For Aristotle, our unique capacity to reason is what defines us as human beings. Therefore, our happiness, or our flourishing, consists in leading a life that enables us to use and develop our reason, and that is in accordance with reason.

Article 1 of the Universal Declaration of Human Rights (1948) states that all human beings are ‘endowed with reason’, and it has long been held that reason is something that God gave us, that we share with God, and that is the divine, immortal element in us.

At the dawn of the Age of Reason, Descartes doubted everything except his ability to reason. ‘Because reason’, he wrote, ‘is the only thing that makes us men, and distinguishes us from the beasts, I would prefer to believe that it exists, in its entirety, in each of us…’

But what is reason? Reason is more than mere associative thinking, more than the mere ability to move from one idea (such as storm clouds) to another (such as imminent rain). Associative thinking can result from processes other than reason, such as instinct, learning, or intuition. Reason, in contrast, involves providing reasons—ideally good reasons—for an association. It involves using a system of representation such as thought or language to derive or arrive at an association.

Reason is often amalgamated with logic, also known as formal logic or deductive reasoning. At the very least, logic is seen as the purest form of reason. Yes, logic is basically an attempt to codify the most reliable or fail-safe forms of reasoning. But logic, or at any rate modern logic, is concerned merely with the validity of arguments, with the right relationship between premises and conclusion. It is not concerned with the actual truth or falsity of the premises or the applicability of the conclusion. Reason, in contrast, is a much broader psychological activity which also involves assessing evidence, creating and testing hypotheses, weighing competing arguments, evaluating means and ends, developing and applying heuristics (mental shortcuts), and so on. All this requires the use of judgement, which is why reason, unlike logic, cannot be delegated to a computer, and also why it so often fails to persuade. Logic is but a tool of reason, and, in fact, it can be reasonable to accept something that is or appears to be illogical.

It is often thought, not least in educational establishments, that ‘logic’ is able to provide immediate certainty and the authority or credibility that goes with it. But logic is a lot more limited than many people imagine. Logic essentially consists in a set of operations for deriving a truth from other truths. In a sense, it merely makes explicit that which was previously implicit. It brings nothing new to the table. The conclusion merely flows from the premises as their inevitable consequence, for example:

1. All birds have feathers. (Premise 1)
2. Woodpeckers are birds. (Premise 2)
3. Therefore, woodpeckers have feathers. (Conclusion)

Another issue with logic is that it relies on premises that are founded, not on logic itself, but on inductive reasoning. How do we know that ‘all birds have feathers’? Well, we don’t know for sure. We merely suppose that they do because, so far, every bird that we have seen or heard about has had feathers. But the existence of birds without feathers, if only in the fossil record, is not beyond the bounds of possibility. Many avian species are hatched naked, and a featherless bird called Rhea recently took the Internet by storm.

Inductive reasoning only ever yields probabilistic ‘truths’, and yet it is the basis of everything that we know or think that we know about the world we live in. Our only justification for induction is that it has worked in the past, which is, of course, an inductive proof, tantamount to saying that induction works because induction works! To rescue it from this Problem of Induction, Karl Popper argued that science proceeds not inductively but deductively, by making bold claims and then seeking to falsify those claims. But if Popper is right, science could never tell us what is, but only ever what is not. Even if we did arrive at some truth, we could never know for sure that we had arrived. And while our current paradigms may represent some improvement on the ones that went before, it would be either ignorant or arrogant to presume that they amounted to the truth, the whole truth, and nothing but the truth.

Putting these inductive/deductive worries aside, reason is limited in reach, if not in theory then at least in practice. The movement of a simple pendulum is regular and easy to predict, but the movement of a double pendulum (a pendulum with another pendulum attached to its end) is, as can be seen on YouTube, extremely chaotic. Similarly, the interaction between two physical bodies such as the sun and the earth can be reduced to a simple formula, but the interaction between three physical bodies is much more complex—which is why the length of the lunar month is not a constant. But even this so-called Three-Body Problem is as nothing compared to the entanglement of human affairs. God, it is sometimes said, gave all the easy problems to the physicists.

