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Fun With Metalogic

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Posted by Harvey on April 17, 2002 15:42:41 UTC

Hi Alan,

***(Note: Any argument you bring I'm aware might be not necessarily your own view but a representation of a particular logician's view; regardless I reply to the argument itself- I do not constrain you to actually holding to whatever logic you try out here!)***

I hold to the notion that we don't have ontological knowledge of these matters, but I believe 'logic' at least of some form is a requirement to exist. Logic would be the rules or absence of rules that happens if you take a Big Ice Cream Scooper, and scoop all material stuff. What those rules or non-rules are, I cannot begin to tell you. It seems reasonable (to me) that some form of similarity to classical logic describes those rules or non-rules.

***Now, some of your arguments appeal to the idea of regarding something as "a formal system". But appealing to that idea already involves APPLYING the Law Of Non-contradiction. You would not have either "formality", or "system", if everything "kept contradicting" - I use quotation marks because I strictly cannot describe such a concept- violation of LNC is so impossible it cannot be described or conceived.***

You are referring to metalogic (the logic of logic). How can we know logic unless we use logic to know it. It sounds either recursive or circular. Well, we need to establish a sequence to what is occurring:

1) We are 'here' and we naturally find ourselves making decisions and observations about nature.
2) We assume that nature follows certain rules that we can somehow manage to make predictions and gain confidence in our ability to understand it. We make this assumption because of all the success we experience by anticipating these assumed rules. This confidence only occurs if we limit our thoughts along a certain line of thought.
3) By analyzing these rules we notice that they flow from certain basic rules which are primitive.
4) We label these primitive rules the axioms of logic, along with what we call rules of inference. We add enough syntax, symbols, and definitions (both defined and undefined) and we conceive of these rules as a formal system. One of the axioms is the LNC.
5) Someone by the names of Harv and Alan come along and discuss the above situation. Harv says that (4) is not the only axioms that we can accept to approximate nature, there may be others that replace key axioms (e.g., LNC) that are actually better at describing (2) and our (4) may just be a human approximation of what (2) really is.
6) Alan says that we need to have the rules of (3) to be able to deduce (4). Therefore Harv is wrong that (4) is not required since any alternative that we can conceive to (4) would still require (3) which is why we have (4) in the first place.

If the above is correctly stated, then I think you can see what is wrong with (6). We don't know what the rules of (2) really are since we are assuming there are rules in the first place according to (2). This is the problem. Whenever we start analyzing these rules in (3), we cannot assume that we can arrive at the ultimately correct rules of (2). We know this because of our experience with (2) (i.e., we can never achieve any high confidence about the flow of nature when making poor assumptions - we have low confidence because poor assumptions lead to unsuccessful events). Hence, the reasoning of (6) is invalid since it depends on (3), but (3) depends on (2) and (2) tells us that all of our assumed rules are based on human success (i.e., pragmatism).

So, Alan, using as your metalogic the rules of classical logic (including LNC) is not valid reasoning. Even metalogic would come from pragmatic success with nature, and this by itself does not tell us what the 'logic' of reality really is. It is all based on assumptions of success, but as (2) also teaches us, assumptions can be wrong.

***I hold that by its very nature, the conceptual framework of honesty (paying attention to Existence) is unlimited; the only limit is our very being (created by Existence). That is: we ARE the limit.***

You based this on (2). But, this is all based on pragmatic success. From a biological perspective, it is in our genes which accrued from billions of years of pragmatic success that our ancestors experienced in their survival and competition with other species.

***We can know the ultimate reality. To know thyself, is to know the Existence of one-self ; to detect Existence through one's own Existence. In other words, in Heaven you will meet "YOU"; and be aware of "God (Existence) creates You".***

You are basing all of these assumptions on the successes that you experience when you are rewarded with food, love, warmth, etc. These 'rewards' teach you through association that if you think along these lines (i.e., classical logic) then you will be rewarded. That's not enough to say what nature is really like beyond our ability to observe it.

***What really exists is not determined by logic; it IS logic.***

Commonsense logic is merely pragmatic logic. However, our experience with nature is very limited. Not nearly enough to generalize our pragmatic logic to the whole of reality.

