(Disclaimer by request: this is going to involve, necessarily, transmorlative functions, so in many aspects, it is not traditionally explicable; ergo, don't feel that you're missing something if you're not already familiar with many of the issues discussed.)
On the Justifications for War
Posit that we have two groups of people, Group War ("GW") and Group Peace ("GP"). Posit also that GW and GP are engaging in a dialogue about their desired outcomes for the future. GP's argument is that war is too horrible to contemplate, while GW argues that war is indeed horrible, but is necessary, because it accomplishes some desired end.
Many of us have likely faced this situation in what we would call "real life." For example, you're chatting with a friend about international politics. You are staggered by your friend's seeming inhumanity, and reference American drone strikes. You reference the horror of civilian casualties, and you think that the discussion will undergo a massive change right there: e.g., you believe that, in order for anyone to advocate for war, that person would have to deny the occurrence of such horrors. You might think that your friend would begin arguing that reports of civilian casualties were false, or that the "civilians" killed were actually bloodthirsty terrorist combatants, or other such nonsense.
Sometimes, that does happen. Sometimes, members of GW argue that there are no real civilian casualties. They approach the problem from a framework of racism or cultural supremacy: insisting, for example, that all Muslims, all Arabs, all Pakistani, or all of "those people" are terrorists, therefore there are no civilian casualties. Other times, they argue that a bleeding heart liberal media makes up civilian casualties in order to stir emotions and gain readership.
When the latter argument is made, you might conclude, "Oh, this person is just stupid." That's a reassuring conclusion in many ways: maybe the person isn't really a callous or bloodthirsty killer of children, but rather, someone so dimwitted that they don't really believe in the existence of so many humans in the middle east who are being killed as part of a war they want no part of. Maybe members of GW simply subscribe to an old-fashioned, ignorant racism--inhuman in its own way, but also strangely reassuring, because if they learned to overcome that racism, their deeper humanity would then cause them to oppose the killing of innocents.
The American Liberal
Far more imposing an opponent than the ignorant racist is the intelligent apologetic, which you may have encountered in the form of the American liberal. This is Bill Clinton; Barack Obama; Digby; any of the other intense warmongers who thoroughly disavow open racism, but who still advocates for imperial war. The standard American liberal, confronted with tales of robotic drones killing two-year-olds in the night, agrees that it is horrible, and is aghast at the notion that "racism" might play a part in drone war.
However, the standard American liberal has many reasons to still be a part of Group War. They include:
1) "It's their fault [the "real" Arab terrorists' faults] for putting their families in harm's way;"
2) "We're acting on the best information we have available, we take every step possible to avoid killing people, but sometimes it just happens as a by-product of war, which I agree is horrible;"
And, to top them all off, the best possible argument for modern warfare, which is filled with so many levels of justified-yet-disguised pigheaded racism and subtly archaic ignorance and self-interest that it appears, paradoxically, rational:
3) "For civilization [or "the human race"] to survive in a world of proven constant conflict and the great game of states, thereby preserving a few pockets of decency for a few lucky people to live in reasonable comfort, many non-progressive, medieval peoples have to be forced to stop using violence, which requires the use of drones, and we can't afford to risk so many soldiers' lives to stop them with targeted raids, so we have to just bomb neighborhoods and hope for the best, while never forgetting our humanity, and deeply regretting the necessary loss of innocents."
Recognize #3? If you get an American liberal with the emotional strength to withstand the discussion, they will always end up at #3. It's the only plausible retreat from the other justifications for war: a plea to the inevitabilities of natural selection, capitalism, free markets, and the American need to survive in a harsh jungle of realpolitik states.
Cold, indeed. Horrible, yes. And yet, this gets spouted, on occasion, from people who are otherwise quite decent--people who, if they're able to move past their comfortable blinders of American exceptionalism, might actually get it. There are American liberals who were active in the "American Civil Rights" (TM) struggle; people who resisted the Vietnam War and understood the racist notions and corporate lies that drove said War...and yet, these same liberals then fall for the same arguments when it comes to the Iraq War a few decades later. People who cried--really cried--about Vietnamese kids burned by napalm, and who cursed Henry Kissinger to high heaven, find themselves, forty years on, "the establishment," explaining away chunks of six-month-old Afghan viscera as glibly as Hillary Clinton.
