Final answer:
Anselm's ontological argument is based on the assumption that existence is a perfection and that the very concept of God necessitates His existence, presented in a Reductio Ad Absurdum form.
Step-by-step explanation:
The key assumption of Anselm's ontological argument for God's existence is that existence is a perfection and that, if God is defined as 'a being than which nothing greater can be conceived,' then this being must necessarily exist. Anselm's argument begins with the concept of God as the greatest possible being and then reasons that if this being exists in the mind, it must also exist in reality, as a being that exists only in the mind is less great than one that exists both in the mind and in reality. This line of reasoning is presented in the form of a Reductio Ad Absurdum (RAA), which seeks to demonstrate that the opposite position (that God does not exist) leads to a contradiction and is therefore untenable. Additionally, Anselm posits that because God is the supreme being, and the concept of God includes all perfections, actual existence must be one of those perfections, hence God must exist.