In many philosophical works and ideas*, it seems like the number 3 gets a major, unexplained emphasis (mostly as a trichotomy).

One of the major ideas that uses trichotomy is the Thesis-Antithesis-Synthesis method of deduction:

  1. provide thesis (a)

  2. give it a contradiction by antithesis (b)

  3. unite/solve the contradiction of (a) and (b) through a "higher" synthesis (c)

Here we see 3 parts of a solution; and using this 3-part solution the philosophers start building many many systems.

For example Schelling in the "First Outline of a System of the Philosophy of Nature" gives an explanation to planetary formation using gravity by postulating that for every 2 opposing masses there is a "higher", uniting mass (which is double the size of the opposing masses) that keeps the opposing masses from becoming one (thus destroying one of the planets); the third mass being usually a sun.

There is, though, many other ideas in philosophy that uses trichotomy, and the division to three.

For example Kant's categories: for each class of categories (Quantity, Quality, Relation and Modality) there are 3 categories derived by 3 types of judgements. You can also note, perhaps by chance, perhaps deliberately, that Kant divided his Critiques to 3.

There are many other examples, ranging from Plato to 20th century philosophers (thanks for @Conifold for the citation in the comments: trichotomy in philosophy).

What I'd like to ask is:

A. Is there a clear explanation as to why philosophers so often incline to a 3-part division? Is there an aesthetic reason here?

B. Can you please provide critics of this method of thought? What are the most popular criticisms? [Edit: most of the answers attempt to answer A, but none have tried answering B, which is equally important to me.]

*The original version of this question emphasized German idealism; I've corrected it according to Conifold that the trichotomy is a theme that runs throughout all of history. I still think that the Germans emphasized this number more than the rest, but it could be my own biased reading.

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    You mention neo-Kantians, but the examples are of German idealists. Wikipedia lists examples of philosophical trichotomies from Plato to Merleau-Ponty and Eric Berne. Then there is Pythagoras, Kabbalah, and, of course, the Holy Trinity. It might be the most popular number ever, 1, 2 and 4 are easy to find too. To the extent that there is a "method" there, it is not due to Kant specifically. It has more to do with our basic cognitive psychology, how pattern recognition and memory work. – Conifold Aug 23 '19 at 18:44
  • @Conifold wow, I always thought Fichte, Schelling, Hegel were considered Neo-Kantians (in addition to them being German Idealists). Thanks for the correction. And thanks, I thought there would be other philosophers that use trichotomies, but couldn't recall (I'm reading mostly German Idealism). There is a major step in my opinion here that the trichotomy is used as a basic deductive method that help builds the entirety of the philosophical foundations of these philosophers; but that doesn't help the question at hand. Could you elaborate on the cognitive psychology you're referring? – Yechiam Weiss Aug 23 '19 at 20:10
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    "Miller argued that we have a hard time retaining more than seven to nine digits in short-term memory... Contemporary scientists, however, have put the number of items we can easily recall in short-term memory closer to three or four"Gallo, Thomas Jefferson, Steve Jobs, and the Rule of 3 Content is split up in a way convenient for memorization, and then high-minded "reasons" are made up to "justify" it. – Conifold Aug 23 '19 at 20:31
  • Fichte was a Freemason, so this is a link to the number 3 and Mozart deploys the 3 note motif, he was a Freemason I think. I think the Masons were linked to the Enlightenment project. So was Kant. On the other hand, this goes deeper than Freemasonry. It resolves an apparent contradiction and keeps a unity in many cases. – Gordon Aug 23 '19 at 21:11
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    @ttnphns So is "automobile" and a long list of other hybrids. Etymology makes little difference after the word gains currency, "trichotomy" is far more common now. @ Yechiam I do not know what to say about the "method", beyond involuntarily keeping memory from overloading, or how one would "criticize" our memory limitations. – Conifold Aug 25 '19 at 0:25

Kant himself brings this up in the third Critique, saying something like, "Some readers have thought it suspicious that my divisions in transcendental philosophy so often come in threes," not the exact words but close... His explanation iirc is that the other divisions are all instances of the scheme of conditions, which is threefold: condition, conditioned, and I don't remember the other but there WAS a third.

