Parmenides, Modal Metaphysician

The philosopher regarded by some as the first metaphysician and modal theoretician to reflect systematically on the nature of possibility, necessity, and impossibility is the Greek presocratic philosopher and founder of the “Eleatic” school of philosophy, Parmenides, born around 515 BC. His one surviving work, On Nature, is a fragmentary poem describing the poet’s mystical journey by chariot to the temple of an unnamed goddess who instructs him in the two ways in which human beings approach reality, the “Way of Truth” and the flawed “Way of Appearance” or mere “Opinion” (doxa). In her discourse on the Way of Truth, the goddess further distinguishes three ways in which reality may be thought about or conceived: “that it is and must be,” “that it is not and it cannot be,” and “that to be and not to be are the same yet not the same.”

What Parmenides meant by these three paths (along with much else in his opaque and oracular poem) has been the subject of much debate, but one interpretation relevant to the history of the possibles has seen his three-fold path as an early distinction between the three modal categories of necessity, impossibility, and possibility, respectively.[1] On this reading, Parmenides’s “what is and must be” refers to those things which are necessary, “what is not and cannot be” to those things that are deemed to be impossible, and the intermediate realm of “what both is and is not” is presumably his way of characterizing the merely possible.

[1] Merrill Ring relates Parmenides’s interest in modality to the likelihood of his mathematical training among the Pythagoreans:

If, as there is good evidence for, he did begin his intellectual career among the Pythagoreasn, he was there exposed to sophisticated mathematical thought. One clear and obvious feature of mathematical discussion is frequent use of the various modal notions. For instance, an early mathematical discovery was that the result of multiplying any integer by 2 has to be an even number. A more complicated realization was that it is impossible to construct a right triangle whose hypotenuse is shorter than iether of the other twos sides. Even possiblity is easily spotted in mathematicians’ talks: “Can (say) 2,372 be divided by 3 without remainder?”

Very probably, Parmenides’ interest in modal concepts arose from his exposure to the frequent use of those notions in the mathematical work of the Pythagoreans. (Ring 91).


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