| Line 1: |
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| | {{DISPLAYTITLE:Factorization Issues}} | | {{DISPLAYTITLE:Factorization Issues}} |
| | | | |
| − | ==Note 1==
| + | <pre> |
| | + | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| | + | |
| | + | IDS -- FI |
| | + | |
| | + | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| | + | |
| | + | FI. Factorization Issues |
| | + | |
| | + | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| | + | |
| | + | FI. Note 1 |
| | | | |
| − | <pre>
| + | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| − | | Things are equivocally named, when they have the name only in common,
| |
| − | | the definition (or statement of essence) corresponding with the name
| |
| − | | being different. For instance, while a man and a portrait can properly
| |
| − | | both be called "animals" [Greek 'zõon' means 'living' or 'true to life'],
| |
| − | | these are equivocally named. For they have the name only in common,
| |
| − | | the definitions (or statements of essence) corresponding with the name
| |
| − | | being different. For if you are asked to define what the being an animal
| |
| − | | means in the case of the man and the portrait, you give in either case
| |
| − | | a definition appropriate to that case alone. ("Categories", p. 13).
| |
| − | |
| |
| − | | Aristotle, "The Categories", in 'Aristotle, Volume 1',
| |
| − | | Translated by H.P. Cooke & H. Tredennick, Loeb Classics,
| |
| − | | William Heinemann Ltd, London, UK, 1938.
| |
| | | | |
| | I would like to introduce a concept that I find to be of | | I would like to introduce a concept that I find to be of |
| Line 35: |
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| | f : X -> Y, just about as generic as it needs to be: | | f : X -> Y, just about as generic as it needs to be: |
| | | | |
| − | | Source X = {1, 2, 3, 4, 5} | + | o---------------------------------------o |
| − | | | o o o o o | + | | | |
| − | | f | \ | / \ / | + | | Source X = {1, 2, 3, 4, 5} | |
| − | | | \|/ \ / | + | | | o o o o o | |
| − | | v o o o o o o | + | | f | \ | / \ / | |
| − | | Target Y = {A, B, C, D, E, F} | + | | | \|/ \ / | |
| | + | | v o o o o o o | |
| | + | | Target Y = {A, B, C, D, E, F} | |
| | + | | | |
| | + | o---------------------------------------o |
| | | | |
| | Now, it is a fact that any old function that you might | | Now, it is a fact that any old function that you might |
| Line 47: |
Line 49: |
| | example just like so: | | example just like so: |
| | | | |
| − | | Source X = {1, 2, 3, 4, 5} | + | o---------------------------------------o |
| − | | | o o o o o | + | | | |
| − | | g | \ | / \ / | + | | Source X = {1, 2, 3, 4, 5} | |
| − | | v \|/ \ / | + | | | o o o o o | |
| − | | Middle M = { b , e } | + | | g | \ | / \ / | |
| − | | | | | | + | | v \|/ \ / | |
| − | | h | | | | + | | Middle M = { b , e } | |
| − | | v o o o o o o | + | | | | | | |
| − | | Target Y = {A, B, C, D, E, F} | + | | h | | | | |
| | + | | v o o o o o o | |
| | + | | Target Y = {A, B, C, D, E, F} | |
| | + | | | |
| | + | o---------------------------------------o |
| | | | |
| | Writing the functional compositions f = g o h "on the right", | | Writing the functional compositions f = g o h "on the right", |
| | as they say, we have the following data about the situation: | | as they say, we have the following data about the situation: |
| | | | |
| − | X = {1, 2, 3, 4, 5} | + | X = {1, 2, 3, 4, 5} |
| − | M = {b, e} | + | M = {b, e} |
| − | Y = {A, B, C, D, E, F} | + | Y = {A, B, C, D, E, F} |
| | | | |
| − | f : X -> Y, arbitrary. | + | f : X -> Y, arbitrary. |
| − | g : X -> M, surjective. | + | g : X -> M, surjective. |
| − | h : M -> Y, injective. | + | h : M -> Y, injective. |
| | | | |
| − | f = g o h | + | f = g o h |
| | | | |
| | What does all of this have to do with reification and so on? | | What does all of this have to do with reification and so on? |
| Line 105: |
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| | and injective factors. | | and injective factors. |
| | | | |
| − | Observe, however, that here is where the battles begin to break out, | + | Observe, however, that here is where all the battles tend to break out, |
| | for not all factorizations are regarded with equal equanimity by folks | | for not all factorizations are regarded with equal equanimity by folks |
| | who have divergent philosophical attitudes toward the creation of new | | who have divergent philosophical attitudes toward the creation of new |
