I probably incorrectly understand some basic things, so I'll show my layman thinking process for easier identification of where lies the problem.

Let's start with basic dichotomy - materialism vs. idealism of what's more primal - matter or mind. As far as I understand, idealism operates only on concepts of human mind and perception thus it's strictly anthropocentric approach.

As materialism states that only matter ontologically exists, idealism states that only ideas (i.e. human cognitive apparatus and perception) ontologically exist.

Thus if we want to stick with idealism, we fall into correlation loop - we are constricted by the ideas we are able to think, as if we assume something that we can't think, it automatically becomes thinkable.

So if idealist wants to say that some object "exists" that would mean something like "we are able think that this object exist (exist in intersubjective consensus reality)".

Then Plato's states his Forms - entities that are not material objects (thus, it's not a materialism), but also not a results of human mind, as they ontologically exist, independent from our cognition. So why is it idealism? Forms doesn't fall in any category of mind and matter. Is it implicitly assumed that Form are results of human cognition? In another words, who thinks the Forms for them to exist in idealistic approach?

As far as I understand, by Plato "actual" reality constitutes only from From, by they are inaccessible by any meaning. Would it be correct to say that the Form might as well not exist at all from this standpoint?

Why does Platonism falls into a mathematicism category? If we say that everything is math concepts, not correlated with human perception and cognition, wouldn't it be a materialism?

  • "Idealism operates only on concepts of human mind and perception thus it's strictly anthropocentric approach" is incorrect. Idealism claims that mind/ideas are the primary mode of being contra materialism, but this mind does not have to be human or human-related, human mind is just an example most familiar to us. Just as solids and liquids are the most familiar kinds of matter, but there are plenty of others, gases, plasmas, fields, dark matter, etc. Plato's ideas are completely human-independent and self-sufficient, so his idealism is as objective as typical materialism. – Conifold May 22 at 23:11
  • I would not use materialism but use appearance. Think of essence (Idea) [fixed] and appearance [changeable]. – Gordon May 22 at 23:13
  • In addition, “Theory of Forms” en.m.wikipedia.org/wiki/Theory_of_forms – Gordon May 23 at 0:14
  • A discussion of the different ways "idealism" has been used to describe both Greek/European and Buddhist and Hindu philosophies and religious views: web.archive.org/web/20100314020538/http://kelamuni.gaia.com/… – Hypnosifl May 23 at 10:06

As the term 'idealism' is used in epistemology and metaphysics there is nothing common and distinctive to all forms of idealism except the claim that reality is non-physical. This accommodates Berkeleley's view that all that exist are immaterial minds and their ideas. It also fits with Plato's theory of Forms, where the Forms are pure essences (e.g. the Form of the Beautiful is alone really beautiful) transcendent of the physical world although the physical world 'participates in' or 'imitates' the world of Forms.

Mathematical 'platonism' holds that immaterial mathematical objects such as numbers and sets exist independently of the human mind. (Apologies to mathematicians, who can state it better.)

Your question raises the whole issue of the role of classifications ('labels') in philosophy: idealism, empiricism, realism, antirealism, pragmatism, conceptualism, &c. I think it is far better to establish what a philosopher holds exactly than to see what classificatory box s/he fits into. Boxes suppress differences: for instance Locke, Berkeley, and Hume are standardly put into the box marked 'empiricism' yet this conceals points of wide, even vital, difference between them. Locke recognised a physical world of primary qualities; Berkeley denied it in any sense Locke would have acknowledged. Berkeley has to do double duty in the box marked 'idealism' as well as 'empiricism' yet there is no significant similarity between Berkeleian idealism which posits God, mind or spirits, and their ideas, and Platonic idealism posits a transcendent world of pure essences.

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  • Apparently, you are looking for a meaning of " idealism" that applies both to Plato and , say, to Berkeley.

Let us then say that " idealism" is the doctrine according to which " the objects of sensible perception only have a mind dependent being".

Berkeley is ok with this : for him, sensible objects are real, but only inasmuch as they are perceived ( by a finite mind , or by God).

Plato is also OK : for him, sensible objects do not have absolute properties, their qualities depend on each one's point of view. Their being is a relative one, not an absolute one.

  • Now, Berkeley's idealism is a generalized idealism, for, according to him, there are no objects besides sensible objects. ( The other entities are not " objects " but " subjects" , that is minds : being is " percipi" or " percipere". )

Plato's idealims is not incompatible with the realist thesis according to which, besides sensible objects , there are mind-independent objects: that is Ideas, intelligible objects.

So Plato is idealist in our sense ; but he is a realist regarding Ideas.

As I understand your question, you are asking why Plato's commitment to Forms can be called idealism.

The terme " form" is the translation of Plato's " idea" or "eidos".

These words mean etymologically " what mind / intelligence sees, the intelligible ad-spect of a thing".

For example, when you have a desk in front of you, your physical eys sees its colour, it's shape, your hand feels its hardness , your muscles feel its heaviness, but your mind sees its " table-made-to-write-on-it-ness". " Being a desk" is not something your physical eye can see. Only your intellect ( mind's eye) can see this.

Your mindf grasps the Concept of a desk.

The Concept of a desk is not something that is in your mind; it is an object that faces your mind's eye. Other minds can also grasp it.

The Concept of a desk is not dependent on material / physical desks. If all physical desks were destroyed, the desk Concept would remain. After all desks have been destroyed, we could produce a new instantiation of this Concept.

Note : in Timaeus, Plato admits the existence of some " stuff" on which Ideas " reflect" ; in a way, this stuff is " matter" , or rather " space".

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