I am not a mathematician, although in solving programming problems with the usage of mathematics, logic - I manage somehow. A fewer days ago, erstwhile commenting on topics related to Artificial Intelligence (SI) and the issue of its gaining consciousness, I came back to the conclusion and hypothesis that quantum phenomena must be active in consciousness. This is not a fresh thought, due to the fact that the aged Nobel laureate Roger Penrose besides went this way, looking for quantum phenomena in the axona neurons.[1] If that's the case, then we can dream of a conscious SI - either not fast or never. due to the fact that we don't realize quantum physics – we don't see it.
Mathematics and logic have known for millennia many paradoxes that tangle our ability to think logically. Like the liar paradox! Saying, "I am a liar" - am I telling the fact or lying?[2] The problem of paradoxes always arises erstwhile in 1 conceptual arrangement there is no anticipation of command and reasoning without feedback, and omission of feedback creates a incomplete and imperfect system. The loops form and logic is trapped.[3] In defining concepts these are problems: ignorance per ignorance (definition unknown by unknown); idem per idem (translation of something utilizing the same). This problem frequently arises besides erstwhile drafting parts of defining agreements, regulations - in the legal field. But let's not turn. Let's get back to math.
Math for millennia was available to everyone and utilized natural language. Signs of plus, minus – only appeared in the 15th century! As fresh evidence emerges, hypotheses, in different languages, mathematicians have come to the conclusion that they must make a complex, uniform, symbolic recording system, which present is simply a magical paravan for many Mathematics adepts, as for many musicians, the barrier is notes. In the early 20th century, many mathematicians were proudly convinced that mathematics and logic could explain everything possible to analyse and prove - on David Hilbert's tombstone we read: "Wir müssen wissen. Wir werden wissen". We request to know, we'll know.[4]
Bertrand Russel – aware that classical axioms and mathematical assumptions face the problem of troublesome feedback, paradoxes and traps he issued in 1910. Mathematical Principles - in which he created from scratch all conceptual mathematical logic, trying to avoid logical errors in command and definition.[5] In his introduction to work he believed that his strategy could perfectly cope with the problems of infinity and infinite collections (e.g. troublesome division by zero). You gotta admit that he was crazy about it - just look at his work - after 52 years of release Principles He said that only 6 people understood his work, including 3 Poles.[6]
Perhaps his work fell into disfavor due to the fact that in the 1930s Kurt Gödel proved that it was physically impossible to make a full set of actual and at the same time proveable claims (proof of the incompleteness of arithmetic and proof of the inference of irreconcilability).[7]
What does that mean? That we must be more humble. That absolute fact will never be known, and that part of this nonsubjective fact will always should be the object of religion on the 1 hand, and on the another hand, on the another hand, we can begin to accept as axioms the hypotheses which may belong to the set of these untrue--that is, easy for cunning traps.
So we conclude with a alternatively pessimistic message – that we will never know the fact and unfortunately we gotta come to it by trial and error. Even if Gödel did not prove arithmetic incompleteness, it would suffice for the same conclusion to rather accept the reasonably apparent axiom that there are infinitely many hypotheses to prove and claims – the more we know, the little we know!
There is besides something affirmative about this human mistake and the pursuit of truth. This is simply a kind of breaking of a paradox, which gives any hope. It would seem that utilizing a metric measurement it would be hard for us to find a better nanometer pattern. It would seem that utilizing the pendulum clock it would be hard to find a more perfect pattern of the second. It would seem that it would not be possible to find the gram pattern by utilizing a kilogram. Yet We do so and we are approaching this nonsubjective truth. However, we must have more humility and remember that it will only and always be asymptotic with the growth of our cognition and our imperfect pursuit of the Absolute Truth. We'll never research it.
What's easier to imagine? Eternity or nothingness? due to the fact that in the end, these 2 things come down to command.
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1. ]]>https://en.wikipedia.org/wiki/Orchestrated_objective_reduction]]>
2. ]]>https://pl.wikipedia.org/wiki/Paradox_k%C5%82amcy]]>
3. ]]>https://en.wikipedia.org/wiki/Self-reference]]>
4. ]]>https://www.comsol.com/blogs/a-tour-of-the-famous-scientists-laid-to-res...]]>
5. ]]>https://danielwharris.com/teaching/380/readings/Printipia.pdf]]>
6. ]]>https://hsm.stackexchange.com/questions/783/3-poles-and-3-texans-who-had...]]>
7. ]]>https://en.wikipedia.org/wiki/Affidavits_G%C3%B6for]]>
