Timeline for Impredicativity
Current License: CC BY-SA 2.5
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 7, 2019 at 11:32 | comment | added | Tommy R. Jensen | I notice that the Wikipedia entry has been changed to saying "Roughly speaking, a definition is said to be impredicative if..." which used to begin "More precisely, ...". It is frustrating for someone who is interested in distinguishing between ways of talking about mathematics that are predicative or not. E.g. in Nelson's "Predicative Arithmetic", Princeton 1986, the introduction "The impredicativity of induction", which precise definition of impredicativity has he got in mind, does anybody know? | |
| May 29, 2010 at 8:26 | vote | accept | dumb student | ||
| May 28, 2010 at 23:57 | comment | added | Rachid Atmai | @Andrej Bauer: actually I must thank you, Mummert and Krishnaswami. After reading the posts, I realize that this is really useful for mathematics. Thank you for proving me wrong, I would otherwise have kept my disappointment. | |
| May 28, 2010 at 22:06 | comment | added | Andrej Bauer | @alphaomega: The philosophers and their theories that bother you so much are irrelevant to this question. The question is about mathematics, not about philosophy of mathematics. Read the answers and you will see we are not discussing pseudo-math but actual math. Take your pet peeve elsewhere, please. | |
| May 28, 2010 at 19:54 | answer | added | Christoph-Simon Senjak | timeline score: 1 | |
| May 28, 2010 at 18:49 | comment | added | Rachid Atmai | I am sorry I offended you but I still maintain this point of view until seeing compelling arguments that these philosophies ask real mathematical problems. For now, all these theories seem to only be fashionable psychological theories about "how humans come to perceive mathematical objects" which is surely not a mathematical question. I used to believe that Frege's logicism gave rise to real problems in mathematics until I got to know about Cantor's work! | |
| May 28, 2010 at 17:11 | comment | added | Peter LeFanu Lumsdaine | @alephomega: It's true that plenty of bad philosophy has been written (by mathematicians and philosophers) about predicativitity, constructivism, etc., and that it can become a distraction from doing maths. But it guides some very real choices we have to make in doing maths (what definitions and constructions to use), and some issues that can't be avoided as soon as we start formalising anything. There are very real mathematical questions here! | |
| May 28, 2010 at 13:36 | answer | added | Carl Mummert | timeline score: 9 | |
| May 28, 2010 at 12:46 | answer | added | Neel Krishnaswami | timeline score: 10 | |
| May 28, 2010 at 8:48 | comment | added | Andrej Bauer | @alphaomega: What is the point of your comment, other than a display of your own ignorance? | |
| May 28, 2010 at 6:22 | answer | added | Andrej Bauer | timeline score: 32 | |
| May 28, 2010 at 5:53 | comment | added | Theo Johnson-Freyd | Not being a philosopher, I looked up "impredicativity" on Wikipedia, which gives: "More precisely, a definition is said to be impredicative if it invokes (mentions or quantifies over) the set being defined, or (more commonly) another set which contains the thing being defined." The definitions I know for all your examples do not fit Wikipedia's gloss. | |
| May 28, 2010 at 5:50 | comment | added | Rachid Atmai | continued: My point of view might itself be a caricature of this philosophical debate but that is the impression I got out of this debate by the time I finished my MA in phil of math. | |
| May 28, 2010 at 5:50 | comment | added | Rachid Atmai | I think predicativism is just some pseudo theory that some philosophers like to play with because they want to talk about mathematics but don't really want to do mathematics. All these pseudo theories such as predicativism, contructivism, finitism, formalism anything else -ism are just a philosopher's caricatures of mathematics in some imaginary world of his own without taking into account the full complexity of mathematical objects and of mathematics itself. All these caricatures have become fashionable and subject of intense (and fruitless) debate while mathematics itself is for eternity | |
| May 28, 2010 at 2:43 | history | asked | dumb student | CC BY-SA 2.5 |