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My scales has been accurate for the past year. I weigh something today using my scales and it says that it weighs 1kg. Should I assume that the measurement is accurate? If so, why?

Here is the explanation for the question.

It seems to me that when we have two mutually exclusive options and we wish to decide which to assume is true for a practical purpose, we should gather evidence for each side (and gather evidence against each side if possible), and we should assume that the option with the most evidence in favour of it overall is the most reasonable one to assume true for our practical purpose.

In the case above, it seems to me that there is no evidence in favour of each side that the other side cannot explain:

  • It's possible that my scales gave me the accurate result, but its accurate performance in the past doesn't seem to provide evidence towards this, since it's possible that at some point it will malfunction.

  • It's also possible that my scales has finally malfunctioned, but there is clearly no evidence in favour of this whatsoever.

If my reasoning is correct, there is no reason to accept either option more than the other since there is no evidence in favour of any side. If so, which option should I choose? It seems intuitively clear to me that I should assume that my scales has not malfunctioned but I cannot explain why this should be true.

This question also applies to many results established by the scientific method: e.g. if we have 1000 observations made by instruments of a given phenomenon, it seems to me that we could simply claim that the instruments malfunctioned, as above.

It seems to me that probability might contain the answer, but I cannot see how.

Thank you for your help.

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    You are just stating the en.m.wikipedia.org/wiki/Problem_of_induction Look to consilience, which is to say convergence of evidence; & 'real patterns, especially continuous symmetries under transformation - see philosophy.stackexchange.com/questions/92058/…
    – CriglCragl
    Jul 23 at 19:53
  • If the battery power indicator reads zero and the 1kg weight is you, you should believe it's out of batteries. To borrow an aphorism from medicine: treat your patient, not the monitor. That is: consider the totality of available observations about the expiriment, the apparatus, and the apparatus readout, not just the latter.
    – g s
    Jul 23 at 21:41
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    If it's an important measurement, you should calibrate your scale every single time.
    – user4894
    Jul 23 at 22:18
  • @CriglCragl Thank you for directing me to this, that is exactly my question. Are there any generally accepted solutions to the problem?
    – A-Level Student
    Jul 25 at 18:54
  • @A-LevelStudent: Sure, there are a range of ways to address it, if not exactly 'solve' it, eg: plato.stanford.edu/entries/induction-problem Mainly it's about changing how we think about scientific truth into a en.wikipedia.org/wiki/Deflationary_theory_of_truth I see this as arising from deciding the status of mathematics, a divisive issue in philosophy. I give my views in this answer: 'The Unreasonable Ineffectiveness of Mathematics in most sciences' philosophy.stackexchange.com/questions/92058/…
    – CriglCragl
    Jul 25 at 19:43

2 Answers 2

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This is a question relating to the portion of statistics dealing with measurement theory. Anyone using a measurement tool repetitively over long periods of time must understand and apply certain foundational principles from that field to ensure the accuracy of the results over time, as follows.

CONTROL CHARTING

every time you take a measurement, you plot the result on a chart with the measurement on the y-axis and the calendar date on the x-axis. a sharp change in the measurement value occurring at a specific date which persists suggests an event which knocked the measurement tool out of whack, which event can be read straight off the control chart.

CALIBRATION

Any tool which is used to make measurements over long periods of time must be intermittently calibrated against a test standard of precisely known value to ensure that the measurements are reliable. Those calibration events are likewise marked on the control chart; measurements taken during the period between two calibration events where the calibration measurements reveal no error can be considered reliable.

As such, philosophical considerations do not enter into the picture at all.

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  • Suppose that I have made a control chart for and have calibrated my scales every day of the past year as you have suggested. Surely my question still applies - even with all of the above surely it is possible that my scales has suddenly malfunctioned?
    – A-Level Student
    Jul 23 at 21:31
  • What I describe is the bare minimum. any and all deviations from the control limit on the chart must be investigated. control charts and calibrations do not prevent malfunctions- they allow you to detect them as soon as possible after they occur.
    – niels nielsen
    Jul 24 at 3:49
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My scales has been accurate for the past year. I weigh something today. Should I assume that the measurement is accurate? If so, why?

This is a risk assessment. Your "assumptions" are measured against the consequences of being wrong. If I weigh myself daily and my weight for the year (180lbs) never fluctuates more than 2 lbs between measurements then any measurement of my weight within 2 lbs can be trusted. If one day I step on the scale and it says 300 lbs or 15 lbs then I should probably check the owners manual and a mirror. But the consequences to me of my scale being off are negligible.

For safety-critical systems where the risk is much higher, there are both redundant measurements and redundant measurement systems to ensure accuracy. Usually in odd numbers where the accepted measurement is determined by a "majority rules" system.

Finally, some wisdom my father drilled into me about assumptions: When you assume you make an "ass" out of "u" and "me".

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