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The problem of induction is the philosophical question of whether inductive reasoning leads to knowledge understood in the classic philosophical sense,highlighting the apparent lack of justification for:
Philosophy is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language. The term was probably coined by Pythagoras. Philosophical methods include questioning, critical discussion, rational argument, and systematic presentation. Classic philosophical questions include: Is it possible to know anything and to prove it? What is most real? Philosophers also pose more practical and concrete questions such as: Is there a best way to live? Is it better to be just or unjust? Do humans have free will?
Inductive reasoning is a method of reasoning in which the premises are viewed as supplying some evidence for the truth of the conclusion. While the conclusion of a deductive argument is certain, the truth of the conclusion of an inductive argument may be probable, based upon the evidence given.
Knowledge is a familiarity, awareness, or understanding of someone or something, such as facts, information, descriptions, or skills, which is acquired through experience or education by perceiving, discovering, or learning.
The problem calls into question all empirical claims made in everyday life or through the scientific method, and, for that reason, the philosopher C. D. Broad said that "induction is the glory of science and the scandal of philosophy." Although the problem arguably dates back to the Pyrrhonism of ancient philosophy, as well as the Carvaka school of Indian philosophy, David Hume popularized it in the mid-18th century.
The scientific method is an empirical method of acquiring knowledge that has characterized the development of science since at least the 17th century. It involves careful observation, applying rigorous skepticism about what is observed, given that cognitive assumptions can distort how one interprets the observation. It involves formulating hypotheses, via induction, based on such observations; experimental and measurement-based testing of deductions drawn from the hypotheses; and refinement of the hypotheses based on the experimental findings. These are principles of the scientific method, as distinguished from a definitive series of steps applicable to all scientific enterprises.
Charlie Dunbar Broad, usually cited as C. D. Broad, was an English epistemologist, historian of philosophy, philosopher of science, moral philosopher, and writer on the philosophical aspects of psychical research. He was known for his thorough and dispassionate examinations of arguments in such works as Scientific Thought, published in 1923, The Mind and Its Place in Nature, published in 1925, and An Examination of McTaggart's Philosophy, published in 1933.
Pyrrhonism was a school of skepticism founded by Pyrrho in the fourth century BC. It is best known through the surviving works of Sextus Empiricus, writing in the late second century or early third century AD.
In inductive reasoning, one makes a series of observations and infers a new claim based on them. For instance, from a series of observations that a woman walks her dog by the market at 8 am on Monday, it seems valid to infer that next Monday she will do the same, or that, in general, the woman walks her dog by the market every Monday. That next Monday the woman walks by the market merely adds to the series of observations, it does not prove she will walk by the market every Monday. First of all, it is not certain, regardless of the number of observations, that the woman always walks by the market at 8 am on Monday. In fact, David Hume would even argue that we cannot claim it is "more probable", since this still requires the assumption that the past predicts the future.
Inferences are steps in reasoning, moving from premises to logical consequences. Charles Sanders Peirce divided inference into three kinds: deduction, induction, and abduction. Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular premises to a universal conclusion. Abduction is inference to the best explanation.
David Hume was a Scottish Enlightenment philosopher, historian, economist, and essayist, who is best known today for his highly influential system of philosophical empiricism, skepticism, and naturalism. Hume's empiricist approach to philosophy places him with John Locke, George Berkeley, Francis Bacon and Thomas Hobbes as a British Empiricist. Beginning with his A Treatise of Human Nature (1738), Hume strove to create a total naturalistic science of man that examined the psychological basis of human nature. Against philosophical rationalists, Hume held that passion rather than reason governs human behaviour. Hume argued against the existence of innate ideas, positing that all human knowledge is founded solely in experience.
Second, the observations themselves do not establish the validity of inductive reasoning, except inductively. Bertrand Russell illustrated this point in The Problems of Philosophy :
Bertrand Arthur William Russell, 3rd Earl Russell, was a British philosopher, logician, mathematician, historian, writer, essayist, social critic, political activist, and Nobel laureate. At various points in his life, Russell considered himself a liberal, a socialist and a pacifist, although he also confessed that his skeptical nature had led him to feel that he had "never been any of these things, in any profound sense." Russell was born in Monmouthshire into one of the most prominent aristocratic families in the United Kingdom.
