First, +1 for an implied endorsement of the Hegelian dialectic.
That's kinda where I am.
I'm not sure what incremental benefit the wall will have in security (our border security really isn't in too bad a shape now IMHO) for the cost of it. But, I do know that the cost is getting more and more expensive with the gov't shutdown rooted in the issue.
No matter which side is at fault (really, both), a direct line has been drawn between this government shutdown and that wall. Those costs become sunk costs for the wall itself.
I was serious about the dialectic, but I was joking about the likelihood that two deterministic inputs could synthesize an accurate output. That outcome requires both sides to make honest and reasoned arguments. If the arguments are politically motivated (which means they're likely deterministic), I doubt the arguments from opposing sides would be accepted by the other as honest and reasoned. Both sides would be more interested in proving their side is right than resolving the differences between the two, accepting that their own position may be wrong.