We seem to disagree on what the nature of facts is so I'll focus on that in this reply:
Bruno Loff:
Of course, because I can't but agree that the ball does fall, that makes it seem like an irrevocable truth.
Just because people agree on something doesn't make it a fact.
Bruno Loff:
Yet the recognition that the ball falls is based on a sensory apparatus we both share, and that is unable to interpret that stimulus any differently. That the ball is falling is not a fact, it is a consensus.
It's unable to interpret that stimulus any differently because sensory apparatus for the most part accurately senses things in the independently-existing world, and in this independently-existing world, a ball is falling. Whether the ball falls is a fact - either it falls, or it doesn't. This is independent of anybody perceiving the ball falling. If you disagree that there is a reality independent of your perception of it then there is no point talking, really.
The recognition of a fact is another matter. If your sensory apparatus is broken in the right way, then you won't be able to recognize that a ball is falling. This doesn't mean the fact is that the ball didn't fall - it means you can't recognize the fact that the ball fell.
It is unsurprising that the consensus for something as simple as a ball falling is usually that the ball is falling. This doesn't mean the consensus makes the fact, or that the consensus is the fact - it means that the fact is simple to ascertain.
Bruno Loff:
Also worth pointing out, with regards to usually-consensual facts --- there is a fun social experiment you can do with 30 people or so, in which you play a game where you have to label the colors of a given object. One person is unaware that the other 29 have arranged to claim that there is a slight shade of, say, blue, in a purely black object. Just put enough pressure and presto, the person who was singled out, in most cases, will come to see that shade of blue.
I'm not sure where this particular set-up comes from: 30 people, and seeing blue in black. Can you provide a link to the study?
In the original Asch conformity experiment (
source), 25% of the subjects always answered correctly, i.e. in accordance with the facts. (Note that there are *facts* here outside of anyone's perception of them!) 75% were incorrect (conformed) at least once. 36.8% of total responses by the participants were incorrect. So far from it being "in most cases", it's rather "in 36.8% of cases". Asch said in "Group Pressure and the Modification of Judgments" that "The preponderance of estimates in the critical group (68%) was correct despite the pressure of the majority." (
source).
Now it wasn't always because they came to actually see the answer the wrong way. There were three possibilities for giving the wrong/conformity answer:
1) distortion of perception: they really did think the wrong answers were right (e.g. came to see that shade of blue)
2) distortion of judgement: they suspected the wrong answers were wrong (they didn't see it that way), but they thought they must be wrong because the group was right
3) distortion of action: they didn't want to be ridiculed so they went along with the group even though they thought the group was wrong
The "distortion of perception" category were
relatively few. The distortion of judgement was the largest group. And the distortion of action was the second largest (
source).
So far from it being that "the person who was singled out, in most cases, will come to [actually perceive the incorrect answer]", it's in the fewest cases that that actually occurs.
And even in the cases that that does actually occur, it doesn't mean that the fact was different for that person. The fact is the same - the person just perceived it incorrectly due to group pressure. Indeed this is a good reason to avoid group pressure.
Bruno Loff:
Your view that the world is made of facts, and that the only thing standing in the way to clearly seeing them are feelings, is that itself a fact?
Because to me it sounds like a very tempting assertion that justifies your particular choices. It sounds like the kind of abstract, unfalsifiable statement that there is nothing I could possibly do to argue against.
Well not the only thing, but there are definitely many and various ways that feelings stand in the way of seeing facts - and this is indeed a fact that is falsifiable! The very experiment you cited is proof of this - the majority choices caused such doubt and anxiety in some subjects that despite their experience of the correct answer, they figured they must be wrong! In some cases the subjects even actually experienced the wrong answer as being the correct one! It is far from unique to actualism that feelings cloud judgement and get in the way of ascertaining facts.
As to the world is made of facts, that is tautological, since a fact is defined as something which actually happens in the world. Of course there are things that are not known and things that cannot be known, but yes, the world is made of facts. This isn't even something that needs to be proven in the scientific sense - science is *based* off of the notion that things actually happen and that they can be measured. You might say it is an axiom but I'm not sure that's entirely correct. In any case, as the wonders of scientific progress has shown, there are many clear and obvious benefits to understanding that the world is made of facts that can be measured.
As to it being an assertion that justifies my particular choices - by the very nature of what a fact is, I am extremely limited as to what my choices can be. That's because I do not make up the facts - they exist independent of me. If I really do care about facts, then I will always be willing to change my mind based on new information if that information shows a new fact that challenges my understanding, or shows that something I previously thought was a fact, wasn't. For example, I used to think the scientific consensus a few decades ago was that the earth was cooling. Yet after seeing the facts that only a minority of scientific papers predicted cooling and it was in fact the media that popularized the notion of cooling despite the scientific evidence, I changed my understanding/dispelled my belief (for it had become a belief at that point).
