One plus one equals two. Oh yeah? Prove it. Some old letters on what is “proof?” Sheesh. I was a bit disjointed 20 years ago but now I am fine. Joke. Peter
From: "Peter Taylor" To: atlantis Subject: Re: ATL: Re: Scientific Determinism Date: Thu, 10 Aug 2000 04:09:32 GMT. George H. Smith wrote an excellent letter but I will only reply to one of his points at this time: (8) In short, we should always bear in mind the crucial difference between science per se and the philosophy of science. The latter is not itself a "scientific" discipline, but is a branch of philosophy. end of quote
By asserting that all science was subsumed under philosophy and Objectivism, (and stretching it a bit, and fishing I was sure I would tick off Dennis May sufficiently to answer me. Instead, George answered, saying he Disagreed with some points of mine, but that he actually Agreed with me, just a bit. George, are you being culturally assimilated? I've wondered if you are doing some investigative journalism (perhaps even a hatchet job) about these quaint folks, who call themselves Objectivists. Maybe you won't burn us, after becoming friendly with us? (If so, imagine Sally Fields saying, "You like us! You genuinely like us!") The more I thought about the crucial difference between science per se and the philosophy of science, I decided my Big Point, was hinted at in some recent letters questioning the difference between Randian Objectivism (Rand's own words) and Objectivism (which includes Rand's own words and philosophical words written by others, about Objectivism.)
And that got me thinking about: If *it* is objectively true, then *it* is provable using Objective (Aristotelian, Randian, and Scientific methods (observable, verifiable and repeatable). In contrast a strictly linguistic assertion that human epistemology is deterministic, or that the earth is 6000 years old, or that 13 angels can dance on the head of a pin is provable if the bible is used as the sole reference. Though these false assumptions may be logically true, based on false basic premises, they are not true in fact. But I am just a cave-man philosopher (who is not laughing at his most basic values, BB, just being objective.) Let me quote from the "Masters," while keeping in mind that Objectivism is a cohesive whole.
Selective, non - consecutive quotes from OPAR by Leonard Peikoff and Ayn Rand, pages 112-120. According to Objectivism, epistemology is necessary for practical purposes, as a guide to man in the proper use of his conceptual faculty. We are ready to concretize this claim. We can now begin to identify the rules men must follow in their thinking if knowledge, rather than error or delusion, is their goal.
These rules can be condensed into one general principle: thinking, to be valid, must adhere to reality. Or, in the memorable words of the old "Dragnet" TV series, which can serve as the motto of all reality-oriented thought: "Just give us the facts, ma'am." But how does one reach "just the facts"? The answer lies in the concept of *objectivity*; it requires that one grasp the full philosophic meaning and implications of this concept.
When you grasp this concept, you will have an invaluable tool enabling you to assess and, if necessary, improve the quality of your own thinking. You will also understand why, out of all the possibilities, Ayn Rand chose to call her philosophy, "Objectivism."
. . . Since definitions ‘are' condensations of observed data, however, they are determined by such data; they are not arbitrary; they flow from the facts of the case. In this respect, as we have seen, definitions are "empirical" statements, and reality *is* the standard of what is essential.
Definitions are statements of factual data - as condensed by a human consciousness in accordance with the needs of a human method of cognition. Like concepts, therefore, essences are products of a volitional relationship between existence and consciousness, they too (properly formed) are *objective.*
. . . As Miss Rand points out, it is mandatory to conceptualize certain types of concretes, including: (a) the perceptual concretes with which men deal daily, represented by the first level of abstractions; (b) new discoveries of science; ( c ) new man-made objects which differ in their essential characteristics from the previously known objects (e.g., "television"); (d) complex human relationships involving combinations of physical and psychological behavior (e.g., "marriage," "law," "justice").
These four categories represent existents with which men have to deal constantly, in many different contexts, from many different aspects, either in daily physical action or, more crucially, in mental action and further study. The mental weight of carrying these existents in one's head by means of perceptual images or lengthy verbal descriptions is such that no human mind could handle it. The need of condensation, of unit-reduction, is obvious in such cases.
. . . "Proof" is the process of establishing truth by reducing a proposition to axioms, i.e. ultimately, to sensory evidence. Such reduction is the only means man has of discovering the relationship between non-axiomatic propositions and the facts of reality. end of quotes
Now to tie it all together. The difference between Randian Objectivism (Rand's own words) and Objectivism (which includes Rand's own words and the philosophical words which will be written by others, about Objectivism, ON INTO THE FUTURE,) and asserting that all science was subsumed under philosophy and Objectivism -
My fellow Atlanteans, am I stretching it a bit? Is this an end run? Scientific facts, at their most basic level are always consistent with Objectivism, but not strict Randian Objectivism which, though true within its context, cannot be infallibly true. If Objectivism is open, and to the greatest extent possible INFALLIBLE, AS IT IS PROVED, WITHIN A CONTEXT ON INTO INFINITY, then we will rarely be wrong. Am I making sense, or am I saying, "I can have my cake and eat it too?" Peter Taylor
Again, I will repeat, Causality pertains to EVERYTHING in the universe except sentient, rational, volitionally conscious HUMANS. quote (first from Leonard, then from Ayn,) OPAR page 64: The principle of causality does not apply to consciousness, however, in the same way that is applies to matter. In regard to matter, there is no issue of choice; to be caused is to be necessitated. In regard to the (higher-level) actions of a volitional consciousness, however, (continuing the sentence with a quote from Ayn Rand,) "'to be caused' does not mean 'to be necessitated.'" And "Man chooses the causes that shape his actions."
