2. The Problems of Metaphysics: the “Old” Metaphysics
2.1 Being As Such, First Causes, Unchanging Things
2.2 Categories of Being and Universals
2.3 Substance
3. The Problems of Metaphysics: the “New” Metaphysics
3.1 Modality
3.2 Space and Time
3.3 Persistence and Constitution
3.4 Causation, Freedom and Determinism
3.5 The Mental and Physical
3.6 Social Metaphysics
Since I'm an old fogy, defining Essences in the infinite (undefinable) context of zillions of possible (not yet real) worlds just hyperbolically complicates the concept for me. Why not just define Forms in terms of concepts, patterns & meanings (Essences) in human minds, in the only uni-verse (one world) we know anything about? {i.e. parsimony} Wouldn't plain old Aristotelian Logic suffice to deal with that narrow definition*1?There is a clear way of talking about essences, as those properties had by an object in every possible world in which it exists. We can deal with the consequences of essences using this stipulation. — Banno
Yes. Plato used the formal structure of geometry (e.g. triangles) to describe the Truth & Utility of immaterial Ideas relative to material Objects*1. Likewise, modern quantum physics deals with the invisible structure of matter that can only be known by means of mathematics*2. Hence, we accept the statistical wave nature of subatomic "particles" as True, even though they don't behave like ordinary matter (e.g. quantum tunneling ; two-slit experiment).1. The Forms are a separate domain of discourse, which one is only able to grasp with understanding of mathematics. — Shawn
Some relevant domain distinctions are Abstract vs Concrete & Relations vs Things & Ideal vs Real & Mental vs Material & Cultural vs Natural. The Forms, like Math, are logically true even though materially false. In their relevant cultural domain (psychology ; philosophy), Forms are useful tools for thinking, even though useless for manipulating matter, until trans-formed into a natural domain (physics ; science). — Gnomon
SO, what are your thoughts about the ineffability of mathematics and the problematic translation of Truth rendered in mathematics, which is poorly understood as a language that can be seen in informal languages? — Shawn
Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago.
Platonism, as mathematician Brian Davies has put it, “has more in common with mystical religions than it does with modern science.” The fear is that if mathematicians give Plato an inch, he’ll take a mile. If the truth of mathematical statements can be confirmed just by thinking about them, then why not ethical problems, or even religious questions? Why bother with empiricism at all?
Mathematical objects are in many ways unlike ordinary physical objects such as trees and cars. We learn about ordinary objects, at least in part, by using our senses. It is not obvious that we learn about mathematical objects this way. Indeed, it is difficult to see how we could use our senses to learn about mathematical objects.
Ironically, although Strings are defined as vanishingly small --- smaller than sub-atomic particles --- they are still assumed to be material & physical, not just mathematical. The image below indicates that some physicists imagine Strings as physical things : building blocks of Quarks, which themselves present no physical evidence to support their theoretical existence.I believe that string theory is closest one can approach the Forms in terms of mathematics and physics as one would or could imagine. It's the only field in physics that is entirely dependent on mathematical relations. — Shawn
...the inherent difficulties of the materialist theory of the atom, which had become apparent even in the ancient discussions about smallest particles, have also appeared very clearly in the development of physics during the present century.
This difficulty relates to the question whether the smallest units are ordinary physical objects, whether they exist in the same way as stones or flowers. Here, the development of quantum theory some forty years ago has created a complete change in the situation. The mathematically formulated laws of quantum theory show clearly that our ordinary intuitive concepts cannot be unambiguously applied to the smallest particles. All the words or concepts we use to describe ordinary physical objects, such as position, velocity, color, size, and so on, become indefinite and problematic if we try to use them of elementary particles. I cannot enter here into the details of this problem, which has been discussed so frequently in recent years. But it is important to realize that, while the behavior of the smallest particles cannot be unambiguously described in ordinary language, the language of mathematics is still adequate for a clear-cut account of what is going on.
