2.5.5
Logic Part 5 Induction, Abduction and Mechanistic Thinking

Induction

When I let go of a coffee cup, while seated at the kitchen table at home, it will always fall.  The law of falling coffee cups is based on an invariance of evidence and is therefore inductively strong.  (‘Inductive strength’ is the nearest equivalent to ‘soundness’ in deductive arguments). In this case, where the evidence is completely invariant, there is indeed a law of falling coffee cups.  We can then generalise that into a law of everything falling.  With the aid of (mathematical) deduction, we can then generalise this local law still further into a law of gravity that goes beyond the behaviour of things that fall towards the surface of the earth.  

There seems at first glance to be no practical value in pretending that there is a theoretical possibility the cup will magically levitate or by the mysteries of quantum physics ‘tunnel’ to another place in space and time. Nevertheless, one can ask are there circumstances in which our apparently invariant descriptions might not be accurate. There might even be situations that I cannot presently conceive of given the information available to me where even my view of the ‘laws of nature’ no longer applies. For the 15th-century coffee drinker, it would have been utterly inconceivable that her coffee might float out of her cup and her cup then float away in conditions of microgravity experienced in an orbiting spacecraft. Her observations of nature would not include or even permit the possibility of such an event. This limitation is not a matter of deductive restriction but one of repeated similar observations that produce the same result. The 15th-century coffee drinker has used invariant and repeated observations to come to a general conclusion that does not apply in different circumstances.

The Basis of Induction

Induction is based on the practical and very reasonable assumption that the world around us maintains the same properties or approximately so. Atoms of iron, for example, do not suddenly become atoms of carbon. The earth will continue spinning on its axis tomorrow. People will continue to die for as long as our species exists. The list of pragmatically reasonable assumptions that support the basis of induction is endless.

Nevertheless, the problem arises that we cannot always account for all of the relevant circumstances that could influence phenomena that we wish to analyse. Even the empirically determined value of the ‘universal gravitational constant‘ varies very slightly over time.  Despite these variations, the underlying assumption of the uniformity of nature is still very strong especially concerning this very fundamental quantity. Instead of assuming that nature is fundamentally variable, the fluctuations in gravitational measurements are presently explained as a combination of experimental difficulty and some, as yet unaccounted for, local and periodic change within the earth. The alternative would be perhaps to devise a new deductive physics based on incomplete and perhaps unreliable evidence.

It intuitively feels that there are situations that we can treat this close approach to certainty as being so absolute that it would be ridiculous to think otherwise. The coffee cup falling is one. However, if I asked you it is possible that there are or could be ducks with regular patterns of pink, green, blue and black striped feathers you might not be quite as certain that such birds could not occur, despite the fact that you have never seen one. In this situation, we might consider our arguments to be inductively weaker.

Inductive conclusions are at their strongest in the natural sciences when ideas have been arrived at by repeated and related observation. The relatedness might, of course, be partially deduced. In many circumstances, we think of inductive truth only as an enumerated probability – a probability that is specified as a number ratio such as 95 times out of 100 or 95%. We try to determine whether what we have observed has just happened by chance or is uncharacteristic of the run of random events. In this case, we are dealing with the strength of a logical argument based on fallible supporting evidence not a conclusion that is absolute.  By contrast when we develop a theoretical or mechanistic explanation our thinking switches from being probabilistic to another mode of deductive mechanistic reasoning (described below). In so doing we tend to revert back to a  binary way of thinking and ask is the proposed mechanistic explanation either true or false.

It is not a problem that induction is less than absolute. As previously argued, there is no ‘problem of induction‘, although a great deal has been written on the subject. Briefly put, the ‘problem of induction’ is said to be the fact that when we try to extrapolate our explanations to as yet unobserved situations they might not be predictively accurate. My attitude to this way of thinking is, “So what? That’s life. Get over it. Chasing absolutes can be time-wasting. There is no way out of this supposed dilemma. Why see our most valuable way of learning about the world as a problem?”

Inductively reached conclusions cannot possibly be ‘sound’ in a deductive sense. Given that deduction can at best only be truth-preserving, why should we worry? Of course, we can be very interested in what distinguishes predictively useful inductions from those that are not. Rather than be a problem, induction should be viewed as a triumph of human memory, intellect and culture and is part of the basis on which science and its applications flourish. We should regard the evolutionary process that has led us to the point where we can make inductive inferences as awe-inspiring.

If a large number of inductions produce useful, elegant and satisfyingly simple explanations then we have a worthwhile demonstration of the power of induction. More generally the pragmatic success of induction in helping us deal with the world is itself an inductive justification of induction.  This meta- or secondary-level of inductive justification is not absolute or axiomatically based. Again, that is not problematic.

