The Big Think’s “Errors we live by” site has a post called “Reason is larger than science,” which makes a number of statements intending to do down science. Some of them are fine, and others are wonky, but the ones that are fine are bloody obvious. The piece is illustrated, though, with this figure, so you can see where it’s going:
It contains 9 claims, some not obviously connected with its thesis. Here are just four examples of a superbly stupid article that makes no clear point at all:
1. The closer we get to human patterns, the more useful the logic and lexicon of the humanities is. If well practiced, science reduces biases and errors, but it grants no immunity to nonsense.
Who said that science never was nonsensical, for, after all, some scientists are weird and crank out crazy stuff, like cold fusion. But science itself as a set of tools will drive out nonsense. The humanities won’t do that, as clearly demonstrated by the persistence of postmodernism. As for “the logic and lexicon of the humanities” being better for understanding “human patterns,” I’d like to see an example that’s not based on empirical observation and testing, i.e., science broadly conceived.
2. Scientists often seek a mathematical “totalizing” theory, however such “monotheorism” risks “theory-induced blindness.” And mathematics is a subset of logic. Plus its tools aren’t always useful.
Yeah, and some of us don’t seek a mathematic totalizing theory, which isn’t useful in biology (there’s not a single equation in Darwin’s On the Origin of Species). And even if mathematics isn’t science per se, it is useful to find out what’s real, which is in the ambit of science. And really, mathematics isn’t always useful? That’s true, but doesn’t leave a mark on science because not every bit of science rests on mathematics, much less “mathematical totalizing.” Yes, math wasn’t useful for Darwin, but how does that show us that his theory is fallacious, or that something’s wrong with science?
8. Not all non-science is nonsense. Far from it, much of non-science is logical; its reasoning is locally reliable. Many reliable skills and arts are unscienced (deploying qualitative facts without underlying unified theory). And all that’s subjective remains unscience-able.
Another straw man. Logic may not be science, but it still is a useful tool in helping us weed out nonsense. I wouldn’t say that the Pythagorean theorem is a piece of science, because it is absolutely true in all the right reference frames, and, unlike claims of science, can be “proven”. No sane scientist, though, would deny that the theorem is extremely useful. So is Plato’s Euthyphro argument, which I consider one of the most useful bits of philosophy around, for it proves logically that morality cannot come from God.
And of course neither music nor art as practiced are “scientific,” but who would dismiss them as “nonsense”? They’re palliatives, consciousness-expanders, and emotional stimulants.
Nevertheless, science is the only game in town if you want to ascertain what’s real in our universe. It is the only reliable “way of knowing”, if by that we mean “finding out stuff that everybody agrees is true.”
9. Many tend now to defer to “the science” mindset. It would be wiser to use diverse thinking tools, to reason humbly, and artfully fit the tool to the task. Much is logically true without “the numbers.”
Logical truths or mathematical truths are not “scientific” truths, which depend on empirical observation. But logic and mathematics are part of the scientific toolkit that helps us find out what is true in our universe. They are not separate from “the science mindset”, but part of them.
I’m not sure who Jag Bhalla is, but if he was paid more than one cent to crank this stuff out, he was overpaid. If you want, try your hand at the other five propositions.
h/t: Steve
All those quoted pieces didn’t really make a lot of sense to me. I think the author needs to go back and rethink what he’s trying to say.
I suspect there is confusion about what is meant by science and that confusion informs the whole piece.
I also don’t really understand what the first picture is supposed to be about.
Same here – if the article hadn’t been attached to a Jerry-piece, I wouldn’t have finished it, short as it is. It was, to me, a lot of nonsense. And I’m a humanities graduate who also studied economics.
Perhaps the picture means that science is not as good as the humanities in describing and explaining humanity.
As a Humanities graduate I must point out the phallic nature of those telescopes. 🙂
As a fine arts graduate I must point out that those are not telescopes.
(http://www.wikiart.org/en/rene-magritte/the-treachery-of-images-this-is-not-a-pipe-1948)
😉
Perhaps the meaning is that the humanities needs bigger telescopes than science does?
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I think it means that the humanities like to pack people into megaphones.
(Is it just me or does that science tripod look as if it’s about ready to walk off?)
Maybe it’s that bigger people are in the humanities. Bigger people who therefore live in bigger telescopes.
