Anselm's Classical Ontological argument was based on ontology( the study of the nature of being). It was intended as a means of proving the existence of God on an a priori basis which doesn't require the use of empirical (sensory) evidence. Anselm starts by arguing that the idea that the definition of God is as a perfect being who greater than anything else that could be imagined. Even if a person didn't believe in God, in order to say he doesn't exist they'd have at the very least have a concept of him in their mind (in intellectu). However, for something to be perfect he argued it must have every possible quality. Anselm believed existence was a quality, so if God has every quality he must surely have the quality of existence. If he didn't have the quality of existence then we could theoretically imagine a being which does has the quality of existence, which would make this being greater than God - which Anselm believed was logically impossible. Therefore he believed that God had to exist, and this could be proved entirely through these logical premises (steps).
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