[ORG] is the mode that changes scales, that creates boundaries, that changes magnitudes, that is related to creating the sense of parts and wholes. In this sense it sounds as the most mathematical of all modes.
Again I go to Lawvere through Rodin
"Arising [..] from the needs of geometry, category theory has developed such notions as
adjoint functor, topos, bration, closed category, 2-category, etc. in order to provide
(i) a guide to the complex, but very non-arbitrary constructions of the concepts and
their interactions which grow out of the study of space and quantity.
It was only the relentless adherence to the needs of that basic subject that made category
theory so well-determined yet powerful. [..] If we replace \space and quantity"
in (i) above by \any serious object of study", then (i) becomes my working de nition
of objective logic. Of course, when taken in a philosophically proper sense, space and
quantity do pervade any serious eld of study. Category theory has also objecti ed
as a special case
(ii) the subjective logic of inference between statements. Here statements are of
interest only for their potential to describe the objects which concretize the concepts."
I see all this tweets in AIME about parts and wholes and I wonder why people don't take advantage of others (mathematicians) who happen to have thought about these issues some time now!
As far as I see AIME would say something like the following for a simple system like a triangle:
a "side in a triangle" has to pass through the "triangle" in order to say some interesting things about it. And the same happens for two other "sides in a triangle", for the "angels in the triangle" etc.
So "triangle" is the whole and "sides" are the parts in the sense that the "sides" (etc) have to "pass through" the "triangle" in special ways , so that different interesting things are told about them.
In this sense Latour's insistence of not creating a higher level of "wholes" relative to parts can be satisfied (although geometrically the part-whole relation seems to me to be a primitive one)
All this sounds to me a very algebraic way to deal with part-whole relations and I find it extremely improbable that the relevant concepts have not beed already worked out by mathematicians.
Please, some mathematician teach them how to speak!
Again I go to Lawvere through Rodin
"Arising [..] from the needs of geometry, category theory has developed such notions as
adjoint functor, topos, bration, closed category, 2-category, etc. in order to provide
(i) a guide to the complex, but very non-arbitrary constructions of the concepts and
their interactions which grow out of the study of space and quantity.
It was only the relentless adherence to the needs of that basic subject that made category
theory so well-determined yet powerful. [..] If we replace \space and quantity"
in (i) above by \any serious object of study", then (i) becomes my working de nition
of objective logic. Of course, when taken in a philosophically proper sense, space and
quantity do pervade any serious eld of study. Category theory has also objecti ed
as a special case
(ii) the subjective logic of inference between statements. Here statements are of
interest only for their potential to describe the objects which concretize the concepts."
I see all this tweets in AIME about parts and wholes and I wonder why people don't take advantage of others (mathematicians) who happen to have thought about these issues some time now!
As far as I see AIME would say something like the following for a simple system like a triangle:
a "side in a triangle" has to pass through the "triangle" in order to say some interesting things about it. And the same happens for two other "sides in a triangle", for the "angels in the triangle" etc.
So "triangle" is the whole and "sides" are the parts in the sense that the "sides" (etc) have to "pass through" the "triangle" in special ways , so that different interesting things are told about them.
In this sense Latour's insistence of not creating a higher level of "wholes" relative to parts can be satisfied (although geometrically the part-whole relation seems to me to be a primitive one)
All this sounds to me a very algebraic way to deal with part-whole relations and I find it extremely improbable that the relevant concepts have not beed already worked out by mathematicians.
Please, some mathematician teach them how to speak!
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