Marchetto of Padua, Lucidarium, authentic, plagal, perfect, imperfect, pluperfect, mixed, odd numbers, even numbers, Aristotle, Metaphysics, Alcmaeon of Croton, causa significationis, dyapente, diatesseron, concord, senaria, Pomerium, Donatus, Vetulus, mode 5, commixed, corda, discant, dyad, voice leading.

Philosophical reflection on the conditions of knowledge did not begin in a cultural vacuum. Several centuries before the Ionian thinkers began their investigations, the Homeric bards had identified various factors that militate against a secure grasp of the truth. In the words of the ‘second invocation of the Muses’ in Iliad II: “you, goddesses, are present and know all things, whereas we mortals hear only a rumor and know nothing.” Similarly Archilochus: “Of such a sort, Glaucus, son of Leptines, is (...) the mind of mortal man, whatever Zeus may bring him for the day, for he thinks such things as he meets with.” When one adds the truism that the scope of human experience pales in comparison with the synoptic view of events enjoyed by the gods, it follows that for most matters it is for the gods to know and mortals merely to conjecture. Traces of the older ‘poetic pessimism’ can be seen in the teachings of many of the first philosophers. Alcmaeon reaffirms that “while the gods enjoy clear and certain knowledge of all things, mortals must conjecture from signs” (B 1). Although Xenophanes encourages inquiry into a wide range of phenomena, he concludes that “No man has known nor will there be anyone who knows the clear and sure truth concerning the gods and what I say about all things” (B 34). And when philosophers begin to affirm a more optimistic view they often do so in terms that invite comparison with the older outlook. The chief truth Heraclitus claims to have discovered is the logos or ‘basic formula’ which holds everywhere and forever (B 1, 30, 80, and 90). Parmenides provides reason to think that human beings can discover the truth even about things located “far off” (B 4). And both Empedocles and Democritus contrast the inferior awareness of those “who think in terms of what they have met with” with the wisdom available to those who have heard and ponder their teachings (B 131). For these thinkers, separation in space and time—the old ‘locality problem’—no longer posed an impediment to knowledge. -/- . (shrink)