I'm operating under some kind of assumption that there is a Law of Nature ... most influential attempts to tackle this Problem where made by David Hume, Karl.
THE PROBLEM OF INDUCTION A Brief Discussion of Influential Works on the Matter of Induction and its Legitimacy
Joe Robbins Gustavus Adolphus College
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When I pick up a cup of coffee, there is generally a process involved. A very small, unobservable process, but a process nonetheless. I visually observe the cup situated within a certain zone in front of me, I observe stimuli within my own brain chemistry that tell me that coffee is a phenomenon that I have experienced in the past and would very much like to experience again, and of course I have back up observations about how the world works, such as: solid objects such as coffee mugs, tend to remain solid objects, that is, retain their coffee muggishess, until some other force is acted upon them to make them change, like my hand breaking the mug, or the mug being heated at a temperature that makes its proteins denature. With all this data safely in hand, I can make the decision to pick up a cup of coffee. However, even though this vast store of empirical data is being utilized to perform this action, there are assumptions that cannot be accounted for. In order to pick up a mug of coffee, even if I can take all these observations and assume them to be true, I am also making the ancillary assumption that, in the naturally observable, empirically verified world that I live in, objects that have certain characteristics at one point in time will continue to exhibit those characteristics at later points in time. I’m operating under some kind of assumption that there is a Law of Nature
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that exists somewhere that dictates if an object is a certain way, it will continue to be that way until another object acts upon it, and that other object will have its own set of characteristics that allow one to predict exactly how it will affect the object it has acted upon. This is known as the problem of induction, and it has been a topic of much contention in the philosophical community for some time. Three of the most influential attempts to tackle this Problem where made by David Hume, Karl Popper, and David Stove.In this paper I will present a synoptic account of the conclusions these men came to and then articulate my own suppositions on the matter.Now, some background: Hume was a philosopher/economist from Scotland who lived in the first half of the 16th century. 1 Popper was an Austrian professor who was born in 1902 and lived to be 92.2 Stove was an Australian philosopher of science who published most of his works during 1970 to 1980. 3 The point of all that is to demonstrate that these are men from different time periods, countries, and professional backgrounds, all who are grappling with the same question posed roughly two thousand years ago. This shows the importance of the problem to both science and philosophy, and the vast difference in how various thinkers have come to terms with it.4
1
Mossner, E. C. (2001). The life of David Hume. Oxford University Press. p. 206 Stephen Thornton, "Karl Popper", in The Stanford Encyclopedia of Philosophy (Summer 2009 Edition), Edward N. Zalta (ed.) 3 Kimball, Roger.” Who Was David Stove? ". The New Criterion -. January 1, 1997. Accessed March 19, 2015. 4 NOTE: Normally, as part of the discussion of these expert’s theories, the author would include reference to contemporary criticisms of their work; however Stove’s paper is mostly composed of discussing the flaws he 2
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David Hume wrote an extensive composition titled “An Enquiry concerning Human Understanding” that deals exclusively with this Problem and the implications of one’s conclusions about it must have on epistemology. 5 He primarily approaches the issue through the first problem raised by Empiricus; the predictive capacity of induction. In Section 4, page 26, Hume begins his argument by making an observation about the nature of truth: “Matters of fact, which are the second objects of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. The contrary of every matter of fact is still possible; because it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness, as if ever so conformable to reality.” He goes on to explain this using the example of the sun rising. Take this statement, Statement A: The sun will rise tomorrow. Now a second statement, Statement B: The sun will not rise tomorrow. A and B state opposing things, however, Hume says they are not contradictory, that is to say, one is not true and the other false, because even if tomorrow the sun can be observed rising, the statement has the capacity to be false the day after that. Of course it turns out, with the knowledge presently available about how the sun functions, it is plausible, even likely, that there will in fact be a day that A will be perceived in Popper and Hume’s work, therefore criticisms will be addressed there rather than in the section specifically devoted to each one’s theories. 5 Hume, David. "An Enquiry concerning Human Understanding." Davidhume.org. 1777 (original was published in 1748, but the republished version in 1777 with additions and revisions by Hume is what is used here). Accessed March 19, 2015.
