Hatata by his pupil and patron’s son, Walda Heywat (Wäldä Hewat).
Socrates and Ọ̀rúnmìlà: Two Patron Saints of Classical Philosophy
Oluwole’s teachings and works are generally attributed to the Yoruba school of philosophical thought, which was ingrained in the cultural and religious beliefs (Ifá) of the various regions of Yorubaland. According to Oluwole, this branch of philosophy predates the Western tradition, as the ancient African philosopher Orunmila predates Socrates by her estimate. These two thinkers, representing the values of the African and Western traditions, are two of Oluwole’s biggest influences, and she compares the two in her book Socrates and Orunmila.
The Philosopher Queens: The Lives and Legacies of Philosophy’s Unsung Women
For all the young women and girls sitting in philosophy class wondering where the women are, this is the book for you. This collection of 21 chapters, each on a prominent woman in philosophy, looks at the impact that women have had on the field throughout history. From Hypatia to Angela Davis, The Philosopher Queens will be a guide to these badass women and how their amazing ideas have changed the world. This book is written both for newcomers to philosophy, as well as all those professors who know that they could still learn a thing or two. This book is also for those many people who have told us that there are no great women philosophers. Please pledge, read this book and then feel free to get back to us.