I'd say, it is a state in a logic table, connecting initial or known states, to variables or unknown outputs. Computing involves two-valued logic, and so true is often equated to signal, and false to no signal - these can often be gate voltages that control larger currents, it's important to have accurate enough voltage discrimination. In practice true is always contextual, it depends on your model, & circuits are just one type of implementation.
To link to physics, I'd say the fundamentals are signal vs noise. This can link via Shannon entropy, to a ground-up picture of entropy in relation to signal loss or uncertainty, and to a generalisation beyond two value logics (neurons for instance involve continously varying or analogue logic, & there is quantum logic)
Edited to add: Ok I see I didn't link to the context of your question explicitly, counting and errors. It is an area of the highest importance to actual professional scientists, things like measuring gravity waves wholely depended on minimising errors.
Basically, we generalise, from small groups of things where we can check, to large groups. This clearly makes you uneasy, but it's the same principle as calculus is based on, taking the limit - we find a model that as the number of elements goes up, gets more accurate. Flip a coin once, unpredictable: flip a coin 1,000 times, we can predict the mix of outcomes very well. Errors on counts are like this, count one thing, & you can be certain how many; count 1,000 things and errors get more likely; get 1,000 people to count 1,000 things, errors get less likely. We can model it, as like a pipe, what Shannon calls a channel. We know there is a true number, (usually, quantum things get weird), the actual coin flips in a specific case. It goes through the pipe, 'counting', and we find comparing many counts that there is an average - and we think that's more accurate. We also get how many people are wrong, by how much, and that tells us how accurate the counters are - like how much a data signal is degraded by going through a pipe.
We build the model, where we can check the coin flips. But mostly in life we never get to check. So we use the average of many counts, as the true answer. You are right in a way to feel uneasy, because not only does this tend to break down on small numbers, it's also very important we are modelling what kind of source of error there is, and there are different modelled distributions, but I assume you don't want that.
You ask a deep question, and on the quantum scale we never get to know the 'true' answer of linked variables at the same time, like position and momentum. That also makes many people uneasy. We live in a world full of errors & uncertainties, but that doesn't make knowledge impossible. The real problem is our intuition that 'true' always means getting to look behind the curtain - 'getting our homework marked by god'. When we think hard though, we find 'true' isn't in the 'facts', it is in the whole situation of evaluating them, and never stand separately from them.