A MARGINAL NOTE ON THE MENO 'EXPERIMENT'
A marginal note on the Meno ‘experiment’
In many of my writings I strongly opposed the commonly sanctioned view (which we have Aristotle to thank for in the first place) that Socrates in his elenctic discourses aimed at reaching definitions. I have expounded and defended my unorthodox position throughout my writings but particularly in “The Socratic Elenchus” (Chapter Three of Plato: An Interpretation) and in “The Euthyphro as a Philosophical Work” http://www.philosophos.com/philosophy_article_101.html (also to be found on this blog). Here I wish merely to add the following marginal note:
Although in the Meno ‘experiment’ the boy in the end reaches a positive, true, answer, this does not contradict Socrates’ usual elenctic procedure. Up to 83e10 we have the common elenchus, leading to aporia, and at 84a2 the boy confesses: alla ma ton Dia, o Socrates, egôge ouk oida. But at this point Socrates had already moved from refuting to showing. He says to the boy: peirô hêmin eipein akribôs· kai ei mê boulei arithmein, alla deixon apo poias. — The significant phrase here is mê arithmein, alla deixon and Socrates goes on to help the boy to ‘show’ or rather to see. For, as Kant insisted, geometry rests on intuition, and I will venture – although here I am uncomfortably conscious that I am swimming out of my depth – that when mathematicians calculate (arithmein) for such a problem, they work backwards from intuition. So the boy in the ‘experiment’ is helped to look and see just as in the properly elenctic discourses the interlocutor is led to look within her/his own mind to behold the meaning sought after in the immediacy of active intelligence (nous, phronêsis) and realize that there is no other explanation than “It is by Beauty that all that is beautiful is beautiful” and that it is in vain to seek understanding in the objects of the phenomenal world.
D. R. Khashaba
Cairo, Egypt, August 1, 2007
In many of my writings I strongly opposed the commonly sanctioned view (which we have Aristotle to thank for in the first place) that Socrates in his elenctic discourses aimed at reaching definitions. I have expounded and defended my unorthodox position throughout my writings but particularly in “The Socratic Elenchus” (Chapter Three of Plato: An Interpretation) and in “The Euthyphro as a Philosophical Work” http://www.philosophos.com/philosophy_article_101.html (also to be found on this blog). Here I wish merely to add the following marginal note:
Although in the Meno ‘experiment’ the boy in the end reaches a positive, true, answer, this does not contradict Socrates’ usual elenctic procedure. Up to 83e10 we have the common elenchus, leading to aporia, and at 84a2 the boy confesses: alla ma ton Dia, o Socrates, egôge ouk oida. But at this point Socrates had already moved from refuting to showing. He says to the boy: peirô hêmin eipein akribôs· kai ei mê boulei arithmein, alla deixon apo poias. — The significant phrase here is mê arithmein, alla deixon and Socrates goes on to help the boy to ‘show’ or rather to see. For, as Kant insisted, geometry rests on intuition, and I will venture – although here I am uncomfortably conscious that I am swimming out of my depth – that when mathematicians calculate (arithmein) for such a problem, they work backwards from intuition. So the boy in the ‘experiment’ is helped to look and see just as in the properly elenctic discourses the interlocutor is led to look within her/his own mind to behold the meaning sought after in the immediacy of active intelligence (nous, phronêsis) and realize that there is no other explanation than “It is by Beauty that all that is beautiful is beautiful” and that it is in vain to seek understanding in the objects of the phenomenal world.
D. R. Khashaba
Cairo, Egypt, August 1, 2007
posted by D. R. Khashaba at 10:12 AM
1 Comments:
KHASHABA:
In many of my writings I strongly opposed the commonly sanctioned view (which we have Aristotle to thank for in the first place) that Socrates in his elenctic discourses aimed at reaching definitions. I have expounded and defended my unorthodox position throughout my writings but particularly in “The Socratic Elenchus” (Chapter Three of Plato: An Interpretation) and in “The Euthyphro as a Philosophical Work”
COMMENT:
You seem to neglect INDUCTIVE ARGUMENT (and UNIVERSAL DEFINITION) as Aristotle's stated [Metaphysics] 2 contributions of Socrates to philosophy.
With respect to Meno's slave, we have an example of INDUCTIVE ARGUMENT, rather than of UNIVERSAL DEFINITION, for "squaring" was a well defined Geometrical Technique in Socrates's time. Meno failed to give Socrates a UNIVERSAL DEFINITION of "virtue". His slave, in contrast, eventually gave Socrates a correct answer to a geometry problem involved with the geometrical technique of "squaring", as distinct from the Grammar and Philosophical "problems" of DEFINING.
KHASHABA:
Although in the Meno ‘experiment’ the boy in the end reaches a positive, true, answer, this does not contradict Socrates’ usual elenctic procedure. Up to 83e10 we have the common elenchus, leading to aporia, and at 84a2 the boy confesses: alla ma ton Dia, o Socrates, egôge ouk oida.
COMMENT:
My English translation of the passage quoted in Greek seems to be, SLAVE:- It's no use Socrates. I just don't know.
That seems to be what Mr. Khashaba calls "aporia", although it is only a confession of ignorance on the plough boy's part. But, as a matter of fact, his answers to how one "doubles" a 4 foot square figure (to obtain an 8 square foot figure) went from 16 square feet, which was "way off", down to a 9 foot square figure, which was much closer to the 8 square foot figure Socrates asked him to construct. So the slave's answers were improving.
