What is Knowledge? Plato’s Theaetetus

In Theaetetus Plato plunges into epistemology, the theory of knowledge. What is knowledge? How do we know things? How do we really know what reality is? and similar questions are the topics of discussion.

The dialog opens with a flashback to Socrates, at the end of his life shortly before his trial, talking to the geometer Theodorus about his current pupils. Theodorus tells Socrates that one, Theaetetus, shows particular promise. The youth arrives on the scene and Socrates decides to test him dialectically. After some preliminary banter, he asks Theatetus to define knowledge, Theaetetus initially starts by listing different kinds of knowledge such as geometry, calculation, shoe making, and others. After some prompting from Socrates, he states that knowledge is perception. Socrates accepts this provisionally but points out that different observers perceive things differently. Does this mean that knowledge is relative? This begins a section which introduces the debate between objectivism and subjectivism which has been a perennial question of Western philosophy. According to most of the pre-Socratic philosophers, including Protagoras, Heracleitus, and Empedocles, reality is not only relative but in a state of constant flux, so knowledge about reality is also relative and mutable.

"Theaetetus crater 4103 h1 4103 h2" by James Stuby based on NASA Images [CC0 via Wikipedia]

“Theaetetus crater 4103 h1 4103 h2 (on Luna)” by James Stuby based on NASA Images [CC0 via Wikipedia]

This argument is the precursor not only to later Epicurean theories of the universe, such as we read about in Lucretius, but also foreshadows both postmodern theories of subjectivism and much of modern physics including thermodynamics, relativity, and quantum theory. For example, the passage,

Yes, Theaetetus, and there are plenty of other proofs which will show that motion is the source of what is called being and becoming, and inactivity of not-being and destruction; for fire and warmth, which are supposed to be the parent and guardian of all things, are born of movement and of friction, which is a kind of motion;–is not this then the origin of fire?

Expresses at least the glimmerings of an intuitive understanding of the laws of thermodynamics.

Socrates leads Theaetetus to explore the implications of these ideas further. He also introduces the point that mad men and dreamers see things that are not there, so perception does not necessarily lead to true knowledge. This struck me as interesting, since at the same time I was reading Hermann Hesse’s novel Steppenwolf, in which the main character certainly seems to gain knowledge from events which occur only in his own mind. Be that as it may, however, Socrates’ arguments are more than enough to force Theaetetus to rescind his definition of knowledge as perception.

Socrates then steers the dialog into a discussion of the nature of memory. What about a man who has obtained true knowledge but then forgets or makes mistakes based on that knowledge?

At this point, Theaetetus needs a little help and, at the urging of Theodorus, begins to argue the opposite position. Among other things, he mentions the point that while all men might perceive things differently, wiser men and those with reason and specialized training in the subject at hand, are more likely to perceive correctly and gain true knowledge.

Socrates has another trick to spring, though, when leads Theaetetus to explore the question “What is perception?” and points out that sensory inputs are meaningless until processed by the mind (soul). He then asks about abstract concepts which can not be perceived with the senses. Theaetetus soon agrees that “[K]nowledge does not consist in impressions of sense, but in reasoning about them in that only, and not in the mere impression, truth and being can be attained[.]”

If knowledge is actually a sort of opinion, though, what about false opinions? This line of inquiry leads them back into an exploration of memory, since failure of memory is one possible cause of false opinions. This leads them back into deep waters. Socrates then points out that they have not adequately defined the verb “to know”, nor the concept of “false opinion”. With these points clarified he leads the boy on another discussion in which they define knowledge as “a way of understanding something by understanding it’s component parts.”

From this position, Socrates introduces yet a third conception of knowledge, understanding things by understanding the differences between them. But after discussing this, they conclude,

But how utterly foolish, when we are asking what is knowledge, that the reply should only be, right opinion with knowledge of difference or of anything! And so, Theatetus, knowledge is neither sensation nor true opinion, nor yet definition and explanation accompanying and added to true opinion?”

Since the definition itself includes the word “knowledge” and is thus circular. However, even though they have failed to provide the definition for which they were seeking, they are better for the attempt itself. Socrates then leaves for his indictment before the king archon, possibly never to see Theaetetus again.

Never mentioned explicitly, yet ever present in the dialog, is Plato’s theory of ideas. Plato believed that even though the material world is indeed mutable, imperfect, and subjective, everything in it partakes of perfect ideals or ideas which are unchanging and objective. Perhaps Socrates doesn’t bring up the theory of ideas because he wants to see if Theatetus will discover the concept on his own. Perhaps Plato is simply trying to keep the dialog to a manageable size and complexity. Or perhaps the state of epistemology conveyed in the dialog is actually as far as Socrates ever got on the subject, and this particular dialog is meant to express the master’s views without Plato’s later additions.

Book Review: At The End of An Age

Lukacs, At The End of An Age, cover picture

At the End of an Age is a small book, and John Lukacs’ elegant yet simple prose could easily lull you into thinking it is an easy read.  It doesn’t take many pages, though, to realize that every paragraph in this book (or rather, book-length essay) is laden with complex ideas and meaning.  I found myself rereading whole pages to make sure I understood, and I suspect that I would need to read the whole book two or three times to pick up on all of his points.  That being said, the book is worth it.

