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Topic: Problem of induction

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	Problem of induction - Wikipedia, the free encyclopedia
		The problem of induction is the philosophical issue involved in deciding the place of induction in determining empirical truth.
		Karl Popper sought to 'bypass' the problem in the philosophy of science by arguing that science does not actually rely on induction, developing the notion of falsification instead.
		Nelson Goodman presented a different description of the problem of induction in the article "The New Problem of Induction" (1966).
	en.wikipedia.org /wiki/Problem_of_induction (526 words)

	Problem of Induction
		The problem of induction is concerned with logical justification.
		Induction is like writing "Gold" on a box into which I then place a nugget of gold, and then another, and then another, and so on, until the observer of my actions is challenged to predict the material of the next nugget to go into the box.
		Induction is logically inconsistent in that the number of possible cases which might be observed is infinite and no number of observed cases which give the same result can therefore increase the probability of that result occurring in the next observed case, because no number can make a dent on infinity.
	www.faragher.freeserve.co.uk /induct.htm (1373 words)

	The Problem of Induction, by Sir Karl Popper
		In other words, the logical problem of induction arises from (1) Hume's discovery (so well expressed by Born) that it is impossible to justify a law by observation or experiment, since it 'transcends experience'; (2) the fact that science proposes and uses laws 'everywhere and all the time'.
		The place of the problem of induction is usurped by the problem of the comparative goodness or badness of the rival conjectures or theories that have been proposed.
		For the problem is, of course, whether 'the unanimous testimony of historians' is to be accepted, or whether it is, perhaps, to be rejected as the result of their reliance on a common yet spurious source.
	www.dieoff.org /page126.htm (13219 words)

	Metaphysics and Induction’: Reply and Rejoinder
		The key to Whitehead’s understanding of the problem of induction and of its solution lies in his recognition of our direct experience of causal efficacy, that vector aspect of experience by which the immediate past is felt as imposing limitations on the present, and the present felt as making a difference to the future.
		One may grant Gutting’s point with regard to the epistemological problem without in the least admitting that causality is neither a sufficient nor a necessary condition for the metaphysical problem of induction.
		To minimize the significance of (2) is precisely to ignore the fact that the concrete locus of the problem of induction is the particular inductive inferences made by individuals.
	www.religion-online.org /showarticle.asp?title=2342 (1874 words)

	Strange Loops - Problem of Induction
		Induction would state the general conclusion that around ninety percent of bullets fired from the gun (be they in the future, or hypothetical shots that never actually take place) will land within two inches of the target.
		The obvious problem with the view of the ordinary language philosopher is that induction defined this way seems useless; we are after a reasoning that leads to likelihood that the conclusions are true, which this type of induction does not do.
		The problem of induction is focused on the fact that an induction that does not lead to likelihood of truth means that we have no reason to accept much of science and human knowledge (which is based around inductive reasoning) as true.
	www.strange-loops.com /philinduction.html (1736 words)

	Bonjour on Induction
		The problem of induction arises in the first place after all from viewing induction as a mode of reasoning or argument that claims to be rationally cogent, that is, one in which the (probable) truth of the conclusion is at least claimed to follow in a rationally intelligible way from the truth of the premises.
		A view of inductive generalization as non-inferentially perceived suggests that the epistemological problem of induction is at least poorly formulated in terms of a mistaken conception of how general empirical beliefs are formed and accepted.
		Armstrong undermines the prospects of a solution to the problem of induction on his own view by allowing nomic relations to hold between “quasi-universals,” universals indexed to particulars or spatio-temporal regions (such as being a negatively charged body on earth).
	facweb.bcc.ctc.edu /wpayne/bonjour_on_induction.htm (3313 words)

	Popper on induction (Site not responding. Last check: 2007-11-07)
		This solves the problem of the alleged clash between the principles (1), (2), and (3), and with it Hume's problem of induction.
		It is essentially merely a slight extension of Hume's logical problem of induction formulated here, earlier, in section V. The answer to this problem is: as implied by Hume, we certainly are not justified in reasoning from an instance to the truth of the corresponding law.
		Induction is logically invalid; but refutation or falsification is a logically valid way of arguing from a single counterinstance to — or, rather, against — the corresponding law.
	www.cavehill.uwi.edu /bnccde/ph29a/popper.html (5281 words)

	Diettrich (1995) A Constructivist Approach to the Problem of Induction (Site not responding. Last check: 2007-11-07)
		Summary The unsolved problem of induction is closely linked to "the unreasonable effectiveness of mathematics in the natural sciences" (Wigner 1960) and to the question "why the universe is algorithmicly compressible" (Davies, 1990).
		The problem of induction is approached here by means of a constructivist version of the evolutionary epistemology (CEE) considering both, the perceived regularities we condense to the laws of nature and the mathematical structures we condense to axioms, as invariants of inborn cognitive and mental operators.
		The difficulty of classical approaches towards the problem of induction follows from the idea that the operators generating the regularities of our perceptions are exclusively non-mental external mechanisms.
	www.vub.ac.be /CLEA/people/diettrich/induction.html (14277 words)