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| | In this case, we factor the function f : O -> S | | In this case, we factor the function f : O -> S |
| | | | |
| − | | Source O :> x_1 x_2 x_3 | + | o---------------------------------------o |
| − | | | o o o | + | | | |
| − | | | \ | / | + | | Source O :> x_1 x_2 x_3 | |
| − | | f | \ | / | + | | | o o o | |
| − | | | \|/ | + | | | \ | / | |
| − | | v ... o ... | + | | f | \ | / | |
| − | | Target S :> y | + | | | \|/ | |
| | + | | v ... o ... | |
| | + | | Target S :> y | |
| | + | | | |
| | + | o---------------------------------------o |
| | | | |
| | into the composition g o h, where g : O -> M, and h : M -> S | | into the composition g o h, where g : O -> M, and h : M -> S |
| | | | |
| − | | Source O :> x_1 x_2 x_3 | + | o---------------------------------------o |
| − | | | o o o | + | | | |
| − | | g | \ | / | + | | Source O :> x_1 x_2 x_3 | |
| − | | | \ | / | + | | | o o o | |
| − | | v \|/ | + | | g | \ | / | |
| − | | Middle M :> ... x ... | + | | | \ | / | |
| − | | | | | + | | v \|/ | |
| − | | h | | | + | | Middle M :> ... x ... | |
| − | | | | | + | | | | | |
| − | | v ... o ... | + | | h | | | |
| − | | Target S :> y | + | | | | | |
| | + | | v ... o ... | |
| | + | | Target S :> y | |
| | + | | | |
| | + | o---------------------------------------o |
| | | | |
| | The factorization of an arbitrary function | | The factorization of an arbitrary function |
| Line 299: |
Line 313: |
| | and this is the topic that | | and this is the topic that |
| | I will take up next. | | I will take up next. |
| − | </pre>
| |
| | | | |
| − | ==Note 2==
| + | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| | + | |
| | + | FI. Note 2 |
| | + | |
| | + | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| | | | |
| − | <pre>
| + | Let me illustrate what I think that a plethora of our controversies |
| − | Let me illustrate what I think that a lot of our controversies | |
| | about nominalism versus realism actually boil down to in practice. | | about nominalism versus realism actually boil down to in practice. |
| | From a semiotic or a sign-theoretic point of view, it all begins | | From a semiotic or a sign-theoretic point of view, it all begins |
| Line 310: |
Line 326: |
| | is quite literally taken to denote each object x_j in a whole | | is quite literally taken to denote each object x_j in a whole |
| | collection of objects {x_1, ..., x_k, ...}, a situation that | | collection of objects {x_1, ..., x_k, ...}, a situation that |
| − | I would normally represent in a sign-relational table like so: | + | I'd normally represent in a sign-relational table like so: |
| | | | |
| | o---------o---------o---------o | | o---------o---------o---------o |
| Line 377: |
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| | Notice the subtle distinction between these two cases: | | Notice the subtle distinction between these two cases: |
| | | | |
| − | 1. A sign denotes each object in a set of objects. | + | 1. A sign denotes each object in a set of objects. |
| | | | |
| − | 2. A sign denotes a set of objects. | + | 2. A sign denotes a set of objects. |
| | | | |
| | The first option uses the notion of a set in a casual, | | The first option uses the notion of a set in a casual, |
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| | of the dyadic components of any relation. | | of the dyadic components of any relation. |
| | | | |
| − | Okay, there are a few pieces of this that I
| + | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| − | will need to think over once or thrice more.
| |
| − | </pre>
| |
| − | | |
| − | ==Note 3==
| |
| − | | |
| − | <pre>
| |
| − | JA = Jon Awbrey
| |
| − | SR = Seth Russell
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| − | | |
| − | JA figured:
| |
| − | | |
| − | o-----------------------------o
| |
| − | | Denotative Component of L'" |
| |
| − | o--------------o--------------o
| |
| − | | Objects | Signs |
| |
| − | o--------------o--------------o
| |
| − | | |
| |
| − | | i |
| |
| − | | /|\ * |
| |
| − | | / | \ * |
| |
| − | | / | \ * |
| |
| − | | o o o >>>>>>>>>>>> y |
| |
| − | | . . . ' |
| |
| − | | . . . ' |
| |
| − | | ... ' |
| |
| − | | . ' |
| |
| − | | "i" |
| |
| − | | |
| |
| − | o-----------------------------o
| |
| − | | |
| − | SR: Your diagrams dont tell the whole story.
