There are no facts. There are only observations, hypotheses, approximations, and interpretations.
It’s a hot day. You glance at the old thermometer on the wall. It’s 96ºF. That’s a fact, right?
Wrong. First, you have an observation, not a fact. You saw that the top of the vertical red column on your mercury thermometer lined up with the mark for 96ºF. That’s an observation, not a fact. An observation is what your senses tell you. A fact is objectively real. Your eyes are not objective sources of information.
Second, your observation is not that the temperature is 96ºF; you observe only that the top of the vertical red column of mercury aligns with the mark for 96ºF. You conclude that the temperature is 96ºF only because you have been assured that the observations you make are indeed factual representations of reality. But if you delve into the workings of the thermometer, you realize that this conclusion is based on the assumption that the mercury expands linearly with temperature. That’s a fairly reliable assumption, being based on some solid physics. But in truth, you are engaging in syllogistic thinking, something along these lines:
Mercury expands linearly with temperature.
The void in the glass containing the mercury is a perfect cylinder.
The temperature scale next to the glass is correctly calibrated to the volume of the cylinder and the coefficient of thermal expansion of the mercury.
The temperature of the mercury is equal to the temperature of the air.
Therefore, the observation of the position of the top of the mercury is a correct measurement of the temperature.
The syllogism is valid — the logic yields correct results. However, each of the premises is actually a hypothesis, not a statement of fact. Not one of the premises is an objective fact. We might call these premises ‘assumptions’, but I think it more precise to regard them as hypotheses; this phrasing makes more clear the subjunctivity of the premises. This makes it easier for us to recognize the possibility that our conclusion might not be true.
Third, the temperature is almost certainly NOT exactly 96ºF. Perhaps it is 96.1ºF or 95.9ºF. Perhaps it is 96.2378149ºF. There is indeed some actual temperature that could be measured with precision to many digits — but we don’t have that number. What we have is an approximation of the actual temperature.
Worse, there is no such thing as “the” temperature. Temperature is a measurement that can be applied to tiny portions of a material. The temperature of the ink for the ink mark for the letter “m” in the word “temperature” on the thermometer might be 96.0239ºF, while the temperature for the ink mark for the letter “a” might be 96.0241ºF. Your reading of the temperature is a gross approximation of many slightly different temperatures.
Now, this may all seem egregiously pedantic. I just want to know roughly how hot my environment is, not split airs over different spots of ink! But this kind of thinking is crucial to avoiding error in dealing with more complex problems.
There’s a fourth factor that does not appear in this simple example, but can be of immense importance in more complex situations: interpretation. This is of particular significance in dealing with witness reports. A particularly revolting example of the way that interpretation can kill people comes from an incident in Arizona in which police terrorized and murdered an unarmed man. (I caution you: the video is deeply upsetting; if you are of gentle disposition and empathetic, do not watch it.) The police officer who shot the victim defended himself with the observation that the victim might have been reaching for a gun when he accidentally fell. The key fact I want to point out is that the killer interpreted an observation of movement to infer murderous intent. We interpret everything we see, and often our interpretations are not justified by the observation.
Think in terms of hypotheses, not facts.