The grip of neuroscience on the academic and popular imagination is extraordinary. In recent decades, brain scientists have burst out of the laboratory into the public forum. They are everywhere, analysing and explaining every aspect of our humanity, mobilising their expertise to instruct economists, criminologists, educationists, theologians, literary critics, social scientists and even politicians, and in some cases predicting a neuro-savvy utopia in which mankind, blessed with complete self-understanding, will be able to create a truly rational and harmonious future.

So the smile-worthy prediction, reported in the Huffington Post, by Kathleen Taylor, Oxford scientist and author of The Brain Supremacy, that Muslim fundamentalism "may be categorised as mental illness and cured by science" as a result of advances in neuroscience is not especially eccentric. It does, however, make you wonder why the pronouncements of neuroscientists command such a quantity of air-time and even credence.

It would be a mistake to assume their authority is based on revelatory discoveries, comparable to those made in leading-edge physics, which have translated so spectacularly into the evolving gadgetry of daily life. There is no shortage of data pouring out of neuroscience departments. Research papers on the brain run into millions. The key to their influence, however, is the exciting technologies the studies employ, notably various scans used to reveal the activity of the waking, living brain.

The jewel in the neuroscientific crown is functional magnetic resonance imaging (fMRI), justly described by Matt Crawford as "a fast-acting solvent of the critical faculties". It seems that pretty well any assertion placed next to an fMRI scan will attract credulous attention. Behind this is something that goes deeper than uncritical technophilia. It is the belief that you are your brain, and brain activity is identical with your consciousness, so that peering into the intracranial darkness is the best way of advancing our knowledge of humankind.

Alas, this is based on a simple error. As someone who worked for many years, as a clinician and scientist, with people who had had strokes or suffered from epilepsy, I was acutely aware of the extent to which living an ordinary life was dependent on having a brain in some kind of working order. It did not follow from this that everyday living is being a brain in some kind of working order. The brain is a necessary condition for ordinary consciousness, but not a sufficient condition.

You don't have to be a Cartesian dualist to accept that we are more than our brains. It's enough to acknowledge that our consciousness is not tucked away in a particular space, but is irreducibly relational. What is more, our moment-to-moment consciousness – unlike nerve impulses – is steeped in a personal and historical past and a personal and collective future, in cultures that extend beyond our individual selves. We belong to a community of minds, developed over hundreds of thousands of years, to which our brains give us access but which is not confined to the stand-alone brain. Studies that locate irreducibly social phenomena – such as "love", the aesthetic sense, "wisdom" or "Muslim fundamentalism" – in the function or dysfunction of bits of our brains are conceptually misconceived.

The greatest excitement, orchestrated by the most extravagant press releases, surrounds the discovery of correlations between the responsiveness of certain areas of the brain and particular aspects of our personality. This neo-phrenology is actually based on shakier grounds than is usually appreciated. Few people realise how indirect is the relationship between what the scan detects and what is happening in the brain. There are many steps in the processing of the data that generates the beautiful coloured pictures that command such credence.

The much-touted idea that neuroimaging will soon be able to see "thoughts" – so that brain scans will be mind scans – fails to reflect the fact that even simple thoughts (such as "I live in Stockport") belong to a nexus of significance called a world and have a multitude of meanings and implications. Taylor's neuroscience of fundamentalism is absurd in principle because "fundamentalism" is an ill-defined cluster of propensities that will be realised differently in different people and will anyway be subject to normative judgments by others. It will not boil down to something a scan could pick up, such as overactivity in the brain's Qur'an interpretation centre.

Encouragingly, some scientists have started to sound the alarm, beginning in 2009 with Ed Vul and his co-authors' savage attack in a paper initially called "Voodoo Correlations in Social Neuroscience". They found serious problems with the localisations observed in such studies. The links between brain regions and feelings such as social rejection, neuroticism and jealousy used methods that artificially inflated the strength of the connection. Katherine Button's more recent review of the field in the prestigious Nature Reviews Neuroscience is even more devastating. She concludes that the statistical power of most studies is very low. On top of this, there is publication bias towards picking out positive correlations, with little incentive for checking for repeatability after the excitement has died down.

The will to believe that brain scans reveal our deepest secrets and will give us the tools to manipulate our fellow humans for our collective benefit probably has quite deep origins. The idea that we are our brains, and that we are destined to act in certain ways prescribed by this biologically evolved organ, relieves us of some of the responsibility for our behaviour. There is also the erroneous idea that if, as many of us wish, we are to reject a supernatural account of the world, along with the idea of the self as an eternal soul planted in the material body, answerable to god, then we are obliged to embrace a naturalistic account of ourselves as organisms, and the self as identical with the key part of that organism, namely our brain.

This mistake was anticipated by the Oxford philosopher Gilbert Ryle in The Concept of Mind: Man need not be degraded to a machine by being denied to be a ghost in a machine. He might, after all, be a sort of animal, namely a higher mammal. There has yet to be ventured the hazardous leap to the hypothesis that perhaps he is man.

Neuroprattle that locates our experiences, propensities and character in the activity of parts of our brain stops us taking this hazardous leap and gets in the way of the humanist project of truly understanding ourselves.

Next time you see a prettily coloured brain scan next to an article burbling on about breakthroughs in understanding our humanity, reach for the salt.

• This article was amended on 2 June 2013, the sentence "We belong to a community of minds, developed over hundreds of thousands of years, to which our brains give us access but which is not confined to the stand-alone brain" initially said it was confined to the stand-alone brain.