In the week that Totness seems to have become the CAM capital of the UK (apparently it’s twinned with Narnia), my mind turned to the ways in which we can so easily believe in things that are on reflection, obviously not so.
The media certainly has its share of the blame here, often whipping up a sensationalist frenzy of interest in stories that turn out to be untrue. An interesting one this side of the Atlantic was the 2008 case of a reported “pregnancy pact” between 17 teenage girls in Gloucester, MA. This stirred up considerable media interest and has spawned two movies and at least one book I know of. Nevertheless, it was actually not true, and the teenage pregnancy rate in Gloucester was really lower than many other towns in the USA.
However, our own brains can easily mislead us too, as cognitive psychological research frequently tells us. I have also found this area fascinating, and the following example is a great brain twister that illustrates the point.
One area of reasoning can easily give rise to erroneous results is that of memory and illusory inference. The brain uses specific parts of the brain to process and store information (such as the hippocampus for working memory and cerebellum for motor skills). Psychological research has suggested that we can only actually think about seven things at once before we overload our working memory capacity (Miller, 1956). This working or so-called “short-term” memory limits our reasoning ability, but the theory is, has evolved to represent more-than-sufficient working memory for everyday life (Johnson-Laird, 2008).
Indeed. Some people with hippocampus and other brain-injuries have demonstrated short-term memory loss, whilst some “memory athletes’ train to improve their memory capacity for competitions and achieve some remarkable results remembering names, cards, faces and numbers (Foer, 2011). Nevertheless, the memory athletes use techniques that help store information in areas outside of working memory and all appear bounded by the same cognitive processing limitations as the rest of us. We also know there are conscious (declarative) and unconscious (non-declarative) processes that result in memorization, but as yet we still do not fully understand the complex inner workings of memory processing and cognition in the brain.
The limit of about seven things to process at a time seems fairly consistent, and more recent work suggests the human mind also tends to ignore things that are false (also known as falsity).
Falsity involves leaving out or ignoring information in the reasoning process to leave a proposition that is false. Mary Newsome and Philip Johnson-Laird of Princeton University reported in a 2006 experimental study that for certain sorts of premise individuals reliably infer invalid conclusions (Newsome & Johnson-Laird, 2006). Complex propositions may confuse us into making the wrong decision. Lets take an example, only one of the following statements is true for a hand of two cards:
- If there is a king in the hand, then there is an ace
- If there is not a king in the hand, then there is an ace
Which is more likely the king or the ace in the hand of cards? You might want to try and figure out your own answer before reading further.
We generally mentally map out this problem of probability as follows on the basis that we consider each separate statement as true:
- King & Ace
- Not King & Ace
So the answer most of us come up with is the ace. It seems we would more likely have a ace in the hand without a king compared to having no king and an ace, as the ace occurs in both sets of statements whereas the king only in the first. However, this is an illusory response as what we overlook is that when one conditional statement is true, the other must be false i.e. there is an exclusive disjunction in the statements (only one of them can be true). We can see this if we fully map out the problem more explicitly:
EITHER: If “King then Ace” is true, and “Not King then Ace” is false,
OR: If “Not King then Ace” is true and “King then Ace” is false,
Using the mutually exclusive nature of the two statements the two possible models are:
- Not King & Not Ace (where the first statement is true and second false)
- King & Not Ace (where the second statement is true and first false).
In this above rationale we can now see the Ace is not only less likely to occur, but an ace is also logically impossible in the hand given the requirement that the other statement must be false. This is actually the correct solution.
Lastly, let us consider a third option, what if both statements could be true?
This is what is technically known as a bi-conditional interpretation of two conditionals and if we write out all the possible hands using an “and” rule: (that is to say if and only if “king then ace,” and if and only if “no king than ace” we would get these possibilities:
- King & Ace
- Not King & Ace
- Not King and Not Ace
- King & Not Ace.
In this case there would be an equal chance of holding a king or an ace, but again this answer is also incorrect as it ignores our conditional “either or” statement in the initial premise. In an experiment by Johnson-Laird and Savary experiment in 1996, using this problem administered to students, 79% of participants gave the initial response that an ace was more likely, 13% got the correct answer that the king was more likely, and 8% also incorrectly thought they had an equal chance (Johnson-Laird & Savary, 1996).
They suggested people reason from a mental model that is constructed according to a “principle of truth”, i.e. a model of a possibility representing clauses in the premises only when these clauses are considered true, i.e. we ignore things that are not explicitly stated as false (Johnson-Laird, 2008; Newsome & Johnson-Laird, 2006). This form of reasoning arises from our prior knowledge and experience and reduces the mental processing load, but for this type of problem the consequence is an erroneous result.
Confused yet? Well, that is the point. There are lots of other examples of cognitve and sensory issues that can mislead our brain, but I quite like this one. If you got all this on the first reading I suggest you immediately grab an application form for MENSA and get working on your acceptance speech for an inevitable Nobel prize. However, for the rest of us this serves to indicate why science remains an important epistemological approach.
Anyone can challenge anything in science and the peer review and verification processes (although flawed) are powerful tools in discriminating evidence. Scientists, as much as anyone else, certainly hold things to be true now that will be proven otherwise in future, but the beauty of science is it encourages us to do so. Modern science recognizes the dynamic, and changing nature of our knowledge, and more importantly, our ability to be deceived by our own thinking.
Foer, J. (2011) Moonwalking with Einstein: The art and science of remembering everything . New York, NY: Penguin Press.
Johnson-Laird, P. N. (2008). How we reason: A view from psychology. The Reasoner, 2, 4-5.
Johnson-Laird, P. N., & Savary, F. (1996). Illusory inferences about probabilities. Acta Psychologica, 93, 69–90.
Miller, G. A. (1956). The magical number seven, plus or minus two: Some limits on our capacity for processing information”. Psychological Review, 63(2), 81-97.
Newsome, M. R., & Johnson-Laird, P. N. (2006). Falsity dispels fallacies. Thinking and Reasoning, 12(2), 214 – 23.