1 of 1- Discens
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I need clarifications on genus and essential definition
I have some questions about genus and essential definition.
1) How does the scholastic concept of genus differ from the mathematical concepts of class and set?
In mathematics, a set is any collection of objects which can be proven to exist from the ZFC axioms. A class is an even more general kind of thing. Every collection of objects which have a given property make a class. For example, there is a class of all the x such that x is ( (a fish & red) or (a horse and not blue) ). I guess that such a feature does not make a genus. Moreover, there are sets/classes which are defined just enumerating their elements. But I guess there is no genus such as G= { Archangel Michael, Archangel Gabriel, Archangel Raphael } .
2) An essential definition is a definition of the proximate-genus-specific-difference kind. Now, my question is: is the essential definition of an essence unique? It seems to me that it's not. Let's say that there is an essence such as being A&B&C. I could say that the genus is being A&B and the specific difference is being C. Or I could say that the genus is being A&C and the specific difference is being B. So there could be a lot of different essential definition for one essence. But there is probably something wrong with my argument; otherwise, it seems strange that man is always defined as rational animal and is never defined in another way.
- seigneur
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Re: I need clarifications on genus and essential definition
Discens wrote:
I have some questions about genus and essential definition.
1) How does the scholastic concept of genus differ from the mathematical concepts of class and set?
Probably the most relevant distinction here is that mathematical concepts are intended as purely logical or analytical, whereas scholastic concepts have ontological implications. Scholastics aim at ontologically real categories, whereas mathematicians are only interested in concepts as analytical tools, not as any sort of ontological categories.
This difference between mathematics and scholasticism becomes evident when considering the concepts of essential versus accidental. AFAIK, mathematics does not have the distinction of essential versus accidental. Math is happy with merely properties. And the objects that math describes do not seem to be things like man and animal and the like and an attempt to describe men and animals in terms of mathematical classes and sets should fail, insofar as the analysis would fail to identify the essential properties.
2) An essential definition is a definition of the proximate-genus-specific-difference kind. Now, my question is: is the essential definition of an essence unique? It seems to me that it's not. Let's say that there is an essence such as being A&B&C. I could say that the genus is being A&B and the specific difference is being C. Or I could say that the genus is being A&C and the specific difference is being B. So there could be a lot of different essential definition for one essence. But there is probably something wrong with my argument; otherwise, it seems strange that man is always defined as rational animal and is never defined in another way.
Man is always defined as rational animal as species of a certain genus. For other purposes, man can be defined differently.