Some math musing re philosophy of mind

About: About: Representationalism


Let us assume ( "if we may") that X1 == X2, and Y1 == Y2,  in all contexts.

Examine the formula:
C1 { X1 r1 Y1; ... }
C2 { X2 r2 Y2; ...}
Where C1 and C2 name the contexts within the curlies and ";" separate true statements in those contexts.

Now we wish to inquire about the the copula between r1 and r2 for different perdicaments.
  1. Does r1 == r2 if C1 == C2 , err yes else we kidd ourselves. This serves to define what identical contexts are.
  2. Can r1 == r2 even if C1 =/= C2 ?
  3. Can r1 == r2 if C1 subset C2 ?
  4. Assume that there is a one-to-one correcpsondance between the statements in C1 and those in C2.
    1. Yes there are identical contexts which cannot be distinguished.
    2. ?
    3. ?

Tags

  1. math
  2. context
  3. representationalism
  4. logic
  5. ai
  6. representation

Comments


Mark de LA says
seth 2006-03-28 07:18:51 3177
M 2006-03-28 06:39:56 3177
M 2006-03-28 06:25:43 3177
you missed explaining what the r's are - presumably relationships ? My instinct tells me that unless the r's are elements of the same sets as the X's and the Y's that only the first of your bulleted statements is a true identity.
To tease it out a little more. You and I have a genetic relationship. You and I also have a relationship over the web thru FastBlogIt. The word "can" is a rather like "not <=>" (NOT "if and only if" - iff). If your thesis is that the context Ci defines the relationship then the second bullet will never be true. In the third bullet one would have to define or illustrate what a subcontext is.

Work on an exampe:

In real life {Seth interactsWith Mark; Seth doesn'tAlwaysAgreeWigh Mark; ... }
In fastblogit {Seth interactsWith Mark; Seth doesn'tAlwaysAgreeWigh Mark; ... }

So far (4,2) holds.  Add something that would break it.

Note that we are (only?) interested in cases where there is a one-to-one correspondance between true statements within the context.
Maybe the statements are true but the actual relationships are texturally different between the 2 contexts - which in my book means they are not identical.

Seth says
M 2006-03-28 06:42:24 3177
I don't see what this has to do with representationalism.
Try this ...

Assume that there is a one to one correspondance between every statement in C1 and C2.  Assume that C1 is brain processess and that C2 is the person's awareness of same.  Also note that for all cases that the Xs and Ys are assumed identical between the two contexts.  This obviously is only theoretical. 

Seth says
M 2006-03-28 06:42:24 3177
I don't see what this has to do with representationalism.
Perhaps i need to rephrase my first attempt here:

Try this ...

Assume that there is a one to one correspondance between every statement in C1 and C2.  Assume that C1 is brain processess and that C2 is the person's awarenesses caused by those brain processes.  Also note that for all cases that the Xs and Ys are assumed identical between the two contexts.  This obviously is only theoretical.

Mark de LA says
M 2006-03-28 06:25:43 3177
you missed explaining what the r's are - presumably relationships ? My instinct tells me that unless the r's are elements of the same sets as the X's and the Y's that only the first of your bulleted statements is a true identity.
To tease it out a little more. You and I have a genetic relationship. You and I also have a relationship over the web thru FastBlogIt. The word "can" is a rather like "not <=>" (NOT "if and only if" - iff). If your thesis is that the context Ci defines the relationship then the second bullet will never be true. In the third bullet one would have to define or illustrate what a subcontext is.

Seth says
M 2006-03-28 06:39:56 3177
M 2006-03-28 06:25:43 3177
you missed explaining what the r's are - presumably relationships ? My instinct tells me that unless the r's are elements of the same sets as the X's and the Y's that only the first of your bulleted statements is a true identity.
To tease it out a little more. You and I have a genetic relationship. You and I also have a relationship over the web thru FastBlogIt. The word "can" is a rather like "not <=>" (NOT "if and only if" - iff). If your thesis is that the context Ci defines the relationship then the second bullet will never be true. In the third bullet one would have to define or illustrate what a subcontext is.

