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It is worth noting that there are two separate issues. The first is the question of proving the statement. The second is the question of the rationality of persuasion.�
If we don't have proof that something exists, it certainly doesn't prove that the object doesn't exist in principle.Everyday example: if a crime was committed, but no one saw it and there is no evidence that the crime took place, then this, however, does not mean that there was no crime.
On the other hand, the question of the rationality of beliefs is a separate issue. The same “Russell teapot” is an example rather about how to think rationally and whether it is rational to believe in something that we cannot demonstrate or prove. That is, in those questions where it is impossible to give an unambiguous answer, it is appropriate to put the question not in terms of “yes” or” no”, but in terms of which picture of the world is more rational and what are the pragmatic consequences of accepting this or that answer.
There may be different strategies. If we take faith in God as an example, we can start a discussion about what is more rational – to believe or not, and such a discussion, in fact, has been going on for more than one century. Believers will cite as an argument, for example, “Pascal's wager”, atheists – “Russell's teapot”, believers will refer to Brownburn's logical analysis, atheists will poke at Dawkins, etc. etc. There is no simple solution here, it should be noted, both sides have their own arguments.
You can take a different approach and link rationality with a pragmatic understanding of truth, i.e. evaluate a particular decision based on the results. This is what James did, for example, in his classic work “The Diversity of Religious Experience”, when he argued that one should evaluate religious faith not from the point of view of logic, but from the point of view of its fruits.
Thus, the lack of evidence is not a sufficient argument for claiming that something does not exist. The lack of evidence for and against rather takes our discussion to another level, where we start talking in terms of the rationality or non – rationality of a particular decision, the logical correctness of our conclusions and the pragmatic consequences of their acceptance or non-acceptance, but even here the lack of evidence alone is not enough to automatically recognize the statement as irrational-stronger arguments are needed.
If we make a positive statement about the existence (or non-existence) of an object, then we must have the appropriate evidence. If we do not have such evidence, then we should refrain from making any statements in this regard. For example, we don't have evidence of extraterrestrials, but that doesn't automatically mean that there aren't any extraterrestrials themselves. We just don't know if they exist or not. And the evidence for the absence of anything at all is logically contradictory.
NO, it is impossible to assert such a thing and not fall into contradiction, because, according to the S5 form, if there is a CONSISTENT POSSIBILITY of something existing, then such a POSSIBILITY is mandatory for All Worlds (according to A. Plantinga), and therefore, such an existence is necessarily feasible, regardless of whether it is possible to confirm it with experience, or there is no such possibility. Hence, if the argument for the existence of God is UNIVERSALLY CONSISTENT, then the proof of such UNIVERSAL CONSISTENCY is a perfectly logical argument for recognizing the existence of a Deity. Moreover, being a Likeness of the Deity, a person simply does not have the resources (in likenesses) to argue the immediate necessity of the nature of the existence of God, but only modally, as a kind of similarity of such a strong argument of existence, i.e., no more than in a weak sense.
You can say anything you want. And a lot of people do! :- ) If the scientific approach is meant, then in the absence of evidence of existence, by default, existence can be accepted as a hypothesis, but no more. And if, with numerous attempts, evidence of existence cannot be obtained , it is assumed that it does not exist.