Does Milk Go Bad at Exactly Midnight of The Expiration Date?

Or, if you prefer, here are similar questions:

- Are people suddenly responsible enough to drink at midnight of their 21st birthday?

- Does driving become much more dangerous at 65.001 mph?

- Are you obese if your BMI is 30.0, but not if your BMI is 29.999?

These specific definitions are intended to address the problem of vagueness by pretending that there is precision where there is none. They're forms of the continuum fallacy, which is illustrated by trying to figure out how many grains of sand it takes to make a sand pile. If you have a some sand that is smaller than a sand pile, adding one grain will never convert it to a "pile". But that implies that achieving a sand pile is impossible if you only add one grain at a time.

So, how can vagueness be addressed? Or, more accurately, how can vagueness be managed? Mathematically, it cannot be addressed; it will remain a paradox.

A) Minimize one error, and ignore the other -- which seems to be the usual solution. That is, set an expiration date that will ensure that only 5% of milk will go bad -- and accept the negative consequence that lots of otherwise good milk will be discarded. Or, set a speed limit that will reduce fatal accidents to 5% of unrestricted speed fatalities, and accept that many people will pay the price of wasting lots of time by driving too slow. There's nothing magic about 5% in these cases; in fact, one would have to need to balance the two types of error to find the "correct" solution. But as long as the solution is "one size fits all", there will be inefficiencies and equity concerns. ("Why should that inept person be allowed a drivers license when it is denied to me because I am under the cutoff age? I'm a better driver; I should be driving him!")

B) Redefine these terms to have more categories; i.e. milk can have a "fresh" date, a "probably fresh" date, a "little curdling" date, and a "foul" date. This provides more useful information, though it can be unnecessarily confusing. Also, it does not address the vagueness issue because each of these new categories would be defined by artificially precise dates.

C) Assign probabilities to freshness; i.e., develop a thermometer-like scale from 0% freshness to 100% freshness. However, this doesn't address the problem; it ignores it. By analogy, this would be like replacing the vague word "fever" with only a numerical gauge.

D) Evaluate every product and person individually. This addresses equity issues, but not vagueness. That is, it doesn't explain exactly when someone becomes obese or bald.

E) Use plain-English and common-sense intuition to either override or complement numerical data and express the evaluation in plain English. Milk sitting at room temperature, someone driving 75 mph with no traffic nearby, and a psychopath 35-year old reaching for a case of beer are all examples of where unanticipated factors invalidate the original "rules" and would make us say, respectively, that the milk might be getting old, that there is minimal added danger in driving faster, and that the psychopath should probably not drink too much, regardless of age. It's related to fuzzy logic, and though it doesn't resolve the vagueness paradox, it does help solve the problem.