Work on an exampe:

In real life {Seth interactsWith Mark; Seth doesn'tAlwaysAgreeWigh Mark; ... }
In fastblogit {Seth interactsWith Mark; Seth doesn'tAlwaysAgreeWigh Mark; ... }

So far (4,2) holds.  Add something that would break it.

Note that we are (only?) interested in cases where there is a one-to-one correspondance between true statements within the context.

Seth says
M 2006-03-28 06:55:41 3177
Actually I don't like the first bullet either. Two things can have 2 different relationships in the same context. Let's say the context is "Living in the World or the Universe" and the X's & Y's are you and I. Well, you and I have many different relationships in this context. The algebra doesn't help!

Sure:

C { X a Y; X b Y; X c Y; ......}

So what?

And yes, the a,b,c .... are relationships.

Mark de LA says
seth 2006-03-28 06:56:09 3177
M 2006-03-28 06:42:24 3177
I don't see what this has to do with representationalism.
Try this ...
Assume that there is a one to one correspondance between every statement in C1 and C2.  Assume that C1 is brain processess and that C2 is the person's awareness of same.  Also note that for all cases that the Xs and Ys are assumed identical between the two contexts.  This obviously is only theoretical. 
Who is aware of brain processes? I'm not aware of the processes of visual perception only the end results. I'm usually only aware of my brain when I have a headache!

Seth says
M 2006-03-28 07:55:00 3177
seth 2006-03-28 07:18:51 3177
M 2006-03-28 06:39:56 3177
M 2006-03-28 06:25:43 3177
you missed explaining what the r's are - presumably relationships ? My instinct tells me that unless the r's are elements of the same sets as the X's and the Y's that only the first of your bulleted statements is a true identity.
To tease it out a little more. You and I have a genetic relationship. You and I also have a relationship over the web thru FastBlogIt. The word "can" is a rather like "not <=>" (NOT "if and only if" - iff). If your thesis is that the context Ci defines the relationship then the second bullet will never be true. In the third bullet one would have to define or illustrate what a subcontext is.

Work on an exampe:

In real life {Seth interactsWith Mark; Seth doesn'tAlwaysAgreeWigh Mark; ... }
In fastblogit {Seth interactsWith Mark; Seth doesn'tAlwaysAgreeWigh Mark; ... }

So far (4,2) holds.  Add something that would break it.

Note that we are (only?) interested in cases where there is a one-to-one correspondance between true statements within the context.
Maybe the statements are true but the actual relationships are texturally different between the 2 contexts - which in my book means they are not identical.

The contexts are identical so far. The interesting thing is to make them not identical and then investigate how the (prior to that identical relationships) change.  Note the statement in the body that i will shortly change to red.  The whole point is to:  inquire about the the copula between r1 and r2 for different perdicaments.   As one adds corresponding true statements to the contexts in question how do the previsoulsy true relationships change ?

Seth says
M 2006-03-28 07:06:17 3177
seth 2006-03-28 06:56:09 3177
M 2006-03-28 06:42:24 3177
I don't see what this has to do with representationalism.
Try this ...
Assume that there is a one to one correspondance between every statement in C1 and C2.  Assume that C1 is brain processess and that C2 is the person's awareness of same.  Also note that for all cases that the Xs and Ys are assumed identical between the two contexts.  This obviously is only theoretical. 
Who is aware of brain processes? I'm not aware of the processes of visual perception only the end results. I'm usually only aware of my brain when I have a headache!

No!  We are not talking of your awareness of the brain processess.  We are talking of the brain processess as awarenesses.  Assume for a moment, if you can, that the brain processess ARE the awarenesses.

