Rickless construes Plato's middle-period account of the Forms as a theory comprising axioms, auxiliary principles, fundamental theorems, and specific premises and conclusions constituting particular arguments. This book attempts to reconstruct that theory (the "high theory"), to trace its further development (the "higher theory") and subsequent criticism in Parmenides 126a–35c (Parm I), and to show how Plato salvages the theory by alterations undertaken in 137c–66c (Parm II). Rickless's reconstruction of the "high theory" includes two axioms, seven auxiliary principles, and thirteen fundamental theorems. The "higher theory" adds another axiom and eight further principles.
To save the theory from Parmenides' criticism, Rickless thinks this additional axiom must be rejected, along with three of the original theorems. The main purpose of Parm II, he says, is to justify rejection of these four theses, thus saving the theory (244). What remains are the two initial axioms (that, for every plurality of F things, there is a form of F-ness that makes each thing F by participating in it, and that every Form "is itself by itself"), along with [End Page 169] several theorems not depending on the rejected theses. Rickless finds this truncated theory operating in all subsequent dialogues save the Timaeus. According to this final theory, the Forms might turn out to be sensible and yet unknowable by human minds (249).
The primary culprit among the theses slated for rejection is the axiom (RP)—that no Form G can have contrary properties F and con-F—which Rickless believes underlies all the problems pointed out by Parmenides. It is important for Rickless's project that the theory criticized by Parmenides contains RP, and not just the weaker theorem (P), that no Form G admits a property (con-G) contrary to itself. Rickless introduces RP into his reconstruction on the basis of 129b–c, rejecting with scant argument the readings of other commentators he mentions who find only P in that passage (49). Since he thinks the main purpose of Parm II is to resolve the logical problems posed by RP, if Rickless's reading of this ambiguous passage is wrong, then the rest of his reconstruction would appear largely unmotivated.
The dependency of Rickless's reconstruction on RP is shown by his interpretation of Parmenides' methodological advice at 135e–36c. Relying on the seemingly gratuitous insertion by Gill and Ryan of 'between opposites' at 135e2 (modifying te¯n plane¯n, which they render 'their wandering'), Rickless takes the basic hypothetical format called for by Parmenides to be "If the G is (or is not), then G is (or the others are) both F and con-F." For reasons never clearly spelled out—beyond "as becomes evident after only a cursory look" (108)—Rickless further expands the ranges of contraries in the consequent to include "G is (or the others are) both not F and not con-F." He then adds the pros (in relation to) qualifications, "pros itself (or themselves)" and "pros themselves (or itself)," to each consequent. As a result, deduction I takes the form, "If the one is, then the one is both not F and not con-F pros itself and pros the others," and deduction II the form, "If the one is, then the one is both F and con-F pros itself and pros the others," while the remaining six follow suit (109–10). He does not discuss the fact that neither I nor VI appears to say anything about the one's relation to the others except that there is not any.
Rickless's general strategy in refuting RP is the following. Each of the first four deductions shows independently that if the one is, then RP is false. Deduction V then shows that, if the one is not, then RP is false. Since the one either is (by each of I–IV) or is not, RP is false. Moreover, deduction VI shows that the one is, hence (with any one of I–IV) that RP is false. Rickless does...