No matter how many observations of a system are made, there will always be a set of trajectories in model state space indistinguishable from the actual trajectory of the target system
A mathematical description of all the possible conditions or configurations a simplified representation of something could be in.
observations of a system(in philosophy of science and epistemology)
The data or measurements you collect about something (like temperature readings from a weather system or position measurements from a moving object).
trajectories(as used in physics and philosophy)
The paths that objects follow through space over time, like the arc of a thrown ball.
underdetermination (implicit concept)(in epistemology and philosophy of science)
The philosophical problem that multiple different explanations or models can fit the same observations equally well, so observations alone can't tell you which one is actually true.
Of course, we do not have perfect models. But even if we did, they are unlikely to live up to our intuitions about them (Judd and Smith 2001; Judd and Smith 2004). For example, no matter how many observations of a system are made, there still will be a set of trajectories in the model state space that are indistinguishable from the actual trajectory of the target system. Indeed, even for infinite past observations, we cannot eliminate the uncertainty in the epistemic states given some unknown on