The missing premise can only follow from the intuition about his existence. Descartes denies that the Cogito is a truncated syllogism because the second premise is not beyond doubt. First, it may be an immediate inference-an inference from a single premise without need for any second general premise such as ‘Everything that thinks exists’ secondly it may be a truncated syllogism needing that further premise. There are two possible logical structures for this argument. The structure of this syllogism would be: For it to be a correct syllogism, however, Descartes needs to introduce another premise: “everything that thinks exists”. The traditional formulation of the Cogito-‘I think therefore I am ‘-is structured like an argument with a premise (I think) an operator (therefore) and a conclusion (I am). Whereas when it is interpreted as an intuition, cogito and sum follow immediately from each other, there is no movement of thought. The difference between the two interpretations is that where the Cogito is interpreted as an inference, there is movement from the premise to the conclusion. Descartes, however, denied that it is to be interpreted as an inference, but he argues that the sum follows as a direct intuition from cogito. At first glance the expression cogito ergo sum appears to be an inference because ergo is the mark of an argument, where sum (I am) follows from cogito (I think). He has expressed this idea in several different ways in his writings this famous formulation comes from Descartes’ Discourse on Method. He finds this foundation of knowledge in the dictum cogito ergo sum. He is seeking an Archimedean point, something which he can believe to be true even beyond unreasonable doubt. He feels like he has “fallen into a deep whirlpool”, tumbling him around so that he can “neither stand on the bottom nor swim on the top”. Descartes feels uncomfortable with his self-inflicted doubt about the existence of the world.
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