Logos

The PTBT evolved out of a series of diplomatic negotiations between the governments of the U.S., the U.K., and the USSR. These talks went on for years.

Given all the talking, it's entirely likely that the conversations between people like Eisenhower and Khrushchev became heated. You might think that each invested party would have engaged a whole spectrum of rhetorical devices, from emotional appeal to ethical conjecture, during the lengthy negotiation process so as to get what they wanted out of the deal. If one tactic doesn't work, you try another, right?

While that might work when you're trying to talk your way out of trouble, you'll be hard-pressed to find anything beyond stone-cold reason here.

That's because the PTBT is an international treaty about preventing catastrophic warfare, not a holiday newsletter from those cousins you only see at family reunions. Considering the intensity of the situation and the strains caused by the capitalist/communist disagreement, emotive content would have been not just inappropriate but volatile.

Furthermore, using something like ethos to drive the decision-making process while writing the PTBT would have been pointless, if not damaging, because—philosophically speaking—the U.S. and the U.K. had a different sense of what defined moral character and ethics compared to the USSR. If anything, ethos could have been seen as one party staking claim to a moral high ground and passing judgment on another party.

Not a great scenario for a nuclear crisis.

It's just as well. Pathos and ethos would have opened a whole can of subjective worms and possibly halted negotiations altogether. It was extremely important that the PTBT presents its content as neutrally and logically as possible so as to be agreeable to all parties involved. This accounts for its tedious language and detailed procedures, which you might have noticed in Articles I, II, and particularly III. They are describing the rules laid out by the treaty—rules for which there is no room for interpretation or error.

There is one exception, however, that is a blend of pathos and logos, and that's line 3:

Seeking to achieve the discontinuance of all test explosions of nuclear weapons for all time, determined to continue negotiations to this end, and desiring to put an end to the contamination of man's environment by radioactive substances [...]. (3)

The idea here is that the original parties are dedicated to eventually ending the use of nuclear weapons because they poison the planet and threaten to kill every living being on it. That's pretty basic logic, but with a strong emotional element to it. The thought of everyone and everything dying because of a nuclear bomb is terrible.

To put it simply, it's a thought that makes us feel bad, and there you have your pathos. Sometimes the most straightforward arguments are successful because they carry with them the strongest emotional appeal.