Why is the law of non-contradiction a real law?

These tautological games, even if flawlessly proven with logic symbols, have their problems.

It’s inconsistent with how we choose to describe the physical world. You can have the premise “if the ball is in my hand” and say it can’t not be in your hand at the same time. But look at the premise. The ball is arguably not “in” your hand. It’s “on” your hand. Furthermore, it’s technically NOT on your hand, it rests on some microscopic barrier of energy particles that may not technically be your hand.

What is a hand anyway? The dermis or the electron layer? Is it merely opinion when the hand starts? So in a sense the ball could be “in the hand” and “not in the hand” depending on how you choose the perceive these variables, let alone temporal is-was illusions, and we rarely talk like this or think like this, so our tautologies involving real world examples are rife with fallacies and unknowns. You might argue that depending on how we agree to arbitrariliy define our variables, once they are defined, it holds that it can’t be and not be true simultaneously. But when variables are so hapharzardly arrived at, what good is the efficacy of non-contradiction? What good is p or not p when we might not know precisely what any p is, p including objects, words, neuronal concepts, including non-contradiction itself. Which is why, while it is sexy, it’s relegated to the same bin as causality, time, space, and other fun tools that fall short of licking God’s face.

siatd, i’ll read the big derrida essay when i have time, it doesnt seem to be challenging what i said though. Perhaps you could quote some stuff, or present your own view?

“In” and “on” can be the same, they are not contradictory terms. It could also be “at” or “with” my hand, all at once. Each has different focus (different connotations), but each is describing the same event legitimately, using similar terms and not contradicting anything.

What entity would you call your hand if it is not the effects if has? All you are doing is describing the properties of the hand.
[pedantry]it is not even microscopic btw[/pedantry]

Since the dermis has an “electron layer”, it must have both (and more besides, a lump of formless skin is not a hand).
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Or rather, the ‘real world’ context is so familiar that we dont observe when we are using its conventions. I dont see a fallacy here.

Which is why we have specific language, and get confused when we use the everyday conventions. You cant have it both ways though; if we have an agreed set of definitions, arbitrary or not, haphazard or not, we can use non-contradiction effectively to clarify our thoughts.

In any case, non-contradiction is about the form of the world, not about any given statement. It will never tell you anything about “p” (this is in the original post), and so why would it matter if you cant agree on what “p” means?

Philosophy may have binned those (though im not so sure they have), but thats only because we have either worked them out or science has taken over the discussion. Non-contradiction however, is not on same par with those things, as i have just shown, it is always the case. :smiley:

You can’t divorce the process from the premise. The ever-present premisory uncertainties brought on by physics and worsened by language have a direct relationship to the tools we use to manipulate and explore the premise statement.

In p is t and therefore p tilda f you’re suggesting that p=p, the law of identity, which is essential to non-contradiction. And a=a is highly suspect as there is no real world analog for numbers or variables and therefore every time we conceive of a variable, or it’s immediate facsimile, doppelganger or recollection taking place a nano second later to make a point, we’re constructing a new referent in our brains and a new object. To believe in a foundational real-world analog to p is faith, like believing in causality. You have demonstrated the rules to a particular game, but not a law of the universe. And don’t smile at me unless it’s in agreement. Otherwise it’s condescending, and that’s a law of the universe you can take to the bank.

Nice post Mr. Age.

Dunamis

I’m unclear here.

I dont see why. QM is a tricky subject for logic to be sure, but not a damning one i dont think. There are currently a couple of actions that would be completely unproblematic: accept that QM is rationally uninterpretable and treat it solely as a mathematical model. Or, reconcile QM to logic. Trying to reconcile logic to a subject with no stable interpretation yet seems too hasty.
As for linguistic uncertainties, this is the very issue, and not one I am convinced about.
In anycase, surely these linguistic uncertainties are about the content (the meaning) of statements, not their logical form. If so, any exploration of statementness would be unnaffected.
Is grammar per se meant to be ambiguous too?

Im not sure what the distinction is meant to be between something being true and “not-false”. But this seems fine.

Woah, wait up there. I thought “a” was a name and “x”(&co.) was a variable? Am I missing something subtler here, or is this just a different convention?

I hold there is difference between an idea and a thought. Thoughts can be repeated, shared, analysed, etc, while ideas are simply unreproducable mental events. Am I right in assuming you are opposed to this distinction? If so, why?

A variable in an argument, whatever it may be, no matter how many copies of it are made, or how many times it is referred to, remains the same because it is part of the form of the statement. All logical statements are of this kind, as they are of course, contentless, and are solely interested in expressing form.

There need not be any analogue to p, p just represents any possible statement, not a particular one I could be mistaken about.
I cannot of course demonstrate to you that any logical law is universal or even true, because i would have to use logic to do so and that would be question begging, but i can ask you practically: show me an example of something which breaks the law of non-contradiction. Your previous example held no water for me.

