“. . . the membership relation for sets can often be replaced by the composition operation for functions. This leads to an alternative foundation for Mathematics upon categories -- specifically, on the category of all functions. Now much of Mathematics is dynamic, in that it deals with morphisms of an object into another object of the same kind. Such morphisms (like functions) form categories, and so the approach via categories fits well with the objective of organizing and understanding Mathematics. That, in truth, should be the goal of a proper philosophy of Mathematics.” ShouldWellsKindPhilosophyFormUnderstandingGoalDealsObjectsFitApproachFunctionRelationMathematicsFoundationObjectivesAlternativesOperationsCategoriesCompositionReplacedOften IsMembership Author:Saunders Mac Lane
“Genitive is a funny word because it means "from," but it also is the gender in European languages for objects: the masculine, feminine, and neuter. So if you have a genitive present, there's room for everybody to fit in. I just did a project in Vienna about rock, paper, scissor; you change the gender and it simply changes the whole thing. Rock is no longer a male. It doesn't function the same way.” IfsWayMeanWholeLanguageRoomsRocksObjectsFitPaperProjectsFunctionMalesGenderFeminineMasculineVienna Author:Lawrence Weiner