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More Fun With Meta-metalogic

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Posted by Harvey on April 21, 2002 21:01:01 UTC


I brought this reply to the top so that we can stay current. I'm replying to your post to mine ("Fun with Metalogic").

***Hi, just a few very quick coments now; I have to delay replies to cut costs (it's getting too expensive to participate- I have no problem dealing precisely with the debate though).***

Either you are stark poor, or you live in another country where internet costs are much more. However, I'm assuming you are an American or Canadian. If so, then why are you spending so much for internet access?

***H: "(1) We are 'here' and we naturally find ourselves making decisions and observations about nature." A: Already you have introduced LNC by default. "We are" requires "We are" cannot contradict and become 'zero'.***

Not necessarily. I could hold that "We are" questions have a different answer than "We are not" questions (and thereby use reasoning that is not dependent on the LNC). In the case of (1) with "We are not 'here'" means that (2)-(4) do not follow, but I can rule out that line of reasoning since any thoughts about us really not being 'here' doesn't affect the answer of (1)-(4).

In any case, you have now jumped to meta-metalogic? That is, you have added (0) as follows:

0) Any metalogic reasoning necessarily involves the axioms of classical logic - specifically the LNC. Therefore pragmatic explanations for logic and the LNC are invalid.

But, how do you know that your reasoning for (0) did not come from pragmatic experiences? If we happened to experience the wave/particle duality on a day to day basis, then the LNC would not be part of our logic. Even if our classical sense of logical reasoning is a priori required (i.e., beyond pragmatic experience), you cannot show that reality is ultimately like that.

Obviously if you jump to metalogic when discussing the rules of logic, and meta-metalogic, when discussing the rules of metalogic (which indicates pragmatic explanations), then this explanation that limits meta-metalogic will mean that you will jump to meta-meta-metalogic and so on. The point, though, is that in order to defend your thesis you must keep jumping to another metalevel in order to keep your viewpoint from running into logical problems at the current metalevel. As you stated in your ending sentence: "[a]ctually this dawns on me as a very serious finding: that the very power to deny LNC is granted by LNC", which indicates that you have started to grasp the problem that even human logical thinking limits our logical truths to human logical truths - and not ultimate truths of the universe.

***"Things ARE" is a complete sentence: it has a verb "to be", it has an object "things".***

In that case you are using 'are' not as a copulative verb (i.e., verbs that connect to descriptions), but as an existential verb (verbs that indicate the state of something, e.g., "Q: Are you happy right now? A: I am",). However, in that case, you are not saying anything since 'things are' is just another way of stating that things have physical existence; which is what physical things are by definition. So, again, you are not saying anything of substance. I find this problematic since often I get the sense that you think you have said something meaningful and profound when all you have done is restating the definition using simple words (e.g., things are, reality is, to be is to be, etc).

***LNC requires no proof; it is a contradiction to seek a proof of an ultimate proof, there is nothing left in terms of which to prove it.***

As you can see above, we can imagine a world that doesn't obey LNC. So, I don't see how you can say that it is proven true. It is an axiom (or assumption) of classical logic. Assumptions about reality can't be true by definition since we don't know our assumptions are necessarily restrictive to reality.

***The axioms of logic are an exercise in fantasy; a double-defining and recursive program. Ultimate Logic requires no axioms; it stands unsupported, requiring no support. It can be found though, providing the support to everything else; (so differs from a fantasy, that would not have that property of supporting everything else).***

Again, we can reason without presupposing a particular logical axiom. It definitely opens up possibilities that we have never imagined, but it just might be so.

***I am not just speaking from the framework of "my experience". Whatever "experience" that is, it has EXISTENCE; I am speaking from the 'framework' of Existence itself.***

Here's another meaningless, true by definition phrase. Experience has existence? The word experience necessarily requires some form of existence in order to experience something. Really Alan, what is your fascination in trivial sentences?

***There is no "because", or "reason" to regard LNC "as right"; it is "right-ness". It requires no reason, as it is ultimate.***

In other words, stop thinking and believe it because I say so. Hmmm...

***My contention remains un-defeated: any attempt to deny LNC can be easily refuted, as no argument can be bought against me as by definition the logician cannot appeal that I am contradicting myself.***

The point is not that contradiction is impossible without the LNC, the point is that you cannot demonstrate that the rules of ultimate reality must somehow obey the LNC. All of your appeals that the LNC is required have failed. You have only been able to appeal to a higher metalogic. Each time we dwelve into that metalogic we see that your reasoning is not valid at that particular metalevel. That's why you must continue making higher and higher appeals, because each metalevel rejects your claim by the very rules in which you cite are universally true. You, yourself, have recognized this. Obviously, you cannot state that the LNC must make-up the ultimate rules of reality, because even with the LNC we can see reasons to believe that the ultimate rules of reality could live without the LNC.

***I cannot refute the logician, as he can just contradict anything he likes (if he can't, then he has allowed LNC into his system). He cannot even have a system without conservation of pattern, which requires LNC.***

As I said above, you can have conversations without the LNC.

***Whatever paraconsistency is, it is still "consistency" enough to involve pattern conservation; and thus LNC is involved.***

No, a rule like LNC is involved. It can be something other than the LNC. That's the point, we don't know what rules there really are. They may be like the LNC and in our particular experience they almost appear identical to the LNC. But, this appearance could be deceiving to our pragmatic experiences that give us our sense of what logic happens to be in the world.

***You see, even the power to contradict is given by God, this freedom is granted by Existence Himself. To have a contradiction at all, requires something common to the two contradictory elements; the pairing (or matching , defining) together of those elements. That something common (that common MATCH) is itself LNC.***

Does God make the LNC true, or is God restricted by the LNC because he lives in an LNC world? If the former, then the LNC is not the ultimate reality. If the latter, then the LNC is a higher principle of truth than God (or Existence as you call God). It seems that a theological view of God as the 'highest' requires God to be the ulimate reality which is a Mystery (i.e., not quantifiable). For that reason alone, you should have doubts about the LNC.

***Actually this dawns on me as a very serious finding: that the very power to deny LNC is granted by LNC.***

Keep thinking along these lines. You're gradually getting it.

Warm regards, Harv

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