In logic it is a mistake to assume that because one condition implies another (P → Q), that the truth (or falsity) of the second implies the truth (or falsity) of the first (Q → P). This is a formal fallacy called affirming the consequent or denying the antecedent. In order to express this symmetrical relation, we need to supply additional information. This is a discipline, and the tendency on the part of those who do not exercise it is one that I have begun to call biconditionalism.

In biology, however, the opposite appears to be true. Biological systems are biased toward symmetry and need extra information to break from it. For evidence of this phenomenon, consider the birth defects that occur in the extremities. Deformation of the hands, when it happens in certain places, tends toward either a lobster-like claw or an even number of fanned-out fingers, but nothing like the familiar and decidedly asymmetrical four fingers and a thumb.

To examine how this happens, we can think about an individual cell as running the same program over and over, to grow and divide, until it gets a message to do something different, like change into something else or retire itself. It's this process that gives shape to living things. But if a cell misses a message for whatever reason, it continues along in the wrong direction, just like missing an exit on a highway.

It's strange, though. Why does symmetry in logic work the opposite way from symmetry in us, the ones who invented it?

I wonder often if it's just a side effect of biological—and ultimately physical—parsimony. In other words, what if it's just so much more convenient to encode the symmetrical form in our brains and deviate selectively from it than the other way around—just like the process of the development of our bodies?

This question is itself an example of the utility of such a structure. We like logical biconditionals because they provide us with enormously powerful heuristics for reasoning, imagery and communication. You might know them by a more familiar name such as analogy or metaphor.

The problem with analogies and metaphors, however, is that they aren't especially accurate. There are always edge cases. Where there's smoke, there's fire is a convenient rule to remember, but it won't apply to flames (like gas or chemical) that don't produce smoke. Nevertheless these constructs usually enable us to make quick and usually satisfactory, and therefore evolutionarily expedient, assessments of our environments.

When the rigour matters is when we really need to know what happened, like in science and forensics, and when we need to assert what ought to happen, like with public policy and technology. Screw up the logic in the wrong place and start a war, send the wrong person to prison or topple a skyscraper (assuming it could even be built in the first place). And that never happens, right?

I've been thinking about this idea because I've been considering our relationship, as humans and as mammals, with logic and with reason. The Enlightenment-age delusion of rationality as an ideal form seems finally to be wearing off. The verdict is that we're irrational, emotional creatures—and predictably so. Recent research suggests that even reasoning itself evolved as a rhetorical tool rather than a forensic one. If this is true, it would appear that logic is a mere side effect.

To this I'd like to add another animalistic intuition: logic works, or rather it demarcates the difference between works and doesn't work. If you create a system which is logically consistent, the only way it can behave unexpectedly is by interference from the outside. If you pick a durable enough medium, it is possible to preserve the reliable behaviour of the system indefinitely. In other words, solve a problem once and you'll have a solution that lasts forever, or at least as long as the problem does. Half-solve it and it'll be as if you never put any effort into solving it at all.

Perhaps when we contort ourselves into the straitjacket of logic, which is an extremely unnatural and costly process, we do it so we can take things with us when we crawl out. We exit logic's crystal palace and return to the mud puddle of primate intelligence carrying a gem that we can use over and over. Day to day, we don't have to worry about how it works, we just have to know that it works. It's only when we forget how to make more like it that we get into trouble.