Editing Formal concept analysis (section)

== Motivation and philosophical background ==
In his article "Restructuring Lattice Theory" (1982),<ref name="restructuring">{{cite book |first1=Rudolf |last1=Wille |chapter=Restructuring lattice theory: An approach based on hierarchies of concepts |chapter-url=https://link.springer.com/chapter/10.1007/978-3-642-01815-2_23 |editor1-last=Rival |editor1-first=Ivan |title=Ordered Sets. Proceedings of the NATO Advanced Study Institute held at Banff, Canada, August 28 to September 12, 1981 |series=Nato Science Series C |volume=83 |publisher=Springer |date=1982 |pages=445–470 |doi=10.1007/978-94-009-7798-3 |isbn=978-94-009-7800-3 }}, reprinted in {{cite book |editor1-last=Ferré |editor1-first=Sébastien |editor2-last=Rudolph |editor2-first=Sebastian | title=Formal Concept Analysis: 7th International Conference, ICFCA 2009 Darmstadt, Germany, May 21–24, 2009 Proceedings |date=12 May 2009 | page=314 | publisher=Springer | isbn=978-364201814-5 }}</ref> initiating formal concept analysis as a mathematical discipline, Wille starts from a discontent with the current lattice theory and pure mathematics in general: The production of theoretical results—often achieved by "elaborate mental gymnastics"—were impressive, but the connections between neighboring domains, even parts of a theory were getting weaker.

{{Quote |text=Restructuring lattice theory is an attempt to reinvigorate connections with our general culture by interpreting the theory as concretely as possible, and in this way to promote better communication between lattice theorists and potential users of lattice theory |author=Rudolf Wille |source=<ref name="restructuring" />}}

This aim traces back to the educationalist Hartmut von Hentig, who in 1972 pleaded for restructuring sciences in view of better teaching and in order to make sciences mutually available and more generally (i.e. also without specialized knowledge) critiqueable.<ref>{{cite book |last=Hentig, von |first=Hartmut |date=1972 |title=Magier oder Magister? Über die Einheit der Wissenschaft im Verständigungsprozeß |publisher=Klett (1972), Suhrkamp (1974) |isbn=978-3518067079}}</ref> Hence, by its origins formal concept analysis aims at interdisciplinarity and democratic control of research.<ref name="AttrExGeneRegProc">{{cite thesis |first=Johannes |last=Wollbold |title=Attribute Exploration of Gene Regulatory Processes |date=2011 |type=PhD |publisher=University of Jena |page=9 |url=http://www.db-thueringen.de/servlets/DerivateServlet/Derivate-24615/Wollbold/Dissertation.pdf |arxiv=1204.1995 |id=urn:nbn:de:gbv:27-20120103-132627-0 }}</ref>

It corrects the starting point of lattice theory during the development of [[formal logic]] in the 19th century. Then—and later in [[model theory]]—a concept as unary [[predicate (logic)|predicate]] had been reduced to its extent. Now again, the philosophy of concepts should become less abstract by considering the intent. Hence, formal concept analysis is oriented towards the categories [[extension (semantics)|extension]] and [[intension]] of [[linguistics]] and classical conceptual logic.<ref name="GW">{{cite book |last1=Ganter |first1=Bernhard |last2=Wille |first2=Rudolf |title=Formal Concept Analysis: Mathematical Foundations |year=1999 |publisher=Springer |isbn=3-540-62771-5 |pages= |url=}}</ref>

Formal concept analysis aims at the clarity of concepts according to Charles S. Peirce's [[pragmatic maxim]] by unfolding observable, elementary properties of the [[Minor premise|subsumed]] objects.<ref name="AttrExGeneRegProc" /> In his late philosophy, Peirce assumed that logical thinking aims at perceiving [[reality]], by the triade concept, [[judgement]] and [[Consequent|conclusion]]. Mathematics is an abstraction of logic, develops patterns of [[Logical possibility|possible]] realities and therefore may support rational [[communication]]. On this background, Wille defines:

{{Quote |text=The aim and meaning of Formal Concept Analysis as mathematical theory of concepts and concept hierarchies is to support the rational communication of humans by mathematically developing appropriate conceptual structures which can be logically activated. |author=Rudolf Wille |source = <ref>{{cite book |first=Rudolf |last=Wille |chapter=Formal Concept Analysis as Mathematical Theory of Concepts and Concept Hierarchies |chapter-url= |editor= |title={{harvnb|Ganter|Stumme|Wille|2005}} }}</ref>}}