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erence 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 edit david hume a scottish thinker of the enlightenment era 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 hume situates his introduction to the problem of induction in a treatise of human nature within his larger discussion on the nature of causes and effects book i part iii section vi he writes that reasoning alone cannot establish the grounds of causation instead the human mind imputes causation to phenomena after repeatedly observing a connection between two objects for hume establishing the link between causes and effects relies not on reasoning alone but the observation of constant conjunction throughout one s sensory experience from this discussion hume goes on to present his formulation of the problem of induction in a treatise of human nature writing there can be no demonstrative arguments to prove that those instances of which we have had no experience resemble those of which we have had experience in other words the problem of induction can be framed in the following way we cannot apply a conclusion about a particular set of observations to a more general set of observations while deductive logic allows one to arrive at a conclusion with certainty inductive logic can only provide a conclusion that is probably true non primary source needed it is mistaken to frame the difference between deductive and inductive logic as one between general to specific reasoning and specific to general reasoning this is a common misperception about the difference between inductive and deductive thinking according to the literal standards of logic deductive reasoning arrives at certain conclusions while inductive reasoning arrives at probable conclusions non primary source needed hume s treatment of induction helps to establish the grounds for probability as he writes in a treatise of human nature that probability is founded on the presumption of a resemblance betwixt those objects of which we have had experience and those of which we have had none book i part iii section vi non primary source needed therefore hume establishes induction as the very grounds for attributing causation there might be many effects which stem from a single cause over repeated observation one establishes that a certain set of effects are linked to a certain set of causes however the future resemblance of these connections to connections observed in the past depends on induction induction allows one to conclude that effect a2 was caused by cause a2 because a connection between effect a1 and cause a1 was observed repeatedly in the past given that reason alone can not be sufficient to establish the grounds of induction hume implies that induction must be accomplished through imagination one does not make an inductive reference through a priori reasoning but through an imaginative step automatically taken by the mind hume does not challenge that induction is performed by the human mind automatically but rather hopes to show more clearly how much human inference depends on inductive not a priori reasoning he does not deny future uses of induction but shows that it is distinct from deductive reasoning helps to ground causation and wants to inquire more deeply into its validity hume offers no solution to the problem of induction himself he prompts other thinkers and logicians to argue for the validity of induction as an ongoing dilemma for philosophy a key issue with establishing the validity of induction is that one is tempted to use an inductive inference as a form of justification itself this is because people commonly justify the validity of induction by pointing to the many instances in the past when induction proved to be accurate for example one might argue that it is valid to use inductive inference in the future because this type of reasoning has yielded accurate results in the past however this argument relies on an inductive premise itself that past observations of induction being valid will mean that future observations of induction will also be valid thus many solutions to the problem of induction tend to be circular nelson goodman s new riddle of induction edit main article new riddle of induction nelson goodman s fact fiction and forecast 1955 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 14 15 observed to be green before a certain time t and 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 given the observations of a lot of green emeralds someone using a common language will inductively infer that all emeralds are green therefore he will believe that any emerald he will ever find will be green even after time t given the same set of observations of green emeralds someone using the predicate grue will inductively infer that all emeralds which will be observed after t will be blue despite the fact that he observed only green emeralds so far one could argue using occam s razor that greenness is more likely than grueness because the concept of grueness is more complex than that of greenness 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 and 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 original research willard van orman quine offers a practical solution to this problem 16 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 17 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 edit hume edit see also david hume induction and causation 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 18 the result of custom is belief which is instinctual and much stronger than imagination alone 19 john maynard keynes edit in his treatise on probability john maynard keynes notes an inductive argument affirms not that a certain matter of fact is so but that relative to certain evidence there is a probability in its favour the validity of the induction relative to the original evidence is not upset therefore if as a fact the truth turns out to be otherwise 20 this approach was endorsed by bertrand russell 21 david stove and donald williams edit 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 22 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 23 biting the bullet keith campbell and claudio costa edit an intuitive answer to hume would be to say that a world inaccessible 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 24 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 25 karl popper edit karl popper a philosopher of science sought to solve the problem of induction 26 27 he argued that science does not use induction and induction is in fact a myth 28 instead knowledge is created by conjecture and criticism 29 the main role of observations and experiments in science he argued is in attempts to criticize and refute existing theories 30 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 31 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 clarification needed 32 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 many 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 33 david miller has criticized this kind of criticism by salmon and others because it makes inductivist assumptions 34 popper does not say that corroboration is an indicator of predictive power the predictive power 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 35 see also edit a priori and a posteriori two types of knowledge justification or argument abductive reasoning inference seeking the simplest and most likely explanation bayesian inference method of statistical inference consilience principle about evidence hasty generalization conclusion made on the basis o...
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