## Have philosophers explored the ideas of accuracy and precision when considering the truth of a statement?

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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 – 2018-03-18T22:22:10.523

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 – 2018-03-19T06:11:29.307

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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 http://www.oxfordbibliographies.com/view/document/obo-9780195396577/obo-9780195396577-0193.xml for a more thorough account of the literature.

– None – 2018-03-19T19:51:03.347

Possible duplicate - https://philosophy.stackexchange.com/questions/47885/are-there-degrees-of-truth

– Yechiam Weiss – 2018-03-21T10:42:26.383