Of course I might not actually be after the facts, but distorting my understanding of what the facts are and thus forming beliefs instead, ignoring facts that contradict my understanding, etc. Maybe I am deluding myself so I see as factual what isn't. Maybe, but that's not what I'm going for. And if something is truly factual then it should be able to be verified by other people.
As to math, that was indeed an interesting diversion:
Bruno Loff:
Even mathematics, which is logic in its purest form, and, if truth exists consistently anywhere, it is there first and foremost ---- even mathematics is a social activity of consensus building, and even it has statements which can not be proven true or false (see Godel's theorem).
No, it's not consensus building, it's starting from axioms and applying the axioms regularly to get proofs. These are simply definitions and rule-following. These are logical constructs which exist only as abstract entities and has nothing to do with consensus. Now all mathematicians might indeed have a consensus that a proof is accurate when in fact it isn't, but this doesn't change the mathematical truth of that proof, and indeed eventually it will be discovered to be false by the very nature of mathematics. As for Godel's theorem, yes, it is a mathematical truth that in a sufficiently advanced mathematical system, not all mathematical statements in that system can be proven true or false.
Bruno Loff:
EDIT: curiosity, Godel's theorem says that given any "mathematical perspective", if you will, there are statements which can neither be proven true nor false --- these statements are called "undecidable". That these statements are undecidable, however, is something that must be ascertained from a different "mathematical perspective" than the one that is under scrutiny.
Almost, but not quite. It is a proof within a given "mathematical perspective", as you put it. That is, for any sufficiently advanced mathematical perspective, there is a proof within that perspective that there exists a true statement that is unprovable by that perspective. It's actually delightfully awesome. Godel, Escher, Bach provides a full, detailed explanation of the proof that I was able to follow - that's when I first really understood the proof. EDIT: Seems I misunderstood and was mistaken. Godel's theorem is a proof
within the perspective that there exist undecidable statements - but you were right, the proof of undecidability of a particular statement does have to lie outside the system - otherwise the system itself would be inconsistent and thus useless.
Bruno Loff:
Furthermore, as a consequence of the theorem, one can also conclude that there must be statements that are undecidable, but whose undecidability is itself undecidable --- one won't be able to prove that the statements are undecidable, i.e., there is a statement S that one won't be able to prove that one won't be able to prove that S is true or false. Such statements are utterly beyond mathematical scrutiny --- by their very nature, I wouldn't be able to present you such a statement, and be able to convince you that I had done so.
I'm not sure that follows from the incompleteness theorem itself - see
these questions that don't mention it - but this does seem to be the case, yes.
Although I'm not sure these statements are utterly beyond mathematical scrutiny. There are a large number of
unsolved problems in math. Maybe some of these are undecidable - there's no way to know yet, since nobody has proven them undecidable. Maybe the decidability of some of these is undecidable - again no way to know yet, since nobody has proven that their decidability is undecidable. So maybe the fit into the category you described, yet they're still pretty scrutable. But perhaps I am missing something.
Bruno Loff:
Now this VERY COMPLICATED state of affairs is how things work in something like mathematics: where everything is describable with the utmost precision and rigor, not at all like messy things such as balls and falling and me wanting this or feeling that. It should be no surprise that in the real world things are even more complicated.
Well the real world is of an entirely different nature than mathematics. Real world things are ultimately based on sense experience, not abstract systems of axioms and rules.
Bruno Loff:
But the fact of the matter is: if someone were to believe in an undecidable statement, I could not prove him or her wrong, no matter how hard I tried. At best, I might point out the fact that it is undecidable, in case that itself was known.
Actually this would prove them wrong. They would say I believe this is true or this is false, and you would say, no actually it is mathematically impossible to show that to be the case because the statement is undecidable. Interestingly, I think you can use such a statement as an axiom to extend a system - another term for undecidable is "independent" - and then you can see how that system (original system + new axiom) behaves.
Bruno Loff:
If someone were to believe in an undecidable statement whose decidability is itself undecidable, then there would be absolutely nothing that I could say against it, no matter what.
Well you could say that there exists no proof as of yet showing that statement to be true or false. This would apply to Fermat's Last Theorem 100 years ago, for example. So they could believe until they're blue in the face, but in mathematics it's always starkly obvious whether a statement has an existing proof of truth or falseness. It's simply illogical to believe in a statement that hasn't been proven yet. You can strongly suspect and not be able to disprove it, but that doesn't make it true.