Identity Entails the Laws of Logic

About: Wikipedia - law of thought


Logical implication (or entailment) is a well understood logical function.  I represent the entailment in the diagram with the arrow labeled "implies".  The three boxes contain the three classical laws of logic.  I used the classical expressions for them. 

The first law is the law of identity.  It merely says that every time you talk about A, you mean the same identical thing. 

The other two formulas are variations on the afeard Law of the excluded middle.   Don't try to use logic in a situation where the Law of the excluded middle does not obtain ... in other words where it is not ... err entailed.   Identity entails it.  That's what the diagram says. For example If A might not be A, then not (not A) might not be A either.  Here is another example of where identity is failing.

In other words:  My diagram lays down a precise formula for when you can, and can not, apply the classical laws of logic.  If my diagram does not do so, then i surely want to know.

My diagram is the three laws of binary logic (see Barbara Cubed) expressed in second order logic notation showing (for the first time) the precise relationship between them.

I said that to say,  we are always in this predicament; it is the way our representations work.

Tags

  1. 3 laws
  2. item 12567
  3. logic
  4. lem
  5. notnota
  6. identical
  7. fidenity

Comments


Seth says
MR 2009-09-08 15:01:38 12567
Symbols representing things not in the real world are talking about chaos not yet become Cosmos - i.e. imaginations.
perhaps so.  But i was talking about symbols representing things in the real world.

Mark de LA says
MR 2009-09-08 13:42:00 12567
seth: ... Don't try to use logic in a situation where the Law of the excluded middle does not obtain ... in other words where it is not ... err entailed.
...?
using entails entails another word.  Identity is self sufficient.
... & so in what real world is a thing not itself or not either itself or not itself; the latter being somewhat like Crowley’s unbornedness - something you can’t really talk about? Or as CFR said once muddling about in Chaos not yet become Cosmos?

RS on un-bornness (ungeborenheit) 
  https://wn.rsarchive.org/Lectures/GA203/English/ZS4417/ZS4417_index.html?utm_source=dlvr.it&utm_medium=facebook  

Seth says
Well your right "entails" takes an object ... as in A entails B.  In my usage the object was implied.  So to restate my confusing sentence above:  Use classical logic only where identity entails it.

Now we get to your more interesting question: in what real world is a thing not itself or not either itself or not itself?   But of course we are not talking about just a "real world" here. Instead we are talking about a world of symbols (A, B, C, x ....) which is suppose to represent a real world of actual things.  The problem in such a symbol world, and we are always talking about such a world when we are talking about using logic, is that the symbol "A" may not always represent the same thing in the real world.  Obviously when that happens, an error has been made; but we fall into making those kind of errors frequently just when we over estimate how accurately we can identify the same thing when we see it again.  For example a Google news front.

Btw, the 12561 bug exists on your 2009-09-08 13:49:21 comment even though it did not contain a ending image.

C says
On a Wednesday, February 18 of 1981, a man published the following sentence:
Truth is a sentence which states a fact .
~
That works for me.
~
    Your sentences & examples are much more muddy & confused than that.
Your diagram says nothing about garbage in or out. Your link to an A & B blue dot diagram with an x etc. seems to include something traveling implying time & distance/&-or change. If you change the context of a fact (time,place,universe, etc.) between the premise & your conclusion, don't be surprised that you get garbage out. All of your presentation is not convincing that the so-called law of excluded middle is incorrect or yields bad results when logic is applied correctly to the facts.

Seth says
MR 2010-03-25 10:29:23 12567
seth 2010-03-25 08:45:10 12567
Some discussion on facebook. Let it not be said that i would ever let an oppurtunity to show my diagram go by. 
Well, logic is a garbage in - garbage out practice; getting out of it what you put into it.  If you use logic to deconfuse your language in thinking about something to the point that you actually grok exactly what you are thinking about & exactly what are the questions you are pondering about the subject then there is a possibility of a benefit, for some, in using logic.
Well, yes, my diagram is kind of saying "garbage in barbage out".  But, no, logic does not help with knowing "exactly what you are thinking about".  That is some other kind of process involved with binding of symbols and signs to what they refer to.  Logic is applied after that process yields specific absolutely referential symbols.  People who expect that logic will help them think practically, are confused.

