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cientific view c d broad once said that induction is the glory of science and the scandal of philosophy 3 in contrast karl popper s critical rationalism claimed that inductive justifications are never used in science and proposed instead that science is based on the procedure of conjecturing hypotheses deductively calculating consequences and then empirically attempting to falsify them formulation of the problem edit in inductive reasoning one makes a series of observations and infers a 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 but 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 even argued 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 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 ancient and early modern origins edit pyrrhonism edit part of a series on pyrrhonism pyrrhonists pyrrho timon of phlius aenesidemus agrippa the skeptic sextus empiricus concepts ataraxia acatalepsy adiaphora aporia dogma epoché similar philosophies academic skepticism modern influence münchhausen trilemma benson mates robert fogelin philosophy portal v t e the works of the pyrrhonist philosopher sextus empiricus contain the oldest surviving questioning of the validity of inductive reasoning he wrote 4 it is also easy i consider to set aside the method of induction for when they propose to establish the universal from the particulars by means of induction they will effect this by a review either of all or of some of the particular instances 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 thus on both grounds as i think the consequence is that induction is invalidated 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 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 indian philosophy edit 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 philosophy edit 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 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 fo...
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