How? Why? Many of us have come to this point of confusion, marveling at the colossal levels of concealed racial supremacy and cognitive dissonance conjoined to such GW viewpoints. Here's where the math comes in.
Life and Death as Functions
The problem here is an improper weighting of variables in transmorlative functions. More traditionally put, members of the group "GW" are "putting too low a value on life," or "arguing that, when a tree falls in the forest, it makes no sound if no one is around to hear it." Here are earthly versions of some of the functions:
C - W > Q
Here, let C equal "civilization," let W equal "the tangible costs of war," and let Q equal "chaos," e.g., something like anarchy. As a sentence, this goes, "Civilization suffers the costs of War, but even after suffering them, still trumps the costs of unrestrained and widespread anarchy."
Now, there is a lot to quibble over in that one equation, and that's where most political arguments end up. Anarchists will suggest that Q is in fact zero, and that a lack of order is not a negative thing. Civilization may be greater than nonexistence, but it is not greater than "the costs of chaos," e.g., "anarchy." Let "N" equal nonexistence, and look at the anarchist argument as a function:
C - W > N < Q
Anarchists, then, are saying, "We could do it better," or rather, in a more Nate Doggish way, "Nobody does it better": an unplanned, decentralized system of not-states would produce a superior result. American liberals will argue the opposite, advocating for the first equation, which, with anarchy added in, would look like this:
American liberal's equations:
C - W > N, or Civilization, less the horrible costs of War, is nonetheless greater than Nonexistence
C - W > Q, or Civilization, less the horrible costs of War, is nonetheless greater than the horrible costs of Anarchy
It seems a bit clunky, and more than a bit ridiculous, to attempt to "force" math to explain this stuff, right? There's a good reason, though. Continuing, with anarchists' preferred two versions of the equation:
(White) Anarchist's equations:
N > C - W, or Free People Without States are greater than State Civilization less the horrible costs of War necessary to maintain it
AND, the more daring, insightful version of anarchy's argument:
N > C + W, or Free People Without States are greater than State Civilization and the horrible costs of War upon which State Civilization thrives
Really, the same point, but the latter version pulls fewer punches, and better characterizes entities like Barack Cheney.
The Part Where Math Helps
"Contorting" these arguments into a mathematical format often seems ridiculous, but it does actually help us realize something that might not be apparent without the math. First, we must understand that the arguments haven't been contorted--these are the arguments, directly expressed as equations. American liberals argue what they argue because they are making a cost/benefit analysis of the situation. They "don't like" drone strikes, and dislike some of Obama's policies, but feel they're necessary, and go along with it all, because they're running the C - W > N rubric. Anarchists, and many progressives, counter them using the N > C + W, so it's essentially a mathematical argument.
So, where does the math actually help us? Easy. If you remember your basic algebra classes, you know that variables can be shifted around on either side of an equation, provided the equation remains balanced. Ergo, in the case of the following:
2 + x = 4
x must equal 2, right? Because if 2 + x = 4, we figure it out by subtracting 2 from each side, like so:
2 + x = 4
x = 2
And there we have the foundation of algebra--balancing the equation yields results. We all know that, right? So, let's use the tangible mathematical arguments from above, and apply that kind of algebra to them.
C - W > N
C > N + W
...adding a War to each side, to get rid of the negative W, proves that Civilization is better than Anarchy plus War. Easy, right? And for the anarchists:
N > C + W
- W -W
N - W > C
Revealing, this last equation--it shows the truth of the anarchist argument, namely, that anarchists hate states so much that even Anarchy and War combined are better than (state) Civilization. What? Take a look at the most recent equation, N - W > C, with the variables spelled out:
Natural Freedom and Anarchy less the horrible costs of War is still better than State Civilization Without War.
Revealing indeed, of the western middle class' affection for what they call "anarchy," and their dark envy of the elites who control civilization. So many sheltered westerners claim to be anarchists, disavowing a need for any kind of collective police force that would require the extremely mentally retarded to be kept away from kids at the playground, just because they're so used to the comfort of life under a state umbrella that they don't believe there are benefits to collective action, be it called "state" or otherwise.
