“The true function of logic…as applied to matters of experience…is analytic rather than constructive; taken a priori, it shows the possibility of hitherto unsuspected alternatives more often than the impossibility of alternatives which seemed prima facie possible. Thus, while it liberates imagination as to what the world may be, it refuses to legislate as to what the world is.”

— Bertrand Russell

 I love logic. One of the few free electives I took in college was symbolic logic, which became one of my favorite courses. What I learned is that logic is a fun way to do math and prove or disprove textual statements. But most people misunderstand what logic is and how it is used, and, more importantly, what it cannot do. As Russell (who knew more about logic than anyone) says, “…it refuses to legislate as to what the world is”. In other words, logic ain’t science.

It’s true that logic was at one time the language of what passed for science, but that time has long gone. Contrary to the ideas of Aristotle and the wisdom of the ancient Greeks, truth cannot be grasped by the application of logic. In fact it is only in very limited circumstances, mostly related to mathematical proofs of theorems, that logic is a useful path to truth.

One of the premier principles of logic is that what it is designed to determine is not truth, but validity. Any system of logic is based on the discovery of theorems that are derived from basic premises. Some of the premises are self-evident, or assumed to be true based on universal experience. Proofs are only as valid as the truth of their premises. Once we leave the rarefied territory of pure math and symbolic logic, premise truth becomes a serious issue of concern.

Even when we have 2 or more true premises, the ability to draw a true conclusion from them requires the strict following of a set of rules. In formal logic it isn’t enough to list the premises and the conclusion; you must also specify by which rule the conclusion follows the premises. For example

1. If a man is tall, he can reach the top shelf.
2. I cannot reach the top shelf.

Therefore I am not tall, by Modus Tollens (If A, then B. Not B. Therefore Not A).

That is a logically true statement. The second premise might be false (maybe I am lying about not being able to reach the top shelf), but the proof is still valid, even if not guaranteed to be true.

However, if I used the same two premises and then concluded that no woman can reach the top shelf, the argument would be fallacious, because such a conclusion is not based on either of the premises, and there is no rule (there are 19 altogether) that allows such a conclusion from those premises.

What logic can do is determine the likely truth of a theorem assuming that the underlying premises are known to be true. But logical systems cannot, and are not meant to, deal with the underlying truth of a proposition.

The major contribution of the thought of Francis Bacon, and of all the inductive reasoning from Galileo on, was that the truth of basic propositions can be determined not by logic but by experiment and observation. This was the beginning of a new philosophical way of seeing the world, and it would be eventually called science.

We now know that there are scientific laws and truths about the universe that defy logic, Natural law can only be discovered by observation of, and experimentation with, the natural world as it is.

Is it logical that it is impossible to know the position and the momentum of a photon at the same time? No, but it’s true. Is it logical that that the universe started out as a singularity which was also the beginning of time? No, but that’s true too. How about the fundamental logic of the fact that a wave function for the probable state of a particle collapses to a particular value only when observed? True, but not at all logical as we generally use the term.

Biology is worse. A great deal of biological reality cannot be reduced to logic, even though we know a great deal of the truth about how cells function. It isn’t terribly logical to have so much unused DNA in cells that must get copied over and over again. (And no, the idea that all of the DNA is used is wrong. It was an awkward error by the ENCODE group.) It isn’t logical that genes are broken up by exons or contain so many transposons, or that humans lost so many genes for smell.

But there is a good side to the illogic of biology and physics and all other sciences. It means we are always being surprised by what we find out – it’s usually not at all what we expected. We have the powerful method of science to discover truth about our natural world, and it’s up to us to make sense of our findings, whether they are logical or not.