I’m sorry. My cheerfulness was not at your expense.

In my mind every example breaks the law of non-contradiction, because the idea of contradiction at all requires there to be an object, as case, a state of affairs, and that these are never set or certain or definable and constantly in flux. I tend to look at a “form” as nothing more than a big seething chunk of stuff, that’s right, matter, disguised as some ghostly map of relationships that never actually comes into contact with matter. But this is a disguise. Like a recipe for apple crisp, it needs to be written on something. A recipe is a piece of paper with ink on it. Nothing more. Perhaps a voice on a recording or a memory stamped electronically in a neural net. A recipe, a form, an identity can not be divorced from its physical host, which is the actual idea in its entirety and can’t be reproduced or stretched over infinity and all things like a constant.

Surely this is easily remedied with temporal quantifiers? ie. “x is the case at such and such a point in time”.

You could add in perspective quantifiers if you wanted too, but you would only need one: “from my point of view, x is the case”.

Ah, you claim you cant divorce form from content, and so are suspicious of any claims by mathematics and logic? Does this suspicion stretch so far as any abstracting process, to include all the sciences?

What’s so important about licking God’s face anyway? Maybe even God can’t lick his own face. Maybe he’s just as practical-minded as we are. Just a stranger on the bus and all that.

The law of non-contradiction is a statement about truth and falsehood, so perhaps we should talk a little about what truth is. Specifically, does truth matter? Why do I care about truth, and why do others? Once we answer these questions, we will begin to understand what truth means to flesh and blood human beings. What truth means to us practically is the matter of first importance.

Here’s an example of what I mean. Today I used the law of excluded middle. I have two green notebooks, one of which is for physics and one of which is for math. I pulled one of my green notebooks out of my backpack today, hoping it would be the math one. Alas, it was the physics one. For some mystical reason I reached into my backpack for the other green notebook, in the confidently hopeful expectation that it would be my math notebook. And my hope was rewarded as I found that the notebook I pulled out was indeed the math notebook. How can we explain my bizarre behavior? I would explain it by my confident belief in the law of excluded middle. This is the essence of the law of excluded middle. The law is true because I used it to find my math notebook, NOT the other way around! :smiley:

Truth matters because we use it; we don’t use truth because it matters. This is the spirit in which logic, science, and philosophical thought should be taken.

Oreo: You said: “You could add in perspective quantifiers if you wanted too, but you would only need one: “from my point of view, x is the case”.”

From which point of view? The one when you said “my” or the one when you said or thought “point…” etc. Besides, that state of affairs is technically a new and different one each time, because it carries in its DNA the description of time, place and, most importantly, perspective and recollection, and the object passes from one shape to the next name seamlessly, in a flux state. Even if you try to group everything, the whole of the cosmos from all point of views, you still ignore the fact that this is yet another physical idea at a certain time, i.e. “the time you cited all things at 3:00, then the time you cited all things at 3:05,” or “the time at 3:06 when you cited the time at 3:05 when you cited all things…”

For some reason we are adrift in the universe, and in a very real sense, logically speaking, we can look but we can’t touch.

This next point is addressed to both oreo and aporia, I’m not interested in licking God’s face, and I do have tremendous, unshaking faith in science, causality and identity, logic, etc. These things are rules of a game, not laws of the universe. For whatever reason I am inextricably a game piece. Logic of this kind is undoubtedly functional and useful, and for our purposes, highly reliable. I hesitate to point at universal laws, though, because it’s just plain metaphysical. There has never been a perfect triangle, anywhere, ever. Not at the level of atomic measurement. Not in the image in your mind. There have never been two identical triangles. The thing that gives triangles triangleness blurs at the edges.

When the biblical God (whom I do not believe in) was to destroy Sodom and Gomorrah, Abraham pleaded “if I can find fifty righteous people will you spare the city?” God says “fine.” Then a hilarious thing happens. The lovable jew actually talks God down to like ten, saying “well surely forty-nine would suffice. How about forty-eight? Well then why not forty-seven…”

At what point is a triangle a triangle, a number a number, an object itself, a town worthy of damnation? Just like in the story, God only knows.

Gamer, I just want to bounce off your ideas a little more:

When we say that logic “is highly reliable”, what we mean is simply “I rely heavily on logic, for I feel confident that it will not break its promises.” As Socrates noted in the Euthyphro, an object is carried because someone carries it; similarly, logic is reliable because someone relies upon it, not the other way around.

I’m not attempting to contrast my position with yours here, just emphasizing something I think is important…

“I feel confident it will not break its promise” = “I feel logic is reliable” = “Logic is reliable.” The “I” can be omitted, as it was in my post, because it’s implied in every first-person assertion.