Mark de LA says
With a changing context & a lack of specificity it is no wonder why you might be confused about logic or what comes out of it.  A point about logic: asking questions with increased specificity until you are ready to make a valid inference will get you farther.  If you throw doubt & confusion into the mix you will get them back out as your conclusion. Such is the meat of governments, lawyers & politicians !


Seth says
It's not about logic ... it's about what is NOT logic.  Hallelujah ! How to shoot somebody who outdrew you !

Mark de LA says
seth 2010-03-27 09:58:10 12567
It's not about logic ... it's about what is NOT logic.  Hallelujah ! How to shoot somebody who outdrew you !
I'm glad you mastered the art of what's not logic & then accordingly, what's not useful. See 13511 for the what it's not meme. Frankly, the song Hallelujah is one of my favorites - so many covers & versions are out there. My favorite version is on YouTube & sung by Allison Crowe. It's not the durge as Leonard Cohen sang it, but I think Crowe better understands the song.

Seth says
C 2010-03-26 13:38:32 12567
seth 2010-03-26 08:38:47 12567
Well, for example, my diagram actually describes our discussion here.  First i say "my diagram is kind of saying garbage in garbage out"; but you contradict that saying "Your diagram says nothing about garbage in or out".  In a logical system such a contradiction can not be allowed to exist.  Let us look at it more closely.  I do believe that we are referring to the same diagram, so for the symbols "my diagram" and "your diagram" we have (Ax  == Ay) and all if fine.  But for my symbol "garbage" and your symbol "garbage" we must be talking about different things.  My "garbage" refers in this context to a situation where in one instance a symbol is used to refer to one thing, but in another instance that same symbol is used to refer to something else.  So what did you mean by "garbage" such that my diagram could not refer to that?
Something much simpler, your diagram does not use the word for garbage at all. There isn't even a picture of a garbage pile/can or such. I have to assume that you say it is talking about garbage when you say so, but then we could just be talking about pelic or anything else.

Thing is we can choose what goes into the context.  I tend not to like to choose that kind of argumentative literalness.

Seth says
M 2015-10-10 10:59:20 12567
seth 2015-10-10 10:56:37 12567
yep.

what nobody seems to assert is the relationship between the laws ... not even GW.  instead everyone seems to think like: well all three laws always apply and are independent of each other ... but that is not the case where humans apply them.  So when a human is really using these laws logically, beore he uses the 2nd and 3rd law, he should first see if they have been entailed in the matter at hand by the 1st, the law of identity ... er, because in most cases they have not.
Humans who apply the laws of logic will all get the same result unless they confuse themselves by accident or on purpose as to what they are focusing on.


... which, of course, is true .

... but focuses on blaming error ... it assumes that we should always be in a situation where the law of indentiy triggers X or not X.  but, strangely enough, that is almost never the case ... especially where more than one human is conversing.  The chance that X would refer to be the same identical thing in my mind, that it does in yours, is almost minuscule. 
(if you must have it)

and i really do not know what "" means to you ... see discussion here.

Mark de LA says
Of course GW mapped them onto a cube - his version anyway. One can see the truth.

Seth says
yep.

what nobody seems to assert is the relationship between the laws ... not even GW.  instead everyone seems to think like: well all three laws always apply and are independent of each other ... but that is not the case where humans apply them.  So when a human is really using these laws logically, beore he uses the 2nd and 3rd law, he should first see if they have been entailed in the matter at hand by the 1st, the law of identity ... er, because in most cases they have not.

Seth says
M 2015-10-10 11:37:52 12567
Yep everything below the thumbs up was what I mean by confusion of what the focus is.
Nice illustration.


