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Most people agree that knowing something one acquired from inductive reasoning is knowledge, that is justified true belief. For example we observed for years, that Sun rises from the East, we still claim that "we know, that tomorrow Sun will rise from the East", even if from epistemological point of view this position is not justified neither via evidentialism nor via reliabilism.

Basically, something isn't true yet, but there is an ultra-high probability of truthfulness, and there is also no justification, yet we call it knowledge. Does that mean that any conclusion got from inductive reasoning is strictly speaking not knowledge? How do epistemologists call and explain this phenomenon?

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Similar, but not a duplicate –  stoicfury May 15 '13 at 3:48
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We know, that tomorrow Sun will rise from the East, even if from epistemological point of view this position is not justified neither via evidentialism nor via reliabilism. Does that mean that any conclusion got from inductive reasoning is strictly speaking not knowledge?

Answer: The skeptic needs a language

Suppose a Bizarre Brain, BB, that is, the computer of the "brain in the vat" skepticism, the brain of the Descartes' devil that deceives us, a permanently dreaming brain, or the solipsistic brain that create the "universe" for itself or for us. If the BB makes her mind the object of scientific study, it will find that it behaves with the same complexity as the universe described by a Common Sense Brain, CSB. Thus what CSB calls "the universe", the BB calls "one's own mind." Understood this way, the distinction between CSB and BB collapses and amounts to different ways of describing the same thing: a massively complex process that causes all the BB's experiences. Presumably having made the case that the BB scientist is actually a CSB scientist, the BB applies Occam's Razor, and suggests to the BB scientist to prefer the CSB's standard external “reality” over something like a BB's "reality". This is because the standard "reality" fits all the data available to the scientist, and on the skeptic's hypothesis is impossible to find differences, rendering superfluous the other more complicated possibilities.

Unobservables such as atomic particles, the force of gravity, and the quantum physics, are useful representation models. "The brain in the Vat" skepticism and the solipsism are interpretations or models too. Any language which provide a practical way of thinking and make sense about natural laws, a common mind-independent world, must provide a way of expressing common true inductive inferences about this world, or a description that relates representation to prediction. What varies are the models and interpretations, but if they are to be true, what they predict does not change. There is no more an objective basis for choosing one theory/representation over another than there is for preferring the Fahrenheit to the Celsius scale for temperature ascriptions. In an interpretation, it is the meaning that is significant and that remains invariant between different, but equally adequate, theories or representations.

If too many of speakers utterances are false, then the link between what speakers say and the world is severed; and the enterprise of interpretation each other halts. Too much error in statements about the world is not an option if speakers are going to interpret each other. Therefore meaning is objective in the sense that most of what speakers say about the world are truths about the world. This is an assumption an interpreter makes because the only path into the world speakers share are the events in the world that cause them to hold those sentences true. Meaning is essentially inter-subjective.

An interpreter’s two most important assumptions are the Principle of Logical Coherence and the Principle of Correspondence. Assuming that a speaker reasons are in accordance with logical laws is not an empirical hypothesis, because satisfying the norms of rationality is a condition on speaking a language and failing to find consistency means there is nothing to interpret. The assumption that someone is rational is a foundation and condition on which the project of interpreting rests as possible. The Principle of Correspondence applies to speakers’ observation sentences, the points of causal contact between the world shared by speakers and interpreters, and the utterances of speakers. That there is no distance between the speaker’s observation and which sentences the speaker puts forward as true, is the another foundation on which the project of interpreting rests, is a condition on speaking a common language.

