Editing Inductive reasoning (section)

===Early modern philosophy===
In 1620, [[Early modern philosophy|early modern philosopher]] [[Francis Bacon]] repudiated the value of mere experience and enumerative induction alone. [[Baconian method|His method]] of [[inductivism]] required that minute and many-varied observations that uncovered the natural world's structure and causal relations needed to be coupled with enumerative induction in order to have knowledge beyond the present scope of experience. Inductivism therefore required enumerative induction as a component.

====David Hume====
The empiricist [[David Hume]]'s 1740 stance found enumerative induction to have no rational, let alone logical, basis; instead, induction was the product of instinct rather than reason, a custom of the mind and an everyday requirement to live. While observations, such as the motion of the sun, could be coupled with the principle of the [[Uniformitarianism|uniformity of nature]] to produce conclusions that seemed to be certain, the [[problem of induction]] arose from the fact that the uniformity of nature was not a logically valid principle, therefore it could not be defended as deductively rational, but also could not be defended as inductively rational by appealing to the fact that the uniformity of nature has accurately described the past and therefore, will likely accurately describe the future because that is an inductive argument and therefore circular since induction is what needs to be justified.

Since Hume first wrote about the dilemma between the invalidity of deductive arguments and the circularity of inductive arguments in support of the uniformity of nature, this supposed dichotomy between merely two modes of inference, deduction and induction, has been contested with the discovery of a third mode of inference known as abduction, or [[abductive reasoning]], which was first formulated and advanced by [[Charles Sanders Peirce]], in 1886, where he referred to it as "reasoning by hypothesis."<ref>{{Cite journal |last=Plutynski |first=Anya |date=2011 |title=Four Problems of Abduction: A Brief History |url=https://philpapers.org/rec/PLUFPO |journal=HOPOS: The Journal of the International Society for the History of Philosophy of Science |volume=1 |issue=2 |pages=227–248 |doi=10.1086/660746 |s2cid=15332806 |access-date=16 April 2022 |archive-date=11 April 2023 |archive-url=https://web.archive.org/web/20230411064730/https://philpapers.org/rec/PLUFPO |url-status=live |url-access=subscription }}</ref>  Inference to the best explanation is often, yet arguably, treated as synonymous to abduction as it was first identified by Gilbert Harman in 1965 where he referred to it as "abductive reasoning," yet his definition of abduction slightly differs from Pierce's definition.<ref>{{Cite journal |last=Mcauliffe |first=William H. B. |date=2015 |title=How did Abduction Get Confused with Inference to the Best Explanation? |url=https://www.jstor.org/stable/10.2979/trancharpeirsoc.51.3.300 |journal=Transactions of the Charles S. Peirce Society |volume=51 |issue=3 |pages=300–319 |doi=10.2979/trancharpeirsoc.51.3.300 |jstor=10.2979/trancharpeirsoc.51.3.300 |s2cid=43255826 |issn=0009-1774 |access-date=16 April 2022 |archive-date=16 April 2022 |archive-url=https://web.archive.org/web/20220416041215/https://www.jstor.org/stable/10.2979/trancharpeirsoc.51.3.300 |url-status=live |url-access=subscription }}</ref>  Regardless, if abduction is in fact a third mode of inference rationally independent from the other two, then either the uniformity of nature can be rationally justified through abduction, or Hume's dilemma is more of a trilemma.  Hume was also skeptical of the application of enumerative induction and reason to reach certainty about unobservables and especially the inference of causality from the fact that modifying an aspect of a relationship prevents or produces a particular outcome.

====Immanuel Kant====
Awakened from "dogmatic slumber" by a German translation of Hume's work, [[Immanuel Kant|Kant]] sought to explain the possibility of [[metaphysics]].  In 1781, Kant's ''[[Critique of Pure Reason]]'' introduced ''[[rationalism]]'' as a path toward knowledge distinct from ''[[empiricism]]''.  Kant sorted statements into two types.  [[analytic-synthetic distinction|Analytic]] statements are true by virtue of the [[syntax|arrangement]] of their terms and [[semantics|meanings]], thus analytic statements are [[tautology (logic)|tautologies]], merely logical truths, true by [[logical truth|necessity]]. Whereas [[analytic-synthetic distinction|synthetic]] statements hold meanings to refer to states of facts, [[contingency (philosophy)|contingencies]]. Against both rationalist philosophers like [[René Descartes|Descartes]] and [[Gottfried Wilhelm Leibniz|Leibniz]] as well as against empiricist philosophers like [[John Locke|Locke]] and [[David Hume|Hume]], Kant's ''[[Critique of Pure Reason]]'' is a sustained argument that in order to have knowledge we need both a contribution of our mind (concepts) as well as a contribution of our senses (intuitions). Knowledge proper is for Kant thus restricted to what we can possibly perceive (''[[phenomena]]''), whereas objects of mere thought ("[[Thing-in-itself|things in themselves]]") are in principle unknowable due to the impossibility of ever perceiving them.

Reasoning that the mind must contain its own categories for organizing [[sense data]], making experience of objects in ''space'' and ''time ([[phenomena]])'' possible, Kant concluded that the [[Uniformitarianism|uniformity of nature]] was an ''a priori'' truth.<ref name="Salmon" />  A class of synthetic statements that was not [[contingency (philosophy)|contingent]] but true by necessity, was then [[synthetic a priori|synthetic ''a priori'']].  Kant thus saved both [[metaphysics]] and [[Newton's law of universal gravitation]]. On the basis of the argument that what goes beyond our knowledge is "nothing to us,"<ref>Cf. {{Cite book|last=Kant|first=Immanuel|title=Critique of Pure Reason|year=1787|pages=B132}}</ref> he discarded [[scientific realism]].  Kant's position that knowledge comes about by a cooperation of perception and our capacity to think ([[transcendental idealism]]) gave birth to the movement of [[German idealism]].  [[Georg Friedrich Wilhelm Hegel|Hegel]]'s [[absolute idealism]] subsequently flourished across continental Europe and England.