By Daniel Hubbard | February 13, 2011
I like thinking about thinking. A few lines I wrote and then deleted in a report reminded me of some concepts that come up when thinking about proving a hypothesis. The sentences that I erased went something like this—”Though the year in her birth record is two years before the one claimed or implied by nearly all other records, there is one exception. Her age at marriage agrees with this earlier birth date.”
I erased those lines (and rewrote them) because of that word “agrees.” It is tempting to say that someone’s age on a specific date agrees with a birth date but that can also be misleading. If I want to be picky, and being careful about wording when working through a hypothesis is a good sort of pickiness, an age can only be consistent with a birth date and “consistent” isn’t the only way that “agree” might be interpreted. If two statements are said to agree it can mean at least two things. One is that they have virtually identical meanings. A relative might remember that someone was born on Christmas. You might then find that person’s birth certificate reads December 25. The wording is clearly different but the meaning is clearly the same. The other possibility when two statements agree is that they are consistent. Maybe that relative only remembered that the birth happened during holiday celebrations. That would certainly be consistent with a December 25th birthday but the information isn’t identical. Too often we slip from only having the less specific type of agreement to thinking we have the more specific type and the distinction can be important.
Statements can drift toward greater accuracy as they are repeated and reworked in what we write, and also in what we read in our quest for information. In a way, that is only human nature. People want to be accurate. We want to know things with precision. Yet, there is a catch. If a statement drifts toward higher and higher accuracy, less and less of the evidence will support it and more and more will simply be consistent with it. As we read or write it is easy to not notice that not only is the precision of a statement going up but that the pool of evidence for the statement is shrinking. We tend to remember that there was plenty of evidence and not realize that what helped to prove the original point may not help with the newer, more precise statement.
For example, an age can’t be used as proof that a questionable birth date is correct but it can support the possibility that the birth date is correct. That is, an age can be consistent (or inconsistent) with a birth date but it doesn’t actually prove a date. That age doesn’t give identical information.
The question is the accuracy that one is considering. A piece of accurate information can support the correctness of a less accurate piece, but trying to work the other way around leads to problems. Knowing that a man was in Tennessee doesn’t do nearly as good a job at proving he was in Memphis as knowing that he was in Memphis does of proving he was in Tennessee. That may seem obvious when put directly like this but if you keep your eyes open, I’m pretty sure that you will notice that there are all too many examples of something inaccurate being used to claim that something more accurate must be correct. It isn’t that people are always setting out to use fuzzy language to pull the wool over anyone else’s eyes. Sometimes that is the case, but often when language is a bit imprecise, our thoughts end up with the same imprecision and pretty soon a few small steps that all seem more or less OK, give you an argument that just isn’t right.
There is another way that accuracy plays into this question. What is the accuracy that is being sought? Say you suspect that someone needs to go turn off a light. That is your hypothesis. If you ask two people if it is possible that the light is on in the kitchen and one person is sure that the light is on and the other has no idea, both will answer “yes” and they would be conveying identical information. If the question had been “Is the light on in the kitchen?” then one answer would be “yes” and the other would answer “I don’t know.” The information that each person has is the same, one feels certain that the light is on and the other is unsure. Nevertheless, the question no longer results in identical answers because this question demands more precision. The two answers are still consistent with each other. On the other hand you, can’t say they are in full agreement. The information conveyed is not identical. The more precise the questions we try to answer, the more often the information we have will only be consistent with our hypothesis instead of directly supporting the hypothesis.
This brings up another ambiguous term—accuracy. What do I mean if I say a statement is accurate? Colloquially, I might mean that it is correct or I might mean that it gives a precise bit of information. Data can be precise without being correct or can be correct without being precise. A death certificate might give a precise date of birth but that date might very well turn out to be incorrect. Alternatively, that death certificate might just give a year for the birth, which is not as precise as you’d like if you are hoping for a birth date but it could be correct.
Time for some Exercise
The next time you are reading a secondary source, try reading it with an eye out for these sorts of problems. If I go back to my question about the lights being on, look for the equivalent of asking if the lights might be on, getting some yes answers and then slipping into the conclusion that the lights actually are glowing. That they are on might be the most likely thing and it is fair enough to write that it seems to be the most likely explanation but it isn’t fair to say that it is proven at that stage.
The next time you write something, think about the different bits of evidence. Do they independently state the same thing, reinforcing each other and supporting a precise claim, or are there less precise pieces of information that are consistent with what you believe but don’t literally prove it with the precision that you imply?Twitter It!