But are people more likely to accept the axioms of Principia Mathematica (and the soundness of every logical step from page 1 to 300) than they are to accept the notion that 2 + 2 = 4 based on intuitive notions of what twoness, fourness and plusness are?
Of course they are more likely to believe their intuitions. They also believe that it makes no difference whether or not you swap doors in the Monty Hall problem, and don't believe that with only 23 people the odds of a shared birthday are more than 50%.
To some extent, there is the problem. People trust their intuitions, and their intuitions are often wrong. That's why for some things we need proper proofs.
But proofs always come back to axioms, and on what basis do we accept axioms? That they sound intuitively right. So we've just kicked the problem upstairs a bit, we can't avoid using our intuition.
Personally I'm more likely to believe 2 + 2 = 4, something I can easily check to my own satisfaction using four objects, than I am to believe the Axiom of Choice.
We still use our intuitions, but now everyone knows the starting set of assumptions.
As for the axioms in use, I think the big reasons they were chosen is: They lead to results we already wanted/proved to be true.
Another thing to keep in mind, not everyone works with the same sets of axioms. Which, as someone with a formalist[2] view on mathematics, I find interesting. For example, not everyone studying logic assumes the principle of the excluded middle[1]. One of the consequences of this is that you can no longer do proofs by contradiction.
The axiom of choice is another example of this where two groups of mathematicians accept it or not. I'm a formalist, so I don't have issues with this (as long as both sets of axioms are interesting and "intuitive"), other philosophies of maths might.
It comes down to levels of assurance. The rules of inference you are using are part of your design space. Mathematics at its core is about clever problem solving. When you encounter a problem you have to decide what you would accept as a proof, and this forces you to accept certain reasoning principles.
The caveat is that this is non-trivial and it's very easy to make people accept assumptions which are completely wrong. That's really the main reason to accept the axioms of set theory: People have been trying to poke holes in them for a hundred years and nobody has managed it yet. If you can use set theory (or something equiconsistent) to solve your problem, chances are that nobody will be able to call you out on a mistake.
Well, the whole idea is to pick simple axioms, so it's harder to get wrong. And also, every successful prediction that math makes based on the axioms, is in a sense a verification of them.
Vimana are not unique to India and there are references from all over the world and include the Egyptian Saqqara Bird, the pre-Columbian golden airplane models, the Greek Icarus legend, the Chariot of Ezekiel, the Nazca runways (lines), The Abydos carvings, The Tassili rock paintings from Algeria and the Chinese references to Lu Ban’s wooden aircraft that flew great distances. Naturally, these references are often dismissed by modern historians as simply impossible but there can be no doubt that humanity has a collective memory of have once been able to fly in ancient times.
Or even just to have worshiped flying beings. Modern fiction is full of fantastical and impossible things. Are we to believe that people in the ancient world were incapable of flights of fancy and everything they wrote and made must be taken absolutely literally?
> Today, we can kill everyone off with an exchange of the already existing nuclear weapon inventory
I'm not convinced we can. For starters, the nuclear weapon inventory is a lot smaller than it was back in the 80s when those sorts of statements were popular. And secondly, as I understand it, it was always a bit of a lie, an estimate based on some silly assumptions (e.g. that everybody in the world lives in cities), which in repetition eventually lost those assumptions.
And yes, I agree with the other poster that it's pretty much impossible to kill everyone on earth with climate change.
Species-ending diseases I do worry about, but maybe that just means I don't know as much about immunology as I do about nuclear weapons.
There are many fewer weapons available for an impromptu nuclear war, and despite the horror that I think many readers here underestimate, that reduction is a Very Good Thing. The problem is that the nuclear explosives may have been taken apart to some extent, but they can also be put back together.
The nuclear arsenal is predominantly hydrogen bombs, and they are insanely powerful. The Hiroshima bomb was 16 kilotons. A W-87 and W88 warheads are a bit under half a megaton, or roughly 30X more powerful. The W-78 is about 350kilotons, about 20X larger. The B-83 bomb lets you dial in just how spectacular you want a return to neolithic life to be, all the way up to 1.2 megatons, about 70X larger than the Hiroshima bomb. There are fewer than 250 cities with over 1M population. With just the ready US arsenal you could blanket most of the populated parts of the planet.
