The problems of induction in scientific inquiry: Challenges and solutions Table of Contents 1.0 Introduction... 2 2.0 Defining induction... 2 3.0 Induction versus deduction... 2 4.0 Hume's descriptive problem of induction... 3 5.0 Hume's solution to the descriptive problem, emergence of the narrative problem. 3 6.0 Is there a solution to the narrative problem of induction?... 4 7.0 Conclusion... 5 References... 7 1
1.0 Introduction Inductive inferences play a significant role in the development of scientific research and thinking. First developed by Francis Bacon, induction is perceived to be a useful tool for the derivation of universal principles from a finite subset of instances. This theory of induction and its role in scientific inquiry has however been a subject of a long-standing discourse. Questions which relate to how an inference may be justified and whether a universal claim may be hinged upon a finite number of observations have emerged as major questions challenging the validity of the theory. It is in this atmosphere that this paper aims to analyse what the problems of induction may be and question if there may be a solution to these problems. This essay aims to achieve this by defining induction, setting it apart from deduction, analysing the arguments regarding the validity of induction made by David Hume and analyse the solutions to these problems which were proposed by Karl Popper. The argument of this paper will be that despite the practicality of Popper's proposal, a full resolution of Hume's problems remains unattainable. 2.0 Defining induction Imagine you landing on a deserted, undiscovered island and encountering a family of rainbow coloured dogs with three legs. You continue to scout around the island, encountering more dogs, most of which fit your conceptions of normality. All the other types of dogs you have seen on this island have four legs, and none of them have rainbow coloured fur coats. On your trip, you continue to come across more three legged rainbow coloured dogs. Assuming that you have seen enough of the dogs on this island, you can then conclude that all the three legged dogs on this island are rainbow coloured. This method of generalisation is known as induction. In layperson's terms, induction is then defined as the process of forming a general conclusion after examining a particular number of instances, a reduction of multiplicity to a single unity (Thilly, 1903). 3.0 Induction versus deduction Induction should not be confused with deduction, which is the process of reaching a general conclusion from its premises, with the assumption that if the premises are valid, the conclusion cannot be falsified (Rodrigues, 2011). As a 'top down' approach, deduction moves from the general to the specific, in scientific terms involving the forming of a theory, the derivation of 2
a specific hypothesis, the collection of observation and finally the confirmation of the theory (Rothchild, 2006). Applying deduction to the story of the dogs, you will first set out the theory that all three legged dogs are rainbow coloured, after which you will travel to the island to find instances of three legged dogs. If all the three legged dogs that you have encountered on the island are rainbow coloured, then your theory cannot be falsified. However, the opposite does not apply and there may be a chance that you may come across a rainbow coloured dog that is not three legged. On the other hand, induction is the opposite of deduction, a 'bottom up' approach working from the specific to the general (Rothchild, 2006). It begins with the observation, generating patterns from this subset of observations, forming some hypothesis and finally concluding with a theory (Rothchild, 2006). As such, conclusions reached by inductive reasoning do not depend on the validity of its premises, which is where the problem of induction has been identified. 4.0 Hume's descriptive problem of induction The problem of induction is usually credited to David Hume who is the first to question induction and analyse its problem. Hume's problems of induction can be divided into two categories, the descriptive and the normative. The descriptive issue questions the mode in which people generate opinions about unobserved matters. It may be trivial and related to his concept of relation of ideas which affirms the truth of various propositions by virtue of the relationships between their concepts or by the fact that they are a priori knowledge (Earman and Salmon, 1992). For example, I do not need to examine every single square in the universe in order to claim that they have four equal sides as the denial of this logic is inconceivable. Evidently, this problem is elementary and does not pose much of a problem to scientific knowledge, since falsification of logically and rationally vivid inductions based upon a priori knowledge is almost impossible. 5.0 Hume's solution to the descriptive problem, emergence of the narrative problem With the problem of induction exemplified in the logic of the squares, Hume's proposed solution that induction is made upon one's experiences is justified (Earman and Salmon, 1992). However, one touching issue remains in this explanation, which is whether all predictions derived from experience about the future which we have not yet observed are always justifiable. 3
This issue is best described by Hume (1955, p.32) as such: "When it is asked what is the nature of all our reasoning and conclusions concerning the relation of [cause and effect]? It may be replied in one word, experience. But if we ask [ ] what is the foundation of all conclusions from experience? This implies a new question, which may be of more difficult solution and explication". This new question is the premise of the normative problem. An example popularised by Hume of such an event is the predictability of the sunrise (Lange, 2008). Hume commented that even though our observation shows that the sun has risen every day, we cannot infer that the sun will rise tomorrow since it is an unobserved future that we have no absolute certainty of (Lange, 2008). He further adds that there is no degree of confidence with regards to the claim that the sun will rise tomorrow since it is an unobservable phenomenon. Hume's demand for a justification to the uniformity of nature is detrimental to the advancement of scientific knowledge as it argues that a logical basis for putting one's confidence in any forms of scientific hypothesis does not exist. Hume's narrative problem questions the very foundations of scientific knowledge which is based upon validity and inferences. He asserts that all