2.5.5 The Value of Inductive Reasoning
Inductions are generalised explanations which are formulated as a result of making one or more relevant observations. Inductive inferences vary in their degree of generality and the breadth of the context in which they can be reliably, applied. Without knowing anything about the tilt of the earth’s rotational axis I can make the highly reliable induction that here in Scotland winter will be colder than summer. By collecting temperature data I can even apply a statistically calculated probability to show that my observations have not occurred by chance. By relying on the reports of residents in other countries I can then make the more general induction that the northern hemisphere will be colder in winter. By also consulting people whole live in equatorial regions and in the southern hemisphere I can develop more encompassing inductions of global annual variations in atmospheric temperature. As we all know, in the absence of a mechanistic explanation, I cannot make reliable inductions about weather conditions by calendar month in New Zealand if my observations are entirely restricted to Scotland.
As stated previously, induction is the process of creating imaginative explanations. Please note that explanations do not arise spontaneously in the sense that they leap out of a spreadsheet. Inductive explanations are narratives that we create about our data or observations.
When we all combine our knowledge of local variations in weather throughout the globe with an understanding of the tilt of the earth’s axis of rotation and the elliptical orbit of the earth around the sun we have then gone beyond a local induction to a more generalised explanation. By observing the tilt of the Martian axis of rotation and also observing that it has a more elliptical orbit than earth we can make the prediction that on Mars “The southern hemisphere has “harsher” seasons than in the north“. These kinds of explanations are normally referred to as coherent for they combine many inductions and many types of observations with mechanistic descriptions. Indeed, when we arrive at predictive valuable outcomes based on the coherence of ideas we tend to apply the term scientific.
The Metaphysical Basis of Induction
Induction is based on the practical and very reasonable metaphysical assumption that some aspects of the world around us maintain 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 thermodynamic properties of definable systems will remain invariant. The known properties of substances such as water will not change although we might learn more about them. The earth will continue spinning on its axis tomorrow. Galaxies will continue to rotate around their centres. Life will continue to evolve even although genetic code will remain remarkably stable. Humans will continue to suffer pain and disease and biological aging, and some will be violent towards others. People will continue to die for as long as our species exists. Currently extant species will become extinct. The list of pragmatically acceptable assumptions and explanations that support the material or physical basis of induction is endless.
Human inductive reasoning is not based on an all pervasive metaphysics of everything that exists, and a completely comprehensive description of the properties and interactions of things. Human inference is instead limited by our perceptions, our profound ignorance and our limited abilities to formulate descriptions of the world. There are no theoretical frameworks, either scientific or philosophical, or grand schemas of an Aristotelian or Kantian nature that can give us a basis for definitively creating the generalities of description that we might like to formulate. Instead, we are limited to the error prone expansion of human understanding by the elaboration of new ideas that come from observation, prediction and human intervention, and by methods of reasoning that are both imaginative and ampliative . It is frequently, or even generally, the case that we cannot 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 have been many suggestions that there can be informal ways of attributing subjective prior probabilities (or feelings about beliefs), to create a sounder or more defined basis for induction, which are not based on empirical data. To put it bluntly, the Subjective Bayesian idea that we can specify a credence, or subjective degree of belief, as a numerical probability without counting, measuring or calculating seems strangely lax. There could of course be an figuratively expressive need to state 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 and nothing more. Using the language of probability in the absence of calculations is merely metaphoric. The Subjective Bayesian view does not, in my opinion, have anything useful to say about the epistemology of belief or induction.
Clinical Drug Trials as an Example of Induction
Even when we accept the need for counting and measuring to develop probabilistic reasoning, we must realise that even the probability calculus applied to measured or countable data is based on axioms and some very important assumptions. For example, in clinical trials we might wish to test the idea that a potentially new drug if tested on a limited number of patients and is shown to be beneficial will also provide a much benefits to the adult population. This type of reasoning is known as inductive inference for it says that what we have seen in small sample will generally apply to the wider community. In other words we wish to use ampliative reasoning to say that what applies to a few patients will apply to many However it is important to realise that the inductions resulting from clinical trials, can involve very restricted conclusions. At best, a small clinical trial might give us the basis for inducing that a specific medical treatment is beneficial for the partial alleviation of a specified range of symptoms, in particular groups of people, at a particular stage in their life, during particular periods of a disease, treated within a particular dose range, while at the same time producing unwanted ‘side’ effects occurring at different frequencies and with varying degrees of severity within the treated group. In other words the context and applicability of our conclusions can be very limited in extremely important ways.