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false. What Hume is demonstrating by making this seemingly nit-picky distinction, is that a statements truth is determined by its ability to be observed or recorded empirically in some way. Hume is making the point that on the day he wrote his book and the day I wrote this, the sun had in fact risen, but since Statement A used the word “tomorrow”, it could not be evaluated for truth. That is, it was unobservable. The only way any scientist or philosopher could evaluate the statements for truth is to make an inference, that is, the sun has been observed rising with much regularity and precision for an extended period of time, therefore Statement A can be assumed to be more likely to be true than Statement B. On page 27 of Section 3, Hume makes another distinction: that inductive inferences are not an a priori form of reasoning, or, without experience people would not make these inductions, whereas reasoning, or logic, is a priori knowledge that can be shaped by experience, but is not dependent on it. In this way, Hume is separating reason and induction into two different modes of knowledge production. Finally Hume addresses possible justifications for induction. 6 He asserts that unless a deductive rationalization can be found in support of induction, it cannot be called a valid form of reasoning. He goes on to contest one possible deductive justification, the idea of statistical probability. His reasons why this answer can easily fall into the same circularity of the Problem are best explained by an
6
See footnote five, E 7.30, SBN 78-79 of the same.
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example. Say one rolls a five-sided die and does not want to roll a five. Now a mathematician would say “roll the dice, you only have a 20% chance of rolling a 5”. Hume would say this is actually false. Hume would posit that the logical probability of rolling a five in one roll is actually 50-50. It is 50-50 because there are two options, rolling a five or not rolling a five and regardless of statistical probability there’s no way to say what the outcome will be, other than five or not five. Of course one would expect that since it is only one option out of five, one could roll five times and expect to only get five once. However, if one asked the mathematician from before, who has been following along and is justifiably seething with rage at this point, if it would be possible to roll said die five times and get five every time, they would have to say yes. In fact, if you asked this mathematician if it would be possible to roll this die 1,987 times and get a five every time, the mathematician would again have to say, albeit through gritted teeth, yes. Which begs the question: what does the statistical probability actually say about the dice roll? It definitely says something, and Hume accepts the pragmatic value of induction as valid, but the arguments he puts forth make it hard to assume that the statistical probability can say anything about the truth, in a logical sense, about the statement: One will not roll a five with this die. Hume, therefore, only allows for induction as a pragmatic tool if it employs logical probabilities as a deductive justification for the inference being made.
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One of the most thorough and controversial works on the Problem is Karl Popper’s “The Logic of Scientific Discovery”. 7 8 He addresses the issue by condensing the Problem down to a matter of empirical truth and non-empirical truth. He states: “principle of induction would be a statement with the help of which we could put inductive inferences into a logically acceptable form. In the eyes of the upholders of inductive logic, a principle of induction is of supreme importance for scientific method….To eliminate it from science would mean nothing less than to deprive science of the power to decide the truth or falsity of its theories. Without it, clearly, science would no longer have the right to distinguish its theories from the fanciful and arbitrary creations of the poet’s mind.” 9 In order to have induction, this principle of induction must be attained through deductive reasoning, which is what Hume also observed. In fact, the whole first half of Popper’s book is essentially rehashing Hume’s theories and strengthening them. Where Popper diverges from Hume, is in his conclusion: ‘The theory to be developed in the following pages stands directly opposed to all attempts to operate with the ideas of inductive logic. It might be described as the theory of the deductive method of testing, or as the view that a hypothesis can only be
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Popper, Karl R. The Logic of Scientific Discovery. 1st English ed. London: Routledge, 2002 (digital publication of 1980 print publication, exact copy). 8 Also one of the best book covers. 9 See footnote 7, Part 1, Chapter 1.1, page 4 of the same.