Mark de LA says
seth 2006-03-28 08:56:28 3177
M 2006-03-28 08:26:06 3177
seth 2006-03-28 08:15:39 3177
M 2006-03-28 07:58:38 3177
2006-03-28 07:35:49 3177 Assume for a moment, if you can, that the brain processess ARE the awarenesses.
Basically I am saying that I can't assume your assumption - their textures are magnificiently different.
And can you conceed that a neurologist can easily make this assumption ?   What is it about your belief structure that prevents you from making that assumption ?
I am not a neurologist nor would I conceed that a neurologist can easily make such an assumption. I say, except for the brainwashing of materialism, that most humans beings don't make that assumption. My more or less direct experience of the world doesn't even come close to the experience of some kind of electro-chemical storm going on in my neurology. My relationship to the electro-chemical storm in my neurology is one of driver & vehicle.
Yep, i kind of suspected that would be the problem for you.  Your belief in dualism and another world block this gestalt.
I am not a dualist! I am more into Zen. In your gestalt you seem to be assuming your conclusion. Anyway you are arguing against my experience which is likely to fail

Mark de LA says
uri http://dictionary.reference.com/search?q=predicament

Seth says
M 2006-03-28 08:15:13 3177
 You have two different relationships between those subjects in 2 different contexts. If the contexts are the same that does not mean the relationships are the same because two entities can have different relationships depending on the context or independent of the context.

You have a point here.  There must be some thing that establishes the correcpondance between the statements in the different contexts. Perhaps a uber-context.  That is the week part of the algebra.

A context does not determine a relationship
I disagree.  If you start out with a blank context and utter {Seth grunt Mark} and then keep adding statements some of which also have grunts in them, eventually the grunts will start to mean something.   Consequently the context determined the meaning of the grunt.  Using those same grunts in a diffeent context will make the grunts mean something entirely different even if the grunts are the same identical sound pattern.


Mark de LA says
seth 2006-03-28 07:55:20 3177
M 2006-03-28 07:09:59 3177
seth 2006-03-28 07:02:41 3177
M 2006-03-28 06:55:41 3177
Actually I don't like the first bullet either. Two things can have 2 different relationships in the same context. Let's say the context is "Living in the World or the Universe" and the X's & Y's are you and I. Well, you and I have many different relationships in this context. The algebra doesn't help!

Sure:

C { X a Y; X b Y; X c Y; ......}

So what?  - The first bullet is true if and only if  a==b==c

And yes, the a,b,c .... are relationships.
I can't figure out what you are getting at here.  "The first bullet is true if and only if  a==b==c is not even defined in my example because i just listed one context. 
Well your algebra is somewhat specious. In point one (which changed from bullet one during the discussion) you have two entities identical in all contexts which means to me that they are the named subjects you are talking about no matter what context. You have two different relationships between those subjects in 2 different contexts. If the contexts are the same that does not mean the relationships are the same because two entities can have different relationships depending on the context or independent of the context. A context does not determine a relationship nor is a context "the" relationship. From one ontology I get that there are distinctions & contexts & contexts are distinctions. A particular relationship may show up differently in different contexts. But, the context is NOT the distinction unless you are talking about a context.

Seth says
M 2006-03-28 07:58:38 3177
2006-03-28 07:35:49 3177 Assume for a moment, if you can, that the brain processess ARE the awarenesses.
Basically I am saying that I can't assume your assumption - their textures are magnificiently different.
And can you conceed that a neurologist can easily make this assumption ?   What is it about your belief structure that prevents you from making that assumption ?

Mark de LA says
seth 2006-03-28 08:03:22 3177
M 2006-03-28 07:55:00 3177
seth 2006-03-28 07:18:51 3177
M 2006-03-28 06:39:56 3177
M 2006-03-28 06:25:43 3177
you missed explaining what the r's are - presumably relationships ? My instinct tells me that unless the r's are elements of the same sets as the X's and the Y's that only the first of your bulleted statements is a true identity.
To tease it out a little more. You and I have a genetic relationship. You and I also have a relationship over the web thru FastBlogIt. The word "can" is a rather like "not <=>" (NOT "if and only if" - iff). If your thesis is that the context Ci defines the relationship then the second bullet will never be true. In the third bullet one would have to define or illustrate what a subcontext is.

Work on an exampe:

In real life {Seth interactsWith Mark; Seth doesn'tAlwaysAgreeWigh Mark; ... }
In fastblogit {Seth interactsWith Mark; Seth doesn'tAlwaysAgreeWigh Mark; ... }

So far (4,2) holds.  Add something that would break it.

