Supplement to Ancient Greek Philosophy. It is an example of philosophizing in the old way, written in the old way, the way before Wittgenstein's logic of language, which makes no distinction between concepts and facts, between language and phenomena.
If reasoning shows that change is not real, then how can the appearances (phenomena as perceived by the senses) be saved (from its negation by reason)?
The One and the Many - Parmenides versus the Appearances
The question of Aristotle's metaphysics or First Philosophy is: What is real and ultimate? The following comparison is based mostly on W.K.C. Guthrie's The Greek Philosophers (1950), Chapter 3.
Plato who, despite his reverence for Parmenides, was not a monist, asked, If it cannot be said that what-is-not is, then what can be our meaning in saying it? (Sophist 237a) In answering this question Plato invents the notion of "logical form" in contrast to apparent form.
Note that "common sense" and "thinking in the abstract" are Guthrie's terms, and their meaning in philosophy is often unclear.
By 'common sense' Guthrie appears to mean: 'the evidence of the senses and the consensus among mankind about the validity of that evidence'.
And by 'thinking in the abstract' Guthrie appears to mean: 'reasoning that prescinds from the evidence of the senses'. Plato's axiomatic method in Phaedo 99d-100a (tr. Jowett) is an example of this type of reasoning: "I was afraid that my soul might be blinded altogether if I looked at things with my eyes or tried by the help of the senses to apprehend them ... [And so] this was the method which I adopted: I first assumed some principle which I judged to be the strongest, and then I affirmed as true whatever seemed to agree with this ... and that which disagreed I regarded as untrue."
A comparatively ancient account of Parmenides' thought
[Parmenides] divided his philosophy into two parts dealing the one with truth, the other with opinion ["the opinions of mortals in which there is no sure trust"].... He made reason the standard and pronounced sensations to be inexact. At all events his words are:
And let not long-practiced wont force thee to tread this path, to be governed by an aimless eye, an echoing ear and a tongue, but do thou with understanding bring the much-contested issue to decision.
He is believed ... to have been the first to use the argument known as "Achilles [and the Tortoise]" ...
From Diogenes Laertius (ca. 200-250 A.D.), Lives and Opinions of Eminent Philosophers, ix, 22-23, tr. R.D. Hicks.
Note.--The following are not the paradoxes as found in Aristotle, but instead only the second and third paradoxes retold using the argument of Zeno's first paradox (Aristotle, Physics 232a20). All four of Zeno's paradoxes prove that what we perceive to be reality is logically impossible, and therefore that sense perception is false. In the example below, our perception is that Achilles catches the tortoise, which, however, reasoning demonstrates is impossible.
Achilles and the Tortoise
In the race if the tortoise is given a head start, Achilles can never catch up with tortoise, because in order to catch up Achilles must pass through an infinity of spaces, for consider that once he has gone half the distance to the tortoise, he must then go the next half, then the next half, and the so on forever, because any space can be indefinitely divided in half.
Paradox of the Arrow (Zeno of Elea)
Likewise an arrow shot from a bow can never reach its target, because it must travel through an infinity of halves (half-way points) to arrive there.
The two proofs are mathematical (Any number may be divided in half) contra sense-perception, because the senses perceive that Achilles does catch up with the tortoise, and the arrow does reach its target, which has been proved to be impossible. The two contradictions are examples of reason ("understanding") disproving the evidence of the senses ("an aimless eye, an echoing ear and a tongue").
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