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empirically tested —and only after it has been advanced.”10 So Popper strengthened Hume’s analysis to the point where he actually decides to scrap the entirety of inferential science and begins to form the idea of a deduction-only scientific method. This method is actually very thoroughly explained and reasoned out, however just a brief synopsis of how it functions is necessary for the purposes of this paper. Popper starts by laying out the one exception to his all-deductive system. He allows for the creation of hypotheses through non-deductive means. 11 For example, when a former patent officer “discovers” the theory of relativity while looking at the reflection of his sailboat moving through the water, this is not deduction, but something else, something beyond deduction.12 Once this is out of the way, Popper goes on to explain his method: that a theory is tested until it is falsified. If it is falsified, then it can be said to be false; if it is not, then it can only be said to be not yet falsified. A theory may be put into practice, or allowed to have pragmatic applications if it is subjected to A) strict tests and B) many strict tests.13 He then lays out criteria for evaluating the stringency of tests, such as simplicity, probability of negative outcomes, and ease of falsification.14 He goes into great detail addressing these criterion and the logicality of their various applications, but most of them are reasonably intuitive and are not significantly different than any 10
See footnote 7, Part 1, Chapter 1.1, page 6 of the same. See footnote 7, Part 1, Chapter 1.2, of the same 12 Inspiration perhaps? Popper cites Henri-Lois Bergson’s idea of “creative intuition” and leaves it at that. 13 See footnote 7, Part 1, Chapter 1.3 of the same. 14 See footnote 7, Part 2, Chapter 4-8, 10 of the same. 11
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other way of determining quality of a scientific experiment, other than perhaps the notion of falsifiability. If a theory is easily falsifiable it can said to be a “good” theory under a normative scientific paradigm simply because it lends itself to easy experimentation. Popper holds that this property can actually speak to the validity of a scientific theory because if it is easy to falsify a theory and then it is tested and not falsified, then that makes it better than other theories. Again, Popper would not say this is positive evidence in support of the theory, but a reason to prefer it over other theories nonetheless. This begs the question of whether or not a reason to prefer a theory over another is actually different than positive evidence, but Popper wholeheartedly believed it was a valid distinction. While Popper claims to do away with the scientific method and create a new one, his model only differs significantly in the manner in which the conclusions of these tests are interpreted. An important preface to any discussion of Stove is to point out two things: first that Stove was a very big proponent of Hume’s work, and second, he very much enjoyed critiquing philosophical work, and he essentially made a career out of literary critique, and delighted even when he found inconsistencies in Hume’s works.15 Stove first critiques Hume’s acceptance of logical probability as a way to justify induction. “Stove points out, once you accept the principles of logical probability then any statement of logical probability will commit you to an
15
Kimball, Roger. 1997. "Who was David Stove?" New Criterion 15, no. 7: 21. EBSCO MegaFILE, EBSCOhost
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indefinitely large class of other such statements; moreover these are so connected, as Stove’s argument shows, if one makes a skeptical judgement at one point one may be bound to accept credulous judgements at others. This is the trap in which he catches Hume (and, to the extent that other sceptics must embrace Stove's formulation of Hume, those sceptics also)” 16 The problem here that Stove is pointing out, is that Hume acknowledges the relatively obvious fact that, regardless of logical validity, induction is pragmatic. It is usable and accurately so. To explain this, he developed the idea of logical probability discussed earlier. Stove points out that this fails to break the cycle of circularity of the Problem. Now Stove’s conclusion here is not that Hume was mistaken because he should have rejected both logical probability and statistical probability, but that Hume’s reasoning behind making this distinction, pragmatism, is strong enough to stand alone and answer the Problem. This is where he attacks Popper’s conclusions; he says that while it is difficult to deductively justify induction, deduction and induction are two different things. Stove makes the claim that induction is a form of knowledge production, in that “new” thoughts are produced and tested, whereas deduction is not a form of knowledge production at all, but rather a way of reordering knowledge that is already available to be seen differently. He also employs Carnap’s idea of intuition as a logical way of justifying things like statistical 16
Hooker. A. Clifford. April, 1975 “Review of Probability and Hume’s Inductive Skepticism” Hume Studies Volume 1, Issue 1 (accessed March 18, 2015).
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probability and the ability of subsets to relay accurate information about whole groups.17 Stove says that normative scientific networks are intuitively justified, and therefore the discussion of induction in terms of deduction is maybe not moot, but unnecessary.