Note that we are (only?) interested in cases where there is a one-to-one correspondance between true statements within the context.
Maybe the statements are true but the actual relationships are texturally different between the 2 contexts - which in my book means they are not identical.

The contexts are identical so far. The interesting thing is to make them not identical and then investigate how the (prior to that identical relationships) change.  Note the statement in the body that i will shortly change to red.  The whole point is to:  inquire about the the copula between r1 and r2 for different perdicaments.   As one adds corresponding true statements to the contexts in question how do the previsoulsy true relationships change ?
Too many pronouns in this one. I think you went into outer space.

Seth says
M 2006-03-28 08:26:06 3177
seth 2006-03-28 08:15:39 3177
M 2006-03-28 07:58:38 3177
2006-03-28 07:35:49 3177 Assume for a moment, if you can, that the brain processess ARE the awarenesses.
Basically I am saying that I can't assume your assumption - their textures are magnificiently different.
And can you conceed that a neurologist can easily make this assumption ?   What is it about your belief structure that prevents you from making that assumption ?
I am not a neurologist nor would I conceed that a neurologist can easily make such an assumption. I say, except for the brainwashing of materialism, that most humans beings don't make that assumption. My more or less direct experience of the world doesn't even come close to the experience of some kind of electro-chemical storm going on in my neurology. My relationship to the electro-chemical storm in my neurology is one of driver & vehicle.
Yep, i kind of suspected that would be the problem for you.  Your belief in dualism and another world block this gestalt.

Mark de LA says
If you have 2 contexts R & L.  R is what we will call Reality & L is what we call Language.  When Language agrees with Reality in your gestalt we have what I call T or TRUTH ! 


Mark de LA says
Incidentally what you have said above works well with context being a collection  ... but you seem not to want to pin that down.  Instead you seem to want to keep that a mystery.  Well that is fine, but then forget about the mathmatics of context ... try to work through it in some cloud of mystery where whatever cannot be made objective must be taken on faith or imagination.
I said a lot above & wonder what your sudden explosion of pronouns refer to. It would help if you define what you mean by an extensional set. Here are the last few meanings of extensional in an online dictionary :
  1. Logic. The class of objects designated by a specific term or concept; denotation.
  2. Mathematics. A set that includes a given and similar set as a subset.
I tend to think in terms of things like number, measure, weight etc. the things in the Categories of Aristotle .  Anything else needs some definition and agreement betwixt you & I. To make a set or collection of disparate items and say context is one of them doesn't make what you are talking about any clearer. Context tends to change the meaning of something linguistic or something ontological.  If you look at something in two different ways, one from one context and one from another - they may look different. A relationship between two different things may look different in two different contexts. Language assists in your looking and the metamorphosis of your attention while you are looking. ...

Seth says
M 2006-03-28 11:10:07 3177
I use context to provide the meaning for distinctions. In an ontology class discussion the difference provided for what might be called a bed in one context is not a bed in another.  Please refer to the description of Odysseus' bed (see the description in Wikipedia) . In one context it is a bed and in another it is a large tree stump. Objective reality is a context which provides that my existence & being is accompanied outside by something else & is not just my personal mind experence.   Context in the context of language provides a bit of resolution to ambiguities. 

We need to have some mechinism to cut through the misunderstandings that crop up when you use natural language.  The word "context" is subject to those misunderstandings; so it is useless for these purposes. But the concept of a collection (substitute set if you like) is more useful.  So we define a context as a set.  It is more convenient to use linguistic statements than the real thing just because we cannot collect the real things.  It is understood, however, that the linguistic statements represent or stand in the linguistic collection for the real things which stand in the real collection. 

See you can (and did) come back to me saying, "well context means this or that to me" ... and i would have to retort "but context means that and this go me" ... and so it goes around and around.  But if we talk about extensional sets of things instead, then once we agree on what elements are in the set, we at least have an agreement on the terms of our mechinism. 

Incidentally what you have said above works well with context being a collection  ... but you seem not to want to pin that down.  Instead you seem to want to keep that a mystery.  Well that is fine, but then forget about the mathmatics of context ... try to work through it in some cloud of mystery where whatever cannot be made objective must be taken on faith or imagination.

