The intentional arc of consciousness binds past and present in a single act of presentation, which the Extensional model's additive summation of atomic moments cannot capture without distorting the unity of temporal experience.

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Additive summation(as used in logic and philosophy): Adding separate pieces together one by one, as if the whole is just the sum of its independent parts.
Atomic moments(as used in philosophy of time): Individual, isolated points in time treated as the smallest possible units, like separate beads on a string.
Extensional model(Contrasted with Retentional models; said to struggle with temporal illusions involving apparent retro-active causation.): A theory of time consciousness on which each stimulus is represented exactly once, so conflicting perceptual data about the same moment t produces contradictory experiences.
Intentional arc of consciousness(as used in phenomenology and philosophy of mind): The way your mind reaches out toward and connects with things you're thinking about or experiencing, treating them as a unified whole rather than separate pieces.

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