What The Hell Is "The Exception That Proves the Rule"?
What does this phrase even possibly mean?
Born and raised in New York City, Nick studies philosophy at Trinity College Dublin, specializing in Mathematical Logic and in the crossroads of free will, determinism, and personhood. His particular interests are: Logic, Philosophy, Motorsports, Kurt Vonnegut, Bertrand Russell, 20th Century American Literature, The Automotive Industry, and Debate.
I am irritated and confused by my complete lack of understanding what people mean when they say "the exception that proves the rule."
What am I missing? Please help me out here.
Exceptions, by their very definition, disprove rules. For example, consider the rule: "Every swan is white." Translated into logic, it reads: "For all X (if X is a swan, then X is white)."
This is actually a real and famous example. It used to be an expression in England, which expression communicated rarity, to call something a Black Swan. The force of the term came from the fact that, as far as they knew, no such thing actually existed. But then, a Dutch explorer actually found black swans in Australia.
At this point, philosophers like Hume and Mill who were concerned with induction, the method in which you draw general rules from a pattern of particular instances, began using it as an example. Induction, you see, is a good but logically imperfect way of figuring things out.
Just because every swan you have seen so far has been white, that does not mean that the next one will be.
Deduction, the method in which you draw particular instances from general rules, is superior. We could deduce from the formal logical proposition above, for example, that any given swan is going to be white.
But, as we mentioned, any given swan is not going to be white. Which brings me to the heart of my confusion: Since a black swan is forbidden by the rule, a single black swan overturns it. Exceptions, by their very nature, disprove rules. The fact of the existence of a black swan means that we have to deny that proposition.
So what does "the exception that proves the rule"" mean?
Is this just a failure of creativity on my part? I think I can remember using it and understanding it in the past, though I have no idea now what that understanding was. Since the company I keep, to which I might address a question about this, consists mainly of students of logic and the related subjects, nobody has been able to help me understand this so far.
Wikipedia has been similarly unhelpful. They say that it is "frequently misused", but that its real meaning is that an exception in a specific case indicates that the rule exists outside of that case.
Which is emphatically does not.
They give the example of a sign which says: "Parking prohibited on Sundays." They say that that exception proves that parking is not prohibited on the other six days of the week.
Which it does not. I suppose it indicates the likelihood of that, but it by no means tests one's imagination to conceive of a case in which parking is prohibited on Sunday and also on one or more other days.
So I am back in the fog in which I started. I don't even have a candidate answer. Help me!
It's just the current cycle that involves opiates, but methamphetamine, cocaine, and others have caused the trajectory of overdoses to head the same direction
- It appears that overdoses are increasing exponentially, no matter the drug itself
- If the study bears out, it means that even reducing opiates will not slow the trajectory.
- The causes of these trends remain obscure, but near the end of the write-up about the study, a hint might be apparent
Through computationally intensive computer simulations, researchers have discovered that "nuclear pasta," found in the crusts of neutron stars, is the strongest material in the universe.
- The strongest material in the universe may be the whimsically named "nuclear pasta."
- You can find this substance in the crust of neutron stars.
- This amazing material is super-dense, and is 10 billion times harder to break than steel.
Superman is known as the "Man of Steel" for his strength and indestructibility. But the discovery of a new material that's 10 billion times harder to break than steel begs the question—is it time for a new superhero known as "Nuclear Pasta"? That's the name of the substance that a team of researchers thinks is the strongest known material in the universe.
Unlike humans, when stars reach a certain age, they do not just wither and die, but they explode, collapsing into a mass of neurons. The resulting space entity, known as a neutron star, is incredibly dense. So much so that previous research showed that the surface of a such a star would feature amazingly strong material. The new research, which involved the largest-ever computer simulations of a neutron star's crust, proposes that "nuclear pasta," the material just under the surface, is actually stronger.
The competition between forces from protons and neutrons inside a neutron star create super-dense shapes that look like long cylinders or flat planes, referred to as "spaghetti" and "lasagna," respectively. That's also where we get the overall name of nuclear pasta.
Caplan & Horowitz/arXiv
Diagrams illustrating the different types of so-called nuclear pasta.
The researchers' computer simulations needed 2 million hours of processor time before completion, which would be, according to a press release from McGill University, "the equivalent of 250 years on a laptop with a single good GPU." Fortunately, the researchers had access to a supercomputer, although it still took a couple of years. The scientists' simulations consisted of stretching and deforming the nuclear pasta to see how it behaved and what it would take to break it.
