LOGICAL GEOMETRIES

Logical Geometries and Information in the Square of Oppositions

The Aristotelian square of oppositions is a well-known diagram in logic and linguistics. In recent years, several extensions of the square have been discovered. However, these extensions have failed to become as widely known as the square. In this paper we argue that there is indeed a fundamental difference between the square and its extensions, viz., a difference in informativity. To do this, ...

Metaphysics of Logical Realism

با اینکه اغلب به غلط تصور می­شود که فلسفۀ تحلیلی، به عنوان یک جنبش ضد-متافیزیکی، هیچ ارتباطی با متافیزیک ندارد، اما دلایل خوبی وجود دارند که بر اساس آن می­توان تمایلات متافیزیکی فیلسوفان تحلیلی را تصدیق نمود و متعاقباً ماهیت ضد-متافیزیکی فلسفه تحلیلی را در تمام مراحل شکل­گیری­اش به حداقل رساند. چون فلسفه تحلیلی یک جنبش تاریخی است که ماهیت اصلی آن در چند مرحله شکل یافته است، لذا با پیگیری این مرا...

Logical Grammars, Logical Theories

Residuated lattices form one of the theoretical backbones of the Lambek Calculus as the standard free models. They also appear in grammatical inference as the syntactic concept lattice, an algebraic structure canonically defined for every language L based on the lattice of all distributionally definable subsets of strings. Recent results show that it is possible to build representations, such a...

Homogeneous Geometries

For the purposes of this paper, a geometry will consist of a set together with a closure operation on that set, satisfying the exchange condition, and under which singletons are closed (for more precise definitions, see §2.1). The geometry is homogeneous if in the automorphism group of the geometry, the pointwise stabilizer of any finitedimensional closed subset of the geometry is transitive on...

Plantinga and the Logical Problem of Evil