What were China's thoughts on the possibility of a nuclear exchange, during the Cold War?
We know, sorta, what the Soviets, and Americans thought, what about China?
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During Mao's reign, the predominant strategic doctrine was People's war. That is, when suffering a large scale invasion, the defenders would avoid direct engagements and allow the invaders to enter deep into home territory, harass them while mobilising the people, then counterattacking only when an overwhelming numerical advantage is available. Under such a doctrine, the threat of nuclear strikes is downplayed:
In both the moderate and extreme versions of People's War, the response to the nuclear bomb was the same: it had to be assessed in terms of the impact on morale of the guerilla army and those masses in the process of being mobilised. The Maoist view was that the destructiveness of nuclear weapons ought not to be exaggerated lest the masses be demoralised. The view was best expressed by describing the nuclear weapons as paper tigers, basically highlighting the outwardly strong, inwardly feeble aspect. Not only was it stated that the weapons were not for use but also the fact that they were inappropriate for guerilla warfare. The assumptions were that even if an attack was launched on China there was very little it could do except resort to civil defence and concealment. Second, while the attack would wreak havoc on China's industrial centres, it could not destroy rural China. Since China was predominantly rural, it could not be subjugated by nuclear strikes.
Chinese Nuclear Doctrine, Savita Pande, Research Fellow, IDSA, http://www.idsa-india.org/an-mar00-2.html
This doctrine was held, with minor amendments, almost to the end of the Cold war. From 1964 - the first successful nuclear detonation - to 1985 when Deng abandoned People's war, China's nuclear strategy evolved from anti-nuclear blackmail to minimal deterrence. Neither strategy could guarantee MAD but can prevent war by making attacks unnecessarily costly. Combined with People's war, this was called "People's war under modern conditions". But it would take time for such deterrence to become credible, especially against adversaries such as USA and USSR, whose nuclear arsenals were advanced enough to eliminate the second strike capabilities of China.
Interestingly, the same views were shared by the Soviets; their anxiety was that due to People's war, China could shrug off a nuclear first strike and launch an overwhelming conventional retaliation.
Further reading: Impacts of China’s Nuclear Doctrine on International Nuclear Disarmament, Xia Liping http://www.nti.org/media/pdfs/Xia_Liping.pdf
There was a quote attributed to Mao tse-tung "What if they killed 300 million of us? We would still have many people left."
It's possible that he never said that in public. But it has become part of the Chinese "lore." Statements of the sort were released during the period leading up to the 1964 announcement of the Chinese atomic bomb, and reflected the Chinese view that "when we have a bomb, we can play the "MAD" (mutually assured destruction) game as well as anyone."
More to the point, the quote reflects the ultimate Chinese defense strategy: In the event of an all out war, nuclear or not, against say, a coalition of the US, Russia, and Japan, China would "cede," if necessary, the eastern one-third of the country and hold out by "holing up" in the western two-thirds, just like in World War II.
Most historians agree Mao was quite crazy, almost as crazy as Stalin, but it remains the general consensus that development of nuclear weapons and nuclear threats were only part of the "MAD game", so that China got its way diplomatically/politically. The most prominent events, as mentioned above, are the Taiwan Strait Crises. Mao wanted Taiwan because (1) he wanted to unite China under his power (2) Taiwan received aid from the USA so there was a constant threat of attack in the far south (3) Taiwan was strategically important as she was key to sea lanes linking Malaya to Japan, which supplied the Japanese with tin and rubber for industry (she was a model democratic society, a state all capitalist countries could point to and say, see, capitalism works. Thwarting its progression would be seen as Communist victory ideologically.)
According to Mao's China and the Cold War by Jian Chen, which in turn is according to Gromyko's accounts of what happened, despite PRC official accounts condemning them as false (Jian believes Gromyko):
In discussions with Gromyko while shelling the islands of Quemoy and Matsu, Zhou Enlai told him "Inflicting blows on the offshore islands, the PRC has take all the hard blows, including atomic bombs and the destruction of its cities." Also, although he advised that the USSR should not take part in the Sino-American war "even if the Americans used tactical nuclear weapons," he said if Washington risked broadening the war by resorting to using "larger nuclear weapons", the USSR should "respond with a nuclear counterstrike." Mao then stated that should the Americans invade the Chinese mainland or use nuclear weapons, the PLA would retreat, drawing American ground forces into China's interior, after which Moscow should use "all means at its disposal [i.e. Soviet nuclear weapons] to destroy them."
Furthermore, Jian sees Mao had "unique" and "unconventional" views towards the nuclear issue, repeatedly claiming that "even if the American atom bombs were so powerful that, when all dropped on China, that they would make a hole right through the earth, or even blow it up, that would hardly mean anything to the universe as a whole, although it might be a major even for the solar system". He also described nuclear weapons as nothing but a "paper tiger" - this may refer to Eisenhower's policies of massive retaliation and brinkmanship that threatened war without genuine belief in those threats, but it is more likely a reflection of Mao's indifference to its power and effect.
Nonetheless, the CCP leadership retained caution in approaching the US military, insisting that the PLA "concentrate the strength of their artillery force and navy to bombard Jiang's vessels ... However, no strike should be aimed at American ships" and unreasonably demanded that they in the event that American and GMD ships were mixed together, only GMD ships could be fired at.