Not (not A) is still not A.


(The shade of A) = (The shade of B).  Here is the proof.  And here is a brain twister ... see if you can use this optical illusion to illustrate Not not A is still not A.

Tags

  1. logic
  2. context
  3. paradox
  4. notnota

Comments


Mark de LA says
The paradox is not true!  The error is in the assumption that B is not-A.  B is some not-A, not all of the not-A.  Also, if you are traveling through the Universe making distinctions & you run into a second one that is in not-A you should be aware that there are many other distinctions that are not-A & don't assume that not-B goes back to A. 


Mark de LA says
Hmmm.. I just used my ordinary senses for logic to break through the paradox - no problem. I don't have a bugaboo about formal logic. An optical illusion or any other illusion is after all not real. Why start out with one?

Seth says
M 2007-02-13 05:34:55 6044
Hmmm.. I just used my ordinary senses for logic to break through the paradox - no problem. I don't have a bugaboo about formal logic. An optical illusion or any other illusion is after all not real. Why start out with one?
Well if you actually are interested in what i am driving at you might start with (1) it has nothing to do with a paradox, (2) it is not a "bugagoo" with formal logic, (3) it is not about a optical illusion, but rather is wanting to use that illusion to illustrate the weekness of applying LEM, and (4) i have already told you that the x traveling in not A is flawed.  Should you still be interested you might start by rejecting all of those misconceptions and then reading my large paragraph above again. 

Mark de LA says
seth 2007-02-13 09:01:26 6044
M 2007-02-13 05:34:55 6044
Hmmm.. I just used my ordinary senses for logic to break through the paradox - no problem. I don't have a bugaboo about formal logic. An optical illusion or any other illusion is after all not real. Why start out with one?
Well if you actually are interested in what i am driving at you might start with (1) it has nothing to do with a paradox, (2) it is not a "bugagoo" with formal logic, (3) it is not about a optical illusion, but rather is wanting to use that illusion to illustrate the weekness of applying LEM, and (4) i have already told you that the x traveling in not A is flawed.  Should you still be interested you might start by rejecting all of those misconceptions and then reading my large paragraph above again. 
I guess I'm not interested.  I do not see any problem with LEM. I don't feel any pain about it nor see anything useful in getting rid of it. People don't think in syllogisms anyway. They don't think like computers either. Formal logic is linguistic & symbolic. It's GIGO. I have it built-in in the low-priced meat computer; no need for re-wiring.


Seth says
M 2007-02-12 11:13:17 6044
The paradox is not true!  The error is in the assumption that B is not-A.  B is some not-A, not all of the not-A.  Also, if you are traveling through the Universe making distinctions & you run into a second one that is in not-A you should be aware that there are many other distinctions that are not-A & don't assume that not-B goes back to A. 
Well i know that my example may have some flaws, you need to know how to look at it to see it for what it is. 

Thing to realize is that the law of the excluded middle (LEM) is just a rule in a mechinism that evolved over time.   Many people think this mere rule is inevitable, necessary and unbreakabel; but it is not. Oh, it is fine to consider it as such as long as you are working out academic problems of logic; but when you apply it to sort out the actual universe, you will need to consider the context of your logical symbols, the reliability of their identity, and the process with which they are bound to the real universe.   The problem is that this invented LEM rule is just too strong to work with all of that other process.  People who hold to it do not adequeatly question their conclusions, instead they will, holding LEM as sacred, draw erronious conclusions and believe them.   What they should do instead is to allow LEM's breaking to challenge the  symbolic process under way. I've been looking for a example of this and i have a gut feeling that this optical illusion might be better used to illustrate the problem than my traveling x in the world of not A. 

Seth says
M 2007-02-13 09:17:50 6044
I guess I'm not interested.  I do not see any problem with LEM. I don't feel any pain about it nor see anything useful in getting rid of it. People don't think in syllogisms anyway. They don't think like computers either. Formal logic is linguistic & symbolic. It's GIGO. I have it built-in in the low-priced meat computer; no need for re-wiring.
The problem is not with LEM, the problem is being able to sense when not to apply LEM.  Btw, what does the "it" refer to in your sentence "I have it built-in in the low-priced meat computer; no need for re-wiring."  ?

Seth says
Ask yourself this:  if you discover a situation where x cannot be A and yet x must be A, then will your meat computer suspend your belife in LEM .. or not?

