Wisdom is the ideal that animates Russell's thought more than any other: perhaps this is only to be expected – Russell was, after all, a philosopher, and "philosophy" is derived from Greek words meaning "love of wisdom". But wisdom has an inescapably practical, ethical aspect that is missing from much philosophical work. Knowledge can be specialised or abstract, instrumental or purely for its own sake; what matters is that it is correct. Genuine wisdom, on the other hand, is not just a matter of correctness: it must be in some way life-enhancing. When we are presented with so-called wisdom that lacks this quality, we recognise it as hollow, vacuous, inauthentic.

Russell reflects on wisdom in his essay The Expanding Mental Universe, which first appeared in the Saturday Evening Post, an American weekly, in 1959. The essay is quintessential Russell: imaginative and stirring, but also wittily commonsensical. Russell begins by posing the question of "the effects of modern knowledge upon our mental life", and by emphasising that "mental life" encompasses willing and feeling as well as intellectual thought.

Inspired by the scientific theory of the expanding universe, Russell envisages an expansion of mental life. In modern times we have become used to dizzying statistics about the weight of the sun, the size of our galaxy, the number of other galaxies, the distance of the stars from earth, and – given the millions of years that light from some of these takes to reach us – the length of time for which there has been something rather than nothing. But, Russell cautions, "there is no reason to worship mere size". It may be true to say that scientific knowledge expands as we understand more about the size and complexity of the universe. However, when Russell talks about "the growth of man" he means the development of wisdom, which is "a harmony of knowledge, will and feeling".

"Will and feeling should keep pace with thought if man is to grow as his knowledge grows," writes Russell. "If this cannot be achieved – if, while knowledge becomes cosmic, will and feeling remain parochial – there will be a lack of harmony producing a kind of madness, with disastrous effects."

Considering the growth of what he calls "will", Russell reflects on how technology has increased our capacity for both creation and destruction. Of course, human beings have always exhibited a range (and usually a mixture) of good and bad tendencies. In the past, remarks Russell, "man has survived by virtue of ignorance and inefficiency" – but now our technical knowledge enables us to go more drastically wrong than hitherto.

This means that we should prioritise moral improvement alongside intellectual and scientific advances: "If, with our increased cleverness, we continue to pursue aims no more lofty than those pursued by tyrants in the past, we shall doom ourselves to destruction and shall vanish as the dinosaurs vanished … I foresee rival projectiles landing simultaneously on the moon, each equipped with H-bombs and each successfully exterminating the other. But until we have set our own house in order, I think that we had better leave the moon in peace. As yet, our follies have only been terrestrial; it would seem a doubtful victory to make them cosmic."

In past centuries, economic prosperity may have been won by imperialistic aggression. But in a technologically developed world, argues Russell, the Earth becomes like a single organism whose parts need to co-operate if the whole is to survive and flourish. "Religion has long taught that it is our duty to love our neighbour and to desire the happiness of others," he writes, "but in the new world, this kindly feeling towards others will be not only a moral duty but an indispensable condition of survival."

Indeed, the "unification and expansion of self-interest" that Russell envisages here is naturalistic and pragmatic rather than moral: "When you eat, the nourishment profits every part of your body, but you do not think how kind and unselfish your mouth is to take all this trouble for something else … This enlargement in the sphere of feeling is being rendered necessary by the new interdependence of different parts of the world."

Perhaps Russell's vision of global co-operation looks, to us, more like fantasy than prophesy. Reading his essay on The Expanding Mental Universe today, one is struck by how much has changed since the era of the cold war and the space race.

Russell might have been surprised by the new forms of violence that technology has brought us: drones and chemical warfare, fracking and internet pornography. But I think he would be even more shocked to find his appeal to wisdom and human "growth" being met with apathy and cynicism. Fifty years ago, a philosopher's reflections on these ideals were taken seriously not only by a small group of professional academics, but by the wider public. Would this happen if Russell was writing in 2014? And would Russell still be able to express his faith in ethical progress?

It is true that Russell's wonderful prose sometimes disguises patchy, vague, or shallow thinking. But when we consider whether his writing remains relevant today, we should be thinking as critically about the state of our society – and in particular its stunted spirituality – as about the quality of his philosophy. If Russell's words of genuine wisdom fall on the stony ground of our hardened hearts, that means we have work to do before new growth is possible.