Melissus was reputed to have been the pupil of Parmenides,[8] and the teacher of Leucippus,[9] though one must regard such claims with a fair amount of skepticism.

Much of what remains of Melissus’s philosophical treatise, later titled On Nature, has been preserved by Simplicius in his commentaries on Aristotle’s Physics and On the Heavens, and several summaries of his philosophy have come down to us.

[11] Unlike Parmenides, Melissus wrote his treatise in prose, not poetry, consequently making it easier to follow than that of his teacher.

The existence of a changeless, motionless, eternal present is an arguable position (as Time, by its nature, is merely made by change and motion and that, there would exist no such thing as Time if there were no change in quality or quantity); however, the existence of a changeless, motionless, infinite succession of moments is a much more difficult position to defend as moments are distinguished from one another by the change in quality or quantity of the one space that they exist within, otherwise, there would have been an infinite number of moments of the same quality and quantity, which is, in actuality, one continuous moment as Parmenides argued.

Fragments 7 and 8 apparently indicate that Melissus is speaking in terms of spatial infinity, although regarding fragment 3, which first argues this point, Simplicius explicitly denies this: “But by ‘magnitude’ he does not mean what is extended in space.”[16] Simplicius undoubtedly had more of Melissus’s treatise at his disposal, as well as other commentaries and notes which have not survived to the present day.

In the former case, unless the argument is based on a now lost theory on the relationship between time and space, it is, as McKirahan says, “grossly fallacious”.

[17] In the latter case, granting the “beginning” and “end” of fragment 2 spatial as well as temporal qualities leaves Melissus open to the charge of equivocation.

The argument is as follows: and further: In fragment 5, Melissus makes the remarkable claim that The One is incorporeal.

Just as his insistence that The One is unlimited, this claim may also be his attempt to address a potential problem inherent in Parmenides’s philosophy (8.42–9).

Melissus's version of Eleatic philosophy was the chief source for its presentation in the works of Plato and Aristotle.

[24] The later Peripatetic philosopher, Aristocles of Messene, also had little admiration for Melissus, calling several of his arguments "absurd".

[25] Melissus has fared somewhat better in the eyes of modern scholars; he was an inventive philosopher and had the good quality of offering clear and direct arguments.

Although he follows Parmenides in his general views and the framework of Eleaticism, he made original contributions and innovations to the substance of Eleatic philosophy.