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| − | | |
| − | JA: No diagram, no form of representation, tells the "whole" story.
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| − | A representation becomes pretty useless if it tries to do that.
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| − | | |
| − | SR: .... here is the rest of the story all in one diagram.
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| − | | |
| − | SR: http://robustai.net/mentography/intensionExtension.gif
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| − | | |
| − | Seth,
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| − | | |
| − | Just off the bat, the arrows that are labeled "connotes",
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| − | "extension of", "intension of", and "isa" seem off base.
| |
| − | | |
| − | Just some random notes:
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| − | | |
| − | y and "i" are both signs.
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| − | | |
| − | x_1, x_2, x_3, and i are all objects
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| − | in the augmented sign relation L'''.
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| − | | |
| − | The intension (property, quality) i gets to be
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| − | an "object of conduct, discussion, or thought"
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| − | as soon as any agents (interpreters, observers)
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| − | start to act, to talk, or to think in some way
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| − | or another with regard to it.
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| − | | |
| − | Later, I will build separate hierarchies for the objects
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| − | and for the syntactic entities (signs, interpretants).
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| − | | |
| − | I forget now, but I don't remember saying anything yet
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| − | about interpretants in this example. I will go check.
| |
| − | </pre>
| |
| − | | |
| − | ==Note 4==
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| − | | |
| − | <pre>
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| − | JA = Jon Awbrey
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| − | SR = Seth Russell
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| − | | |
| − | JA glyped:
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| − | | |
| − | o-----------------------------o
| |
| − | | Denotative Component of L'" |
| |
| − | o--------------o--------------o
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| − | | Objects | Signs |
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| − | o--------------o--------------o
| |
| − | | |
| |
| − | | i |
| |
| − | | /|\ * |
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| − | | / | \ * |
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| − | | / | \ * |
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| − | | o o o >>>>>>>>>>>> y |
| |
| − | | . . . ' |
| |
| − | | . . . ' |
| |
| − | | ... ' |
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| − | | . ' |
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| − | | "i" |
| |
| − | | |
| |
| − | o-----------------------------o
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| − | | |
| − | SR giffed:
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| − | | |
| − | http://robustai.net/mentography/intensionExtension.gif
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| − | | |
| − | JA: No diagram, no form of representation, tells the "whole" story.
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| − | A representation becomes pretty useless if it tries to do that.
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| − | | |
| − | SR: Point taken :)
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| − | | |
| − | JA: Just off the bat, the arrows that are labeled "connotes",
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| − | "extension of", "intension of", and "isa" seem off base.
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| − | | |
| − | SR: Why?
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| − | | |
| − | JA: Just some random notes:
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| − | y and "i" are both signs.
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| − | | |
| − | SR: You mean 'y' and 'i' , I presume. And yes, I agree,
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| − | and my mentograph shows both of those things in the
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| − | context labeled signs.
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| − | | |
| − | No, let me explain ...
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| − | | |
| − | I'm trying to stay within what I'm able to say using
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| − | just one level of quotation marks, so bear with me.
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| − | To do any better in a truly systematic way requires
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| − | the explicit introduction of "higher order" (HO)
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| − | sign relations. Maybe later.
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| − | | |
| − | I resort to analogy:
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| − | | |
| − | I am saying that y is a sign in S, much like the way I might say
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| − | that k is an integer in J = {..., -3, -2, -1, 0, 1, 2, 3, ...}.
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| − | | |
| − | I am saying that "i" is a sign in S, much like the way I might say
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| − | that |j| is an integer in J, where the vertical bars indicate the
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| − | absolute value function -- this is just an example, it could have
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| − | been any other functional value f(j).
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| − | | |
| − | The point is that once we have a sign domain S, for example,
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| − | something like S = {"a", "b", "c", ... A", "B", "C", ...},
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| − | then we can use the elements listed to talk about signs in S,
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| − | or we can use other constant names and variable names to talk
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| − | about the elements of S. For example, I can ask you to think
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| − | about a sign z such that z = "a", and so on.
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| − | | |
| − | JA: x_1, x_2, x_3, and i are all objects
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| − | in the augmented sign relation L'".
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| − | | |
| − | > Yes I agree and have shown them as such in the context labeled objects in
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| − | > the mentograph. I presume the 'sign relation L' to which you refer to is
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| − | > all the arcs labeled 'connotes', 'denotes', and 'represents' in my diagram.
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| − | > I may or may not have chosen correct words for these labels. What words
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| − | > would you choose?