True enough, I have to rely on memory to create a persistant identity. I dont think that’s so terrible though. Regardless of whether my identity is ACTUALLY stable, I experience that it is. You are speculating about the nature of the inexperiencable, and I think thats nonsense.

Sure the weight of causality and induction are psychological (they are not the strict ‘rules of the game’), but having a psyche myself, I’m gonna use them where appropriate.

If I can only ever experience the game, then the game IS the universe, finding its laws, is finding universal laws.

You misunderstand what understanding a perfect triangle is, at risk of sound like a platonist, the perfect triangle is a form that all other triangles emulate. These ‘rules of the game’ are contentless, and arent meant to be ‘observed’ because they are more than just experiencable events (contentful); they are in fact, a guide to the form of all experience (contentless).

Its probably nievete, but i dont see the problem in accepting it both ways round; a priori knowledge and all that.

You stated : “Regardless of whether my identity is ACTUALLY stable, I experience that it is. You are speculating about the nature of the inexperiencable, and I think thats nonsense.”

It’s not mere speculation to say that while we might EXPERIENCE a stable identity, or a stable chair, or a stable triangle, we’re actually experiencing flux, and the word “triangle” is attempting an imperfect grouping of unique moments. We EXPERIENCE causality. We EXPERIENCE identity. But we also experience science, which illuminates that causality and identity as absolutes are inconsistent to the way the universe works.

“Sure the weight of causality and induction are psychological (they are not the strict ‘rules of the game’), but having a psyche myself, I’m gonna use them where appropriate.”

So will I. This is to Aporia’s point. Having faith in identity is pragmatic.

“If I can only ever experience the game, then the game IS the universe, finding its laws, is finding universal laws.”

The reason I bother distinguishing between game and universe is because we have indispensible pragmatic game tools (time, space, causality, free will, identity, ego) that help us survive, yet they are all capable of contradicting our other ideas about the natural universe, which are many times extreme cases of logic or pure observation.

Finally, I don’t misunderstand what it means to understand a triangle. If anything, I misunderstand the moment when something begins to pass for a triangle. I also misunderstand where this perfect form you speak of resides. The usual suspects would be it resides in the brain, which is physical and bound by imperfections. My point is that the idea of “1” in your brain can not be the idea of “1” in my brain. I don’t believe in the concept of “1.” I don’t believe there is math out there, even though i experience there is clear as day. Because to me, believing in perfect ones, twos and threes, and the pure form of a triangle, is no different than believing in God.

All forms are ideas. All ideas are thoughts. All thoughts are psychological. All psychological events involve matter. All matter is in flux, undefinable and certainly induplicable in an absolute way. Ergo, forms themselves are in flux, undefinable and induplicable. Forms include one, triangle, horse and non-contradiction.

Rest assured you will not find me devoid of non-contradiction. Dunamis would probably take that to be my point all along.

this is fine and dandy.

Not the case. Without ever seeing a triangle, you could formulate one. The imperfect triangles we see are only representations of the eternal mathematical principle.

Then I’d say we interpret identity and causality wrong by taking them as ‘absolutes’. Are you saying these things are unreconcilable?

Could you give us an example of a contradiction?

They dont reside anywhere, its a silly question as we’re talking about form here, not contentful things.
Its hardwired into how our brains work, and how the universe works. If the world is a 3D model, then these principles are the vertices: invisible but utterly necessary because its these that give the world shape.

Kinda spurious connection there. :smiley:

My idea of “1” is not 1 itself, but the form of 1 placed into words, as if it had content.

Nope, forms can be represented by ideas, but this is really just relating the form to a something familiar and contentful (a particular visual representation of a triangle, “1” item).

You’re right, that was spurious. It’s different than believing in God, but shares certain similarities.

To summarize, my problem isn’t with non-contradiction, because that’s playing soundly upon the fallacious premise of identity.

You can’t use ideas like 3-D space to demonstrate how identity is a more sound concept than other concepts, including space.

Not sure why people think mathematical eternal pure forms exist, or that we’d have any access to knowing that. It’s not unlike what Hume said of causation. i haven’t found the words yet, and at the very least you’ve convinced me that I probably won’t.

Ideas of pure form or eternal lasting instructions that define things like perfect triangle…these ideas are all stand-ins for the actual thing which was never there, it is an undefined chunk of flux and beyond defining, and the ideas themselves are in flux, too. I guess I’m an extreme materialist, and I think all forms INCLUDING NUMBERS can be seen as undefinable brain events, like everything else.

Nothing is definable. There is never a point where something, including a number, (which is) a thought, and more obviously, a ball in your hand, can accurately be considered a mere “a” because in order to do this you must perfectly contain the object or concept-thought within absolute boundary points, and such boundary points are impossible. Therefore, every constituent of the phrase a=a is a babbling absurdity, a supreme delusion, and can hardly be called an eternal truth. “A” stands for absurd.

