- Problem of induction
- 2. Reconstruction
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- Problem of induction | imuwenikywax.tk
The question posed by Hume is: What rational justification is there for making this inference? More generally, what reason do we have to believe that our conclusions about observed instances may be extended even with probability to include unobserved instances? The same basic question is most frequently framed in temporal terms: What reason do we have to think that we can draw reliable conclusions about future unobserved instances on the basis of past observed instances?
The need for such an answer is immeasurable, since the majority of scientific research is based on inductive reasoning — not to mention most of our everyday inferences about what to expect in the world. I will also briefly explain why each of these attempts is unsuccessful. The reasoning of such a reply may be spelled out in more detail as follows. Whenever we have observed instances in the past, and have drawn conclusions about at that time future unobserved instances, our conclusions invariably turn out later to be confirmed via direct observation i.
Since it has always been the case that unobserved instances have been found to resemble observed instances, we can confidently conclude that at least probably all unobserved instances will resemble observed instances. The trouble with this answer, as Hume was at pains to point out, is that it begs the question. The reply itself takes the form of an inductive argument — reasoning about the future on the basis of the past — and thus must presuppose the very thing it aims to establish: the inductive principle.
It is therefore guilty of fallacious circular reasoning. As Hume succinctly puts it: 1. To say [the inference that the future will be like the past] is experimental [i. For all inferences from experience suppose, as their foundation, that the future will resemble the past, and that similar powers will be conjoined with similar sensible qualities.
If there be any suspicion that the course of nature may change, and that the past may be no rule for the future, all experience becomes useless, and can give rise to no inference or conclusion. It is impossible, therefore, that any arguments from experience can prove this resemblance of the past to the future; since all these arguments are founded on the supposition of that resemblance.
Frederick L. Will has provided no answer. Furthermore, second-level induction can be justified via a third-level inductive argument applied to second-level arguments , and so forth as required. This response to the problem, while creative, is entirely unsatisfactory. As BonJour notes, not only does it lead to an infinite regress in which the actual justification of the first-level induction is indefinitely deferred , but it also misses the point. Popper argues, rightly, that a scientific theory involving predictions about future instances can indeed be shown to be false by present or past observations.
Lange Proponents of this point of view point out that even deductive inference cannot be justified deductively. Achilles is arguing with a Tortoise who refuses to perform modus ponens. The Tortoise accepts the premise that p , and the premise that p implies q but he will not accept q. How can Achilles convince him? But the Tortoise is still not prepared to infer to q. Achilles goes on adding more premises of the same kind, but to no avail.
It appears then that modus ponens cannot be justified to someone who is not already prepared to use that rule. It might seem odd if premise circularity were vicious, and rule circularity were not, given that there appears to be an easy interchange between rules and premises. After all, a rule can always, as in the Lewis Carroll story, be added as a premise to the argument.
But what the Carroll story also appears to indicate is that there is indeed a fundamental difference between being prepared to accept a premise stating a rule the Tortoise is happy to do this , and being prepared to use that rule this is what the Tortoise refuses to do. Still, a possible objection is that the argument simply does not provide a full justification of X. After all, less sane inference rules such as counterinduction can support themselves in a similar fashion.
The counterinductive rule is CI:. Therefore, it is not the case that most CI arguments are unsuccessful, i. This argument therefore establishes the reliability of CI in a rule-circular fashion see Salmon Argument S can be used to support inference X , but only for someone who is already prepared to infer inductively by using S. It cannot convince a skeptic who is not prepared to rely upon that rule in the first place. One might think then that the argument is simply not achieving very much.
The fact that a counterinductivist counterpart of the argument exists is true, but irrelevant. It is conceded that the argument cannot persuade either a counterinductivist, or a skeptic. Nonetheless, proponents of the inductive justification maintain that there is still some added value in showing that inductive inferences are reliable, even when we already accept that there is nothing problematic about them. The inductive justification of induction provides a kind of important consistency check on our existing beliefs. It is possible to go even further in an attempt to dismantle the Humean circularity.
Maybe inductive inferences do not even have a rule in common. What if every inductive inference is essentially unique? Norton puts forward the similar idea that all inductive inferences are material, and have nothing formal in common Norton There have long been complaints about the vagueness of the Uniformity Principle Salmon The future only resembles the past in some respects, but not others. Suppose that on all my birthdays so far, I have been under 40 years old. This does not give me a reason to expect that I will be under 40 years old on my next birthday. He might have explained or described how we draw an inductive inference, on the assumption that it is one we can draw.