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| − | | |
| − | Just for clarity, here is the tabular version
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| − | of the twice augmented sign relation L'":
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| − | | |
| − | o-----------------------------o
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| − | | Sign Relation L'" |
| |
| − | o---------o---------o---------o
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| − | | Object | Sign | Interp |
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| − | o---------o---------o---------o
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| − | | i | "i" | ... |
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| − | | x_1 | "i" | ... |
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| − | | x_2 | "i" | ... |
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| − | | x_3 | "i" | ... |
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| − | o---------o---------o---------o
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| − | | i | y | ... |
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| − | | x_1 | y | ... |
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| − | | x_2 | y | ... |
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| − | | x_3 | y | ... |
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| − | o---------o---------o---------o
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| − | | |
| − | Okay, this has gotten way too abstract for me!
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| − | Let us back up and remember why we got into this
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| − | in the first place. It had to do with some of the
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| − | hard cases of the ontology development process that
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| − | I commonly think of as "inquiry", and especially the
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| − | abductive generation of a new concept, hypothesis, or
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| − | term, or what is very similar, the semeiosis/semitosis
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| − | of some old such notion that has gotten too posh to be
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| − | useful without undergoing some further distinctions or
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| − | divisions in the over-extenuated mass of its extension.
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| − | | |
| − | Were you here when we were talking about metonymy?
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| − | There is something about this that reminds of that.
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| − | | |
| − | Here is one old note I found:
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| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o | |
| − | | |
| − | Subj: Re: Meaning-Preserving Translations
| |
| − | Date: Sat, 31 Mar 2001 23:00:31 -0500
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| − | From: Jon Awbrey <jawbrey@oakland.edu>
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| − | To: Stand Up Ontology <standard-upper-ontology@ieee.org>,
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| − | SemioCom <semiocom@listbot.com>
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| − | CC: John F. Sowa <sowa@bestweb.net>,
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| − | Mary Keeler <mkeeler@u.washington.edu>
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| − | | |
| − | John F. Sowa wrote:
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| − | >
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| − | > Jon,
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| − | >
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| − | > Your quotation from Hugh T. is very helpful, because it
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| − | > illustrates a universal principle of natural languages:
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| − | >
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| − | > > | It is worth noting in this connexion that the use of the words
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| − | > > | 'oros' (bound or limit), 'akron' (extreme), and 'meson' (middle) to
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| − | > > | describe the terms, and of 'diastema' (interval) as an alternative
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| − | > > | to 'protasis' or premiss, suggests that Aristotle was accustomed to
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| − | > > | employ some form of blackboard diagram, as it were, for the purpose
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| − | > > | of illustration. A premiss was probably represented by a line joining
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| − | > > | the letters chosen to stand for the terms. How quality and quantity
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| − | > > | were indicated can only be conjectured.
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| − | > > |
| |
| − | > > | Hugh Tredennick,
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| − | > > |"Introduction" to Aristotle's "Prior Analytics", page 184 in:
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| − | > > |'Aristotle, Volume 1', Translated by H.P. Cooke & H. Tredennick,
| |
| − | > > | Loeb Classical Library, William Heinemann, London, UK, 1938.
| |
| − | >
| |
| − | > This example illustrates a kind of "metonomy", which refers to
| |
| − | > something by using a term (often more concrete or "diagrammatic")
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| − | > to refer to something abstract. This usage is common not only in
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| − | > ordinary language, but also in the most formal of all sciences,
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| − | > mathematics. We use terms like "limit", "boundary", or "interval"
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| − | > to refer to numbers, which are the entities denoted by numerals.
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| − | > In fact, it is very rare for mathematicians to mention the
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| − | > distinction between numbers and numerals explicitly, unless
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| − | > they are talking about the actual syntax of decimal, binary,
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| − | > or other representation.
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| − | | |
| − | Let me think.
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| − | | |
| − | Metonomy = "use of the name of one thing for that of another
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| − | of which it is the attribute or with which it is associated --
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| − | as in 'lands belonging to the crown'" (Webster's).
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| − | | |
| − | Accordingly, in this figure of metonymy, the term "crown" denotes
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| − | what the term "regent" denotes by virtue of the fact that a crown
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| − | is an associate or an attribute of a regent.
