janw@inmet.UUCP (09/28/86)
[Adam Reed (ihnp4!npois!adam)] >Rand's suggestion is that an axiom can be identified by the fact >that it cannot be denied without self-exclusion, since such a de- >nial would *necessarily* have to be either meaningless or self- >contradictory. For example, the claim that "awareness does not >exist" expands to "I am aware that it is true of reality that >there is no such thing as awareness", which is self- >contradictory. Hence Rand's claim that awareness is an axiom. It seems possible to justify axioms of existence in this way; but how does one justify, e.g., A=A ? It is true that no one denying A=A can help using implicit as- sumptions of the form A=A; but this only implies that *sometimes* A=A, not that *always* A=A. [William Dwyer: dwyer@vixie.UUCP ] >>Templeton states: >> "(It's too complex to go into here, but if you really want some >> consistent metaphysical systems where A is not A or consciousness >> does not exist, I and others on the net can provide them. This >> article is long enough already.)" >>Since it is the law of identity that defines consistency, a con- >>sistent metaphysical system in which A is not A is worse than a >>contradiction in terms. It is a contradiction in terms that ex- >>plicitly forbid contradictions! If you can have a consistent >>metaphysical system in which A is not A, then what would an IN- >>CONSISTENT metaphysical system be? One in which A is A? >>sistency means is a context in which you do not have both A and >>not A (at the same time and in the same respect). It is never the same time and the same respect. The two mentions of A come one after the other in a text; and their context is al- ways different. The object denoted has also changed; if it is an event, then the memory of it has changed. It requires a conven- tion, implicit or explicit, to ignore these differences in some cases - and in this class of cases, A is A. E.g., in a programming language, we may have B = A = NOT (A); IF ( NOT (A == A) ) FAIL (); In the first line, the values of A have to be different; in the second, identical. Or consider "Cramer vs Cramer". Are the words "Cramer" used in the same respect? First define respect... In each case, Cramer means "the litigant we are talking of". A is A is a useful rule. But it is not simple. It can, for exam- ple, be reformulated like this: "It is often worth while to use terms in such a way that the name changes when the meaning does". Of course, it is not completely practicable. I changed while writing this, yet I still sign Jan Wasilewsky