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I am studying mathematical logic, though some of it crosses over into (or is perhaps part of?) what I think is called traditional logic, formally, which seems to be basically philosophical logic, that used by aristotle and the likes.

Anyway, I am reading up on tradional logic, specifically about the nature of contradiction. The ending of this passage on importanceofphilosophy.com however, eludes me:

If the content of your knowledge contains contradictions, then some of your knowledge is in error. Because in order to be successful in reality one must know reality, success requires correct knowledge. It is therefore important to continually search for and root out contradictions in your knowledge in order to make sure that your knowledge corresponds to reality. The two primary methods for doing this are logic, the art of non-contradictory identification, and integration.

Okay then, so I don't know logic, but I know of it and am studying it. However, I have no idea what integration is in a philosophical sense. I doubt it's the same as integration in maths.

Part of the reason I am asking this is because I can't seem to find any information on this term, when searching for 'philosophical integration', or 'logical integration', nothing of relevance seems to be returned. Also, the sheer importance of this seems to be colossal, as it's paired up with logic itself. So it seems like a worthy endeavour to find out what integration is. Though, it kinda seems strange that it's somehow separate from logic, but anyway, perhaps you could shine some light.

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    Welcome to Phil.SE! Given that it's an unfamiliar term, it's probably useful sourcing the quote ie naming the book it came from. – Mozibur Ullah Dec 14 '15 at 17:24
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The materials in the site to which you referred (http://www.importanceofphilosophy.com/) seem to be based on objectivism, the philosophical system of the writer Ayn Rand. The quote on the home page is taken from Rand's essay Philosophy:  Who Needs It

In objectivism, the term integration refers to the formation of concepts. In a word, one forms concepts by grouping together (=integrating) similar percepts (perceptual data) and/or previously formed concepts. Rand believed that a correct method of concept-formation (=integration) was crucial to every individual human being, in order to avoid false and disastrous ideologies, like (by her) religion,  marxism, fascism.

See the entry on integration in the Ayn Rand Lexicon for some more details. 

  • Wow, just wow, I had no idea that what I read was the basis of a whole type of philosophy, I thought it was just sort a collection of common philosophical ideas from various types of beliefs, but never that it was an entire system, full fledged system. Thank you for introducing me to this! :) – user108262 Dec 16 '15 at 21:04
  • @user108262 You're welcome :) – Ram Tobolski Dec 16 '15 at 22:19
  • Philosophy is nothing other than rooting out contradictions and integrating concepts. I know of no other way to do it. I can never grasp why Rand did not follow her own advice. That she did not is why few people view her as a philosopher, or fewer than she would have liked. – PeterJ Jul 17 '18 at 10:33
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The answer by Ram is a good one, and he correctly identifies that "integration" can refer to the act of concept formation (i.e., integrating percepts into concepts) within Objectivism. However, Rand also used the term "integration" more broadly to refer to the broader requirement to integrate different principles, concepts, ideas, empirical data, etc., into a coherent non-contradictory whole. She was critical of philosophers who spurned "system building" (i.e., the integration of ideas into a full system of thought). In a discussion of the disintegration of modern art, she wrote:

While the alleged advocates of reason oppose “system-building” and haggle apologetically over concrete-bound words or mystically floating abstractions, its enemies seem to know that integration is the psycho-epistemological key to reason...

The notion of "integration" within Objectivism has been further developed in Leonard Piekoff's book The DIM Hypothesis where he asserts that many philosophical ideas fall into a tripartite distinction between Disintegration (D), Integration (I), and Mis-integration (M). Piekoff argues that integration is a crucial element of Objectivism and that many serious philosophical errors occur as a result of disintegration and mis-integration. This is probably the best book to read if you would like a detailed account of "integration" within the Objectivist system.

Within the context of the quote you give in your question, "integration" is referring to this type of activity --- i.e., "integrating" your ideals to make sure they all fit together without contradiction. And yes, this is a completely different meaning to "integration" in calculus!

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I'm not aware of a technical use of integration that would match the context, nor is the term listed in the dictionary on the site that I assume you found the quote on (http://www.importanceofphilosophy.com/Dictionary.html). For those reasons, I suspect the term is just being used in its ordinary sense, meaning combining disparate parts into a unified whole. In this case, it would mean combining your separate pieces of information and/or knowledge. I think the general idea is that contradictions that might be hidden when your knowledge is compartmentalized may become clear when your knowledge is "integrated."

With that said, my quick glance at the site referenced doesn't indicate it is particularly authoritative on the subject of philosophical logic.

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