Who’s Afraid of Inconsistent Mathematics
Bibliographic Data
| ID | 19475490 |
|---|---|
| Authors | Mark Colyvan (0000-0002-9789-4527, The University of Sydney, corresponding author), ProtoSociology Project |
| Year | 2008 |
| Volume | 25 |
| Pages | 24-35 |
| Publication date | 2008-01-01 |
| Peer Reviewed | Yes |
| Open Access | No |
| Type | ARTICLE |
| Venue | ProtoSociology (JOURNAL) |
| Journal identifiers | ISSN: 1434-4319 |
| Publisher | Philosophy Documentation Center (PUBLISHER • US) |
| DOI | 10.5840/protosociology2008252 |
| OpenAlex | W2505882798 |
| Language | EN |
| Citations received | 4 |
In formal logic, a contradiction is the signal of a defeat: but in the evolution of real knowledge it marks the first step in progress towards a victory . Alfred North Whitehead (1861–1947) Contemporary mathematical theories are generally thought to be consistent. But it hasn't always been this way; there have been times when the consistency of mathematics has been called into question. Some theories, such as naive set theory and (arguably) the early calculus, were shown to be inconsistent. In this chapter we will consider some of the philosophical issues associated with inconsistent mathematical theories. Introducing inconsistency A five-line proof of Fermat's Last Theorem Fermat's Last Theorem states that there are no positive integers x , y , and z , and integer n > 2, such that x n + y n = z n . This theorem has a long and illustrious history but was finally proved in the 1990s by English mathematician Andrew Wiles (1953–). Despite the apparent simplicity of the theorem itself, the proof runs to over a hundred pages, invokes some very advanced mathematics (the theory of elliptic curves, among other things), and is understandable to only a handful of mathematicians. But consider the following proof of this theorem
Mathematics education · History and Theory of Mathematics · Mathematics · Psychology
| Unique citing works | 4 |
|---|---|
| Citations per year | 0,33 |
| Citation span | 2014 - 2022 (9) |
| Citation velocity | historical |
| Highly cited | No |
| Citation types | Neutral: 4 |