Mark de LA says
seth 2007-02-13 09:24:34 6044
M 2007-02-13 09:17:50 6044
I guess I'm not interested.  I do not see any problem with LEM. I don't feel any pain about it nor see anything useful in getting rid of it. People don't think in syllogisms anyway. They don't think like computers either. Formal logic is linguistic & symbolic. It's GIGO. I have it built-in in the low-priced meat computer; no need for re-wiring.
The problem is not with LEM, the problem is being able to sense when not to apply LEM.  Btw, what does the "it" refer to in your sentence "I have it built-in in the low-priced meat computer; no need for re-wiring."  ?

IT=sense for logic = sense for language.

Mark de LA says
seth 2007-02-13 09:30:16 6044
Ask yourself this:  if you discover a situation where x cannot be A and yet x must be A, then will your meat computer suspend your belife in LEM .. or not?
My senses would tell me that that is a paradox which can't occur except in diseased minds.

Seth says
M 2007-02-13 09:32:38 6044
seth 2007-02-13 09:30:16 6044
Ask yourself this:  if you discover a situation where x cannot be A and yet x must be A, then will your meat computer suspend your belife in LEM .. or not?
My senses would tell me that that is a paradox which can't occur except in diseased minds.
Doesn't matter what you call it, matters what you do about it.  Me thinks it occurs all the time in a healthy active mind and is usually accompanies by a sensation of surprise.  Such a healthy mind will then examine the context, and identity, and binding of the symbols "x" and "A".  The problem does not really occur very often in human minds ... but it does occur cybernetic systems ... which is why we need to know when to suspend LEM in such systems.

Mark de LA says
IMHO, it's easier to see the problem if you divide your logical Universe into peanutbutter & that which is not peanutbutter. (;-))

Mark de LA says
 The problem does not really occur very often in human minds ... but it does occur cybernetic systems ... which is why we need to know when to suspend LEM in such systems.

So far you have not come up with one single concrete example that applies to the real world except a bunch of rhetorical bullshit!

Seth says
M 2007-02-13 09:41:47 6044
 So far you have not come up with one single concrete example that applies to the real world except a bunch of rhetorical bullshit!
Try the one above:  the shade of A = the shade of B,  yet the shade of A not = shade of B.

Mark de LA says
seth 2007-02-13 10:10:54 6044
M 2007-02-13 09:41:47 6044
 So far you have not come up with one single concrete example that applies to the real world except a bunch of rhetorical bullshit!
Try the one above:  the shade of A = the shade of B,  yet the shade of A not = shade of B.
It's not true as the link shows you.  It is an illusion.  You have 2 states or points of view which must qualify your logic. In one case you have the illusion condition & the other case you have reality.   Where you are confused in your mind is where the illusion is equivalent to reality for purposes of seeing your paradox. Your example is flawed.


Mark de LA says
i.e. (GIGO) start out with a paradox & you end up with a paradox. What else would you expect.

Seth says
M 2007-02-13 10:25:21 6044
seth 2007-02-13 10:10:54 6044
M 2007-02-13 09:41:47 6044
 So far you have not come up with one single concrete example that applies to the real world except a bunch of rhetorical bullshit!
Try the one above:  the shade of A = the shade of B,  yet the shade of A not = shade of B.
It's not true as the link shows you.  It is an illusion.  You have 2 states or points of view which must qualify your logic. In one case you have the illusion condition & the other case you have reality.   Where you are confused in your mind is where the illusion is equivalent to reality for purposes of seeing your paradox. Your example is flawed.
The human mind does a fair job of suspending LEM when it does not apply.  The problem is to devise cybernetic systems (automated systems) that are equally as flexible.  Consider the problem of getting useful implications out of big database like Cyc using only LEM and not providing for suspending it.  If you would give up the idea that i am confused, you might actually be able to see my point.

Mark de LA says
seth 2007-02-13 11:11:44 6044 -snip-
 Consider the problem of getting useful implications out of big database like Cyc using only LEM and not providing for suspending it.  If you would give up the idea that i am confused, you might actually be able to see my point.
Just because you are confused does not mean that the thing itself is confused. I don't understand what you are talking about regarding Cyc. If your database contains contradictions & errors then clean it up (GIGO) - don't throw away your logic.   If you are talking about the P vs NP problem (math) - that isn't solved yet.

