***I realise that. Such a "mathematical world" is a particular viewpoint of reality***
Your example was one of missing all the physical details, but still assumed that we live in a mathematical world. That cannot be assumed.
***Quote: "impute our sense of logic ('restricted' or 'unrestricted') on what we cannot know about what we don't know." You say "on what we CANNOT know"? That is itself an example of imposing a law, a dogma about reality. One must not assume that we CANNOT know; prefer "might not know".***
No, we cannot know. We can look only in our conceptual framework that necessarily limits our conceptual framework to our own perspective. We cannot leave our conceptual framework to 'see' everything. Even if we could leave our conceptual framework, we would need another conceptual framework that also could be limited. Without this absolute knowledge we do not know the ultimate reality - hence we cannot know. If this view appears to be absolute in itself, it is really not. It is an approach based on how we define knowledge, so given this definition we can see how our knowledge must be inherently limited. Seeing that limitation is enough to humanly justify the statement that we cannot know the ultimate reality (at least in this current state of being).
***"On what..." this implies "on something that IS" so the logic of existence MUST apply by definition as whenever you imply IS-ness, the logic of existence applies.***
By existence I'm assuming you mean ontological existence (i.e., what really exists). Unfortunately we don't know if there is a logic that determines what really exists. We merely observe order in the material universe, but there's no way to know if that order is based on limitations of our conceptual scheme or can be reduced to other 'logics' that are much more fundamental than the order that we observe. It is a mistake to think that we can successfully apply this logic to whatever fundamental order is 'out there'.
***H: " The only reference that we are making is to 'all that is out there'. That may be nothing at all if the solipsists are correct." A: As soon as "we" are "making a reference" you have got "we" existing and "action" so there cannot be nothing. The question is how much somethings?***
That is, there may be 'nothing' outside ourself - according to the solipsist.
***H: "On the other hand, it might be all the things that exist, or things that don't fall into a category of existing and not existing, etc. We don't allow reality to be restricted by our words." A: By definition things MUST BE or not BE; you cannot have some other category other than that they MIGHT be (but you don't know yet, or haven't chosen an alternative from several choices yet). It is true that reality should not be restricted by our words, to have this discussion more accurately requires telepathy and then the discussion would be unnecessary as the issue would I think be solved by such insight as is associated with telepathic ability!***
Well, there are a few logic axioms that can be played with and changed. The definitions aren't fixed and each 'logic' proposes a different sense of 'MUST BE'.
***H: "Reality is 'all that is out there' or perhaps 'all that is not out there'. What we don't know is the real property of a thing. Maybe it has muliple properties that contradict each other (e.g., exist and not exist)." A: Any multiple properties could only pseudo-contradict (e.g. ten choices that are mutually exclusive "contradict" but not really, choices by their nature may be mutually exclusive. You make a choice, and it does not contradict, that choice-decision exists). We do know that the ultimate reality of a thing is "existence".***
What you just said was: "the ultimate reality of a thing is [the ultimate reality of a thing]." You didn't say anything.
***H: "The LNC states -(P & -P). You cannot say things that break this law do not exist entirely since they are speculated to exist as P and not exist as P. What prevents them from existing and not existing? "
You seem to be confusing "speculation" with reality. A: Speculating that something can be and not be is just nonsense; what prevents this from happening is that the very verb "to be" prevents it.***
It's good to know that the English language can effectively constrain the nature of the universe. I was concerned for a moment.
***Your question becomes "What prevents the existence of something existing and not existing?" which becomes "What prevents the existence of the existence and supposed non-existence of something existing and non-existing" which becomes.....etc. ad infinitum. Your question grows longer and longer in this way as it is nonsensical.***
No. The answer to a "Do you have?" question may be different than "Do you not have?" question. For example, here is a series of hypothetical questions and answers where we can count on getting true answers from reality about its basic constituent form of matter:
(Q1) Are you a particle? Yes
(Q2) Do you have particle properties that we can know to some degree? Yes
(Q3) Can you tell us something about your particle properties? Sure
(Q4) Do all these properties you are telling me correctly infer that these particles exist? Yep
And now for the 'have not' questions?
