This essay discusses whether inductive reasoning is justifiable in both science and philosophy in order to provide a qualitative analysis on the topic given. It first gives a simple introduction of Hume's problem of induction and clarifies some key definitions used in this essay. In the body paragraph, this article provides several evidences and arguments to support the thesis to a certain extent. It illustrates the contributions of inductive reasoning done to the field of science, meanwhile it also shows that problem of induction is still an ongoing dispute among contemporary philosophers. With the aid of some examples, this essay also illustrates many counter-arguments to refute the thesis. It also points out that the glory today may change to scandal tomorrow, and vice versa. In the conclusive part, the article agrees with the thesis question to a large extent but it also leaves some room for opposite opinion to stand.
'Induction is the Glory of Science but the Scandal of Philosophy'. Discuss.
The thesis is based on the oft-quoted aphorism by C.D. Broad in year 1926. These well-known words had summarized the key conflict of the inductive methodology between science and philosophy. In the field of science, especially empirical science, inductive reasoning has long been the most effective and dominating method widely applied. It seems to remain the fact that induction is capable to make science triumphant in the future and evermore. On the other hand, the "problem of induction", first introduced by David Hume in the eighteenth century, had been under heated debate among philosophers and natural scientists for centuries. Numbers of philosophers have made lots of effort in solving the problem but in the end there are still no commonly accepted answers to it, although some inspired attempts had been made to solve this problem. It is undeniable that the problem of induction has puzzled philosophers ever since its first day. These facts did tell us that inductive reasoning had been beneficial to science but problematic to philosophy, but it also would mislead us to a cursory agreement with "induction is the glory of science but scandal of philosophy" without proper analysis. Therefore in this essay, a further discussion will be given based on the problem of induction.
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Before any formal discussions, the meaning of induction has to be clearly elucidated to remove any confusion in this essay. Although the so-called "problem of induction" was posed by Hume, the term "induction" appeared rarely in any of his published books, journals and papers. Traditionally, Aristotle denoted "induction" as a progression from particulars to a universal. But Hume mainly used "inference" instead of "induction" and gave a broader meaning to it which includes all the non-demonstrative reasoning founded on experience (Hume, D., 1777). Inductive reasoning here means reasoning about matters of fact. Briefly speaking, induction could even help people derive unobserved fact from the observed instances. Suppose that we have observed numerous objects with property X and all of them also have property Y, it is natural or even instinctive for us to conclude that all objects with X also possess Y including those objects with property X that have yet to be observed. A famous example can be seen from: All Ravens examined so far are black, so we can conclude that all Ravens are black or the next Raven to be examined will be black. Moreover, self-evident statements (axioms) were excluded from the usage of induction. The conclusion of such reasoning is logically implied by the premises, such as self-defined statement "No bachelor is married", complete enumeration "1+1=2" and so on. Hence in my discussion, the usage of "induction" is the same as Hume's of "inference".
Almost all the sciences, from main streams to side branches, have been adopting inductive reasoning as one of the most important and fundamental methodologies. Empirical scientists even used to believe that induction was the only way to discover and answer so many "What"s and "Why"s. The famed Caltech physicist Richard Feynman lauded induction in saying that, "Experiment is the sole judge of scientific 'truth'" (Feynman et al, 1963) Together with deduction, inductive method had really made loads of contributions to the scientific area in the modern world. The basis of scientific method is making observations, sometimes in the form of experiments. When the observation is confirmed by many competent observers, it can become a fact. A scientific hypothesis must not only link existing observations and facts, but suggest new observations (predictions). If a hypothesis that describes/explains how nature works survives many experimental tests (observations), it may become a law/theory. The above depiction, though is oversimplified, has summarized the key steps of how inductive reasoning works as a scientific method. Observation of nature is the authority in scientific studies, therefore "the sun will always rise tomorrow" for scientists.
