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Of course he did. But I can not think of a justification available to Aristotle that wouldn't equally justify that Sun revolves around the Earth. Yet "Aristotle knew that Sun revolves around the Earth" would be seen as a misuse of "knew". Did Aristotle know that water is heavier than air? Sure, but to him it meant that the natural place of air is above the natural place of water. Are we still answering "yes"? Did he know that the universe is finite? Did Newton know the law of inertia? Keep in mind that to him inertial motion happened relative to the absolute space, and means of formulating the law without it weren't worked out until late 19th century. Did Eistein know about the dark energy? Cosmological constant was introduced to stabilize the universe, not to accelerate its expansion.

These are historical examples of the Gettier problem of knowledge as justified true belief (JTB), when a person is justified in her belief, and the belief is true, but the justification relies on elements that are false. To put it plainly, a person believes the right stuff for the wrong reasons, but this "wrongness" is external to justification. Officially, Gettier knowledge is not knowledge, but "X knew that p" is colloquially interpreted as "X believed that q, which is translated into modern terms as p, and comes out as true", otherwise if X still believed that q then "X mistakenly believed that p".

I used to think that Kuhn's "incommensurable paradigms" are an exaggeration, and perhaps they are, but there is a genuine problem there. Let us grant downward correspondence, that is that "less advanced" paradigms can be imported into "more advanced" ones using anachronistic translation, and cheerfully assume that today we know what's true. This still leaves the problem of Gettier knowledge. The justifications historical figures had for their beliefs invariably depended, at one place or another, on something that we now hold false. People often ask on the history site if people knew p before modern times, or who first discovered p. I usually give a colloquial answer, with reservations, and then try to explain how modern concepts emerged, and differ from the historical ones. Is there a more principled way? Kuhn's dissolution of the question as meaningless seems extreme, but the colloquial interpretation is hardly a satisfactory philosophical position.

What do we count as "knowledge" in centuries past? How do we measure dependence on "false lemmas", and how slight is it supposed to be to still produce knowledge? What are the approaches to the Gettier problem in the context of the history of science, in particular concerning the growth of knowledge? How is the flaw it reveals in the notion of the downward correspondence addressed? Are alternatives to JTB, that SEP barely mentions, more suitable in historical contexts?

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    What is the question you want the SE to answer? – virmaior Dec 9 '15 at 1:51
  • More and more I think the distinction between 'knowing' and simply 'believing' is just a philosophical red herring. Yes, the truth of a belief matters, but the correspondence of belief to truth should always be thought of as a likelihood. Think of Bayesian probabilities, where any 0% or 100% belief in an idea breaks the ability of the system to ever respond to new evidence. – kbelder Dec 9 '15 at 19:03
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John McLaughlin used to host a talk show on PBS called the McLaughlin group, with two conservative and two liberal panelists; McLaughlin was conservative. When one of the liberal panelists (especially Mort Kondracke) made an insightful point, McLaughlin would say that the panelist had "stumbled uncontrollably into the truth".

There is a certain amount of historical wisdom that is only accidentally right--the proponents did stumble into the truth, despite their justification being wholly wrong. Whatever label you give to it ("knowledge" or something else), the key is that if the rightness of their justification had really mattered at the time, people would have been doing things that were wrong, which demonstrates that it wasn't a good model of reality. If it didn't matter at the time, pragmatically, they had functional knowledge.

When it comes to the relationship between the Sun and Earth, however, the ancient Greeks did have some compelling evidence that the Sun was more likely to be at the center of the system. And if some of the details of Aristarchus' calculations were wrong, the logic did not require them to be correct to that degree of accuracy, just like many proofs will go through just fine if a function is merely continuous instead of smooth. The rationale may have made stronger assumptions than necessary, or two conceptual structures may be largely isomorphic such that even if the wrong one was used, you'll get the right answer in many cases.

And that, if you care to employ it (at least conceptually) is a reasonable method for assessing degree of functionality of "knowledge" (or whatever you call it).

So you have to be careful when thinking about historical knowledge; people may have had good enough reasons to believe what they believed for you to want to credit those beliefs with some positive tag like "knowledge".

But in many ways it's simply the wrong question. Reality does not seem to be structured such that we can cleanly separate things into "knowledge" and "not". This is, to my mind, much of the point of Popper's ideas of falsification and corroboration: you don't, in the end, have "knowledge", only beliefs with varying degrees of corroboration and problems. I don't think Kuhn meaningfully expanded upon that basic point even if he viewed the process as rather different (at once more mundane, between revolutions, and more radical, during them).

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    In the case of ancient heliocentrism the empirical evidence (absence of parallax, non-uniformities etc.) was largely against it, nor did the accuracy of available observations provide theoretical grounds that Copernicus later had. But I am interested not in judgement calls on history but in positive proposals on how to analyze "good enough for knowledge", especially in historical contexts. If it is phrased in degrees so much the better. But Popper and Kuhn are equally unhelpful, one is blind to context, the other sees nothing but. Maybe something like Carnap's analysis applied to history. – Conifold Dec 9 '15 at 4:48
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    @Conifold: The Ancient Greek built at least one metallic mechanistic calender which included a mechanic representation of some quite exact maths regarding the movement of Sun, Earth, Moon and even some planets like Jupiter and Venus in exaclty the correct relations. I think they went there through accepting the giveness of perceptions, theorizing about them and pragmatistic trial and error. In other words: scientific method. They where much more developed we want them seen. – Philip Klöcking Dec 9 '15 at 8:28
  • @Philip Klöcking You probably mean the Antikythera mechanism, it is based on Babylonian data transmitted to Greeks after Aristarchus. It was modeled by Hipparchus with at most one epicycle for each planet. One of the strongest arguments Copernicus had, that to match observations geocentrism requires unwieldy towers of epicycles complete with ad hoc equants, was not available to Hipparchus, let alone Aristarchus. Aristarchus's main motivation seems to have been that the Sun is larger than the Earth, but he could not explain the absence of parallax and fly-off effects, or unequal seasons. – Conifold Dec 9 '15 at 21:31

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