Wow, that’s pretty dire stuff.
This, however, is good stuff (IMO):
http://www.compoundchem.com/2014/04/02/a-rough-guide-to-spotting-bad-science/
“Not all non-science is nonsense. Far from it, much of non-science is logical; its reasoning is locally reliable.”
LOL! I love that phrase “its reasoning is locally reliable.” It’s an academic sounding way of saying, “an opinion can be reasonable, as long as you don’t hold it up to objective scrutiny.”
Also, “It would be wiser to use diverse thinking tools, to reason humbly, and artfully fit the tool to the task.”
Please. I’m so sick of the calls for humility from some in the humanities. It’s the same weak plea we hear from religious apologists asking atheists to quiet their criticisms down. This is nothing but a ploy to try to give subjective, artsy reasoning the same credibility as objective reasoning. Objectivity has no reason to humble itself before subjectivity.
“This is nothing but a ploy to try to give subjective, artsy reasoning the same credibility as objective reasoning. Objectivity has no reason to humble itself before subjectivity.”
—
I can remember reading something once (I think it was by Noam Chomsky), that the origin of all of the post-modernism nonsense came about from a desire to make the humanities more like the sciences. Apparently, university humanities departments were envious of the science departments’ big budgets, impressive sounding specialist language, and the real progress they made in primary research and understanding the world.
So, they tried to replicate this with their own specialist jargon, impressive-sounding projects, and attempts to uncover fundamental truths about reality from deconstructing and analysing the text of books, or coming up with convoluted theories about society etc.
Unfortunately, none of this was based on real logic, experimentation, evidence, or reason – so it’s never made any objective progress. And, unfortunately (possibly due to the deliberately impenetrable language that they use) many people haven’t yet realised this.
I watched Chomsky speak about this in an interview thst can be found on YouTube. I don’t have time right now to search for it, but did want to confirm that it was indeed Chomsky.
Yes, whatever one thinks of Chomsky’s views, he’s a pretty clever chap. His life-long study of how language gives meaning makes me think that, if he cannot extract sense from a text, no-one else can.
He says he fails to understand postmodernist writing.
This?
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That is the very clip.
Echoing what Mr. Huxley writes above, whatever you think of some of his views, Chomsky seems like a down-to-earth guy you (I) could really get along with and enjoy talking to (even being the intellectual dilettante that I am).
I can’t figure out what “locally” means. This person isn’t very good at Humanities if he can’t make himself understood.
That locally sounded like a Deepakitty.
sub
I think it means that the means by which content or (what passes for) knowledge in a given field works for that field, even if those means are not applicable to other fields.
Basically it’s a post hoc rationalization for the way things are being and/or have been done in any given humanities field.
Even more basically, it’s the new-age theist’s “it’s true for me.”
As I’ve heard here and there, “That’s my story and I’m stickin’ with it.”
The illustration shows the three legs of the tripod in a straight line, which makes it foolishly unstable.
Very fitting.
That’s what happens when you have a humanities major doing a fine arts major’s job while they’re frantically insisting at the sciences that they’re not useless.
Ugh.
I’m so tired of these articles claiming that science is somehow fundamentally flawed because it is “too logical”, “too demanding of evidence”, “too narrow-minded” etc.
Humanities aficionados often make very large claims about how their subjects have a lot to offer to science and scientists.
In many cases, this may be true. But, humanities graduates, please take the time to learn something about how science operates, and to learn some of the basic facts of the subject area before you start telling us that our work is flawed. Otherwise, don’t get upset if no one takes you seriously.
And leave out the post-modernist nonsense. No one is interested.
Yet another word salad.
I’m going to sound like a humanities-apologist, but here we go:
I see no conflict between humanities and science. When studying history, we too apply the scientific method. Yet because humans are complicated human beings, we must apply different perspectives and be aware of different perspectives in our field of research. A catholic historian would have a very different view of the revolt of the protestant Dutch against the catholic Spanish than a protestant historian.
If only we could work with math too. Math is great because it’s just a matter of taking logical steps. There is no bias in mathematics.
You don’t sound like a Humanities apologist. This foolish tribalism of arts vs. science is something the relatively recent divisions set up in universities, for the convenience of administration, has caused. I personally so no conflict out in the real world or honestly within Humanities or Science classrooms.
Do = see. I don’t know why my brain is so broke lately.