Seth says
M 2006-03-28 09:17:36 3177
seth 2006-03-28 08:30:07 3177
M 2006-03-28 08:15:13 3177
 You have two different relationships between those subjects in 2 different contexts. If the contexts are the same that does not mean the relationships are the same because two entities can have different relationships depending on the context or independent of the context.

You have a point here.  There must be some thing that establishes the correcpondance between the statements in the different contexts. Perhaps a uber-context.  That is the week part of the algebra.

A context does not determine a relationship
I disagree.  If you start out with a blank context and utter {Seth grunt Mark} and then keep adding statements some of which also have grunts in them, eventually the grunts will start to mean something.   Consequently the context determined the meaning of the grunt.  Using those same grunts in a diffeent context will make the grunts mean something entirely different even if the grunts are the same identical sound pattern.
While some don't make this distinction I can & do make a distinction between language and what language is talking about. This is part of your confusion about context. I think you accurately describe the process of language & semantics but these latter things are not what they are attached to.  In other words all the language & semantics about an apple is not in fact an apple.

Look this is just algebra.  It is not interesting to observe that: although F=M * A describes the dynamics of a situation, it is not that situation.  We know that.  The point of the algebra is to have some normative way to talk about things rather than by using natural language words which, as you can see, change their interpertation according to which person is using them.  If you cannot make the assumptions of the formula, then you are simply not playing the game.  Which, of course, is ok.  Once you get the algebra to the point (which has not happend yet) where it says something within the assumptions stated, then you can go back and fiddle with the assumptions and see how what the algebra says changes. 

Seth says
M 2006-03-28 09:49:29 3177
Well, whether I participate or not, you have to be consistent in what your algebra represents if you want to persuade others to use your algebra or see your point. It seems to be a mashup of set algebra with language & some of your private theories. If you consistently used set algebra I would probably see it's flaws.  If you consistently used mentography I would likewise probably be able to see them. Right now seem to reign. One thing that is very confusing is that you use the word context in a different way than I use it.
context Look up context at Dictionary.com1432, from L. contextus "a joining together," orig. pp. of contexere "to weave together," from com- "together" + textere "to weave" (see texture)I use the word more in alignment with meaning #2 in this dictionary definition .

I'm using "context"  in the traditon of the pioneering AI work by Gupta and McCarthy ... when i get a chance i'll post some references.  In that tradition context is a collection of linguistic statements.  One can ask who collected them and from where the collection was made, but those are just variables into your inquiry.

Seth says
I think we covered the extensional nature of a set already in extensional.

Seth says
source:  M above
To make a set or collection of disparate items and say context is one of them doesn't make what you are talking about any clearer. 
Nor is that what I am suggesting.  For this to match your natural understanding of context the process of collection has to be a real one; for example: the collection of that includes this item and all the comments on this item.  That collection which was created in the real world by you and I creates a real context.  It is not just a collection of "disparate items".
source: M above
Context tends to change the meaning of something linguistic or something ontological.  If you look at something in two different ways, one from one context and one from another - they may look different. A relationship between two different things may look different in two different contexts. Language assists in your looking and the metamorphosis of your attention while you are looking. ... 
I have no troubles with any of that.  That is a pretty good summary of what i would call our common sense knowledge about context.



Mark de LA says
M 2006-03-29 05:59:46 3177
seth 2006-03-29 05:47:19 3177
I think we covered the extensional nature of a set already in extensional.
Seems to make context into what you have which pretty much makes context an empty word.
I mean like it's zen, but so what ?

Mark de LA says
The length & nesting on this item suggests a need for something creative in the way of inter-relating comments like 2952. I couldn't figure out the data structure on that item just zooming to place comments & pictures & new stuff at a specific level unless I keep track of the zoom level and the attention coordinates. Maybe we could talk about that somewhere else. 


