Abstract

Gödel proves the contingency of Cantor’s generalized continuum hypothesis through the proof of non-impossibility; on the other hand, according to Avicenna’s claim in the previous section to the last of al-Isharat, not having proof of impossibility suffices for contingency. Now, the question is whether Gödel’s effort is superfluous or Avicenna’s claim is false. My answer is a third option: neither the former nor the latter. The “contingency” in the Avicenna’s claim means “probability” which is mental and subjective; so, it does not need anything but "nothaving proof of impossibility". But, the contingency of the generalized continuum hypothesis is external and objective; therefore, it does need the proof of non-impossibility. Consequentely, neither Gödel’s effort is superfluous, nor Avicenna’s claim is false.