While they were able to discover just how strong nuclear pasta seems to be, no one is holding their breath that we'll be sending out missions to mine this substance any time soon. Instead, the discovery has other significant applications.
One of the study's co-authors, Matthew Caplan, a postdoctoral research fellow at McGill University, said the neutron stars would be "a hundred trillion times denser than anything on earth." Understanding what's inside them would be valuable for astronomers because now only the outer layer of such starts can be observed.
"A lot of interesting physics is going on here under extreme conditions and so understanding the physical properties of a neutron star is a way for scientists to test their theories and models," Caplan added. "With this result, many problems need to be revisited. How large a mountain can you build on a neutron star before the crust breaks and it collapses? What will it look like? And most importantly, how can astronomers observe it?"
Another possibility worth studying is that, due to its instability, nuclear pasta might generate gravitational waves. It may be possible to observe them at some point here on Earth by utilizing very sensitive equipment.
The team of scientists also included A. S. Schneider from California Institute of Technology and C. J. Horowitz from Indiana University.
Check out the study "The elasticity of nuclear pasta," published in Physical Review Letters.
Scientists think constructing a miles-long wall along an ice shelf in Antarctica could help protect the world's largest glacier from melting.
- Rising ocean levels are a serious threat to coastal regions around the globe.
- Scientists have proposed large-scale geoengineering projects that would prevent ice shelves from melting.
- The most successful solution proposed would be a miles-long, incredibly tall underwater wall at the edge of the ice shelves.
The world's oceans will rise significantly over the next century if the massive ice shelves connected to Antarctica begin to fail as a result of global warming.
To prevent or hold off such a catastrophe, a team of scientists recently proposed a radical plan: build underwater walls that would either support the ice or protect it from warm waters.
In a paper published in The Cryosphere, Michael Wolovick and John Moore from Princeton and the Beijing Normal University, respectively, outlined several "targeted geoengineering" solutions that could help prevent the melting of western Antarctica's Florida-sized Thwaites Glacier, whose melting waters are projected to be the largest source of sea-level rise in the foreseeable future.
An "unthinkable" engineering project
"If [glacial geoengineering] works there then we would expect it to work on less challenging glaciers as well," the authors wrote in the study.
One approach involves using sand or gravel to build artificial mounds on the seafloor that would help support the glacier and hopefully allow it to regrow. In another strategy, an underwater wall would be built to prevent warm waters from eating away at the glacier's base.
The most effective design, according to the team's computer simulations, would be a miles-long and very tall wall, or "artificial sill," that serves as a "continuous barrier" across the length of the glacier, providing it both physical support and protection from warm waters. Although the study authors suggested this option is currently beyond any engineering feat humans have attempted, it was shown to be the most effective solution in preventing the glacier from collapsing.
Source: Wolovick et al.
An example of the proposed geoengineering project. By blocking off the warm water that would otherwise eat away at the glacier's base, further sea level rise might be preventable.
But other, more feasible options could also be effective. For example, building a smaller wall that blocks about 50% of warm water from reaching the glacier would have about a 70% chance of preventing a runaway collapse, while constructing a series of isolated, 1,000-foot-tall columns on the seafloor as supports had about a 30% chance of success.
Still, the authors note that the frigid waters of the Antarctica present unprecedently challenging conditions for such an ambitious geoengineering project. They were also sure to caution that their encouraging results shouldn't be seen as reasons to neglect other measures that would cut global emissions or otherwise combat climate change.
"There are dishonest elements of society that will try to use our research to argue against the necessity of emissions' reductions. Our research does not in any way support that interpretation," they wrote.
"The more carbon we emit, the less likely it becomes that the ice sheets will survive in the long term at anything close to their present volume."
A 2015 report from the National Academies of Sciences, Engineering, and Medicine illustrates the potentially devastating effects of ice-shelf melting in western Antarctica.
"As the oceans and atmosphere warm, melting of ice shelves in key areas around the edges of the Antarctic ice sheet could trigger a runaway collapse process known as Marine Ice Sheet Instability. If this were to occur, the collapse of the West Antarctic Ice Sheet (WAIS) could potentially contribute 2 to 4 meters (6.5 to 13 feet) of global sea level rise within just a few centuries."
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