applied philosophy, deep democracy, sustainability / by A.R.Teleb
|Plato’s dialogue “Parmenides” is notoriously enigmatic. Viewing it through the proper (wide-angle) lens, however, it is quite readable and well worth the effort. In it, the philosopher critiques his own theory of ideas as he illustrates some of the most critical philosophical riddles (paradoxes) of his time. It is also a satisfying demonstration of the progress that’s been made in philosophy, language, logic, and mathematics.|
What does it still have to tell us 2400 years later?
People often wonder, does philosophy make advances like natural sciences? Or is it meaningless to ask, like asking if literature or art make progress? Does philosophy even matter to anything except itself? Is it in any way “useful”?
This dialogue does not even present any of these questions. But, as a sketch of the arc of philosophy and its possibilities, I know of no better text. Incidentally, it also happens to answer the above about the nature of philosophy and work as an optimum pedagogical tool.
After giving a quick outline, I will lay out a few of the paradoxes presented, then give an explanation of each and why they matter. And yes, this will include why the egg came before the chicken.
The characters of the dialogue are the young Socrates, the elder Parmenides, his pupil Zeno, and a young companion new to philosophy, Aristotles. Parmenides, founder of the school of thought associated with the city of Elea, famously used logic to deny the very possibility of change or the multiplicity of objects in the world.
Parmenides was renowned as the Philosopher of the One–that there is only one indivisible, unchanging thing in the universe! After his death, this thesis was still taken seriously by some, namely, Plato who supposedly held him in high esteem and thought of him as the father of philosophy. Others did not agree so much, viz. Aristotle, who said that his idea “follows logically, but to believe it is next door to madness.” Of course, Plato had his own controversial theory, and that’s what brings them together in the dialogue. Plato, as usual, employs Socrates as a stand-in for himself.
The dialogue has two marked parts. In Part I, Socrates talks to Zeno and Parmenides about his theory of ideas. In Part II, Parmenides demonstrates the “new art of talk,” as he calls it, on his own theory of the one. He appears to dismantle his own theory for the benefit of his pupil Socrates.
The kernel of the argument begins when Parmenides addresses Socrates, “I admire the bent of your mind towards philosophy; tell me now, was this your own distinction between ideas in themselves and the things which partake of them?”
His initial responses set Parmenides off on a relentless logical assault on the “theory of ideas” that Socrates is unable to parry. It poses no difficulty for today’s reader, keeping in mind that “idea” could mean thought, concept, or representation.
When Socrates admits that he does not have adequate responses to the objections, Parmenides digs his knife deep,
“if a man, fixing his attention on…difficulties, does away with ideas of things and will not admit that every individual thing has its own determinate idea which is always one and the same, he will have nothing on which his mind can rest; and so he will utterly destroy the power of reasoning.”
“But…what is to become of philosophy? Whither shall we turn, if the ideas are unknown?”
Plato presents a deep issue in doing philosophy, or using language at all for that matter. How do we know whether the thoughts in our minds correspond with “the world of perceptions?” If we are seeking the true, the good, the absolute–not mere opinion–not mere convention–how do we get there? If we construct a consistent world of ideas through our dialogues, or through the “dialectic,” how do we know this functions in the material world?
Part II begins.
Parmenides, at the imploring of Socrates, Zeno et al., but only after coquettishly lamenting how he’s no longer so young as to rise to the performance, offers to demonstrate “the new art of talk” he believes the young Socrates needs to practice. He even chooses his own “theory of the one” to place on the operating table.
By first assuming one hypothesis than its opposite, and arriving at similarly impossible conclusions, he leaves us in a quandary. Here is the skeleton of the first of the argumentative fugues:
“If one is…the one cannot be many?”
“And the one, when it changes and ceases to be itself, cannot be any
“Then the one cannot possibly partake of being?…
Then the one is not at all?
Then the one does not exist in such way as to be one; for if it were
and partook of being, it would already be; but if the argument is
to be trusted, the one neither is nor is one?”
And there lies the paradox: “if the one is then it is not; if it is not one than it is.”
Why should Parmenides do this? Why would a teacher demonstrate that his own theory is susceptible to such attack? Is he saying that his theory is merely a play on words? Surely not.
Interpretation of Part II as a parody would not hold water, neither would it be interesting. It is known that Plato held Parmenides in the highest esteem and judged him a master in the art of thinking. Moreover, Socrates admits the very difficulties that Parmenides and Zeno brought up regarding the “theory of ideas.”
There’s a more satisfying reading. Parmenides steps in to teach us, and all subsequent generations of system builders, that something is amiss. We must either accept making some logical jumps or be contented with saying little about the world of perceptions—or, there is something about the way we speak that is inadequate to some of the issues.
The dialogue illustrates some paradoxes, some of which Plato himself hints at resolving, some of which were “solved” quite recently, and at least one of which is still disputed.