judgements with regards to the validity of a hypothesis and people's ability to predict the findings of a specific procedure are purely based upon probabilities with undefinable confidence levels ranging from 0-100% (Rothchild, 2006). Such an argument deconstructs the certainty and confidence we place in an induced scientific law, which reveals this law to be no more reliable than single events on which it is based.. Such a disturbing challenge to the foundations of scientific knowledge have inspired the efforts of various philosophers to seek a solution to Hume's problem so as to continue to justify the inductive predictions that science has made thus far. 6.0 Is there a solution to the narrative problem of induction? A proposed solution which is of significant mention is that of Karl Popper's. Popper's solution has moved away from the commonly addressed question of whether induction can be justified and how it can be justified (Musgrave, 2004). Instead, Popper acknowledges Hume's claim that inductive reasoning is logically invalid (Booth, 2004; Musgrave, 2004). Furthermore, Popper proposes that induction should not be employed as a mechanism for scientific knowledge if scientific method is supposed to be rational and only make claims to logically intact knowledge (Booth, 2004). 4
Claiming that scientific inquiry should shift away from universalism to the study of specific events, Popper offered falsificationism as the alternative to induction (Booth, 2004; Lange, 2008). Popper adds that the quest of scientific knowledge is an on-going process of forming conjectures and of rejecting these non-logical 'inductive' laws through falsification (Musgrave, 2004; Lange, 2008). Based on this argument, an inductive conclusion that is incapable of being falsified is considered unworthy of being scientific, and the job of scientists is then to search for observations that will falsify the universal laws being produced and hence refine and evaluate our operational knowledge (Booth, 2004; Lange, 2008). One major fallacy of Popper's argument is that in cases whereby instances to falsify a universal law cannot be found, it will be left sitting on the shelf waiting for a solution since Popper's solution is premised on the conjecture that there exists no justification for universal laws. Moreover, Popper's theory presupposes Hume's principle of the uniformity of nature which cannot be justified, hence it can only be considered as a partial solution to Hume's problem. Claims from Chalmers (1999) and Ladyman (2002) have also demonstrated that the complexities of scientific knowledge through observations and experimentations will require more than one falsification to deny its truth, and that the dependence on historical antecedents as a justification is inadequate. Popper's lack of auxiliary assumptions and the notion of a degree of falsifiability identified by both Chalmers (1999) and Ladyman (2002) is supported by O'Hear (1989), claiming that both probability and repeatability, which are important concepts in scientific inquiry, have not been addressed by Popper's solution. 7.0 Conclusion In conclusion, this essay has revealed that the problem of induction presents itself in two folds, as both descriptive and narrative. While the formal is trivial and can be dealt with by means of a priori knowledge acquired through experience, the latter cannot fully be solved. Hume's questioning of the justifiability of universal laws has introduced scepticism into scientific knowledge and the quest for an answer to his question still persists. To the above, Karl Popper has to be credited with proposing a unique and convincing solution to Hume's narrative problem. Boldly agreeing with Hume that universal laws are illogical and unjustifiable, Popper proposes abandonment of these laws and of the method of induction for that of falsification. In this aspect, Popper asserts that scientific knowledge should not be a 5
collection of truths, but rather a constant readjustment and refinement of our claims to universal knowledge through readapting it to new discoveries in our experiences of everyday life. However, a gap in knowledge exists in every solution, and Popper's argument is not spared from this. A major issue of Popper's proposal is that it has been premised upon Hume's principle of the uniformity of nature, which Popper himself claims cannot be justified, hence introducing a certain degree of circularity to his work. Moreover, issues of probability and repeatability, foundations of scientific inquiry, have also not been discussed through his solution. Despite all these inadequacies, both Popper and Hume have challenged you as the reader to rethink the principle of universal truths. It is up to you to decide if universal law is your cup of tea, or if Russell's (1912, p.81) preference for a collection of individual truths, eloquently expressed as such: " A body of individually probable opinions, if they are mutually coherent, become more probable than any one of them would be individually. It is in this way that many scientific hypotheses acquire their probability. They fit into a coherent system of probable opinions, and thus become more probable than they would be in isolation", better fits your purpose. 6
References Booth, J. (2004), Scientific knowledge: Truth, induction and falsification, Richmond Journal of Philosophy, 7 Chalmers, A. F. (1999), What is the thing called Science?, St. Lucia, Queensland: University of Queensland Earman, J., and Salmon, W. C. (1992), The confirmation of scientific hypotheses, in Salmon, M. H. (editor), Introduction to the philosophy of science, Englewood Cliffs, N.J.: Prentice Hall Hume, D. (1955), An Enquiry Concerning Human Understanding, Indianapolis: Bobbs-Merrill Educational Publishing Ladyman, J. (2002), Understanding philosophy of Science, London; NewYork: Routledge Lange, M. (2008), Hume and the problem of induction, Handbook of the History of Logic, 10, pp. 43-91 Musgrave, A. (2004), How Popper [might have] solved the problem of induction, Philosophy, 79(307), pp. 19-31 O'Hear, A. (1989), Introduction to the philosophy of science, Oxford: Clarendon Press Rodrigues, C. T. (2011), The method of scientific discovery in Peirce's philosophy: Deduction, induction and abduction, Log. Univers, 5, pp. 127 164 Rothchild, I. (2006), Induction, deduction, and the scientific method. An eclectic overview of the practice of science, Cleveland, Ohio: Society for the Study of Reproduction Russell, B. (1912), The Problems of Philosophy, Oxford: Oxford University Press Thilly, F. (1903), The Theory of Induction, The Philosophical Review, 12 (4), pp. 401-411 7