Talk:First principle

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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.

The subject of first principles is sufficiently fundamental in philosophy that we should view references to Godel's incompleteness theorem as also being related to the incomputability results. This is an awfully difficult area of mathematics to get into when talking about first principles, but the relationship between the incompleteness theorem and the definition of an algorithm suggests that we should not include restrictions on the incompleteness theorems to talk about only arithmetic theories.

--Peterbbishop (talk) 21:04, 15 November 2010 (UTC)[reply]

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)[reply]

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)[reply]

Not relevant, but if I remove someone will claim religion is being systematically deleted from the interwebs.

Somebody else do it, I'm a wimp. --142.179.5.252 (talk) 06:25, 7 July 2008 (UTC) (thezeus18)[reply]

I think that the English and the German text cover different subjects. The German "Begriff" means something like "the idea behind a (single!) word", while first principles deal with propositions which connect several Begriffe.--Jkbw (talk) 15:06, 28 January 2009 (UTC)[reply]

The title of the section on "Descartes" links to the page on this person. Should this link be moved to the first time the name is mentioned in the main paragraph? This is the first time I have seen a title linked like this in Wikipedia.--Kuliwil (talk) 06:06, 30 August 2009 (UTC)[reply]

I have moved the link to the first in-paragraph reference. --Kuliwil (talk) 22:40, 13 October 2009 (UTC)[reply]

From the section on Aristotle's contribution: "Aristotle [..] formulated a principle (the Aristotelian tautology denoted A=A ) [...] called the first principle"

This is wrong, surely? My reading of the linked pages is that Aristotle's First Principle is not A=A (identity) but the principle of contradiction ¬(P ^ ¬P). That is, Aristotle's First Principle is actually the Second of the three classic laws of thought.

Helvetius (talk) _"A=A"" class="ext-discussiontools-init-timestamplink">10:23, 2 September 2009 (UTC)[reply]

I agree that the Greek text does not give the Law of Identity, but the Principle of Contradiction. As the three classic laws of thought were also known as "prnciples", "the first principle" simply means the first of these three laws in the conventional order of presenting them, and the juxtaposition of "first" with "principle" here has nothing to do with "reasoning from first principles". Therefore I've removed the whole section as being irrelevant to the topic of the article.  --Lambiam 09:51, 8 February 2011 (UTC)[reply]

Wrong or not, just deleting it is worse. I have replaced it with a stop-gap quote. Hpvpp (talk) 04:24, 9 February 2011 (UTC)[reply]

I take issue with your edit summary don't just remove something you don't like - replace it with something better and your statement "just deleting it is worse". I've presented my argument for removing it above, and it is obviously not just "because I don't like it". The argument is, basically, that the section was based on a misrepresentation of the meaning of "first principle" applied to the three classic laws of thought – a meaning that is quite unrelated to the topic of this article. The content of the section clearly did not belong in this article, which is an entirely valid reason for removing it without having to replace it by "something better".  --Lambiam 10:46, 9 February 2011 (UTC)[reply]

Regarding the "don't like", I offer my apologies; I will try to be less hasty. Regarding your reasoning, I beg to differ. Aristotle is the place to go for First Principles and so the better move would have been here to leave the heading, but with a {{Empty section}} tag. Hpvpp (talk) 23:05, 9 February 2011 (UTC)[reply]

When we compare two separate mathematical theories for equivalence, we find that two theories are completely equivalent if the axioms of the first theory can be proven as propositions of the second theory and the axioms of the second theory can be proven as propositions of the first theory.

Thus, the philosophical concept of first principles is a little shaky in relationship to this kind of mathematical observation. This means that in mathematics, the concept of first principles is not very meaningful because you can have an alternative equivalent mathematical theory with a different set of axioms.

The philosophical idea of first principles is much more important, because it is related to how people think about things. This is very much related to the axioms of a mathematical theory, but the possibility of a different person operating with an equivalent, but different mathematical theory with different axioms, or first principles, is an ever-present danger in philosophical debate.

Often, arguments over which principles are really the first principles are a favorite subject of debate, but it is as useful as arguing over how many angels can dance on the head of a pin.

This does not cause the concept of first principles to stop being important; it merely means that we should not get too excited about which principles are actually the first principles.

--Peterbbishop (talk) 21:20, 15 November 2010 (UTC)[reply]

Changed lead sentences meanings, first sentence more general, second sentence more exact, linked and cited, ^[1], Arnlodg (talk) 18:50, 16 October 2019 (UTC)[reply]