The white swan and red pen

Note that this post is focussed largely on science and how it works.

If you think that it is possible to accumulate evidence for a theory then a red pen is evidence in favour of the claim “all swans are white”. How is this so? And, Brett, aren’t you one of those people who keeps on saying you cannot have evidence for a theory anyway? Yes, I am. But let’s understand the reasons against this claim at a deeper level than some realise.

It’s not enough to know falsification works - that the existence of one black swan refutes “All swans are white”. You have to also know why the alternative perspective - almost universally subscribed outside of what is called “critical rationalism” is false. It needs to somehow become a deep part of your thinking that *positive evidence* just is not a thing and never can be. Which is to say you cannot have evidence for a theory; evidence that supports a theory or makes it more likely to be true and so on. That is not only unnecessary but it is absurd and let us see why momentarily. Let us first recap why it’s unnecessary. 

Once you have an explanation of the evidence, it no longer cries out for “support me” because there are no alternative theories. There’s just the one - the explanation. But, ok, imagine you’re in the rare position of having two good explanation. Well then if you find yourself in that rare position of having two or more good explanations then the function of evidence is to decide between those theories already guessed. When evidence does this it also serves the simultaneous purpose of serving as the so called “explicandum”: the thing to be explained. The explanation is there to explain the evidence. The evidence is there to decide between explanations. Ok, so all of that means “evidence in support” of a theory is unnecessary. But why is it also absurd?

Now we shall take a little lesson in logic. Consider if you like the claim “All swans are white” - so often held up as the pedestrian example of either “how falsification works” (find the unexpected - a black swan in other words, or maybe a translucent one these days) or as a way of teasing out exactly what Bayesian “epistemology” is trying to get at. How many swans need to be observed before we can say it’s “probably the case all swans are white”? Or likely? What is the threshold? And once you do employ Bayes’ theorem (that almost never happens, by the way: what is called “Bayesianism” never much involves Bayes’ theorem being actually deployed) - say you “update your initial prior probability in light of more white swans to 85% confidence that “All swans are white”) well then you can conclude, with something less than certainty, that “All swans are white”. Of course how certain you are that the 85% is 100% correct no one can say. 

But let us put aside all of those concerns about how many white swans need to be observed before concluding “all swans are white” - put aside that no finite list of observations (like seeing one millions swans) can never logically be equivalent to a universal claim about “All” anythings -  and let us even put aside science is not about making claims like “all swans are white” in the first place (it’s about explaining the world). 

All that aside. The idea that one can have “evidence in support” of a theory or claim like “All swans are white” by finding ever more white swans is logically equivalent to my looking on my desk any seeing any random thing there - like a red pen as also evidence in support of “All swans are white”.

If that seems absurd to you, it is. But this is one of the counter intuitive things about logic and one of the absurd consequences of the “evidence can support a theory” account of how science functions. It is a problem for that idea - but not a problem for falsification or explanation. What on Earth am I talking about?

The red pen on my desk is…a non white non swan.

“All swans are white” is logically equivalent to: “all non-white things are not-swans”. (In formal logic this is known as the “contrapositive”).

So given this rock solid logical fact of reality, anything at all in the universe you can point to that is not a swan and isn’t white is evidence in favour of “all swans are white” if you think there is such a thing as evidence in favour or support of any claim at all. So on the inductivist or Bayesian account of things every time you observe non white non swans (basically everything in the universe) your confidence in your theory about the truth of “All swans are white” should increase precisely because it amounts to being evidence in support of your theory.

Do you see how absurd the inductive account of science is? Of Bayesianism? Of non-explanatory, falsifiable conjectural scientific knowledge?

Science does not consist of claims like “All swans are white”. It consists of explanations. Evidence cannot be used to support a theory. It serves only to decide between explanations already guessed.

No amount of gathering more evidence about the world allows us to extrapolate general truths about it. What we have are problems - that’s where we begin. Our ideas at times fail to account for what is out there in the world. In science to resolve this clash of ideas between what we think and what we observe we have to use our imaginations to conjecture - guess - into existence a new and better explanation. Once we’ve done that, once we can explain the “problematic observation” we have a solution. And once we have that, there’s no need to further support it because, it’s all we’ve got. It’s the solution. It’s the good explanation. 

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Credit to my lecturer at The University of New South Wales, Professor Michaelis Michael who, aside from being the only professor of logic I know to have a name which is itself a tautology (Michael is Michael) - was the lecturer I most admired. His lectures were always fun. He meandered through the luminaries of philosophy and his encounters with some of them and peculiar stories of their lives and his as well as diving very deep in the classes I took with him on formal logic. It was Michaelis who set us the challenge of proving the soundness and completeness of sentential logic for one assignment. Sometimes assignments can be fun - and that one I remember was. And it's him I credit for leaving our class one afternoon at the end of the lecture with the problem as to why, as he held his red white board marker up, it was “evidence in favour of the claim that all swans are white”. It was on the bus ride home I realised I had the answer. Of course next lecture so did many others. It was class of logic students after all.