But he leaves untouched the question of how we distinguish between cases where we extrapolate a regularity legitimately, regarding it as a law, and cases where we do not. Goodman considers a thought experiment in which we observe a bunch of green emeralds before time t.
We could describe our results by saying all the observed emeralds are green. Using a simple enumerative inductive schema, we could infer from the result that all observed emeralds are green, that all emeralds are green. But equally, we could describe the same results by saying that all observed emeralds are grue. Then using the same schema, we could infer from the result that all observed emeralds are grue, that all emeralds are grue. In the first case, we expect an emerald observed after time t to be green, whereas in the second, we expect it to be blue.
Thus the two predictions are incompatible. One moral that could be taken from Goodman is that there is not one general Uniformity Principle that all probable arguments rely upon Sober ; Norton ; Okasha , a,b. Rather each inductive inference presupposes some more specific empirical presupposition. A particular inductive inference depends on some specific way in which the future resembles the past. It can then be justified by another inductive inference which depends on some quite different empirical claim.
This will in turn need to be justified—by yet another inductive inference. There is no circularity. Rather there is a regress of inductive justifications, each relying on their own empirical presuppositions Sober ; Norton ; Okasha , a,b. Hume says that there exists a general presupposition for all inductive inferences, whereas he should have said that for each inductive inference, there is some presupposition.
Different inductive inferences then rest on different empirical presuppositions, and the problem of circularity is evaded. Here different opinions are possible. On the one hand, one might think that a regress still leads to a skeptical conclusion. So although the exact form in which Hume stated his problem was not correct, the conclusion is not substantially different Sober Another possibility is that the transformation mitigates or even removes the skeptical problem. For example, Norton argues that the upshot is a dissolution of the problem of induction, since the regress of justifications benignly terminates Norton It is also necessary to establish that inductive inferences share no common rules—otherwise there will still be at least some rule-circularity.
Okasha suggests that the Bayesian model of belief-updating is an illustration how induction can be characterized in a rule-free way, but this is problematic, since in this model all inductive inferences still share the common rule of Bayesian conditionalisation. Hume is usually read as delivering a negative verdict on the possibility of justifying inference I , via a premise such as P8. There are however some who question whether Hume is best interpreted as drawing a conclusion about justification of inference I at all we will discuss these interpretations in section 5.
There are also those who question in different ways whether premise P8 really does give a valid necessary condition for justification of inference I sections 5. Some scholars have denied that Hume should be read as invoking a premise such premise P8 at all. The reason, they claim, is that he was not aiming for an explicitly normative conclusion about justification such as C5.
However, one could think that there is no further premise regarding justification, and so the conclusion of his argument is simply C4 : there is no chain of reasoning from the premises to the conclusion of an inductive inference. The thesis is about the nature of the cognitive process underlying the inference. For Owen, the message is that the inference is not drawn through a chain of ideas connected by mediating links, as would be characteristic of the faculty of reason.
Under this interpretation, premise P8 should be modified to read something like:. The question of how expansive a normative conclusion to attribute to Hume is a complex one. The question is then whether this alternative provides any kind of justification for the inference, even if not one based on reason. On the face of it, it looks as though Hume is suggesting that inductive inferences proceed on an entirely arational basis.
He clearly does not think that they do not succeed in producing good outcomes. It is also not clear that he sees the workings of the imagination as completely devoid of rationality. For one thing, Hume talks about the imagination as governed by principles. Thus, there may be grounds to argue that Hume was not trying to argue that inductive inferences have no rational foundation whatsoever, but merely that they do not have the specific type of rational foundation which is rooted in the faculty of Reason.go to site
Problem of induction
And thus there is also room for debate over exactly what form a premise such as premise P8 that connects the rest of his argument to a normative conclusion should take. No matter who is right about this however, the fact remains that Hume has throughout history been predominantly read as presenting an argument for inductive skepticism. Even if one does attribute a normative conclusion to Hume, one may question his argument by asking whether premise P8 is true.
This can prompt general reflection on what is needed for justification of an inference in the first place, and what Hume is even asking for. For example, Wittgenstein raised doubts over whether it is even meaningful to ask for the grounds for inductive inferences. If anyone said that information about the past could not convince him that something would happen in the future, I should not understand him. One might ask him: what do you expect to be told, then?