	Problem of Induction (Site not responding. Last check: 2007-11-07)
		For induction to be rationally justified, it is not enough that i-arguments have been reliable in the past.
		The commonsense problem of induction is based on the ‘bucket theory of the mind’—roughly, the assertion that ‘there is nothing in our mind which has not entered through our senses.’ But we do have expectations and we strongly believe in regularities.
		But for Popper, there is no such thing as induction by repetition (simple enumerative induction), as is shown by the fact that it is false that "The sun will rise and set once in 24 hours" (counterexample: the midnight sun at the Earth’s poles) and "All bread nourishes" (counterexample: ergotism in a French village).
	philosophy.wisc.edu /Forster/220/Notes2.html (3028 words)

	Problem of induction (Site not responding. Last check: 2007-11-07)
		The Problem of Induction is the philosophical issue involved in the place of induction in determining empirical Thus I know from direct sensations (vision...) that you dropped a rock on toe.
		David Hume addressed this problem in the 18th century in a particularly influential way and analysis since has managed to evade Hume's Hume looked at ways to justify inductive He pointed out that justifying induction on grounds that it has worked in the begs the question.
		Sir Karl Popper sought to 'bypass' the problem in philosophy of science by arguing that science does not rely on induction developing the notion of falsification instead.
	www.freeglossary.com /Problem_of_induction (785 words)

	Hume's Problem Of Induction - Objectivism Online Forum (Site not responding. Last check: 2007-11-07)
		Now if the question were about how induction should work, that would be an interesting question, but to say "error is possible in knowledge" is a fairly useless statement (especially if you neglect to complain about "the problem of deduction").
		It was addressed in the sense that she combined (i) a proper conception of the law of causality (which Hume, by means of a long series of historical errors, arrived at an opposite conception) with (ii) a correct theory of concept formation and (iii) a contextual theory of knowledge acquisition.
		First, induction is classically defined as deriving general principles from particulars (in contrast to deduction, which is deriving particulars from a general principle).
	forum.objectivismonline.net /index.php?showtopic=3974 (2365 words)

	Station Information - Problem of induction
		Such a conclusion is reached by what is called inductive reasoning, but the problem of induction is whether inductive reason works.
		Prior to Hume, Sir Francis Bacon had made a strong claim that science was based on induction.
		Sir Karl Popper sought to 'bypass' the problem in the philosophy of science by arguing that science does not actually rely on induction, developing the notion of falsification instead.
	www.stationinformation.com /encyclopedia/p/pr/problem_of_induction.html (506 words)

	Secular Responses to the Problem of Induction
		The induction applied at the second level (to arguments) is distinct from that applied at the first level (to objects in the world), thus no objectionable circularity is involved.
		While many philosophers, such as Reichenbach, concede that the problem of induction is indeed a real problem and acknowledge that the demand for a justification of induction is legitimate and important, other philosophers have argued that demanding a justification for induction is improper — or worse, incoherent.
		Wesley Salmon, ‘The Pragmatic Justification of Induction’ in Swinburne (1974), pp.
	www.ccir.ed.ac.uk /~jad/induction.html (2501 words)

	The Problem of Induction (Site not responding. Last check: 2007-11-07)
		The problem of induction was first raised by David Hume.
		Hume considers the suggestion that every inductive argument has a principle of induction as a suppressed premise and it is this principle of induction that renders the inference from premises to conclusion rational.
		However, if this principle of induction is to render inductive inferences rational, then we need some grounds for thinking that it is true.
	facweb.bcc.ctc.edu /wpayne/problem_of_induction.htm (286 words)

	Peter Suber, "Mathematical Induction"
		Prove that the property of complying with the theorem is "hereditary" and extends to all the successors of the minimal case.
		The induction step is the proof of a conditional statement, namely, "if the theorem is true of the ancestor case, then it is true of the descendant cases." The if-clause of this conditional statement, asserting that the theorem is true of the ancestor case, is called the induction hypothesis.
		Notice that the induction step is to prove a conditional statement, of which the induction hypothesis is the antecedent.
	www.earlham.edu /~peters/courses/logsys/math-ind.htm (1191 words)

	Math Forum - Ask Dr. Math
		Date: 10/14/97 at 20:30:20 From: sharon wesolowski Subject: Induction Hi, I am having a problem with the reasoning of the left side of an induction problem.
		Here's the original problem: Use math induction to prove that (1 + 2 + 3 +....n)^2 = 1^3 + 2^3 + 3^3....n^3 This is what I have done: p(k) = (6)^2 = 36 n^2 = [(n)(n+1)(2n+1)]/6{p} = {pk} [n^2(n+1)^2]/4 [k(k+1)(2k+1)}/6 = [k^2(k+1)^2]/4 Pk+1 = [(k+1)^2(k+2)^2/4 = (4k-3) + (4k+1) Here I am stuck.
		Actually, induction was involved, since you need it to prove the two formulas that you used.
	mathforum.org /library/drmath/view/52413.html (397 words)

