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I was going through the categorization article in Wikipedia and happened to read this line:

In the classical view, categories need to be clearly defined, mutually exclusive and collectively exhaustive. This way, any entity in the given classification universe belongs unequivocally to one, and only one, of the proposed categories.

If John is both a doctor and a carpenter. Isn't the element 'John' part of both the doctor and carpenter category at the same time? Does this make the categorization non-classical (in the Aristotelian sense)?

In the Criticism of the Aristotelian model section of this page: https://cogling.fandom.com/wiki/Aristotelian_model_of_categorization, It is also written that:

Further research into the categorization of shapes, organisms and other non-scalar phenomena, category boundaries also tend to be fuzzy, and, moreover, that certain entities are considered members of more than one category.

I just wanted to know how being in more than one category is in conflict with the Aristotelian categorization model. I get how the absence/difficulty finding necessary/sufficient conditions is an issue but why is being in multiple categories an issue?

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  • Categories are the most fundamental kinds, not just any predicates used in a classification. Aristotle has only ten of them, and doctors and carpenters are not on the list. Indeed, it is hard to imagine a categorization where those would be fundamental, classical or otherwise. For a non-classical example see e.g. Husserl's joint formal/material categorization.
    – Conifold
    Nov 29, 2020 at 12:44
  • @Conifold Looks like Aristotle's is something like a consistent system on its own rather than a general mechanism to structure things in the world? Actually I was reading Criticism of the Aristotelian model in this page: cogling.fandom.com/wiki/Aristotelian_model_of_categorization, and it said (specially the last line) : Further research into the categorization of shapes, organisms ... moreover, that certain entities are considered members of more than one category. I just wanted to know how entities being in multiple category is in conflict with Aristotelian Categorization.
    – Tangent
    Nov 29, 2020 at 13:38
  • It is an ideal mechanism for structuring things, it is something we want if it can be had. But real life is messy and common categorizations are just surrogates. Overlapping categories mean either that something more fundamental is in play, or that things are categorized based on a mix of principles instead of a single one. Ideally, we would want to clean that up, but it is not always possible.
    – Conifold
    Nov 29, 2020 at 14:08

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If John is both a doctor and a carpenter. Isn't the element 'John' part of both the doctor and carpenter category at the same time? Does this make the categorization non-classical (in the Aristotelian sense)?

In Aristotelian terminology, "doctor" and "carpenter" are accidents. A person can become a doctor, then a carpenter, then any other profession. It doesn't affect his essence, which is what the categories (and genera and species) describe him as. The person himself who is a doctor or carpenter is a human, which is a species of the genus animal, which is a genus of the category substance.

The profession of doctor and carpenter aren't discussed in particular by Aristotle, but professions might all be in the category of relatives, like the slave which he does discuss (the concept of doctor presupposes a relation towards the patient, the concept of carpenter presupposes a relation towards the building).

I just wanted to know how being in more than one category is in conflict with the Aristotelian categorization model. I get how the absence/difficulty finding necessary/sufficient conditions is an issue but why is being in multiple categories an issue?

Aristotle himself (Categories 7) is unsure about whether it's possible to belong to two categories.

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