TL;DR: Ukraine will eventually either get nuclear protection by NATO or its own nukes, which in both cases will likely lead to the nuclear war with Russia. Knowing this, Putin may want to attack first or credibly threaten to do so.

The whole world is looking at the Ukraine-Russia conflict. Will it lead to nuclear war?

My general view is that the Ukraine-Russia conflict is structurally similar to the conflict between India and Pakistan. There are many differences, but it is a good reference point. Pakistan appeared after the British empire breakdown and it was a relatively new country whose borders was not well established. Kashmir is like Crimea in this conflict.  

The bottom line of this analogy is that there will be many wars between Ukraine and Russia and that Ukraine will eventually become a nuclear power, the same way as Pakistan did, or will get similar military capabilities via drones and membership in NATO.  

Putin also knows this and also knows that his large tank armies are almost obsolete. Therefore, he tries to limit future Ukraine military capabilities by attacking (or threatening) now. He does actually say this: we see Ukraine (in NATO) as an existential threat. He may also have some other irrational motives but the rational motives go beyond Putin, so any other Russian leader will be in the same strategic situation.

A nuclear war between Russia and Ukraine is rather possible from a long-term perspective, no matter how the current escalation will end. Unless the current war ends with the complete occupation of Ukraine.  

Therefore, the real goal of the war may be taking (or permanently damaging) almost all Ukraine including all nuclear power stations and industrial capabilities. Personally, I do not think it will make Russia safer, as new military technologies (drones) will continue to evolve in other countries and Russia will be cut from new tech by enormous sanctions. In my view, the large war with Ukraine will end in large crimes and will be eventually lost because of international help.

Therefore, Putin may see the current moment as the only chance to stop future nuclear-protected Ukraine and to prevent a nuclear war with it.

Ukraine now is slowly developing medium-range missiles which can reach Moscow according to some accounts. ( Hrim-2 declared distance is 500  km, Poroshenko said 1000 km is possible.)

A rocket attack from Ukraine against Moscow, even if with a conventional warhead, will trigger Russian nuclear-powered anti-ballistic missiles. The nuclear explosions of such anti-missiles will be small (15kt?) and high-altitude, so there will be no harm, but it will be the first use of nuclear weapons in conflict for decades. A hypothetical future nuclear war of Russia with Ukraine could spill to other countries, as an attack by Ukraine on Russia could be seen as a hidden US attack. 

Ukraine has a very large civil nuclear power – several stations of the size of Chernobyl (15 reactors). They could be used to produce plutonium. Ukraine has uranium ore mines. In 2019, the construction of nuclear fuel production plant was started (centrifuges?) 

Ukraine non-nuclear status is based on the Budapest memorandum. 19 Feb in Munich Ukrainian president Zelensky almost threatened Ukraine’s rejection of the Budapest Memorandum: “I am initiating consultations in the framework of the Budapest Memorandum. The Minister of Foreign Affairs was commissioned to convene them. If they do not happen again or their results do not guarantee security for our country, Ukraine will have every right to believe that the Budapest Memorandum is not working and all the package decisions of 1994 are in doubt.”

The memorandum was signed on December 5, 1994, by the United Kingdom, Russia, the USA and Ukraine and provided guarantees of the security and territorial integrity of Ukraine in exchange for the renunciation of nuclear weapons. After the annexation of Crimea, the memorandum was clearly violated and Ukraine has “technical” right to demand its nuclear status back, or exchange this right for membership in NATO. 

While NATO is a defence organization, Ukraine hopes that the membership in NATO will help Ukraine to attack Donbas and Crimea, which are its territories according to international laws – without risks of Russian retaliation. This situation will quickly deteriorate to war between NATO and Russia. Actually, nobody wants neither nuclear Ukraine, nor Ukraine in NATO, so NATO continues to feed Ukraine with promises without exact substance.  

Ukraine unlikely will openly start to work on nukes soon, but it can ask for equal weapons in exchange for not doing so. 

Therefore, for Putin, it is like a trolley problem: bad war now or hypothetical very bad war in the future. Personally, I am against changing the track in the trolley problem, as it is killing the real people for the possible safety of hypothetical people. Possible people and risks are more likely to be products of imagination and therefore many trolley-like problems are subject to biases – or just good words to cover some bad intentions. 

In December 2021 Putin put a rather broad ultimatum to NATO: either provide safety guarantees to Russia or deal with military-technical consequences. 

The wars are known to be unpredictable, so there is a risk that the current confrontation will spiral out of control into a global nuclear war. I even thought about moving to a county house from Moscow but decided to stay for now.

In some sense, it is a game of chicken on the trolley track.

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Thanks for this analysis. This part is the part that seems least convincing to me:

A nuclear war between Russia and Ukraine is rather possible from a long-term perspective, no matter how the current escalation will end. Unless the current war ends with the complete occupation of Ukraine.  

