Talk:Fallibilism

message: 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)
thread_title:  Knowledge in an axiomatic system versus knowledge about an axiomatic system 

message: 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)
thread_title:  The 1+1=2 Deal 

message: 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)
thread_title:  Re: Fallibilism and Human Error 

message: The claim that fallibilism is in conflict with the theological defense of Papal Infallibility doesn't belong in this article as currently written.  In the first place, it's not sourced at the present.  Secondly, Catholics are at pains to distinguish beween epistemelogical infallibility, and the Pope's (putative) position as the infallible interpreter of Catholic tradition.  As canons of interpretation present different problems than the question of the certainty of knowledge, I believe this contribution compares apples to oranges, in a way that gives short shrift to both.  I'm removing the line. Innocent76 (talk) 08:02, 9 January 2011 (UTC)
thread_title:  Removing line on "papal infallibility" 

message: Could anyone add a section to explain the difference between fallibilism and skepticism?
--Roland 20:15, 20 September 2011 (UTC)
thread_title:  Fallibilism vs. Skepticism 

message: This statement at the bottom of the first (opening) paragraph -- "This position is taken for granted in the natural sciences" -- is problematic.  First of all, it's not really at all what Kuhn is saying in his thesis broadly speaking, and, more certainly, it suggests that modern science is value-free.  Nazi science, for example, was not fallibilist.  A strong case can be made (and has been -- post-colonial; poststructural; feminist social theory) that modern western anthropology itself was and continues to be rife with ideological baggage.  I think I know what the writer is trying to say, but I also think this statement needs to be qualified or else removed.  — Preceding unsigned comment added by 200.252.139.132 (talk) 14:45, 10 August 2012 (UTC)
thread_title:  Kuhn's insight