I find it rather interesting that the foundations of both logic and democracy can be traced back to ancient Greece. Here in the US, we’ve taken the Greeks’ idea of democracy and brought it to a new level, but at the same time our political discourse seems anything but logical. We owe to Aristotle the “Three classic laws of thought”, which are as follows:

1. The law of identity. Anything object must be the same as itself. $$ P \to P $$
2. The law of noncontradiction. Something can’t be and not be at the same time. $$ \neg(P \land \neg P) $$
3. The law of excluded middle. Either a proposition is true, or it’s negation is. $$ P \lor \neg P $$

It’s worth while to note that these statements are neither verifiable or falsifiable, qualities true of any “axiom”. An axiom is supposed to be a self-evident truth, that gives us starting point for a discussion. The universe described by these axioms is one where “TRUE” and “FALSE” form a dichotomy. These axioms don’t handle things like quantum particles or Russell’s paradox in which things can be both true and false simultaneously. Nevertheless, they provide a useful tool for discerning truthhood. Politicians, however, are more concerned with “votes” than “truths”. The following “Three Axioms of Political Alogic” are the negation of the “three classic laws of thought”, and generally indicate situations where a politician is distorting the truth for personal gain. Although, that could change if Schrodinger’s Cat decides to run for office.

The Three Axioms of Political Alogic

#1: The law of deniability

Just because something is, doesn’t mean that it is.
First order (a)logic: $$ \neg (P \to P) $$
Sometimes politicians don’t have their facts straight, but that won’t stop them from proclaiming that a lie is the truth. The most common form of this seems to be the denial of evolution and climate change, despite the overwhelming scientific evidence. When the majority of the population is poorly informed about scientific issues, its much easier for a politician to appeal to these voters by reaffirming their misconceptions than it is to actually educate them. Just ask Rick Santorum.
There’s a corallary to this rule, and that is that if you repeat the lie often enough then eventually the public will believe you. The right-wing media repeatedly refers to President Obama as “Socialist” or “Muslim”, despite neither being true, in the hopes of eventually convincing the public that they are true.

#2: The law of contradiction

Just because two positions contradict each other, doesn’t mean you can’t hold both of them simulatenously.
First order (a)logic: $$ P \land \neg P $$
Politicians seem to have a natural immunity to cognitive dissonance, allowing them to hold two contradictory positions without feeling any guilt or embarrassment. Republicans like to call themselves “pro-life” while simultaneously supporting the death penalty — something I never fully understood. How can one be pro-life and pro-death at the same time?
President Obama’s 2012 State of the Union had a few subtle contradictions worth noting. President Obama begins by praising the General Motors bailout and goes on to speak out against bailouts near the end. He also called out “the corrosive influence of money in politics”, while he himself was the largest beneficiary of Wall St donations during the 2008 campaign. When you consider that this President has built his position on the principles of compromise and cooperation, taking both sides of the issue seems to be his way of encouraging both parties to work together. Unfortunately, this strategy hasn’t really worked out that well in the past.

#3: The law of the included middle

You don’t need to choose between a position and its negation. You can always change your mind later.
First order (a)logic: $$ \neg (P \lor \neg P) $$
Politicians try to appeal to the widest possible base of voters. Since the voters don’t always agree with each other on a particular issue, you’ll often find politicians changing their stance depending on which voters they’re speaking to. This law is the “flip-flop” rule of politics. Mitt Romney is a popular example, having changed his stances on abortion, Reaganomics, and no-tax pledges. These changes make sense from a vote-maximization point of view. Romney’s earlier campaign in Massachusetts required him to appeal to a moderate voter base. In the GOP Primary, he now needs to contend with the far-right wing voters. If the votes he potentially gains by changing stance outnumber the votes he’d lose from the flip-flop, then he gains votes overall. Likewise, President Obama has also “flip-flopped” on some issues he campaigned on now that he’s actually in office — like single-payer healthcare versus individual mandates. Again, the President is dealing with a change in audience. “Candidate Obama” needed to appeal to the general population, while “President Obama” needs to appeal to members congress. He’s still trying to maximize votes, it’s just a different type of vote that counts now.

Parting Thoughts

This post started with a joke on Twitter about politicians’ inability to do basic math or logic. After giving it some thought, perhaps they’re better at math than I originally gave them credit for. They may not be able to answer simple arithmetic problems, but when it comes down to maximizing the number of votes they receive they are actually quite skilled. They may tell bold faced lies and flip-flop all over the place, but they do so in such a way that gets them elected and keeps them there. If we want politicians to tell the “truth” then we to start voting that way. We also need to start educating others about how to tell a “lie” from the “truth”, and I hope someone finds these “Three Axioms of Political Alogic” a valuable tool for doing so.