David asked:

I'm translating into English an excerpt from a paper on Parmenides, yet I'm a novice in the subject of
Philosophy. Can anyone tell me if the following terms are well-used in Philosophy, and if not, are
there more appropriate synonyms?

1. The term "formulation": Does this just mean "statement"? Which is better to use.

"Fragment 6 explains this new formulation (of the two paths of enquiry), but the interpretations differ
considerably ..."

2. The term "negation": At first I thought "negation" and "antithesis" are synonyms. Is that not the
case?

"Parmenides' thesis and its negation are represented by two paths of enquiry, one of which,..."

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1. If I make a statement, and then make a second statement intending to put the point made in the
first statement more clearly, or from a different angle, or in response to a different question, then one
would say that I had 'reformulated' my statement. It is appropriate to use the term 'formulation' when
one is dealing with two or more statements which would be described as 'reformulations' of one and
the same thought.

2. You are right to be worried about the use of the term 'negation' in Parmenides.

The key premise of Parmenides' two paths of inquiry is that there are only two alternatives, for any
assertion of the form 'X is', namely, 'X is and needs must be', or 'X is not and cannot be'.

Consider the case where 'is' means 'exists'. (Similar things can be said when we are talking about the
'is' of predication, e.g. 'Pegasus is a horse'.) According the law of excluded middle, either Pegasus
exists Pegasus does not exist. However, Parmenides reads this as saying that either Pegasus
necessarily exists or Pegasus necessarily does not exist. But that is not a consequence of the law of
excluded middle, since the logical negationof 'Pegasus necessarily exists' is not 'Pegasus
necessarily does not exist' but rather, 'Pegasus does not necessarily exist'. 'Antithesis' is closer to
what Parmenides is trying to say, than 'negation'.

Geoffrey Klempner

For a fantastic source on Latin and Greek originals and translations, with dictionaries, go here:

http://www.perseus.tufts.edu/

Steven Ravett Brown