The intricacies of human affairs often lead to a paralysis of reason, and we are left undecided, sometimes for years or even into the grave. To cut through all this complexity, we rely heavily on forces such as emotions and desires—which is why Aristotle’s Rhetoric on the art of arguing includes a detailed dissection of what used to be called the passions. Our emotions and desires define the aims or goals of our reasoning. They determine the parameters of any particular deliberation and carry to conscious attention only a small selection of all the available facts and alternatives. Brain injured people with a diminished capacity for emotion find it especially hard to make decisions, as do people with apathy, which is a symptom of severe depression and other mental disorders. Relying so heavily on the emotions comes at a cost, which is, of course, that emotions aren’t rational and can distort reasoning. Fear alone can open the gate to all manner of self-deception. On the other hand, that emotions aren’t rational need not make them irrational. Some emotions are appropriate or justified, while others are not. This is why, as well as coming to grips with science, it is so important to educate our emotions.

Another shortcoming of reason is that it sometimes leads to unreasonable conclusions, or even contradicts itself. In On Generation and Corruption, Aristotle says that, while the opinions of certain thinkers appear to follow logically in dialectical discussion, ‘to believe them seems next door to madness when one considers the facts’. In Plato’s Lesser Hippias, Socrates manages to argue that people who commit injustice voluntarily are better than those who do it involuntarily, but then confesses that he sometimes thinks the opposite, and sometimes goes back and forth:

My present state of mind is due to our previous argument, which inclines me to believe that in general those who do wrong involuntarily are worse than those who do wrong voluntarily, and therefore I hope that you will be good to me, and not refuse to heal me; for you will do me a much greater benefit if you cure my soul of ignorance, than you would if you were to cure my body of disease.

The sophists of Classical Greece taught rhetoric to wealthy young men with ambitions of holding public office. Prominent sophists included Protagoras, Gorgias, Prodicus, Hippias, Thrasymachus, Callicles, and Euthydemus, all of whom feature as characters in Plato’s dialogues. Protagoras charged extortionate fees for his services. He once took on a pupil, Euathlus, on the understanding that he would be paid once Euathlus had won his first court case. However, Euathlus never won a case, and eventually Protagoras sued him for non-payment. Protagoras argued that if he won the case he would be paid, and if Euathlus won the case, he still would be paid, because Euathlus would have won a case. Eualthus retorted that if he won the case he would not have to pay, and if Protagoras won the case, he still would not have to pay, because he still would not have won a case!

Whereas philosophers such as Plato use reason to arrive at the truth, sophists such as Protagoras abuse reason to move mobs and enrich themselves. But we are, after all, social animals, and reason evolved more as a means of solving practical problems and influencing people than as a ladder to abstract truths. What’s more, reason is not a solitary but a collective enterprise: premises are at least partially reliant on the achievements of others, and we ourselves make much better progress when prompted and challenged by our peers. The principal theme of Plato’s Protagoras is the teachability of virtue. At the end of the dialogue, Socrates remarks that he began by arguing that virtue cannot be taught, but ended by arguing that virtue is no other than knowledge, and therefore that it can be taught. In contrast, Protagoras began by arguing that virtue can be taught, but ended by arguing that some forms of virtue are not knowledge, and therefore that they cannot be taught! Had they not debated, both men would have stuck with their original, crude opinions and been no better off.

Why does reason say ridiculous things and contradict itself? Perhaps the biggest problem is with language. Words and sentences can be vague or ambiguous. If you remove a single grain from a heap of sand, it is still a heap of sand. But what happens if you keep on repeating the process? Is a single remaining grain still a heap? If not, at what point did the heap go from being a heap to a non-heap? When the wine critic Jancis Robinson asked on Twitter what qualifies someone to call themselves a sommelier, she received a least a dozen different responses. Another big problem is with the way we are. Our senses are crude and limited. More subtly, our minds come with built-in notions that may have served our species well but do not accurately or even approximately reflect reality. Zeno’s paradoxes, for example, flush out the limits of our understanding of something as rudimentary as movement. Some of Zeno’s paradoxes side with quantum theory in suggesting that space and time are discrete, while others side with the theory of relativity in suggesting that they are continuous. As far as I know (I am not a physicist), quantum theory and the theory of relativity remain unreconciled. Other concepts, such as infinity or what lies outside the universe, are simply beyond our ability to conceive. A final sticking point is with self-referential statements, such as “This statement is false.” If the statement is false, it is true; but if it is true, it is not false.

In concluding, I want to make it very clear that I hold reason in the highest regard. It is, after all, the foundation of our peace and freedom, which are under constant threat from the forces of unreason. In highlighting its limits, I seek not to disparage or undermine it but to understand and use it better, even to exalt it.

‘The last function of reason’, said Blaise Pascal, ‘is to recognize that there is an infinity of things which are beyond it. It is but feeble if it does not see so far as to know this.’