The Geometry Of Cosmic Horror

It is impossible for anything immaterial or physical to violate the laws of logic, but it is entirely possible for a person to encounter something that is very abnormal by comparison to familiar emotional or sensory experiences.  Although the "alien" geometric designs associated with the cosmic horror genre are sometimes said to defy logic, it is by necessity impossible to do so--yet the foreign shapes and figures of cosmic horror are certainly meant to contrast with "normal" experiences.  In doing so, they implicitly reinforce themes of human helplessness and insanity.

Of course, seeing or feeling a surface that lacks the relative smoothness of many material objects in everyday life is possible, as is discovering objects or environments that lack the kind of architectural consistency that is present in so-called normal environments.  This kind of geometric landscape is not contrary to the laws of logic, but is rather permitted by them.  Foreign architecture and unusual shapes are completely different from geometry that "defies reason," as if such a thing could be done!  The use of strange environments in storytelling can certainly expose the arbitrary nature of what most people consider "normal" with regards to sensory experiences, yet this is the most it can ultimately accomplish.

Right angles can only be right angles; a circle cannot be anything other than a circle.  Furthermore, parallel lines cannot intersect by their very nature, and an acute angle must be smaller than a right angle.  These truths would inescapably apply even on a world shaped by an eldritch entity of the Lovecraftian kind.  While the language used to express mathematical facts and some of the ideas used to explain geometric facts, such as the notion that a circle "contains" 360 degrees, are nothing but mere constructs, the elements of true geometry--that is, the truths about shapes and numbers revealed solely by reason--are necessary truths.

By definition, necessary truths cannot be altered or negated by even the most alien, powerful, and subjectively terrifying cosmic entities which could hypothetically be in existence.  Logical possibility is the same as possibility: if someone ascribes to Cthulhu, Azathoth, or any other entity from cosmic horror the ability to supercede reason, then their conception of that being is a total impossibility.  Fiction can use the concept of something that differs from expected sensory experiences to communicate ideas about reality which are logically possible, but going beyond this is self-refuting.

There is no such thing as an object or truth that contradicts the laws of logic, which means that all necessary truths about geometry cannot be violated.  Certain information about moral and aesthetic values, sensory stimuli, and similar things are subject to a variety of epistemological limitations that prevent humans from knowing anything more than specific logical truths about them.  Logic itself, however, which genuine truths about geometry and the whole of valid mathematics reduce down to (as opposed to the educational constructs used to explain some of them), is the light by which both itself and all other things are seen.


[1].  https://thechristianrationalist.blogspot.com/2020/01/the-concept-of-circle.html