Intuition and Reason

In math and other fields of rational inquiry there are two degrees of understanding. The first is intuitive knowledge. Whether because we experience something directly or because we conceptualize it through example, intuitive facts just feel right. For example, it seems obvious that the angles opposite the equal sides of an isosceles triangle will be the same. At times, concepts are not immediately intuitive but can become so through analogy, such as the realization that the total resistance of two wires connected in parallel is less than the resistance of each wire individually because one can draw a comparison to the amount of water that can flow simultaneously through two pipes rather than one. The second mode of understanding is formal proof. We may intuitively know that all of the angles of an equilateral triangle are sixty degrees, but we also must prove it to be sure. Math and science abound with examples in which the common-sense answer is utterly wrong: heliocentrism, relativity, and quantum mechanics, just to name a few. Complete understanding of something generally requires both degrees of thought.

The same process of understanding applies to morality. Ethical questions should not be solely decided on the basis of pure intuition or on the basis of pure reason. (Indeed, it's hard to even imagine what it would look like for something to be decided purely on the basis of reason. At some point, one needs to establish why things matter, and it's hard to imagine how this could be done without emotion.)

The basis of morality must always be intuition: this grounds and gives meaning to any reasoning that one hopes to undertake. For example, one must intuitively establish that "suffering is bad" before the rational realization that "this action will reduce net suffering" has any moral significance. To use Toulmin's terminology of argument, one must establish a warrant before an audience will make the leap from one's grounds to one's claim. At the foundational level, such warrants can only arise from intuitive emotion.

In the same way, mathematics can only arise from certain core axioms that one takes for granted. Like basic intuitions in ethics, these fundamental postulates cannot be debated because doing so would require that both sides share some set of even deeper assumptions, which is not the case once one has gone down to the foundation of the theory. In the same way that two people can disagree about the core values of ethics, two people may take for granted different core axioms in math and arrive at two different theories (take, for example, Euclidean and non-Euclidean geometry).

Once basic assumptions have been established, however, it is best to let reason take its course, both in mathematics and ethics. While intuitive mathematical conclusions do often turn out to be correct by logical proof, there are some instances in which that is not the case; sometimes theorems that are clearly proved from basic axioms turn out to be counterintuitive. When it comes time to apply mathematics in practical situations, we trust knowledge derived from logic, not "what feels right."

I assert that we should do the same in ethics. Beyond the most basic, axiomatic expressions of value, pure intuition becomes fuzzy, capricious, and self-contradictory. It is here that reason must take hold and guide our emotional energies toward those decisions that genuinely are most in line with our fundamental intuitions.

Thus, in spite of my early aversion to Intuitional Ethics [...], I was forced to recognise the need of a fundamental ethical intuition.

The utilitarian method [...] could not, it seemed to me, be made coherent and harmonious without this fundamental intuition. [...]

And I had myself become, as I had to admit to myself, an Intuitionist to a certain extent. For the supreme rule of aiming at the general happiness, as I had come to see, must rest on a fundamental moral intuition, if I was to recognise it as binding at all. And in reading the writings of the earlier English Intuitionists, More and Clarke, I found the axiom I required for my Utilitarianism [That a rational agent is bound to aim at Universal Happiness], in one form or another, holding a prominent place [...].

--Henry Sidgwick, Methods of Ethics, ``Preface to the Sixth Edition" (1901)