(Q5) Are you not a particle? Yes
(Q6) Do you not have particle properties? Yes
(Q3) Can you tell us something about your anti-particle properties? Sure
(Q4) Do all these negative properties you are telling me correctly infer that you are also a wave? Yep
As you can see, ask different questions and the answer comes back differently. So, let me rephrase my comment so that you can see more clearly the possibility of LNC being false.
"What prevents the existence of something existing and not existing?" becomes: "What prevents a correct answer of something existing also being correctly answered with something not existing?" In other words, change the wording of the question from affirmative questions to negative questions and the answer is contradictory. This is just one example how it is possible that the LNC could be false and that it could make sense from our human inquiry. Funny thing, the wave-particle duality issue is close to being the kind of situation that one would expect if such a thing were possible. This is why so many Taoists, Buddhists, and other Eastern beliefs have really grabbed onto quantum mechanics as endorsing their philosophical view of the world (i.e., historically the Eastern philosophies have more often refuted LNC than the Western philosophies).
***The very nature of existence EXCLUDES non-existence.***
No, the very nature of existence questions excludes non-existence. Non-existence questions about God, for example, which is called negative theology, have long been viewed as providing more insight. I believe that negative theology is more often associated with denial of the LNC.
***Any logician who denies that; cuts themselves off from the universe because they cannot be refuted (since they permit themselves to contradict everything) nor can they repel my refutation (they cannot answer my refutation- as what are they going to say? That I'm contradicting myself? Hardly, that would be appealing to the LNC which would end their case. They cannot even string two thoughts together with justification in that such consistency is forbidden by their denial of LNC.***
Alan, Alan, Alan. The LNC is just one axiom among manner. You'd be surprised how well those logicians sleep at night. Billions of Taoists, Buddhists, etc would think of us as quite the limited minds for accepting the LNC. They might think of it as one of the main ignorant beliefs of our culture.
***In the case of the LNC; one does not assume it applies. It IS applied the moment you conserve a pattern sufficient to even consider a question at all. Those logicians who think they can avoid assuming it forget that they are constantly applying it.***
There's a few axioms that deal with all of these issues: LNC, bivalence, excluded middle, and identity. I think you are confusing LNC for these other axioms and that the LNC is seen as absolutely needed. You can have identity (pattern matching as you call it) without requiring LNC. Identity is the whole of itself compared to the whole of itself (e.g., P=P). The whole could be (P and not P) compared to (Q and not Q). If the properties exactly match, then in classical logic they are the same identity (called Liebniz's law or principle of the identity of indiscernibles). This principle doesn't require LNC since we are only concerned with wholes. For example, you wouldn't compare P to not Q. Rather, you compare P and not P with Q and not Q.
***Reality and the LNC are unseparable; any attempt to separate them involves category errors- applying multiple categories or perspectives that give illusions of avoiding assumptions.
Such strange logics may appear productive; because there exists the phenomenon of "alternatives" in "Choice systems"; and alternatives are allowed to contradict each other. But that is not a real contradiction.***
Alan, think of what you are doing. You are taking a formal system having axioms and stating that this formal system is unseparable from reality. There is a distinct separation in the mere fact that formal systems are interpreted. You are saying there is no chance that your interpretation of reality cannot be wrong. You use the formal system to prove that is the case, but you are again interpreting the formal system to show that you are properly interpreting the formal system. Do you see that you are using the interpretation to prove the interpretation? Do you have any idea what is wrong with doing that?
***"Logic" is not in the category "descriptive" (as Dr. Dick might note); it is the framework of description. Muddling these categories leads to the illusion that there is a question as to whether logic accurately describes reality. But "logic" DOES NOT DESCRIBE. Layers of pattern-matching describe; not logic. Logic is just the framework.***
I agree that logic is part of our conceptual framework, but let me emphasize the word 'our'. We are using our conceptual framework to apply it to our experiences, and that is fine. But, when we use it to limit what is 'out there', that's human arrogance at its worst. We cannot do that.
Warm regards, Harv