Sigh. “So” = see. That one was the iPad’s fault.
It’s the do-see-do of the Humanities Square Dance.
Thanks! As soon as I typed the words ‘I see no conflict between…’ my fingers cramped. 😛
Fun fact: The word science is often translated into Dutch as ‘wetenschap’, the same word as the German ‘wissenschaft’. But the Dutch and German words encompass both the natural sciences and the humanities.
Pointing out the nudity of a given emperor whose domain just happens to lie in the humanities does not make one anti-humanities.
I’m a musician and I’m constantly seeing naked emperors sachaying about.
I just wish they’d put some damn clothes on, that is, emend their reasoning and their epistemological methods.
Your first paragraph got me all mixed up. At first I thought you were referring to how ancient Romans didn’t like seeing nude statuary of their emperors because that implied they thought of themselves as gods.
What the hell is going on with my brain? I think lesions. Or maybe legions. 🙂
lol
Hopefully it’s not legions of lesions.
Or legionnaire’s disease …
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PS. “lol” looks like somebody drowning …
Well, in that case at least it’s appropriate for my current work situation.
Ugh.
Or should I say “gurgle”.
“A catholic historian would have a very different view of the revolt of the protestant Dutch against the catholic Spanish than a protestant historian.”
I hope that at the very least both the catholic and protestant historians can agree as to the historic facts, and do not engage in rewriting the history to suit their biases and sensibilities.
Depends on the matter at hand. Describing a siege can be done in a fairly neutral manner, although some historians might pick the word ‘defeated’ where ‘slaughtered’ might be better. A historian shows his bias most profoundly when he tries to investigate the motives of historical actors.
In 1567 Philip II send the Duke of Alba with an army to the Netherlands to put down the rebellion. This might be a simple troop movement from A to B, but as historians we don’t stop there. Historians say Philip II was either a cruel and ruthless tyrant, or a pious catholic who simply tried to bring lost sheep back into the fold.
Maybe if they are historians and not theologians. When they’ve been the latter, it hasn’t gone so well.
> Plato’s Euthyphro argument, which I consider one of the most useful bits of philosophy around, for it proves logically that morality cannot come from God.
Well, I know the theologians try to find a way around it by claiming that god is “wholly good” so he couldn’t order an evil act if he wanted (which pretty bears on his almightiness, but let’s leave that aside for a moment) and the holy command theory of morals is saved.
I also know there’s a counterargument to that, as well – but I never really understood it.
The theologians try to solve the dilemma by equating “God” with “Good” as its intrinsic nature. That’s empty wordplay, though. It only moves the problem down to our capacity to recognize the Good.
Do we know that God is good because God sets the standard (and thus the standard can be anything?) Or do we know God is good because we can measure God against standards we already know?
Whenever I read one of these “science isn’t everything” essays I try to suss out the Bogie Man. What is the writer really afraid of?
Are they worried that people will try to make “scientific” pronouncements on matters of taste, becoming bullies by asserting that people who enjoy jazz or ballet or country living are objectively right or wrong?
Are they concerned about a “scientific temperament” overtaking the modern world and all the romance, love, beauty, and emotion draining out because those are now deemed “illogical?”
Do they think science is going to be used to justify racism, sexism, or some economic or government system which is cruel, unfair, and/or oppressive?
OR…
are they bothered that people are weighing religious beliefs in light of modern science and thus they are working themselves into a frothy panic over the first three because if we can grant that THOSE encroachments of science are bad then they can slip in the idea that it’s equally wrong to include the supernatural because Same Thing.
I don’t know. If the Bogie Man isn’t atheism then I don’t see the real problem. Jerry’s right; it seems they’re attacking a Straw Man. If the Bogie Man is atheism, however … then tough. Not the Same Thing. Nice try.
Often, when you dig into these articles, you find a theist lurking behind them.
🙀
Not even wrong. Jag Bhalla appears to have thought about what science is and how it can be corrected while drinking a margareta.
I must leave with Anderson’s advice about the unmistakable utility of simplicity and it leads to insight so few people outside of science ever understand.
“Very often a simplified model throws more light on the real workings of nature than any number of ab initio calculations of individual situations, which even where correct often contain so much detail as to conceal rather than reveal reality. It can be a disadvantage rather than an advantage to be able to compute or to measure too accurately, since often what one measures or computes is irrelevant in terms of mechanism. After all, the perfect computation simply reproduces Nature, does not explain her.” P. W. Anderson, Nobel Lecture, 1977
Oh, you posted that quote just last month!
