Second Freshman Lab Paper
First Semester
Mr. Davis
Regarding a Proposition, a Dissection, and a Translation
On first consideration of this question, the connection between dissection, translation, and proposition seemed obvious. Each of these processes involve a series of steps, each follow a set of rules, and each lead to a furthered understanding of the problem in question. However, when I began to examine more closely the ways in which these arts are conducted, I realized that there is a vast distinction between translation and proposition, and dissection. Dissection sits apart from the other two; a divide which calls to be explored.
One of our more fruitful discussions in language stemmed from the nature of the word μεθεξις. Our idea of the participle is derived from a derivative word, μετοχη, meaning “partaking,” though μεθεξις can mean much more than “participle” or “partaking.” μεθεξις is participation, it is politics. μεθεξις is grammar, as every use of language involves a participation with the language. When we speak, we play by a set of rules. If we didn’t participate, language would fall apart. This led us to discuss John 1:1, “In the beginning was the Word, and the Word was with God, and the Word was God.” “Ἐν ἀρχῇ ἦν ὁ Λόγος.” λὸγος can be translated many ways, but it too has strong ties with μεθεξις. If, according to the Liddell-Scott-Jones Lexicon, μεθεξις is “a participation in an idea”– λὸγος can be seen as that idea. With this in mind, John takes on new meaning: In the beginning there was reason/participation/grammar, and the grammar was God. This way of thinking has exciting implications. In discussing José Ortega y Gasset’s article The Misery and Splendor of Translation, we even began to question whether human “sentience” would be possible without μεθεξις– without language, without participation. It is only when someone can address the other through language that one can begin to separate oneself from one’s surrounds. From the chaos of the natural world arises a dichotomy: the other, and the Self. If this Self is sentience, then surely it has its roots in μεθεξις.
Where Socrates attempted to avoid the other, and to synthesize the natural world through the medium of the self, Heraclitus took a different approach. Socrates sought to eliminate conflict in all things– to create a State without conflict, to try and find the true Form at the root of all visible forms. Heraclitus presents a world at war with itself, a world in a constant conflict of states: fire, water, and air. But Heraclitus doesn’t portray war as an opposition to a desirable equilibrium, like Socrates. To Heraclitus, “war is the father of all things.” War is fate, war is necessity. War is also essential, and natural: like the lyre, or bow, a thing can be in conflict with itself and still remain one. μεθεχις is a participation between oneself and the other: it is the stringing of the bow. Synthesis is an opposite process: it is an assimilation of the other into oneself. A deconstruction, and a resolution of conflict. It is with these words, μεθεξις, and synthesis, that the distinction between dissection and translation/proposition can be explored.
Dissection is a synthesis. It is a very Socratic/Platonic process. Dissection requires no μεθεξις with the natural world (no participation). When we dissected the cats, we took our observations and synthesized them with prior knowledge. We observed form and function in an attempt to better understand the Form of cat. We took a conflict between ourselves and the natural world (the other), and Socratically resolved that conflict. We unstrung the bow, and were left only with the self. Heraclitus might say that we won the war. Not only dissection, but all of science, and much of observation, is rooted in finding a synthesis between the other and the self. Whether this is a benefit of science or a shortcoming is open to interpretation.
Translation and Proposition, on the other hand, are μεθεξις. As we also discussed in the Gasset essay, all communication is a translation, in a way. In speaking, concepts must be translated into language. The listener, then, translates that language back into concepts. All understanding is reached through an ability to translate. If one should step away from translation, grammar, and μεθεξις, one begins to also stray from language. To explore a sentence like a digestive system doesn’t translate, it synthesizes. To synthesize a sentence is to take it from its author and make it one’s own: to strip away all conflict in an attempt to arrive at a Form. To take the conflict out of language is to take away the participation– without participation, every person is left with their own private language. The loss of μεθεξις in language can result in nothing but babel. This, Gasset argued, is what is so often wrong with the practice of translation in general. Translators seek to synthesize ancient concepts with modern taste. In the process of that synthesis, the original meaning is lost. Translation must not be afraid to be at war with its audience. Conflict is the core of participation.
A proposition employs μεθεξις in much the same way. Just as participating in language involves cooperation with an established set of rules, so does participation in mathematics involve a cooperation with established absolutes. Euclid begins his Elements with postulates, common notions, and definitions for a reason: these are the λὸγοι through which one can conduct μεθεξις. If mathematics were to deviate from these rules, the participation would dissolve, and there would be only a personal mathematic for each individual. A proposition, like a translation, involves a conflict between the self and the other. In the same way that language evolves through that conflict, so does mathematics evolve, and so too does the student’s ability to accept new concepts, and adapt new methods of thought to suit them.
To engage in translation, or demonstrate a proposition, is to join a community– to engage in politics. To conduct a dissection, or any observation, involves an assimilation. Neither μεθεξις nor synthesis are necessarily better than the other, but one should be careful to use each in the field that it is suited, and not to confuse one for the other. This is, I feel, why a translation and a proposition are not like a dissection.