In metaphysics, nominalism is a philosophical view which denies the existence of universals and abstract objects, but affirms the existence of general or abstract terms and predicates. There are at least two main versions of nominalism.

Dr. John Sowa is a leading semantic ontologist who has had significant influence on this project. Below is a brief quote from a recent email sent to the "Ontolog" mailing list, introducing some of these issues

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John Sowa, Ontolog, Jan 26, 2021

I sympathize with both of you, and I'll add a bit more to explain some of the philosophical issues.

The most long-lasting and fundamental philosophical debate is among the realists and the nominalists. The term 'realist' in philosophy is applied to Plato and others who believe that the abstract mathematical forms are "really real" and the physical things are imperfect imitations of the forms.

Aristotle is also considered a realist, but he modified Plato's theory by claiming that mathematical forms and the physical things both exist, but that the forms primarily exist as possibilities, and they only exist as actualities when they are embodied in something physical.

The nominalists claim that only the physically observable things are real, and the mathematical forms exist only as descriptions of things that do or might exist. For the medieval scholastics, Duns Scotus was considered the most characteristic realist and his student, William of Ockham, was considered the most characteristic nominalist.

Today, mathematicians are often considered (and consider themselves as) realists because they believe that the theories that they discover represent something really real. But many other philosophers today are considered nominalists.

Some philosophers, such as Quine, considered themselves to be nominalists, but they recognized the importance of mathematics. They therefore modify their ontologies to include things like sets and sets of sets, which they can use to define the foundations of mathematics. That decision moves them somewhere to a mixture of nominalism with some realism.

There are also the laws of nature. Many scientists, who would like to consider physical actuality as fundamental, also believe that the laws of nature are really real. That pushes them over the border into the realist camp.

The version I summarize below is by C. S. Peirce, who was a logician, mathematician, scientist, engineer, and philosopher. The three universes of discourse (UoDs) are based on his writings. He considered himself to be a realist along the lines of Aristotle and Duns Scotus. However, it is possible to interpret his three universes as abstract descriptions without making a firm commitment to either side of the realist/nominalist debate.

Recommendation: For any theory of ontology that is adequate to support science and, engineering, mathematics is essential. It's also essential to have a firm belief that the well tested laws of science are good approximations to the real laws of nature (as far as they have been tested).

If you use the term "Universe of Discourse" rather than "Universe", it's possible to make good progress in ontology without getting bogged down in endless philosophical arguments about what is "really real".

And by the way, this is the core of my major disagreements about BFO. Barry has adopted an extreme nominalist interpretation that limits mathematics to just mereology. I admit that mereology is useful, but it is just an insignificant fraction of the total amount of mathematics that is required for modern science, engineering, and especially computer science and systems.

Any adequate ontology must include *all* mathematical theories as options for any branch of science, engineering, business... The math must be available as an integral part of the ontology (right at the top), not as some kind of "artifact".

Wed, Apr 14, 2021