Timeline for What is the difference between formalism and logicism
Current License: CC BY-SA 3.0
8 events
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| Mar 26, 2013 at 15:50 | history | edited | Dennis | CC BY-SA 3.0 |
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| Mar 26, 2013 at 14:44 | vote | accept | Amr | ||
| Mar 26, 2013 at 14:23 | comment | added | Dennis | @Amr This article does a good job of explaining the difference between these schools in a broad and accessible way. In general, I recommend the Stanford Encyclopedia of Philosophy as a first stop for these sorts of questions. The articles are all commissioned and written by experts so there is a bit more clarity and reliability than Wikipedia (generally). | |
| Mar 26, 2013 at 14:16 | comment | added | Dennis | @Amr As the last sentence of my previous comment might suggest, intuitionists reject the law of excluded middle (p or not-p), since there are some instances of that they will say are not true. Also, intuitionists tend to regard mathematics as an essentially mental (perhaps even "creative"/"inventive") activity and might take mathematical objects to be mind-dependent (this is true of old-school Brouwerian intuitionism, at least). | |
| Mar 26, 2013 at 14:14 | comment | added | Dennis | @Amr Yes to your first question. The difference between intuitionism and logicism is (at least) two-fold. Intuitionists typically don't take the axioms to be justified on the basis of logic alone (rather, on some forms of intuitionism they are given to us by (mathematical?) intuition). In addition they tend to understand "p is true" as "there is a proof of p", so they collapse truth into proof. As a result, they think that certain statements (the unproven ones like Goldbach's Conjecture) are neither true nor false. They would say something similar about all statements which are undecidable. | |
| Mar 26, 2013 at 14:03 | comment | added | Amr | If this is true, then what is the difference between intuitionism and logicism ? | |
| Mar 26, 2013 at 14:02 | comment | added | Amr | It seems to me that logicists treat axioms as statements with meaning and not just a string with characters. Am I right about that ? | |
| Mar 26, 2013 at 13:53 | history | answered | Dennis | CC BY-SA 3.0 |