However, for many philosophers and logicians, tomorrow might be completely dark without sunrise. Ever since he posed his problem of induction, Hume believed that it was unjustifiable to presuppose that future (unknown) will be similar to the past (known). He also argued that no inductive argument is able to ever justify uniformity of nature because every inductive argument employs uniformity of nature as a premise (Hume, D., 1777). To a large extent, this problem remains to be a scandal of philosophy because there is still no solution in sight nor even a consensus about what a possible solution could look like, although we believe we understand Hume's problem much better today. Along the history, there were many famous and brilliant thinkers trying to justify induction and bring back this glory to philosophy. For example, some philosophers had argued that the inductive premise can be supported by inductive evidence. Frederick L. Will agreed that past observations can serve as an evidence for its authenticity by pointing out a concealed ambiguity on the word "future" in the problem of induction (Wills, F. 1947). However, this response to the problem is entirely unsatisfactory as rebutted by BonJour stating that proving induction premises inductively would lead to an infinite regress in which the actual justification of the first-level induction is indefinitely deferred (BonJour, L. 1998).
Inductive reasoning is an instinctive action of human logic system. Human beings have been adopting inference, sometimes called educated guess, for ages even before they realized its underlying problem. It has been so many years for us to apply induction as an obstinate habit regardless of how the human race began, evolved from apes or created by the God. A case in point can be seen from the famous remarks of Rene Descartes that "it is truth very certain that, when it is not in our power to determine what is true, we ought to follow what is most probable" (Lafleur, J. 1960). This celebrated quote was defended more recently by Wesley Salmon in order to provide a reasonable justification from a pragmatic point of view (Salmon, W. 1978). Wesley pointed out that it is a wiser "bet" to choose inductive reasoning than any other experience-based methods, because inductive logic has a higher chance of success compared to other alternative means as long as the inductive principle is true. This response to the problem seems to be creative and rational; nevertheless, in my point of view, it is still improper. The statement is pragmatically correct but it does not imply an epistemic justification. This means, while it may serve as an incentive for us to think inductively, it still does not show the actual successful rate of induction. That is to say, the number of observed cases is always finite and that of unobserved ones is possibly infinite, hence the probability may never reach anything close to unity. A real solution to get rid of this scandal requires an epistemic justification. It still remains a fact that no satisfactory solutions have been drawn to justify inductive inferences; in this sense, induction is still the scandal of philosophy.
There are numerous criticisms as well as praises heaped upon the inductive reasoning, but we will be blind from the other side of the coin if we completely accept the opinions from a single side. The answer to the problem of induction is uncertain; this determines that we have to believe it with a skeptical attitude. Ironically, it is paradoxical to conclude that induction is still the glory of science and scandal of philosophy in the future, because we could not look at the past to predict the future.
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As mentioned previously, inductive logic seems like the most effective way to perform science. Very often, scientific experiments work in an opposite fashion. Albert Einstein commented that "the really great progress of natural science arose in a way which is almost diametrically opposed to induction" (Einstein, A. 1919). If this is true, is the induction still a glory of science? To a certain extent, inductive inference may slow down the scientific development. For instance, in early days many scientists were reluctant to accept the fact of discovery of a positron (positively charged electron), as their inference told them that electron could only be negatively charged in order to balance with the positively charged nucleus and make the whole atom neutral. Inductive reasoning therefore hinders people from thinking outside the box. When a new observation violates the old principles which are established on past experience, the first thing on one's mind is to question and even reject this observation. The chemical composition of water now is H2O but no one can be absolutely certain that this composition will not change in the future, say a million years' time. The water at that time is possibly in the form of X2Y-only God knows. This may turns out to be that no scientific theory based on induction can be absolutely true but only tentatively validated. It is not rare that induction might lead to underdetermination thesis, especially in the scientific study of some unknown instances. The point can be demonstrated by the following example: There is a sequence 2, 4, 6, 8, 10â€¦, what will be the next number? We may guess inductively that the 6th number is 12, and this intuitive assumption is based on our inference from the common sense of arithmetic sequence. However, such educated guess is extremely risky if no "true" premise is given in advance, e.g. the 6th number could be 132 as well if the sequence follows as f(n)=2n+(n-1)(n-2)(n-3)(n-4)(n-5). In other words, this example of the mathematical formula illustrates that there can be infinite number of distinct futures to be found on the basis of an identical past. The reality is crueler for empirical science than that for mathematics. Mathematics deals with relations of ideas so that concrete premises and conclusions could be derived from various methods such as contradiction. But the essence of empirical science is matters of fact-nothing is capable of certifying the given premise. In empirical science, the premise of an inductive argument can never warrant its conclusion, so it is still finitely possible that, inductive logic may cease to become the glory of science right after tomorrow.
