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My view is that mind, matter, and mathematical objects are all that exist. What is the name of that view? Dualism is the view that both mind and matter exist. So, perhaps my view should be called Trialism, but that doesn't seem to be a real word. So, is there a standard name in the philosophical literature for my belief?

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    Trialism was already coined by John Cottingham and it admits mind, body, and sensation which is the union of body and mind. Your spec sounds like Popper's famous Three Worlds Ontology: By world 3 I mean the world of the products of the human mind, such as languages; tales and stories and religious myths; scientific conjectures or theories, and mathematical constructions; songs and symphonies; paintings and sculptures... Feb 23, 2022 at 4:57
  • The idea of abstract entities (of which mathematical entities are a special case) as a "third realm" in addition to physical and mental goes back to Bolzano, Brentano and Frege, Popper's "third world" is in the same vein. A label sometimes used for this sort of view is platonism with a small "p", but "the use of the terms platonist (for those who affirm the existence of abstract objects) and nominalist (for those who deny existence) is somewhat lamentable, since these words have established senses in the history of philosophy".
    – Conifold
    Feb 23, 2022 at 9:38
  • To clarify what @Conifold said, "platonism" with a small "p" stands for the position that abstract objects are real. It doesn't say anything specifically about mind or matter. Feb 23, 2022 at 11:48

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Dualism is the view about X that there are two X. Likewise, monism is a view that there is one X, nihilism - no X, pluralism - >2 X.

When talking about mind, there are two kinds of dualism - substance dualism and property dualism. Under substance dualism there are two substances - material and mental; under property dualism there are two kinds of properties - material and mental.

Math is typically viewed as something other than a substance or a property. The most widespread view under which math exists is called platonism. The shortest you can call such view will have to be "substance (or property) dualism + platonism."

If you still want to have math as a substance, you can have three substances (material, mind, and math), so the view can be called substance trialism or substance pluralism. I am not aware if there are any coined names for such view.

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