“Problem of induction”的意思、由来-开放百科全书

The problem of induction is the philosophical question of whether inductive reasoning leads to knowledge understood in the classic philosophical sense,^[1] highlighting the apparent lack of justification for:

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.

Formulation of the problem

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.

Second, the observations themselves do not establish the validity of inductive reasoning, except inductively. Bertrand Russell illustrated this point in The Problems of Philosophy:

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.^[3]

Ancient and early modern origins

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 Quarterly^[5] that although Sextus's approach to the problem appears different, Hume's approach was actually an application of another argument raised by Sextus:^[6]

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.^[7]^[8]

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.^[9]^[10]

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.^[11] 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.{{'"}}^[12] 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.^[13]

David Hume

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",^[14] 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".^[15] 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.^[16]

Nelson Goodman's new riddle of induction

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^[17]^[18]) 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 problem^[19] by 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.^[20] 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.

Notable interpretations

Hume

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".^[21] The result of custom is belief, which is instinctual and much stronger than imagination alone.^[22]

David Stove and Donald Williams

Biting the Bullett: Keith Campbell and Claudio Costa

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 taken into account by Keith Campbell by considering that, to be built, a concept must be reapplied, which demands a certain continuity in its object of application and consequently some openness to induction ^[25]. 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.^[26].

Karl Popper

He argued that science does not use induction, and induction is in fact a myth.^[29] Instead, knowledge is created by conjecture and criticism.^[30] The main role of observations and experiments in science, he argued, is in attempts to criticize and refute existing theories.^[31]

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.^[32]

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.^[33] 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).

See also

Notes

1. ^Vickers, John, "Can induction be justified?", The Stanford Encyclopedia of Philosophy (Fall 2011 Edition), Edward N. Zalta (ed.)
2. ^{{cite book |first=David |last=Hume |title=An Enquiry Concerning Human Understanding |url=http://www.gutenberg.org/cache/epub/9662/pg9662.txt |work=Gutenberg Press |date=January 2006 }}#9662: Most recently updated in 16 October 2007
3. ^This story is found in Alan Chalmers, What is this thing Called Science, Open University Press, Milton Keynes, 1982, p. 14.
4. ^Sextus Empiricus. Outlines of Pyrrhonism, trans. Robert Gregg Bury (Loeb ed.) (London: W. Heinemann, 1933), p. 283.
5. ^Weintraub, R. (1995). What was Hume's Contribution to the Problem of Induction? The Philosophical Quarterly 45(181):460–470
6. ^Sextus Empiricus. Against the Logicians, trans. Robert Gregg Bury (Loeb ed.) (London: W. Heinemann, 1935), p. 179
7. ^Dr. S. Radhakrishnan, Indian Philosophy Vol I, p. 279
8. ^S. Dasgupta, A history of Indian philosophy, Vol III. pg 533
9. ^Piotr Balcerowicz, "Jayarāśi"
10. ^Franco, Eli, 1987, Perception, Knowledge and Disbelief: A Study of Jayarāśi's Scepticism
11. ^Franklin, J. (2001), The Science of Conjecture: Evidence and Probability Before Pascal (Baltimore: Johns Hopkins University Press), 232–233, 241.
12. ^Duns Scotus: Philosophical Writings, trans. A. Wolter (Edinburgh: 1962), 109–110; Franklin, Science of Conjecture, 206.
13. ^Franklin, Science of Conjecture, 223–224.
14. ^Enquiry, §4.1.
15. ^Enquiry, §4.2.
16. ^The Problem of Induction
17. ^Goodman, Nelson. Fact, Fiction, and Forecast (Fourth Edition). Harvard University Press, 1983, p.74, "will each confirm the general hypothesis that all emeralds are grue"
18. ^Goodman’s original definition of grue
19. ^{{cite book |editor=Nicholas Rescher|title=Essays in Honor of Carl G. Hempel| publisher=D. Reidel |location=Dordrecht |author=Willard Van Orman Quine |contribution=Natural Kinds |year=1970 |pages=41–56 |contribution-url=http://fitelson.org/confirmation/quine_nk.pdf|display-editors=etal|title-link=Carl G. Hempel}} Reprinted in: Quine (1969), Ontological Relativity and Other Essays, Ch. 5.
20. ^{{Cite book|title=A Realist Theory of Science|last=Bhaskar|first=Roy|publisher=Routledge|year=2008|isbn=978-0-415-45494-0|location=New York|pages=215–228}}
21. ^Enquiry, §5.1.
22. ^Enquiry, §5.2.
23. ^{{cite book | author=Donald Cary Williams | title=The Ground of Induction | location=New York | publisher=Russell and Russell | year=1947 }}, {{cite web |url=https://plato.stanford.edu/entries/williams-dc/ |title=Donald Cary Williams |date=2015 |publisher=Stanford Encyclopedia of Philosophy |access-date=2017-03-04}}
24. ^D. Stove, The Rationality of Induction, Clarendon Press, Oxford, 1986, ch. 6.
25. ^"One form of Skepticism about Induction", in Richard Swinburne (ed.) The Justification of the Induction. Oxford, Oxford University Press, 1974.
26. ^Claudio Costa: Philosophical Semantics: Reintegrating Theoretical Philosophy, Appendix to Ch. V, CSP, 2018.
27. ^{{cite book| title = The Logic of Scientific Discovery| author = Karl Popper| year = 1959| pages = Ch. 1| quote = ... the theory to be developed in the following pages stands directly opposed to all attempts to operate with the ideas of inductive logic.| isbn = 978-84-309-0711-3| title-link = The Logic of Scientific Discovery}}
28. ^{{cite news| url = http://www.abc.net.au/rn/science/ss/stories/s75303.htm| title = A Portrait of Sir Karl Popper| author = Alan Saunders| work = The Science Show| publisher = Radio National| date = 15 January 2000| accessdate = 27 December 2007}}
29. ^{{cite book| title = Conjectures and Refutations| author = Karl Popper| year = 1963| page = 53| quote = 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.| isbn = 978-0-06-131376-9| title-link = Conjectures and Refutations}}
30. ^{{cite book| title = Conjectures and Refutations| author = Karl Popper| year = 1963| page = 53| quote = The actual procedure of science is to operate with conjectures: to jump to conclusions – often after one single observation| isbn = 978-0-06-131376-9| title-link = Conjectures and Refutations}}
31. ^{{cite book| title = Conjectures and Refutations| author = Karl Popper| year = 1963| page = 128| quote = 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| isbn = 978-0-06-131376-9| title-link = Conjectures and Refutations}}
32. ^{{cite book| title = Conjectures and Refutations| author = Karl Popper| year = 1963| page = 25| quote = 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?'| isbn = 978-0-06-131376-9| title-link = Conjectures and Refutations}}
33. ^{{clarify|date=October 2018}}Logic of Scientific Discovery, section 43
34. ^{{cite book| title = The Foundations of Scientific Inference| author = Wesley C. Salmon| year = 1967| pages = 26}}
35. ^{{cite book |last1=Miller |first1=David |title=Critical rationalism: A restatement and defense |date=1994 |publisher=Open Court |location=Chicago}}
36. ^Thomas Bullemore, [https://www.academia.edu/4154895/Some_Remarks_on_the_Pragmatic_Problem_of_Induction "Some Remarks on the Pragmatic Problem of Induction"], Academia.edu