It is apparent in the foregoing discussion that no ultimate vindication has been provided to free induction from the scandal of philosophy. But a complete denial of the inductive reasoning from a philosophical perspective must be cursory and inadequate. I am not fully convinced by Hume's conclusion to the problem of induction, which has stated that we have no good reason to justify the induction. Personally I do acknowledge the difficulties in solving the problem, but I strongly believe that it is not insurmountable. Similar to the progress of proving Goldbach Conjecture by mathematicians, the problem of induction may be conquered by philosophers someday in the future. The principle of the uniformity of nature is not a simple conception that can be proven in finite steps. Before we can thoroughly interpret this principle, it is only a belief or even a faith for us. In fact, Euclidean geometry and Newtonian mechanics, before the discovery of the more updated and advanced theories (Non-Euclidean geometry and Einstein's relativity), were all kinds of scientific beliefs. Mankind was born and designed to think inductively (also deductively). This nature of human beings, to a certain extent, determines that inductive reasoning is reasonable in the eyes of Mother Nature. Although problem of induction has been an unsolved riddle in philosophy, inductive reasoning had provided considerable amount of topics to be studied by philosophers. A very well-known lemma in point was by Rene Descartes: Cogito ergo sum (I think, therefore I am), which was based on inductive reasoning. Today there are many philosophers like Descartes who are applying inductive method to the study and understanding of philosophical issues. Therefore it is probable for philosophy to embrace the inductive method in a day not far away.
Last but not least, if there is a way to evade the problem of induction, then it would become pointless to distinguish between glory and scandal. Karl Popper (Popper, K. 1979) raised such arguments stating that science, instead of being inductive, proceeds only deductively by "conjectures and refutations". He also listed down some non-sciences, such as Astrology and Alchemy, to counter the argument of "the hallmark of science is observation". If this is true, induction would no longer be the glory of science since science is free of induction from this perspective. But Popper's response contributed so little to the justification of inductive reasoning because it was actually begging the question rather than solving it. The problem of induction asks whether it is reliable to predict future occasions on the basis of past events, while Popper indicated that scientific theories or predictions can be demonstrated to be wrong by former observations.
From the foresaid arguments, I have shown that attitudes towards the inductive reasoning may vary from one extreme to another. With further analysis of each response, almost all of them can fall into the three prevail categories: first, approve Hume's conclusion as a basis for skepticism; second, find suitable approaches to strengthen inductive arguments; third, oppose to the construction of the "problem of induction". None of these stands is absolutely correct or essentially wrong, since there is no flawless argument to solve or dissolve the problem of induction. But I am a person who inclines to take the skeptical point of view. From our past experience, induction might be the glory of science and the scandal of philosophy, and the only thing I can conclude is that this situation will be very likely unchanged but there is still a chance to overturn. No matter what the result is, we will not stop ourselves from reasoning inductively because it has been an unjustifiable habit for us to assume the future will resemble the past. In conclusion, it is regrettably to say that there currently has no feasible solutions to the problem of induction, but this does not mean that all the effort put into is going to be futile. Maybe someday inductive reasoning is justified so that we could confidently yell out "induction is the glory of both science and philosophy".
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