In 1967 the US maintained an arsenal of about 30,000 (!!!!!) nuclear weapons. You have to wonder. Now the stockpile is about 4500 and about 1500 are deployed and ready at a moment's notice.
Recent research has shown that nuclear winter after even a limited exchange would be worse than previously thought. We don't know how/if our technological society would bounce back from N billion starvation deaths.
Indeed, just 100 small warheads would (maybe) do it. See Mills' Multidecadal global cooling and unprecedented ozone loss following a regional nuclear conflict [0] which models the effects of a limited nuclear conflict between India and Pakistan.
I believe you misunderstand the cause of a nuclear winter.
The cause isn't the nuclear radiation per se. It is the extreme destruction of many large urban centres simultaneously. The problem is that all of those cities burning simultaneously would send up a tremendous amount of ash and smoke that would block the sky for quite a while.
This would cause a reduction in the amount of sunlight that would be available for growing crops and combined with the almost total destruction of global economy could result in the destruction of the entire human race through mass starvation.
I believe that would 100 users for the service that you would write using their api. See bottom of this page: https://plaid.com/products/ (playing around with the api to help make a self-use budgeting app - under the current terms, this use case would be free).
It's not about portrayal, it's about actual physiology.
The percentage of alcohol users (ie almost everybody) who become alcoholic is quite low. The percentage of heroin or meth users who become heroin or meth addicts is very high indeed.
Alcohol still of course does plenty of damage, unsurprisingly since it's the only such substance which the majority of the population consumes. Maybe the world would be a slightly better place if we hadn't started drinking booze all those thousands of years ago. But I don't buy the idea that because we accept one particular form of stupid behaviour that we should tolerate all the others... any more than I buy the idea that just because I tolerate my unemployed brother living in my apartment that I should open the doors to let everyone else live there too.
>The percentage of alcohol users (ie almost everybody) who become alcoholic is quite low. The percentage of heroin or meth users who become heroin or meth addicts is very high indeed.
Do you have a source for this? Every study I've seen shows addiction rates among users in the 10-15% range for all three.
It is difficult to look at "% of users who become addicts" in a vacuum, since it's a population selected for willingness to take illegal drugs and hang out with the sorts of people with access to them.
I think it is because society tolerates alcohol abuse more, and the delineator between alcoholic and non-alcoholic is biased.
See my other comments in this thread. People openly admit to their peers being hungover when showing up to work, or bragging about their crazy, drunk weekend. There's a lot of denial about alcohol's impact on society, and what constitutes an alcoholic when it is legal, and widely accepted. Just substitute heroin or meth for some of the things people say about their alcoholic adventures, and you will see this very clearly.
I heard it was around 10% for heroin users. No idea what the numbers for alcohol are. I imagine social circumstances play at least as large a role as the actual drugs.
True, although I'd guess that the massive decrease in mortality in infants under 1 (who are still massively more likely to die than older children) is probably due to improved medical intervention.
For older children and teenagers it's probably better safety equipment, particularly in cars. I guess we've also got improved treatments now for the few diseases which actually do kill children, such as various cancers.
But hey, it's still good news, even if "healthier" isn't the way to describe it.
> If you think about it logically for the era, it's incredibly unlikely that Jesus was actually unmarried
Only on the assumption that "being married" is uncorrelated with "starting some weird travelling hippie Jewish tradesman cult", which I assume it isn't. Having a wife and family obligations tends to hamper the travelling-and-preaching lifestyle somewhat.
Also, people who spend their 30s claiming to be the Messiah and getting crucified for it probably spent their 20s being a bit weird as well, even if nobody bothered to write about it.
If you're thinking that your calling may invite persecution, or are inclined to do stuff like wander the desert and eating locusts, it's not so strange that you would choose not to get married. Never mind that getting married may not be so easy in this case!
