I am studying a bit of this and so far it seems that, apart from math and computer science, the discipline of Logic is very self facing, with logicians proving things for other logicians. It left me wondering about interdiscipliary work. Specifically, can classical(propositional and first order predicate) and/or non-classical (i.e., fuzzy, intuitionist, relevant etc) logics provide unique insights or analysis in the following domains:

  1. History,
  2. Law,
  3. Psychology,
  4. Engineering?

I know this is a bit broad, just looking for smattering of concrete examples indexed to these domains.



closed as too broad by Najib Idrissi, Bruno Joyal, TZakrevskiy, Davide Giraudo, Daniel Fischer Dec 2 '13 at 19:14

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    $\begingroup$ Most of the uses I am aware of are actually abuses that make me cringe and die a little bit whenever I see them. $\endgroup$ – Asaf Karagila Nov 22 '13 at 16:33
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    $\begingroup$ Fuzzy Logic does have a few things to say about Linguistics, according to K. H. Lee's First Course in Fuzzy Theory and Applications, which I suppose is pertinent to both Psychology and History (in some sense); other applications will surely be found ibid. $\endgroup$ – Shaun Nov 22 '13 at 16:50
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    $\begingroup$ "Applications of Modal Logic in Linguistics" indiana.edu/~iulg/moss/linguistics.pdf $\endgroup$ – Matthew Towers Nov 22 '13 at 18:38
  • $\begingroup$ @mt_ : Thanks for that. Although it is still very theoretical in its applicaiton in linguistics, at least it is related to human activities. I can't help but think that the use of logic here is more of a diagramming tool than as a way to get insight. This is different than, say, math as applied to physics, where math provides actual insights not already apparent to the practitioner. $\endgroup$ – user76844 Nov 22 '13 at 18:53
  • $\begingroup$ Modern logic has applications to other areas, but mostly to other areas of mathematics. For example, descriptive set theory (especially invariant descriptive set theory and the study of Borel equivalence relations) has many applications. $\endgroup$ – Trevor Wilson Nov 23 '13 at 6:11

I think that Mathematical Logic is not the "foundation" of Mathematics; refer to Y.Manin, A Course in Mathematical Logic for Mathematicians (2nd ed, Springer - 2010; pag.xi) :

Foundational problems are for the most part passed over in silence. Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life.

Math Logic is Mathematics : Proof Theory, Model Theory, Computability Theory. But ML is a "strange" branch of Math because it has as his object of study Math itself.

The impressive success of Math is with application (through physics, engineering, economy) to the understanding of the external world.

ML has its application in the study of a particular "human activity" : the mathematician's one and its "products" : mathematical theories.