Plato
by Annaelle
Philosophy in CEGEP sucks, which is a weird slur because I never met any person or thing that sucked and wasn’t all kinds of awesome. Maybe it’s supposed to mean that CEGEP’s Philosophy is a damn tease and that we have to wait until university until we can have a full-fledged intercourse with Philosophy ?
Does that make sense ?
Ermm…
Sex joke aside, everyone who’s had a philosophy class in CEGEP is familiar with some ancient dude in a toga, who wrote about being tortured in a cave, or also that time he wrote about drinking wine and fantasizing over having sex with pubescent boys and it’s somehow supposed to be profound and enlightening about the meaning of truth, love and beauty.
I mean, yes, it’s actually enlightening. A little. Except that it’s all wrought in the now obscure and dated pop culture of ancient Athens, so most of it seems alien to modern readers. And while the books sure have some lovely prose, it always seems that the teacher who’s presenting Plato is pulling an interpretation out of their ass.
So here’s something more modern to understand what Plato was all about.
What kind of things exists ? Do properties exists independently of the individuals that have them ? (Those are the questions that Plato tried to answer with his famous theory of forms).
Imagine a number. Like 3. That number, it seems obvious, exists. It is manifest in all sets of 3 objects, and all ratios of length or size where one particular object is 3 times larger than another. We can observe the property «being a set of three objects» in those sets, and we can see the property «being three times as large as» in objects that are larger by this ratio to other objects, and both those property, collectively, instantiate three-ness.
Point is – it’s not controversial that the number 3 exists when we can experience that number so frequently in our day to day lives.
Now the harder part :
Imagine a number. Larger. Pick a larger number. Much, much larger. Go larger, and stop at a prime number. Let us say that you managed to pick a prime number arbitrarily large. A number so large, in fact, that it is larger than the number of possible combination of all the parts of the Universe. Which means that it cannot possibly be exemplified by any quantity of anything there is – except by the being larger than the number 1 by a factor of itself. For that reason, let’s call it a «vacuum number (VN)». VN is, obviously, an odd number – because 2 is the only even prime number, and it is much too small to be a vacuum number. Because VN is an odd number, it is preceded and followed by two even numbers, both of which can conceivably be «twice as much» as quantities that can, in fact, be expressed by at least one combination of some parts of the Universe.
The question is : does VN exist ?
We can have four possible cases : 1- VN exists. 2- VN doesn’t exist. 3- VN is partially existent. 4- VN is fully existent and fully non-existent at the same time. Because cases 3 and 4 raise important semantic and philosophic problems about existence, let us not consider these cases further today.
Let us instead consider option 2 : VN doesn’t exist. That means that, in the set of numbers that exist, we have two consecutive even numbers, and this is an extremely bizarre thing to consider.
That leaves us with option 1 : VN exists. This means that it is possible for numbers to exist even thought they are not represented in a corresponding set of objects. But now, does that mean that the idea of a unicorn can exist in the physical absence of a unicorn in the same way that the number VN can exist in the physical absence of a set of VN objects ?
If you can see why someone would want to say «yes», than you now understand Plato.
You are welcome.
Rekindled light 
Hello. Nice post!
Can I ask a question without picking a fight? Can I gently disagree? 3 is completely controversial! 3 is a shadow on the cave wall!
But, you might say, 3 is so famous! Everyone knows 3. It is obvious. Only to humans. Hmmm.
What is 3 made of? Can we find it? Is it matter or energy?
Only hoping to stir the pot. Enjoy your day!
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The property of being 3 is instantiated in every set of three objects. It is not made of matter nor of energy – it is a property, not an individual : where it can be found, it is its worldly instantiation which, according to platonists, is less perfect than the eidos of 3.
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But the property must “instantiate” in the mind of an individual. Plato is trying to say the “eidos” exists, when he’s simply invented it.
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Plato does not believe that he invented the eidos. He believed to have discovered it. Plato’s ontology also has the advantage of being able to explain that uninstantiated predicates such as «Is inertial» have a definite meaning. However it has the disadvantage that such predicates as «Is non-self instantiating» have absurd consequences for the theory.
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Thanks for the thoughtful reply. Oddly enough, invent and discover are synonyms. Part of my question here relates to your second conclusion above:
“Let us instead consider option 2 : VN doesn’t exist. That means that, in the set of numbers that exist, we have two consecutive even numbers, and this is an extremely bizarre thing to consider.”
Gently suggesting that option 2 is not complete enough. VN doesn’t exist and neither does any other number. Here is where it seems helpful to carefully define ‘exist’. Could there be two “realms” of existence? One physical, where there are no numbers at all. And the other metaphysical, where all the numbers can ‘exist’ along with my precious unicorn.
If all the humans disappeared from the planet simultaneously, where would 3 exist? Where would VN exist? Where are my unicorns!? Cheers!
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Aristotle would have believed that every number other than VN existed, because they were instantiated. Plato would say it’s absurd – VN must exist otherwise we have to consecutive even numbers, which makes no sense. And that led him to posit a metaphysical realm for numbers to exists independently of the physical.
Plato believed that the metaphysical realm was just as real as the physical realm, if not more-so. I’m not saying Plato is right, though, I’m just trying to explicit his line of reasoning.
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