Does science really explain everything?

It has often been suggested that the scientific method is the best way of explaining things – that "the scientific method represents the most effective use of our reasoning powers yet developed and thus is the most adequate method for obtaining truth" (A. Cornelius Benjamin, "Science and Its Presuppositions," Scientific Monthly, Sept 1951, 150–153).

As a scientific professional (an applied mathematician), this seems to me clearly nonsensical – there are at least three widely accepted kinds of truth not derived from the scientific method:

Mathematical truths

Mathematical truths, for example, are proved using mathematical techniques, not experimental ones:


These mathematical truths are assumed before science even begins – in interpreting these stroboscopic observations of a bouncing ball, for example, we assume certain mathematically-proved properties of parabolas:

Metaphysical truths

From Plato onwards, metaphysical truths have been proved using philosophical arguments. Many metaphysical truths are also assumed by science – that's what philosophy of science is about.

Ethical truths

A fundamental principle of ethics is that "is" does not imply "ought" – more formally, modal operators of obligation have no introduction rule. Consequently, systems of ethics need at least one axiom (such as Kant's categorical imperative) as a starting point for ethical arguments.

Again, we are outside of the scientific method, and again, science must use these truths – in particular, in discussions of whether scientific discoveries should or should not be used. Such debates may use scientific facts (and mathematical ones), but they must also use ethical principles and ethical arguments.