The Ontological Argument by Anselm

The Ontological Argument

The argument was formulated by Anselm of Canterbury (1033-1109 CE)

(1) God is that than which a greater cannot be conceived.
(2) Now that which exists in the understanding (in intellectu) and in reality (in re) is greater than that which exists in the understanding alone (in solo intellectu).
(3) If that than which a greater cannot be conceived exists in the understanding (in intellectu) and not in reality (in re), then that than which a greater cannot be conceived is one than which a greater can be conceived (reductio ad absurdum).* But surely that cannot be.
(4) Therefore, that than which a greater cannot be conceived without a doubt exists both in the understanding (in intellectu) and in reality (in re).

*The logical move "reductio ad absurdum" (reduction to absurdity) involves proving an utterance (U) by showing that its denial (not-U) leads to or entails a contradiction or absurd conclusion (Alvin Plantinga).

The Internet Encyclopedia of Philosophy says the following about reductio ad absurdum:

“In its most general construal, reductio ad absurdum - reductio for short – is a process of refutation on grounds that absurd - and patently untenable consequences would ensue from accepting the item at issue. This takes three principal forms according as that untenable consequence is:

1. a self-contradiction (ad absurdum)
2. a falsehood (ad falsum or even ad impossibile)
3. an implausibility or anomaly (ad ridiculum or ad incommodum)”