Michael Stuart Kelly Posted June 11, 2007 Share Posted June 11, 2007 Since we have been discussing Objectivism and science for a while, here are a few Peikoff quotes on proof to chew on. Ayn Rand did not write very much on the process of proof itself. She did mention that the fundamental axioms cannot be proven, but instead must already be used in any process of proving them. She usually implied that identification of facts and logic were to be used. Peikoff has built on the implications of this to try to form an Objectivist approach to proof.Since Peikoff stated so much about science in the DIM Hypothesis lectures, including the phrase, if I remember it correctly, that all scientific truths were ultimately based on induction, I think it is pertinent to look at his written statements about proof. The following quotes are all from Objectivism: The Philosophy of Ayn Rand.("Chapter 1—Reality," p. 8)Proof is the derivation of a conclusion from antecedent knowledge, and nothing is antecedent to axioms. Axioms are the starting points of cognition, on which all proofs depend.("Chapter 2—Sense Perception And Volition," p. 39)Proof consists in reducing an idea back to the data provided by the senses.("Chapter 4—Objectivity," p. 120) "Proof" is the process of establishing truth by reducing a proposition to axioms, i.e., ultimately, to sensory evidence. ("Chapter 4—Objectivity," p. 138)Proof is a form of reduction. The conclusion to be proved is a higher-level cognition, whose link to reality lies in the premises; these in turn eventually lead back to the perceptual level. Proof is thus a form of retracing the hierarchical steps of the learning process. (As with conceptual reduction, so with proof: the process identifies not the optional variants, but the essential links in the chain, the necessary logical structure relating a mental content to observational data.)Proof is not a process of deriving a conclusion from arbitrary premises or even from arbitrarily selected true premises. Proof is the process of establishing a conclusion by identifying the proper hierarchy of premises. In proving a conclusion, one traces backward the order of logical dependence, terminating with the perceptually given. It is only because of this requirement that logic is the means of validating a conclusion objectively.("Chapter 5—Reason," p. 183)A process of proof commits a man to its presuppositions and implications. It thus commits him to an entire philosophic approach—to the validity of sense perception, the validity of reason, the need of objectivity, the method of logic, the processes of conceptual knowledge, the law of identity, the absolutism of reality.We have a number of scientifically oriented people on OL. I am curious to hear what they have to say.Michael Link to comment Share on other sites More sharing options...
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