Martin Seligman is the inventor of positive psychology and a major figure in the wellbeing movement. This makes him a significant figure in world culture and also makes him a target for attack. I think he is right. A happier society requires us to attend much more to the quality of our inner life, and to proven methods for improving it.

That is what positive psychology is about – it goes beyond the treatment of depression and anxiety to ways in which we could all live more rewarding lives. The exercises it offers include the systematic practice of kindness, gratitude to others, counting your blessings, and exploiting your strengths rather than attacking your weaknesses. It also teaches resilience and optimism. These two characteristics are apparently better predictors of a person's educational achievement than their IQ. And they can reduce your annual chance of dying by 20%.

So this is important. It is now being taught in 60 English schools. (I have to admit having a hand in this.) And it is being taught to every US soldier – a pretty extraordinary development. In Smile or Die, Barbara Ehrenreich has attacked positive psychology as the psychology of Pollyanna. But it is not. It is about how you can construct your own reality by developing the positive side of your nature.

The book is full of fascinating detail of how this extraordinary venture is developing, including a good deal of autobiography which can be skipped if you don't like that stuff. But there are two important areas where I disagree with Seligman. First, flourishing versus happiness. In his great book, Authentic Happiness, Seligman focused on just that, and I agreed with his argument. He now prefers a different objective: flourishing, which consists of "Perma" (positive emotion, engagement, relationships, meaning and accomplishment). But how do we add these five together? If I ask you: "Is your child happy at school?", you know the answer exactly. "But is your child flourishing?" Well, it depends.

Seligman is against the "monism" of focusing on happiness alone. In this respect, he is what Isaiah Berlin called a fox rather than a hedgehog. He is especially keen to bring into his ultimate goals some objective elements like accomplishment, on the basis that people's feelings of joy and contentment, rather than despair and torment, do not provide a sufficiently complete objective for the good society.

But surely Abraham Lincoln was great because he did a lot for human happiness – not, as Seligman says, because he accomplished highly, as though accomplishment were sufficient without some external criterion for deciding what accomplishment is valuable. Rational public policy requires a single criterion for comparing the benefits of different types of expenditure – and for comparing the costs of different cuts. So Seligman will have to come up with a system of weights for combining his different objectives, and where will they come from? I dare guess that, in the end, the weights he chooses will in fact depend on how far positive emotion, engagement, relationships, meaning and accomplishment each affect human happiness.

Which brings me to my second issue: the happiness of the individual versus the happiness of the group. Positive psychology can come over as very individualistic – a strategy for each individual to find his own way to wellbeing, full stop. But of course our wellbeing depends hugely on how others behave towards us. So, we will never achieve a better life for all of us unless we each take more trouble about the wellbeing of others.

This is not mentioned in Seligman's final chapter on the politics of wellbeing. He does, of course, mention that we are deeply social animals with an innate capacity for empathy. This enables us to have rewarding relationships with others. However, in his book we should cultivate empathy because it is good for us, not because of what it does for others. But this source of wellbeing requires special prominence precisely because it benefits the rest of the group as well as the individual. For Seligman, it is just one of the five elements of Perma. This needs some rethinking.

For me, that means going back to the great ideal of the 18th-century Enlightenment, from which this whole tradition of thought springs. We want a society in which there is the most possible happiness and especially the least possible misery. Where Seligman wants to have 51% of the world's population flourishing by 2051, I would add less than 5% in misery.

But Seligman is dead right when he says that, wherever we want to go, people's values will be the main force that determines the outcome. That is why the new Action for Happiness movement is asking its members to pledge to try to produce the most happiness in the world around them, and the least misery. We hope Seligman will join.

Richard Layard is director of the Wellbeing Programme at LSE's Centre for Economic Performance and the author of Happiness: Lessons from a New Science.