Ontological priority is a philosophical concept that was first introduced by Aristotle (384–322 BCE) in his influential book Categories, in about 350 BCE. For over two millennia, this concept has influenced the reasonings of many philosophers (e.g., Aristotelians) and has influenced some discussion in ontology and logic. (Aristotle also makes numerous references to priority, as well as posterity, in two of his most influential works, Physics and Metaphysics.)
When something (be it an idea or a physical object) is said to be "ontologically prior" to something else (i.e., idea/object/property, tone, or quality), it is literally to say something exists before something else exists. To use René Descartes' famous phrase, "cogito ergo sum," in a slightly different context than the one he originally intended, Aristotle would have agreed with Descartes' reasoning that a person/thinking thing is ontologically prior to the activity of thinking. So, in this case, a positive formulation would be that a thought requires a thinking thing, i.e., the thinking thing has ontological priority over their (or his/her) thought, whose existence depends on the former to exist. Conversely, the negative formulation is that thoughts cannot exist without a thinking thing.
One thing's ontological priority over another may be chronological, by reciprocally and non-reciprocally implied existence (i.e., a thing's nature), order, "esteem," or "truth-maker," depending on the formulation used.
Ontological Priority in Aristotle's Categories
An ontological priority is an existential type of relationship, between two or more things, that occurs whenever a thing exists only because another thing exists; moreover, that existential relationship only becomes an ontological priority when at least one thing exists before (prior) another thing (posterior). Whereas if both things came to exist at the same time or bear no meaningful relationship (even if one came before the other), then an ontological priority cannot be said to occur.
With modal reasoning in mind, two of Aristotle's five ontological-priority formulations have it so that if the prior-existing thing were not to exist, then it would be impossible for the posterior-existing thing to exist (in the same way that five is the sum of two plus two is false in all possible worlds). These would be among the strongest forms of reasoning in philosophy and logic, since they carry the same certainty as analytic truths, and the denial of any one of them would result in an impossibility.
A "thing" can be a physical object/particular, idea/universal, or a tone/quality and can share an ontological/existential before-after relationship with any of the aforesaid three types of entities. But according to Aristotle, ideas/universals and tones/properties/qualities cannot exist without a particular/physical object; this means that it is impossible, according to Aristotle, for any universal or quality to be ontological prior to any physical object (see his fifth formulation in the subsection below), which was made clear in his arguments against Melissus, and his mentor, Parmenides, among others, in his first book of Physics (e.g., 185a29–b5), as well as other books throughout his Physics and Metaphysics.
If one suspected that the aforementioned trichotomy (viz., particulars, universals, and qualities) bears similarities to the type-token-tone framework of C. S. Peirce, a theorist who was not born until about 2,161 years after Aristotle's time, one would be correct. Aristotle's implicit understanding of this trichotomy is already quite evident by his first book of Physics, for example; he makes references and distinctions between the three abundantly. But these similarities between Peirce's trichotomy and Aristotle's implicit one may or may not coincidental. However, "trichotomy" is not the best description for it, since they are interrelated and, in all cases imaginable, inseparable; for example, the property of being a rational or thinking thing and the idea of bipedalism are inseparable from a particular man. (It is true that some persons lose the capacity for thought or the ability to walk, but these are two of many examples of particulars and ideas that are integrated with things, which helps understanding the perspective of how ontological priorities work.) For this reason, "triadic" would be a better term, since the three types of ontological phenomena are not mutually exclusive or an either/or. But triadic is a term that must be used with caution to avoid confusion with other ideas that also go by "triadic."
In Aristotle's terminology, this triadic relationship would have much to do with what he calls substance, essence, and accidental attributes, among other things, and according to Aristotle, universals (which are similar to his mentor Plato's Forms/Ideas) cannot be prior to substance, and accidental features (which are qualities, tones, or properties), such as the quality of whiteness (the example Aristotle uses many times against Melissus and Parmenides), cannot exist without substance either. Bear in mind that C.S. Peirce was influenced by Aristotle and was well-aware of Aristotle's use of particulars, universals, and qualities.
Aristotle's Five Formulations of Ontological Priorities
There are five ways, Aristotle states, that something is ontologically prior to something else, namely, time, reciprocity/non-reciprocity (or prior by nature), order, "esteem," and "truth-maker." (The last two are nicknames for the sake of keeping the two distinct from the other three Aristotle named.)
The first of Aristotle's five formulations of priority is time (which is the second easiest to understand in terms of its simplicity); for when one thinks about "priority," it is usually to do with the timewise sense in terms of "before" and "after" or Aristotle's prior and posterior. An example of a timewise ontological priority would be that of a father and son: Aristotle would say that the father is ontologically prior to the son because the father came to exist temporally before the son.