I am not totally sure what you are highlighting about what i said below the "". 

Don't we agree that confusion can be different things being represented in different minds (or contexts) by the same sign?  ... or all kinds of variations on that.  Our knowing that is not confusion. 

The diagram just tells us not to use binary logic when such confusion exists ... and i emphasize that is most of the time.  Out knowing that is not confusion. 

So what particular confusion did you see illustrated in your comment above?

Seth says
M 2015-10-10 13:38:10 12567
seth 2015-10-10 13:33:26 12567
M 2015-10-10 11:37:52 12567
Yep everything below the thumbs up was what I mean by confusion of what the focus is.
Nice illustration.


I am not totally sure what you are highlighting about what i said below the "". 

Don't we agree that confusion can be different things being represented in different minds (or contexts) by the same sign?  ... or all kinds of variations on that.  Our knowing that is not confusion. 

The diagram just tells us not to use binary logic when such confusion exists ... and i emphasize that is most of the time.  Out knowing that is not confusion. 

So what particular confusion did you see illustrated in your comment above?
Something IS or IS NOT is not something to dispute in the domain of logic

Well yes, perhaps it should not be disputed in the domain of classical academic logic, but this implication tell us when we can apply that logic in real life. 

Seth says
choy 2015-10-11 07:58:55 12567
choy 2015-10-10 18:34:37 12567
seth 2015-10-10 17:44:54 12567
M 2015-10-10 13:43:40 12567
Liber Legis & the occult/Thelemic domains have all kinds of shit where IS/IS NOT might be attained or questioned.


i am sure they do, perchance they are even closer to "real life" than is academic classical binary logic.
.. only if you forget to take your meds.
The challenge here is finding something that IS not what it IS.  Such would violate the meaning of the words IS & not.


No challenge at all really ... this happens all too frequently.  You are looking at this from a perspective that is not allowing you to see the point.  Every time you write a word which refers to something, and i interpret your word as referring to something that it did not mean to you, then we have a case of a thing that within our collective minds is not what it is. 

Seth says
source: mark

There is only confusion in the collective mind. There is lack of focus & confusion in an individual mind that does not use logic or becomes irrational. In reality there is no collective mind - just a collection of individual minds. To believe otherwise is to say that the library of Congress is smart. I've been there - it's just a collection of books.


Well "only" is a gross exaggeration, there is lots and lots of very precise communication going on outside of individual minds ... were it not, then there would be no civilization.  But i think that the "Tower of Babel" metaphor actually speaks of the collective confusion to which you refereed.  But don't get me wrong, I see the confusion only too poignantly ... which is why i so dearly love fidenity

I think that believing in a collective mind would require a person to "cast aside the selfie" ... not an easy thing for a person to do.

Seth says
source: mark
Too much abstract munge for me to continue here. Enjoy!
fine, its not a problem for me when your mind does not want to absorb something from my mind.  In fact it is kind of a example of what i am saying.  It is the way the ball bounces in this multi-mind universe ... my selfie would have it no other way.


Seth says
incidentally there is a grand distinction between a collection of representations, and a active processing mind.  it is not something that is easily confused, at least in my mind.

Eiammy.. says
seth 2015-10-11 10:06:12 12567
Eiammy.. 2015-10-11 09:56:37 12567
seth 2015-10-11 09:52:26 12567
source: mark
Too much abstract munge for me to continue here. Enjoy!
fine, its not a problem for me when your mind does not want to absorb something from my mind.  In fact it is kind of a example of what i am saying.  It is the way the ball bounces in this multi-mind universe ... my selfie would have it no other way.

The reflection is perfect!

FYI, i don't really know what you precisely mean there.  But who cares ... not me.

Mark de LA says
seth 2015-10-11 09:01:21 12567
incidentally there is a grand distinction between a collection of representations, and a active processing mind.  it is not something that is easily confused, at least in my mind.
The world of abstractions & the Meta-World that you seem to live in require a lot of healthy grasp of the physical world in order not to confuse it for  what is real & slide off into solipsistic selfiehood  . . Malkuth versus Yesod- the physical versus the astral.

