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This question came up for me when I began considering metaphysical realism and metaphysical idealism.

Realists claim that there exists an objective world independent of consciousness, though we only have indirect access to it via our sense perceptions. On the other hand, idealists essentially claim that nothing can be known outside of consciousness and therefore positing an entire world independent of consciousness is un-parsimonious and unjustifiable. Therefore, there is no world outside of consciousness as a category. It may very well be that there is an objective consciousness beyond our personal consciousness (objective idealism), but idealists think that claiming an entire (physical) world exists beyond consciousness is wrong.

Although I am sympathetic to both realism and idealism in some ways, it seems as though both positions are unverifiable. For the realist, the idealist makes a very powerful point that we cannot escape consciousness and subjective experience to go beyond it and verify that there indeed is a world independent of consciousness. However, for the idealist, the realist can claim that just because we cannot go beyond consciousness to verify the existence of a world independent of it does not necessarily mean that it isn’t there.

Is this dilemma between realism and idealism ultimately irresolvable? In other words, how could we ever possibly know which of them is true? Or do we just have to use principles such as Occam’s Razor and parsimony to conclude that one is at least more likely to be true over the other?

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    "how could we ever possibly know which of them is true?" It is hard to answer... we have 2,5 millenia of discussion in "Western world" (since Plato and Aristotle) and no ultimate decision. Oct 8, 2021 at 15:56
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    "All models are wrong, but some are useful". We cannot "definitively determine" even the "correct" physics, see Underdetermination of Scientific Theory, and physical theories are much more amenable to testing. Even there epistemic values, like unification, fruitfulness, explanatory power, parsimony and coherence, play a role in deciding which one to adopt. Much more so in philosophy.
    – Conifold
    Oct 8, 2021 at 17:47
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    If one presumes that evolutionary psychology is explanatory of the need for metaphysics, then we should expect that a plurality of metaphysics will maximize the likelihood of human survival, and endorse that plurality should we care about the continuance of the species.
    – J D
    Nov 7, 2021 at 21:27

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