This isn't meant to devolve into an argument over anarchism, though, so put that aside for now. Focus on the American liberal's apologia for war. We want to find the functions' missing variables. Being able to add and subtract things on either side of the equation produces many ridiculous results, which, when expressed mathematically, show us how ridiculous many of our arguments are. Like geometric proofs, shifting the variables in our little rationalizations show how flawed they are from inception.
Ridiculous, right? A stilted attempt to say nothing at all by reducing complicated issues to math? I promised to show how these explain otherwise-liberal war-apologists, and so I will--using those equations.
Challenging the Apologist
When you approach the apologist, your argument is, "The costs of war are so great and horrible that what you call civilization is not worth those costs." E.g., your argument is, indeed, a mathematical one: "The greater-than sign should be changed to a less-than sign." What you are arguing is:
C - W < N
While what the Obama-apologist is arguing is:
C - W > N
So, your argument is mathematical. You're also arguing that quantity "W," i.e., "The costs of war," is larger than the American liberal says it is. And that's a big argument--you can spend dozens of hours arguing, correctly, about (1) how inaccurate drone strikes are, or (2) how you can't trust tribal Pakistani informants who are accusing neighbors from other tribes of al Qaeda "membership" in exchange for briefcases of cash to feed their families and try to escape the killing zones. You can argue that (3) fewer drone strikes occur in larger cities, not because there are fewer potential terrorists there, but simply because corrupt local politicians are able to better protect their cities from American murderers, and direct the wrath of American murderers toward poorer rural villages.
All of these things are true--and eventually, if you find a patient enough liberal, all of these things will be conceded. And yet, the argument will not be won. No matter how big you make "W," the American liberal's unalterable position is that the greater-than sign starts off facing "C," or civilization.
You can assault the value placed on "civilization," next. You can discuss the millions of Americans in prison; the millions of starving children; the international police state and the financial fraud and environmental devastation of civilization...and still lose, because the "greater than" sign is there.
So you turn to the only place you can, the place I said you would in the beginning: trying to argue that the greater-than sign should be switched into a "less than." You want to tell the killing-apologist, "These things simply aren't worth it. They are too horrible." But because you lack the tools that could properly address the problem, you lose. The greater-than sign stays there for the liberal, it remains a less-than sign for you, and life goes on (for some of us).
The Missing Variable
The variable that we're missing here is an integral part of the transmorlative function, which, expressed in this mathematics, is the "turner" of greater-than/less-than signs. Variables of this type cannot often be expressed in Earth maths, so they sound speculative and pointless, however, one has been an acknowledged part of Earth arithmetic from the beginning, and you're probably already familiar with it: dividing by zero. We all know that you can't divide by zero; when working with fractions, if you have:
...you have a problem. Math teachers will tell you to just write the solution as "zero," but the real answer here is, "Error," as in, "What your calculator says when you try to divide something by zero." Dividing by zero is another of the lovely paradoxes of this perspective that we all kindly ignore, so long as we're able to keep using the rest of the system to calculate the trajectory of flying objects, and other such things. Dividing by zero is not expressly related to what we're doing here, but for purposes of this discussion, it demonstrates the unexplored attic rooms in the old Victorian manor of our maths--so, if you accept that you can conceptualize, but not properly solve, dividing by zero, you're able to acknowledge other "Error" functions, and realize that any arguments worked out that way are flawed.
Dividing by zero, or partitioning nothing into something and representing it as a quantity, is fun, and related to costless energy production, but again, ignore that for now. Focus on the old equation, C - W > N. Our problem here is that it is an equation; restated, the problem is that neither the "equals" sign, or the "greater-than" sign, or the less-than sign, work out in this place. That's why the argument can't be won, and why arguing for a larger W, a smaller C, or an inverted greater-than symbol is inherently faulty. Here, that's like trying to divide by zero. It's an error, even if your heart's in the right place.
The missing variable is L, which we can define in almost the same words as "W": the costs of war. We should even replace "W" with "L" in our original function, like so:
C - L > N
L has different characteristics than W, though, which makes it invaluable for working things here: L cannot exist. Said another way, L must not exist, e.g., there can be no equations in which L is weighted, for L is the ending of equations, so its appearance in any function in Earth maths is anathema. Like the sudden appearance of zero as the denominator of a fraction, the appearance of L indicates a flawed equation; an impossible equation; an irrefutable proof that the original setup, no matter how complicatedly it was presented, had a fundamental flaw. C - L > N, then, is wrong without argument. That has to be accepted in order to achieve the desired result: a world where the existence of L is not reasonably contemplated.
