# Categories, Universals, Particulars

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### Patrick Browne

Jul 25, 2011, 5:18:29 AM7/25/11

Hi,
Below are some assumptions, followed by two questions.
1. Categories are high level generic concepts e.g. Region
2. Universals are classes of actual things and particulars e.g. Country
3 Particulars are individual occurrences of universals e.g. Ireland
4. Categories are organized using subsumption hierarchies
(mathematically a sub-set relation).
5. Universals are organized using subsumption hierarchies
(mathematically a sub-set relation).
6. Individuals are elements of sets (mathematically element-of or set-
membership relation)

Question 1: Are these assumptions correct?
Question 2: Is the relationship between Categories and Universals also
a subsumption relation, with the caveat the categories are higher up the hierarchy than universals?

Thanks,
Pat

### Erick Antezana

Jul 25, 2011, 7:08:30 AM7/25/11
Pat,

this paper might be of help:

"Towards a Reference Terminology for Ontology Research and Development
in the Biomedical Domain"

http://ontology.buffalo.edu/bfo/Terminology_for_Ontologies.pdf

Erick

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### Barry Smith

Jul 25, 2011, 10:51:14 AM7/25/11
On Mon, Jul 25, 2011 at 5:18 AM, Patrick Browne wrote:

Hi,
Below are some assumptions, followed by two questions.
1. Categories are high level generic concepts e.g. Region

We do not use 'concept' -- since it has so many different definitions
Categories are high level universals

2. Universals are classes of actual things and particulars e.g. Country

For us, the extension of a universal is a class; but other sorts of collections of particulars are classes also

3 Particulars are individual occurrences of universals e.g. Ireland

avoid 'occurrence' since not all particulars are occurrents. Instead write

Particulars are individual instantiations of universals e.g. Ireland

4. Categories are organized using subsumption hierarchies
(mathematically a sub-set relation).

categories are just highest-level universals -- they do not have a separate subsumption hierarchy
Their extensions are organized in a mathematical sub-set relation.

5. Universals are organized using subsumption hierarchies
Yes. The structure of the hierarchy is analogous to a mathematical sub-set relation, but only analogous thereto, since universals are not set-theoretic entities.

6. Individuals are elements of sets (mathematically element-of or set-
membership relation)

Everything can be an element of a set, including a universal.

Question 1: Are these assumptions correct?
see above

Question 2: Is the relationship between Categories and Universals also
a subsumption relation, with the caveat the categories are higher up the hierarchy than universals?
yes
BS

### Patrick Browne

Jul 26, 2011, 11:15:00 AM7/26/11
On 25/07/11, Barry Smith <phis...@buffalo.edu> wrote:

6. Individuals are elements of sets (mathematically element-of or set-
membership relation)

Everything can be an element of a set, including a universal.

What I am trying to establish with point 6 is the nature of the hierarchy.

Is it the case that at the bottom of the hierarchy there is a switch from the subset relation to the element relation? This  could be expressed as follows:

[6a] aParticular is-element-of aUniversal is-subset-of aCategory

If the universal Dog is a subset of the category Animal then the particular Fido is an element of Animal. Whereas, if I assume that Dog is an element of Animal, then I do not think that I can say that Fido is an element of Animal (because the element relation is non-compositional).

Is [6a] the correct interpretation of the hierarchy?

Regards,

Pat

Jul 26, 2011, 11:27:13 AM7/26/11
On Jul 26, 2011, at 11:15 AM, Patrick Browne wrote:

On 25/07/11, Barry Smith <phis...@buffalo.edu> wrote:

6. Individuals are elements of sets (mathematically element-of or set-
membership relation)

Everything can be an element of a set, including a universal.

I don't totally see this---"individuals are elements of sets". What's the relationship, if there is any systematic one at all, between an individual's being an instance of the lowest-level universal it instantiates, and being an element of a set (the set of things instantiating the lowest-level universal? Of some other set?)

What I am trying to establish with point 6 is the nature of the hierarchy.
Is it the case that at the bottom of the hierarchy there is a switch from the subset relation to the element relation? This  could be expressed as follows:

[6a] aParticular is-element-of aUniversal is-subset-of aCategory

If the universal Dog is a subset of the category Animal then the particular Fido is an element of Animal. Whereas, if I assume that Dog is an element of Animal, then I do not think that I can say that Fido is an element of Animal (because the element relation is non-compositional).
Is [6a] the correct interpretation of the hierarchy?

I would have thought that Fido is an instance of Animal and an instance of Dog and that the instantiation does not behave in the same way that set membership does, which accounts for the composition problem. Right?

Regards,
Pat