During the coming years, the high-energy accelerators will bring to light many further interesting details about the behavior of elementary particles. But I am inclined to think that the answer just considered to the old philosophical problems will turn out to be final. If this is so, does this answer confirm the views of Democritus or Plato?
I think that on this point modern physics has definitely decided for Plato. For the smallest units of matter are, in fact, not physical objects in the ordinary sense of the word; they are forms, structures or — in Plato's sense — Ideas, which can be unambiguously spoken of only in the language of mathematics.
I agree. The ancient Greeks didn't have the technology to dissect real material things into their substantial elements (e.g. Atoms). So instead, they tried to analyze Reality into the Ideal/Mathematical essences of the world (e.g. Forms). We now call that "pursuit" of abstraction Philosophy. Over time though, technological inventions, such as the telescope and microscope, allowed Natural investigators to actually see what before could only be envisioned via Mathematics and imagined by Reason.In this way, it is the pursuit of the ideal that allows us to calculate the behavior of objects in motion sufficiently enough to visit other bodies in space. In my view, by doing so humanity clearly demonstrated that the ideal was real. — David Hubbs
In quantum physics today, the "smallest units of matter" (e.g. quarks, preons) are statistical probabilities rather than physical objects. Yet, the units of Statistics are data : bits of Information. And the four main types of statistical data are nominal, ordinal, discrete, and continuous. All of which are categories of mental concepts, not instances of material objects*1.I think that on this point modern physics has definitely decided for Plato. For the smallest units of matter are, in fact, not physical objects in the ordinary sense of the word; they are forms, structures or — in Plato's sense — Ideas, which can be unambiguously spoken of only in the language of mathematics.
Yes. And the Quantum physics of early 20th century seems to have required a Philosophical return to Platonic logistikon*1 (reasoning ability) after years of reliance on technological mēkhanikos*2. When subatomic particles proved to be too small for their devices to resolve, scientists were forced to resort to statistical math*3 to determine the structure & properties of unseen things. Thus, modern Physics became more Theoretical, and less Empirical. For example, Einstein & Planck didn't work in gadget-filled laboratories, but in pencil & chalk provisioned offices.The concept of Forms in Plato is not about invisible particles or mathematical abstractions per se, but about the intellect’s ability to grasp stable, intelligible principles that underlie the flux of experience. — Wayfarer
Philosophy Now magazine (April 2025) presents the Question of the Month : Is Morality Objective or Subjective? And one writer said "Objective moral principles are necessary to reconcile worldviews". So, it occurred to me that his theory of universal Forms might have been an attempt to objectify-by-edict ("thus saith the Lord") mandatory ethical rules that would otherwise be endlessly debatable.So does the distrust of Platonism really come down to the fact that Plato's 'ideas' are not things that exist in space and time, and that the only reality they could possess are conceptual? — Wayfarer
So it seems we must accept them on Plato's authority, or by agreement of our own reasoning with his. Similarly, the ancient Hebrews were presented by Moses with a compendium of ethical rules, that were supposed to be accepted as divine Laws. And violations would be punishable by real-world experiences, up to and including death & genocide. — Gnomon
Philosophy Now magazine (April 2025) presents the Question of the Month : Is Morality Objective or Subjective? And one writer said "Objective moral principles are necessary to reconcile worldviews". So, it occurred to me that his theory of universal Forms might have been an attempt to objectify-by-edict ("thus saith the Lord") mandatory ethical rules that would otherwise be endlessly debatable. — Gnomon
Ha! I didn't mean to equate them as "historical types", such as a messianic prophet. I imagined them as more like analogous divine intermediary types, handing down the Truth of God (Laws vs Forms) to ordinary mortals.Many would say that Plato and Moses were completely different historical types — Wayfarer
...the ancient Hebrews were presented by Moses with a compendium of ethical rules, that were supposed to be accepted as divine Laws. And violations would be punishable by real-world experiences, up to and including death & genocide. — Gnomon
Plato’s dialogues are meticulously rational albeit with some mythological elements. — Wayfarer