Eliminating the Unwanted Variable
From this perspective, that appears to be pie in the sky, wishful thinking, et cetera, and yet, it's necessary to get where you (may) want to go. C - W > N is an insane argument; a heartless argument; and, maybe less importantly, a wrong argument, even if all you read is the New York Times. The quite literal and hard-headedly-grounded economic costs of war are too expensive to make C - W > N sensible.
Nonetheless, it's still an arguable equation. You can have a rational disagreement about C - W > N, where one party may be provably wrong, but still making a valid, internally consistent point. To argue about the weight of C, W, or N brings into play opinions about the merits of, say, "clean streets" or "food stamps," and leaves open for speculation the merits and responsibilities of both sides. The war apologist may be confused, heartless, or simply stupid, but s/he may still have that argument rationally.
The argument that needs to be had to settle the issue here is the quintessentially simple argument that dividing by zero is impossible, and that so too is the existence of L. What is "L"? Well, it's not measurable here, which is why it has no place within this rational framework. In this case, L is:
1) Four seconds of the encapsulated agony of one thirty-eight-year-old woman who has just found her infant crushed beneath a fallen first-floor roof and who realizes that she probably won't be able to have another;
2) Two seconds of the encapsulated terror of one infant when it hears the loudest, scariest noise ever and realizes the roof is getting closer really fast.
Granted, L could be called "emotional" here, which is why we've been trained to avoid it in our rationality--but just like dividing by zero, there are places where there aren't actually any emotions involved, but things as tangible and measurable as our ability to weigh barrels of cabbage. In this particular shadow, our ignorance of what makes the scale move causes us to work with broken equations. Unavoidable in some arenas, but once we figure out that certain operations don't "work," we need to stop employing those operations. Trying to have rational arguments with people about inverting the greater-than symbol is fail, even if you're right, because your counter-argument will also be wrong. C - W < N is wrong, because if you add a W to each side, you get C < N + W, or C < N + L, or "Anarchy plus the costs of War is still better than awful state Civilization," which is wrong because it includes L. If you hate the idea of Barack murdering families in their sleep, then you can't stand for the existence of L.
To have any chance, however small, of being effective, you have to be willing to address the real point: the existence of L. You need to suggest the bane of modern realpolitik, namely, the impossibility of taking any action which could cause L to appear anywhere on the board. Any other form of equation is flawed, because any equation which leads to an L variable being stuck inside Earth maths is going to be wrong.
Your Levelheaded Take
When you haven't been told about certain variables, you still understand this. It was not by "cold, rational" means that you came to oppose drone-strikes against Arab kiddies; rather, you already recognized the infeasibility of L, and you were just trying to express it in the best way you could, by saying, "C - W < N." Wrong, but your heart was in the right place. Yet, because you were wrong, the American liberal senses an instinctive wrongness in your argument--their own humanity, telling them that your argument will lead, also, to L...and so, they feel justified in resisting it, even if their resistance is in the form of an impossible defense of L.
If you're into realpolitik, and don't like any of the presumably mushy stuff, look at it this way: the only way to be actually right, and the only way to address the issue at the core of the disagreement, is to point out the characteristic impossibility of L. L can't be weighed or valued, here, except to call it something like "negative infinity," or "the destroyer of worlds and equations," which must be wholly prevented. Using L that way solves a lot of other arguments had here too, including the white western anarchy one--because leaving kiddies to the whims of roving gangs is impossible, there must be some sort of communal safety arrangements.
Anyhoo, looking forward. There are places where L can be used, but it's not here or now. The operative thing to remember is that, like it or not, you'll have to employ so-called mushy variables in order to be correct. Most war apologists don't actually believe in C - W > N, even though they think they do. What they're actually trying to do, by supporting war, is to subtly argue the insane, impossible position that L is weighable and usable here. That's why they so easily dodge stuff like, "The CIA decides who to murder based upon cash-purchased testimony from the local drunk," or, "The police could arrest the suspect rather than the military blowing up the suspect's entire family." They're not actually invested in the variables they claim; what they are invested in is the ridiculous notion that L can become part of a measurable debate.