can logical contradictions, like a set S of all sets that don't contain themselves, represent a superposition of being true and false and be valid within the framework of quantum reasoning? basically, you creative a wavefunction of truth values.

>>16726097 (OP)
No because quantum mechanics eliminates things with a probability of 0 as in the Pauli exclusion principle. Wavefunctions only calculate probabilities within the possibilities of physics.

>>16726097 (OP)
Superposition refers to addition in a vector space. Vector spaces are sets. You go figure out why what you just said makes no sense.

>>16726097 (OP)
There are already logical systems which do not use the law of excluded middle as a foundation.
Look into intuitionist logic as an example.

>>16726097 (OP)
Let's try doing that thing in science where we explain some hypotheses and watch everyone else tell us how stupid we are.

Science has a language problem, specifically a language and grammar which permits the construction of sentences like OP. There have been *many* attempts at a linguistic standard, similar to the attempts to standardize mathematics notation. not. gunna. happen. everrrrr.

Still, E-prime and General Semantics with all their woo and grift had some good ideas. The idea here is specificity.

Are your true/false wavefunctions better called truthfunctions, and just like the wavefunctions, we get to have all kinds of little operators, transforms, matrices, exotic numbers, etc... which make it all work under the hood? You've got true/false situations which vary temporally, by location, hell even based on temperature. We could make a set of all water molecules with a thermal energy high enough to be considered steam, but that true/false changes based on exterior influences.

The burden is on you to generate an example wavefunction/truthfunction which illustrates what you are doing, and some possible examples which others need to look over... you know, that science thing where you make some examples, maybe a story about a goat and some doors, and badabing, we're jazzin.

>>16726251
>maybe a story about a goat and some doors
You mean the one people get wrong due to linguistic quirks?

>>16726259
yup. when the grammar of a language permits making little hidden logic traps... among other things. sort of a neurogrammatical programming capability too, like how the innuendo and double-entendre tricks used in neuro-linguistic programming do in fact work, but sporadically and often in unintended ways.

https://www.youtube.com/watch?v=7KDYEjGecZc

linguistic weapons and all that.

>>16726259
another good example of using linguistic quirks/weapons is guiding a glowie operation under the nose of surveillance and not getting caught.

https://www.youtube.com/watch?v=XPFRaCnkVzE

>>16726097 (OP)
They represent useless statements with no possible value. Not a possible future value, not even at an infinite point in time (like Thomson's lamp), not a real number value, not even a complex number value, but no value that could ever be useful for anything other than proving the incompleteness of the logic system itself or the silliness of another statement. Not even the empty set, just nothing because you crashed or froze the logic machine before it could arrive at a result.

>>16726097 (OP)
OP... do you even know what those words mean?

How does a set that contains itself make sense in the first place?

>>16726712
The set of all sets is a set. Therefore it contains itself.

>>16726712
https://en.wikipedia.org/wiki/Non-well-founded_set_theory
it still disallows "the set of all sets that do no contain themselves", so that's why it works

>>16726712
>recurssion
>infinity
it doesn't make sense, is merely an error

>>16726800
That's the stipulation but as >>16726834 said, you just get an infinite recursion anyway. My point is that you don't even have to construct a set of all sets that don't contain themselves, it already fails one step before that imo.

>>16726983
why would it fail? first order logic has no constraints on infinite recursion or reflective properties. hell, transfinite recursion itself is a fundamental concept in set theory.

>>16726097 (OP)
No because true false are logical axioms that cannot change for the purpose of rules. A wavefunction is a non deterministic probability distribution. You mesure the the distribution for the mean of or average occurrence of the data that appaears the most like 1 appearing 200 times and 5 appearing 40 times and 3 appearing 20 times you measure that distribution on the x and y axis as a curve. There is no such thing as a non deterministic truth value. 1+1=2 is a truth value because it’s deterministic. Chaotic distribution have no truth just more likely occurrences or patterns

>>16727240
but what if you impose a fuzzy logic notion to it to represent how far away your reasoning is from the axioms? like a metric that encapsulates the proof-theoretic ranking for your.

basically, we have to rely on some system of logic. and while one proposition might be false in one system, it could be true in another. by using this quantum framework where you have probability densities for being true or not, you could make a function that gives you the probability that your reasoning is true under that system, and by extension, its ranking in the hierarchy of logical systems when it comes to proving/reasoning strength.

>>16727245
I see what you’re getting at. And I agree with your theory the problem is that it’s not specific enough.


What proposition would be false in one system? All systems here on earth obey some universal law.


Maybe in space systems behave differently like for example the solar system doesn’t seem to obey thermodynamics nor does the sun. In a frictionless system earth seems to spin perpetually.


So this example shows you must be specific. It shouldn’t be ambiguous or universal. Because what you’re essentially saying is a “thing” behaves this way under these conditions. And this thing doesn’t behave this way under some other conditions.


Math has to have some physical dimension you can apply it to. Like it can’t be too abstract in theory.


An example is time. Time isn’t real but the frequency oscillation is connected to a physical pendulum. Tick tock. No we can say the frequency and speed of the pendulum = 1sec. The we can take that measures distance and the rate of change over the pendulum and get speed or velocity. My car goes 60mph

You see the physical non abstract dimension is important otherwise you sound like a schizophrenic in his head and not in reality.

>>16727256
i get that it has to be rooted in reality on some level, but i'd rather that be a consequence of a truth value rather than a fundamental tether for the whole system, because what if you want to operate beyond the physics of this world and develop any model of your choosing? i think that type of versatility and generality is what i'd wanna preserve. like if you say "given these laws, these are all possible truths about the world" you can try and encode that for various worlds with various laws. it's like a template rather than a specific truth system. that's the mathematical abstraction of it i want to preserve.

i think it would be cool though to have a function that could take any proposition or postulate, and not just tell you if it's true or false, but instead where it could be true if it's false, and where it could be false if it's true. something stronger than a truth value, like a model value.