What I'm still struggling with is the Subjective vs Objective nature of the Forms. Sure, Plato assures us that there is an ideal Concept, Pattern, Design of everything, but not in the Real world, so why should we believe him? As a professional designer myself, I like the idea that there is a perfect house for this couple, for example. But I've never even come close.While Moses's revelation is of eternal commandments, Plato's noetic apprehension of the Forms (especially the Form of the Good) is more intellectual ascent. — Wayfarer
Yes. I'm sure you are not used to thinking of Forms in such irreverent terms. But my ignorant subjective/objective question about ideal Forms vs real Things, is "which is the caricature, and which is the original"? Did Plato discover the Forms, or did he invent them? It's just a rhetorical thought, no need to answer. :wink:Your depiction of the forms is something of a caricature. All I can say is, do more readings. — Wayfarer
Thanks for that insight. I hope you'll pardon me for my layman's playful use of less technical terms for discussing "spooky" invisible concepts that are only apparent to highly intelligent beings. Although Principles are of primary importance for philosophers, they may be un-intelligible to non-philosophers. I suppose that all humans have some minimal ability to broadly categorize their environment, but only a few go so far as to break it down into fundamental (essential) concepts for understanding (intellectual comprehension). For example, most people can count up to ten, but only a few can deal with infinities & differentials.↪Gnomon
Plato’s so-called ‘Forms’ might be better understood as principles of intelligibility —not ghostly objects in another realm, but the structural grounds that make anything knowable or what it is. To know something is to grasp its principle, to see what makes it what it is.
And they’re neither objective - existing in the domain of objects - nor subjective - matters of personal predilection. That is why they manifest as universals — Wayfarer
most people can count up to ten, but only a few can deal with infinities & differentials. — Gnomon
as you implied, Universals may be an overarching third class of knowables, and yet we only know them via rational extrapolation from objective observation. They are not obvious, but must be discovered (revealed) by means of rational work. — Gnomon
Forms...are radically distinct, and in that sense ‘apart,’ in that they are not themselves sensible things. With our eyes we can see large things, but not largeness itself; healthy things, but not health itself. The latter, in each case, is an idea, an intelligible content, something to be apprehended by thought rather than sense, a ‘look’ not for the eyes but for the mind. This is precisely the point Plato is making when he characterizes forms as the reality of all things. “Have you ever seen any of these with your eyes?—In no way … Or by any other sense, through the body, have you grasped them? I am speaking about all things such as largeness, health, strength, and, in one word, the reality [οὐσίας, ouisia] of all other things, what each thing is” (Phd. 65d4–e1). Is there such a thing as health? Of course there is. Can you see it? Of course not. This does not mean that the forms are occult entities floating ‘somewhere else’ in ‘another world,’ a ‘Platonic heaven.’ It simply says that the intelligible identities which are the reality, the whatness, of things are not themselves physical things to be perceived by the senses, but must be grasped by reason. — Eric D Perl, Thinking Being, p28
Like Plato & Kant, due to the Materialistic bias of our language, I have been forced to borrow or invent new words (neologisms) to describe Metaphysical*1 concepts that don't make sense in Physical terms. In my Enformationism thesis, I describe those "occult entities" as Virtual or Potential things. I'm appropriating terms that scientists use to describe not-yet-real particles and incomplete electrical circuits for use as metaphors of un-real Forms. At my advanced age, I am still learning the lingo.This does not mean that the forms are occult entities floating ‘somewhere else’ in ‘another world,’ a ‘Platonic heaven.’ It simply says that the intelligible identities which are the reality, the whatness, of things are not themselves physical things to be perceived by the senses, but must be grasped by reason. — Eric D Perl, Thinking Being, p28
So much of this has actually filtered through to the way we understand the world today - after all the Greek philosophers are foundational to Western culture. So to understand principles, to see why things are the way they are, is to see a 'higher reality' in the sense that it gives you a firmer grasp of reality than those who merely see particular circumstances. Indeed the scientific attitude is grounded in it, with the caveat that all of Plato's writings convey a qualitative dimension generally absent from post-Galilean science. — Wayfarer
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