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This is one of the main questions of epistemology: what are the foundations of human knowledge in general, what can we say that we know it absolutely reliably, and by what right can we deduce from these foundations all that we use in practice?
If you think for five minutes and review the film “The Matrix” (the first part, of course), it becomes obvious that the question is not limited to scientific theories and strict logic. You hit your little toe on the leg of the sofa. The sensation is perceived as real, but who says that the sofa or finger is real, and you are not a brain in a jar with wires connected to it? Yes, and the feeling is also difficult to recognize as real: ten seconds have passed and all that you have left of it is not a very pleasant memory, which may turn out to be “induced”.
Have you experienced an unearthly happiness and religious ecstasy and are sure that this feeling is higher than some kind of scientism that reduces everything to platitudes? No, it's just Agent Smith added a little ecstasy to the nutrient solution your brain is swimming in.
But even in such a crazy world, where everything is shaky and uncertain, you need to rely on something. The system that we rely on must be at least internally consistent and allow us to make decisions.
It is better to assume that there is an objective reality that lives according to strict laws that are accessible to human understanding. This is easily challenged, for example, by the “Matrix” method, but what can we offer in return?
It is better to assume that there are other people who have the same subjective qualia as me. That we have free will and interact with them in a world that has a moral aspect, and we can do it for good or for evil, and all this in general is not in vain. This is easily challenged, for example, by imagining the universe as a giant finite automaton that deprives people of any choice, but what can we offer in return?
It is better to assume that these two views of the world do not contradict each other and can complement and enrich each other. Let's be optimistic, why not?
You don't even need a trilemma here. Godel's theorems are sufficient for mathematics and modern scientific methodology. Starting with postpositivism, science does not claim to be truly true knowledge, but only plausible reliable models that have passed all the tests that competitors could not pass.
Empirio-criticism: In the 1930s, the Austrian mathematician Kurt Godel proved two theorems – the consistency theorem and the inverse incompleteness theorem, which state that any consistent system is incomplete and, conversely, any complete system is always contradictory. If we say that scientific knowledge is constructed logically and consistently, then we are saying that it is incomplete.
Empirio-criticism: In the 1930s, the Austrian mathematician Kurt Godel proved two theorems – the consistency theorem and the inverse incompleteness theorem, which state that any consistent system is incomplete and, conversely, any complete system is always contradictory. If we say that scientific knowledge is constructed logically and consistently, then we are saying that it is incomplete.
The first is Descartes ' idea “I think therefore I exist”. It can be tested by any experimenter at any time without any effort.
The second is the axiom of the Scientific Method of cognition – ” True representations of reality are consistent.” It is obvious and unavoidable, without it, discussion and communication immediately disappear, so the one who denies it is immediately deleted because he contradicts himself.
All those who try to impose on the Real Me, for example, the ideas of solipsism about a completely imaginary world = – automatically call themselves imaginary and this is deleted, as well as those who do not recognize the Axiom of the scientific method.
After all, only one solipsist can be alive )) and this is Me )) all imposed collective solipsists, absolute solipsists, divine and” brahman ” solipsists, all also automatically delete because I still exist ))
And this fact can be said about the beloved by every capable intelligent Object.
At the same time, Mathematics does not use the concept of “object – object interaction”, it has its own apparatus of proof. But physics, on the contrary, only talks about object – object interaction, and it has other ways of testing Scientific theories.
Actually, it is the Real World Sciences (natural sciences) that use the Full Unambiguous concept of”proof”.
Therefore, the Scientific Method has one hundred percent predictive power, repeatability and verifiability of the experiment, with the result obtained regardless of the Personality of the observer.
There is nothing more “absolute” than 100% predictivity ))
PS – why philosophers and even many prof scientists do not understand the difference between Physics and Mathematics (more precisely Algebra), I do not understand )) After all, it is obvious that in one case there is a duty to prove the real interaction between objects, and in the other case there is pure modeling.
PS-2 at the same time, in geometry, for example, there is already an “interaction”, the shapes intersect, are located at a certain measured distance from each other, etc.
And the order of proof immediately changes, anyone who makes a statement must prove it, including “assumptions about refutation”.
Therefore, in mathematics it is necessary to prove strictly and there are all sorts of gaps and nuances with infinities, and in geometry and physics it is enough to show a certain area of application and everything – in this area with the same experimental conditions-there will always be 100% absolute proof.
PS-3 It is precisely by clarifying the “duties of the disputing parties” to prove their statements that the Absolutely Exact Proof of all the famous “Euclidean theorems” about parallel straight lines and all sorts of impossible “Lambert tri-straight lines” with an allegedly “unknown” fourth angle for infinity is perfectly established.
A sample of the “final” distance is taken, there are strictly four right angles on it, and everything is absolutely observed. And then the “doubter” comes and demands to prove separately for an infinite distance-oops!- and his counterclaim, and first prove yourself that there is a Lambert rectangle without a fourth right angle?
And all on this, strictly as in jurisprudence )) Prove yourself all your doubts )) But of course not as in mathematics, where the theory is proved initially by the author of the theory, taking into account all possible infinities and doubts.
So there are different Sciences and” epistemologies ” of proof are the subject of controversy – but in the Scientific Method of cognition of the real world, everything is absolutely and 100 percent.