The Problems of Philosophy is a 1912 book by Bertrand Russell, in which the author attempts to create a brief and accessible guide to the problems of philosophy. Focusing on problems he believes will provoke positive and constructive discussion, Russell concentrates on knowledge rather than metaphysics: If it is uncertain that external objects exist, how can we then have knowledge of them but by probability. There is no reason to doubt the existence of external objects simply because of sense data.
Domestic animals expect food when they see the person who usually feeds them. We know that all these rather crude expectations of uniformity are liable to be misleading. The man who has fed the chicken every day throughout its life at last wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to the chicken.
In several publications it is presented as a story about a turkey, fed every morning without fail, who following the laws of induction concludes this will continue, but then his throat is cut on Thanksgiving Day.
Pyrrhonian skeptic Sextus Empiricus first questioned the validity of inductive reasoning, positing that a universal rule could not be established from an incomplete set of particular instances. He wrote:
Sextus Empiricus, was a physician and philosopher, who likely lived in Alexandria, Rome, or Athens. His philosophical work is the most complete surviving account of ancient Greek and Roman Pyrrhonism.
When they propose to establish the universal from the particulars by means of induction, they will effect this by a review of either all or some of the particulars. But if they review some, the induction will be insecure, since some of the particulars omitted in the induction may contravene the universal; while if they are to review all, they will be toiling at the impossible, since the particulars are infinite and indefinite.
The focus upon the gap between the premises and conclusion present in the above passage appears different from Hume's focus upon the circular reasoning of induction. However, Weintraub claims in The Philosophical Quarterlythat although Sextus's approach to the problem appears different, Hume's approach was actually an application of another argument raised by Sextus:
Those who claim for themselves to judge the truth are bound to possess a criterion of truth. This criterion, then, either is without a judge's approval or has been approved. But if it is without approval, whence comes it that it is truthworthy? For no matter of dispute is to be trusted without judging. And, if it has been approved, that which approves it, in turn, either has been approved or has not been approved, and so on ad infinitum.
Although the criterion argument applies to both deduction and induction, Weintraub believes that Sextus's argument "is precisely the strategy Hume invokes against induction: it cannot be justified, because the purported justification, being inductive, is circular." She concludes that "Hume's most important legacy is the supposition that the justification of induction is not analogous to that of deduction." She ends with a discussion of Hume's implicit sanction of the validity of deduction, which Hume describes as intuitive in a manner analogous to modern foundationalism.
The Cārvāka, a materialist and skeptic school of Indian philosophy, used the problem of induction to point out the flaws in using inference as a way to gain valid knowledge. They held that since inference needed an invariable connection between the middle term and the predicate, and further, that since there was no way to establish this invariable connection, that the efficacy of inference as a means of valid knowledge could never be stated.
The 9th century Indian skeptic, Jayarasi Bhatta, also made an attack on inference, along with all means of knowledge, and showed by a type of reductio argument that there was no way to conclude universal relations from the observation of particular instances.
Medieval writers such as al-Ghazali and William of Ockham connected the problem with God's absolute power, asking how we can be certain that the world will continue behaving as expected when God could at any moment miraculously cause the opposite. '" Some 17th-century Jesuits argued that although God could create the end of the world at any moment, it was necessarily a rare event and hence our confidence that it would not happen very soon was largely justified.Duns Scotus, however, argued that inductive inference from a finite number of particulars to a universal generalization was justified by "a proposition reposing in the soul, 'Whatever occurs in a great many instances by a cause that is not free, is the natural effect of that cause.
David Hume is the philosopher most often associated with induction. His formulation of the problem of induction can be found in An Enquiry concerning Human Understanding , §4. Here, Hume introduces his famous distinction between "relations of ideas" and "matters of fact." Relations of ideas are propositions which can be derived from deductive logic, which can be found in fields such as geometry and algebra. Matters of fact, meanwhile, are not verified through the workings of deductive logic but by experience. Specifically, matters of fact are established by making an inference about causes and effects from repeatedly observed experience. While relations of ideas are supported by reason alone, matters of fact must rely on the connection of a cause and effect through experience. Causes of effects cannot be linked through a priori reasoning, but by positing a "necessary connection" that depends on the "uniformity of nature."
