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 fig.26—Kantian schematism meets logic­-inflected linguistics

 We can now revisit Kant with our cyclical Square/Plot model: while the chiastic twist ‘sublates’ our original Y­-axis, we retain the X-axis of imagination along which it grasps perceptual manifolds by apprehension. Kant’s ‘transcendental synthesis’ thus returns expansion toward materially­-real noumenal space via contraction into psychically­-ideal phenomenal space. Kant’s transcendental engine is driven, as Deleuze notes, by “subjective faculties which differ in nature (receptive sensibility and active understanding)”—yet which conspire to set it into rotation, as “to reduce this synthesis to conceptions is a function of the understanding” (Kant). As this engine is reciprocated by language, we can source a new Y­-axis for fig.26 from modern linguistics: extension takes in the quantitative range of objects subject to classification under a concept, as signified by a term’s denotation. Conversely, intension (or ‘comprehension’) measures the properties and attributes (i.e. qualitatively analyzed percepts) convoked in a subject by a term’s connotation

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 fig.27—(cf. Heidegger’s vorhanden/zuhanden on the X­-axis)

 Finally, by harking the nom­-inal jargon back to its verb-al roots, we return abstract to concrete. As we ‘read out’ the four phases of fig.27, the X/Y Plot terms drive the (inset) A/B Square terms inward and outward. Where to begin? (­-X:) Like all primates, our primordial engagement with the world (and every newborn’s first situated act) is to apprehend (literally, to grasp toward) what objects are immediately given to our nascent ability to perceive. (­-Y:) To comprehend (literally, to hold together) what we touch and see, we first must take it in. (+X:) To ‘figure out’ our world, we imagine possible past, present and future events—syntheses that subjectivize our situation sufficient to form a response. (+Y:) Last but not least, in order to gather identifiable objects (or pieces of information), we must first form a concept sufficient to classify them, and second, conceive a well­-ordered place to put them. Or, in sum, to paraphrase Heidegger (by way of the A/B fourfold): given a world, we take what we see, form it into itself, then put it back.

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