Appearing in the UK four years after its original US publication, Proust Was a Neuroscientist is an assured debut by Jonah Lehrer, best known here for The Decisive Moment, a popular, Gladwellesque exploration of how we make up our minds. Lehrer fancies himself – and not without reason – as a sort of one-man third culture, healing the rift between sciences and humanities by communicating and contrasting their values in a way that renders them comprehensible to partisans of either camp.

In this book, Lehrer asks why, when it comes to understanding the mind, neuroscience has been pipped to the post, not once, but time and time again, by writers, artists, composers and cooks, especially those working in the early part of the 20th century.

In the most powerful, well-argued and carefully condensed of his biographical essays, Lehrer says of the paintings of Paul Cézanne: "Instead of giving us a scene of fully realised forms, Cézanne supplies us with layers of suggestive edges, out of which forms slowly unfurl. Our vision is made of lines, and Cézanne has made the lines distressingly visible." In other words, Cézanne got the eye right, long before Hubel and Wiesel transformed our understanding of the visual cortex in 1959. Around the time Cézanne was making migranous perceptual puzzles out of the Bibémus quarries, Gertrude Stein was working in William James's Harvard psychology lab. Her own neuroscientific safari, attempting to abstract grammar from sense, hit a much-lampooned stylistic brick wall – but her failure was far ahead of its time, straightening paths for Noam Chomsky's hunt (again, in the 50s) for a human's innate, hard-wired "universal grammar".

One of the great pleasures of this book is to read intensely felt, cogently argued apologias for people whose towering achievements you might not otherwise be able to stomach. (This card-carrying anti-modernist was persuaded – positively charmed – by Lehrer's chapter on Virginia Woolf.)

The trouble is, in writing a series of accessible, linked essays, Lehrer deprives himself of the chance to explain why modernism ran so far ahead of contemporary science in its exploration of the working mind.

At the end of the 19th century, surrealism, occultism and psychoanalysis were all born out of a growing awareness that science, narrowly conceived, had no way of studying the mind. After all, the sciences can only study what they have the means to study, and in the first half of the 20th century, the only analytical tool capable of exploring subjectivity was "guided introspection" – a rather overworked form of meditation in which subjects tried to describe what their thinking felt like.

Artistic experimentation, informed by the science of the day, turned out to be a much more robust analytic technique, and over time perceptual-cognitive experiments of the Cézanne/Stein/Stravinsky sort have found their way into the laboratory. They have become precise, repeatable, scientifically respectable – and fodder for a shelf full of pop-science books a lot less interesting than this one. This lends Lehrer's energetic and passionate prose a stridency he may not have meant. He seems, with his first book, to have burst, gun in hand, through a door that is already open.

He writes several too many "So-and-so was Right and Science was Wrong" passages. To say that Auguste Escoffier was "right" about the fundamental taste umami is like saying Democritus (460-370BC) was right about atoms which (let's be clear) he jolly well wasn't. Indeed, nobody discovers anything for ever, and nobody discovers anything first. The truth is always too complicated, the world always too big, for claims of that sort.

But it is impossible to stay grumpy with a writer who calls the three tiny bones that enable us to hear "a skeleton locked inside the ear", while dropping cheerful quips about Proust's "weak spot for subclauses and patisserie". Anyway, Lehrer's central point holds. Science had, has, and always will have a problem with subjective experience.

Scientific accounts of the world offer us a user's manual – a description of how we interact with the world. They say nothing whatsoever about the way the world really works – what vision scientist Donald Hoffman in 1998 dubbed "the relational realm": "We might hope that the theories of science will converge to a true theory of the relational realm. This is the hope of scientific realism. But it's a hope as yet unrealised, and a hope that cannot be proved true."

Carried away by his own enthusiasm, Lehrer sometimes writes as if he thought scientists were unaware of their bind. Elsewhere he summarises the problem in words so right, they sing: "It is ironic but true, the one reality science cannot reduce is the only reality we will ever know."

Not everything that is true can be proved. Lehrer's quotation from Escoffier is well chosen: "No theory, no formula, and no recipe can take the place of experience."

Simon Ings's The Weight of Numbers is published by Atlantic.