First, Hume ponders the discovery of causal relations, which form the basis for what he refers to as "matters of fact". He argues that causal relations are found not by reason, but by induction. This is because for any cause, multiple effects are conceivable, and the actual effect cannot be determined by reasoning about the cause; instead, one must observe occurrences of the causal relation to discover that it holds. For example, when one thinks of "a billiard ball moving in a straight line toward another",one can conceive that the first ball bounces back with the second ball remaining at rest, the first ball stops and the second ball moves, or the first ball jumps over the second, etc. There is no reason to conclude any of these possibilities over the others. Only through previous observation can it be predicted, inductively, what will actually happen with the balls. In general, it is not necessary that causal relation in the future resemble causal relations in the past, as it is always conceivable otherwise; for Hume, this is because the negation of the claim does not lead to a contradiction.
Next, Hume ponders the justification of induction. If all matters of fact are based on causal relations, and all causal relations are found by induction, then induction must be shown to be valid somehow. He uses the fact that induction assumes a valid connection between the proposition "I have found that such an object has always been attended with such an effect" and the proposition "I foresee that other objects which are in appearance similar will be attended with similar effects".One connects these two propositions not by reason, but by induction. This claim is supported by the same reasoning as that for causal relations above, and by the observation that even rationally inexperienced people can infer, for example, that touching fire causes pain. Hume challenges other philosophers to come up with a (deductive) reason for the connection. If a deductive justification for induction cannot be provided, then it appears that induction is based on an inductive assumption about the connection, which would be begging the question. Induction, itself, cannot validly explain the connection.
In this way, the problem of induction is not only concerned with the uncertainty of conclusions derived by induction, but doubts the very principle through which those uncertain conclusions are derived.
Nelson Goodman's Fact, Fiction, and Forecast presented a different description of the problem of induction in the chapter entitled "The New Riddle of Induction". Goodman proposed the new predicate "grue". Something is grue if and only if it has been (or will be, according to a scientific, general hypothesis) observed to be green before a certain time t, or blue if observed after that time. The "new" problem of induction is, since all emeralds we have ever seen are both green and grue, why do we suppose that after time t we will find green but not grue emeralds? The problem here raised is that two different inductions will be true and false under the same conditions. In other words:
Goodman, however, points out that the predicate "grue" only appears more complex than the predicate "green" because we have defined grue in terms of blue and green. If we had always been brought up to think in terms of "grue" and "bleen" (where bleen is blue before time t, or green thereafter), we would intuitively consider "green" to be a crazy and complicated predicate. Goodman believed that which scientific hypotheses we favour depend on which predicates are "entrenched" in our language.
W. V. O. Quine offers a practical solution to this problemby making the metaphysical claim that only predicates that identify a "natural kind" (i.e. a real property of real things) can be legitimately used in a scientific hypothesis. R. Bhaskar also offers a practical solution to the problem. He argues that the problem of induction only arises if we deny the possibility of a reason for the predicate, located in the enduring nature of something. For example, we know that all emeralds are green, not because we have only ever seen green emeralds, but because the chemical make-up of emeralds insists that they must be green. If we were to change that structure, they would not be green. For instance, emeralds are a kind of green beryl, made green by trace amounts of chromium and sometimes vanadium. Without these trace elements, the gems would be colourless.
Although induction is not made by reason, Hume observes that we nonetheless perform it and improve from it. He proposes a descriptive explanation for the nature of induction in §5 of the Enquiry, titled "Skeptical solution of these doubts". It is by custom or habit that one draws the inductive connection described above, and "without the influence of custom we would be entirely ignorant of every matter of fact beyond what is immediately present to the memory and senses".The result of custom is belief, which is instinctual and much stronger than imagination alone.
David Stove's argument for induction, based on the statistical syllogism, was presented in the Rationality of Induction and was developed from an argument put forward by one of Stove's heroes, the late Donald Cary Williams (formerly Professor at Harvard) in his book The Ground of Induction.Stove argued that it is a statistical truth that the great majority of the possible subsets of specified size (as long as this size is not too small) are similar to the larger population to which they belong. For example, the majority of the subsets which contain 3000 ravens which you can form from the raven population are similar to the population itself (and this applies no matter how large the raven population is, as long as it is not infinite). Consequently, Stove argued that if you find yourself with such a subset then the chances are that this subset is one of the ones that are similar to the population, and so you are justified in concluding that it is likely that this subset "matches" the population reasonably closely. The situation would be analogous to drawing a ball out of a barrel of balls, 99% of which are red. In such a case you have a 99% chance of drawing a red ball. Similarly, when getting a sample of ravens the probability is very high that the sample is one of the matching or "representative" ones. So as long as you have no reason to think that your sample is an unrepresentative one, you are justified in thinking that probably (although not certainly) that it is.