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| − | | |
| − | Apparently, we have a sign relation of the following form,
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| − | in which the figure of metonymy is embodied by the triples
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| − | of the form <o, s, i> in the lower four rows of the table:
| |
| | | | |
| − | ¤~~~~~~~~~~¤~~~~~~~~~~¤~~~~~~~~~~¤
| + | FI. Factorization Issues -- Discussion |
| − | | Object | Sign | Interp |
| |
| − | ¤~~~~~~~~~~¤~~~~~~~~~~¤~~~~~~~~~~¤
| |
| − | | | | |
| |
| − | | Crown | "Crown" | "Crown" |
| |
| − | | | | |
| |
| − | | Regent | "Crown" | "Crown" |
| |
| − | | Regent | "Crown" | "Regent" |
| |
| − | | Regent | "Regent" | "Crown" |
| |
| − | | Regent | "Regent" | "Regent" |
| |
| − | ¤~~~~~~~~~~¤~~~~~~~~~~¤~~~~~~~~~~¤
| |
| | | | |
| − | This may be diagrammed as follows, with denotative arcs
| + | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| − | extending from signs to objects and with connotative arcs
| |
| − | extending from signs to interpretant signs:
| |
| | | | |
| − | Crown = o1 <----- s1 = "Crown"
| + | FI. Discussion Note 1 |
| − | / ^
| |
| − | / |
| |
| − | / |
| |
| − | / |
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| − | v v
| |
| − | Regent = o2 <----- s2 = "Regent"
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| | | | |
| − | The projection of this sign relation on its SI-space forms an
| + | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| − | equivalence relation, a "semiotic equivalence relation" (SER),
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| − | on the signs "Crown" and "Regent". However, this SER does not
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| − | constitute a "referential equivalence relation" (RER), because
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| − | the parts of the associated partition of the syntactic domain,
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| − | the union of S & I, do not faithfully represent the structure
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| − | of the object domain O.
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| | | | |
| − | > I would interpret Aristotle's use of diagrammatic terms in
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| − | > the same way I would interpret the use of the word "top"
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| − | > to refer to the most general category of the ontology:
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| − | > it refers explicitly to the place where the mark occurs
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| − | > on the paper or blackboard, by metonomy to the word instance
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| − | > written in that place, by further metonomy to the word type,
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| − | > and by further metonomy to the concept expressed by that word.
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| − | >
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| − | > In programming languages, a related term is "coercion", which
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| − | > refers to the automatic type conversion that takes place when
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| − | > necessary:
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| − | >
| |
| − | > - Integer to float: In the expression, "2 + 3.75",
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| − | > the integer value of the numeral "2" is automatically
| |
| − | > converted (or "coerced") to float.
| |
| − | >
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| − | > - Character string to numeric: In some languages,
| |
| − | > arithmetic can be performed directly on numbers that
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| − | > are represented by character strings. In "2.6 + '55'"
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| − | > the string '55' is coerced to the integer 55, which is
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| − | > then coerced to the floating-point value.
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| − | >
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| − | > Metonomy in natural language is extremely common and,
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| − | > I would say, extremely valuable in general. And I admit
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| − | > that it can sometimes cause confusion. But I would much
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| − | > rather take advantage of metonomy in what I read, write,
| |
| − | > and speak than to force myself and others to insert
| |
| − | > "conversion" operators for every change of type.
| |
| − | >
| |
| − | > Bottom line: I am willing to say "By 'top', I mean
| |
| − | > the concept expressed by the mark that occurs at the
| |
| − | > top of the type lattice." But I'm only going to say
| |
| − | > that once. From then on, I would just say "top".
| |
| − | >
| |
| − | > > ... The more pertinent question,
| |
| − | > > from the standpoint of a pragmatic theory of signs is:
| |
| − | > > "Exactly what roles does the given thing play within
| |
| − | > > a given moment (= elementary relation = triple) of
| |
| − | > > the relevant sign relation?" So, of course, signs
| |
| − | > > can be objects -- no sooner do we talk about them
| |
| − | > > than they become objects of discussion, if others
| |
| − | > > would say "potential objects" (PO's), reserving
| |
| − | > > the honorific title "object" for the PO of some
| |
| − | > > consistent style of discussion and predication.
| |
| − | >
| |
| − | > Yes, such analysis can be valuable. But once the analysis
| |
| − | > has been done, I would go back to using language the way it
| |
| − | > has always been used: take advantage of metonomy whenever
| |
| − | > it makes the expression more concise.
| |
| | | | |
| − | Sadly, until our computers get to understand the way we talk,
| |
| − | with all of these figures of speech, metaphor, metonymy, and
| |
| − | many more, somebody will have to do the dirty job of getting
| |
| − | them to grok it.