First, Plato suggests that in saying “one is,” and “the one is one,” Parmenides uses “is” in two different senses. In logic this is called “the fallacy of equivocation.” Since the meaning of “is” in the first instance involves existence, it’s called the “existential is.” The second, indicating a property of the verb’s subject, is called the “predicative is.” Although he did not use the exact words, Aristotle himself pointed out that the solution to this riddle is that Parmenides uses it in two different senses. Anthony Gottlieb called Parmenides’ equivocation “a clever mistake” because it revealed something about how we use language.
As an aside, not all languages use “is” in both senses, it just happens that both Greek and English (along with many European languages) have this ambiguity. For example, neither Arabic and Hebrew use the verb “to be” in the predicative sense; they simply place subject and complement adjacently. This is conclusive evidence that the paradox is not universal and therefore not part of thinking itself.
Second, the seeming impossibility of talking about “what is not” (what does not exist) likewise no longer poses a problem for philosophy. How can we talk about what a unicorn is if unicorns do not exist? Surely if it “is not” then we can make no statements about it. This conundrum was nicely solved by Bertrand Russell, the philosopher–mathematician that made a name for himself working on such paradoxes. See, Sorensen‘s “A Brief History of the Paradox.”
When Parmenides rhetorically asks Socrates, “And can there be individual thoughts which are thoughts of nothing?” he is referring to what is now called “negative existentialism.”
Russell’s elegant explanation is that when we talk about hypotheticals we are making no claim as to existence at all. We could for example, create a “set of red flying pigs” and a “set of black flying pigs” and the third, containing the second, “set of black pigs.” It only at a second step that we further distinguish “pigs that exists” from “pigs that do not exist.” It is not a paradox that the different hypothetical sets may or may not overlap, no more difficult than the fact that the “set of all triangles” overlaps with the “set of all purple triangles.”
Third is a riddle that we’ve all heard of before, that is not a paradox at all, at least not anymore if you believe in natural selection. After Darwin, science would categorically answer that the egg came first. Because mutations in the genes are passed on only at the time of procreation, a non-chickens zygote would have first mutated (into chicken DNA) then hatched the first chicken (or rooster) after fertilization and incubation.
As an aside, another example of a “solved” paradox, quite literally in this case, comes from Zeno. Here’s one version of it. If a turtle starts with a one yard lead on Achilles, and Achilles cuts the separation in half every second, will he ever catch up? Mathematically the question is does 1/2 + 1/4 + 1/8 + 1/16 + … add up to 1? Yes, indeed, as most high school Algebra students could show.
Fourth is another riddle that no longer troubles (most) thinkers. When Parmenides instructs Socrates to “consider not only the consequences which flow from a given hypothesis, but also the consequences which flow from denying [it],” he is referring to argument in “reductio ad absurdum” or argument from contradiction.
Although at the time it was considered a kind of trickery, or even sophistry, it is now a generally accepted method of argumentation in science and mathematics. All the same, a rather elegant (and intuitively gratifying) school of thought in mathematics “The Constructivists” will not accept proof of existence based on a contradiction. For them, a mathematical object is only real if it can be put together following a step by step algorithm. There’s even an impressive sub-group “The Strict Constructivists” that will only accept proofs that can be done using “collapsible compass, unmarked straight-edge, a method of accounting, and nothing more.”
Finally, the “real paradox,” and perhaps THE grand riddle of philosophy, Parmenides tells Socrates that he has a much bigger problem. If the “world of ideas” [to us thoughts and concepts] is intractably separate and distinct from the “world of perceptions” [to us sense experience] how could either realm know anything about the other? Said in another way, just because something works logically, it does not follow that it is true in the external world–at least, without a further assumption.
Parmenides continues, “the greatest of all is this: If an opponent argues that these ideas, being such as we say they ought to be, must remain unknown, no one can prove to him that he is wrong, unless he who denies their existence be a man of great ability and knowledge, and is willing to follow a long and laborious demonstration.”
Voila the heart of the issue. This is where philosophers have continued to debate for many centuries, and where I will spend more time in upcoming posts on the history of philosophy.
Philosophy is at once analytic and synthetic, reductive and creative, clarifying and complicating. But even in complicating it reveals the contours of our own imaginations, and simply, opens up possibilities. Ultimately we choose whether to entertain this or that particular possibility, and in so doing philosophy has served a “useful” function.
[The above parallels Episode 4 of my short and sweet “philosophy 101″ talk that “aired” on Moondog Medicine on Hollow Earth Radio on Dec 23. Previously, I discussed one of Plato’s first dialogues “Meno.” I find it elucidating and compelling to read the two dialogues together. My next philosophy post will reflect Episodes 5 & 6 on Aristotle’s Ethics and Politics, relating them to modern political science.]
[For alternative interpretations of the dialogue see the Stanford Encyclopedia of Philosophy.]
Update, November, 2014: Looking back at this post almost two years on, I must say that there appears to be more to this dialogue than I have begun to articulate or even understand. A better philosopher, one with a deeper understanding of Parmenides, and probably Hegel, could do it more justice.
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