Group Members: David Johnson, Michelle Hollinger, Jessica Crawford, Paige Irwin, Lindsay Clawson, Dave Lowery, Serena McMurdie, Rachelle, Rachelle McNiven, Mary Howard
Definition of Platonism
There exist abstract objects (i.e. completely non-spatiotemporal, nonphysical, and non-mental). There are true mathematical sentences that provide true descriptions of such objects.
Theses
Abstraction: Non-Physical
Platonists believe that abstract objects exist such that abstract object are non-spatiotemporal. This means that objects exist independently of people and their minds, but do not exist in the physical universe. But even though the abstract objects are non-physical, they have existed and will continue to always exist. Also, not only are abstract objects timeless, they are changeless. The objects basic properties stay the same throughout time. Finally, an abstract object is independent of its relationship with other items, because they are not made of physical matter. They cannot have a cause-and-effect relationship with other objects.
Independence:
Abstract objects are not located anywhere in the physical universe, and they are non-mental, but they always exist and they will always exist. Abstract objects are real, objective, and independent. What does it mean to be independent? X is independent of Y if X would exist even if Y did not. So math, or any abstract object, would exist even if there were no rational activities. Even more than this, independence means that things would have their same properties if rational activities were different than they currently are.
Arguments
Quine-Putnam Indispensability Argument:
This argument appeals to science in order to determine the question of existence of mathematical objects. The indispensability argument borrows a Naturalist “bottom-up” view of ontology in contrast to other “top-down” approaches that attempt to define existence based on first principles or axioms. This argument asserts the premise that our most accurate theories for describing our universe are scientific theories. From there, one can note that because these theories are expressed and considered on the basis of mathematical ideas, (i.e. mathematics is indispensable to our scientific theories), consequently we are ontologically committed to the existence of mathematical objects. This addresses fundamental philosophical questions such as “what exists?” and “how do we know what exists?” An essential element of this argument is Quine’sConfirmational Holism—that the correctness of theories is not determined on an individual basis. Rather, theories are interrelated and proven or disproven as a whole. That we can observe and predict physical phenomena is evidence that our scientific theories are correct. Scientific theories are inseparable from mathematical principles and therefore, the acceptance of these theories necessarily implies the existence of the mathematical objects used to describe them. These arguments, while drawing on other philosophical stances establish the first thesis of Platonism-existence of mathematical objects or entities.
Full Blooded Platonism:
The main idea behind full blooded Platonism is that most humans have systematically and purposefully true beliefs about a platonic mathematical realm; a realm where we do not influence it and it does not influence us.
There are several theses that result from this belief. First the schematic reference- the relation between theories and the realm are purely schematic or very close to it. Second, plenitude- the realm is extremely large and contains entities related to each other in all possible ways of relation. Third, theories embed constraints on the structure of a part of the realm that must be in order for it to be used as true. Lastly, the existence of any part of a theory in the realm is sufficient to make the theory true.