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    "If there is to be an a priori division it must be either analytical, according to the law of contradiction, which is always twofold... or it is synthetical. And if in this latter case it is to be derived from a priori concepts (not as in Mathematic from the intuition corresponding to the concept), the division must necessarily be trichotomy. For according to what is requisite for synthetical unity in general there must be (1) a condition, (2) a conditioned, and (3) the concept which arises from the union of the conditioned with its condition." CJ, footnote 11. – Conifold Aug 23 '19 at 18:54
  • that's really interesting, thanks @Conifold is "the concept which arises from the union" of synthesis always a unified, single, thing? – user38026 Sep 3 '19 at 5:14

I'm not certain whether you're looking for a philosophical or psychological answer to this question, and I suspect the question naturally blurs that distinction in any case, so let me just say this...

The natural focus of human cognition is the object. We perceive the world in terms of objects, we define objects in terms of various characteristics and classify them according to similarities in those characteristics. In this sense, an object is a monad (in Leibniz' sense of an indivisible, simple entity). However, objects are only properly understood in terms of their negations. If we think of a 'cat' as an object with a certain collection of characteristics, then we implicitly recognize that there are not-cats (things that do not share that collection of characteristics), because if everything in the world shared the characteristics of 'cat' then the category 'cat' would be meaningless. To have a cat means to have objects that are not cats; to have a monad automatically implies a dyad.

Now, much of simple logic deals with dyads: relationships of 'is' and 'is not', and the licit and illicit transfer of properties from categories of objects to objects themselves. But one of the first things we learn when we deal with simple logic is how limited the 'is'/'is not' dichotomy is for any functional purpose. Most things in the world cannot be categorized in simple true/false/ terms. there are, for instance:

  • Continuums, with a range of values between extremes (e.g. the liberal/conservative spectrum)
  • Non-diametric oppositions, in which objects are distinct but non-negating (e.g. cats and dogs, where a cat is not a dog, but is not a not-dog in the logical sense)
  • Orthogonals, which are continuums that vary independently of each other (like x/y coordinate systems)
  • Processes and syntheses, which evolve or integrate dyads into new forms (e.g. syllogisms or dialectics)

Once we start entertaining these more complex considerations, we must invoke (at least) triads: liberal, conservative, and the spectrum that contains them; cats, dogs, and non-cat non-dogs; x, y, and the xy plane; major premise, minor premise, conclusion. Triads are the simplest construct in which philosophy in its proper sense is possible. Most philosophy builds these simple triads into more complex forms, of course — e.g., hermeneutics is best thought of as an ongoing serial dialectic — but triads are the necessary and sufficient condition for the exercise of any philosophy.

Now, we could go back to the root and start questioning this naturalistic, a priori 'object' concept, and maybe develop a new philosophical approach; some philosophers I've read have aimed for that. But even there, the triadic structure seems essential for any kind of movement in philosophical thinking, so at best we would end up reconstructing focal objects in different terms, and then following the same pattern onward.

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  • I like that. I added onto your thinking en.wikipedia.org/wiki/Benford's_law – J D Aug 24 '19 at 19:04
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    To see a continuum or a spanning dimension as simply a third option compared to its two much smaller sources, so small they have zero measure compared to the remainder, as a trichotomy misses all rational perspective. Notions of one, two, many are silly ways to go at math. There are not just red, violet, and all those colors in between. We divide the spectrum up according to our cultural or individual focus. So I think this fails to be a good reason. We do not go Thesis, Antithesis, All other possible configurations... – user9166 Aug 26 '19 at 5:24
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    No, what's silly is suggesting that a whole is not conceptually distinct from its parts. That is the worst sort of reductionism. If you're going to have a relationship between two distinct objects, then there must be a context in which those objects have a relationship, and bringing that context into the analysis creates the trichotomy. – Ted Wrigley Aug 26 '19 at 6:32
  • But we can still go on with blue, yellow, green, and the palette of all colors. Meaning, it might be possible that trichotomy is the simplest division possible for philosophy, but that does not mean it's always the correct one. My emphasis is on that - what reason does the philosophers that use trichotomies have to using just a 3 part division? Who says that should not be a 4 part division, or more (or less)? The arbitrary use of trichotomy in, at least most of the concepts I've encountered, is simply that - arbitrary, without any real explanation to invoke specifically that number. – Yechiam Weiss Aug 31 '19 at 8:21
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    Using less than 3 (as I suggested) does not allow one to do proper philosophy: mere dyads can't really reflect the richness of the world, or allow for intellectual movement in an analysis. Using more than three is perfectly feasible, but why use more than 3 if 3 suffices? It's not arbitrary, it's pragmatic. If you won't accept pragmatism as an explanation, then you'll have to resort to mysticism or psychologism. – Ted Wrigley Aug 31 '19 at 13:49

It's a shame that Peirce never completed his book on the importance of triads and trinities. The best book I've read on the topic is God and the World of Signs: Trinity, Evolution, and the Metaphysical Semiotics of C. S. Peirce by Andrew Robinson. Unfortunately the last time I looked the price was about £80. It's something of a masterpiece.

