Is there anything infallible?

[Jaded Sage]

Do human beings have access to anything infallible? The first thing that comes to mind is math. Plato said reason is infallible. Some Christians believe the pope is sometimes infallible. What do you think?

[thedoc]

Do human beings have access to anything infallible? The first thing that comes to mind is math. Plato said reason is infallible. Some Christians believe the pope is sometimes infallible. What do you think?

Apart from math, (if it's done correctly), and logic, (if it's done correctly), I think it's a very short list.

[Jaded Sage]

I suppose the question then becomes how do we know we are doing it correctly. That may seem like a small assumption, but Descartes would argue it is a massive assumption. How can I be sure that I haven't made a simple error in a two step math problem every time, even when I'm checking my work. It's as easy as losing your glasses on your nose.

[surreptitious57]

Axiomatically deductive systems of logic like mathematics and sound syllogisms and also reasoning devoid of logical fallacies

[Jaded Sage]

Yeah, but the problem is they are axioms! That means they are based on nothing. They are simple assumptions.

(Actually, there are exceptions. Sometimes we reason to axioms instead of from axioms, but most of the time, and in this case, we are reasoning from them, which means they are grounded on nothing.)

[Greta]

Even maths breaks down at infinity and zero. Maybe there's another kind of math that can deal with absolutes?

Also, the humans who perform maths are fallible. Even AI has fallibility in its design, courtesy of limited humans. Maybe many generations of AI built by AI could come very close to mathematical perfection?

[Jaded Sage]

Honestly, I think that's the closest we could ever get to actual infallibility. Otherwise, the best we can hope for is potential infallibility.

[surreptitious57]

Mathematics uses proof to validate its conclusions and so it is not based upon untested assumption
The laws of physics are derived from observable phenomena and are written in mathematical form

[Jaded Sage]

I'm fairly certain it ends up begging the question.

Also the laws of physics are not written in math, they are described with math.

[surreptitious57]

Mathematics is the most perfect system that is known to exist and nothing is superior to it including science

[Jaded Sage]

Most perfect does not equal perfect. Also, what about logic?

[Durian_Freak]

A few random thoughts:

It seems to me, first of all, that the question is somewhat misleading: surely it is not a thing which is fallible or infallible, but our (putative) knowledge of that thing. A tree is neither fallible nor infallible; it just is. The same goes for reality, mathematics, logic and all the rest. More correctly, I think, we should rephrase the question as : "Are there any statements -- regarding trees, reality, or those cast in the language of mathematics, logic, etc -- about which we cannot be mistaken?"

Re: mathematics. I'm no expert, so correct me if I'm wrong, but didn't Gödel demonstrate the incompleteness of mathematics? In other words, there are certain statements in mathematics which are undecidable; their truth cannot be known. This would suggest to me that our knowledge of mathematics as a whole -- even when all the proper rules of inference are adhered to (i.e. no slip-ups) -- cannot be infallible.

How about individual statements of mathematics and logic then? W V O Quine famously argued that any statement can be held firm come what may if we so desire; and conversely, that every statement is potentially subject to revision, even those that seem most impregnable (2+2=4). It's kinda all up to us, if I understand him correctly. What tends to happen in practice on Quine's account is that those statements most deeply entrenched (those of the 2+2=4 variety) in our 'web of belief' are held firm, while those at the periphery of the web are revised according to a principle of minimal mutilation. We could, if we so wished, and without contradiction, cling to the belief that the world is flat, or decide that two plus two does NOT equal four, but this would require a massive reorganization of the entire system of beliefs. Likewise, if we were determined, for whatever reasons, to defend Newtonian mechanics against the assault of Einsteinian relativity, we could do so without inconsistency by positing the existence of undetected (or undetectable) forces that, under certain conditions, shrink meter sticks and make clocks run faster.

Then again, I see no reason to think Prof Quine is any less fallible than the rest of us.

[surreptitious57]

That is what mathematics is namely an axiomatically deductive system of logic though there are also others

[Jaded Sage]

I don't think Quine is relevent here. Certainty and infallibility are two different things.

[Durian_Freak]

I don't think Quine is relevent here. Certainty and infallibility are two different things.

I'm not sure I understand. It seems to me that "the truth of a statement S is known with certainty" is just another way of saying "our knowledge of the truth of statement S is infallible". If a proposition is known with certainty then we cannot be wrong about it; which is simply to say we enjoy infallible knowledge of that proposition.

No?

If not, can you please clarify the distinction you're trying to draw? Thanks!