Epistemological solipsism
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Epistemological solipsism is the variety of idealism according to which only the directly accessible mental contents of the solipsistic philosopher can be known. The existence of an external world is regarded as an unresolvable question, or an unnecessary hypothesis rather than actually false.
Epistemological solipsists claim that realism begs the question: assuming there is a universe that is independent of the agents mind, the agent can only ever know of this universe through its senses. How is the existence of the independent universe to be scientifically studied? If a person sets up a camera to photograph the moon when they are not looking at it, then at best they determine that there is an image of the moon in the camera when they eventually look at it. Logically, this does not assure that the moon itself (or even the camera) existed at the time the photograph is supposed to have been taken. To establish that it is an image of an independent moon requires many other assumptions that amount to begging the question.
Realists wonder, in response, how solipsists know, without begging the question themselves, that reality is known only indirectly through the senses.
This relates to Kantian transcendental aspects of the world, in which a new factor can be included, once it is clear that the current axioms neither support or refute it. The continuum hypothesis and the axiom of choice, are examples of possible transcendental decision points. Solipsism in its weak form is characterized by the repeated decision to not take transcendental steps, a logical minimalism. In its strong form, the denial of the existence of an argument for the existence of an independent universe may be justified in principle in an empirical manner. Whether the non existence of a proof means that non existence of the entity is a transcendental choice.