2.5.5 Inductive Reasoning
As stated before, induction is the process of creating imaginative explanations that are supported by repeatable observations. Please note that explanations do not arise spontaneously in the sense that they leap out of the spreadsheet. Inductive explanations are narratives that we create about our data or observations.
In addition it seems likely, as John Norton argues, that there are no general rules or formalisms of induction that apply universally to all situations. Norton successfully argues that there is no general formulation or theory of induction since each induction has a distinctive relationship to the relevant background knowledge and assumptions. (I do find Norton’s choice of the word ‘fact’ to describe background knowledge a bit irksome, as if the so-called ‘facts’ were to be clearly distinguished from inductions especially in scientific practice.)
Induction is based on the practical and very reasonable assumption that the world around us maintains the same intrinsic properties or at least approximately so over short time periods. Atoms of iron, for example, do not suddenly become atoms of carbon. As the alchemists found out, there is no way to turn ‘base metal’ into gold. 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 acceptable assumptions that support the basis of induction is endless.
Nevertheless, it is frequently the case that we cannot always account for all of the relevant circumstances that could influence phenomena that we wish to understand. 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 or periodic change within the earth. The alternative would be perhaps to devise a new deductive physics based on incomplete and perhaps unreliable evidence.
There are situations in which it intuitively feels that that we can treat the close approach to certainty, which induction affords, as being so absolute that it would be ridiculous to think otherwise. It is in this situation that some pragmatists might find the conversational use of the words ‘true’ and ‘fact’ to be perfectly acceptable. For example, when we let go of a coffee cup it will always fall if unsupported, unless you and your coffee cup were floating around the confines or boundaries of a spacecraft in conditions of microgravity. [Notice it would have taken the actions of building and flying a ‘vomit comet‘ in a particular way, or building and launching a space rocket for the law-like certainty of the falling coffee cup to be violated. For the 15th century coffee drinker the floating coffee cup would not have been possible, even if flying magic carpets existed.]
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 it being the case 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 after repeated and related observations, which can from a coherent explanation. In many circumstances, we think of outcomes, expressed as inductive assertions, only as an enumerated probabilities for different 2 reasons:
1) We might be pragmatically concerned about whether our not our sampling is representative of a large population of occurrences or is uncharacteristic of the longer run of events.
2) We might wish to express our subjective uncertainty as a pseudo-enumerated degree of belief, by saying I am 90% sure, for example. From a pragmatic perspective such enumerations cannot have any firmer status than our use of descriptive terms that express degrees of belief. Numerically expressed credences are just a convenient shorthand where the desirable vagueness of descriptive words run out of explanatory power.
In the either 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. For example we do not explain sunrise in probabilistic terms, although we could in principle rate the probability as 100% every day for the next few billion years. Instead, we imaginatively invent the idea of the earth orbiting the sun. In so doing we tend to revert back to a binary method of assessment of our ideas and ask is the proposed mechanistic explanation either acceptable or unacceptable given the available observations.
Inductively reached conclusions cannot possibly be ‘sound’ in a deductive sense. Given that, deduction can at best only maintain acceptability (or be truth-preserving for the traditionalist), why should we worry? Of course, we can be very interested in what distinguishes predictively useful inductions from those that are not, and see the later as a motivation for new lines of enquiry. Rather than be an epistemic problem, induction should be viewed pragmatically as a triumph of human memory, intellect and culture and as 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 complex inductive inferences about future weather as awe-inspiring.
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 that when we try to extrapolate our explanations to as yet unobserved situations they might not be predictively accurate. My pragmatic 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 should see our most valuable way of learning about the world as a problem?’ The only type of proposition that can be stronger than an induction is a law-like mechanistic explanation.
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 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.
In short induction ‘works’ in the sense that it is practically useful in ordinary living and scientifically fruitful. However induction is not a route to a guaranteed explanation and so results in the need to revise theories from time to time. When deduction is combined with, the imaginative thinking that is the mechanistic explanations of our induction, this is our only route to ampliative inferences and causal explanations.
Version 2.4
Steve Campbell
Glasgow, Scotland
2017, 2019, 2022, 2024