Mathematical Nominalism Mathematical nominalism can be described as the view that mathematical entities—entities such as numbers, sets, functions, and groups—do not exist. However, stating the view requires some care. Though the opposing view (that mathematical objects do exist) may seem like a somewhat exotic metaphysical claim, it is usually motivated by the thought that mathematical objects are required to exist in order for mathematical claims

Modal Illusions We often talk about how things could have been, given different circumstances, or about how things might be in the future. When we speak this way, we presume that these situations are possible. However, sometimes people make mistakes regarding what is possible or regarding what could have been the case. When what seems possible to a person is not really possible, this person

Truthmaker Theory Truthmaker theory is the branch of metaphysics that explores the relationships between what is true and what exists. Discussions of truthmakers and truthmaking typically start with the idea that truth depends on being, and not vice versa. For example, if the sentence ‘Kangaroos live in Australia’ is true, then there are kangaroos living in Australia. And if there are kangaroos living in Australia,

Humor The philosophical study of humor has been focused on the development of a satisfactory definition of humor, which until recently has been treated as roughly co-extensive with laughter. The main task is to develop an adequate theory of just what humor is. According to the standard analysis, humor theories can be classified into three neatly identifiable groups:incongruity, superiority, and relief theories. Incongruity theory is

Predicative and Impredicative Definitions The distinction between predicative and impredicative definitions is today widely regarded as an important watershed in logic and the philosophy of mathematics. A definition is said to be impredicative if it generalizes over a totality to which the entity being defined belongs. Otherwise the definition is said to be predicative. In the examples below, (2) and (4) are impredicative. Let π be

Logical Paradoxes A paradox is generally a puzzling conclusion we seem to be driven towards by our reasoning, but which is highly counterintuitive, nevertheless. There are, among these, a large variety of paradoxes of a logical nature which have teased even professional logicians, in some cases for several millennia. But what are now sometimes isolated as “the logical paradoxes” are a much less heterogeneous collection: