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:
- For any proposition p, reasons can be given for/against p.
- q and r are reasons for/against p.
- If q and r are propositions, then reasons can be given for/against q and r.
- q and r are propositions.
- (Therefore) Reasons can be given for/against q and r.
- s and t are reasons for/against q.
- If s and t are propositions, then reasons can be given for/against s and t.
- s and t are propositions.
- (Therefore) Reasons can be given for/against s and t.
- u and v are reasons for/against s.
- If u and v are propositions, then reasons can be given for/against u and v.
- u and v are propositions.
- (Therefore) Reasons can be given for/against u and v.
What do you think about Aristotle's regress argument? Is there any way out?
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