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Abstract:
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In the Critique of Pure Reason , Kant defends the mathematically deterministic world of physics by arguing that its essential features arise necessarily from innate forms of intuition and rules of understanding through combinatory acts of imagination . Knowing is active : it constructs the unity of nature by combining appearances in certain mandatory ways . What is mandated is that sensible awareness provide objects that conform to the structure of ostensive judgment : “This (S ) is P .”
Sensibility alone provides no such objects , so the imagination compensates by combining passing point -data into “pure” referents for the subject -position , predicate -position , and copula . The result is a cognitive encounter with a generic physical object whose characteristics—magnitude , substance , property , quality , and causality—are abstracted as the Kantian categories . Each characteristic is a product of “sensible synthesis” that has been “determined” by a “function of unity” in judgment .
Understanding the possibility of such determination by judgment is the chief difficulty for any rehabilitative reconstruction of Kant’s theory . I will show that Kant conceives of figurative synthesis as an act of line -drawing , and of the functions of unity as rules for attending to this act . The subject -position refers to substance , identified as the objective time -continuum ; the predicate -position , to quality , identified as the continuum of property values (constituting the second -order type named by the predicate concept ) . The upshot is that both positions refer to continuous magnitudes , related so that one (time -value ) is the condition of the other (property -value ) .
Kant’s theory of physically constructive grammar is thus equivalent to the analytic -geometric formalism at work in the practice of mathematical physics , which schematizes time and state as lines related by an algebraic formula . Kant theorizes the subject–predicate relation in ostensive judgment as an algebraic time–state function . When aimed towards sensibility , “S is P” functions as the algebraic relation “t → ƒ (t ) .” |