Conclusion While all these very smart men have written very smart things about this subject, none have definitively answered the question. In this case, a definitive answer would be one that preempts the question; causing it to be no longer asked. If one was reading this paper under the assumption that somewhere hidden in its paragraphs would be such an answer, I am afraid they would be disappointed. I can do no more than the fine gentlemen before me; illustrate how I have answered the question for myself so that I no longer need to puzzle about it, and hope it does the same to you or at least speed you on your way to finding your own answer. An easy reply that many philosophers of science have offered is that inductive reasoning is intuitive; the human mind for some reason accepts it as valid and so that in itself lends legitimacy to the concept. A breakdown of the intuitivism of inductive reasoning is one reason that I would suggest that inductive reasoning can be found to be logically valid. Here is an illustration of the logical intuitionism
17
Vickers, John, "The Problem of Induction", The Stanford Encyclopedia of Philosophy (Fall 2014 Edition)
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entailed by inductive reasoning: say there is an ecosystem populated only by geese and flamingos. In order to in some way predict the behavior of this ecosystem, a study is conducted using a small portion of the population. Now, this study aims to test behaviors of a sample population and then, through inductive reasoning, use the conclusions of this test to make statements as to the behavior of the population as a whole. Intuitively, this process would not seem problematic, in fact it seems quite legitimate. Now, borrowing a bit from Popper’s philosophy here, let us ask: what would it take to make this process seem intuitively illegitimate? What if the study was conducted only using flamingos? Right away this seems, again intuitively, illogical. This example reveals a logically intuitive “law” of inductive reasoning: that a sample set must be representative of a whole population if conclusions about behaviors of that sample set are to be inferred onto the whole population. Now, how does this intuitive logic implicate a discussion of inductive reasoning as logically legitimate? Let us engage momentarily in some formal logic. Returning to the earlier example, let us refer to the ecosystem containing only flamingos and geese as Set A. The goal of the experiment conducted is to prove that set A has Characteristic X. Now, in order to use inductive reasoning to prove this, a sample set must be tested that is perfectly representative of population A. This sample set will be called Set a. Since Set a is perfectly representative of Set A, Set A could be depicted as follows: Set A= {a,a,a,a,a,a,a,a…}. If the experiment
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could then demonstrate that Set a has Characteristic X, it is absolutely logical to say that Set A, being completely made up of Set a’s, also entails Characteristic X. Of course most will make the observation that it is impossible to obtain a perfectly representative sample set. This is a flaw I believe that I can freely admit to without compromising the logical integrity of the inductive reasoning being used. The reason for this is twofold. The first reason I believe I can get away with this is because the testing model can predict its own margin of error. This Set A idealization is of course not realistic, but in a well-constructed study, the ideal/perfectly representative Set a can be compared to the realized Set a. The points at which the realized Set a deviates from the ideal Set a can be catalogued and used to predict where and to what degree the inference will not be applicable. If the Set a only includes flamingos and excludes geese, then the study can accurately say 50% of Set A has Characteristic X. Indeed, all of formal logic deals with idealization. One would be hard pressed to find a tautological statement outside of an idealized formal logic system. The point at which formal logic becomes useful is when it is held up to realized systems and, measuring points of departure between the two, can be used as a standard of truth. This is not different than the use of inductive reasoning illustrated above, and seems to be standalone confirmation that inductive reasoning is legitimate. Another common attack on inductive reasoning is the temporality argument. This is illustrated by the
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Humerian example of the sun rising day after day, with the inference being that since the sun has risen every day in the past, it will continue to behave in a similar manner tomorrow. I have two responses to this, which may very well contradict each other. I advance both of them as possible solutions to the logical challenge of this reasoning, not to be evaluated in tandem, but to be considered as two separate possibilities. The first is this: predictive statements are not subject to deductive logical analysis. The idea in question is that inferential statements about the future are illegitimate because of their inductivity. I would make the claim that deductive logic behaves in a way that is inherently atemporal. To illustrate this, I will unapologetically use the classic example: All men are mortal> Socrates is a man.> Therefore, Socrates is mortal. Deduction takes the general statement, all men are mortal, to derive its conclusion. Now this begs the question, does the phrase “all men” make a temporal claim? If it does, the temporal claim would be either “All men that have existed are mortal”, or “All men that have existed and all men that will exist in the future are mortal”. If it is the first case, then the distinction between inductive claims and deductive claims would be arbitrary. If inductive reasoning only lays claim to things that have happened already then there is nothing predictive about it. . If it is the second case, then as far as deductive logic is concerned, the future does not exist; things that happen in the future cannot be
