What is the difference between Platos view on mathematics, and the view of a mathematical platonist? — LisaVardy

Mainly historical. But, the divergence is stipulated by science.

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Why does it take time? Because most of what philosophers write is a reaction to something, and without being at least somewhat aware if not conversant with what that something is, it is no easy matter to understand what the philosopher is saying. But that does not stop or even slow down many people, hence the fool. — tim wood

Correct. Didn't Socrates say that he couldn't understand why the oracle called him the wisest man?

Philosophy as understood in Ancient Greece was a way of life. It had to be lived to be understood. This is not to say that no fake philosophers existed even in those times. However, nowadays, in the absence of a living teacher, people read stuff like Plato's Symposium and imagine that philosophy was about quaffing wine mixed with water, admiring pretty boys and making speeches. Nothing further from the truth.

Few people in those days would have written a theoretical paper on philosophy without knowing what they were talking about, quite apart from the fact that the most important teachings were transmitted orally, from master to disciple. But, obviously, this day and age things are slightly different.

... hence the fool. — tim wood

:smirk:

Mathematical objects were for Plato hypothetical. This does not mean that he denied they existed but that the mathematician does not know them directly. She relies on reason, images, and the imagination.

Plato's mathematicians do not ask about the ontology, that is, the existence of mathematical objects. The mathematical Platonist asserts their existence.

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see a parallel between language and mathematics - taking them to be different things. Being familiar with language, we think we know language. And in an informal and uncritical sense, of course we do. And similarly with mathematics, or at least those part of mathematics we severally "know."

The book is on the table and 2+2=4. Eezy-peezy, and we find find as well that we can create in language, as well as just know it.

Alas, my recent experiences with learning a new (to me) language has reminded me of a more basic and fundamental reality. Which I will simply state briefly: we memorize language, and we memorize mathematics. And what we memorize is collective wisdom, practice, and knowledge, itself hard-earned and refined. There ain't no two, or three,..., but that someone decided there should be such, and a lot of other someones agreed was a good idea. And the same for candles, watermelons, and screwdrivers, and nouns, verbs, and the other parts of speech (which I actually know), in those languages that possess them. .

If anyone cares to argue that underlying these is a necessary mind, I agree. But the mind is/are just the human mind(s) that had the ideas and thought them good enough to embrace. — tim wood

Mr Wood,

Oh my. What relevance does this have with platonism and mathematical structures (other than substandard philosophy/jibbering)?

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What relevance does this have (in the OP) with platonism and mathematical structures ?

Second request, please answer.