I would recommend a study of Peirce's semiotics. I seem to remember that the number three is also crucial in 'chaos theory' and it would be vital in metaphysics. Here we constantly faced with an impossible binary choice that needs a third option for a solution.

I would say it's a productive area of study

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  • I always thought of Pierce as part of this school :-) – Yechiam Weiss Aug 23 '19 at 16:15
  • yes, i'm surprised pierce didn't come up more – user38026 Aug 24 '19 at 9:09

From a logical point of view threefold divisions are errors. Logic allows only binary yes-no predicates; two predicates can be either independent or not. If they are independent 4 cases are inevitably produced. if they are related one of them appears as a condition and the the second is applicable only within bounds. The paradigmatic case of fallacious trichotomy is ''lesser'', ''greater'' ''equal''; they exhaust possibilities, but logically first comes 'Equal or Unequal', then Unequal is divided into greater and lesser. Otherwise one uses greater and not greater. In scholastic parlance threefold division involves a genus species confusion: one genus + two species.

Aristotle mostly uses independent predicates and 4-fold divisions but occasionally he also errs. For instance according to his Physics movement is from the centre, toward the centre or around the centre. Actually movement either changes distance to the centre or not. If distance changes it either increases or decreases.

Kant is aware of the fact and in his Logik (113) points that polytomies are not to be studied in logic. Synthesis is a three step procedure just as the syllogism.

A highly recommended piece isThe Myth of 'Thesis, Antithesis, Synthesis' in Hegel and refs. therein.

Hegel says that Kant rediscovered triadic form, not that it derives from Kant. Further, Hegel says...that triadic form is unscientific 'when it is reduced to a lifeless schema'...

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  • "In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating true, false and some indeterminate third value. This is contrasted with the more commonly known bivalent logics (such as classical sentential or Boolean logic) which provide only for true and false." - Wikipedia – sfmiller940 Aug 29 '19 at 21:46

From a Jungian point of view, where metaphysics is cultural psychology, this is tied to a succession of magic numbers that are laid out in the tradition springing from Hermes Trismegistus. Mystical texts like the Hermetcs' are taken to embed the anchors of human psychology, rather than as primitive attempts at science or psychology.

Three as 'the number of man' (following the numbers of God/mind and the material world of strife and division) captures the triad of the Cardinal, Fixed and Mutable from Hermes, and becomes deeply embedded in our religious history, and therefore in our philosophy.

The proposed cause is that it is a symbolic expression of one of the primary psychological problems -- freedom arising from two unfree states -- the internal will/idea (cardinality, that of God) and the outside world (fixedness, that of the world) require a battlefield on which to work out their differences (mutability, that in but not of the world). Lacan captures this most consciously, but Jung prefigures it, and prominent Jungians have done extensive studies of mythological numbers, most prominently three and four.

From this POV three is the number of 'man' because is expresses the recognition of the Freudian ego, 'Ich'. We know that something happens when the seemingly unchangeable animal need 'es' that seems to be the core of being in infancy meets the seeming inflexible outside world 'sie'. Neither of these latter things feels exactly like 'me'. They both feel like pressures imposed on some other thing that is more realistically 'me'. So we make up a third thing for 'me' to be and slowly discover what it means. It is empty, as a mere creation, but its first use is as a place to put free will.

The reason this shows up in Kant then, is just that it is part of a larger human metagrammar of abstract and internal, rather than concrete and adaptive causes. This thread would theorize that any equally abstract thinker would probably also devolve on a tendency to segment domains into threes. We can find an equal number of fours in more functional thinkers. And to some degree we find some sets of fives, such as the Chinese elements or the inner planets (and related tens) in skepticisms or naturalisms like Sextus Empiricus, Astrology, Chinese medicine, or reconstructed Witchcraft. etc.

But this kind of 'observation' may often be an injected sort of monomania over numerology. It has some very weird adherents and manifestations leading to, for instance, the Thelematic obsession with the absence of a rotationally symmetric unicursal hexagram, or John Dee's construction of the tarot with four suits, each divided into a ten and a three and a set of twenty-one trumps made of three sevens, each a three and a four.