***What really exists is the logic of existence. This is not circular, there are no more powerful grounds to which you can appeal than this.***

The 'logic' of existence may not equate to our pragmatic logic.

***Even "freedom" has to exist to be real freedom. And on existing, an item has freedom (If a cat didn't exist, it would not have the freedom of being "cat" and doing "cat stuff".)***

It sounds like you own a cat. I prefer dogs.

***Of course if I said the ultimate reality of a thing is the ultimate reality of a thing; I didn't say anything new. There is a false assumption that one can always say "this" is "that".***

All we can work with is the pragmatic logic that got us to the point of a formal system, and from there we start to play with the axioms to see where it takes us. The interesting aspect of doing so is that we can begin to conceive of a fundamental reality which is substantially different from our own.

***But ultimately you run out of "that"s. Things just ARE. That is why you cannot treat LNC as just another axiom system. You have to apply LNC to address the issue at all. It permeates everything.***

Once you come to the point of playing with the axioms of formal systems, we can see that LNC may not be necessarily the ultimate logic of (2).

***English language doesn't constrain the nature of the Universe; but Existence does. Because Existence is freedom-constraint; to BE is to have a boundary that gives a freedom.***

In other words, to get rewards we end up with a logic about the world that experience, and that logic limits the world that is experiencable. What if the world disagrees? Do we send in the Marines?

***Your example of "Do you have?" and "Do you not have?" questions are about two categories, two perspectives. There is no contradiction; just a distinction not being made. They say in philosophy: when you meet a contradiction, make a distinction.***

The point is that the answers are opposed to each other and all we did was change the question from a positive to a negative state. This is how we define a contradiction (not P). If not P questions get different answers than P questions, then we should think that LNC is violated.

***When you change the question from "What prevents something existing and not existing?" to what prevents a correct answer of something existing being correctly answered with something not existing?" you have completely changed the issue.***

I don't know what you mean.

***Ontologically, LNC is absolute. But DESCRIPTIVELY, that is in terms of making "models", of course you can get pseudo-contradictory answers wherever the modelling confuses DIFFERENT aspects of the one entity. The "contradiction" appears in the error-margin, in the generalisation, in the multiple-category or multiple-perspective inherent in the generalisation modelling upon which the questions are based.***

As you can see from above, we humans think based on pragmatic success, so that is where our logic ultimately comes from. It also shows that if it originates from pragmatic success, then it is limited to our experience of nature. Since our experience of nature is very limited to this planet at this point in history, we cannot with extreme confidence generalize this experience (or logic of our experience) to things far beyond, and even more so when we talk about a world where we have absolutely no experience (e.g., the foundation of reality).

***The LNC is not JUST one axiom among many. Without it, you can have no axioms. It is far more than an "axiom". You cannot raise "axiom" as a higher power than LNC. All the power comes from LNC.***

I don't think you have demonstrated why the LNC holds this priveledged role. Personally, I think Identity and the Law of the Excluded Middle (LEM) are more difficult to do without than the LNC.

***If "those logicians" claim they can deny LNC, they are kidding themselves. As I said, they can never refute my refutation; because they cannot appeal that I am contradicting myself. And anything they say can be contradicted; so they are so easy to refute. Yet they can just contradict that, and so avoid refutation. So they are left alone chasing their tails in delusion!***

There are wrong answers using the paralogics that these logicians create. The issue is what are those rules and how do they manage their paraconsistency that comes with denying the LNC. That doesn't make it incorrect, it merely means that such logics begin to depart from our experiences. But, as I've said, maybe our experiences of logic are just approximations of some 'logic' that doesn't involve the LNC. Perhaps there's another axiom such as the LANC (the law of approximately no contradiction, etc).

***Identity is a myth. There is no such thing as identity. Things ARE. They are not things. They just ARE. "Identity" talk is "double defining". Note the quote: "When you mean "yes", say "yes"; when you mean "no", say "no"; all else comes from the evil one". (Quote goes something like that).***

Oh Alan, are you always so dramatic? I think it is interesting that you deny the axiom of identity but cannot do away with LNC. In any case, when you say 'things ARE' you should finish the sentence. Things are what? This is an incomplete sentence. When I say 'reality is', I mean that reality is what it happens to be - itself (identity). There is nothing more fundamental in our understanding of logic than the identity tautology. Something is itself means that it is identical with itself. What do you mean by 'things ARE'?