Basic Theory of Surface States gives the year as 1978… Did his Nobel Prize lecture lag the award?
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* Ah, no: The book is wrong: The date of the lecture was 8 December 1977.
** Ah, no. The book was not wrong. It was just citing “Nobel lectures in Physics for 1977”, Review of Modern Physics, Vol. 50, 1978.
…”But science itself as a set of tools will drive out nonsense. The humanities won’t do that, as clearly demonstrated by the persistence of postmodernism”
So true! So true!
Nonsensical science would not have survived Alan Sokal’s detailed exposure through his hoax article.”Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity”.
From Wikipedia:
Sokal reasoned that, if the presumption of editorial laziness was correct, the nonsensical content of his article would be irrelevant to whether the editors would publish it. What would matter would be ideologic obsequiousness, fawning references to deconstructionist writers, and sufficient quantities of the appropriate jargon. Writing after the article was published and the hoax revealed, he stated:
“The results of my little experiment demonstrate, at the very least, that some fashionable sectors of the American academic Left have been getting intellectually lazy. The editors of Social Text liked my article because they liked its conclusion: that ‘‘the content and methodology of postmodern science provide powerful intellectual support for the progressive political project’. They apparently felt no need to analyze the quality of the evidence, the cogency of the arguments, or even the relevance of the arguments to the purported conclusion.”
I wonder if the picture meant to represent the Freudian competition on who has the biggest telescope, or is it a contrast of humanities versus science as being over-bloated and over-clouded with personal views that nearly block the true picture of reality.
I’m unwilling to sit through Wieseltier’s entire piece, leaving me unsure whether Jag Bhalla’s bit is supposed to be a refutation or a “me too” commentary. So, I just read Dan Dennett’s rejoinder to Wieseltier instead.
This says it all
Nobody seems to have addressed Jerry’s unspoken question who is Jag Bhalla?
“Jag Bhalla is an entrepreneur, inventor and writer. His current project is Errors We Live By, a series of short exoteric essays exposing errors in the big ideas running our lives, details at http://www.errorsweliveby.com. His last book was I’m Not Hanging Noodles On Your Ears, a surreptitious science gift book from National Geographic Books, details at http://www.hangingnoodles.com. That explains his twitter handle @hangingnoodles.”
http://bigthink.com/experts/jag-bhalla
So, nothing do so with a need for a Viagra prescription? Good to know.
“And of course neither music nor art as practiced are “scientific,” ”
However, I’d be willing to bet that both music and art as practised today owe a large part of their existence to science.
I would imagine (I stand to be corrected) that modern instruments, even non-electronic ones, owe much of their design to the science of acoustics. As for every electronic instrument, and the amplifiers, and recording / transmission media, do I need to spell it out?
And for art, just take painting for example, how much do modern artists’ colours owe to chemistry?
I agree with their music/art’s non-scientific merits in inspiring the listener/viewer, but my life has become vastly richer in musical terms since I discovered the wealth of music on Youtube, for example.
About painting:
CMU recently held a course on the chemistry of artistic pigments, which got various science, environment and art students. It was apparently so popular they don’t know how they are going to pull off running it.
Apparently the key topic was figuring out how to do environmentally friendly, but art-friendly, pigments. (A lot are transition metal coordination compounds of things like chromium, which aren’t too fun for the environment.)
Interesting. Ironwing would likely have some interesting comments to add to this, but I haven’t seen her around her in some time. I recall that in addition to her science experience (geology I think?) she is an artist and makes at least some of the pigments she uses from natural resources she finds herself.
Of course, my memory could be completely wrong.
I got … emotional … so I responded over there, sorry. I couldn’t bother with the details of the long series of strawmen after showing that they a were such.
Luckily that piece won’t drive much traffic there anyway.
Behind every cliché science stereotype is a romanticist trying to get out.
You know them when they contrast “cold, unfeeling, mathematical-logical” science with special “warmer, experienced, intuitive” humanity, as if to score a line in the sand between spirit and machine. Dualism, human exceptionalism, and moralizing are sure to follow:
1. The emphasis on science’s “mathematical” side pops out more than any other, as if whole scientific fields were nothing more than number crunching.
