Recently, across Europe, children have been dying from measles. The World Health Organisation blames the resurgence of the disease on low MMR vaccination rates. Confidence in the vaccine fell after a 1998 article in The Lancet, later retracted, claimed a link to autism. Despite massive evidence against any link, populist parties in France and Italy oppose mandatory vaccination. In August, the Italian coalition government fulfilled election pledges to abolish a law making vaccinations compulsory. On a larger scale, political inaction over manmade global warming, facilitated by public scepticism about climate science, threatens the future habitability of the planet. What non-scientists believe about science is literally a matter of life and death.

Well-informed public debate over significant or contentious issues is clearly important in a liberal democracy. A necessary condition for such debate is the fair and accurate reporting of scientific results. Although this need is generally granted in principle, it is not always respected in practice.

One problem is that it is often unclear what constitutes a scientific “result”. Real science is inherently a much messier, more complicated, and less straightforward process than the traditional stereotype of discovery in a dramatic “Eureka!” moment. Evidence is accumulated gradually, and its significance is typically probable rather than certain. The biological and environmental processes that matter most for human life are themselves so messy and complicated that they cannot be traced and studied in full detail.

Often, the only feasible approach to understanding complex natural and social processes is by building theoretical “models”, sets of highly simplified assumptions in the form of mathematical equations, which can then be studied and tested against observed data. The models can be improved, sometimes to a very high degree of accuracy, but they will never do better than approximate reality “out there” in the world. Still, they give us our best shot at predicting the natural processes that will make or break our future. For instance, computer simulations based on such models generate predictions of climate change over coming decades for contrasting hypotheses about future carbon emissions. Such results should inform rational expectations and policy-making.

Accurate, effective reporting of science must be honest about the nature of the scientific arguments without losing the reader in technicalities. Achieving even an elementary understanding of the science requires distinguishing three dimensions: its subject (such as the past, present, and future climate), evidence about the subject (such as measurements of temperature), and theories about it (such as a hypothetical mechanism for global warming). To confuse any two of these three dimensions leads to alarming mental muddles, in which no theory lacks evidence, or nothing happens unobserved, or a change of theory is a change of climate.

In other words, public discussions of science had better avoid basic mistakes in the philosophy of science, on pain of distorting scientific discoveries and their practical impacts. Accuracy in reporting science includes accuracy on these philosophical matters. Alas, this fundamental requirement is often neglected, even by institutions that pride themselves on their fact-checking.

A case in point is a recent article in the the New York Times by the journalist Ava Kofman on Bruno Latour, a central figure in the sociology of science, famous for his richly detailed studies of what goes on in laboratories. Latour has often been depicted as a post-modern relativist and enemy of the idea that science investigates a reality “out there” in the world, an image of himself which he contests. More recently, Latour has been using his conception of science in an attempt to repel the attacks of climate change sceptics. Indeed, Kofman’s broadly sympathetic piece is entitled: “Bruno Latour, the Post-Truth Philosopher, Mounts a Defense of Science.”

The article contains some striking passages. Kofman assures us that what Latour’s critics “have always missed” is that he “never sought to deny the existence of gravity”. She then adds: “Gravity, he has argued time and again, was created and made visible by the labour and expertise of scientists.” In short, scientists created gravity.

Really? Did no apples fall before gravity was thought of? Or did scientists magically employ backwards causation to make gravity work before they created it? Of course, scientists created theories of gravity, but to confuse gravity with a theory of gravity is to commit one of the basic mistakes listed above. It is like confusing water with a theory of water. You can drink water; you cannot drink the theory.

It is no serious defence of the claim that scientists created gravity to grant it some sort of poetic licence. That would be like defending the claim that Nasa created the moon as poetic licence, since Nasa created a moon rocket. What journalist would confuse the moon with a moon rocket? Confusing gravity with a theory of gravity is no better, but it sounds less gross because the items confused are less palpable.

Such confusions cannot be dismissed as inconsequential, for politically what is often at stake is precisely the relation between a scientific theory and what it is a theory of, say, between a theory of the climate and the climate itself. Without distinguishing the two, one cannot make proper sense of questions about the theory’s correctness or incorrectness. And how much weight can one expect one’s interventions to carry in public debate after it is pointed out that one thinks that scientists created gravity?

The writer oscillates between the harmless point that scientists create knowledge of facts and the attention-seeking idea that scientists create the facts themselves. She speaks as if the two were interchangeable. They are not. To deny that we know that there is life in other galaxies is not at all to deny that there is life in other galaxies.

The point is worth labouring because failures to distinguish between what is and what we know are far from unusual and Kofman’s piece is by no means exceptional. Steve Fuller, professor of social epistemology at Warwick University, sympathetically expounds a post-truth view of science on which, concerning truth, “science differs from politics only in that the masks of its players rarely drop”, and it is merely elitist to exclude proponents of intelligent design against evolutionary theory from a scientific conference.

Alas, there is a temptation to let these failures go. “Who cares?” That is the post-truth attitude, simply shrugging one’s shoulders when a politician one likes is caught out in a lie. But accuracy matters in philosophy as in politics and science. Indeed, the three areas interact in complex ways. When things go wrong in one of them, there can be knock-on effects in the others. If climate change sceptics get to say that climate scientists created climate change, what stops them from further muddying the waters and saying that climate scientists can reverse climate change by reversing the science?

Of course, the distinctions I have been insisting on – between the roles of reality, evidence, and theory – are not totally uncontroversial in the sociology and philosophy of science.

One reason is that there are many genuine complexities in their application. First, scientists have access to the reality under study only through the lens of evidence and theory. Second, the observer may be part of the system being observed, as when humans study humanity. Third, what counts as data is sometimes unclear, as when scientific fraud or incompetence has been alleged. Fourth, it may be unclear whether a theory is well enough established to be used as evidence in assessing another theory. And so on. Although careful reflection shows that such subtleties do not really undermine the distinctions between reality, evidence, and theory, they are sometimes misinterpreted as if they did.

Cases like MMR vaccination and climate science show how much it matters for there to be the clearest possible public understanding of science, which includes carefully distinguishing between the different parts evidence, theory, and the reality in question play in scientific practice. Getting such broadly philosophical matters right is just as important as getting the numbers right for understanding what science is telling us.

Timothy Williamson is the Wykeham professor of logic at New College Oxford. His latest book is Doing Philosophy: From Common Curiosity to Logical Reasoning.