Reality
Introduction
In the conventional view of reality, truth founds itself on sensible reality grounded on perceptions, and reflection concerning perception, of the world as we experience it. This view is related to, but not identical with, empiricism. Conventional reality has its basis in perspectives and is, accordingly, dependent on a particular point of view. For this reason it is considered to fall within convention since it relies to some extent on shared beliefs concerning experience that in turn rely o perceptions from a particular point of view. There could be as many perspectives as there are people, these appearing with greater or lesser degrees of refinement with some perspectives being highly organized conceptualizations of the world, e.g., scientific theories of reality that use highly specialized methods to verify their findings.
Because of the regress problem, establishing a foundation of truth and reality is a problematic that underlies all disciplines, including mathematics. The desire to establish an underlying ground of all or part of reality, that is, to say what reality "really is," has been a long-standing preoccupation of philosophy and the sciences.
Platonic Realism
In Plato, philosophy concerns itself with the nature of Being itself, "what is." Platonic philosophy distinguishes between "what is" and material existence. What is Real is "what is" in itself. In Plato, these are the Forms. Here is derived the term "Platonic Realism" which refers to a view of reality that grounds truth, the ultimate Reality, in a Being outside sensible reality, the Forms, and beyond the Forms, in the Good that is beyond Being. The Platonic Theory of Forms does not depend on sensible perception as a means to ascertain truth but, rather, on another form of 'seeing' only possible for the soul[Ψυχή]. In the myth of the charioteer, in the Phaedrus dialogue, Plato argues, "For a human being must understand a general conception formed by collecting into a unity by means of reason the many perceptions of the senses; and this is a recollection of those things which our soul once beheld, when it journeyed with God and, lifting its vision above the things which we now say exist, rose up into real being (249c) [1].
In Plato, being is itself and nothing but itself. The Form of Justice is simply Justice itself. To define, we use predicates but a Form would have no predicates in the usual sense we are accustomed to thinking of such things, since a Form's definition would give you something that has the same thing on either side such that Justice=Justice. No matter what predicates you add to a thing itself - the Form - for Plato, it remains the same. On the other hand, when we say that Mary has blue eyes and Bill has brown eyes, we refer to items pertaining to sensibility and particular biological traits.
Given his definition of Reality, it is easier to see why, for Plato, knowledge is not 'acquired' but instead involves anamnesis. Real knowledge involves a vision of the shining of the Beautiful, its Eidos. For one thing, how would we bring something immutable into material life, such that we could acquire it? For another, would we acquire the Being of the Beautiful or merely another image of the Beautiful? Contrary to this, the objects of immanent, sensible experience remind us of the things themselves. We see a bed and this evokes the Idea of a bed, and so on. Knowledge is the extent to which you can connect the bed of experience to the immutable Form of the bed (597a-598b)[2].
So there is a Form of the relation between numbers, the Form of specific numbers, and the Form of the abstraction of 'number' itself. In immanent existence, the forms are all mixed up in matter and predicates abound. But what of the varying degree to which some of us are able to make these relations, to gain knowledge? I may see a beetle climbing on a branch and think about bugs. If I am no entomologist I may not go to the specific Form of beetle, only the form of a beetle in general. My inability to understand the intricacy of number does not prevent me from a vision of the form of 'number' in general or its abstraction but may prevent me from seeing the intricacy of their relationships.
Because the Forms are external to the sensible copies of reality, it does not seem that there can be change in something like Beauty or Justice. Immanent life seems to confirm this finding because objects of sensation appear to be all mixed up together. We see justice and truth in varying degrees, as composed in matter, rather than by themselves. These break, degrade, disperse or scatter. Plato's explanation is that the beautiful we experience is beautiful because it participates in the Form of Beauty, not because it is beautiful in itself. Accordingly, if I want to know if a a sunset is beautiful, I go to the Form that gives the sunset its beauty. The relation of the particular sunset to Beauty remains temporary. The sun goes down although the beauty of the sunset cannot fade. Perception of beauty in this world involves establishment of such a relationship between objects of sensation and that which is truly Beautiful. Unlike finite beauty, the Form of the Beautiful has no beginning or end. When we perceive the beautiful sunset as being present, we are soon dissuaded of this reality when we perceive that the facts have changed and are now otherwise once the sun goes down. Futher, in order to understand Plato's conception of Reality, we must get around the idea of causality. The Real does not come to be and cease to be in a material sense. The scientific cause of the 'appearance' of a sunset, the appearance that the sun moves, for us has to do with the movements of bodies in space but from a Platonic view implies a connection to the Form that is the underlying cause of the sun or of a sunset seen in in our experience. The bond to the Beautiful of the sunset or to the Form of the sun itself is real but the objects we think of as sun or sunset do not amount to things in themselves. All we have done in locating these objects is to establish a relation to Reality.
Conventional reality, for Plato, is less than satisfactory and knowledge of this type of reality can be categorized as doxa,the stuff of beliefs and opinions, rather than the act of real knowledge but from this it should not be concluded that Plato rejects all doxa. Including "geometry and the kindred arts," Plato asserts that through the power of dialectic, as he conceives of it reason is able to treat "its assumptions not as absolute beginnings but literally as hypotheses, underpinnings, footings, and springboards so to speak" (511b)[2].