You might reasonably argue that induction lacks the intuitive sense of ‘validity’ that can be applied to deductive arguments. At its core deduction can seem more conceptually complete and classical logic can appear more conceptually ‘closed’. Nevertheless, when we consider the origin of the premises in the deductive argument we can see that for many practical purposes there is little merit in privileging one of these forms of argument over another.

Abduction

Abductive argument is said to be the kind of logical argument that we use in everyday life, during a scientific enquiry or that a jury might hear in court when they listen to the final arguments of a prosecutor or defence counsel who provide what they consider to be the best explanation available. The difference between induction and abduction is in the nature of the conclusion reached. Induction seeks to produce some form of generalisation whereas abduction is restricted to an explanation of the particular circumstances under consideration.

Abductive explanation can involve the use of the logical connectives AND  & OR that were considered aboveFor example, in legal evidence where the more statements we have supporting the proposition that the accused is guilty of a criminal offence the surer we are of that verdict.

If,    1) the accused stated in front of the first witness he hated the defendant

AND 2) the second witness said he heard him threaten to kill the victim
AND 3) he was seen by a third witness to strike the victim with a curved sword
AND 4) the complainant (or victim) had a deep cut on his neck
AND 5) a police officer found a curved sword in the apartment of the accused
AND 6) the fingerprints of the accused were found on the sword
AND 7) there was blood stains on the shirt of the accused
AND 8) a forensic scientist stated that the blood matched that of the complainant

we would have a convincing story.  We could, if we were Scottish jury members, take the analysis a stage further and agree that the legal requirement for demonstrating the intention of the accused to commit the crime of attempted murder was fulfilled. In addition, we could deductively reason that there exists corroborating evidence, as required in Scots criminal law, to convict the accused.

An argument to the best available explanation does not require ‘truth’ in any absolute sense only a description that meets an individual person’s chosen criteria of acceptability whatever they may be. The Scottish criminal case above would require the jury to be convinced beyond ‘reasonable doubt’. In addition, there is a set of background assumptions and previous experience that will inform what we do and the way we interpret.  We, of course, need to consider what ‘best’ means, for if the concept is to be useful we need a way of deciding between competing explanations.

Complex examples of abductive (and inductive) reasoning inevitably lead us to the notion of partial truth. In the legal story above, where I used  ‘conjunction’, expressed by the logical connective AND,  it is apparent that the conjunction of statements has more legal or logical force because it is more comprehensive or elaborate and as a consequence has acquired a more cohesive or logically coherent appeal. Each piece of evidence is literally part of the whole picture available to us. Although each component might be regarded as true, there seems a stronger and more complete truth in the conjunction.

There is also ‘partial truth’ in senses that do not include the idea of logical conjunction. It is possible that an assertion could be partially true in that it might not be totally exact or correct in all circumstances. The purists might, of course, argue otherwise if applying some form of non-modal classical logic in which the idea is simply not permitted (see below).

Mechanistic Thinking

The long-term aim of scientific enquiry is to go beyond the simple alternatives laid out above and whenever appropriate produce what are taken to be the ‘laws of nature’. These laws are mechanistic explanations and are very numerous. Mechanistic thinking aims to draw together observations, measurements, inductions and deductions.

For example, we do not think of the sun rising in the sky each morning in terms of a probability. Instead, we explain the appearance of the sun each day, the seasonal variations in its observed path and the movement of the planets with a mechanistic explanation. We reason that the earth is spinning on a tilted axis as it orbits elliptically around the sun. By including the planets in our explanation and grouping them together with the earth we then derive the ontological declaration of a solar system. We then generalise the explanation even further and claim the existence of an invisible force field of gravity that causes objects to fall, projectiles to follow parabolic courses before crashing to the ground or stars to revolve around the centre of the galaxy.

When mechanistic explanations are highly speculative and come before observation or experimental testing  they are commonly referred to as hypotheses. In highly complex systems such as the human body, for example, speculative mechanistic explanations might be produced that provide a reasoned form of argument but still remain far from certain. If you told me that   Vitamin D reduced respiratory infection because there are cells of the immune system which require that molecule for proper functioning, that assertion of itself should not lead me to take a large dose of it on a daily basis.  I need controlled tests of taking the vitamin and observation of subsequent infection rates to provide direct evidence. And even if such a test proves effective that is not an establishment of a mechanism or causal attributions.  By contrast in physics which tends to deal with trivially simple idealisations, when compared to the complexity of living things,  mechanisms and causal attribution are easier to arrive at in a convincing fashion.

 Over extended periods of development, mechanistic thinking in physical sciences (or applied sciences such as engineering) has tended to become mathematized so that the relationship of relevant factors is expressed logically and precisely in the form of formulae that involve variable parameters, constants and mathematical operators. In so doing, the mathematicians or theoreticians are trying to produce a deductive form of reasoning that is mathematically expressed

Steve Campbell
Glasgow, Scotland
2017, 2019

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