norm@ariel.UUCP (N.ANDREWS) (08/12/84)
> Ahem. Cause and effect may exist, and indeed, in order to function as > human beings, we seem to need to behave as if it exists, but I don't > think the principal of cause and effect can be *proved* to exist. The > association of two events in time does not imply a connection between > the two. > > (For a more detailed argument, read Hume and Kant) > > --Ray Chen The concept of proof depends upon the concepts of cause and effect, among other things. Even the ideas "anything" and "functioning" depend upon the idea of cause and effect. All of these concepts depend on or are rooted in the concepts of identity and identification. Here's why: To be is to be something in particular, to have a specific identity, or having specific characteristics. What does it mean to have specific characteristics or a specific identity? It means that in a particular context, the entity's existence is manifested in a particular way. An entity IS what it can DO (in a given context). So what's causality? The law of identity applied to action. Things do what they do, in any given context, BECAUSE they are what they are. "What they are" includes or consists of "what they can do". This is true irrespective of our ability to identify what they are. Hume's and Kant's arguements re causality are the analytic-synthetic dichotomy. For the original presentation of the views that smash this false dichotomy, see Leonard Peikoff's article "The Analytic- Synthetic Dichotomy" in the back of recent editions of Ayn Rand's "Introduction to Objectivist Epistemology". For the epistemological basis of Peikoff's article, read Rand's Intro. (I almost posted this to net.cooks, but GOOD cooks know this already...) -Norm Andrews, AT+T Information Systems, (201) 834-3685
kissell@flairvax.UUCP (Baba ROM DOS) (08/14/84)
(Norm Andrews challenges Ray Chen's agnosticsm on cause and effect) > The concept of proof depends upon the concepts of cause and effect, among > other things. This is simply not true. The notion of logical proof involves implication relationships between discrete statements in discourse. This is an agreed upon rule of the game. Causality assumes implication relationships between discrete events in the world. The universe may or may not argue like a philosopher, and it is not always clear what constitutes a "discrete" event. > So what's causality? The law of identity applied to action. Things do > what they do, in any given context, BECAUSE they are what they are. This is a denial of causality, not a definition. If things do what they do because they are what they are, then they certainly can't be *caused* to do anything by something else. Unless, of course, the only *thing* is everything. uucp: {ihnp4 decvax}!decwrl!\ >flairvax!kissell {ucbvax sdcrdcf}!hplabs!/
TONH%alvey@ucl-cs.arpa (09/01/84)
From: TONY HASEMER (on ALVEY at Teddington) <TONH%alvey@ucl-cs.arpa> (Tony Hasemer challenges Norm Andrews' faith about cause and effect) You say: "logical proof involves implication relationships between discrete statements...causality assumes implication relationships between discrete events". Don't think me just another rude Brit, but:- > in what sense is a statement not an event A statement (as opposed to a record of a statement, which is a real-world object) takes place in the real world and therefore is an event in the real world. > what do you mean by "implication" This is the nub of all questions about cause and effect, and of course the word subsumes the very process it tries to describe. One can say "cause and effect", or "implication", or "logically necessary", and mean ALMOST the same thing in each case. They all refer to that same intangible feeling of certainty that a certain argument is valid or that event B was self-evidently caused by event A. > what do you mean by "relationship" Again, this is a word which presumes the existence of the very link we're trying to identify. May I suggest the following- The deductive logical syllogism (the prototype for all infallible arguments) is of the form All swans are white. This is a swan. Therefore it is white. Notice that the conclusion (3rd sentence) is only true iff the two premises (sentences 2 and 3) are true. And if you can make any descriptive statement beginning "All..." then you must be talking about a closed system. Mathematics, for example, is a set of logical statements about the closed domain of numbers. It is common, but on reflection rather strange, to talk about "three oranges" when each orange is unique and quite different from the rest. It is clear that we impose number systems on the real world, and logical statements about the square root of the number 3 don't tell us whether or not there is a real thing called the square root of three oranges. I'm saying that closed systems do not map onto the real world. Mathematics doesn't, and nor does deductive logic (you could never demonstrate, in practice, the truth of any statement about ALL of a class of naturally-occurring objects). On the contrary, the only logic which will in any sense "prove" statements about the real world (such as that the sun will rise tomorrow) is INDUCTIVE logic. Inductive logic and the principle of cause and effect are virtually synonymous. Inductive logic is fuzzy (deductive logic is two-valued), and bootstraps itself into the position of saying: "this must be true because it would be (inductively) absurd to suppose the contrary". There is no real problem, no contradiction, between the principle of cause and effect and deductive logic. There is merely a category mistake. The persuasive power of deduction is very appealing, but to try to justify an inductive argument (e.g. causality) by the criteria of deductive arguments is like trying to describe the colour red in a language which has no word for it. We just have to accept that in dealing with the real world the elegant and convenient certainties of the deductive system do not apply. The best logic we have is inductive: if I kick object A and it then screams, I assume that it screamed BECAUSE I kicked it. If repeated kicking of object A always produces the concomitant screams, I have two choices: either to accept the notion of causality, or to envisage the real world as being composed of a vast series of arbitrary possibilities, like billions of tossed pennies which only by pure chance have so far happened always to come down heads. Personally, I much prefer a fuzzy, uncertain logic to a chaos in which there is no logic at all! Belief in causality, like belief in God, is an act of faith: you can't hope to PROVE it. But whichever one chooses, it doesn't really matter: stomachs still churn and cats still fight in the dark. The very best solution to the problem of causality is to stop worrying about it. Tony.