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said to be logical or illogical from a deductive standpoint because deductive logic cannot account for it. This will be discussed in more detail in my next point. Now if deductive reasoning makes the second temporal claim, than clearly it is no different than inductive logic in that it assumes the future to be consistent with the past. My second point has something to do with the first case above: that deductive reasoning cannot evaluate future events. The concept is most easily explained visually. 18 Picture a number line, representing the passage of time, with plot points on it representing events and all of the facts that those events entail. The center of this line is point P, which is the present. This is the point at which claims are made. Behind point Pare points A, B, and C, all representing events in the past that entail facts and characteristics. For example, A, B, and C, are all of the mortal men (of which there are only three in this case), Phillip, Johnny, and Bob. The person making a claim at point p can observe Phillip, Johnny and Bob and make claim X: since all men are mortal, and Phillip is a man, he must be mortal. On this number line, ahead of point P, are points Q and R. Point Q, is an inductive conclusion made by a person at point P, and point R represents all other possible conclusions. The person at point P observes A, B, and C and makes the claim that; since all men are mortal, if another man is born in the future, let’s call him
18
Figure 1, after Bibliography
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Quentin, he will be mortal. Point R, represents a Quentin that is immortal, or anything that is not mortal. The reason past attempts at deductively evaluating inductive reasoning have failed is because they attempt claim-based evaluation. Deductive reasoning starts at point P and looks back; if it cannot find point Q behind point P somewhere, it cannot possibly evaluate it. What happens if we wait? Point P represents the present, so of course as time passes point P moves up the number line, eventually passing points Q and R. At that juncture, deductive lists can look back behind point P and observe either point Q or point R. This means that at some point, it is possible to deductively prove what was at one point an inductive claim. Alternatively, one can see that claim-based evaluation of inductive reasoning fails because of course at point P it is impossible for deductive reasoning to account for anything to the right of it. The rules of logic are quite clear about things that are not able to be evaluated are not necessarily false; in fact, they are considered true. While I do not make the claim that this inability is not positive reason to validate inductive reasoning, it is enough to delegitimize the claim-based evaluation technique. That leaves us to look for alternative evaluation strategies, more specifically, warrant-based evaluation. Both conclusions made at point P, deductive claim X, and inductive claim Q, use data point A, B, and C to derive their conclusions. From this perspective, one can absolutely deductively validate
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an inductively derived claim. From a deductive standpoint, there are infinite unknown futures, and induction divides tis infinity into two zones; one zone being the future depicted by inference Q, and a second zone that includes all other futures; point R. A deductivist then evaluates zone Q, and if zone Q is compatible with data A, B, and C (which of course is how accurate inductive claims are made), then the deductivist can confirm that Q is logically valid.
Bibliography Bett, Richard, "Pyrrho", The Stanford Encyclopedia of Philosophy (Winter 2014 Edition) Accessed March 18, 2015. Hooker. A. Clifford. April, 1975 “Review of Probability and Hume’s Inductive Skepticism” Hume Studies Volume 1, Issue 1. Accessed March 18, 2015. Hume, David. "An Enquiry concerning Human Understanding." Davidhume.org. 1777 Accessed March 19, 2015. Accessed March 18, 2015. Kimball, Roger. 1997. "Who was David Stove?" New Criterion 15, no. 7: 21. EBSCO MegaFILE, EBSCOhost. Accessed March 19, 2015. Mossner, E. C. (2001). The life of David Hume. Oxford University Press. p. 206 Accessed March 18, 2015. Popper, Karl R. The Logic of Scientific Discovery. 1st English ed. London: Routledge, 2002 (digital publication of 1980 print publication, exact copy). Accessed March 19, 2015.
Robbins 17 Stephen Thornton, "Karl Popper", in The Stanford Encyclopedia of Philosophy (Summer 2009 Edition), Edward N. Zalta (ed.) Accessed March 18, 2015. Vickers, John, "The Problem of Induction", The Stanford Encyclopedia of Philosophy (Fall 2014 Edition) Accessed March 19, 2015.
