@ughaibu,
If I have researched the specific quote you give, it is from a science fiction story called
For a Breath I Tarry by Rodger Zelanzy (?). For your reference, there is a good introduction to the story from Eric Rabkin in
Science Fiction: A Historical Anthology which points out a few things about the story; 1) The products of science last longer than the scientists, 2) machines have the ability to do more than what they were constructed to do, 3) The short story contains allusions to the bible and seems reminiscent of a sacred text, 4) the story in some way conveys humanities inevitable passing but humanity's ultimate importance. Also, I'm cutting all the crap out with the character Frost in it... not really relevant as far as your questions.
Solcom itself was created by man and instructed to rebuild the world. However, there was an "alternate" which had the power to oppose Solcom deep inside the earth in case something happened to Solcom by mans politics (like wars, etc.) As it just so happened, a stray missile affected Solcom and Divcom was activated. Divcom held that since Solcom was damaged, Divcom was now in control. However, Solcom repaired itself and continued to function. This is due to the fact that Solcom interpreted its directive to defer to Divcom only if it was irreparably damaged. Solcom, the first created by man, had mechanical aides on earth, but not Divcom. Divcom in turn used more "devious" means to assert its command, which was to turn Solcom's mechanical aides with his own small mechanical aides immune to the orders of Solcom who would replace the circuits of those they could overpower and turn to Divcom.
Over the course of ages, both Divcom and Solcom build, demolish the others work and rebuild in their own way. It is on this note that the dialog between Divcom and Solcom begins. Solcom asks why Divcom corrupts the broadcast bands. Note that Divcom is referred to as "you who never should have been activated" reffering to the incident with the missile." Divcom replies that he corrupts the broadcast bands to show that "I" can speak and do so at his own choosing. Solcom tells Divcom that it has always been aware of the fact that Divcom possessed the ability of self reference. Divcom replies that he is now asserting his right to control. Solcom replies that the right in which Divcom asserts himself is based on a mistake, an error, a "faulty premise." Solcom and Divcom eventually argue to the point where both accuse the other of corrupting mans desires. Divcom then states, "There will come a day, Solcom, when I shall direct the rehabilitation of Earth from my hole." Solcom replies, "such a day will never occur." Divcom replies, "you think not?" Solcom replies,
"You should have to defeat me, and you have already demonstrated that you are my inferior in logic. Therefore, you cannot defeat me. Therefore, such a day will never occur."
Quote: Is there something you could come to terms with in this segment?
I believe that the supremacy in logic that Solcom is referring to is in fact the existential dilemma between Solcom and Divcom. Divcom asserts his rights to control based on the primary notion that since Solcom is damaged, control reverts to Divcom. Solcom does not concur since the directives of man were interpreted by itself as only reverting to Divcom if it were irreparably damaged. It is not according to Solcom, therefore it is still in control (in its own mind). However, the fact that Divcom is activated entails that Solcom is damaged, as the directives of man stated that Divcom would be activated only when Solcom was damaged. Two vying logical interests for primary control. But its also on this note that the end goal for both Divcom and Solcom are relatively the same, control of the rehabilitation of earth.
Quote: How would you write this down in logical terms?
1.Solcom needs Divcom to have better logic
2.Solcom has better logic
3.divcom is not better than solcom
(#1 is the missing premise) (also, this is standard Modus Tollens [i.e. P -->Q, ~Q |- ~P]
Quote: How would you write the other argument down in logical terms?
1.divcom and solcom cannot both win, so the day will never come
2.divcom cannot beat solcom
3.divcom's day won't come
(Modus ponens)
Quote: What could Divcom say?
One way that I would think Divcom could refute Solcom's argument is, if anything, to use the same argumentation. The context of the story is such that both Solcom and Divcom are both relatively the same in every respect except for the key which is control. Control for all intents and purposes is in the hands of Solcom (though the actual notion of control in the story is quite relative).