See Also

  1. Thought Socrates Cafe Question: Should presidents tweet? with 312 viewings related by tag "context".
  2. Thought There is no intrinsic meaning in signs. with 288 viewings related by tag "context".
  3. Thought A plate of grapefruit with 219 viewings related by tag "representation".
  4. Thought Thinking Domain Math with 203 viewings related by tag "math".
  5. Thought About Seth with 194 viewings related by tag "representation".
  6. Thought Conversation on hash tags? with 111 viewings related by tag "logic".
  7. Thought new days with 108 viewings related by tag "context".
  8. Thought Tools in my peculair bag ... with 101 viewings related by tag "representation".
  9. Thought 3 state logic with 86 viewings related by tag "logic".
  10. Thought Why we represent ... with 85 viewings related by tag "representation".
  11. Thought BARBARA CUBED - The Manual of Pure Logic with 83 viewings related by tag "logic".
  12. Thought Are you introducing a non-existant term? with 63 viewings related by tag "representation".
  13. Thought Thoughts are connected in context, or they are not apprehended. with 60 viewings related by tag "context".
  14. Thought Representation and Representing with 55 viewings related by tag "representation".
  15. Thought Fascinating piece on Internet with 53 viewings related by tag "ai".
  16. Thought Another girl for my nightstand ... with 52 viewings related by tag "ai".
  17. Thought Context and Juice with 46 viewings related by tag "context".
  18. Thought Representing something changes my awareness of it with 42 viewings related by tag "representation".
  19. Thought The binary logic of two distinctions with 34 viewings related by tag "logic".
  20. Thought List of Logical Fallacies with 32 viewings related by tag "logic".
  21. Thought Listening with 32 viewings related by tag "context".
  22. Thought about: Tutorvista.com - Online Tutoring, Homework Help in Math, Science & English By Expert Tutors with 31 viewings related by tag "ai".
  23. Thought Have you ever wondered .. with 29 viewings related by tag "ai".
  24. Thought Representation all the way down with 28 viewings related by tag "representation".
  25. Thought Email Chatbots with SparkPost with 25 viewings related by tag "ai".
  26. Thought zodiac with 21 viewings related by tag "context".
  27. Thought Identity Entails Logic with 20 viewings related by tag "logic".
  28. Thought Other Math Curiosities with 19 viewings related by tag "math".
  29. Thought General overview article ... with 17 viewings related by tag "ai".
  30. Thought What is Cybermind ? with 15 viewings related by tag "ai".
  31. Thought about: Intel Launches Movidius Neural Compute Stick: Deep Learning and AI on a $79 USB Stick with 14 viewings related by tag "ai".
  32. Thought Death of an idea ... with 13 viewings related by tag "context".
  33. Thought [title (23165)] with 12 viewings related by tag "ai".
  34. Thought about: research blog: inceptionism: going deeper into neural networks with 10 viewings related by tag "ai".
  35. Thought Context is King with 10 viewings related by tag "context".
  36. Thought Identity Entails the Laws of Logic with 9 viewings related by tag "logic".
  37. Thought Example of online tutoring by computer circa 2015 with 8 viewings related by tag "ai".
  38. Thought The Rise of Gobbledygook. with 7 viewings related by tag "logic".
  39. Thought about: transcendence (2014) - imdb with 6 viewings related by tag "ai".
  40. Thought about: Semantic Scholar - An academic search engine for scientific articles with 6 viewings related by tag "ai".
  41. Thought about: Thinking Domains as Assistive Technology - comment 61170 with 6 viewings related by tag "ai".
  42. Thought Awareness, Attention is the function of the Ego with 5 viewings related by tag "representation".
  43. Thought Life is boring repitition ... with 5 viewings related by tag "ai".
  44. Thought Context with 5 viewings related by tag "context".
  45. Thought about: A Son’s Race to Give His Dying Father Artificial Immortality with 5 viewings related by tag "ai".
  46. Thought The Ten Commandments of Logic with 4 viewings related by tag "logic".
  47. Thought about: GW Document: Spring - #57 with 4 viewings related by tag "logic".
  48. Thought Good Girl with 4 viewings related by tag "ai".
  49. Thought Quads with 3 viewings related by tag "context".
  50. Thought Waiting for fireworks at Ruston Freedom Celebration with a new "live camera" with 3 viewings related by tag "representation".