From: "William Dwyer" To: <atlantis Subject: ATL: Is proof agent-relative? (was "Does proof require a Sandra ASS U MEd ...) Date: Thu, 15 Nov 2001 19:32:14 -0800. Sandra Mendoza wrote: "As my hero, the Emperor Marcus Aurelius wrote: *If anyone can show me, and prove to me, that I am wrong in thought or deed, I will gladly change. I seek the truth, which never yet hurt anybody. It is only persistence in self-delusion and ignorance which does harm."
Andrew Taranto replied, "Very interesting... because Antony Flew took pains to discuss, in _Thinking Straight_ (and the latter version, _How to Think Straight_) that one does not ~prove to~, one only proves. When someone says, 'Prove X to me,' he means to say, 'convince me of X'; but then proof doesn't necessarily play a role. (Unfortunately, my copies are at home, so I can't provide specific cites.)"
Based on Andrew's summary, I don't think that Flew's analysis does justice to the concept of "proof"; on the contrary, his analysis would appear to be self-contradictory. If, as he says "proof" doesn't necessarily play a role in "proving" X to someone, then one ~hasn't~ "PROVED" X to him; one has simply "convinced" him of X.
One can convince someone of something by a means other than proof, e.g., by sophistry or propaganda. If a person says, "Prove it to me," he is not simply asking to be convinced; he is asking to be convinced ~by an objectively valid justification~.
So, I think that proof does indeed require a person ~to whom~ one proves something, even if that person is only the prover himself. In other words, proof presupposes a consciousness whose requirements of knowledge are satisfied by the fulfillment of certain epistemological criteria.
Therefore, if a person asks for proof, he is indeed asking that something be proved ~to~ him, because he is demanding that it satisfy his own understanding of the truth according to rational and objective criteria.
To put it in standard Objectivist lingo, proof is objective, but not intrinsic! Although proof is certainly not arbitrary or subjective, it still requires a mind to receive and understand it.
The idea that proof is always proof ~to~ someone was also the position of Michael Scriven, whom I had as a professor of philosophy at U.C. Berkeley many years ago! He was a pretty good philosopher and has written quite a good book on epistemology, which I used to own but have since lost track of. Bill
From: "Dennis May" To: atlantis Subject: ATL: Re: Is proof agent-relative? Date: Fri, 16 Nov 2001 09:41:45 -0600. William has written on a topic which has fascinated me since my first geometry class.
I will be the first to admit I have never felt comfortable with mathematical or physics proofs regardless of the thousands I have either read, regurgitated, or done. Proof requires auxiliary assumptions which must also be supported by proof. At some point you fall back upon the most basic axioms. Your tree of logic is only as sound as your correct inclusion of all relevant assumptions.
My lack of comfort comes from observing the many times errors have been discovered in proofs years later because of in-correct assumptions, neglect of required assumptions, technical errors, missed steps, proof by intimidation [appeal to authority], and any number of other errors in logic.
Proof is the holy grail in advancing rational arguments. It is often an elusive goal and very much dependent upon a qualified receptive mind. A thousand qualified rational people can look at the same proof year after year without detecting an error. The person who comes along and discovers an error is to be congratulated but every time it happens I again feel uncomfortable with proofs. I guess proof always remains provisional in my mind. I would greatly appreciate Michael Hardy [as resident mathematician] jumping in on this. Dennis May
From: Ellen Moore To: Atlantis Subject: ATL: Re: Is proof agent-relative? Date: Fri, 16 Nov 2001 14:42:46 -0600 Dennis May wrote, "The person who comes along and discovers an error is to be congratulated but every time it happens I again feel uncomfortable with proofs. I guess proof always remains provisional in my mind."
The answer to Dennis's discomfort is "contextual knowledge", and it would be advisable to understand the context of "truth". This belongs to the issue of epistemology - "how do we know when the truth we know is actually true?" Actually it is when there is no evidence that contradicts what we know to be true. In other words, everything we know is evidence that supports [proves] that it IS true - and we know nothing that contradicts this knowledge. This is "certain knowledge".
An error is a different thing. It means that one has not validly proven that one's information is true - or it means that one has not applied all the facts and principles one does know to be true. In other words, an error, a mistake, occurs when one has muddled one's thinking. An evasion occurs when one has refused to identify and acknowledge the truth one does in fact know.
However, someone may discover new evidence that in effect sets up a new context of knowledge - the new evidence adds new proofs of information adding a new perspective on old knowledge that was true in that earlier context of knowledge. This only means that knowledge of truth is ~open-ended~ - meaning that one does already know one can always learn new things about new discoveries. This does not contradict what one did know, it merely adds new truths proven by new knowledge. This does not make proof or truth provisional". It is "contextual" knowledge.
This should never make one doubt one's knowledge - unless there IS new evidence proven to be true. In fact, it IS just a new contextual certainty of knowledge.
Dennis, it is not that proof is always provisional, it IS that knowledge of truth is contextual -- and whatever one knows to be true IS certain knowledge of reality.
Get it? I'm not offering a formal presentation here, this is simply an off-the cuff expression of what I learned about objective contextuality. Ellen M.