Lets jump right into it…
Premise 1 – None of them want to die.
Premise 2 – Some of them want to nuke the Russians.
Premise 3 – Killing the Russians result in their death.
Conclusion – There for none of them should want to nuke the Russians.
You’ll find some helpful context in THIS video.
The concept of a doomsday device is as a deterrent to nuclear war. If a nuclear attack is launched it will trigger the doomsday machine which will wipe out all human life on the planet. This means that no one will attempt to nuke anyone else simply because of instinctual self-preservation.
In a world where this machine exists, here is what we know. We know its true that instinctually they don’t want to die. We know at this point in the cold war the temptations for the americans to preemptively nuke the Russians is there. In our scenario, because of the doomsday machine, nuking the Russians would mean the end of human life, including the americans.
Premise 1, 3, and the conclusion alone are totally valid and can exist as so. Premise 2 is absolutely paradoxical. All logic says that they should not nuke the Russians, but Dr. Strangelove defies logical explanation. Between him and General “Buck” Turgidson a plan is devised to move the men of office into an underground mineshaft, safe from radiation. Even then they must be the first to strike, so the Russians can’t get a start on their mineshaft plans. Even in the face of extinction they still want to bomb the “damn commys”.
“Mr. President, we must not allow a mineshaft gap!”
General “Buck” Turgidson
Seeing as the premises are all true, and the formula though paradoxical is also indeed true, the logic is sound. The doomsday machine is (was) the solution to the cold war. Leaving the stove unlit and on in a room where everybody’s got a gun on everybody else and saying “now no one go and shoot each other or we’ll all get the shit end of the deal” seems to be a perfectly viable solution.
I’ll finish with a quote from the movie…
He said war was too important to be left to the generals. When he said that, 50 years ago, he might have been right. But today, war is too important to be left to politicians. They have neither the time, the training, nor the inclination for strategic thought. I can no longer sit back and allow Communist infiltration, Communist indoctrination, Communist subversion and the international Communist conspiracy to sap and impurify all of our precious bodily fluids.
– General Jack D. Ripper