(For other posts in this series, see here.)

The idea of scientific infallibility, that the knowledge generated by science should be true and unchanging, suffered a series of blows in the late 19th and early 20th centuries that saw the repeated overthrow of seemingly well-established scientific theories with new ones. Even the venerable Newtonian mechanics, long thought to be unchallengeable, was a casualty of this progress. Aristotle’s idea that scientific truths were infallible, universal, and timeless, fell by the wayside, to be replaced with the idea that they were provisional truths, the best we had at the current time, and assumed to be true only until something better came along.

But despite that reduction in status, it is important to realize that for the practicing scientist, the question of ‘truth’ remains paramount. But what the word ‘true’ means depends on the context.

One form that this commitment to truth takes is that it requires scientists to be truthful when reporting the results of their work, because others depend upon it. The whole structure of scientific knowledge is created cumulatively, each person building on the work of others, and this requires trust in the work of other people because it is not always feasible to independently verify every claim of other scientists. Because scientific knowledge is so interdependent, falsehoods in one area can do serious damage to that structure.

This does not mean that scientists are more truthful as persons. But it does mean that being dishonest is not a good career strategy because you will likely be found out, especially if your work has important consequences. Scientists are not usually suspicious of the work of other scientists and do not reflexively check their work. But the interdependence of knowledge means that a falsehood or error in one area will eventually be detected because people will try to use that knowledge in new areas and will encounter inexplicable results. When the sources of the error are investigated, it will eventually be traced back to the original perpetrator. This is almost always how scientific errors and frauds are discovered.

As a minor example, in my own research experience I once uncovered an error published by others years before because I could not agreement with data when I used their results. Similarly a published error of my own was discovered by others after a lapse of time, for the same reason. It is because of this kind interdependence that science is largely, but not invariably, self-correcting. This is also why in academia, where the search for true knowledge is the prime mission, people who knowingly publish or otherwise propagate falsehoods or commit many errors, suffer serious harm to their reputations and are either marginalized or drummed out of the profession. Some recent spectacular cases of deliberate fraud are those of Jan Hendrik Schon and Woo Suk Hwang . So in the search for knowledge, accurately reporting honestly obtained data and making true statements about one’s work is a prime requirement.

But there is another, more philosophically elusive, search for truth that is also important, and that is determining the truth of scientific theories. It matters greatly whether the theory of special relativity is true or not or whether some chemical is a carcinogen or not. To get those things wrong can have serious consequences extending far beyond any individual scientist. But it is important to realize that in such cases, truth is always a provisional inference made on the basis of evidence, similar to the verdict arrived at in a legal case. And just as a legal judgment can be overturned on the basis of new evidence, so can such scientific truths be overturned, thus eliminating the idea of infallibility.

So how does one arrive at provisional truths in science? In establishing the truth of a scientific proposition, scientists use reasoning and logical arguments that are closely similar to, but not identical with, mathematical and legal reasoning. Being aware of the similarities and distinctions is important to avoid claiming scientific justification for claims that are not valid, as often happens when religious people try to co-opt science in support of their beliefs in god and the afterlife.

The first issue that I would like to discuss is the relationship between truth and proof, because in everyday language truth and proof are considered to be almost synonymous. The idea of ‘proof’ plays an important role in establishing truth because most of us associate the word proof as being conclusive, and it is always more authoritative if we are able to say that we have proven something to be true or false.

The gold standard of proof comes from mathematics and much of our intuitive notions of proof come from that field so it is worthwhile to see how proof works there, what its limitations are when applied even within mathematics, and what further limitations arise when we attempt to transfer those ideas into science.

Next: Truth and proof in mathematics