"Diagrammatic Immanence"

Diagrammatic Immanence

"There is thus a naturally 'pragmatic' epistemology intrinsic to categories: from the standpoint of category theory objects are investigated and known only via their interactions with other objects, not 'in themselves''. The space of possible maps from one object to another determines what can be known of those objects as such. Over the past several decades, category theory has proven extraordinarily successful in unifying diverse fields of mathematics and providing a less arbitrary and more productive foundation for mathematics than set theory. Because of its intrinsic orientation towards relations, it connects more readily and with fewer idealist assumptions than set theory to the real world and its component structures." p.10. 

"A meaning of whatever sort is necessarily determined by its position in a space of various intersecting structures, each with its own rich tangle of relations. Each of the 'single' topics being discussed opens up internally into a complex arrangement of mappings between, words, sentences, semantics, phonemes - all the systematic orders of differential relations that structuralism has taught us to recognise. And these orders are themselves embedded in actual material and historical processes.

The seemingly intractable complexity of actual language (parole and not only langue) is one of the reasons linguistic semantics have tended to resist mathematical and logical formalisation so stubbornly. Meaning is enacted in singular events and in this way resists abstract treatment. Yet at the same time, meaning presupposes translatability.  All the singular grain of the interlocking systems of some actual conversational exchange connects potentially to the systems of innumerable others. Any adequate categorical representation of linguistic events and, more generally, semiotic processes must be both rigorous and and flexible enough to track the logical and structural underpinnings of meaning and at the same time facilitate the blurring and affordances of translation." p.141.

Gangle, R. (2016). Diagrammatic Immanence: Category Theory and Philosophy. Edinburgh University Press. http://www.jstor.org/stable/10.3366/j.ctt1bgzc38