It does not matter that one cannot experience another's subjective sensations. One cannot feel another person’s pain, but only infer it from their behavior and their reports of it. Unless the talk of such subjective experience is learned through public experience the actual content is irrelevant; all we can discuss is what is available in our public language. The idea of a dictionary is constitute a reference of justification for a translation, but justification consists in appealing to something independent. Without justification therefore a dictionary that exists only in private language, is pointlessness, if it were to describe those inner experiences supposed to be inaccessible to others. The last speaker of a dying language would not be speaking a private language, since the language remains in principle learnable. Imagine someone is to associate some recurrent sensation with a symbol S in private language when the sensation occurs. If it is a private language, it is presupposed that S cannot be defined using other terms, such as "the feeling I get when the manometer rises"; for to do so would be to give S a place in our public language. Or consider the example of someone pointing to two nuts while saying "This is called two". How does it come about that the listener associates this with the number of items, rather than the type of nut, their color, or even a compass direction? To participate in an ostensible public definition presupposes an understanding of the process and context involved. If there is a truly particular language, if it can exist, then it must be in principle untranslatable.

Hume challenges other philosophers to come up with a deductive reason for the inductive connection. If the justification of induction cannot be deductive, then it would beg the question. To Hume, induction itself, cannot explain the inductive connection. (Wikipedia)

But I ask, why do we need to show that induction is a necessary truth? We can not demonstrate a necessary truth but we can demonstrate that we have a valid reason to believe.

The principle of uniformity refers to the assumption that the same natural laws and processes that operate in the universe now have always operated in the universe in the past and apply everywhere in the universe.

If nature is uniform, crystal gazing may or may not work, but induction works. If nature is not uniform, then induction will fail, but so will any alternative method. Because if the alternative method did not fail, if it consistently yielded true predictions, and the success of that alternative would constitute a uniformity that could be exploited by the inductive method. Because we could inductively infer the future success of the crystal gazer from her past success. Hence, the inductive method will succeed if any alternative method could.

Why do we need to know whether the inductive method is necessarily true if the inductive method will succeed if any alternative method could? We can’t have a reason for believing that induction is necessarily true because we can’t know in advance whether nature is uniform. We can’t have a reason necessarily true, but we can justify the inductive method by saying that it's the best method for making predictions about the future/unobserved, because if nature is uniform, crystal gazing may or may not work, but induction works. If nature is not uniform all methods will fail.

References: Donald Davidson, Wittgenstein, Quine, David Deutch, Wesley C. Salmon

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Judea Pearl in Causality (2nd ed. 2009), E. T. Jaynes in Probability Theory: The Logic of Science (2003), Eliezer Yudkowsky in Highly Advanced Epistemology 101 for Beginners (2012, unfinished) all give a pretty good picture of what inductive reasoning and truth is.

First of all "truth" isn't something that brains can contain. Truth is the relationship between a model of reality inside a brain, and the external reality. Models are tested by and used for prediction of sensory experiences (and thereby in mental reconstruction, the external reality). From that test, we can see who is closest to the truth: The Wright brothers had a working airplane, thus their model of how heavier-than-air flight works was probably "truer" than others at the time (what with feathers and flapping wing contraptions).

Second of all, if anyone ever says that they don't know if it is true that the sun will rise in the east tomorrow, you can ask them to bet money on the proposition. If they are willing to bet a large amount of money in favour of eastwards sunrise, that is a clear indicator that they don't even know their own internal model of the universe for what it is.

Truth is research and ideas that becomes actually flying airplane, not a question of philosophy.

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Working backwards, that's an idea of truth that is itself a philosophical claim. Second, betting money doesn't demonstrate anything. To say we don't know the sun will rise tomorrow is absolutely true, and a bet that it will isn't even a bet against the claim because that would mean betting that we do know its rise, not that it will rise. Third, the pragmatic idea of truth reduces truth to "what works" not "what is". There are many cases of pragmatically useful lies. However, truth is indeed a relationship: the conformity of the intellect to the real. –  danielm Jan 19 '13 at 1:03
    
@danielm To say that we do not know if the sun will rise tomorrow prompts us to assign a probability. Knowing isn't binary, it is a real number in the range (0, 1). I can rightfully claim I am not 100% sure that the sun will rise tomorrow, but I am in fact 99.8% sure. So I would rather bet money on eastern sunrise than not-eastern sunrise, or more generally not-sunrise. –  Karl Damgaard Asmussen Jan 20 '13 at 19:35
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