Seth says
M 2007-02-13 11:30:56 6044
seth 2007-02-13 11:11:44 6044 -snip-
 Consider the problem of getting useful implications out of big database like Cyc using only LEM and not providing for suspending it.  If you would give up the idea that i am confused, you might actually be able to see my point.
Just because you are confused does not mean that the thing itself is confused. I don't understand what you are talking about regarding Cyc. If your database contains contradictions & errors then clean it up (GIGO) - don't throw away your logic. 
Large databases almost always contain errors and contradictions ... the larger and more inclusive, the more likely these errors will exist.  If you want to get interesting conclusions out of that database, then you must suspend LEM or your logical engine will simply grind to a halt or cycle forever. 

Mark de LA says
Well, if you can't clean up the errors in your database then you obviously have a procedural problem.  You probably should create a bot to crawl the database & find the inconsistencies & errors & then eliminate them. Otherwise confer ibid.


Seth says
M 2007-02-13 12:36:33 6044
seth 2007-02-13 12:24:02 6044
M 2007-02-13 12:18:15 6044
Well, if you can't clean up the errors in your database then you obviously have a procedural problem. 
Obviously we are talking about an application where cleaning up the db is not practical.  What a flexible logical system allows is for you to use real world collected databases and still arrive at interesting conclusions.  Given the same db, a stricter logic would fail to yield anything interesting. 
GIGO notwithstanding, you have reduced the idea to that of a search strategy for a database that has inconsistencies & contradictions.  There is no need in the outside world though to suspend logic. There are things in the outside world that also defy logic - love & suicide for example.
Well yes, "a search strategy for a database that has inconsistencies & contradictions" is close.  I have no idea what "a need to suspend logic in the outside world" means; but i am quite sure that you didn't get it from me.

Seth says
M 2007-02-13 13:58:21 6044
seth 2007-02-13 13:41:04 6044
-snip-
  I have no idea what "a need to suspend logic in the outside world" means; but i am quite sure that you didn't get it from me.
Your desire to get rid of the LEM.
sorry i dont't get that translation ... especially the term "outside world".  LEM is a rule for a mechinism that is useful at times.  You don't just "get rid of it" if you want to use that mechinism.  My only desire is to integrate into one mechinism the ability to suspend LEM when it is not working.  My desire is about when to apply LEM and when to abandon it. 

Mark de LA says
There is the physical world (the outside world) and then there is the world of our minds. The world of logic, mathematics etc is in our minds - mostly mediated by language. Language & logic add to what is so in the physical world - congruent or not. LEM is a device of our minds and language to describe the physical world & (internally, inside) logical objects. Don't confuse the inside with the outside.


Seth says
M 2007-02-14 08:10:16 6044
There is the physical world (the outside world) and then there is the world of our minds. The world of logic, mathematics etc is in our minds - mostly mediated by language. Language & logic add to what is so in the physical world - congruent or not. LEM is a device of our minds and language to describe the physical world & (internally, inside) logical objects. Don't confuse the inside with the outside.
Right, don't confuse them.  I have no problems with your description above.  LEM is a rule in our minds ... it can also be be a rule implemented inside a computing devise that is outside our mind. That is why your sentence "a need to suspend logic in the outside world" didin't make any sense to me ... the only place we can suspend logic is in our mind (inside world) and perhaps in some computing devise that is in the "outside world". 

Mark de LA says
M 2007-02-14 10:11:07 6044
Continuing this theme of the Map is not the Territory also includes programming & the mind that creates it. The correspondence between what is input & what to expect from the output happens in the minds of the designers of the machines & the programs; which may or nor correspond to anything in the real world.
i.e. GIGO extended to the electronic hardware, the software & the specs.  Hence QA still has a job.

Seth says
M 2012-10-24 10:35:07 6044
Obviously neither of us finished the Stanford Thinking Mathematically course, or did you?
https://class.coursera.org/maththink-2012-001/class/index ... the stuff about the implies operator and the <=> was very interesting but I quit after that.


I think i have a pretty good understanding of how to use the implication and entailment relations ... => ... <=> ... see this one, it is one of my favorite.

I really would have liked to finish that course but could not devote the time and focus it required.  I think you got further than i did.  Apparently they don't let you go at your own pace.  Oh well.

Mark de LA says
The part I got new out of the course on the implies operator was that the truth table is different from ordinary language & the <=> truth table has some differences as well. That was where I began to see some stuff. It was also better taught then when I had it at UCLA as abstract algebra.


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