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 (imkan). 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” (imkan) 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.
Azimi, M. (2014). Avicenna and Gödel:
"Not Having Proof of Impossibility"or"Having Proof of Non-Impossibility?''. Avecinnian Philosophy Journal, 18(51), 19-36. doi: 10.30497/ap.2014.59342
MLA
Mahdi Azimi. "Avicenna and Gödel:
"Not Having Proof of Impossibility"or"Having Proof of Non-Impossibility?''". Avecinnian Philosophy Journal, 18, 51, 2014, 19-36. doi: 10.30497/ap.2014.59342
HARVARD
Azimi, M. (2014). 'Avicenna and Gödel:
"Not Having Proof of Impossibility"or"Having Proof of Non-Impossibility?''', Avecinnian Philosophy Journal, 18(51), pp. 19-36. doi: 10.30497/ap.2014.59342
VANCOUVER
Azimi, M. Avicenna and Gödel:
"Not Having Proof of Impossibility"or"Having Proof of Non-Impossibility?''. Avecinnian Philosophy Journal, 2014; 18(51): 19-36. doi: 10.30497/ap.2014.59342
)