| |
| | | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| | | | |
| − | Okay, let's compare and contrast:
| + | FI. Work Area |
| | | | |
| − | o---------o---------o---------o | + | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| − | | Object | Sign | Interp |
| |
| − | o---------o---------o---------o | |
| − | | | | |
| |
| − | | crown | "crown" | "crown" |
| |
| − | | | | |
| |
| − | | regent | "crown" | "crown" |
| |
| − | | regent | "crown" | "regent"|
| |
| − | | regent | "regent"| "crown" |
| |
| − | | regent | "regent"| "regent"|
| |
| − | o---------o---------o---------o
| |
| | | | |
| − | o-----------------------------o
| |
| − | | Sign Relation L'" |
| |
| − | o---------o---------o---------o
| |
| − | | Object | Sign | Interp |
| |
| − | o---------o---------o---------o
| |
| − | | i | "i" | ... |
| |
| − | | x_1 | "i" | ... |
| |
| − | | x_2 | "i" | ... |
| |
| − | | x_3 | "i" | ... |
| |
| − | o---------o---------o---------o
| |
| − | | i | y | ... |
| |
| − | | x_1 | y | ... |
| |
| − | | x_2 | y | ... |
| |
| − | | x_3 | y | ... |
| |
| − | o---------o---------o---------o
| |
| − |
| |
| − | What's similar is this. Signs are typically used in highly
| |
| − | ambiguous, equivocal, non-deterministic ways, and there is
| |
| − | just no substitute for intelligent interpreters, humane or
| |
| − | otherwise, when it gets down to the brass syntax of trying
| |
| − | to pin down the meaning of a text. The way that metonymy
| |
| − | works is that when you hear the word "crown", not knowing
| |
| − | if it is capitalized or not, you have to decide whether
| |
| − | it literally means a crown, or whether it figuratively
| |
| − | means a regent. In the literal case, you are taking
| |
| − | the word at its word and assigning it to a semantic
| |
| − | equivalence class with other words that are used
| |
| − | to denote physical crowns. In the figurative
| |
| − | case, you are associating the word to a very
| |
| − | different sort of semantic equivalence class.
| |
| − |
| |
| − | I need to break here and think about that a while.
| |
| − |
| |
| − | Jon Awbrey
| |
| − |
| |
| − | JA: The intension (property, quality) i gets to be
| |
| − | an "object of conduct, discussion, or thought"
| |
| − | as soon as any agents (interpreters, observers)
| |
| − | start to act, to talk, or to think in some way
| |
| − | or another with regard to it.
| |
| − |
| |
| − | SR: Yes, absolutely ... this is not as yet in that graph.
| |
| − | However I did make a stab in that direction in both
| |
| − | of the mentographs:
| |
| − |
| |
| − | http://robustai.net/mentography/Tarskian3.gif and
| |
| − | http://robustai.net/mentography/AnnBobYouI.gif
| |
| − |
| |
| − | ... which shows the perdicament broken
| |
| − | into the contexts of different agents.
| |
| − |
| |
| − | JA: Later, I will build separate hierarchies for the objects
| |
| − | and for the syntactic entities (signs, interpretants).
| |
| − |
| |
| − | SR: ... looking forward to it.
| |
| − |
| |
| − | JA: I forget now, but I don't remember saying anything yet
| |
| − | about interpretants in this example. I will go check.
| |
| − |
| |
| − | SR: You probably did not, yet I cannot in good conscience
| |
| − | mentograph a sign relation leaving out one of the triads.
| |
| − |
| |
| − | SR: ... thanks for the dialogue.
| |
| − | </pre>
| |
| − |
| |
| − | ==Note 5==
| |
| − |
| |
| − | <pre>
| |
| − | JA = Jon Awbrey
| |
| − | SR = Seth Russell
| |
| − |
| |
| − | Seth,
| |
| − |
| |
| − | Let me try to come up with a more concrete version
| |
| − | that has the same structure as the present example.
| |
| − | Then I'll go back and try to answer your questions.
| |
| − |
| |
| − | JA glyphed:
| |
| − |
| |
| − | o-----------------------------o
| |
| − | | Denotative Component of L'" |
| |
| − | o--------------o--------------o
| |
| − | | Objects | Signs |
| |
| − | o--------------o--------------o
| |
| − | | |
| |
| − | | i |
| |
| − | | /|\ * |
| |
| − | | / | \ * |
| |
| − | | / | \ * |
| |
| − | | o o o >>>>>>>>>>>> y |
| |
| − | | . . . ' |
| |
| − | | . . . ' |
| |
| − | | ... ' |
| |
| − | | . ' |
| |
| − | | "i" |
| |
| − | | |
| |
| − | o-----------------------------o
| |
| − |
| |
| − | SR giffed:
| |
| − |
| |
| − | http://robustai.net/mentography/intensionExtension.gif
| |
| − |
| |
| − | The initial problem had to do with "nominal" thinking versus "real" thinking.
