Monday, February 10, 2014

Counterfactuals: Introduction

Counterfactual reasoning is essential to science. It could also be called hypothetical reasoning. It is at the root of many scientific confusions.

Hypothetical reasoning means formulating some hypothesis, and deducing the consequences. For example, a hypothesis might be that CO2 concentrations in the atmosphere might double in the next century. A deduction might be some global warming. The scientific method could be summarized as formulating a hypothesis, deducing consequences, testing those consequences, and ultimately making an inference about the validity of the original hypothesis.

The German philosopher Ludwig Wittgenstein once asked why anyone would think that it logical to assume that the Sun revolves around the Earth. When told that the Sun appears to be revolving, he asked how it would look if the Earth were rotating instead. The point of that anecdote is that science does not just find explanations consistent with observations. It compares the consequences of different hypotheses that may not be true.

Hypothetical reasoning is usually based on the hope that the hypothesis in going to turn out to be true. Counterfactual reasoning is similar, except that the hypotheses are likely to be false. The purpose is not to prove the hypothesis at all, but to elaborate on some artificial scenario.

If you are giving an hypothesis as a scientific explanation for some observed facts, then you are implicitly saying that alternative hypotheses are inconsistent with the facts. Thus even if you want to stick to truth, you must do some counterfactual analysis.

In the 1865 Lewis Carroll book, Alice in Wonderland says, “There is no use trying; one can’t believe impossible things.” The Queen replies, “I daresay you haven't had much practice. When I was your age, I always did it for half an hour a day. Why, sometimes I've believed as many as six impossible things before breakfast.” Carroll was a mathematician, writing for children.

Believing in counterfactuals does take practice, as it is barely distinguishable from believing in nonsense. It is also essential to quantum mechanics.

Aristotle is commonly quoted (incorrectly) as saying, "It is the mark of an educated mind to be able to entertain a thought without accepting it." An educated mind, or the open mind of a child. Or someone who accepts counterfactuals.

A counterfactual argument often starts with a what-if. Someone might ask, “what if the Axis Powers had won World War II?” It is a historical fact that they did not, and any such discussion seems like nonsense. Nevertheless, it is necessary to consider such questions if we are to come to conclusions about whether the war was worth fighting.

Comic books sometimes have counterfactual plots, such as the 1977 comic “What if Spider-Man joined the Fantastic Four?”. These are entirely fictional characters, but the comic was intended for readers who had accepted the story line that Spider-Man was not part of the Fantastic Four, and it was not trying to convince anyone that Spider-Man was joining the Fantastic Four. It was entirely counterfactual, but still made logical sense for its readers. It was like a dream within a dream. Disney recently tweeted that it was banning counterfactual Star Wars stories.

In case you are still wondering what "counterfactual" means, it is an adjective that means contrary to fact. When used as a noun, it is an abbreviation of "counterfactual conditional". But it does not just mean a false conditional, as false conditionals are meaningless. A philosophy site defines it as:
A conditional statement whose antecedent is known (or, at least, believed) to be contrary to fact. Thus, for example, "If George W. Bush had been born in Idaho, then he would never have become President." Unlike material implications, counterfactuals are not made true by the falsity of their antecedents. Although they are not truth-functional statements, counterfactuals may be significant for the analysis of scientific hypotheses.
I have become convinced that children understand counterfactuals better than adults, and that misunderstandings about them pervade many disciplines. I will be posting more on this topic. I will eventually relate this to relativity and quantum mechanics, but first I want to make sure that the concept is crystal clear in other contexts.


  1. Roger,
    If you want to talk about counterfactuals being useful, you have not succeeded so far. 'Dream within a dream' is a lovely piece of alliteration about complete and utter fantasy for little boys, but a really crappy piece of reasoning to demonstrate something is even possible in reality. Could you provide a useful example to make your case for counterfactuals in science? I would agree with you on one point, children are a lot like the followers of quantum mechanics, when they cover their eyes and makes themselves blind, they actually think the universe disappears. However, the moon is still there, even when you are not looking at it.

    1. It will take me several postings before it is clear where I am going with this. Please be patient.