An intuitive answer to Hume would be to say that a world inacessible to any inductive procedure would simply not be conceivable. This intuition was taking into account by Keith Campbell by considering that to be built a concept must be reapplied, what demands a certain continuity in its object of application and consequently some openness to induction. Recently, Claudio Costa has noted that a future can only be a future of its own past if it holds some identity with it. Moreover, the nearer a future is to the point of junction with its past, the greater are the similarities tendentially involved. Consequently – contra Hume – some form of principle of homogeneity (causal or structural) between future and past must be warranted, which would make some inductive procedure always possible. .
Karl Popper, a philosopher of science, sought to solve the problem of induction.He argued that science does not use induction, and induction is in fact a myth. Instead, knowledge is created by conjecture and criticism. The main role of observations and experiments in science, he argued, is in attempts to criticize and refute existing theories.
According to Popper, the problem of induction as usually conceived is asking the wrong question: it is asking how to justify theories given they cannot be justified by induction. Popper argued that justification is not needed at all, and seeking justification "begs for an authoritarian answer". Instead, Popper said, what should be done is to look to find and correct errors.Popper regarded theories that have survived criticism as better corroborated in proportion to the amount and stringency of the criticism, but, in sharp contrast to the inductivist theories of knowledge, emphatically as less likely to be true. Popper held that seeking for theories with a high probability of being true was a false goal that is in conflict with the search for knowledge. Science should seek for theories that are most probably false on the one hand (which is the same as saying that they are highly falsifiable and so there are lots of ways that they could turn out to be wrong), but still all actual attempts to falsify them have failed so far (that they are highly corroborated).
Wesley C. Salmon criticizes Popper on the grounds that predictions need to be made both for practical purposes and in order to test theories. That means Popperians need to make a selection from the number of unfalsified theories available to them, which is generally more than one. Popperians would wish to choose well-corroborated theories, in their sense of corroboration, but face a dilemma: either they are making the essentially inductive claim that a theory's having survived criticism in the past means it will be a reliable predictor in the future; or Popperian corroboration is no indicator of predictive power at all, so there is no rational motivation for their preferred selection principle.
David Miller has criticized this kind of criticism by Salmon and others because it makes inductivist assumptions. [ according to whom? ] is in the theory itself, not in its corroboration. The rational motivation for choosing a well-corroborated theory is that it is simply easier to falsify: Well-corroborated means that at least one kind of experiment (already conducted at least once) could have falsified (but did not actually falsify) the one theory, while the same kind of experiment, regardless of its outcome, could not have falsified the other. So it is rational to choose the well-corroborated theory: It may not be more likely to be true, but if it is actually false, it is easier to get rid of when confronted with the conflicting evidence that will eventually turn up. Accordingly, it is wrong to consider corroboration as a reason, a justification for believing in a theory or as an argument in favor of a theory to convince someone who objects to it.Popper does not say that corroboration is an indicator of predictive power. The predictive power
... the theory to be developed in the following pages stands directly opposed to all attempts to operate with the ideas of inductive logic.
Induction, i.e. inference based on many observations, is a myth. It is neither a psychological fact, nor a fact of ordinary life, nor one of scientific procedure.
The actual procedure of science is to operate with conjectures: to jump to conclusions – often after one single observation
Tests proceed partly by way of observation, and observation is thus very important; but its function is not that of producing theories. It plays its role in rejecting, eliminating, and criticizing theories
I propose to replace ... the question of the sources of our knowledge by the entirely different question: 'How can we hope to detect and eliminate error?'
In philosophy, empiricism is a theory that states that knowledge comes only or primarily from sensory experience. It is one of several views of epistemology, the study of human knowledge, along with rationalism and skepticism. Empiricism emphasises the role of empirical evidence in the formation of ideas, rather than innate ideas or traditions. However, empiricists may argue that traditions arise due to relations of previous sense experiences.
Foundationalism concerns philosophical theories of knowledge resting upon justified belief, or some secure foundation of certainty such as a conclusion inferred from a basis of sound premises. The main rival of the foundationalist theory of justification is the coherence theory of justification, whereby a body of knowledge, not requiring a secure foundation, can be established by the interlocking strength of its components, like a puzzle solved without prior certainty that each small region was solved correctly.
Deductive reasoning, also deductive logic, logical deduction is the process of reasoning from one or more statements (premises) to reach a logically certain conclusion.
