Talk:First principle
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[edit] Incorrect Godel reference?
I've not directly modified it since my comprehension of the implications of Godel's theorems isn't probably perfect, but from my understanding the sentence:
- contending that any logical system that was consistent could not be complete, and any system that was complete could not be entirely self-consistent.
is rather incorrect. Shouldn’t it be something like:
- contending that any logical system in which basic arithmetical facts are provable that was consistent could not be complete, and any system in which basic arithmetical facts are provable, cannot prove its own consistency
Please see Gödel's incompleteness theorem, in particular the chapter "Misconceptions about Gödel's theorems"
The specification of "in which basic arithmetical facts are provable " maybe can be seen as a detail in the context, but the second result seems completely incorrect to me.
--GozzoMan
I'm not an expert on the topic either, but to me not only the use of Gödel, but the whole article seems to be iffy.
[edit] Aristotle's and Modern Western Contributions
From the end of Aristotle's section:
- "[this principle] cannot be doubted, as all doubting is based on inconsistency, which assumes consistency a priori."
It's not clear to me why must all doubting be based on inconsistency. Couldn't one just doubt it unless it is proven?
And from the end of the Modern Western's section:
- "the need to represent the world, and the dualism that that task, in his view, entails."
Dualism in that sentence is wikilinked, though I don't find in its article a meaning fitting its use here. What's meant by dualism, so?
--euyyn 17:21, 11 March 2007 (UTC)
[edit] It cannot be doubted?
It cannot be doubted, as all doubting is based on inconsistency, which assumes consistency a priori.
You're laying it on pretty thick. Of course it can be doubted. There's no magic that prevents someone from saying "I doubt it" and not being a liar.
It's just that it would not be "rational" to doubt it. It would not be "sane" to doubt it. And these are more complicated concepts which do not derive especially from objective consistency. --76.217.82.113 (talk) 06:58, 12 December 2007 (UTC)