What sort of information do you call a ground for such a belief? Wittgenstein One might not, for instance, think that there even needs to be a chain of reasoning in which each step or presupposition is supported by an argument. Wittgenstein took it that there are some principles so fundamental that they do not require support from any further argument. Entitlement provides epistemic rights to hold a proposition, without responsibilities to base the belief in it on an argument. Crispin Wright has argued that there are certain principles, including the Uniformity Principle, that we are entitled in this sense to hold.
Some philosophers have set themselves the task of determining a set or sets of postulates which form a plausible basis for inductive inferences. Bertrand Russell, for example, argued that five postulates lay at the root of inductive reasoning Russell Arthur Burks, on the other hand, proposed that the set of postulates is not unique, but there may be multiple sets of postulates corresponding to different inductive methods Burks , The main objection to all these views is that they do not really solve the problem of induction in a way that adequately secures the pillars on which inductive inference stands.
Rather than allowing undefended empirical postulates to give normative support to an inductive inference, one could instead argue for a completely different conception of what is involved in justification. Like Wittgenstein, later ordinary language philosophers, notably P.
Strawson, also questioned what exactly it means to ask for a justification of inductive inferences Strawson Strawson points out that it could be meaningful to ask for a deductive justification of inductive inferences. Rather, Strawson says, when we ask about whether a particular inductive inference is justified, we are typically judging whether it conforms to our usual inductive standards. Strawson says that if that person is asked for their grounds or reasons for holding that belief,. In saying this, he is clearly claiming to have inductive support, inductive evidence, of a certain kind, for his belief.
Strawson That is just because inductive support, as it is usually understood, simply consists of having observed many positive instances in a wide variety of conditions. In effect, this approach denies that producing a chain of reasoning is a necessary condition for justification. Rather, an inductive inference is justified if it conforms to the usual standards of inductive justification. But, is there more to it? Might we not ask what reason we have to rely on those inductive standards?
It surely makes sense to ask whether a particular inductive inference is justified. But the answer to that is fairly straight-forward. Sometimes people have enough evidence for their conclusions and sometimes they do not. Does it also make sense to ask about whether inductive procedures generally are justified? Strawson draws the analogy between asking whether a particular act is legal.
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We may answer such a question, he says, by referring to the law of the land. But it makes no sense to inquire in general whether the law of the land, the legal system as a whole, is or is not legal. For to what legal standards are we appealing? It is an analytic proposition that it is reasonable to have a degree of belief in a statement which is proportional to the strength of the evidence in its favour; and it is an analytic proposition, though not a proposition of mathematics, that, other things being equal, the evidence for a generalisation is strong in proportion as the number of favourable instances, and the variety of circumstances in which they have been found, is great.
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Strawson — Thus, according to this point of view, there is no further question to ask about whether it is reasonable to rely on inductive inferences. But effectively what they are doing is offering a whole different story about what it would mean to be justified in believing the conclusion of inductive inferences.
What is needed is just conformity to inductive standards, and there is no real meaning to asking for any further justification for those. The main objection to this view is that conformity to the usual standards is insufficient to provide the needed justification. The problem Hume has raised is whether, despite the fact that inductive inferences have tended to produce true conclusions in the past, we have reason to think the conclusion of an inductive inference we now make is likely to be true.
Arguably, establishing that an inductive inference is rational in the sense that it follows inductive standards is not sufficient to establish that its conclusion is likely to be true. But if it is this question that concerned Hume, it is no answer to establish that induction is rational, unless that claim is understood to involve or imply that an inductive inference carried out according to rational standards is likely to have a true conclusion.
Some philosophers have however seen his argument as unassailable, and have thus accepted that it does lead to inductive skepticism, the conclusion that inductive inferences cannot be justified. The challenge then is to find a way of living with such a radical-seeming conclusion. We appear to rely on inductive inference ubiquitously in daily life, and it is also generally thought that it is at the very foundation of the scientific method. Can we go on with all this, whilst still seriously thinking none of it is justified by any rational argument?
One option here is to think that the significance of the problem of induction is somehow restricted to a skeptical context. Hume himself seems to have thought along these lines. For instance he says:. Nature will always maintain her rights, and prevail in the end over any abstract reasoning whatsoever. Though we should conclude, for instance, as in the foregoing section, that, in all reasonings from experience, there is a step taken by the mind, which is not supported by any argument or process of the understanding; there is no danger, that these reasonings, on which almost all knowledge depends, will ever be affected by such a discovery.
