Deterrence works, you don't need 10,000 nukes for deterrence as North Korea has clearly shown.
No, this is just representing the increased marginal utility of individual nuclear weapons in a world with fewer nukes.
This makes nuclear use more likely, as the required quantities for effective "deterrence" are lower, which means a credible nuclear capability is within reach of more countries. Obviously, more people having nuclear bombs means the inevitable second use of nuclear weapons in war will be accelerated.
If the superpowers each had 10,000 nukes, their expectations of credible nuclear weapon arsenals be higher, and North Korea would probably be priced out of the game just like South Africa was. As there are fewer nuclear weapons in the world, the more attractive it becomes to get nuclear weapons, which means non-proliferation ends up being a race to a point where nuclear weapons arsenals explode. This point is probably maximized at "zero" nuclear weapons in the world, or very close to it.
The last time this happened was the late 1940's and early 1950's, when countries as small as Sweden, Belgium, and Switzerland were actively pursuing nuclear and thermonuclear weapon programs.
Remains to be seen whether it's for deterrence. And let's face it, they were left alone for 60 years before they started developing nukes anyway. The DPRK nukes aren't really the deterrent there, it's China, not that the US is particularly interested in NK anyway, despite how much that little tubby dude craves the attention with his regular announcements.
The DPRK's biggest ally is Russia, not China. It only cares about China for trade and routinely ignores its political demands.
No one in Asia cares about America beyond it simply being there and making its presence known. It is not a primary factor in the pursuit of nuclear weapons, which is why it has not been a primary factor in preventing it. The purpose of the DPRK nuclear program is to replace the entire manpower intensive army (not only is it increasingly unsustainable, it is a political threat to the Kim dynasty) and to prevent South Korea from invading and conquering the country.
The purpose of the public announcements is to keep South Korea's population sufficiently concerned that if its leadership attempts a surprise attack to conquer the country, it will be destroyed by the nuclear weapons, whether or not it is true. It's a fairly normal method of deterrence when dealing with aggressive democracies.
If DPRK thinks anything of America, it might think America controls South Korea, and could command it to invade on a minute's notice.
The reverse is probably closer to reality.
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