Mathematical Platonism, formally defined, is the view that (a) there exist abstract objects—objects that are wholly nonspatiotemporal, nonphysical, and nonmental and (b) there are true mathematical sentences that provide true descriptions of such objects.
Thus, when Platonists say that the number 4 is an abstract object, they mean to say that it is a real and objective thing that, like the Moon, exists independently of people and their thinking but, unlike the Moon, is nonphysical.
This might seem eminently sensible, and one might wonder why Maddy counts as a Platonist at all; that is, one might wonder why a set of eggs counts as a nonphysical object in Maddy's view.
This is the view that numbers are abstract objects, where an abstract object is both nonphysical and nonmental.
It should make him wonder what good it would do to posit any further condition whether a purely physical condition of the brain or a condition of some as-yet-unknown nonphysical substance that a human being, an animal, or a machine must possess in order to have a mental life.
Impulsion is the nonphysical life energy that propels all biological motion and growth, up to and including all activities of the mind.
Functionalism thus vindicated the reasonable insistence that psychology not be replaced by physics while avoiding the postulation of any mysterious nonphysical entities as psychology's subject matter.
Nevertheless, abnormal behaviour in animals often does have a nonphysical, psychological, or emotional origin, which should always be considered in the diagnosis and treatment of the ailments of companion animals.
Inasmuch as some cosmologists even try to define the elementary particles themselves in terms of the curvature of space-time, there is no reason why a philosophy based on such a geometricized cosmology should not be counted as materialist, provided that it does not give an independent existence to nonphysical things such as minds.
A similar departure from the paradigm is a form of what might be called "double-aspect materialism," according to which in inner experience one is acquainted with nonphysical properties of material processes, though these properties are not causally effective.
American social psychologist Leon Festinger proposed that group uniformity pressure is based on the group's ambition to move toward particular goals (group locomotion) and the desire among group members to validate their opinions about the nonphysical world (social reality).
