John Page

Yes, but how do we know for sure whether the universe is constant or not? All we can do is compare effects of the outside world on our senses and analyze the relationships between them (which is how we come to know things).

Words and other symbols are used to describe what we observe as entities, their static and dynamic attributes and relations between them. This applies to logic as well as natural language (and is not affected by interposing a machine or other device between ourselves and the efect we're observing).

Accordingly, in answer to sr's query, I conclude the axioms of logic are observations and not impervious to error.

PJPYSCO suggests the law of non-contradiction was derived. I profess ignorance as to its history, altough I remember it being mentioned as part of classical Greek logic. Anyone know?

PJPSYCO

The proof is the analysis of the concequence, read the paragraph after hypothetical 2.

As noted, it is derived. I don't care how anyone else gets to it, I derived it. You can derive it too, and thats the point. I suspect some else may have thought it up, but that doesn't mean you can't too. (noting I thought it up before I knew someone else did).

John Page

Sorry, Pjpsyco, I don't follow the proof. Consistency doesn't necessarily mean permanence and comparing things doesn't imply they're the same. Indeed, the fact that you are comparing things means that they must different in some regard (see law of identity?). Hence my assertion that the law of non-contradiction as represented in formal systems of logic is self-contradicting:

1. Natural language version: "A cannot be anything other than itself"
2. Propositional Calculus version: "~(A.~A)"
3. The latter form asserts that A exists twice, contradicting the natural language meaning.
4. Conclusion. All systems that employ representations of reality that have two or more instances of the same entity (in one statement) are subject to internal contradictions.

Note: "not A" (or "~A" in Prop Calc notation) is used a little differently in natural and logical languages. In English, not A means "something other than A" whereas in logic it can mean proposition A is negated.

I'm arguing that the underlying mechanisms of (most systems of)logic are contrary to the law of non-contradiction.

PJPSYCO

You say you don't follow my proof.

Perhaps the problem is you don't get the underlying point. The main point of the whole idea behind logic is communication. Do you understand that? Do you understand that the only premice that really matters is communication?

I will elaborate. I perceive something. I get an idea. I want to tell it to you. How do I do that? I could say something, but how do I know it won't come off as something else.

Example:
I express - I like flowers.
You hear - mkhlyghreac
Well, looks like I failed there.

So, how do we talk?
Lets try definition. I will call something by an identifier(it's definition). Defintions follow the form defintion (A) is set of things that make it up ({A}). To communicate effectively we need consistant definitions. You and I must have the same one(A=A). This is one of the places where the different definitions can come from. You could give me the wrong one, and then ours will be inconsistant.

Example:
You tell me your natural hair is black hair
Then you tell me your natural hair is blond hair
I have just obtained two unique definitions, and both can't be true, therein your hair does not have a relevant color, and I have no definition.

So, as we can see consistant definition is required for communication. You could try arguing, "but what if they aren't consistant", this however is futile since I could never obtain a grasp on your point due to its ever changing state. If that is the case you may of as well just go home, and leave all of us people who like talking to each other alone with our consitant interpersonal definitions.

Where does logic fit in to all this, you ask? Well, after obtaining consitant defintions we need to check them against each others. We use logic to obtain coherency out of people. I call you on your claim and say proove it. You have to use basic definitions that we both understand to proove it. That's logic.

So, everything is derived.
perception=>ideas=>communication=>definit ion=>coherency=>logic

So, what don't you understand now?

John Page

Hmmmmmm. In general, there is much I don't understand. Let's try and communicate.

1. You assert that definitions are constant. Maybe there are some definitions like this but most of them are, say, loose. In a dictionary, for example, you will find words defined in terms of other words, the definitions have no meaning without an external reality to define. External reality is not constant.
2. You have not picked up the issue of how identity is created. Identity is created by comparing things that are different and admitting they are sufficiently alike to be of the same type, which is then given a class label or name like "A" and this is defined in terms of other entities.
3. Thus, associated with this class label/name is an axiomatic definition. Sharing an axiomatic definition enables us to say things like "Aha, thats a ball". Please note this does not mean that all balls are identical, only that they conform to the axiom. This is likely where we start to diverge, however, because I follow with the thought: If all balls were identical we would fall foul of the law of non-contradiction.
4. I would say that to communicate effectively, the first precondition is to share a common external reality, through which we form common axiomatic definitions and can develop a language that allows us to reference things more accurately. For example, "Og, get food", and later "Og, not Big Mac again, get real food". (No sponsorship was involved in this example, it was constructed to exemplify the shifting definition of food).
5. I do agree with you that everything (in the mind?) is derived. I do agree that communication is important - its the purpose of langauge. Languages, interestingly, can themselves vary enormously even though they are referencing the same (or very similar) external realiities. Also, languages are prone to error and ambiguity in describing reality.
6. In my previous posting I had tried to pinpoint as precisely as possible, using the language and terms of logicians where appropriate, where the axioms of propositional logic fall over themselves.

Rather than get into a game of automatically gainsaying each other, please attack and attempt to prove whether the following statement is true or false.

"The Propositional Calculus representation of the law of non-contradiction "~(A.~A)" flouts the natural language definition of the same law by implying that A exists twice."

PJPSYCO

There is not two occurences.
It's just A, but it's from two perspectives.

