Talk:Fallibilism
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I have a question: What is the fallibilist response to extremely simple, "easy" statements, such as "x = x" or "1+1 = 2"? Such statements are so easy to understand that it seems they could not possibly be fallible. What would an ardent fallibilist respond to this? SpectrumDT 19:13, 26 November 2005 (UTC)
- This is no editing talk, however I like to answer you (if you are still well and alive - see date):
- Even mathematics is fallible, because there are no certain proofs (see Gödel, see Quine - I am not a specialist in mathematics). Your proof, as far as you put it, is: "statements are so easy to understand that it seems they could not possibly be fallible". Would you maintain "If any statement is easy to understand it must be right"? (Surely not, or do you?)
- My solution to this problem is: "X=X" and "1x1=1" and "I have a head on my shoulders" are "unproblematic propositions". If and only if propositions become problematic they become also worthwhile to investigate them. In this case you propably will find something interesting. --hjn 12:43, 12 March 2006 (UTC)
SpectrumDT, even if the math is infallible, we're not. It's hard to see how we might be mistaken about things like "1+1=2", but I know I've personally added up larger numbers and gotten wrong answers. Clearly, the realistic odds of making an arithmatic mistake decrease to negligible as we use simpler numbers, but they never go away.
That's basically the point of fallibilism: not that we are wrong about "1+1=2", but that we can in principle be wrong about anything. Error, however unlikely, remains possible, so we can't rule it out entirely. In fact, any attempt to do so is itself open to the possiiblity of error.
Note how this stance is incompatible with both infallibilsm and radical skepticism. Alienus 18:52, 12 March 2006 (UTC)
[edit] Knowledge in an axiomatic system versus knowledge about an axiomatic system
I believe there is a consensus that mathematical axioms and systems based purely on such axioms do not contain knowledge. In the case of this discussion, 1 + 1 = 2 (based on Peano axioms) is not knowledge but an instance of non-erroneous application of that particular axiomatic system. As 1 + 1 may be equal to 2 in one axiomatic system and 11 in another.
On the other hand, one may know (possess knowledge about) a method, which may be axiomatic; e.g., the reader may know what Peano axioms are and, based on that knowledge, the reader (or reader's Turing machine) may infer that 1 + 1 = 2. In doing so, the reader (or a Turing machine) does not inject any new information (thus any new belief, thus any knowledge) into the system but simply applies the axioms to the data in order to obtain the result. But a person (or the designer / programmer of a Turing machine) may not be absolutely certain about that knowledge and is fallible as he / she may misinterpret and / or erroneously apply an axiomatic system and reach to false conclusions. Kayaalp 18:34, 23 October 2006 (UTC)
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Quick q: isn't "fall victim to relativism or scepticism" unecessarily pejorative?
[edit] The 1+1=2 Deal
I think introducing statements like "1+1=2" and "x=x" is beyond the scope of what fallibilism is about. Fallibilism mainly concerns the indeterminacy of empirical evidence to theory; There's little sense in applying it to conclusions that involved no inductive inference in the first place. To wit, 1+1=2 is true by definition - ours, that is - and definitions aren't subject to paradigmatic overturning in the same sense that normal theories are. There was no "Oh shoot, -1 had a square root all along" moment; there was an "ooh, giving that a definition would be useful" moment.
As for "even if the math is infallible, we're not", I think that this observation is, again, outside the scope of fallibilism proper. I don't think that any philosophical doctrine seriously doubts that humans are capable of error, and at any rate, turning on your axioms and making them fair game for discarding is not a choice to be taken lightly. The notion "but what if 1+1 doesn't equal 2?" is about as enlightening as "But what if the whole idea of falliblism is bogus?"- being human, we have to start somewhere, and falliblism is nothing if not a pragmatic approach. It is of course healthy to remain skeptical and keep an open mind to re-questioning assumptions etc., but it is also healthy to know our limitations as to what we can effectively question that'd yield any insight beyond self-defeating sophistry. --AceMyth 11:18, 26 October 2007 (UTC)
[edit] Re: Fallibilism and Human Error
Re: "I don't think that any philosophical doctrine seriously doubts that humans are capable of error."
Some people are, or historically have been, infallibilists about some human beings (e.g., some human beings thought to be divinely inspired), or about some methods of knowledge (e.g., "The Scientific Method"--whatever that is supposed to be!). Further, the whole point of much Modern philosophy--e.g. Descartes' knowledge that he exists and so does the world he perceives, and Kant's knowledge about the categorical imperative--is that certain philosophers claimed to be infallibly certain that they infallibly knew some doctrine x. Other historical thinkers also believed that some axiomatic systems, e.g. Euclidean geometry, were based on self-evident, infallibly known axioms and thus were avenues of infallible knowledge. So, even if there is a current consensus (amenable to fallibilism) that axiomatic systems do not give us knowledge, and that induction does not give us certain knowledge, and that No Humans are Immune to Error, fallibilism remains an important and distinctive philosophical position, when seen in its historical context. SCPhilosopher 20:15, 7 November 2007 (UTC)