Seth says
source: mark

Precise communication - if you can find it somewhere - is not the same thing as a mind or a collective mind. I suspect that casting aside the selfie is something you must do to disabuse yourself of the beliefs you are pushing in this regard.  The Tower of Babel mythos is about the change from one to many languages + confusion etc. My hex throw for last Friday. #4,1 .


Well precise communication is what catalyzes a mind working well ... perhaps another word for it might be "focus". 

... i say to believe it, you must cast aside your selfie, you respond that for me to disbelieve it, i must cast aside my selfie ... ahh the symmetry  ...
.

I actually like how you have described the Tower of Bable as "the change from one to many languages"  ... if you think about it, every individual has their own language ... so that totally works
  ... don't forget that "The Tower of Bable" is a myth, a saga, a story.  This confusion of which we speak is something that exists in being today.   Anybody can interpert such myths as referring to whatever works for them ... if it doesn't work in your mind, then just ignore it, no biggie. 


Seth says
M 2010-03-27 07:17:31 12567
[...]  A point about logic: asking questions with increased specificity until you are ready to make a valid inference will get you farther.  If you throw doubt & confusion into the mix you will get them back out as your conclusion. [...]

The strange thing about your apparent lack of comprehension of my formula here is that you have expressed it yourself in your quote above.  I claim you are talking about the same  phenomena described by my formula from the perspective of blaming a person for ignoring it. 

Whereas, it is my intention to call to people's awareness that we are always in this predicament ... regardless of a person intending to "get farther" or a blame a person might suffer for "their" confusion.   Rather this phenomena is built into the way our representations work.

Mark de LA says
More stuff: (ibid)


Seth says
choy 2015-10-12 14:02:05 12567
I haven often repeated the NLP motto "the meaning of your communication is the response you get" - I extend that further to say "the results of your communication is the response you get back, if any & none is a response".
To assign or judge another as if the fault lies with them to understand what you are saying is a bit arrogant & forgets about the lack of ability of you to be clear sometimes in what you are communicating-OR- perhaps what you are serving up just shows up as at the receiving end. Going round & round about my ability or want to "comprehend" you communication is a prime, juicy pile of an example of the latter.  What you value as pearls of wisdom or brilliance may be a hohum when shown to others. Know it, love it & move on is my suggestion. I do respond to less abstract.  If you want a bunch of abstract go for the Occult - Crowley painted some beauties such as: Snowdrops From a Curate's Garden


It is easy to distinguish between the meaning of a communication (to your audience, or to you) and the effect it has on you, or on your audience. 

For successful communication to happen, both ends must be willing and cooperate.

Mark de LA says
seth 2015-10-12 18:32:34 12567
choy 2015-10-12 14:02:05 12567
I haven often repeated the NLP motto "the meaning of your communication is the response you get" - I extend that further to say "the results of your communication is the response you get back, if any & none is a response".
To assign or judge another as if the fault lies with them to understand what you are saying is a bit arrogant & forgets about the lack of ability of you to be clear sometimes in what you are communicating-OR- perhaps what you are serving up just shows up as at the receiving end. Going round & round about my ability or want to "comprehend" you communication is a prime, juicy pile of an example of the latter.  What you value as pearls of wisdom or brilliance may be a hohum when shown to others. Know it, love it & move on is my suggestion. I do respond to less abstract.  If you want a bunch of abstract go for the Occult - Crowley painted some beauties such as: Snowdrops From a Curate's Garden


It is easy to distinguish between the meaning of a communication (to your audience, or to you) and the effect it has on you, or on your audience. 

For successful communication to happen, both ends must be willing and cooperate.
Yep, a 2-way street with someone driving on it.  The RWG tells us that only one driver can drive at a time. Watch out - it will prove itself soon here.


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