That, to my mind, relegates excluded middle and non-contradiction to the useful tool bin.

It was just an analogy. The vertices (lines) are the form of the 3D shape, but what we see is the surface, the texture on the polygons. We can only determine where the vertices are by probing the edges of the polygons.

Likewise, the form of the world is not directly visible as it is obviously not “in” the world, but by probing the edges of what we can think we can determine its form. ~(p&~p) is a good example of this.

“Exist” is the wrong word. They are not in the world, they are part of how it is arranged, its form.

I cant think of a better analagy then geometry, but try this: a house is made entirely of bricks but no particular brick contains the structure of the house. You dont have a pile of bricks, and then add something else and get a house from it. Similarly, the world is not just a pile of stuff: it has a structure that is not found in any particular part of it.

not so. the mathematical ideal of ‘triangle’ could easily exist without actual trianglish objects.
Ah, good idea: what about mathematical principles which have no object tied to them; like riemann surfaces and pi; is this just playing with ideas?

These things have very specific definitions, cos with some things, all they are is definitions for objects we could have no direct experience of.

How do you explain that consensus is reached about these brain events with extraordinarily little fuss?

Im not sure I get what you mean here.
You’re saying identity is impossible because things constantly change? Of course, such boundaries between things is in some sense arbitrary (we cant really carve nature up at the joints) but this isnt an attack on identity, just the legitimacy of naming ordinary objects. Surely, it leaves things like mathematics untouched?

Cheers!
This is extremely clarifying for me, that is to say, it clarifies where I am unclear. :smiley: Good stuff.

“You’re saying identity is impossible because things constantly change? Of course, such boundaries between things is in some sense arbitrary (we cant really carve nature up at the joints) but this isnt an attack on identity, just the legitimacy of naming ordinary objects. Surely, it leaves things like mathematics untouched?”

The boundaries are not arbitrary, they are undefined – there’s a difference. You can not select an arbitrary boundary and use it as a basis for forming a definition. You can only PRETEND to have done this because it is physically impossible to select a boundary that does what boundaries are intended to do: define the bounds of a thing. Also, adjectives are nouns. “2” might seem like an adjective, but beneath that layer is the true layer of any utterance or conception or supposed repetition of “two.” This hidden layer is the noun. All adjectives are actually nouns and every occurence of any adjective is a new noun, and it exists, physically, in your brain, and it looks different every time. It is not measured in terms of “meaning” but imprecise shape in flux. This is why a can not equal a.

This thread is looking great. Oreso, you are one of the more exceptional members to arrive recently. Just wanted to toss a compliment your way.

The mentioning of the idea of “flux.”

There is that same basic logical fallacy of self-referent that makes the concept epistemologically unsound. It turns on itself, Gamer.

According to the proposition that identity does not exist because of “flux,” and “A” must be an identity, then it would be impossible to form a notational sequence for your proposition, and you could not make it.

If “A” (identity) does not exist because of “X” (flux), then X does not exist because it is an A. There is no way to represent “flux” in a proposition, I don’t think, because whenever it is mentioned it cancels itself out- it ironically causes the very organization and stability for the proposition to occur. If “A” is not then “X” is the reason. But there is no X that is both a premise and unidentified at the same time.

Just a thought.

An easy way to understand what I mean in case it isn’t obvious.

So the proposition “Identity doesn’t exist because of flux” is:

  1. A doesn’t Y since X.

If X (flux) is true then it Y (exists) because it is an A (identity) in the 1, and therefore 1 is not possible, and not not true. That is, it isn;t even a question.

Without the 1, there is no question, and without that, no subject.

Firstly, I second Detrop’s notion that oreso is a good member. It takes tremendous character to deal with me and my nonsense without resorting to patronizing language, and he actually attempted to have me believe HE was learning something…not from me, per se, but about organizing HIS point of view, even better. A role I can be satisfied with.

Secondly, this has been, for me, simply a religious conversation. Surely I make no attempt to prove my theory logically. That would be a self-defeating task. I resort to Wittgenstein’s ladder on this…if I’m to contend what I say might be compelling to some. There can not be a more pigheaded argument than that of denying the absolute truth of non-contradiction, which is why I flung myself into it to see what would happen. (It seems oreso’s idea for a thread was so obvious, it was all that was left to do.) Also, I have long held the view that to speak is to lie, to name something is to lie, to have a thought is to lie, to acknowledge a concept as being universal is the pinnacle of human illusion, and the final frontier of oblivion. No combination of words seems to make sense to others, so for now I will rest, and contemplate Wittgenstein’s ladder…the ultimate copout, I know. But we all have our ladder, waiting for us somewhere, or we are forever riding a merry-go-round, and how logical is that?

I thank oreso for his lack of ego. In the past it’s been evident in certain members that no matter how gentlemanly one might cushion their remarks, the goal of superiority can not hide.