The problem of induction then must be seen as a problem that arises only at the level of philosophical reflection. Another way to mitigate the force of inductive skepticism is to restrict its scope. Karl Popper, for instance, regarded the problem of induction as insurmountable, but he argued that science is not in fact based on inductive inferences at all Popper . Rather he presented a deductivist view of science, according to which it proceeds by making bold conjectures, and then attempting to falsify those conjectures. In the simplest version of this account, when a hypothesis makes a prediction which is found to be false in an experiment, the hypothesis is rejected as falsified.
The logic of this procedure is fully deductive. The hypothesis entails the prediction, and the falsity of the prediction refutes the hypothesis by modus tollens. Thus, Popper claimed that science was not based on the extrapolative inferences considered by Hume.
The consequence then is that it is not so important, at least for science, if those inferences would lack a rational foundation. There are always many hypotheses which have not yet been refuted by the evidence, and these may contradict one another. According to the strictly deductive framework, since none are yet falsified, they are all on an equal footing.
Yet, scientists will typically want to say that one is better supported by the evidence than the others. We seem to need more than just deductive reasoning to support practical decision-making Salmon But arguably, this took him away from a strictly deductive view of science. It appears doubtful then that pure deductivism can give an adequate account of scientific method.
That is, it may preclude a justification which gives reason to believe the conclusion of a particular inductive inference is correct, or even likely to be correct. However, it is also possible to move away from the focus on justifying particular inductive inferences, and to consider inductive methods more generally.
For example, it might be the rule that one should infer to a universal generalization, after a certain number of positive instances and reject the universal generalization after observation of a counter-instances. Might it be the case that the general properties of an inductive method give grounds for employing that method, even when we have no reason to think that the method will result in a correct answer in any particular application? Given a particular inductive problem, we can look for an optimal method, or means, for providing a solution.
Such a means-ends argument may then form the basis for following the method, even in the absence of reasons to believe in its success in particular instances. According to this approach, we have a certain aim in making inductive inferences. Even if we cannot be sure we can achieve the aim, we can still argue that if the aim can be met, it will be by following the usual principles of inductive inference.
This provides a reason for making those usual inductive inferences. This provides some kind of justification for operating on the man, even if one does not know that the operation will succeed. Cases such as Hume considered are a special case of this principle, where the observed frequency is 1. The problem then is to justify the use of this rule. Reichenbach argued that even if Hume is right to think that we cannot be justified in thinking for any particular application of the rule that the conclusion is likely to be true, for the purposes of practical action we do not need to establish this.
We posit a certain frequency f on the basis of our evidence, and this is like making a wager or bet that the frequency is in fact f. It is possible that the world is so disorderly that we cannot construct series with such limits. But if there is a limit, there is some element of a series of observations, beyond which the principle of induction will lead to the true value of the limit. Although the inductive rule may give quite wrong results early in the sequence, as it follows chance fluctuations in the sample frequency, it is guaranteed to eventually approximate the limiting frequency, if such a limit exists.
Therefore, the rule of induction is justified as an instrument of positing because it is a method of which we know that if it is possible to make statements about the future we shall find them by means of this method Reichenbach This justification is taken to be a pragmatic one, since though it does not supply knowledge of a future event, it supplies a sufficient reason for action Reichenbach There are several problems with this pragmatic approach.
One concern is that the kind of justification it offers is too much tied to the long run, while allowing essentially no constraint on what can be posited in the short-run. Yet it is in the short run that inductive practice actually occurs and where it really needs justification BonJour ; Salmon It applies, in fact, to any method which converges asymptotically to the straight rule. Reichenbach makes two suggestions aimed at avoiding this problem.
Problem of induction | imuwenikywax.tk
Another problem is whether Reichenbach has really established that there could not be a better rule than the straight rule. For instance, for all that has been said, there might be a soothsayer or psychic who is able to predict future events reliably. Here Reichenbach argues that by using induction we could recognize the reliability of the alternative method, by examining its track record. One might also question whether a pragmatic argument can really deliver an all-purpose, general justification for following the inductive rule.
Surely a pragmatic solution should be sensitive to differences in pay-offs that depend on the circumstances. For example, Reichenbach offers the following analogue to his pragmatic justification:. We may compare our situation to that of a man who wants to fish in an unexplored part of the sea. There is no one to tell him whether or not there are fish in this place. Shall he cast his net? Well, if he wants to fish in that place, I should advise him to cast the net, to take the chance at least. It is preferable to try even in uncertainty than not to try and be certain of getting nothing.
Reichenbach [ —]. But if there is some significant cost to making the attempt, it may not be so clear that the most rational course of action is to cast the net. Similarly, whether or not it would make sense to adopt the policy of making no predictions, rather than the policy of following the inductive rule, may depend on what the practical penalties are for being wrong.
