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A scientist might make a clear distinction about objects that exist, and assert that all objects that exist are made up of either matter or energy.
But in the layperson's worldview, existence includes real, fictional, and even contradictory objects.
Thus if we reason from the statement " Pegasus flies " to the statement " Pegasus exists ", we are not asserting that Pegasus is made up of atoms, but rather that Pegasus exists in a particular worldview, the worldview of classical myth.
When a mathematician reasons from the statement " ABC is a triangle " to the statement " triangles exist ", she is not asserting that triangles are made up of atoms but rather that triangles exist within a particular mathematical model.

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