***Since "identity logic" is a myth, Liebniz's law collapses into the field of pattern-matching of partially differentiated patterns. Whole patterns do not have identity; they ARE. To say they are themselves is double defining.***

Liebniz's principle may not necessarily follow from identity. There have been many arguments against it. I believe the main issue is whether there exists a language which can exactly identify something so that it can be indistinguishable from something else. I tend to agree with this principle for the most part.

***I am not using the formal system to prove the case (I know what is wrong with that). I'm saying that "proof" as Aurino noted, is created by LNC. The assumption that something "must be proved" ceases to apply with LNC; LNC IS proof itself. If you ask for proof of "proof" itself, "proof" is your answer.***

Proof is a term used in a formal system that are derived from unproven axioms. You can't have proof if you don't have a formal system without unproven axioms.

***The formal system you describe that has a "obtains" bucket standing in as an "is true" bucket, is clearly a logic of approximation. It still invokes LNC; but allows pseudo-contradictions because it bundles together different categories and perspectives as singular.***

No, it merely allows the bucket 'is true' to include answers that are contradictory.

***A formal system based on "choice" also contains numerous pseudo-contradictions without difficulty (e.g. you cannot make all possible moves at a given state of play on a Chess board within the rules; only one move is allowed.***

Well, that would be your's and my experience, but we aren't talking about our experience but rather the logic that is 'out there'.

***The virtual moves however do not contradict: they are in the category: virtual. Devising a logic that muddles the distinction between virtual moves and real moves would be a logic of multiplicity-of-perspectives; contradictions between "real/virtual" moves are solved by re-distinguishing their "real" and "virtual" components. Waves are like virtual moves, particles are like real moves.***

You are speaking entirely within the framework of your experience. This is far more limited than what is 'out there'. You are extrapolating on the known to the unknown and are saying what must be the case.

***When you conserve a pattern of any kind, you appeal to LNC even if not stated. To state "snow is white and grey" a second time is to conserve this pattern (and require it hasn't changed into some contradictory pattern already when you next viewed it). In fact, to even deal with it once, requires that it doesn't keep switching into something else.***

These are all attempts to limit what is 'out there' to your experience. You can't limit reality.

***Of course, if it is a pattern of options; what is conserved is whatever has those options. Or in Dick's generalised system; what is conserved is Existence itself- that something (unknown) IS.***

Is what? It is itself! When I use that phrase I mean to say that there is no language which perfectly describes the contents of reality. Rather, language fails, and the only thing that can be said is that reality has an identity with itself. Nothing else can be said.

On the other hand, you've denied identity, you've said that existence is limited by logic (language), so I'm not sure what you think reality is, exactly. Reality is Alan's view of logic? I think that is the answer that I am hearing here.

***Saying that P and not-P are not necessarily false is saying that they are not necessarily singular. That they might be a muddling of categories. This does not deny LNC; it is a pseudo-evasion of LNC. P and not-P is, because of LNC, a generality and not specific. Specific P: IS.***

As I mentioned, the answers to the polar opposite of each question might be a contradiction to what was expected. These aren't separate categorical questions. It is not like asking if someone is tall and fat. It is like asking are they tall and not-tall. The answer is not a different category, but a contradiction of the same category (I consider the polar opposite question to be the same category, e.g., tall and not-tall).

***People who misleadingly label LNC as an axiom like "law of bivalence" are being rather silly; anyone can pseudo-dodge LNC by talking in generalisations and muddling distinctions.***

Oh my gosh. Whenever you state a reason for something being illogical, you must have some original premise that is occuring in your head. The premises of logic are called axioms and all of classical logic can be derived from them. Why is that silly? It makes good sense to state your assumptions.

***BEING is what makes formal systems possible; ultimately everything is reality; whether formal systems are allegedly concerned with reality or not; they EXIST as thoughts etc. and the LNC transcends them and cannot be overruled by them.***

You have a knack for saying the obvious. Of course if there was no earth, people, universe, etc, then there wouldn't be any human formal systems. You also take very dogmatic stances. The LNC is right, because you need the LNC to have successful thoughts of the world? I don't consider that enough of a reason to accept it.

Warm regards, Harv

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