Abduction and the no-miracles argument

The Cheshire cat,
famous invisible cat

In an earlier post in this blog, I explained with an example the mode of reasoning based on abduction. Although not as strong as deduction and induction, abduction reaches high degrees of confidence in fields such as history, art criticism and others, less scientific than mathematics or natural science.

In another post published in March 2016, I described the fallacy of the invisible cat, which confuses a sufficient condition with a necessary condition for something to happen. This situation occurs when there are several possible causes that may have given rise to the same phenomenon.

In some cases, if we apply abduction to a situation where the fallacy of the invisible cat could occur, a conclusion can be reached. Think of the example I proposed to describe this fallacy:

If there were an invisible cat on that table, we would see nothing.

We see nothing.

Therefore there is an invisible cat on that table.

This is a fallacy, because there are other reasons that can lead to the same result (we see nothing on the table), apart from the presence of an invisible cat. For example, we would also see nothing if there is nothing on the table.

If we consider all the possible causes of a phenomenon, we’ll usually find that they have different probabilities. In our example, what does the reader think is the most likely cause for seeing nothing on the table? What is the best explanation? That there is an invisible cat, or that there is nothing? I think we all agree that the second is infinitely more probable than the first. Well, if we choose that explanation, we are applying abductive reasoning. That is why abduction is also called inference to the best explanation, and also the no-miracles argument. The word miracle is used here with the meaning that it would be a miracle if the correct explanation was an invisible cat, for it is much less probable.

Witnesses of the miracle of the Sun,
October 13 1917

In another post in this blog I mentioned the miracle of Fatima, witnessed by 30,000 to 40,000 people. Two explanations can be given: a) something unusual happened; or b) all these people suffered a collective hallucination (something we don’t know that it exists). What is the most likely explanation in this case? Surely an atheist won’t agree with me, but I think the first is the most likely explanation. In other words, in this case, the no-miracles argument would lead us to conclude that there really was a miracle. The argument would run in this way:

The explanation based on a collective hallucination affecting tens of thousands of people is so unlikely, that it would be a miracle if it were true, therefore it is more logical to conclude that these people actually witnessed a miracle.

Hilary Putnam

The American mathematician and philosopher Hilary Putnam uses this type of arguments to justify his position, favorable to the philosophical theory called realism of entities, within the framework of the discussion about whether or not the entities posited by science really exist. His reasoning can be summarized as follows:

The best explanation of the success of science is the assertion that the entities whose existence is postulated are real: atoms, electrons, genes, viruses, and so on. It is extremely unlikely that science can be so successful in its technological applications if all that should be false. We know that true conclusions can follow from a false theory, but it would be a miracle if this had happened so many times, and all those theories were false.

Let's see how Putnam says this in his book Meaning and the Moral Sciences (1978):

[T]he modern positivist has to leave it without explanation [the fact that] ‘electron-calculi’ and ‘space-time-calculi’ and ‘DNA-calculi’ correctly predict observable phenomena if, in reality, there are no electrons, no space-time, no DNA molecules. If there are such things, then a natural explanation of the success of these theories is that they are partially true accounts of how they behave. And a natural account of the way in which scientific theories succeed each other −say, the way in which Einstein's Relativity succeeded Newton's Universal Gravitation− is that a partially correct/partially incorrect account of a theoretical object −say the gravitational field, or the metric structure of space-time, or both− is replaced by a better account of the same object or objects. But if these objects don’t really exist at all, then it is a miracle that a theory that speaks of gravitational action at a distance successfully predicts phenomena; it is a miracle that a theory that speaks of curved space-time successfully predicts phenomena.

What do anti-realists answer to this argument? Are they convinced? We’ll take a look at this in the next post.

The same post in Spanish
Thematic Thread on Philosophy and Logic: Previous Next

Manuel Alfonseca