2. The “quantitative” nature of science is explicitly contrasted with the “qualitative” nature of the humanities. Bizarrely, somehow points four and five entangle this with some reductionist view of people as “money-making machines”, a proud demonstration of a field making a hasty generalization towards some grand unifying theory, as if it were a sign of what happens when social sciences get, well, scientific (as opposed to embracing human diversity and imperfection).
3. The appeal to a “diversity” of tools comes straight out of the NOMA rulebook, which itself is a relic of dualist thinking that thinks you need a second, ontologically distinct world of concepts to even try to discuss phenomena like human minds and experiences and constructs. That’s especially obvious in the third bullet point, which treats social and even biological sciences as “contested border zone”, which is “categorically different from physics”, literally as if you were walking from one territory to a completely different one. It’s also screamingly obvious in point 7, which even explicitly puts forward the dualist position of minds and matter being utterly distinct.
4. There’s transparent human exceptionalism in the first bullet point. There are even echoes of free will in the seventh point – choices are described as if they were fundamentally different phenomena from anything to do with matter – which is a classic human exceptionalist position.
5. In the ninth, there’s an obvious injection of moral piety with the appeals to “humility” and “diversity”. Heck, the whole economics argument in the middle is basically a finger-wagging cautionary tale.
It’s not only nonsense; it’s predictable, regurgitated nonsense. It doesn’t seem to be making a clear point because the point is blindingly obvious due to sheer repetition of clichés.
I think you are correct. I’ve thought that as well and it pisses me off. I am a romantic in many ways myself! And as far as I can tell many science friendly people, hell even scientists, are. Jerry Coyne himself is a good example. Look at his love of cats and other cute animals, of literature and music, of movies, fine foods, different cultures, and how he talks about those things.
It seems to me, therefore, that there must be some other component to it. Something in addition to romanticism. Something, perhaps, that when absent or lacking leaves romanticism relatively unfettered by reason.
I think you are correct. I’ve thought that as well and it pisses me off. I am a romantic in many ways myself! And as far as I can tell many science friendly people, hell even scientists, are.
It seems to me, therefore, that there must be some other component to it. Something in addition to romanticism. Something, perhaps, that when absent or lacking leaves romanticism relatively unfettered by reason.
I think we should be clear that there’s a difference between romantic impulses – such as a love, appreciation, and understanding of beauty, nature, and art – and romantic ideologies – explicit philosophies which try to build complex ideas out of impulsive or emotionally persuasive thinking.
For instance, Dawkins has romantic impulses when he uses poetic metaphors or meaningful literary references to describe scientific ideas, but is firmly opposed to romantic ideologies that are intellectually thin, such as those arguing from tradition, authority, or intuition.
What I was getting at was that a common thread uniting, say, religion, spiritualism, political dogmas, and the drek in this “refutation of reason” is romantic ideology. Symptoms include:
– suspicion and vilification of science and reason.
– elevation of emotional, impulsive, or intuitive ways of achieving beliefs, values, or behaviours.
– resistance to being pinned down coherently or openly.
– excessive moralization of what should strictly be neutral issues.
– anti-urban, anti-industrial, anti-progressive, anti-technology, sometimes to a puritanical degree.
– preferring special and charismatic individuals, especially as standard-setting leaders, to collective action; sometimes explicit contempt of the masses or ordinary people.
– valuing imagination and freedom over reality and constraint; this is notable when treating corrections, realistic thinking, and scientists in general as killjoys.
– prefer persuasion and moral character credentials over genuine argument or expert consultation.
You keep an eye out, and it’s disturbingly surprising how often this keeps lurking under the surface of many discussions.
I’d add one more.
– Looking to the past for greatness and wisdom as opposed to the present and the future. The Golden Age was in the past and we have since lost our way.
Oh god, yeah. I can’t believe I forgot that one, and I’m all the more astonished I didn’t list it because it was a major point in one of my favourite books, Pinker’s Better Angels. That’s got to be one of the worst romantic tropes.
+++++
That said, I’m not so confident about why such ideologies tend to be so seductive, especially since it seems selective from time to time. Environmentalism, for instance, seems to me to readily fit the romanticist category, but I’m never sure I know why I keep seeing it treated as the annoying obsession of single-issue wonks. Could it be a backlash against scientific global warming? Does even the whiff of scientific argument for global warming put it on the Enlightenment side of the Enlightenment versus Romanticist dichotomy?
