Formulation of the problem
In David Hume would even argue that we cannot claim this is the "more probable", since this still requires the assumption that the past predicts the future.
Second, the observations themselves pretend not develop the validity of inductive reasoning, apart from inductively. Bertrand Russell illustrated this piece in The Problems of Philosophy:
Domestic animals expect food when they see the grownup 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.
The workings of the Pyrrhonist philosopher Sextus Empiricus contain the oldest surviving questioning of the validity of inductive reasoning. He wrote:
It is also easy, I consider, to category aside the method of induction. For, when theyto setting the universal from the particulars by means of induction, they will effect this by a review either of all or of some of the specific instances. But whether 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 that although Sextus's approach to the problem appears different, Hume's approach was actually an application of another parametric quantity 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 this is the 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 non been approved, and so on ad infinitum.
Although the criterion argument applies to both deduction and induction, Weintraub believes that Sextus's parameter "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 near 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 contemporary 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 cognition 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(a) as al-Ghazali and William of Ockham connected the problem with God's absolute power, asking how we can bethat the world will come on behaving as expected when God could at anymiraculously cause the opposite. 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 issue of that cause.'" 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.
David Hume, a Scottish thinker of the Enlightenment era, is the philosopher almost 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(a) as geometry and algebra. matters of fact, meanwhile, are not verified through the working of deductive logic but by experience. Specifically, matters of fact are established by making an inference approximately causes and effects from repeatedly observed experience. While relations of ideas are supported by reason alone, matters of fact must rely on the connective 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 number one ordering 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 coming after or as a total of. way: we cannot apply a conclusion approximately a particular set of observations to a more general set of observations. While deductive logical system allows one toat a conclusion with certainty, inductive logic can only administer a conclusion that is probably true.[] 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 specification of logic, deductive reasoning arrives atconclusions while inductive reasoning arrives at probable conclusions. [] Hume's treatment of induction authorises to establish the grounds for probability, as he writes in ]
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 aset of effects are linked to aset of causes. However, the future resemblance of these connections to connections observed in the past depends on induction. Induction permits 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. condition 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 credit 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 or done as a reaction to a question 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 normally 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 ownership 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 intend that future observations of induction will also be valid. Thus, many solutions to the problem of induction tend to be circular.
Nelson Goodman's Fact, Fiction, and Forecast presented a different relation 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, 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:
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.
W. V. O. Quine offers a practical solution to this problem by devloping 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 opportunity 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 conform 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.