Hume's empiricism-the dean paradox-of colin leslie dean
empiricism-science-destroyed by the dean paradox
the dean paradox
Logic insists that between two points lies an infinite set of divisions, making it "impossible" to traverse from start to end. Yet, in practice, the finger does move from the beginning to the end in finite time.
• Dean’s paradox highlights a core discrepancy between logical reasoning and lived reality. Logic insists that between two points lies an infinite set of divisions, making it "impossible" to traverse from start to end. Yet, in practice, the finger does move from the beginning to the end in finite time. This contradiction exposes a gap between the abstract constructs of logic and the observable truths of reality.
Hume’s empiricism is undermined by the very logic he uses, because logic (as shown by the Dean paradox) allows for infinities while empirical reality does not thus Humes reality ie empiricism is destroyed by the very logic he uses to process sensory experience
All sensory experience is processed by logic. However, Hume’s empiricism insists that only those logical structures that have empirical content are meaningful when talking about the world. When logic leads to concepts (like actual infinities) that cannot be experienced, Hume brackets them as “empty” for empirical inquiry
It does not matter what Hume says about bracketing
All sensory experience is processed by logic-including by Hume-- The Deanparadox demonstrates that the very logic used to process sensory experienceinherently allows for constructs-such as actual infinities and infinitedivisibility-that empirical reality does not support (since, for example, wetraverse a line in finite time, not through infinite steps). Thismeans that the logical framework underpinning empiricism [and science] is itself misalignedwith the phenomena it is meant to interpret.
No matter how much Hume tries toseparate “relations of ideas” (logic/math) from “matters of fact” (empiricalreality), the paradox shows that logic is used in both domains, and its resultscan directly conflict with experience.As aresult, Hume’s empiricism is undermined by the very logic it employs: logicproduces paradoxes and constructs (like infinities) that empirical observationcannot confirm or even accommodate.
This exposes a fundamental instability inempiricism/science-its reliance on logic means it inherits all the limitations andcontradictions of logic itself. The Dean paradox thus reveals that empiricism rationalism etc , likeall philosophical systems dependent on human reasoning (Aristotle Plato HumeKant Hegel Schopenhauer Nietzsche Wittgenstein Russell Quine sciencemathematics philosophy ie everyone) is constrained by the inherent flaws oflogic, and cannot guarantee a coherent or reliable account of reality