One of the most important probabilistic assumptions in a clinical trial of a new drug is that the method of randomisation actually resulted in the creation of sufficiently well matched treatment and control groups that it is valid to infer a causative role for the putative drug or intervention. It is the randomisation procedure, the number of people treated, and the ‘blinded‘ nature of assessment of outcome, the magnitude of response that gives legitimacy to the statistical analysis. Even then, we now know that the methods of statistical analysis should to be specified in advance of a particular randomised double-blinded controlled trial so that results are not biased by the post-hoc selection of analytical techniques that might bias our judgment. (see the this EMA document) And after all of that, we still need to ask the question does the treatment apply to the wider population or to a particular patient that an individual doctor is treating. That is why in medicine the practice of conducting further ‘pragmatic trials‘ is now seen as beneficial to patients.
The pragmatism arises in both controlled and pragmatic trials by testing that treatments are beneficial on very large numbers of people of both sexes, over a wide age range, of different body weights, in different countries, in different health care settings (referred hospital patients versus all comers seen by a GP), with varying degrees of disease severity. In addition it is also relevant to know whether or not there are significant long terms benefits and ill-effects that might lead to a discontinuation of treatment. Even then we need to accept that the use of the same drug for other clinical indications needs to be very extensively re-tested.
In short, the contextualization of our inductions can be extremely important.
The Locality of Induction
Medical interventions provide one type of situation where we might all easily agree that our inductions should be very strictly ‘local’ in scope. There is the wider philosophical question of whether or not all inductions are limited in their generality. In addition could there be some wider theory of induction? The answer would appear to be no. We would not expect to learn anything about weather forecasting from clinical drug trials. We would not expect that explanations of the cosmic red-shift of very distant galaxies would explain the movement of the earth’s tectonic plates. Understanding the nutritional requirements of garden plants in springtime would not be expected to teach us anything specific about the metabolic requirements of parasitic bacteria such as Chlamydia trachomatis. In short, since we have distinct domains of knowledge based on different types of actions and enquiries we would expect as a direct consequence that our inductions would in general have an extremely wide range of explanatory justifications. It would seems that there are no general rules, schemas or formalisms of induction that apply universally to all situations. Indeed, the philosopher of science, John Norton, argues in his free (!) books, with reference to a wide variety of examples, that there can be no general formulation or theory of induction, since each induction has a distinctive “material” relationship to the relevant background knowledge and assumptions. That ‘material’ connection certainly applies in medical research and to a very precise degree as described above.
Degrees of Support for Inductions
John Norton argues that inductions rely on ‘material facts’ and that the explanations he offers are not concerned with the epistemology of belief. Presumably he views theory-laden interpretations of experimental data and so-called ‘facts’ differently’? He also argues that each case involves an inductive logic concerning the relevant ‘facts’. As a pragmatist I take the view that induction is very much to do with the epistemology of belief. I envisage support for beliefs as existing on a spectrum between baseless conjecture to very strongly well founded. My view is very well backed up by the types of evidence that are used to support inductions in medical research. The quality of evidence in medicine has been rated in hierarchies, which underpin the actions of doctors when they undertake evidence-based practice. Evidence might range from the experimental treatment of human cancer cells in primary culture with a putative anti-cancer drug all the way to national guidelines based on an extremely large number of multi-national clinicals trials involving hundreds of thousands of people over a period over many years.
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. For the 15th century coffee drinker the floating coffee cup would not have been possible, despite human culture evolves.
Notice it took the actions of building and flying an aircraft in a very particular way, or building and launching a space rocket for the law-like certainty of the falling coffee cup to be locally violated within a very small region of defined space.
References and Further Reading
The Material Theory of Induction by John D Norton, 2021
Large-Scale Structure of Inductive Inference by John D Norton
Pragmatic Trials by Ian Ford and John Norrie New England Journal of Medicine 375:454-463, 2016
Statistical Principles for Clinical Trials, European Medicines Agency, 1998
Issues in Outcomes Research: An Overview of Randomization Techniques for Clinical Trials by Minsoo Kang, Brian G Ragan and Jae-Hyeon Park Journal of Athletic Training. 43(2): 215–221, 2008
Hierarchy of Evidence, Wikipedia
The Problem of Induction by Leah Henderson in the Stanford Encyclopedia of Philosophy, 2022
Bayesian Epistemology by Hanti Lin in The Stanford Encyclopedia of Philosophy, 2022
Probability Axioms, Wikipedia
Deductive Reasoning, Wikipedia
Steve Campbell
Glasgow, Scotland
2017, 2019, 2022, 2024