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a thread on Ibn Sina (Shaykh al Rais) and numbers!
In his major work on Metaphysics, the learned shaykh tells us why meta-physics is named “after nature”
In his major work on Metaphysics, the learned shaykh tells us why meta-physics is named “after nature”
he says that the science of metaphysics occurs to the mind or to our knowledge AFTER our experience with nature ie material things and their properties. we see material existents first, and through that we observe existence as such in its various states.
however, in its ESSENCE metaphysics is prior to material existents or to nature, because the object of knowledge (existence and its states) are prior to matter in terms of their generality and just what they talk about, like oneness vs manyness, cause vs effect, etc
then he considers an objection: isn’t NUMBER also prior to matter? why isn’t the study of numbers (arithmetic) called metaphysics too? in terms of their existence, numbers don’t depend on matter. heck they can’t even be found in matter!
the learned shaykh says: YIKES, that is a concern! okay, but look: arithmetic doesn’t study numbers in EVERY respect. numbers can occur in: 1) things separate from matter, like angels 2) or numbers exist in things not separate from matter
the main mistake of the objector is in thinking that numbers share the same aspects or properties when they exist in 1 vs in 2.
when numbers exist in things separable from matter, they don’t have relations like increasing or decreasing. they stay exactly as they are.
when numbers exist in things separable from matter, they don’t have relations like increasing or decreasing. they stay exactly as they are.
change is associated with matter. non-material things don’t change. (his proof for this isn’t important here.) and all the relations of numbers that arithmetic studies are associated with change!
when number exists in the #2 sense, however, it becomes susceptible to receiving relations or to increasing, because matter changes. so I have 1 orange, I cut it up and it becomes 2 oranges. the accident of number (to the orange) has changed.
arithmetic will take this aspect of change and study the relations of numbers. what’s 2+1 or 10/2?
so in the #2 sense, number exists in natural things (as an accident to the amount of oranges, for instance), OR it exists as the human mind considers it.
so in the #2 sense, number exists in natural things (as an accident to the amount of oranges, for instance), OR it exists as the human mind considers it.
the human mind will abstract number from all sorts of things and then study it. but the abstracted number isn’t studied in and of itself (though we often think it is). rather, its relations and properties are studied, and those are the properties that depend on matter.
so, arithmetic isn’t “after nature” because it studies numbers after they’ve acquired properties from being material accidents (like combining numbers, separating them etc)
ok but I know what you’re gonna say: what about number INSOFAR as it DOESNT change? Who studies that?
NOT arithmetic, says our shaykh. Oneness, manyness, & immaterial things in general are studied in metaphysics. Therefore it is truly the science most fit to be prior to nature
NOT arithmetic, says our shaykh. Oneness, manyness, & immaterial things in general are studied in metaphysics. Therefore it is truly the science most fit to be prior to nature