Scientific evidence is evidence which serves to either support or counter a scientific theory or hypothesis. Such evidence is expected to be empirical evidence and interpretation in accordance with scientific method. Standards for scientific evidence vary according to the field of inquiry, but the strength of scientific evidence is generally based on the results of statistical analysis and the strength of scientific controls.
The following outline is provided as an overview of and topical guide to scientific method:
The hypothetico-deductive model or method is a proposed description of scientific method. According to it, scientific inquiry proceeds by formulating a hypothesis in a form that can be falsifiable, using a test on observable data where the outcome is not yet known. A test outcome that could have and does run contrary to predictions of the hypothesis is taken as a falsification of the hypothesis. A test outcome that could have, but does not run contrary to the hypothesis corroborates the theory. It is then proposed to compare the explanatory value of competing hypotheses by testing how stringently they are corroborated by their predictions.
Critical rationalism is an epistemological philosophy advanced by Karl Popper. Popper wrote about critical rationalism in his works: The Logic of Scientific Discovery, The Open Society and its Enemies, Conjectures and Refutations, The Myth of the Framework, and Unended Quest. Ernest Gellner is another notable proponent of this approach.
Grue and bleen are examples of logical predicates coined by Nelson Goodman in Fact, Fiction, and Forecast to illustrate the "new riddle of induction" – a successor to Hume's original problem. These predicates are unusual because their application is time-dependent; many have tried to solve the new riddle on those terms, but Hilary Putnam and others have argued such time-dependency depends on the language adopted, and in some languages it is equally true for natural-sounding predicates such as "green." For Goodman they illustrate the problem of projectible predicates and ultimately, which empirical generalizations are law-like and which are not. Goodman's construction and use of grue and bleen illustrates how philosophers use simple examples in conceptual analysis.
Henry Nelson Goodman was an American philosopher, known for his work on counterfactuals, mereology, the problem of induction, irrealism, and aesthetics.
Computational epistemology is a subdiscipline of formal epistemology that studies the intrinsic complexity of inductive problems for ideal and computationally bounded agents. In short, computational epistemology is to induction what recursion theory is to deduction.
In logic, counterinduction is a measure that helps to call something into question by developing something against which it can be compared. Paul Feyerabend argued for counterinduction as a way to test unchallenged scientific theories; unchallenged simply because there are no structures within the scientific paradigm (positivism) to challenge itself. For instance, Feyerabend is quoted as saying the following:
Formal epistemology uses formal methods from decision theory, logic, probability theory and computability theory to model and reason about issues of epistemological interest. Work in this area spans several academic fields, including philosophy, computer science, economics, and statistics. The focus of formal epistemology has tended to differ somewhat from that of traditional epistemology, with topics like uncertainty, induction, and belief revision garnering more attention than the analysis of knowledge, skepticism, and issues with justification.
In epistemology, the Münchhausen trilemma is a thought experiment used to demonstrate the impossibility of proving any truth, even in the fields of logic and mathematics. If it is asked how any knowledge is known to be true, proof may be provided. Yet that same question can be asked of the proof, and any subsequent proof. The Münchhausen trilemma is that there are only three options when providing proof in this situation:
The following outline is provided as an overview of and topical guide to epistemology:
Inductivism is the traditional model of scientific method attributed to Francis Bacon, who in 1620 vowed to subvert allegedly traditional thinking. In the Baconian model, one observes nature, proposes a modest law to generalize an observed pattern, confirms it by many observations, ventures a modestly broader law, and confirms that, too, by many more observations, while discarding disconfirmed laws. The laws grow ever broader but never much exceed careful, extensive observation. Thus, freed from preconceptions, scientists gradually uncover nature's causal and material structure.
Epistemology or theory of knowledge is the branch of philosophy concerned with the nature and scope (limitations) of knowledge. It addresses the questions "What is knowledge?", "How is knowledge acquired?", "What do people know?", "How do we know what we know?", and "Why do we know what we know?". Much of the debate in this field has focused on analyzing the nature of knowledge and how it relates to similar notions such as truth, belief, and justification. It also deals with the means of production of knowledge, as well as skepticism about different knowledge claims.
Logic, is the systematic study of the form of valid inference, and the most general laws of truth. A valid inference is one where there is a specific relation of logical support between the assumptions of the inference and its conclusion. In ordinary discourse, inferences may be signified by words such as therefore, hence, ergo, and so on.
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