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How to Derive Aristotle’s Categories from First Principles

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Abstract

We propose a model of cognition grounded in ancient Greek philosophy which encompasses Aristotle’s categories. Taking for First Principles the brute facts of the mental actions of separation, aggregation and ordering, we derive Aristotle’s categories as follows. First, Separation lets us see single entities, giving the simple concept of an individual. Next, Aggregation lets us see instances of some kind, giving the basic concept of a particular. Then, Ordering lets us see both wholes-with-parts as well as parts-of-some-whole, giving the subtle concept of a relational or Gestalt. The basic and the subtle concept give us the major and minor categories. The categories constitute a top-level ontology and describe universal usage so that any other category necessarily describes particular or domain usage.

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Notes

  1. References to Aristotle are given as XX aabcc or XX d.ff, where XX is the abbreviation of the work as per (Shields 2015, p xix) and aabcc are the Bekker pages and d.ff are the book and chapter. All references are to Barnes (1995b).

  2. References to Plato are standardly given as XXX aaBcc, where XXX is the work and aaBcc are the Stephanus numbers. All references are to Cooper (1997).

  3. There is another, brief mention in the dictionary, Book 5 of the Metaphysics, “the first point from which a thing either is or comes to be or is known” (1013a17); this, too, suggests a tri-partition, but would require further study to be substantiated.

  4. For impossible objects, imagine this scene at the Mad Hatter’s tea party. “Look,” said the Mad Hatter as he lifted the lid off the teapot and much to Alice’s surprise, there it was: a perfectly square circle.

  5. Our choice of using classical logic is following Leslie Tharp’s comment “The reasons for taking elementary logic as standard evidently have to do also with certain imprecise – but I think vital – criteria, such as the fact that it easily codifies many inferences of ordinary language and of informal mathematics, and the fact that stronger quantifiers can be fruitfully analyzed in set theory, a theory of EL.” (italics in original) (Tharp 1975, p. 17).

  6. One of the ways in which Aristotle is thought to have arrived at the categories is by asking questions and analysing all possible answers, but the problem with this is that “Aristotle does not have a category corresponding to every one-word Greek interrogative, nor do all of his categories correspond to such interrogatives” (Ackrill 1963, p. 78–79). No, the real problem is that asking questions indiscriminately presupposes that the categories are an unordered set, which is not the case as we pointed out in the Introduction.

  7. Preferring here the translation by Jonathan Barnes (1995a) over the standard one by David Ross. (It would be nice if the community could agree to make Aristotle’s works an open source project so that we can develop a real standard.).

  8. In the classical distinction, what is ‘out there’ is a phenomenon and what is ‘in here’ is a noumenon where the latter constitutes our knowing the former (Sextus Empiricus 1933, I.xiii.33). The problem here is that the current understanding of ‘noumenon’ derives from Kant (1781) notwithstanding Schopenhauer’s (1819) criticism that Kant had hijacked the term to suit his own purposes. Using ‘noumenon’ here might confusingly evoke Kant’s usage.

  9. The Stoic ‘something’ as a ‘super category’ would seem comparable, but their notion appears to be conflicted (c.f. Long and Sedley 1987; Menn 1999; Brunschwig 2003).

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Acknowledgements

Kate Burridge, without whose help this project would not have gotten started; Lloyd Humberstone who introduced one of us to logic; Keith Allan and John Sowa who commented on an earlier version; John Bigelow and Peter Freere who commented on various parts; the anonymous reviewer whose critical comments caused some important pieces of the puzzle to fall into place.

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  1. Monash University, Clayton, VIC, Australia

    Humphrey P. van Polanen Petel

  2. Latrobe University, Bundoora, VIC, Australia

    Karl Reed

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Humphrey P van Polanen Petel: conceptualization, methodology, writing of original draft; Karl Reed: minor contributions, validation, critical review and editing; Both authors approved final version.

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Correspondence to Humphrey P. van Polanen Petel.

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van Polanen Petel, H.P., Reed, K. How to Derive Aristotle’s Categories from First Principles. Axiomathes 32 (Suppl 2), 113–147 (2022). https://doi.org/10.1007/s10516-021-09591-2

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