Plato, Self-Predication, the Verb to Be and the Arity of Relations

Discuss any topics related to metaphysics (the philosophical study of the principles of reality) or epistemology (the philosophical study of knowledge) in this forum.
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Bluemist
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Re: Plato, Self-Predication, the Verb to Be and the Arity of Relations

Post by Bluemist »

ChanceIsChange wrote: December 16th, 2018, 8:43 am In Plato's dialogues, it is sometimes stated that that every Form is itself. For example, the Form of Justice is said to be just. I am wondering whether some characters in Plato's dialogues commit linguistic errors regarding this self-predication of Forms. Specifically, I stumbled over the following two.

a) ... Evenness. This is the property of being divisible by 2. Obviously, only numbers can have this property. But Evenness itself is a Form and not a number. Therefore, it can't possibly be even, i.e. divisible by 2. But of course, Evenness is obviously itself in that it is identical itself.
As far as I can see, there are (at least) four distinct meanings of the word "is":
1. Existence;
2. ... essence;
3. ... has-as-a-property
3.5. ... belongs-to
4. ... identity
... Do Plato's characters mix up these last two meanings of the word "is" when they say that every Form is identical to itself? Obviously, every Form is identical to itself, but, as is shown by the Form of Evenness, not every Form characterizes itself. By realizing the latter, we can also solve the problem of the third man.

b) ... In my opinion, the fact that some Forms, such as Equality, are binary relations and not unary ones proves that not every Form characterizes itself.
This comment is too multi-faceted for simple discussion. It includes metaphysical (I mean 'systematic' here), logical, semantic, translational, and interpretive issues before the specifics can be clearly investigated. As of today, none of these are resolved by commentators, and some of them are not open to resolution. Then there is the issue of Plato's invention and understanding of the then-existent philosophy and of his own developing and changing philosophy, which of course he could not complete for lack of logical and linguistic resources.

Analytic philosophers attempted to unravel the complexities of language, but the complexities of metaphysics await the arrival of newer 21th Century philosophy [should it ever happen].

While it would seem easy to dismiss Plato's Forms as unnecessary castles in the sky and to stick to what is real, as some Aristotelian philosophies would wish, this leads to a philosophical disaster. However, as Aristotle noted, if this were done, the possibility of rational thought and language would be gone [from systematic philosophy].

Plato's Forms, what he called 'really, really real' are quite different from what I called 'stick to what is real'.

For Plato, 'is' also means 'having being' and being 'real',

where these terms have meaning in his attempt to connect the Forms to his Particulars. It is in this sense that Forms are necessary for rational thought and language. Forms impose discrete bounds to the continuous world (which calls entirely unreal) which then can be labeled through the names of the Forms.
If you don't believe in telekinesis then raise your right hand :wink:
ChanceIsChange
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Re: Plato, Self-Predication, the Verb to Be and the Arity of Relations

Post by ChanceIsChange »

Bluemist wrote: March 4th, 2019, 3:38 pm While it would seem easy to dismiss Plato's Forms as unnecessary castles in the sky and to stick to what is real, as some Aristotelian philosophies would wish, this leads to a philosophical disaster. However, as Aristotle noted, if this were done, the possibility of rational thought and language would be gone [from systematic philosophy].
I totally agree except where you say that it would seem easy to dismiss Forms. I think that it’s rather the opposite: Forms are self-evidently real. Otherwise, how could it even make sense to think or say that certain particulars share a common feature?
Bluemist wrote: March 4th, 2019, 3:38 pm Plato's Forms, what he called 'really, really real'
I agree with Plato on this point.
Bluemist wrote: March 4th, 2019, 3:38 pm For Plato, 'is' also means 'having being' and being 'real',
These are basically the meanings of “is” which I have already mentioned when I said that the verb “to be” can mean existence and essence, right?
After all, existence necessarily lets reality follow, doesn’t it? (Of course it’s not the other way around, for e.g. the One is real – or rather over-real – but doesn’t exist since it stands beyond existence and not-existence.)
Bluemist wrote: March 4th, 2019, 3:38 pm It is in this sense that Forms are necessary for rational thought and language. Forms impose discrete bounds to the continuous world (which calls entirely unreal) which then can be labeled through the names of the Forms.
I agree except in the following points:
1. Does Plato really call the continous world wholly unreal? Doesn’t he just regard it as less real than the Forms?
2. I agree with Plato on the reality of Forms, but I do also consider the continous world which our ensouled bodies live in to be real.