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  • Nice. Do you have any reference of a philosopher acknowledging this, or do you propose that this happens unconsciously? – Yechiam Weiss Aug 31 '19 at 8:28
  • @YechiamWeiss The people who care are philologists and psychologists, after all, this is not about the nature of the universe, it is mostly a detail about how a trope underlies a pattern in stories and why that holds significance to individuals. – user9166 Aug 31 '19 at 17:50
  • @YechiamWeiss The overall notion is that it happens unconsciously but we might as welll buy in and help it along. It is one of the clearer parts of the Jungian support for the overall notion of Collective Unconscious. Maria Louse von Franz had the initial idea and published work on 'fours', and the work on 'threes' starts from Jung's own work on the salt/mercury/sulphur part of the Great Work literature. – user9166 Aug 31 '19 at 17:51

Dichotomies and trichotomies do appear frequently in philosophical literature. Instead of suggesting a philosophical or psychological basis for this, let me introduce instead a mathematical one in the form of Benford's Law. It might be a fundamental property of the collections of divisions in philosophy which are themselves probably abstract correlations to neurological properties. Think about this: the mind has to make choices, so neurons grow so that some choices are between two classes, fewer between three, even fewer between four, so on. This would likely be because of the chemical and biological properties of neurons. Just like entropy of information mimics entropy of physical systems that use information, so too would Benford's law apply to the collections of choices made in the mind, like the neurons that do the work to make the choices happen.

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  1. All philosophy is grounded in assumption.

  2. One assumption progresses to two assumption with this progress being assumed in and of itself, thus necessitating a triad: assumption through assumption as assumption.

  3. The Munchauseen trillema observes the forms of thus triad as the "point" of the observer, a linear continuum of assumptions, and the cyclic nature of the assumptions repeating through a self referencing nature. This is observed symbolically through the ⊙ as the Monad, which has a common bond in all the worlds religions with all the religions referencing a trinity.

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Hermes Trismegistus (thrice great) was said to have written the original basis of Hermeticism.

Much of the importance of Hermeticism arises from its connection with the development of science during the time from 1300 to 1600 AD. The prominence that it gave to the idea of influencing or controlling nature led many scientists to look to magic and its allied arts (e.g., alchemy, astrology) which, it was thought, could put nature to the test by means of experiments. Consequently, it was the practical aspects of Hermetic writings that attracted the attention of scientists.[12] Isaac Newton placed great faith in the concept of an unadulterated, pure, ancient doctrine, which he studied vigorously to aid his understanding of the physical world.

As philosophy it seems slightly bizarre and antiquated, but it is still gets quite some coverage in undergraduate classes. It's conceivable (to me anyway) that his status as "thrice great" -- perhaps due to him being priest, philosopher and king -- helped form some contemporary affinity for trinities. In the same way as the Holy Trinity.

This affinity is perhaps most evident in Peirce's theory of categories, which he numbers to three. "Thirdness" has the quality of mediation. Presumably because "secondness" is a dyad linking two things with "firstness", but it itself is already actual, and so in need of something more if it is to be signified or represented.

I wouldn't take it too seriously. While his categories may be a useful paradigm to help thinking, the Chrsitian Trinity is just so ingrained in our culture that it's difficult to treat 'trinity' independent of it. Why not attribute special status to 'duality', given Descartes and the self's separation from the world? It's not like substance pluralists have an easy time of it. Or why not the number ten, given the decimal system?

Nb 'synthesis' could perhaps be thought of as involving two qualities, a greater (in number, action, conception, whatever) and lesser one, and their unity then thought of as a third thing. That doesn't strike me as an especially helpful simplification, however.

Mind you, I'm not sure that wholes are anything in addition to their parts, and then synthesis in the sense of inclusion is just a dyad.

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  • +1 but I feel you're missing a vital point. This is not about ingrained ideas but about logic. A fundamental theory requires a reduction of dualities for Unity and thus a trinitarian structure of explanation. The point you make about 'synthesis' is excellent. It is addressed by noting that in many contexts the dyad is conceptual, not a real division in Unity. Thus in Buddhism the phrase 'Middle Way' is said to be misleading. I reckon your thoughts are mostly correct but Unity (the third term) should not be thought of as a synthesis but an annihilation or denial of the dyad. – user20253 Sep 4 '19 at 14:03
  • not meaning to sound weird or upset, @PeterJ , but where is my +1 haha – user38026 Sep 4 '19 at 18:05
  • ps yeah that's one way of looking at the problem of holism @PeterJ one that confused the heck out of me when i was reading about it (you may know the book or tendency in buddhist studies) – user38026 Sep 4 '19 at 18:06
  • Oops. My bad. It's there now. I'd agree it's a problem of holism - but also of reductionism. I see it as the central problem of metaphysics, from which arise all the others. . . – user20253 Sep 5 '19 at 12:37

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