platonism

Plato’s Idealism

Plato’s theory of knowledge, which Aristotle says is different from that of Socrates, was based on the idea that the object of knowledge must be permanent, eternal, and since nothing under the sun is permanent, we must seek stable knowledge outside this fleeting and deceitful world of material things. When Diogenes ridiculed the theory of Ideas, by saying he could see the cup, but not ―cupness,‖ Plato retorted that that was because he had eyes to see, but no intellect. And it is true that merely to base oneself on sense-perception is not enough. It is necessary to go from the particular to the universal. The fundamental flaw here is to think that the generalisations of the intellect can stand on their own, divorced from, and counterposed to, the material world from which, ultimately, they are derived. Marx and Engels in The Holy Family explained: in the philosophy of Idealism, the real relations between thought and being are stood on their head, ―for the absolute idealist, in order to be an absolute idealist, must necessarily constantly go through the sophistical process of first transforming the world outside himself into an appearance, a mere fancy of his brain, and afterwards declaring this fantasy to be what it really is, i.e., a mere fantasy, so as finally to be able to proclaim his sole, exclusive existence, which is no longer disturbed even by the semblance of an external world.‖ (MECW, Vol. 4, p. 140.) The sophistical trick whereby this is done was wittily explained in the same work: ―If from real apples, pears, strawberries and almonds I form the general idea ‗Fruit,‘ if I go further and imagine that my abstract idea ‗Fruit,‘ derived from real fruit, is an entity existing outside me, is indeed the true essence of the pear, the apple, etc., then—in the language of speculative philosophy—I am declaring that ‗Fruit‘ is the ‗Substance‘ of the pear, the apple, the almond, etc. I am saying, therefore, that to be a pear is not essential to the pear, that to be an apple is not essential to the apple; that what is essential to these things is not their real existence, perceptible to the senses, but the essence that I have abstracted from them and then foisted on them, the essence of my idea—‘Fruit.‘ I therefore declare apples, pears, almonds, etc., to be mere forms of existence, modi, of ‗Fruit.‘ My finite understanding supported by my senses does of course distinguish an apple from a pear and a pear from an almond, but my speculative reason declares these sensuous differences inessential and irrelevant. It sees in the apple the same as in the pear, and in the pear the same as in the almond, namely ‗Fruit.‘ Particular real fruits are no more than semblances whose true essence is ‗the substance‘—‘Fruit.‘ (Ibid, pp. 57-8.) Far from advancing the cause of human understanding, the idealist method does not take us a single step forward. Only a study of the real, that is to say, material world, can deepen our understanding of nature and our place in it. By directing men’s eyes away from ―crude‖ material things towards the realm of so-called ―pure‖ abstraction, the idealists played havoc with the development of science for centuries. ―By this method one attains no particular wealth of definition. The mineralogist whose science was limited to the statement that all minerals are really ‗the Mineral‘ would be a mineralogist only in his imagination. For every mineral the speculative mineralogist says ‗the Mineral,‘ and his science is reduced to repeating this word as many times as there are real minerals.

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Plato was not actually an idealist in the sense that he believed that conscious or mental experience is primary.

Plato takes these ideal forms as starting points. The ideal table is sometimes given as an example, but that’s probably not a core arcchetype of the universe or of god itself, but tables are created by human beings in particular cultural contexts, and they are an archetype in our perception. The way in which we classify the world, there is something like an ideal table. The forms that Plato is talking about are actually dimensions in an embedding space. In some of his texts, he alludes to a world outside of our perception, our mental construction that we experience, and that world is an outside [of our?] simulated world that is isomorphic to the world that we experience in these forms.

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"Traditional platonism"

A complete metaphysical, epistemological, and ethical package:

Theory of Forms: there are abstract, non-physical, eternal, unchanging entities (the Forms / ideas / eidê). For every kind of thing there’s a Form — the Form of Beauty, of Justice, of Circle, of the Good.

Particulars “participate” in Forms: A beautiful thing is beautiful because it partakes of the Form of Beauty. Physical objects are imperfect, shifting copies of perfect, stable originals.

Forms are more real than particulars.
Ontological hierarchy: Forms > physical things > images/shadows.
Plato’s Cave: what you see with your eyes is the shadow, not the thing.

Forms are accessed by reason, not senses. Episteme (knowledge) is of Forms; doxa (belief/opinion) is of the sensible world. The senses mislead.

The Form of the Good is the highest. Like the sun in the cave: source from which all other Forms derive their reality and intelligibility. Has ethical/political content — only philosopher-kings, who know the Forms, should rule.

Recollection (Meno): learning is remembering Forms the soul saw before birth. Ties to soul’s immortality.

Modern "mathematical Platonism" keeps one thin claim

Mathematical objects (numbers, sets, functions) exist mind-independently as abstract entities; we discover them.