Hermetic understanding of the fork

The thing is that they used the world of ideal forms in 3rd edition and it was rejected in 5th.

However what things do have is an unchanging essential nature. In fact you could muto a sapling into a full grown tree, and when the duration expired it would change back into a spaling, where if you us creo to accelerate its growth it remains fully grown. If you change the tree into a slug with Muto then it will resume the form of its essential nature when the spell expires.
Crafting something can make some changes to a thing's essential nature- metal can be refined, and shaped, but the intended use is not part of an object's essential nature.
Purpose is entirely an invention of human consciousness.

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It was my understanding that there is a perfect marker stone, and that the one we percieve is a distorted shadow. Some of those distortions may include anything etched into the real world marker stone.

A shadow of the perfect language? That has a physical form, that exists as a perfect exemplar?
Also I am reminded of the Hermetic Limit of Divinity and the Tower of Babel.

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If all languages are a shadow of a perfect language (language of Adam in ancient magic?) then would it not also follow that there is a perfect message that all texts are a shadow of, and that this is the message that will be revealed, regardless of what the actual message is?
Aside from which, as I mentioned earlier, te whole world of ideal forms was used in third edition and rejected for 5th.

Not quite.

The point is, that even in the case you posit the inmates of the cave are speaking/writing - and their interaction need not be mirrored thought by thought by objective true forms.

It doesn't matter, if there is an objective true form of language, a more perfect language like the (AM p.10ff) Language of Adam, or an original language, like that sought by Psammetich I in Herodot's anecdote.

No ancient or medieval philosopher - certainly not Plato - has claimed, that the interaction by language of the inmates has a true form, of which the actual interaction were just a shadow.

This sounds like an incredible concept for a Criamon or possibly somewhat demented Jerbiton mage: someone who’s looking for the perfect truth that lurks in every text, from the holiest of works to common doggerel.

One could argue that this is the consequence of Babylon. Only True Love can share some true form between caves.

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I agree here and this is crucial for the question in the OP. Since any specific fork is a reflection of the objectively ideal fork, then it is possible with intellego magic to sense the specifics forks belonging to the category of the platonic ideal, and thus its purpose as a fork.

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That is interesting, as it means that the fork exists as a true form, with the purpose of eating, long before it is invented. Then we should assume that space rockets exist too, and while Hermetic magic cannot affect anything beyond the lunar sphere, it can create a rocket that does. I don't know what other true forms exist, of which we have yet to see the shadows even in our time.

Just a thought experiment. I have no idea what conclusion it leads to.

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We should assume this only if space rockets actually can exist in ME. As far as I am aware the majority opinion is that space does not exist and that the physics required to make such a rocket also do not exist.

But assuming that the physics of ars magica are such that space rockets could exist, then yes I would assume that they have an ideal form.

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I don't have anything in canon, but I tend to differentiate the Techniques in that Creo makes the "shadow" of the perfect form crisper/less distorted, while Perdo makes the "shadow" less clear.
The other 3 Techniques fit the analogy less easily, but Muto uses smoke and mirrors to make the "shadow" look like something else, Rego to adjust the cave wall so the "shadow" is no longer in the same situation, and by default Intellego describes the "shadow" very finely.

None of them actually directly affect the perfect form that is casting the "shadow". As if it is some sort of Divine primitive, out of reach of Hermetic magic.

Canon is that there is something beyond the lunar sphere that Hermetic magic cannot affect, and the other planets (including the Sun) form more distant spheres in this -I call it- space. I agree that how this space works is less clear.

Sure. We are talking about the near perfect shadows that Creo can create from nothing.

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OK, I overlooked that.
Does tend to break my analogy. Unless the Creo magician is limited to "shadow" forms that they have already encountered? (like magi can't shapeshift into creatures they are unfamiliar with).

Having encountered it should be irrelevant. The basis is the true form, and in what sense did we ever encounter that?

OTOH the magus has to be able to call the form into being, so he has to be able to address the precise form he wants, whatever that means. It does not mean, however, that he has to be able to describe the form. Then there is the question if the magus can imagine and guess on a form, and have some chance to call forth something truly spectacular and unprecedented.

The Chinese have already invented black powder, and they are able to make rockets which fly into the air without magic, and Marco Polo writes about it AFAIR within the life time of our magi. It does not take a lot of imagination to name a form of some bigger and more powerful rocket which can make it to the moon. Why would such a true form not exist?

Yes, I am aware that 5ed no longer makes reference to Platonic forms. It is, however, not clear to me how their cosmology is supposed to work without them.

Agreed. I was introduced to Platonic forms in 4th Ed and it has stuck in my head since then.
all this wordage over whether Intellego examining a miniature gardening fork (or perhaps a wool comb on a stick), with only the skills appropriate to Terram, can intuit the act of eating, a function that is part of Corpus.

The arguments are so over the place by now I can't even work out if I am responding to the For or Against camp.

That is bound to happen in every sufficiently serious and deep discussion on fantasy roleplaying worlds.

In the real world, we have largely rejected Platonic and Aristotelean ideas, simply because they lead to inconsistencies when we explore their implications in sufficient depth.

Roleplaying is a the study of the what if. In our case, what if Plato and Aristotle are right, and we have magic on top, and then develop the world to the limits of our collective imagination. What do we see? No surprise. It is inconsistent.

Several posters have made the same point in different contexts.

The only conclusion we can draw is that we should not try to comprehend the world in its entirety. We should rather tell some good stories, tossing a coin every time the rules questions become too difficult. Then we should find a closure and a khatharsis, and start over with a new saga, before the old one gets so complex and messy that our heads ache.

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HOH:S rejects the idea of a world of forms and indicates that this can only be used for naturally occurring objects (rocks, trees, etc) not for manufactured objects, so all arguments based on plato's cave of shadows belong to a different Ars Magica universe than RAW.

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The World of Forms is not what HoH:S rejects. They may one or more aspects of Plato's, even if I was not able to find an explicit statement, but the World of Forms is explictly canon. The book also says that artificial things require a finesse roll to Creo, which natural things do not. Presumably this is what you are referring to.

That distinction between natural and artificial things seems to bring us to Herbert Simon (1969) and my initial thought that purpose derive from the contingencies of human society and not from the thing itself. Is anyone able to identify these ideas in medieval thought?

Where then is the world of forms made explicitly canon in 5th edition?

HoH:S:60 «The Creation of Beautiful Things» first paragraph. Wasn't this the section you were referring to too?

As I indicated this only specifies natural objects, not manmade ones, which at best it leaves to undefined metaphysics, and at worst is specifically trated seperately by the rules requiring finesse for manufactured items, suggesting that the world of forms only applies to the natural world, and that purpose cannot be a part of these natural forms unless it is guarded by the limit of the divine, since that purpose would belong to the mind of God.