A foundation ontology purports to describe "what exists", to a sufficient degree of rigor to establish a reasonable method of empirical validation.
Acceptance of these tends to vary drastically from culture to culture: classical Greek and Roman civilization assumed for example that "earth, air, fire, and water" sufficiently described the elements, while 19th century scientists considered the periodic table to be a solid foundation ontology describing all atoms that could exist. As it became clear that theology could vary drastically in all aspects except foundation ontology, a philosophy of science evolved to explain this stability. Over time mathematics became accepted as a neutral point of view.
Within the physics community, the two most common foundation ontologies are the reductionist position, which is held most strongly by particle physicists, and the anti-reductionist position, which tends to be held by solid state physicists. The reductionist position is that one can understand the universe by examining its most basic components and how they interact - producing a foundation and from this understanding derive (even only in principle) an understanding of how the entire universe works. The particle physics foundation ontology is thus one of parts and linkages.
The anti-reductionist position among physicists is that collections of objects sometimes exhibit behaviors which are independent of the objects themselves. Therefore it is incorrect to think of the objects as more fundamental than the collections of objects. It is important to note that this particular debate between reductionists or anti-reductionists does not involve the nature of scientific truth, the process of science, the role of mathematics in science, or any issues involving interpretations of quantum mechanics.
Another debate within the scientific community is between scientists who hold to the Copernican principle and those who believe some variation of the anthropic principle. The Copernican principle states that there is nothing special about the human location in the universe. The anthropic principle on the other hand argues that the universe is special because there are human observers in it and from the existence of human observers one can deduce the properties of the universe.
It may also be that the acts of counting and trusting each other's cognition are more fundamental than the output of any experimental apparatus, or any theory that can be expressed numerically. That is, that the universe may actually be built out of some form of trust, perhaps down to the molecules and entanglement bonds. Although this view is associated with theology, it has increasingly impacted ecology, notably via the Gaia theory, and more deeply biology through the work of Edward O. Wilson, who seeks "a biological basis for morality".
In physics, this view has come to be associated with Lee Smolin and the "fecund universe" theory. In this foundation ontology, new universes are formed "on the other side" of black holes as stars collapse, and vary in their foundation parameters much as bacteria vary slightly in their genetic makeup from their parent. Universes with such life-like characteristics may not just be passive containers of objects, living or otherwise, but "exhibit behaviors which are independent of the objects themselves," i.e. be "alive".
In computer science jargon, a foundation ontology or upper ontology is a hierarchy of entities and associated rules (both theorems and regulations) that attempts to describe those general entities that do not belong to a specific problem domain. See ontology (computer science) for a more detailed description and examples.
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.