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*To*: [email protected]*Subject*: Re: Quibbling about definitions of "proof"*From*: [email protected] (Dr. Frederick B. Cohen)*Date*: Mon, 7 Aug 1995 12:03:22 -0400 (EDT)*In-Reply-To*: <[email protected]> from "[email protected]" at Aug 7, 95 11:21:51 am*Sender*: [email protected]

> All this quibbling about the "validity" of proof checkers is philosophically > inept. It is a basic property of logic that it proceeds from axioms to > conclusions. No proposition can be understood except by reference to some > other proposition. Except that it all starts with language and developes through set theory. > It is not possible to objectively observe anything, all observation is made > through a mechanism which is imperfectly analysed and thus the observation > is subjective to the extent that the interpretation is unknown. And yet it is all based on observations at the initial set theoretic level. > We may obtain an objective statement from a subjective observation by reference > to the source of subjectivity. If however the subjective assumptions are shared > by all participants within the system of being any statement which follows from > only those assumptions may be regarded as objective. Objectivity is thus not > an atomic fact but a relation, a fact cannot have the property of objectivity > except with respect to a system of being. And indded, we are people which gives us some common context. > [Thus I may assert 1+1=2 as an objective fact since the assumptions upon which > it is based are commonly shared. If however someone wished to question this > statement (e.g. phenomological bracketing) then in the context of that > discussion I would accept it as being subjective).] I was taught 1+1=1 in boolean algebra. > The question of prooving the proof checker is thus an extension of a more > fundamental problem, providing proof of proof. Since a proof is a fact and facts > are subjective except with resepct to a system of being the demand for proof of > consistency of proof is an extension of the requirements for proof as normally > understood. But in computers, we are living in a mathematically defined system (except for physical issues which have been suppressed to a very large extent by the design of statistically low error-rate systems) which follows very precisely the logic of its design. Thus proofs work since we are working in this well formed domain. > The requirement for "prooving" a program is thus significantly less onerous than > asserted. It is not necessary to provide a trancendental proof, merely to > establish consistency with respect to a commonly accepted set of axioms. More specifically, within the logic dictated by the hardware designed to assure that the system remains within the mathematical structure defined by its design. -- -> See: Info-Sec Heaven at URL http://all.net Management Analytics - 216-686-0090 - PO Box 1480, Hudson, OH 44236

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