As a practicing quantum mechanic, I'd warn you against the claim that dialetheism is used in quantum computers. Qubits are sometimes described as taking "both states at the same time," but that's not precisely what's going on, and people who actually work on quantum computers use a more precise understanding that doesn't involve interpreting intermediate qubits as truth values.

There are also two people I wanted to see in your post: Russell and Gödel - mathematicians rather than philosophers. Russell's type theory was one of the main attempts to eliminate paradoxes in mathematical logic. Gödel showed how that doesn't quite work, but also showed how things become a lot clearer if you consider provability as well as truth value.

The main problem with paraconsistent logic is that it doesn't exist. That is, there is no formalisation of it that anyone uses. Whatever non-standard logics people study, their metalanguage is always plain old mathematical logic, as foreshadowed by Aristotle, hoped for by Leibnitz, brought to fruition by Boole, Russell, and Whitehead, and embodied into computers by Turing, von Neumann, and whoever else should be mentioned in the same breath as them. There is no other game in town, except perhaps subsystems for constructive reasoning (where e.g. any proof of ∀x.∃y... can be read as a program for computing a suitable y from a given x).

The idea of Buddhist logic has always puzzled me, because I don't recognise anything that could be called logic in those writings, i.e. methods of reasoning,. There are only recitations of various formulas like "true, not-true, neither true not not-true, both true and not-true."

"What do I have in my pocket?" said Gollum, and Frodo knew, and said [LW · GW], without philosophizing on the nature of truth.

Don't Godel sentences rebut the ideas of groundedness or of creating a system where self-referential sentences are blocked? Their existence means that you can create something that behaves as a self-referential sentence and has the associated paradoxes while using only normal arithmetic and without a "this sentence".

I don't get the liar's paradox, why is 'P = ¬P' an interesting statement?

This is a post I, funnily, found both useful, and intend to, in other comments, intend to 'tear to shreds', so to speak. The first thing I would say is this article could be edited and formatted better. This is a relatively long post for LW, that nonetheless covers a great breadth of material rather briefly relative to the scope of the topics. I think having an introduction at the beginning that generally summarizes the different sections of your post at the beginning, it would be helpful for readers. You could also use formatting options for presenting formal logic or philosophy, and others, like subheadings, available on LW, that would make this article more readable on this site. I'd also say that you move through a lot of subjects very fast that it would be unrealistic to expect most readers to know enough about to put them altogether in the way you're intending to understanding your conclusion. If you were to provide some links as resources to learn more about the subjects, or you were to expand on how the central theme(s) of this article relate to the different topics you bring up (e.g., theoretical physics, quantum computing, AI, Bayesian epistemology). I think editing this article to make it more readable is what would get more people to read it to the end, and thus understand the message you're trying to impart.

Edit Note: Fixed your images for you. You were linking to imgur, without linking to the actual image addresses.

Quantum logic differs from classical logic in dropping distributivity, not the principle of non contradiction.

Hi. I'm new to this site and stumbled across it via searching for the "Why is there something rather than nothing?" question. My own thinking about this question makes me think that the statement "The universe exists AND the universe doesn’t exist” can be true. I think that the thing we often think of as “nothing” (the lack of all matter, energy, space/volume, time, abstract concepts, laws of physics/math/logic, “possibilities” and the lack of all minds to consider this supposed lack of all) is, when thought of from another angle, a “something”. That is, asking how you go from “nothing” to “something” in the question “Why is there something rather than nothing?” is like saying that you start with a 0 (e.g., “nothing”) and end up with a 1 (e.g., “something”). Because there’s no mechanism in 0 to change it to a 1, the only way you can do this is if the 0 is really a 1 in disguise, and it just looks like a 0 from the one perspective we’ve always looked at it from.

How can “nothing” be seen as a “something”? To answer this, I think we first have to answer why does any “normal” thing, like a book, exist? That is, why is a book a “something”? I think that a thing exists if it is a grouping. Groupings unite things together into a single unit whole and define what is contained within the whole. This grouping together is visually seen and physically present as a surface, or boundary, that defines what is contained within and that gives “substance” and existence to the thing. Some examples are 1.) the definition of what elements are contained within a set groups those previously individual elements together into a new unit whole called the set, which is visualized as the curly braces surrounding the set and 2.) the grouping together of previously unrelated paper and ink atoms into a new unit whole called a book, which can be visually seen as the surface of the book.

Next, in regard to the question “Why is there something rather than nothing?”, when we get rid of all existent entities including matter, energy, space/volume, time, abstract concepts, laws or constructs of physics and math as well as minds to consider this supposed lack of all, we think what is left is the lack of all existent entities, or “absolute nothing” (here, I don’t mean our mind’s conception of this supposed “absolute nothing”, I mean the supposed “absolute nothing” itself, in which all minds would be gone). This situation is very hard to visualize because the mind is trying to imagine a situation in which it doesn’t exist. But, once everything is gone, and the mind is gone, this situation, this “absolute lack-of-all”, would be it; it would be the everything. It would be the entirety, or whole amount, of all that is present. By its very nature, it defines exactly all that is present (e.g., nothing). Is there anything else besides that “absolute nothing”? No. It is “nothing”, and it is the all. An entirety, whole amount or “the all” is a grouping that defines what is contained within (e.g., everything), which means that the situation we previously considered to be “absolute nothing” is itself an existent entity. Said another way, by its very nature, “absolute nothing”/”the all” is a grouping. It defines itself and is therefore the beginning point in the chain of being able to define existent entities in terms of other existent entities.

So, I don't think all contradictions are true, so I don't support the problem due to explosion argument. I just think this one contradiction is true. In fact, it's not even really a contradiction. It's just that we're thinking of the statement incorrectly in thinking that nothing and something are mutually exclusive.

In regard to the liar's paradox, "this sentence is false”, I think the reasoning about a thing exists if it's a grouping argument applies here, too. This argument would also say that a thing doesn't exist until it's a grouping. In the sentence, "this sentence is false." the words "this sentence" refer to a point in the future when the whole sentence ("this sentence is false.") has been said. Only after the whole sentence has actually been said (or read) does it become a grouping of all 4 words and only then does it come into existence. Once the sentence exists (only after all 4 words have been said or read), you can't then go back and retroactively assume that just the two words "this sentence" are the same as the whole sentence because the sentence didn't even exist until after those two words were said/read.

Anyways, thanks for listening. This is a very interesting website.

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There are lot of interferences used where its unclear whether one can use old defintions for them. For example in paraconsistent logics some sorts of negation propagations are not always available (ie you might not have ~(P^Q)=>~P^~Q or ~~P=>P). It raises a suspicion where the interferences presented are a pre-formal mess. Thus I have a feeling that I am constantly "repairing" the message of the post to get it be relevant to me while it does seem there is substance to be salvaged.

If Gary says "this statement’s metalanguage is false" and Alice says "Vad Gary säger är falsk" and David says "Was Gary sagen ist falsch" does Gary refer to Swedish or German? I think it's plausible that Gary's statement does not by itself succesfully refer to Swedish or German and it remains plausible for me that there is really no good way from the object language to get a refererence to the metalanguage.