A pragmatic solution may not be capable of offering rationale for following the inductive rule which is applicable in all circumstances. As we saw above, one of the problems for Reichenbach was that there are too many rules which converge in the limit to the true frequency. Which one should we then choose in the short-run? Might other goals place constraints on which methods should be used in the short-run? The field of formal learning theory has developed answers to these questions Kelly ; Schulte ; also see Schulte In particular, formal learning theorists have considered the goal of getting to the truth as efficiently, or quickly, as possible, as well as the goal of minimizing the number of mind-changes, or retractions along the way.
Formal learning theory can be regarded as a kind of extension of the Reichenbachian programme. It does not offer justifications for inductive inferences, in the sense of giving reasons why they should be taken as likely to produce a true conclusion. Rather it offers reasons for following particular methods based on their optimality in achieving certain desirable epistemic ends, even if there is no guarantee that at any given stage of inquiry the results they produce are at all close to the truth.
Recently, however, Steel has suggested that formal learning theory offers more, and does provide a solution to the problem of induction. Another approach to pursuing a broadly Reichenbachian programme is to move to the level of meta-induction. Whereas object-level inductive methods make predictions based on the events which have been observed to occur, meta-inductive methods make predictions based on aggregating the predictions of different available prediction methods according to their success rates.
Here, the success rate of a method is defined according to some precise way of scoring success in making predictions. The main result is that the wMI strategy is long-run optimal in the sense that it converges to the maximum success rate of the accessible prediction methods. Worst-case bounds for short-run performance can also be derived. The optimality result forms the basis for an a priori means-ends justification for the use of wMI. Namely, the thought is, it is reasonable to use wMI, since it achieves the best success rate possible in the long run out of the given methods.
Schurz also claims that this a priori justification of wMI, together with the contingent fact that inductive methods have so far been much more successful than non-inductive methods, gives rise to an a posteriori justification of induction. Since wMI will achieve in the long run the maximal success rate of the available prediction methods, it is reasonable to use it. But as a matter of fact, the maximal success rate is achieved by inductive methods. Therefore, since it is a priori justified to use wMI, it is also a priori justified to use the maximally successful method at the object level.
Since it turns out that that the maximally successful method is induction, then it is reasonable to use induction. One point of discussion is whether this amounts to an important limitation on its claims to provide a full solution of the problem of induction Eckhardt Particular thanks are due to Don Garrett and Tom Sterkenburg for helpful feedback on a draft of this entry.
Reconstruction 3. The Necessary Conditions for Justification 5. Living with Inductive Skepticism 7. Means-ends Solutions 7. In general, he claims that the inferences depend on a transition of the form: I have found that such an object has always been attended with such an effect, and I foresee, that other objects, which are, in appearance, similar, will be attended with similar effects. Hume says that All reasonings may be divided into two kinds, namely, demonstrative reasoning, or that concerning relations of ideas, and moral reasoning, or that concerning matter of fact and existence.
And, he says, it implies no contradiction that the course of nature may change, and that an object seemingly like those which we have experienced, may be attended with different or contrary effects. In the Enquiry , Hume suggests that the step taken by the mind, which is not supported by any argument, or process of the understanding … must be induced by some other principle of equal weight and authority. The next instance of A will be B.
All observed instances of bread of a particular appearance have been nourishing. The next instance of bread of that appearance will be nourishing. The negation of the UP is not a contradiction. There is no demonstrative argument for the UP by P3 and P4. Any probable argument for UP presupposes UP. An argument for a principle may not presuppose the same principle Non-circularity.
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If there is no argument for the UP, there is no chain of reasoning from the premises to the conclusion of inference I. There is no chain of reasoning from the premises to the conclusion of inference I. By C3 and P7 P8. If there is no chain of reasoning from the premises to the conclusion of inference I , the inference is not justified.
Inference I is not justified By C4 and P8. Most arguments of form X that rely on UP have succeeded in the past. Therefore, most arguments of form X that rely on UP succeed. Most inferences following rule R have been successful Therefore, most inferences following R are successful. Most observed A s are B s. Therefore, it is not the case that most A s are B s. Most CI arguments have been unsuccessful Therefore, it is not the case that most CI arguments are unsuccessful, i.
Brown, M. Burks, Arthur W. Carroll, John W. Zalta ed. Kyburg ed. Dretske, Fred I. Cited by book. Cited by section. Wood, A. Ellington trans. Kelly, Kevin T.