The assumption is that our external universe is the same. Which is basically another concequence of us talking and desiring to have coherent ideas.
I'm going to use more hypotheticals, if/then cosequence statements. Noting that since we have a desired effect(coherent communication of idea) the 'then' part is more important than confirming the 'if'.

We have possibities on the state of the universe.

First is that it is independant of your mind, second that is an extention of your mind. A third possibility that it is an extention of everyones mind ocould also be possible, since we can't perceive each other without reacting with the universe this one is very questionable though, and veritably has exactly the same concequences as the independant universe if true(since your mind will change my universe as well as your own). So, the two persevable different ideas are independant universe, and dependant universe.
(Note:These are both the self centered versions, I find they make explination easier, though dependant can also be extrantraneous in source)

Now to the hypotheticals.

Hypothetical 1) independant universe
Objects are consitstant. Noting only notable differnces would exist in the temporal parts of the object which should be included in their defintions making them consitant since they should be talked about over the full time range for consistancy.

Example: A dog
(note: I'm simplifying the definition since it wil take to long for a full defintion)
Animal(living being, breaths air, etc.), has a certain characteristics based on certain gene structure(potentials for characteristists such as size, color, hair length, etc.), and temporal equations for things in the previous list applied to their change in time
That is a dog(general defintion, I was not specifying things like breed, etc.)

If this universal idea is true then concequently we will always be talking about the same thing since all things called dog are the same according to their defined characteristics.
This makes them coherent and we can talk about these things and have complete understanding by merely listing the full characteristics. No comparison is nssesary, since if you have never even seen such a thing, it can be fully defined for complete understanding.

Hypothetical 2) Dependant universe
The universe is mearly a figment of your imagination. Which makes the problem of nullifying communication, since there is nothing to communicate anything to. You made it up, and are mearly talking to yourself. Ultimately, it is also yourself that is keeping these imagination fragments that you are trying to communicate to from knowing everything you know.

So, hypothetical 1 is the best senario.

Now, we have the basis the universe is coherent(thought I never said easy) to communicate.

I can go over why time is not a problem some more in coherency if thats still a problem for you(it's most peoples problem with it).
I do not even have any idea what the tangent to any other reason why the universe is not coherent could be, what you have covered is just that you say the universe is not coherent, but not why, unless I already covered that and it was in the last derivation.

So, in the end A is the same thing as other A, it's just:
my A and your A
your A, and your other A
my A, and my other A
and combinations therein(though, I do realize that I'm not including everbody, but again for space purposes - I can expand later if you can't fathom the interaction with A).
Basically for communication purposes they should all be equal if A is an independant body(the independant body part I think we agree apon).

Perhaps the problem is with general and specific defintions, which I will elaborate on now. Dog is general, it only speaks of the dog as defined before. Poodle is more specific, and takes the general defintion and specifies those genetic characteristics. My mothers poodle is very specific and refers to the defintion with all the variables filled in(the temporal equations have exact equations in them now since they are known.
We can use your ball example as well. You say ball, I think of all things spherical whether objects or not. You say ball, I can play with , and you've limmited yourself to only objects. You say rubber ball, and I'm further limited to rubber formed into sphere's. You say my rubber ball, I named "meteorite", and I know that you are reffering to my green rubber ball with glitter in the rubber mix that's aproximately 2 inches in diameter, and when thrown becomes a projectile nearly as dangerous to breakables, as a meteorite is to planets.

That cover it?

John Page

pj:

Thanks for the effort you have put into the response. (Really, I'm not being flip).

1. You said: "There is not two occurences.
It's just A, but it's from two perspectives." Agreed.

2. I concur with your hypothesis of an "independent universe". FYI, I call it "common external reality" to avoid the issue of how you can have an observer that is independent of something that conceptually comprises all reality.

3. I never said the universe was not coherent! I do, however, agree that our minds seemingly have a difficulty making concepts of the universe coherent.

4. "So, in the end A is the same thing as other A, ..." This is where I start to have difficulties because I must reject the law of identity in order to accept this statement. Furthermore, the statement contradicts my quote of you in item 1. above.

5. I'm also having trouble with your examples of general and specific definitions. Dog is (literally) a word used to describe or notate a type of animal. We hold within us an axiomatic concept of Dog against which to test our sensory information for the presence of a Dog. The "consistent universe" allows us to share this information. However, Dog is a representation of an axiomatic concept that characterises real dogs. Internally, when we experience a Dog, we compare our sensory information with our axiomatic concepts and conclude "There is a Dog". However, there is no Dog in my head or yours - all we have is a system of abstract representations and a process for comparing them. Is this OK?

Maybe what I'm trying to say is that we should be careful when making assertions that one thing is the same as another. They can be equivalent in terms of axiomatic comparison, but not the same.

For the above reasons I remain concerned that the Propositional Calculus representation of the law of non-contradiction "~(A.~A)" flouts the natural language definition of the same law by implying that A exists twice, thus sowing the seeds for further contradictions. Truth is arrived at by a process and I don't see any process in the above, whereas "A = A" is a symbolic comparison and less troublesome to me.

Theophage

No, it doesn't, and it could very well be that you are the only person in existance who thinks that it does. I don't really like being so blunt, but there you are...

[ February 28, 2002: Message edited by: Theophage ]</p>

John Page

How come it doesn't? Be as blunt as you like but I'd be grateful for a reasoned response.

PJPSYCO

Let's just cover your little problem with your ~(A.~A). There are not two A's there is two ideas of A. They are the same A.