Some are dualists, puzzled how the immaterial One (usually Mind or the Ideal) can possibly interact with the material Many (the Body or the World). There are other kinds of dualists, but the idealism/materialism divide has a long history in philosophy under dozens of different names through the ages.

Monists generally reduce the physical world to the ideal, or vice versa, or argued that the ideal and physical worlds were somehow both something else - a "neutral monism.". But their underlying dualism is inescapable.

Many philosophers prefer triads, triplicities, or trinities as their fundamental structures, and in these we may find the most sensible way to divide the world as we know it into “worlds,” realms, or orders.

Those who divide their philosophy into four usually arrange it two by two (Schopenhauer, Heidegger, Derrida - who did it in jest, and against Christian trinitues). There are a few who think a pentad has explanatory power. Another handful look to the mystical seven (the number of planets and thus days of the week) for understanding. Since the Pythagoreans drew their triangular diagram of the tetractus, ten has been a divine number for some. Aristotle found ten categories. The neo-Platonist Kabalists have ten sephiroth. In string theory, there are ten dimensions reflecting the components of Einstein’s general relativity equations.

The most important philosopher since Aristotle, Immanuel Kant, structured his architectonic into twelve categories, arranged four by three. We will scrutinize these architectures to see if the thinkers divide their worlds the same way, whatever they call their divisions. There is a surprising amount of agreement among them, considering their disagreements on terminology.

One of the "founders" of quantum mechanics. Niels Bohr, saw the wave-particle dual nature of quantum mechanics as connected to many other philosophical dualisms. We have compiled a semi-chronological list of various philosophical terms used through the ages that seem highly correlated with the fundamental ideal-material duality.

Over the centuries many philosophers have seen a fundamental dualism. Most have invented their own names for this dualism. Not all have meant the very same things, but the great similarities allow us to collect all these dualisms into a quasi-chronological table, where similarities and slight differences become more clear.

Of course many have claimed to be monists. "All is One," they said, as they generally reduced the physical world to the ideal, or vice versa, or argued that the ideal and physical worlds were somehow both something else. But their underlying dualism was inescapable.

Many philosophers saw the need for the two sides to work together.

Immanuel Kant wrote

Gedanken ohne Inhalt sind leer.
Anschauungen ohne Begriffe sind blind.

Charles Sanders Peirce rewrote it as

If Materialism without Idealism is blind,
Idealism without Materialism is void.

With a nod to Kant and Peirce, we can say

Concepts without Percepts are empty.
Percepts without Concepts are blind.

And although Freedom and Values are not a Dualism, they too require one another and we can observe

Freedom without Values is Absurd (Continental Existentialism).
Values without Freedom are Worthless (British Utilitarianism).

After dualisms, the next most popular philosophical architectonic structures are triads, triplicities, or trinities.

Some philosophers describe their triads as three "worlds," just as dualism is often described in terms of an Ideal World and a Material World. The deep philosophical (and scientific) question is - do these divisions "carve Nature at the joints," as Plato put it in the Phaedrus, (265e)?

We analyze examples, and find that the three worlds are most often simply the canonical Ideal/Material dualism with an interpolated third world corresponding to a human world (or more broadly, the biological world), with its obvious connection to the world of "subjective?" ideas above and the "objective" material world below.

Gottlob Frege's Three Realms

• An External Realm of Public Physical Things and Events
• An Internal Subjective Realm of Private Thoughts
• An "Objective" Platonic Realm of Ideal "Senses" (to which sentences refer, providing their meaning)

Karl Popper's Three Worlds (clearly influenced by Frege)

• World I - "the realm of physical things and processes"
• World II - "the realm of subjective human experience"
• World III - "the realm of culture and objective knowledge" - of human artifacts (our Sum)

Charles Sanders Peirce's Three Universes of Experience. Peirce's first and third worlds are both immaterial (our Sum), with the material world in the middle. So a better triad would have had Signs in the middle as human inventions mediating between the ideal and the material. Peirce's triad of Objects - Percepts - Concepts is in the correct order.

• Firstness - Ideas
• Secondness - Things
• Thirdness - Signs.

Those who divide their philosophy into four usually arrange it two by two (Schopenhauer, Heidegger, Derrida - in jest). There are a few who think a pentad has explanatory power. Another handful look to the mystical seven (the number of planets and thus days) for understanding.

Since the Pythagoreans drew their triangular diagram of the tetractus, ten has been a divine number for some. Aristotle found ten categories. The neo-Platonist Kabalists have ten sephiroth.

The most important philosopher since Aristotle, Immanuel Kant, structured his architectonic into twelve categories, arranged four by three.

We will scrutinize these architectures to see if the various thinkers divide their worlds the same way, whatever they call their divisions. We'll see that there is a surprising amount of agreement among them, especially considering their disagreements on terminology.