Yesterday I argued: Aristotle counts words indicating time (pote) as a category; thus time has the same standing as item in any other category. I called this an argument from 'parity'.
This of course raises the question of whether, for Aristotle, there is parity among the categories. And one might argue that clearly there isn't. After all, substance is primary. And then Aristotle standardly gives only four categories when referring to them--substance, quality, quantity, relation--as if to suggest that these are somehow more fundamental. Of these, he seems to regard relation as a low-level sort of existence (Nic. Eth. I.6).
Of course, even if 'time' were somehow ranked lower than other categories, this would no more imply that it is mind-dependent than that 'location' (pou) is, or, indeed, action and passion.
These reflections invite the question, whether there some system in Aristotle's categories. Is his list of ten meant to be exhaustive, or open-ended? If he meant it to be exhaustive, did he implicitly have an argument that it is? In the introduction to his edition of the Metaphysics, Ross gives what is probably the common view:
Aristotle has no 'deduction of the categories', no argument to show that the real must fall into just these divisions. He seems to have arrived at the ten categories by simple inspection of reality, aided by a study of verbal distinctions (lxxxv).But this seems a non sequitur. What is at issue is not how Aristotle arrived at them, or how he presents them in the Categories, but whether, upon reflection he was willing to stand by them, by giving reasons against alternatives, or for his own list.
Since, it is true, there is no such defense in the Aristotelian corpus, if such a defense were contemplated, we would need to arrive at it by the perfectly respectable enterprise of rational reconstruction.
The best effort along these lines that I have seen may be found in a recent article by Kyle Fraser, "Seriality and Demonstration in Aristotle's Ontology", in OSAP, Winter 2003. Since I am writing a review of this volume, to be published elsewhere, I'll say little more about Fraser's article.
However, I do wish to note here the following. In an Appendix, "On the Neoplatonist 'Deduction' of the Categories", Fraser reproduces a standard neoplatonic systematization of the categories, which Ross gives in his commentary introduction, on page lxxxvi. Fraser also gives Brentano's classification (from On the Several Senses of Being in Aristotle). Yet he does not refer to Aquinas' interesting systematization, in his Metaphysics commentary (lect. 9, n. 892), which I'll therefore paste below. (I copy it from the excellent site, Corpus Thomisticum.)
Sciendum enim est quod praedicatum ad subiectum tripliciter se potest habere. Uno modo cum est id quod est subiectum, ut cum dico, Socrates est animal. Nam Socrates est id quod est animal. Et hoc praedicatum dicitur significare substantiam primam, quae est substantia particularis, de qua omnia praedicantur.
Secundo modo ut praedicatum sumatur secundum quod inest subiecto: quod quidem praedicatum, vel inest ei per se et absolute, ut consequens materiam, et sic est quantitas: vel ut consequens formam, et sic est qualitas: vel inest ei non absolute, sed in respectu ad aliud, et sic est ad aliquid. Tertio modo ut praedicatum sumatur ab eo quod est extra subiectum: et hoc dupliciter. Uno modo ut sit omnino extra subiectum: quod quidem si non sit mensura subiecti, praedicatur per modum habitus, ut cum dicitur, Socrates est calceatus vel vestitus. Si autem sit mensura eius, cum mensura extrinseca sit vel tempus vel locus, sumitur praedicamentum vel ex parte temporis, et sic erit quando: vel ex loco, et sic erit ubi, non considerato ordine partium in loco, quo considerato erit situs. Alio modo ut id a quo sumitur praedicamentum, secundum aliquid sit in subiecto, de quo praedicatur. Et si quidem secundum principium, sic praedicatur ut agere. Nam actionis principium in subiecto est. Si vero secundum terminum, sic praedicabitur ut in pati. Nam passio in subiectum patiens terminatur.
Quia vero quaedam praedicantur, in quibus manifeste non apponitur hoc verbum est, ne credatur quod illae praedicationes non pertineant ad praedicationem entis, ut cum dicitur, homo ambulat, ideo consequenter hoc removet, dicens quod in omnibus huiusmodi praedicationibus significatur aliquid esse. Verbum enim quodlibet resolvitur in hoc verbum est, et participium. Nihil enim differt dicere, homo convalescens est, et homo convalescit, et sic de aliis. Unde patet quod quot modis praedicatio fit, tot modis ens dicitur.