Here is the core of the concept of underdetermination; the evidence available to us at a given time may not be enough to determine what we should believe. We might see this with a simple example:
- A dozen eggs cost $6 dollars
- An apple costs $1
- Carrots cost $2 a bunch.
- I spent $12 on apples, eggs and carrots.
- How many of each did I get?
You can deduce that $6 was spent on eggs, leaving $6 for apples and carrots. However, you could buy 2 bunches of carrots and 2 apples, or 1 bunch of carrots and 4 apples. The problem is underdetermined.
We might know that just because a correlation was found between two factors, it does not follow that one causes the other. In short, correlation does not imply causation. This is also an example of underdetermination. See https://ephektikoi.ca/2020/07/13/correlating-fish-and-water/
Various philophers such as Rene Descarte and David Hume discussed ideas that presaged underdetermination, but it came to the forefront of discussion with arguments by Pierre Duhem and later with arguments by W.V.O. Quine. Duhem’s version might be called holist underdetermination, and Quine’s version contrastive underdetermination. Both, if taken seriously, have strong implications for how much we can demonstrate with scientific evidence.
Holist underdetermination argues that within a given research paradigm, we must of necessity, consider our research evidence within a web of supporting hypothesis. We can not rule out that an experimental result is false; it might be that one of the supporting hypothesis is false, and needs to be reconsidered. We need to examine the whole web of belief of the researcher, the discipline, and perhaps society in order to make sense of research results.
Contrastive underdetermination argues that for any research result, or any set of results, we can develop alternative theories which do an equivalent job of explaining the evidence.
It is still a topic of much debate among philosophers just what this implies for our understanding of scientific evidence, or our understanding of the world.
For a more thorough, though somewhat difficult, discussion see Stanford Encyclopedia of Philosophy, Underdetermination of Scientific Theory, Kyle Stanford, https://plato.stanford.edu/entries/scientific-underdetermination/, 2017.