Ideological bullies?
Science has long questioned theism by examining design flaws in the nature. However, it seems to me that some science followers don’t like being questioned about the scientific methodology. Just like theists don’t like being questioned about existence of God.
Of course, science lovers pride themselves on scientific enquiries and methods. But does such pride translate to ego and honour—something that should not be challenged?
I have met several scientists and science Ph.D. students. Some—not all - of them seem to treat fallibists as some kind of nonsense and anti-positivists as a science equivalent of Satan. Although they argue politely, this saddens me. They are not as open-minded as philosophers I know. Philosophers tend to be happy when receiving challenges about their fundamental beliefs. Theists and scientists seem to be otherwise. This is just from my experience though. It is not meant to be generalisable.
Science is not rationalism. It is an attempt to translate empirical results into knowledge with logic and statistics. So, science stands on two foundations—empiricism and rationalism. If one believes in science, they are likely to believe in both empiricism and rationalism. But because empiricism cannot be conclusive, neither can science. Why do scientific ‘facts’ are sometimes spoken as if they were certain? Why do some scientists fail to notice that those ‘facts’ are subject to falsification when new evidence is introduced?
Right, I may have done some silly stuffs like grounded theory, which isn’t compatible with the scientific methods. But I acknowledge that I can be flawed, and my methods are certainly flawed. Some—not all—natural scientists, on the other hand, seem to have so much faith in scientific methods, which I believe is somewhat flawed as well. As a social scientist, I am sometimes intellectually group-raped by scientists as though I offend them by questioning the scientific methods. * sighs *
If you are a scientist or a science follower, may I ask, what do you think about social scientists? Sometimes I feel like scientists look down on social scientists, and I don’t feel comfortable working with them.
“Why do scientific ‘facts’ are sometimes spoken as if they were certain?”
Because one can be certain of facts (where ‘certain’ means ‘assigning a probability arbitrarily close to 1’) even if we’re not certain of the mechanisms behind them. Newtonian gravity was wrong, but if you let go of a lead weight it will drop to the ground. You can be certain of that. Try it as many times as you like.
“Why do some scientists fail to notice that those ‘facts’ are subject to falsification when new evidence is introduced?” If they do, then they’re not scientists. In fact the scientific method is precisely equivalent to Bayesian reasoning—formulate a hypothesis, test the hypothesis, revise based on results. On the other hand, there are some facts (evolution, lead weights falling to the ground, heat never passing from a cooler thing to a hotter one) that are so well established that the probability of their being falsified is effectively zero.
“Some—not all—natural scientists, on the other hand, seem to have so much faith in scientific methods, which I believe is somewhat flawed as well. ” In what way? The scientific method is simply updating of one’s beliefs based on new evidence. That’s all it is. I can’t see how that is flawed, and can’t in fact see any other way to discover truths about the universe. What do you offer as an alternative?
“I am sometimes intellectually group-raped by scientists as though I offend them” This is a horribly incoherent sentence, with some very unpleasant attitudes in it. To start with, disagreement, however vociferous, is in no way comparable to gang rape. Furthermore, while I don’t pretend to understand the motives of rapists, their behaviour is not usually explained by saying they were offended. Perhaps if you rephrased this so it refers to actual people’s actual behaviour, your writing might be clearer.
“If you are a scientist or a science follower, may I ask, what do you think about social scientists? Sometimes I feel like scientists look down on social scientists, and I don’t feel comfortable working with them.” No scientist I know looks down on social scientists. Plenty of scientists I know, however, look down on people who witter on about supposed problems with the scientific method without actually saying what those problems are, and then take disagreement as ‘rape’...
Open-minded does not equal right: it’s wrong to be open-minded about 2+2=4.
I don’t understand what problem you have with scientists. It sounds like they’re right and you’re wrong, plain and simple.
What does open-minded mean? If it is open-minded to agree that there’s some non-zero probability that 2+2=4 then being open-minded is a good thing. If being open-minded means assigning that possibility a high likelyhood then presumably being open-minded is very bad.
As a reasonable person I probably should agree with you, but the truth is I don’t know whether to agree or disagree, or even what it means to agree or disagree with what you said. There’s a mystery and a promising research program hiding behind your words.
Assigning non-crisp probabilities to math statements is very tricky. I haven’t yet seen a satisfactory system that manages to do that. If you ever find one, tell it to Wei Dai because he’s very interested in consistently formalizing “mathematical intuition”, e.g. assigning a credence to P=NP. Just a small example of the troubles that arise: if you’re a Bayesian, assigning <1 probability to 2+2=4 (whatever that means) may make you incoherent and susceptible to Dutch books.