Reciprocity and non-reciprocity of implied existence (or prior by nature) are the second of Aristotle's formulations and are among the more difficult/complex of them all; the example Aristotle gives of a reciprocal/non-reciprocal ontological priority is through the example of numbers:
In Aristotle's second-formulation example, the existence of two implies (or "reciprocates the implication of") one's existence (and cannot fail to do so, unlike other formulations of the ontological priority, such as the fourth a little further below, "esteem"). But one does not reciprocate (hence, Aristotle's use of "non-reciprocate") the existence of two. Two cannot exist without one because two is two by virtue of being two units of one; whereas, by its own nature, one does not need two to exist because one is one unit, not two. Using the same reasoning between two and three, two would, then, become ontologically prior to three because three units reciprocally imply the existence of two units, but two does not reciprocate three (because it does not have three units), and so on. (If formulated properly, the second formulation is among the strongest forms of reasoning in philosophy.)
Order is Aristotle's third formulation of the ontological priority and is somewhat more or as complex as the previous one; a better way to understand this is the organization of something, be it science, speech, etc. Aristotle gives the example of grammar, wherein "the elements are prior to the syllables" (14b1–5). One can extrapolate from the example that words are, by order, ontologically prior to sentences and sentences to paragraphs, etc. Another of Aristotle's examples is, with speeches, the introduction comes before the exposition or explanation (14b1–5), and one can understand from there that the introduction and exposition are ontologically prior to the conclusion.
It is worth reiterating that formulations two (reciprocity and non-reciprocity or by nature) and three (order) are two of Aristotle's strongest formulations, which carry apodictic truth values; by contrast, their denial would result in a contradiction, causing impossibility. An example of formulations two and three are: three cannot fail to imply the existence of two because three is, by its nature, defined by its relationship to the numbers preceding it (i.e., bigger than one and two and comes after two), and a syllable cannot exist without its elements, even under modal realism (viz., in all possible worlds, there exist none in which three units do not imply the units of two, for example, which makes these sorts priorities necessarily true). Whereas no such examples are possible in the first formulation (i.e., time) and the fourth, just below.
While "esteem" is not Aristotle's name for the fourth formulation, he provides none for it. He suggests that it is "perhaps the least proper" of all other formulations because has more to do with how someone esteems themselves or persons they love/admire as ontologically prior to other persons (14b1–5). This formulation starkly contrasts the more substantive formulations of the three other ontological priorities described above.
Aristotle describes the fourth formulation of the ontological priority as "what is better and more valued is thought to be prior by nature: ordinary people commonly say of those they specially value and love that they 'have priority' " (14b5–10). Aristotle's mention of "by nature" implies that the second formulation of the ontological priority (e.g., three is greater than two and reciprocally implies the existence of two) is being misunderstood by people who esteem others, by placing them prior to others by nature; this is so that this aspect of formulation four does not get confused with formulation two. As understandable as it would be that a mother's love for her child, for example, would have her place him as "prior" to other children who are not her own, either by nature (i.e., what the child is) or thought (i.e., what the mother thinks), this form of ontological priority is arbitrary (i.e., what the child is) and opinion-driven (i.e., what the mother thinks), and it is the simplest among all the formulations. As we saw with Aristotle's comment of this formulation being perhaps the least proper, it is made clear by him that he regards this form of ontological reasoning with disdain.
"Truth-maker" is the fifth and last of Aristotle's formulations of what ontological priorities are, and, as a comprehension heuristic, one could think of it in terms of Alfred Tarski's "x makes it true that p." Alternatively, one may think of the similarities between this formulation and the correspondence theory of truth. As a word of caution: these ideas are not the same, but they have remarkable parallels. Furthermore, the Tarski truth-maker formula and the correspondence theory of truth roughly represent half of Aristotle's formulation; the other half goes above and beyond the truth-making and extends into ontology and the cause of a thing's existence, which is what makes it an ontological priority in the first place.
Before going further, the fifth formulation, dubbed "truth-maker" for naming convenience, is the most complex of them all and is a variation of the second of Aristotle's formulations (reciprocity and non-reciprocity or by nature). But although its certainty is not as high as the second and third formulations, it is stronger than the fourth formulation and either on par with the first, i.e., priority by time, or slightly weaker in terms of certainty. Whatever problems the correspondence theory of truth and Tarski's formula have, the fifth formulation is likewise affected by their problems.
Aristotle gives the example of his fifth formulation of a man and a proposition about him: