For example, assume two entities P and Q, where we are using 'proof-by-contradiction' to validate P (by using Q).

Something like:

  • if P then Q;  
  • Not Q. Hence not P

IMO, one can only use such scenario, when P and Q are independent of each other existentially.

In other words, can one use proof-by-contradiction in cases where Q's existence is dependent on P's validity?

For example, Q exists if and only if P exists.

In such case does the proof-by-contradiction still hold valid?

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