Part of the problem is that we do empirically make arithmetic mistakes. We’ve all misadded at some point for embarrassingly small numbers. But yes, I agree that formalizing such notions is particularly difficult with math, especially because our probability calculations themselves use arithmetic.
Is “2 + 2 = 4” about things or statements?
2 raindrops + 2 raindrops = from 0 to to unspecified droplets.
I’m honestly not sure whether this is a fair quibble or not, but if “2 + 2 = 4” is a tautology (a semi-taughtology?) which unpacks to “I’m only talking about things which are sufficiently stable to behave in a “2 + 2 =4″ish manner”, then there might be some wiggle room.
FWIW, I was talking about 2+2=4 as a statement of formal math. Interpreting it as a statement about the material world is a whole other can of worms that I’m scared to even think about, for fear of becoming confused forever. And the nature of human intuition about whole numbers of “things” (an intuition that can’t be captured by any finite system of axioms) is another completely separate mystery.
Here’s a more interesting angle than the water droplets:
There’s presumably some chance that there will be more math discovered—something with an effect like Goedel, but ever so much more so—which will make 2 + 2 = 4 not quite so certain.
For example, PA may turn out to be inconsistent. Here’s a great story about that possibility. Similar things have happened already: many people were surprised when Russell’s paradox broke naive set theory which looked as obviously consistent then as PA looks to us now.
This is another point for my claim that we need to understand how actual humans do math, not invest everything into one set of axioms.
Note that we have good reasons for believing that PA is consistent. Gentzen’s theorem is the most obvious one. I’d say we have much more reason to believe that PA is consistent than someone would have had prior to Russell believing that naive set theory was consistent. But that may involve some hindsight bias.
Gentzen’s theorem assumes a much stronger claim to prove this weaker one. Yes, it grounds consistency of PA in another mathematical intuition, and in this sense could be said to strengthen the claim a bit, but formally it’s a sham.
(Of course, modern mathematics is much stronger than a century ago, so that alone counts for a good reason to believe that PA is consistent.)
No. The minimal axioms needs to prove Gentzen’s theorem are not stronger than PA. There are claims in PA that cannot be proven in the minimal context for Gentzen’s theorem.
There is a lot of weirdness here, once you try to reduce the question.
Imagine an AI programmed to believe in the axioms of PA and nothing else. What credence should it assign to the arithmetical statement Con(PA)? The answer is that there’s no answer. Assuming PA is “in fact” consistent, Con(PA) is formally independent from PA—which means I may add the negation of Con(PA) to PA as an extra axiom and get a consistent system. (Equivalently, that “self-hating” system has a model in ordinary set theory. Building it is a neat little exercise.) So believing or disbelieving in the “actual” consistency of PA, as we humans can, requires some notion of Platonism or semantics that we cannot yet teach to a computer.
And the question why you instinctively believe Gentzen’s proof, which uses transfinite induction up to epsilon zero, is even more mysterious. You’re comfortable relying on the consistency of a stronger system than PA because it sounds intuitive to you, right? Where do those intuitions come from? The very same place where naive set theory came from, I think.
“There’s presumably some chance that there will be more math discovered—something with an effect like Goedel, but ever so much more so—which will make 2 + 2 = 4 not quite so certain.”
Uh, no.
“it’s wrong to be open-minded about 2+2=4.”
right, until you learn something about non-Euclidean systems.
If you don’t understand what I say, you can’t really say I’m wrong without reasonable doubt. But some scientists don’t really listen. Just like some theists who don’t want to listen to atheistic statements.
I wanna learn! What’s a non-Euclidean system and what is 2+2 in it?
It seems that you are talking about many things you don’t know much about.
Non-Euclidean is a term used to refer to certain types of geometries.
In this context, do you mean non-Archimedean? That’s very different. But then 2, +,4 and = will generally have different meanings. It seems pretty damn likely that interpreting these terms in say Peano arithmetic, that 2+2=4 is true.
Not quite; this is a case where reducing certainty from a numeric scale to a yes/no dichotomy loses something very important. As evidence accumulates, it can bring you arbitrarily close to a probability of 0 or 1, just not to 0 or 1 exactly. A more accurate way of phrasing this is: Empiricism can use only a finite amount of evidence, so while science can be arbitrarily certain, it cannot be infinitely certain.
Not defending the poster: just trying to salvage the thread.
Is this right? The probability space reserved for the milieu of extreme skeptical hypotheses seems more like a constant (albeit a very small one) than a range which can be arbitrarily small.
What kind of social scientist are you?