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#generalizing about the properties of a class of objects based on some number of Observations of particular instances of that class of objects (for example, "All ravens we have seen are black, and therefore all ravens are black"); or
#presupposing that a sequence of events in the future will occur as it always has in the past (for example, the attractive force described by Isaac Newton 's Law Of Universal Gravitation , or Albert Einstein 's revision in General Relativity ).

Francis Bacon , Isaac Newton , and numerous others up until at least the late 19th Century have considered Inductive Reasoning the basis of scientific method--indeed inductive reasoning is used today, though in a more balanced interaction with Deductive Reasoning and Abductive Reasoning . By the inductive approach to scientific method, one makes a series of observations and forms a Universal Generalization . If correct and stated in a sufficiently accurate way, an inductively arrived at statement relieves others of the need for making so many observations and allows them to instead use the generalization to predict what will happen in specific circumstances in the future. So, for instance, from any series of observations that water freezes at 0°C at sea-level it is valid to infer that the next sample of water will do the same--but only if induction works. That such a prediction comes true when tried merely adds to the series; it does not establish the reliability of induction, except inductively. The problem is, then, what justification can there be for making such an inference?

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Karl Popper , an influential Philosopher Of Science , sought to resolve the problem in the context of the Scientific Method , in part by arguing that science does not primarily rely on induction, but rather primarily upon deduction, in effect making Modus Tollens the centerpiece of his theory. On this account, when assessing a theory, one should pay greater heed to data which is in disagreement with the theory than to data which is in agreement with it. Popper went further and stated that a hypothesis which does not allow for experimental tests of falsity is outside the bounds of science. However, critics of Popper's approach to solving the problem, such as the famous Utilitarian and Animal Rights advocate Peter Singer , argue that Popper is merely obscuring the role Induction plays in science by concealing it in the step of Falsification . In that, they mean that the proposition of something having been falsified is in and of itself a scientific theory and can only be assumed to be definitive through induction; no matter how many times a proposition is demonstrated to be accurate, when taken as a strict matter of logic it cannot necessarily be assumed that the proposition will always be accurate under the same circumstances. For this reason, among others, contemporary Scientific Research regards all Hypotheses and Theories as tentative, validated in terms of degrees of confidence rather than true/false propositions.

Nelson Goodman presented a different description of the problem of induction in the article " The New Problem Of Induction " ( 1966 ). Goodman proposed a new colour, " Grue ". Something is grue if it is green up until some given time, and blue thereafter. The "new" problem of induction is, how can one know that grass is indeed green, and not grue? The standard scientific response is to invoke Occam's Razor .


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