	PhilSci Archive - The Epistemological Root of the Problem of Induction
		The Epistemological Root of the Problem of Induction
		Badino, Massimiliano (2004) The Epistemological Root of the Problem of Induction.
		This paper analyzes the epistemological significance of the problem of induction.
	philsci-archive.pitt.edu /archive/00002115 (178 words)

	Francis Bacon
		Whereas induction, invention, and judgment presuppose “the same action of the mind”, this is not true for proof in the syllogism.
		Induction implies ascending to axioms, as well as a descending to works, so that from axioms new particulars are gained and from these new axioms.
		His induction, founded on collection, comparison, and exclusion of factual qualities in things and their interior structure, proved to be a revolutionary achievement within natural philosophy, for which no example in classical antiquity existed.
	plato.stanford.edu /entries/francis-bacon (8593 words)

	Popper's Solution to Induction (Site not responding. Last check: 2007-11-07)
		But the guilty lemma in Popper's system is not his solution to induction; rather, what makes his system difficult to accept is his pseudo-formal treatment of the concept of verisimilitude, or approximation to truth.
		According to Popper, induction is "inference from repeatedly observed instances to some as yet unobserved instances" (P 103).
		The "problem of induction" is, given that humans use such inductive inferences, whether induction is justified; the solution, according to Popper, is that humans -- if they are rational -- do not use any induction at all.
	www.stanford.edu /~ecelyft/papers/Popper.htm (945 words)

	IIDB - Problem of Induction (Site not responding. Last check: 2007-11-07)
		The process of induction most often, but not always, argues from a collection of individual instances, a collection of particulars, to a generalization - as I did.The probability of the truth of the generalization is only as good, or reliable, as the size and quality of the sample.
		Induction had led to the belief that 'All swans are white.' 'til the fl swans were discovered.
		Induction isn't groundless, it works with deduction, just as deduction works with the observations we gain from induction.
	www.iidb.org /vbb/showthread.php?goto=newpost&t=90899 (3000 words)

	The problem of induction. (Site not responding. Last check: 2007-11-07)
		Induction in science is not to be confused with mathematical induction.
		Scientific induction is a method whereby general laws (about the ``real'' world) are drawn from specific observations of that world.
		This a burning issue in the philosophy of science; a problem that is by no means solved.
	musr.physics.ubc.ca /~jess/sci1/biol/science/node4.html (509 words)

	my 2¢ on the problem of induction
		Dear Robert and Friends, "The" problem of induction is many problems.
		(But query: What is a "singular" event?) Some observers take the view that "the" problem of induction proper deals with the effort to construct generalizations or the like from "singulars" or single instances or events.
		Another question about induction is whether "the" problem of induction devolves into the question of the "logic" of induction.
	www.mail-archive.com /uai@cs.orst.edu/msg00321.html (604 words)

	The Problem of Induction as Pseudo-Problematic
		problem with believing in causes without appealing to a cause (of the problem).
		There remain problems of another type, however, which must be discussed before concluding our analysis; problems relating to the authenticity of the mystical experience in light of several of the more significant objections commonly brought to bear against it.
		This, of course, is the Problem of Induction forcefully stated by the skeptic David Hume in his Treatise of Human Nature (Bk.
	www.johnofthecross.com /the_problem_of_induction_as_pseudo-problematic.htm (4637 words)

	3 David Hume and the problem of induction
		The problem with this methodology is that it breaks one of the fundamental rules of logic.
		The problem here is that no amount of observations of a consequence will ever prove the antecedent – or in other words – you can’t generalize from particular events to make universal laws or claim to have absolute knowledge of the Universe.
		This alarming conclusion has become known “Hume’s” problem or the “problem of induction” and appears to make scientific theories of the world no more valuable than any other form of “metaphysical” (not empirical) theory of the world.
	www.abdn.ac.uk /physics/px2511/Hume.htm (482 words)

	A problem with double induction (Site not responding. Last check: 2007-11-07)
		The problem: I wish to prove results along the lines of (g1,g2:context)(ceq g1 g2)->(g3:context)(ceq g2 g3)->(ceq g1 g3) by using two inductions, one on the derivation of (ceq g1 g2) and the other on the deriviation of (ceq g2 g3).
		Now, the problem is that g2 is common to both these derivations and when I use the elim tactic for the second induction, Coq generalizes g2 to a new term which is then in no way connected to any previous references of g2 (of which there may be many).
		Can any one explain to me a general way of performing the double induction which unifies both instances of g2 without having to work out the term of the double induction principle itself as this would become unmanageable for other parts of my formalization.
	pauillac.inria.fr /pipermail/coq-club/1997/000094.html (238 words)

	Directory - Society: Philosophy: Philosophy of Logic: Problem of Induction
		The Problem of Induction · cached · Essay by Karl Popper, arguing that there is no such thing as inductive inference.
		Conjectures · cached · PhD thesis of Peter Flach, investigating the `logic of induction' from philosophical and machine-learning perspectives.
		Mathematical Induction · cached · Lecture notes by Peter Suber, explaining the difference between inductive inference and mathematical induction (which is a species of deductive inference).
	www.incywincy.com /default?p=294982 (110 words)

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