Tuesday, August 28, 2012

[PHI 3000] Aristotle's regress argument

In the Metaphysics (1006a, 8-10), Aristotle writes:
It is impossible that there should be demonstration of absolutely everything; [for then] there would be an infinite regress, so that there would still be no demonstration.
Aristotle is making a reductio ad infinitum argument that can be reconstructed as follows:
  1. For any proposition p, reasons can be given for/against p.
  2. q and r are reasons for/against p.
  3. If q and r are propositions, then reasons can be given for/against q and r.
  4. q and r are propositions.
  5. (Therefore) Reasons can be given for/against q and r.
  6. s and t are reasons for/against q.
  7. If s and t are propositions, then reasons can be given for/against s and t.
  8. s and t are propositions.
  9. (Therefore) Reasons can be given for/against s and t.
  10. u and v are reasons for/against s.
  11. If u and v are propositions, then reasons can be given for/against u and v.
  12. u and v are propositions.
  13. (Therefore) Reasons can be given for/against u and v.
And so on, ad infinitum.

What do you think about Aristotle's regress argument? Is there any way out? 

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