| |
| − |
| |
| − | A. Some maxims of nominal thinking are:
| |
| − |
| |
| − | 1. "Do not confuse a general name with the name of a general." (Goodman, I think).
| |
| − | In other words: Just because we find it useful to employ general, plural, or
| |
| − | universal terms, that does not mean that there is any such thing as a general
| |
| − | property, a plurality such as a set, a universal form or a platonic idea that
| |
| − | we are thus talking about, or thereby denoting by means of this general term.
| |
| − | In the way that folks used to talk, the practice of really believing in such
| |
| − | entities would have been criticized as "reifying an adjective" and so on.
| |
| − |
| |
| − | 2. Short versions:
| |
| − |
| |
| − | a. "Generals are mere names."
| |
| − |
| |
| − | b. "Universals are merely signs."
| |
| − |
| |
| − | B. The real thinker does not see the harm in supposing the existence of objects
| |
| − | of thought like abstractions, categories, generalities, intensions, properties,
| |
| − | qualities, universals, platonic ideas, and so on.
| |
| − |
| |
| − | Where I came in, I was trying to explore the conditions under which
| |
| − | it really does appear to be perfectly harmless to talk as if we were
| |
| − | really talking about such things, and so I picked up the classical
| |
| − | notions of "general denotation" and "plural reference", examined
| |
| − | their analogy to function application, and then observed that
| |
| − | the canonical factorization of functions permits us to invoke
| |
| − | a realm of intermediate entities without having to wring our
| |
| − | hands in ontological anxiety about it. That was Phase One.
| |
| − | Phase Two was more tentative and tenuous, trying to shove
| |
| − | these intermediate entities into one or the other or both
| |
| − | of the established domains, namely, objects and/or signs.
| |
| − | In mathematics, they usually do not bother with this,
| |
| − | but just refer to the equivalence classes explicitly.
| |
| − | Maybe that will turn out to be the best way after all.
| |
| − |
| |
| − | Let's try this:
| |
| − |
| |
| − | x_1 = cat_1
| |
| − |
| |
| − | x_2 = cat_2
| |
| − |
| |
| − | x_3 = cat_3
| |
| − |
| |
| − | Options:
| |
| − |
| |
| − | 1. y = "Cat", interpreted as denoting each item of a category.
| |
| − | This is the nominal way of interpreting general terms,
| |
| − | namely, as applying to each separate member of a group,
| |
| − | but without having to posit the group as a whole or
| |
| − | any of its qualities as separately existing entities.
| |
| − |
| |
| − | The nominal option is not to augment the sign relation,
| |
| − | but just keep trying to get by with multiple referents.
| |
| − |
| |
| − | 2. y = "Cat", interpreted as denoting a category of items.
| |
| − | Here, one is asserting that a category is an object
| |
| − | in its own right, over and above its items.
| |
| − |
| |
| − | Here, object i is a new entity like a class or a set.
| |
| − |
| |
| − | 3. y = "Catitude", interpreted as denoting a quality that is
| |
| − | possessed in common or shared by cat_1, cat_2, cat_3.
| |
| − |
| |
| − | Here, object i is a new entity like an intension or a property.
| |
| − |
| |
| − | So, in general, it can happen that a use of the string of char "Cat"
| |
| − | may denote a particular cat, a category of cats, or a catitudiosity.
