Barry> Landgrebe and I have been working on a BFO physics Ontology and on a mathematics Ontology, separate from BFO. I'm glad to hear that you're finally developing an ontology for mathematics and that it's independent of the current BFO. Since it's impossible to do modern physics without a huge amount of mathematics, I suggest that you combine your math ontology with BFO in order to support physics. There are three ways to combine an ontology of actual entities with a math ontology: 1. Platonic: The mathematical forms are really real, and the physical stuff is a degenerate approximation to reality. 2. Aristotelian: The physical entities are the real existents and the forms exist only when they are embodied in physical stuff. 3. Peirce's update to Aristotle: All mathematical forms exist as real possibilities, which may be used to describe or characterize anything that exists in actuality or in any kind of imagined, planned, intended, hoped, feared, described, communicated, or hypothesized aspect of reality. Peirce's version implies that pure mathematicians can talk and act like Platonists (which they frequently do), but applied mathematicians can focus on the actual universe while having an infinite book of mathematical forms to use as they wish when they're doing any kind of engineering, virtual reality, or plans for future things that do not yet exist. Option 3 also supports every kind of pattern on paper, in anyone's imagination, implicit in any spoken or written language or notation, implicit in anybody's knowledge, or implicit in any data structures in any computer or collection of computers anywhere in the universe. In short, Peirce's option #3 supports common sense, the most advanced sciences, and every form of artistic endeavor in any culture in the world -- or even in any alien life anywhere in the universe. I recommend it, John
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