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In philosophy of mathematics, a foundation ontology is an ontology in the formal philosophical sense that is deemed to play a role in the foundations of mathematics. Most notably, the role played by Plato's ontology in some theories of realism in mathematics. Hilary Putnam made the distinction in 1975, arguing that one could believe in a realist philosophy of mathematical foundations without also accepting Plato's ontology or his sacred geometry, thus the labels "Platonist" and "realist" were not to be held equivalent.
This is discussed further in the article on foundations of mathematics.
The term 'standard ontology' should never be used, as any reference to an ontology implies completeness by some definition, and the inability of a system based on one 'standard' to communicate with a system based on any other such 'standard'. Accordingly, the term foundation ontology should be used in all three (philosophy, theology or computer science) senses of the term ontology.