16 February 2020

From Parts to Wholes (BC)

"Further, the state is by nature clearly prior to the family and to the individual, since the whole is of necessity prior to the part; for example, if the whole body be destroyed, there will be no foot or hand, except in an equivocal sense, as we might speak of a stone hand; for when destroyed the hand will be no better than that. But things are defined by their working and power; and we ought not to say that they are the same when they no longer have their proper quality, but only that they have the same name." (Aristotle, Politics, 4th century BC)

"The infinite […] happens to subsist in a way contrary to what is asserted by others: for the infinite is not that beyond which there is nothing, but it is that of which there is always something beyond. […] But that pertaining to which there is nothing beyond is perfect and whole. […] that of which nothing is absent pertaining to the parts […] the whole is that pertaining to which there is nothing beyond. But that pertaining to which something external is absent, that is not all […] But nothing is perfect which has not an end; and the end is a bound. On this account […] Parmenides spoke better than Melissus: for the latter says that the infinite is a whole; but the former, that the whole is finite, and equally balanced from the middle: for to conjoin the infinite with the universe and the whole, is not to connect line with line." (Aristotle, Physics, cca. 4th century BC)

"The proof that the state is a creation of nature and prior to the individual is that the individual, when isolated, is not self-sufficing; and therefore he is like a part in relation to the whole." (Aristotle, Politics, 4th century BC)

"The totality is not, as it were, a mere heap, but the whole is something besides the parts." (Aristotle, "Metaphysics", cca. 335-323 BC)
 
"The whole is more than the sum of its parts." (Aristotle, "Metaphysics", cca. 335-323 BC)
 
"And the whole [is] greater than the part." (Euclid, "Elements", cca. 300 BC)

"We can get some idea of a whole from a part, but never knowledge or exact opinion. Special histories therefore contribute very little to the knowledge of the whole and conviction of its truth. It is only indeed by study of the interconnexion of all the particulars, their resemblances and differences, that we are enabled at least to make a general survey, and thus derive both benefit and pleasure from history." (Polybius, "The Histories", cca. 150 BC)
 
"I say, then, that the universe and all its parts both received their first order from divine providence, and are at all times administered by it." (Marcus T Cicero, "De Natura Deorum" ["On the Nature of the Gods"], 45 BC)
 
"Order gives due measure to the members of a work considered separately, and symmetrical agreement to the proportions of the whole. It is an adjustment according to quantity. By this I mean the selection of modules from the members of the work itself and, starting from these individual parts of members, constructing the whole work to correspond." (Marcus Vitruvius Pollio, "De architectura" ["On Architecture"], cca. 15 BC)

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