As I mentioned in my previous post, the ostensible thesis of the book is that the modern age, which Lukacs calls the “bourgeoisie age” is nearing its end.  He offers cogent arguments and examples in support and, in general, makes a strong case.  As it happens, I agree with him; I wrote something very similar on this blog a couple weeks ago, before I had ever read Lukacs.  I think that anyone with some level of historical awareness can see that our civilization is gearing up for a drastic change.  Other historians I have read would have spent the entire book (or 12, in the case of Toynbee) expanding on their particular theory.  Lukacs, having laid out his arguments, then moves up to a higher, more meta-historical level.  Lukacs is interested not just in how history works, but in the epistemology and metaphysics of history and its relationship to the other sciences.  These are deep waters indeed.  Only Lukac’s strong voice and skill as a writer keep the reader from sinking.  Since I lack his mastery, I will not attempt to explain his points here, but will merely mention a couple of his main themes.

Lukacs believes that in history, as in quantum physics, the phenomena is ultimately inseparable from the observer.  The historian does not just record history but, in the act of writing it, actually influences and creates it.  This means that true objectivity is impossible for the historian, and that a purely deterministic conception of history is as obsolete as deterministic physics was after Heisenberg.  This matches up with comments I have occasionally made about history as a narrative.  History is based on fact but, ultimately, is a literary discipline.  This historian doesn’t just tell the story, he creates it.

Another major theme in the book is the role of the human mind in creating history.  Lukacs asserts that “the inclinations of men’s minds” and their beliefs are more important than their competence or any material factor.  “Mind” in this sense means consciousness or soul, separate from brain and body.  Lukacs believes in the power of the mind to influence reality and manifest different potentialities.  Comparative metaphysics is far from my specialty.  However, this sounds very similar to the writings of various New Thought philosophers,  particularly Earnest Holmes and his Science of Mind disciples.  I wonder to what extent the young John Lukacs was influenced by these metaphysical systems.  Regardless, the take away is that if a historian wants to understand a person or group he needs to go beyond studying their situation and strive to understand their minds.

Overall, I found many ideas in this book which I could agree with, or at least try on for size.  There were a few arguments, however, with which I did take minor issue.  In an early section of the book, as part of an overview of various ways the social structures of the current age are breaking down, he discusses the trend towards women’s equality in the workplace and announces that,

Women thought (or, rather, convinced themselves) that they were reacting against the age-old and often senseless categories and assertions  of male authority; yet their dissatisfaction often arose not because of the oppressive strength but because of the weakness of males.  The rising tide of divorces and abortions, the acceptance of sexual liberties, including pre-marital (and sometimes post-marital) habits of frequent copulation and other forms of cohabitation, the increasing numbers of unmarried women and single mothers, the dropping birth rate–thus the decline of the so-called “nuclear” family–were, especially after 1955, grave symptoms suggesting vast social changes.  They included the perhaps seldom wholly conscious, but more and more evident, tendency of many young women to desire any kind of male companionship, even of a strong and brutal kind, if need be at the cost of their self-respect. (pp. 23-24)

He offers no support for this complex, arguable, and potentially inflammatory claim.  This is not the sort of paragraph you just casually slip into a book without offering evidence to back it up.  This is the sort of thing which would have caused me, when I was still a teaching assistant grading papers, to circle the whole paragraph with red pen and write “BURDEN OF PROOF” in the margin.

Lukacs is also universally deprecatory of post-modernism in all of its forms, seeing it as a basically vague and degenerate direction for scholarship and culture.  That is a legitimate, if somewhat reactionary stance.  However, Lukacs, who escaped communist Hungary as a young man, is also blatantly anti-Marxist.  Since, as a historian, Lukacs could not help but be aware of the many contributions that Marxism has made to post-modern analysis and art, I have to question whether he might not be biased on the whole subject of post-modernism.

Finally, Lukacs is dismissive of any value in mathematics for the study of history.  As a “quant”, I feel compelled to respond.  As evidence, he cites his own non-deterministic, non-objectivist view of history as well as Gödel’s incompleteness theorems, which say that 1) Any non-trivial mathematical system contains some postulates which can not be proven without going beyond the system.  2) No mathematical system is capable of proving its own consistency.  Personally, I have been fascinated by Gödel’s theorems since I first studied them in an Abstract Algebra class that I took as a college junior.   As an illustration of what they mean, consider Euclid’s geometrical system, as set down in the Elements.  Euclid begins “A point is that which has position but no dimension.”  The entire system doesn’t work without this axiom, yet there is no way to prove that a point has no dimension using only Euclidean geometry.  You would need to introduce propositions from topology and/or calculus–which are themselves systems which contain propositions which can not be proven without introducing even more complex systems of mathematics.

Kurt Gödel in 1925 [public domain via Wikimedia]

Kurt Gödel in 1925 [public domain via Wikimedia]

And yet, geometry works quite well enough for most purposes, as do topology and calculus.  Granted, the incompleteness theorems seem to imply that a grand-unified theory of history, in the sense of of a closed form solution (plug all the variables into the equation, predict what will happen next) is impossible.  But applied math and statistics are about approximations, empirical formulas, noisy data, and models that work “well enough”, with a quantifiable margin of error.  The incredible advances over the past fifty years in fields like data mining, complexity theory, machine learning, and signal processing have paved the way for a useful discipline of mathematical history, probably within our own lifetimes.  Such a system will only be one more tool for the historian to use, and the results must not be allowed to dominate the historical narrative itself.  But to dismiss all mathematical history out of hand because it will not be an internally provable system seems like a major error.  Even in a non-deterministic universe, mathematical modeling can still provide startling and useful insights.

Despite these minor qualms, I truly enjoyed this book and would recommend it.  Overall, in fact, it is the kind of book I would like to write myself some day.  I will absolutely be reading (and probably reviewing) more of Lukacs’ works in the future.