I don't see much reason to think nuclear war with Ukraine is significantly more likely than with North Korea, or Iran, or the USA, or the PRC, or India, or any of various other nuclear-armed states. OK sure there are border conflicts with Ukraine so maybe there are more likely to be local clashes that could blow up into nuclear war via brinksmanship... but (a) if Russia retreated from Crimea and the Donbass, I think it would be extremely unlikely that Ukraine would attack Russia, and (b) if Russia's main concern is national security but they still want to keep Crimea and the Donbass, why don't they offer the following deal: Ukraine and NATO recognize Crimea and Donbass as officially and legitimately part of Russia, and also Ukraine permanently banned from NATO, but Ukraine gets to have nukes? I feel like this deal would be acceptable to all parties on the model of the world that you are presenting. Under this deal all parties should feel pretty secure, existentially speaking. Sure Ukraine loses some territory they've already lost, but they get nukes & with nukes comes ridiculous levels of protection against invasion (see North Korea). As for Russia, with Ukraine barred from NATO and officially recognizing Crimea etc. it seems pretty darn unlikely to me that Ukraine would later get aggressive and start attacking Russia.

(My alternate hypothesis, which seems more plausible, is that Russia/Putin have other major goals besides avoiding a future nuclear war with Ukraine, goals such as annexing Ukraine or at least the Donbass and Crimea regions)

I have no experience or expertise in these topics so I'm probably wrong in a bunch of ways... what am I missing?

What I said above was my attempt to reconstruct the line of thoughts of Putin based on game-theoretical considerations and published documents. His real thoughts may be different and there are other goals as well, first of all, the desire to "resurrect" USSR. 

Retreating from Crimea or nuclear Ukraine is unacceptable for their worldview. However, they really want some kind of international agreement which will ensure Russia safety without these two things. I don't think that such agreement is viable as previous agreement of this type was thrown under a bus - the Budapest memorandum. 

If the deal included Ukraine guaranteeing its own protection with nuclear weapons again, the failure case of third-parties deciding they can't be bothered to protect Ukraine isn't a problem.

How do you factor the perception in Moscow of the recent instability in Kazakhstan in your projections?

In January I thought that the whole ukraine story is just distraction to cover Kazakhstan takeover. But not now.

While NATO is a defence organization, Ukraine hopes that the membership in NATO will help Ukraine to attack Donbas and Crimea, which are its territories according to international laws – without risks of Russian retaliation.

Russian retaliation is matter of Russian, not international law. Ascribing such naivety to Ukrainians is a bit too much for my world model. You seem to operate under assumption that Putin wants to attack and struggle to come up with rationale for his motive, while failing to address much simpler possibility of assumption being wrong to begin with. He was supposed to attack yesterday, did he? And a week before, and a week before that? Maybe it is time for update on evidence?

Oh wow, we have interesting development. I did not expect any, so my neck have been chopped somewhat, and I still don't understand why. Apparently there is some urgency at play here.

On the other hand situation is consistent with my understanding of Russian strategy: put actual servicemen there, so any attack will be attack on actual Russian army with dire consequences, international law or no.

So there will be technically invasion, but Russian kind, without dead bodies. I was wondering how situation will resolve and this resolution seems both obvious in retrospect and far more benign than what I imagined. (Of course it is far from actually resolved, this is more of a prediction/hope. In particular I can't answer "why now?")

On meta level, making prediction and being proving wrong is more fun than I expected, should write my thoughts down more often.

The problem is the borders of Donbas which is different from Line of control.

As in it provides (extremely weak) pretext for invasion? It is same as Armenia which is also in defensive treaty with Russia and governments of those regions are dependent on Russia so likelihood of them getting adventurous by themself is low. It is hard to imagine Ukrainian forces leaving Donbas without a fight so we are speaking about actual invasion here, with shooting and a lot of dead bodies. If that happens it will happen because someone wanted it to happen, not because of technical pretext.

Oh wow, we have scary development. I did not believe this can happen til the end. Yugoslavia all over again. This has to mean complete abandon of cooperative relationship with the West. That is big decision, huge economic consequences, did not expect Putin capable of it.

Other big reason why this was unexpected to me is China. China had to knew about it and still agreed to back up Russia. They are not going out of it completely unscathed, are they? That cases me to update on Taiwan invasion significantly (still low but not negligible anymore). Interested to hear official China reaction.

So it seems China knew something and effectively siding with Russia. But one thing got my attention: they seemed to be surprised by the speed of it. From multiple sources I see this surprise again and again. What happened? Is it just favorable weather conditions?

The speed may be not that quick compared to what russian planners tried to achieve. Ukraine is very large and moving in 100-200 km is some direction is only making troops vulnarable. The main question is will they able take Kiyv and will Zelensky choose to capitulate. 

It don't expect war to be quick and easy a priory. Taking Kiev? Thought alone is nightmare fuel.

I was talking about timeline up to war, not war itself. Ah, I see, happening instead of happened, fixed.

It is an issue that I noted myself and it came up repeatedly in other descriptions: recognition of D/LNR, military moving there, war - all happened too fast. Like script on fast forward. Why?

On meta level, making prediction and being proving wrong is more fun than I expected, should write my thoughts down more often.

This comment fills a warm glow in my heart.