norm@ariel.UUCP (N.ANDREWS) (09/07/84)
> > From: TONY HASEMER (on ALVEY at Teddington) <TONH%alvey@ucl-cs.arpa> > > (Tony Hasemer challenges Norm Andrews' faith about cause and effect) > > You say: "logical proof involves implication relationships between > discrete statements...causality assumes implication relationships > between discrete events". > Hold on here! I, Norm Andrews, didn't say that! You are quoting someone going by the name "Baba ROM DOS" who was attempting to disprove my statement that "The concept of proof depends upon the concepts of cause and effect, among other things." Please don't assign other peoples' statements to me! I haven't time now to reply to any other part of your posting... Norm Andrews
rmc@teddy.UUCP (R. Mark Chilenskas) (09/11/84)
nduction. The proof is valid if the accepted community of experts agrees that the proof is valid (see for example various Wittgenstein and Putname essays on the foundations of mathematics and logic). The experts could be wrong for a variety of reasons. Natural law could change. The argument may be so complicated that everyone gets lost and misses a mistake (this has even happened before!) The class of cases may be poorly chosen. etc. The disagreement seems to be centered around a question of whether this community of experts accepts causality as part of the model. If it is, then we can use causality as an axiom in our proof systems. But it still boils down to what the experts accept. R Mark Chilenskas decvax!genrad!teddy!rmc
robison@eosp1.UUCP (Tobias D. Robison) (09/11/84)
References: Mark Chilenskas discussion of inductive proof is not correct for mathematics, and greatly understates the strength of mathematical inductive proofs. These work as follows: Given a hypothesis; - Prove that it is true for at least one case. - Then prove that IF IT IS TRUE FOR A GENERIC CASE, IT MUST BE TRUE FOR THE NEXT GENERIC CASE. Fore example, in a hypothesis about an expression with regard to all natural numbers, we might show that it is true if "n=1". We then show that IF it is true for "n", it is true for "n+1". By induction we have shown that the hypothesis is absolutely true for every natural number. Since true: n=1 => true for n=2, true: n=2 => true for n=3, etc. It is the responsibility of the prover to prove that induction through all generic cases is proper; when it is not, additional specific cases must be proved, or induction may not apply at all. Such an inductive proof is absolutely true for the logical system it is defined in, and just as correct as any deductive proof. When our perception of the natural laws change, etc., the proof remains true, but its usefulness may become nil if we perceive that no system in the real world could possibly correspond to the proof. In non-mathematical systems, it is possible that both deductive and inductive proofs will be seriously flawed, and I doubt one can try to prefer "approximate proofs" of one type over the other. If a system is not well-enough defined to permit accurate logical reasoning, then the chances are that an ingenious person can prove anything (see net.flame and net.religion for examples, also the congressional record). - Toby Robison (not Robinson!) allegra!eosp1!robison or: decvax!ittvax!eosp1!robison or (emergency): princeton!eosp1!robison
jbn@wdl1.UUCP (jbn ) (09/18/84)
Having spent some years working on automatic theorem proving and
program verification, I am occasionally distressed to see the ways in which
the AI community uses (and abuses) formal logic. Always bear in mind that
for a deductive system to generate only true statements, the axioms of the
system must not imply a contradiction; in other words, it must be impossible
to deduce TRUE = FALSE. In a system with a contradiction, any statement,
however meaningless, can be generated by deductive means.
It is difficult to ensure the soundness of one's axioms. See Boyer
and Moore's ``A Computational Logic'' for a description of a logic for which
soundness can be demonstrated and a program which generates inductive proofs
based on that logic. The Boyer and Moore approach works only for mathematical
objects constructed in a specific and rigorous manner. It is not applicable
to ``real world reasoning.''
There are schemes such as nonmonotonic reasoning which attempt to deal
with contradictions. These are not logical systems but heuristic systems.
Some risk of incorrect results is accepted in exchange for the ability to
``reason'' with non-rigorous data. A clear distinction should be made between
mathematical deduction in rigorous spaces and heuristic problem solving by
semi-logical means.
John Nagle