Critical Thinking: An Introduction to Investigations and Recommendations

Recall from above:

Let’s begin by formalising the question as already posed:

The obvious evidence, which is indispensable to this investigation, is (note this is a simple case where a declarative version of the Lead Question is the only Evidence to Explain):

With this simple question and simple piece of evidence, we can come up with a few quick answers:

Explanatory resources, here guided by our possible answers, will help us decide on a best explanation:

Those Explanatory Resources undermine two of the rival answers, which makes the remaining answer seem best. To put it all together:

Given that we found out the sprinklers are not in, the answer RA1 is undermined. Given that we found out there is no filming happening nearby, the answer RA2 is undermined. Therefore, our resources leaving the obvious RA3 as the best explanation.

Formalisation, Detailed Example 2

Let’s work with more complicated example to illustrate all of these concepts:

In this example, there has been an explosion, then a subsequent investigation into the cause of the explosion, then a conclusion drawn from the evidence. To assess the inference, we need to formalise.

Lead Question

Identify the question that needs to be answered. In this case, it was the explosion that stood out as unexpected, and so the Lead Question should be about the explosion. That is, we treat the explosion as indispensable evidence. There are many ways to frame lead questions, all of which will result in subtly different sets of Rival Answers. Consider these:

The first question might be motivated by an investigation into possible negligence on the part of technical staff or crew. The second question might be motivated by a desire to determine whether there was equipment failure. Knowing your motivation guides choices of lead questions.

Answers to the first question might include foul play, negligence, bad weather conditions, and so forth. Generally, in this case, the answers will be about the circumstances of the explosion rather than a chain of events that led to the explosion.

Of course, there might be overlap in the answers to the various questions. The goal here is to develop a sensitivity to the sorts of answers that interest us, and then figuring out which question’s answers will capture that interest.

In the Apollo 13 case, given the narrative includes no indication of negligence, here we will focus on the second question:

Evidence to Explain and Explanatory Resources

Pick out Evidence to Explain. In this case, there is the obvious fact of the explosion. We would list this and the further evidence as follows:

Notice that the evidence is a series of events. Knowing how we divide those events into pieces of evidence is part of our reasoning skills. We could characterise these same events in more detail, perhaps dividing EE4 into two steps: When the fan was switched on, current ran through the wires; when current ran through the wires, an explosion occurred. But it’s sufficiently clear that the flicking of a switch causes current to flow through a connected wire, so that step goes without saying.

However, in this case, we might state that applying too much voltage to a circuit can cause overheating, which can cause damage to insulation. Knowing this fact requires sufficient specialisation that not everyone will necessarily have. Of course, whether to include this fact in our formalised argument is a judgement call. Here we’re best to judge that it’s worth stating clearly. This is an Explanatory Resource, which we will list as follows:

Generally, when in doubt, make Explanatory Resources explicit.

Rival Answers

Craft possible answers to the Lead Question. In this case: What caused the explosion on Apollo 13? Let’s represent possible answers this way:

This is by no means an exhaustive list. RA1 is obviously unlikely, but we include it here in order to illustrate our evaluative process. RA2 and RA3 are subtly different, but sufficiently different to list separately. The subtleties will become increasingly more important as we develop a system to construct recommendations.

We might wonder what keeps an answer off the list. To this point, it might sound as though anything goes, and to an extent, this is true. But anything goes within reason. The idea that a puppy stowed away on Apollo 13 and chewed through a wire at the same time that an astronaut flipped a switch is, clearly, outside the bounds of reasonable. As always, inclusion of the most exotic of explanations is a matter of judgement.

The Favoured Rival

Determine the favoured Rival Answer. To do this, we need to interrogate the Rival Answers based on our minimum standards.

In the case of RA1, that there was a bomb aboard: The answer is consistent with the evidence, as it certainly explains the explosion and none of the evidence at hand rules it out, nor does it contradict any of the evidence we have gathered.

RA1 is not a particularly charitable or uncomplicated answer, though, as it requires introducing evidence of conspiracy. It doesn’t need to address possible damage to wiring, given the catastrophic nature of the answer. But given the need to complicate the case, this is not a preferred rival answer.

More evidence could come to light, which could, in the future, make this a more likely candidate. But at this point in the investigation, this is not the case. This illustrates the value of collecting evidence and answers in one place and accounting for them precisely. Things change, as can best explanations.

RA2, that damage to the wires caused the explosion, is consistent with the evidence at hand. The investigation uncovered a couple of unnoticed pieces of evidence (EE2 and EE3), and these seem intimately related to the explosion, given our general understanding of the world. They seem as though they might be causal factors, or at least potentially so. RA2 deals with them well, and at the same time is charitable and uncomplicated. RA2 does not require us to make any further assumptions or to appeal to unlikely scenarios. RA2 is also comprehensive in that it deals nicely with all the evidence uncovered so far in the investigation.

RA3 is a tricky one, because it appears consistent with the evidence at hand. It could certainly be that a short in a switch was the problem, suggesting that even though there was damage to insulation, that damage was not the cause of the explosion. But given the explanatory resource we introduced, ER1 (that excessive voltage in a circuit can cause damage to insulation), RA2 appears a better candidate than RA3. ER1 is the extra-ordinary circumstance, and RA2 deals with it best. (This demonstrates the value of explanatory resources.)

Overall, we can say that RA2 seems the best explanation. RA3 is close behind, and if we uncovered more evidence, we might come to think RA3 the better explanation (a later exercise asks you to consider this case). RA1 is not close to either of these answers, as its position among its rivals depends on further evidence that is unlikely to be found.

Express the Best Explanation. This will be a combination of our favoured rival answer to the Lead Question, plus the fact that motivated the Lead Question. So:

Complete Structure

This is an instance of our Standard Form of Inference to the Best Explanation, which we can express as follows:

This structure provides a means to see all the evidence, resources, and rivals in one place, which in turn makes it clearer why your chosen answer is the Best Explanation. Furthermore, as investigations uncover more evidence, or determine some evidence irrelevant, you can easily revise the contents in this structure to reflect those changes.