All in all, I regard Plato’s Theory of Forms (ÞoF) and his unwritten Theory of Principles (ÞoP) quite highly and hold many of the tenets of those theories to be true. I’m mainly just saying that:
1. Not all Forms self-predicate, and by giving up the rather obviously false (according to my view) principle of self-predication, we save ourselves and the ÞoF a lot of trouble.
2. Thinking of Forms as prototypes is problematic, firstly because it needs self-predication, and secondly because (imho) it degrades Forms from being the features themselves to being things that merely have those features.
3. Plato or his characters sometimes misuse speech, which might be due to their lack of the needed logical and speech tools that you have mentioned.
4. It is conceivable that sometimes, it is not we, but Plato or his characters who think too concretely. For example, in the Parmenides, there is talk of inside, outside, beginning , middle and end regarding the One, even though all of those concepts look very suspect to me as having been inspired by everyday experience of the physical world. Maybe Plato himself made those mistakes, or maybe he wanted to show us that thinking too concretely leads to problems.
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Bluemist
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Re: Plato, Self-Predication, the Verb to Be and the Arity of Relations

Post by Bluemist »

ChanceIsChange wrote: May 13th, 2020, 4:11 am
1. Does Plato really call the continous world wholly unreal? Doesn’t he just regard it as less real than the Forms?
Plato has often been painted as a precursor of Aristotle. Nothing could be further from the truth. It is not the case that Plato had some Theory of Forms that needed to be corrected and brought down to earth as Raphael's painting the School of Athens with Plato pointing to heaven and Aristotle pointing to the ground would suggest. Plato should be pointing both ways.

Plato as a mathematician was concerned with continuously measured dimensional geometric figures as against discrete arithmetic numbers. He was troubled by the incommensurability of pi and some arithmetic ratios and the infinite divisibility of lines. The real Theaetetus was supposed to have solved some of these problems. Whereas the world is continuous, Parmenidean logic, Plato's only logical tool is discrete. To do philosophy of the visible world Plato needed to be creative.

Where this leads is that Plato suggested two philosophical models for the visible world. A Protagorean+Heraclitean model that is always continuously in flux, never stands still and therefore wholly unreal, and a second Platonic world of phenomenal particulars that momentarily does stand still and is real only for each momentary perception. Plato's particulars thus both are and are not as time flows, therefore somewhat more real for him.

For Plato, it makes perfect sense to say that the sky is blue and gray in parts, or even black at different times. The sky does not have permanent inherent color properties, although it may have other properties that give rise to different perceptions.
ChanceIsChange wrote: May 13th, 2020, 4:11 am
2. I agree with Plato on the reality of Forms, but I do also consider the continous world which our ensouled bodies live in to be real.
Both ensouled bodies and the world are continuous and have being according to Plato. But the only complete reality for Plato is that which never moves or changes and is unhypothetical.

If you want ensouled bodies to be real then you have to look elsewhere than Plato. Reality for non-idealists might be absolute Parmenidean-Aristotelian or maybe relative, as in real for me or real for her/it/them or maybe real in that system.
ChanceIsChange wrote: May 13th, 2020, 4:11 am
All in all, I regard Plato’s Theory of Forms (ÞoF) and his unwritten Theory of Principles (ÞoP) quite highly and hold many of the tenets of those theories to be true. I’m mainly just saying that:
1. Not all Forms self-predicate, and by giving up the rather obviously false (according to my view) principle of self-predication, we save ourselves and the ÞoF a lot of trouble.
2. Thinking of Forms as prototypes is problematic, firstly because it needs self-predication, and secondly because (imho) it degrades Forms from being the features themselves to being things that merely have those features.
3. Plato or his characters sometimes misuse speech, which might be due to their lack of the needed logical and speech tools that you have mentioned.
4. It is conceivable that sometimes, it is not we, but Plato or his characters who think too concretely. For example, in the Parmenides, there is talk of inside, outside, beginning , middle and end regarding the One, even though all of those concepts look very suspect to me as having been inspired by everyday experience of the physical world. Maybe Plato himself made those mistakes, or maybe he wanted to show us that thinking too concretely leads to problems.
This is difficult to discuss because Plato's alleged Theory of Forms (Plato never said anything like that) is current dogma in every classroom.

Plato formulated many different versions of the Forms starting from a corrected version of the One of Parmenides. Socrates' entire aim appears to have been to discover the Good and Virtue. By the Phaedrus, the five elemental forms of Virtue turn out be one and the same.

Analytic critiques of the middle-period Forms are completely logical but are all un-Platonic. Plato would just laugh them off as nonsensical. He in fact moved on from seemingly devastating attacks in the Parmenides completely unfazed to a more complex version of the Forms in the late dialogues. Doing so, he never gave up on any of the earlier versions of the Forms. Analytics need to give Plato the benefit of the doubt here and admit that Plato was more advanced and much smarter as well.
If you don't believe in telekinesis then raise your right hand :wink:
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Re: Plato, Self-Predication, the Verb to Be and the Arity of Relations

Post by Mlw »

The Form of the Even needn't be arithmetically divisible by 2, because we must think of the Forms as qualities. All even numbers have a quality evenness. This is like a smell or a flavour, on which we cannot do arithmetical operations. At least, this is one way of looking at it. But we must remember that this quality is something divine and otherworldly. We can only faintly understand what the quality of a number is, for instance.

Today, I published an article that discusses the nature of the Form: [url=http://mlwi.magix.net/platonicform.htm]The Platonic Form as Self-Generating Triunity : The Resolution of the Third Man Argument[/url].
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Re: Plato, Self-Predication, the Verb to Be and the Arity of Relations

Post by Mlw »

"The Platonic Form as Self-Generating Triunity : The Resolution of the Third Man Argument"
http://mlwi.magix.net/platonicform.htm
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