Final answer:
Anselm accused Gaunilo of the fallacy of composition for misapplying the ontological argument, which asserts the necessary existence of God, to a contingent concept like a perfect island.
Step-by-step explanation:
Anselm accuse Gaunilo of committing the fallacy of composition when Gaunilo critiqued Anselm's ontological argument. Anselm, through his reductio ad absurdum approach, defined God as 'a being than which nothing greater can be conceived' and posited that such a being must necessarily exist as existence is a necessary condition of being the greatest conceivable being. Gaunilo, opposing Anselm's argument, suggested that one could conceive of a perfect island and, by Anselm's logic, be compelled to conclude its existence. Anselm found fault with Gaunilo's critique because Gaunilo mistakenly applied a logical structure meant for a necessarily existent being (God) to a contingent concept (an island), which does not necessarily have to exist. Anselm's main accusation toward Gaunilo was that he misrepresented Anselm's argument by applying it in an inappropriate context, thereby illustrating the fallacy of composition by assuming what is true of a part (the concept of a perfect island) is true of the whole (the concept of God).