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I'm a physicist interested in exploring philosophy. As a motivation, let me give a few contradictory statements about gravity:

"Acceleration due to gravity is a constant 9.81m/s^2"

"Gravity follows Newton's law of gravitation."

"Gravity is due to the warping of space-time, as described by general relativity."

In the context of physics, all of these assertions are generally considered to be true (roughly speaking). Even so, they are all quite contradictory. The first statement says that gravity is constant, while the second tells you how gravity varies. Finally, the third states things that are entirely contradictory with the first two about possible behaviour of gravity (such as gravity waves, or light interacting gravitationally). These statements are all considered true however, because they're accurate and precise enough within some particular context of interest.

Another way of phrasing the question, is the idea of "approximately true" statements explored with any depth in the philosophical literature? Are there any common positions taken for this topic? If so, where would I start for reading on the issue?

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    It is widely recognized that meaning of sentences (and hence their truth) is context dependent, some take it all the way to relativism, see contextualism. In your examples surface of the Earth or small masses and velocities are the implicit contexts that remove "contradictions". But "true" or "approximately true" as applied to empirical theories are generally controversial in philosophy, see e.g. Barrett's Are Our Best Physical Theories (Probably and/or Approximately) True? – Conifold Mar 18 '18 at 22:22
  • These statements are not philosophical statements but scientific ones. And the reason they appear contradictory is because you are leaving out context. For instance the first statement is more better made as "Near the Earth's surface, gravity causes downward acceleration to the amount of 9.81 meters per seconds squared". – MichaelK Mar 19 '18 at 6:11
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    There is an extensive literature on idealizations. Think of the ideal gas law: it assumes that molecules have zero size, and so on, which is false. So the model is only approximately true, and yet it seems wrong to call the ideal gas law “false”. See oxfordbibliographies.com/view/document/obo-9780195396577/… for a more thorough account of the literature. – shane Mar 19 '18 at 19:51
  • Possible duplicate - philosophy.stackexchange.com/questions/47885/… – Yechiam Weiss Mar 21 '18 at 10:42
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You might perhaps like to start your reading with David Lewis’ immensely influential 1979 paper, Scorekeeping in a Language Game (http://www.andrewmbailey.com/dkl/Scorekeeping_in_a_Language_Game.pdf), which addresses this sort of thing, and in part spawned a massive literature spanning multiple disciplines.

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Roy Sorensen has an article on just this topic. He considers vagueness and accuracy in the truth condition (as well as in the belief and other conditions) for knowledge :

Roy A. Sorensen, 'The Vagueness of Knowledge', Canadian Journal of Philosophy, Vol. 17, No. 4 (Dec., 1987), pp. 767-804.

1987 is a long way back but it is still a valuable article.

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