Some historical examples include the Gnostics, Advaita Vedanta, Kant, Schopenhauer, and countless mystics.
I was just wondering if there is a common name for these sorts of worldviews.
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The view you are describing, though possibly not the view you are thinking of, is called indirect realism. It is not a view of mystics, but the view of most materialists and physical realists today. Idealism denies that there is a real world at all. Idealists believe that only the mind exists (along with perceptions in the mind). An indirect realist believes in the real world, but believes that our minds have no direct experience of it.
Indirect realism is a consequence of scientific realism, as was shown by Descartes. The scientific view of perception is that light strikes an object, then gets reflected into your eye, through the lens, and onto your retina. The light knocks electrons around to produce nerve impulses which then travel to your brain which does an enormous amount of processing on the signal before delivering it to your conscious awareness.
The evidence for this view is overwhelming. It comes not only from optics and anatomy, but also from brain studies and instruments such as optical illusions and perspective, which show that what is reflected on the back of our eye is not what is brought to our consciousness.
The conclusion from this is that what you see is not the real world, but a mental image of the real world created by your brain from data that wasn't even the real world when it entered the nervous system, but only a projected image.
And the mental image you see is indistinguishable from images that can occur entirely in the mind without even the projection on the back of the eye. You can have hallucinations or dreams that show the same mental image. This shows that there is no necessary link between a physical object and the mental image you perceive.
Furthermore, not only do you see only a mental image, but science says that a real object really isn't what your mental image shows you. That tree isn't really a whole; it's a swarm of subatomic particles, going in and out of the tree constantly. The particles even go in and out of existence. The tree isn't even physically identical from one moment to the next, yet you see a single tree persisting over time.
All of this leads to the conclusion that we don't see the real world, but rather a mental image of the real world. The real world is a much different thing from what we see.
Other than that, you are probably looking for "idealism" in some form or another.
This is a common concept for those who hold by idealist worldviews. That the world is really consciousness, and the appearance of matter around us, and its solidity, is an illusion. There is a term for this idea in Indian philosophy, and that is Maya -- that the appearance of a material world is an illusion.
The concept of Maya is adopted from its Hindu origins in both Buddhist and Sikh thought, with slightly different but related definitions in both. Note that these religions give somewhat different answers as to what is "real", than mayanic Hinduism does.
This view of our material world as at least partially illusory, or at least created by thought, is not limited to eastern thought. The "New Thought" brand of Christian and near-Christian religion holds that our physical universe is malleable to our willing. This is also a common view in the New Age movement. Modern paganism holds that our material world (and deities) are created by collective presumptions of humanity.
A surprisingly related view is held among eliminative materialists, who hold that the world is "really" elementary particles, and the things we perceive (color, solidity, temperature, etc) are perceptually manufactured "shortcuts" to process the underlying "true" reductive reality, and the shortcuts basically are self-created illusions. This view is often called "scientific realism" https://en.wikipedia.org/wiki/Na%C3%AFve_realism#Scientific_realism_and_na%C3%AFve_perceptual_realism. Scientific realists also present the sensible world as illusory with the true reality being particles in motion. Sellars made the difficulties created by the opposition between "manifest image" and "scientific image" a centerpiece of his philosophy https://plato.stanford.edu/entries/sellars/#PhilEnteImagHumaWorl.
A particular view of mind -- advocated by the materialist Daniel Dennett among others, is that consciousness is an DElusion. IE that it is not just our image of the external world that is seriously mistaken, but that we are also seriously mislead about what our minds themselves do and perceive. The term applied to this theory of mind is "Delusionism". https://aeon.co/essays/what-if-your-consciousness-is-an-illusion-created-by-your-brain?utm_medium=feed&utm_source=atom-feed
A broader term to use across this whole collection of thought might be "illusionism" relative to matter and perception. But the diversity of views collected under the term, might make such a collective term more misleading than helpful.
There's subjective idealism which entails that the reality-generating apparatus of consciousness is itself the entirety of the world that we can have indubitable knowledge of…
Perhaps speculative idealism characterizes the post-Kantian efforts most generally, if at the cost of gathering together some really disparate voices. Kant's closest readers like Solomon Maimon point the way beyond the antinomies and the transcendental ideas towards an abstract synthesis; in later accounts like Hegel's this synthetic process would achieve its formal elucidation as dynamic metaphysical process, yet still seemingly derived however from some form of self-knowledge and transcendental structure -- although the subject here is thoroughly decoded or translated, portrayed as the cosmos itself or the absolute etc