I think some people have science-(math-, technology-) phobia and need to feel superior in a way they can understand.
9. Many tend now to defer to “the science” mindset. It would be wiser to use diverse thinking tools, to reason humbly, and artfully fit the tool to the task. Much is logically true without “the numbers.”
This guy fails on both ends! Something can only be “logically true” if the argument is valid AND the premises are true. Is he suggesting we can somehow infinitely regress with pure logic to validate premises without any input from the outside (also known as “the numbers”)? This guy is a paragon of obscurantism.
I’m majoring in computer science and philosophy. I have some thoughts on this.
If you ask a philosophy professor a philosophical question, then they will say “well, first what are all of the possible positions on this issue that don’t contain explicit contradictions, and how many ways can we divide those up? what did Kant say and is that the right interpretation of Kant, because heaven forbid we ignore what Kant said? I have an intuition that this and that are true, and my colleagues have all of these other intuitions and we have to juggle them all.”
By contrast, if you ask a computer scientist a question about computer science, then they will immediately defer to reality. They will run the program or do the math, regardless of what other computer scientists have said. Quicksort is accepted because it works when we run the program, not because it’s been accepted by some authority.
This is the difference between the sciences and the humanities, in my view. It’s not that the humanities can’t make progress, it’s just that the humanities have accepted toxic patterns of reasoning that inhibit progress. I can’t help noting, by the way, that Dr. Coyne’s example of postmodernism is a perfect illustration of my point here.
Originally, the concept of philosophy was awesome. The idea of developing a way of living that is based on facts is what draws a lot of people into studying philosophy in the first place. But I think that got corrupted at some point into a sterile academic exercise.
You’re illustrating how philosophy is often taught to undergraduates (I too did computing and philosophy for most of my education): historically, and that’s only one approach. Where I was as an undergrauate, history of philosophy was one strength of the department, so that wasn’t surprising. But it is also ‘traditional’, and thus carries (unnecessary?) weight.
Personally, I would teach it as an intersection of other fields of interest, including history of ideas, but …
I really like that thought.
Fatuous is not a strong enough word for this tripe. First off, the accompanying graphic and the cheap shot at Pinker, blow Jag Bhalla’s objectivity out of the water before the reader completes the first sentence. What follows is a parade of over-stuffed straw men. No, Science is not invalidated because economics and physics are not exactly the same thing. The fact that Mill states that economics is more than theorems and numbers does not speak in any meaningful way about the veracity of validity of science and do please elaborate on the desire of economists to create a “grand, unifying theory.” As an English teacher, I’d give it a D. As an editor, I’d laugh in Bhalla’s face for bringing me copy this weak and stilted.
I would really like to know where this place in which science is king and the poor humanities have all their wonderfully useful insights bullied out of existence by the scientific method, exists on earth. I think I’d like to go live there.
I have the perspective of someone with a college education that was entirely in the humanities, and steeped in postmodernism to boot. It was a virtually useless exercise in philosophical criticism which imbued me with no skills I could go trade for money and I am still paying the bill for it today.
Perhaps if I’d been better educated in the evils and shortcomings of math and science, I might not have spent tens of thousands of dollars for a piece of paper on my wall that, aside from the fancy frame, is worth about $.08 anywhere outside of a college campus.
The humanities, as, “palliatives, consciousness-expanders, and emotional stimulants,” are indispensable. But, as a mechanism for acquiring insight and understanding in the form of objective facts about the universe, they suck, and an education steeped in postmodernism with no real math or science is a waste of everyone’s time and money.
There HAS to be some Apologist Central that sends out talking points, because I just saw all these very same things a few weeks ago on the site of a philosophy prof I fight with. He denied the the Origin of Species was science!!! No “quantitative relationships”!
Who was this?
(And there *are* quantitative relationships implicit in evolution by natural selection anyway. Grumble.)
I really enjoy your writings (for sure 🙂
“science is the only game in town if you want to ascertain what’s real in our universe”
It’s probably worth noting that anybody who says “math is just a subset of logic” without qualification probably doesn’t know much about either. The reduction of mathematics to a complete and consistent set of logical axioms is provably impossible.