| |
| − | </pre>
| |
| − |
| |
| − | ==Work Area==
| |
| − |
| |
| − | <pre>
| |
| | The word "intension" has recently come to be stressed in our discussions. | | The word "intension" has recently come to be stressed in our discussions. |
| | As I first learned this word from my reading of Leibniz, I shall take it | | As I first learned this word from my reading of Leibniz, I shall take it |
| Line 1,032: |
Line 549: |
| | analogous to the issue of where to place those other i-words, namely, "idea", | | analogous to the issue of where to place those other i-words, namely, "idea", |
| | capitalized or not, "impresssion", "intelligible concept", and "interpretant". | | capitalized or not, "impresssion", "intelligible concept", and "interpretant". |
| − | </pre>
| |
| | | | |
| − | ==Document History==
| + | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| | | | |
| − | ===Factorization Issues (Standard Upper Ontology, Nov–Dec 2000)===
| + | FI. Factorization Issues -- 2000-2001 |
| | | | |
| − | * http://suo.ieee.org/email/thrd224.html#02332
| + | SUO List |
| − | # http://suo.ieee.org/email/msg02332.html
| |
| − | # http://suo.ieee.org/email/msg02334.html
| |
| − | # http://suo.ieee.org/email/msg02338.html
| |
| − | # http://suo.ieee.org/email/msg02349.html
| |
| − | # http://suo.ieee.org/email/msg02396.html
| |
| − | # http://suo.ieee.org/email/msg02400.html
| |
| − | # http://suo.ieee.org/email/msg02430.html
| |
| − | # http://suo.ieee.org/email/msg02448.html
| |
| | | | |
| − | ===Factorization Issues (Ontology, Nov–Dec 2000)===
| + | 01. http://suo.ieee.org/email/msg02332.html |
| | + | 02. http://suo.ieee.org/email/msg02334.html |
| | + | 03. http://suo.ieee.org/email/msg02338.html |
| | + | 04. http://suo.ieee.org/email/msg02340.html |
| | + | 05. http://suo.ieee.org/email/msg02345.html |
| | + | 06. http://suo.ieee.org/email/msg02349.html |
| | + | 07. http://suo.ieee.org/email/msg02355.html |
| | + | 08. http://suo.ieee.org/email/msg02396.html |
| | + | 09. http://suo.ieee.org/email/msg02400.html |
| | + | 10. http://suo.ieee.org/email/msg02430.html |
| | + | 11. http://suo.ieee.org/email/msg02448.html |
| | + | 12. http://suo.ieee.org/email/msg04334.html |
| | + | 13. http://suo.ieee.org/email/msg04416.html |
| | + | 14. http://suo.ieee.org/email/msg07143.html |
| | + | 15. http://suo.ieee.org/email/msg07166.html |
| | + | 16. http://suo.ieee.org/email/msg07182.html |
| | + | 17. http://suo.ieee.org/email/msg07185.html |
| | + | 18. http://suo.ieee.org/email/msg07186.html |
| | | | |
| − | * http://suo.ieee.org/ontology/thrd111.html#00007
| + | Ontology List |
| − | # http://suo.ieee.org/ontology/msg00007.html
| |
| − | # http://suo.ieee.org/ontology/msg00025.html
| |
| − | # http://suo.ieee.org/ontology/msg00032.html
| |
| | | | |
| − | ===Factorization Issues (Standard Upper Ontology, Nov 2001)===
| + | 01. http://suo.ieee.org/ontology/msg00007.html |
| | + | 02. http://suo.ieee.org/ontology/msg00025.html |
| | + | 03. http://suo.ieee.org/ontology/msg00032.html |
| | + | 04. http://suo.ieee.org/ontology/msg01926.html |
| | + | 05. http://suo.ieee.org/ontology/msg02008.html |
| | + | 06. http://suo.ieee.org/ontology/msg03285.html |
| | | | |
| − | * http://suo.ieee.org/email/thrd128.html#07143
| + | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| − | # http://suo.ieee.org/email/msg07143.html
| |
| − | # http://suo.ieee.org/email/msg07166.html
| |
| − | # http://suo.ieee.org/email/msg07182.html
| |
| − | # http://suo.ieee.org/email/msg07185.html
| |
| − | # http://suo.ieee.org/email/msg07186.html
| |
| | | | |
| − | ===Factorization Issues (Inquiry, Mar 2005)===
| + | FI. Factorization Issues |
| | | | |
| − | * http://stderr.org/pipermail/inquiry/2005-March/thread.html#2495
| + | 00. http://stderr.org/pipermail/inquiry/2005-March/thread.html#2495 |
| − | # http://stderr.org/pipermail/inquiry/2005-March/002495.html
| + | 01. http://stderr.org/pipermail/inquiry/2005-March/002495.html |
| − | # http://stderr.org/pipermail/inquiry/2005-March/002496.html
| + | 02. http://stderr.org/pipermail/inquiry/2005-March/002496.html |
| | + | 03. |
| | | | |
| − | ===Factorization And Reification (Inquiry, May 2005)===
| + | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| − | | + | </pre> |
| − | * http://stderr.org/pipermail/inquiry/2005-May/thread.html#2747
| |
| − | # http://stderr.org/pipermail/inquiry/2005-May/002747.html
| |
| − | # http://stderr.org/pipermail/inquiry/2005-May/002748.html
| |
| − | # http://stderr.org/pipermail/inquiry/2005-May/002749.html
| |
| − | # http://stderr.org/pipermail/inquiry/2005-May/002751.html
| |