Seasons Greetings: The wonders of integrative science

Hello all,

As usual Roger and I have put together a little something extra for our holiday blog. This year we have tackled the brave new world of integrative science. Now many of you may have noticed a growing trend in integrative science which combines traditional scientific methodologies with other more spiritual and intuitive forms of inquiry. So to avoid any confusion we have created a video scribble to explain the intricacies of this important subject.

So kick back, grab a savoury snack and a beverage (or an iced drink, for readers in the southern hemisphere), and click on the link to enjoy this short video presentation that will explain all. We proudly present: the Wonders of Integrative Science…  https://www.facebook.com/photo.php?v=10153646540185074&set=vb.265638800073&type=2&theater

Happy Holidays all!

Roger and Bernie

P.S. It has been suggested that there may be some issues with our critical reasoning here, so in the spirit of good science we will award a fabulous prize to any reader who can identify all of the logical fallacies, and problems in the video!

Scientific reasoning and the problem of induction; the big one!

Hi folks,

Roger is currently tied up with a writing project, and being hounded with menaces by some large henchmen sent round by his publisher. Apparently, something about chapters being overdue. As he has gone into hiding I have volunteered to cover the blog for the next few weeks, and so to kick us off with a good weighty topic to frazzle the grey cells. So here we go with the problem of induction.

Although in essence inductive reasoning appears fairly simple (generate a list of probable explanations to explain an observed phenomenon) there are some underlying assumptions that are more problematic, and together these are known as the Problem of Induction. This is quite complex to grasp, so be warned, if you are new to these arguments, the following may give rise to headaches and palpitations. Here is a synopsis of the problem based on my feeble grasp of it:

Firstly there is the assumption of generalization. Induction requires we generalize about the properties of a set of objects based on repeated observations of particular instance. For example, we may infer that all the sheep are white, based on multiple instances of observing only white sheep, but this would later be found to be false, when we discover a black sheep. This would make any proposition derived from this generalization equally invalid (see the famous black sheep joke for a good example).

Secondly we have the assumption of uniformity. In inductive reasoning we presuppose that a sequence of events will occur in the future just as they have in the past (for example, the sun will rise in the east). This assumption itself relies on inductive reasoning, as the only way we can predict the future is by speculation based on past experience. This is circular reasoning by deriving a conclusion from premises that presuppose the conclusion. I.e. we are basically saying that the future will be the same as the past because in the past the future has been the same as the past!

Causality is the third area raised in criticism of inductive reasoning. Causality is a basic assumption of science and although we generally accept the concept of cause and effect, philosophically it is a challenging principle. Aristotle discussed ideas of deliberate (prior) and accidental causation, but the great thinker David Hume (1711-1776) outlined more detailed principles suggesting three basic elements.

If there is a causal link between A and B:

1) One must always precede the other (temporality),

2) The cause and effect must be in contact (spatial contiguity), and

3) There is some power in A to cause B (necessary connection).

This third point is philosophically a little more problematic in that it requires a theoretical element, “something that exists in the mind, not in the objects” (Hume, 2000). That is to say, a mental notion must be established linking the two types of object or event. Hume suggests it is our mind that makes this connection between objects or events when in reality they should be regarded as separate isolated instances. Relativity and quantum mechanics have also forced physicists to abandon their assumptions of causality, as they don’t seem to apply at the sub-atomic particle level. However they seem to remain valid for what happens at the level of human experience.

The major problem identified with inductive reasoning lies in the fact that to justify generalization or causality we use experience and inductive reasoning, creating a kind of circular logic, as we are justifying an inductive argument with more inductive reasoning.

The Raven Paradox

Carl Gustav Hempel (1905-1995) technically described this problem in logical terms with his Raven Paradox. Inductively to describe ravens we can hypothesize “all ravens are black” based on our observation of a subset of all ravens (as we cannot view them all). Over time with no non-black ravens encountered we accept this hypothesis. Therefore, by logical implication we can also state “everything that is not black is not a raven.”  Our hypothesis “all ravens are black” therefore has the equivalent form “all non-black things are non-ravens,” or more precisely, “if an object isn’t black then it is not a raven.” Logically, if every sighting of a black raven confirms our hypothesis, then every sighting of a non-black non-raven should equally confirm our hypothesis. This is where he argues inductive logic falls down, as if I look at my car, and see it is green, and it is not a raven, this confirms my hypothesis that all ravens are black! This of course makes no sense at all, but by the rules of logic, if I accept inductive hypotheses and confirmation by observation, then every observation (except one that refutes my hypothesis) confirms it, even when totally irrelevant.

The problem of induction is an argument frequently used by philosophers to “beat up” science, by suggesting that science is no better than alternative narratives for explaining the world. However, Karl Popper proposed a partial solution to the problem of induction with falsifiability, and  Charles Saunders Pierce gives us a pragmatic framework that appears quite effective at generating effective outcomes in the hypothetio-deductive model. So practically the problem of induction remains more philosophical than practical in its nature.

At worst the problem of induction represents a set of arguments that show inductive reasoning can only suggest a truthful explanation but cannot ensure it. We should certainly accept that there could well be alternative explanations for a phenomenon that we have not considered and be open to them.

Pragmatically, we should also note that we frequently use inductive reasoning everyday in general learning for the real world. For example, in learning to drive we learn how to start a car engine by turning a key, and generalize this technique to use in other models of cars. For science, we still rely on induction, and it is very much part of the creative (and arguably most interesting) part of scientific inquiry. The inductive conjecture about best treatment options is also a central part of the evidence based practice process in healthcare. Of course, scientists also discovered that inductive reasoning becomes much more powerful for systematic inquiry when combined with deductive reasoning.

Anyhow, in order to stimulate some creative thinking Roger and I are offering a fabulous prize (as yet to be determined, but surely some object of unimaginable wealth and beauty) for the most inventive solution to the problem of induction posted below. Go on you know you want to give it a go…

Onwards

Bernie

P.S. I got reunited with my luggage eventually, so take back all those bad thoughts I had about Virgin Atlantic.

References

Hempel, C. G. (1965). Aspects of scientific explanation and other essays in the philosophy of science. New York: New York Free Press.

Hume, D. (2000). A treatise of human nature (originally published in 1739). Oxford: Oxford Philosophical Texts.

Memory, falsity and how we know what isn’t so.

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:

  1. If there is a king in the hand, then there is an ace
  2. 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.

Bernie

References

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.