But, when asked to correct the "better" 9 square foot figure (based on a 3 foot side) to a perfect 8 square foot figure, that is when the slave admitted his personal "aporia", quoted, in Greek, by Khashaba above. At that point Socrates argued to Meno that they had done his slave no harm and had actually helped him by having him confess his own ignorance --- whereas, at first, he had answered very boldly, but with an equally "bold" wrong answer.
In being once "stung" or "numbed", the slave's 2nd and less confident answer was closer to the correct answer, but still a wrong answer, at which point he confessed that he didn't know upon which LINE he could construct an 8 square foot figure.
KHASHABA:
But at this point Socrates had already moved from refuting to showing. He says to the boy: peirô hêmin eipein akribôs· kai ei mê boulei arithmein, alla deixon apo poias.
QUESTION:
Do you mean, in English, where Socrates says,
SOCRATES:
If you don't want to count it up, just show us on the diagram. (???)
Obviously I don't have the text in Greek. But Socrates was "showing" Meno's slave figures from the very first of his teaching, where the lad eventually confessed ignorance.
He never asked him to define anything. It is only after the slave saw the correct line to use to double a 4 foot square figure (into an 8 foot square figure) that Socrates both showed him and told him the definition of a DIAGONAL line.
To belabor the point, Socrates was "showing" the slave various FIGURES all along the way. And it wasn't Socrates who did the REFUTING. The slave did all the REFUTATIONS of his own previous answers. He refuted the answer 16 with his next answer of 9, at which point he gave up. But with further "showing" Socrates eventually led him to the correct answer that both he and Meno already knew how to obtain, given their common knowledge of Geometrical "squaring".
KHASHABA:
. — The significant phrase here is mê arithmein, alla deixon and Socrates goes on to help the boy to ‘show’ or rather to see.
QUESTION:
Why is that such a "significant" phrase? As a matter of fact in the case of a 1 square foot figure with sides of 1 unit each, one can only "show" the diagonal of such simple squares, but never arithmetically and accurately calulate the length of the diagonal, for that length is the square root of 2 --- an irrational number --- similar to the ratio of circumferences divided by the diameters of circles ("pi") --- also an incalculable ratio.
In other words "pi" can be DEFINED but never perfectly calculated. Similarly, the diagonal of a square, where each side is 1 unit long, can be SHOWN, but never arithmetically calculated to the last decimal point, or at least to a repeating decimal pattern.
KHASHABA:
For, as Kant insisted, geometry rests on intuition, and I will venture – although here I am uncomfortably conscious that I am swimming out of my depth – that when mathematicians calculate (arithmein) for such a problem, they work backwards from intuition.
COMMENT:
Every liberal art begins with INTUITION. eg. No one knows how children eventually grasp their initial understandings of their "mother tongue" --- or in other words "intuit" the initial rudiments of GRAMMAR. Moms, dads, nursemaids, or, in general, infant caregivers, simply POINT AT or "show" children various things and then give children NAMES for what they "point-at" or "show" to them.
So, as Aristotle argues, simple GRAMMAR and simple ARITHMETIC are fundamentally grounded upon INTUITION (non-teaching) and "showing". In contrast GRAMMARIANS and MATHEMATICIANS become competent grammarians and competent mathematicians by TUITION or teaching.
And, Mr. Kashaba, you are "swimming out of your depth" in mathematics because, as almost every mathematician knows, irrational numbers can be "shown" and "defined" but they are impossible to arithmetically calculate into DETERMINED lengths or DETERMINABLE ratios.
KHASHABA:
So the boy in the ‘experiment’ is helped to look and see just as in the properly elenctic discourses the interlocutor is led to look within her/his own mind to behold the meaning sought after in the immediacy of active intelligence (nous, phronêsis) and realize that there is no other explanation than “It is by Beauty that all that is beautiful is beautiful” and that it is in vain to seek understanding in the objects of the phenomenal world.
D. R. Khashaba
Cairo, Egypt, August 1, 2007
TO THE CONTRARY:
Had Socrates not been able to show Meno's slave GEOMETRICAL OBJECTS in the "phenomenal world" of Greek sand, by drawing squares in that sand and showing them to the slave, he would have never been able to teach him how to double a 4 foot square or to both show him and define for him WHAT a hypotenuse was.
But you are right about Socrates's conclusion. He, too, argued to Meno that he hadn't taught the slave anything. He had merely helped him "recollect" the geometrical knowledge in his own soul.
Aristotle refutes that conclusion by PROVING that questions may be turned into assertions with a "turn of the phrase". In other words, Socrates was GIVING Meno's slave good LOADED QUESTIONS in order to help him solve a Geometry problem, based NOT ON INTUITION, but rather "grounded" by the slave's KNOWLEDGE of Greek Grammar and Arithmetic.
In Aristotle's words:- All knowledge proceeds from preexistent knowledge and from the Law of Contradiction.
Since the slave knew both Greek grammar and arithmetic, he KNEW when he was giving Socrates the WRONG Arithmetical answers to his questions.
So, by knowing arithmetic and Greek grammar, the slave eventually obtained the correct Geometrical answer to Socrates question which was "grounded" NOT BY INTUITION, but, rather, upon (1) known arithmetic, (2) his own eventually "Known-wrong" answers and (3) Socrates's questions and (4) reference to or "showings" of geometical diagrams in the sand of the so-called, "phenomenal world".
The slave certainly didn't "intuit" his wrong answers. He calculated them. Then, he knew they were wrong answers because of Socrates's questions and his recalculations based upon known arithmetic and Socrates's INDUCTIVE questions.
In short the "slave experiment" is an example of INDUCTIVE ARGUMENT --- one of the 2 contributions to philosophy which Aristotle attributes to Socrates.
Kevin Byrne
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