Johannes Kepler was one of a new breed of astronomers who followed in the wake of Copernicus during the Scientific Revolution. Of the many changes that occurred during this period, some of the most notable were in the field of astronomical study and natural philosophy, as old paradigms were overturned and replaced with new ones. The proponents of Copernicanism were at the forefront, as they improved upon the traditional theories about the geocentric structure of the universe and the way the fixed stars rotate around the earth. But astronomy did not exist in a vacuum; like most disciplines, it was influenced by developments in other fields like philosophy as Europe began the shift toward modernity. Some of these external influences are represented in Kepler's criticism of the Ptolemaic account of the universe as written in his Epitome of Copernican Astronomy, which was published in three volumes from 1618-1621.
According to Ptolemaic cosmology, the superlunary realm is immutable: the stars are fixed in position on concentric crystalline spheres that rotate about the Earth, which is at the centre of the universe. The spheres ensure that the motion of the celestial bodies is reliable and constant, so natural philosophers might use "the unchanging steadfastness of their movements" as their basis for making judgements about the nature of the universe (Epitome, 142). Conversely, terrestrial things are transitory. Since it is not possible to find "something which stays in the same state perpetually" in the sublunary realm, one ought not to formulate judgements and hypotheses based on the movements of things that can be observed on Earth (142).
This sharp distinction between the sublunary and the superlunary was borrowed from Aristotelian physics, and it is the "excuse" to which Kepler refers in the criticism of Ptolemy presented in the Epitome (142). According to Kepler, Ptolemy's argument relies on this single principle (which Copernicus' work proved to be false) to such an extent that it "undermines the whole possibility of astronomy", and it "satisfies neither the astronomers nor the philosophers" (142). Furthermore, this account of the universe is also unsuitable from a Christian viewpoint as it ascribes to the stars godlike qualities like immortality, even to the point of making them out to be "visible gods", giving them "more [...] than belongs to God Himself the Founder" because of their eternal immovability (143). Of course, since God is omniscient and omnipotent, for the Christian natural philosopher nothing can be greater than Him, and a new account of the stars becomes necessary.
Traditionally, natural philosophy (or physics, anachronistically speaking) had been held to be a discipline apart from astronomy; under the Ptolemaic system it had to be, because of what were thought to be the differing characteristics of celestial and terrestrial objects. But, for Kepler and the rest of the Copernicans, this is where Ptolemy's "excuse" becomes an impediment to full understanding of the nature of the universe. Though in the Epitome Kepler concedes "that we should not judge of the ease of celestial movements from the difficulty of the movements of the [terrestrial] elements" in all cases, he flatly refuses to accept the conclusion which Ptolemy draws out of that argument: that is, that "with respect to the celestial movements no terrestrial cases are akin", so that natural philosophy and astronomy could never be considered as a single discipline (142).
Ptolemy's entire argument is unsuitable from a Copernican view of astronomy -- and also, one might argue, from any carefully-reasoned astronomical viewpoint -- because it "brings all hypotheses under suspicion of falsity [...] so that even reason is put down in erring in its judgement of what is geometrically simple" (142). For instance, Kepler cites Ptolemy's epicycles, which were used to explain away planetary retrograde motion. Epicycles were like circular sub-orbits, described around the perimeter of the planet's main orbital path around the Earth -- this explained the way in which the planets sometimes seemed to travel backward in the sky. Thus it was held that the movement of the planets was "composite", made up of a number of circles, rather than "compounded with one another in order to fashion one movement" (142).
The rationale supporting it is unsound, however, and Kepler details why. Ptolemy's self-declared aim was "to construct hypotheses which are as [geometrically] simple as possible", and so if simpler theories were put forward to explain celestial phenomena (retrograde motion, in this case) he "will not defend his composite hypotheses [...] but will prefer the hypotheses which seem simpler" -- even if to prove the new hypotheses one used "terrestrial examples" to explain them (143). Ptolemy desires simplicity, then, but his position seems equivocatory; his willingness to accept new ideas, provided they are simpler, makes his system seem almost as though it had been put in place pending the discovery of a better idea. As according to Aristotle's Metaphysics "astronomers should be listened to on the form, lay-out, and movements of the celestial bodies", relying on a system which invites replacement -- let alone one which "[elicits] the truth from things which are absolutely false", like Ptolemy's geocentric universe -- would prove disastrous indeed for "the honor of astronomy" (142-3). Thus, with the work of astronomers like Brahe, Copernicus, and Kepler himself to supersede the old theories, there is no real reason for "modern" astronomers to subscribe to anything that Ptolemy put forward.
After proving that Ptolemy's opinion on the movements of planets should be unacceptable to astronomers, Kepler continues to demolish the old system by establishing that it ought not to be accepted by philosophers, either. He argues that Ptolemy was too unclear about the nature of the material in which the crystalline spheres are suspended above the Earth, and "the philosophers will deny that it is sufficient" to know only that it is "liquid" and somehow "permeable by the globes" (143). Ptolemy is also unclear about what it is that moves the planets around the Earth, "as there is no immobile field remaining underneath, and since a round body does not possess the services of feet or wings" to move itself of its own accord. He also fails to explain what guides the planets and stars to orbit the way that they do (143). Leaving all of these questions unanswered makes the Ptolemaic system open to criticism from sceptical thinkers like Kepler, to the point of philosophical inadequacy.
Kepler's final criticism of the Ptolemaic system is that it "cannot be tolerated in a Christian discipline" (142). In many ways, this problem stems from Kepler's philosophical difficulties with Ptolemy: leaving the origins of planetary movement unexplained begs the assumption that the stars and planets themselves are the source of their own movement, like Aristotle's prime mover. Kepler even accuses Ptolemy of "[making] the stars to be visible gods" in their own right (143). The notion of all things celestial being eternal and unchanging also contributes to their illegitimate deification; it is all too easy for one to "[infer] immortal life from their eternal motion", and from there "attribute more to them than belongs to God Himself the Founder", based on Ptolemy's "pagan superstition" (143). Kepler, whose writing displays strong sympathy for this Christian perspective, suggests that this particular problem might be resolved by thinking in terms of an axiom: those things that God wishes to be understood by man "should be simple in the stars" (143).
Kepler's Copernican criticisms of the Ptolemaic cosmology were revolutionary for a number of reasons; one of the foremost is that the Epitome stands at the juncture between the traditional notion of physics as being distinct from astronomy, as reflected in the systematic refutation of the Ptolemaic and Aristotelian notion that the terrestrial must be by definition completely apart from the celestial. Kepler's critique proposed a new sort of physics, one that could encompass both; this would prove to be the forerunner for Newton's universal gravitation theory, in which the same law applies to stars and planets as to things on Earth. Kepler was also important in that he helped reconcile Christian thought with Copernican heliocentricity. Suggesting that "the understanding whereof God wished man His image to have in common with Him" would be revealed simply in the stars would have rendered the idea that the Earth was not the centre of all things less offensive to early modern Christian sensibilities. Perhaps most importantly, Kepler's work rejected the traditional cosmology, providing a reasoned critique to emerge with a new understanding of the universe: such systematic questioning would come to be one of the characterising features of early modern Europe.
Page references above come from Kepler's Epitome of Copernican Astronomy book IV section 2, trans. C.G. Wallis.