One sticking point I reach in certain discussions on this site is trying to pin down exactly what constitutes a fact in science. Let’s try a simple one as a test case.

The temperature is 68° Fahrenheit.

Is this measurement a fact, or a conclusion based on a tall tower of theories? I’ll bet that you forebode where I’m going with this.

First, let’s get legal and precise: The air temperature in the shade in my garden at the location of my thermometer at precisely this moment (as defined by some reading at GMT-6 on the radio-synchronized clock on my wall) is 68°F (292.0K). We cannot conclude (absent other information) what the temperature is elsewhere in the neighborhood, or the rate and direction of the change of temperature from this single reading.

Next, considered as an experiment: The incident radiant heat from reflecting sources is minimal, estimated as an error of increase of less than 0.1°F. The relative humidity and breeze are constant enough to ensure that the thermometer is dry, therefore evaporative cooling can be ignored. The temperature is safely too high for quantum effects, yet far too low for relativistic effects to be measurable. The instrument is viewed at eye level normal to its plane at teh reading height, reducing parallax effects to negligible.

Next, how well is this thermometer calibrated? Um. Well, it has numbers and marks. But those indicate only about one degree of precision, without indicating any accuracy in particular. It is not a laboratory calibrated instrument with a 0.01° certainty over its range. So we need an error bar of at least 2°F until such calibration can be made (based on typical factory quality control standards, taken with a grain of salt).

Let’s now say that we tested the thermometer in boiling and iced water at sea level pressure to get the actual error amounts at those ends of the existing scale, and now have compensated readings that can give us that tenth of a degree accuracy given by the environment.

Unless: What if the column of liquid is not perfectly cylindrical, or if the fluid is not entirely stable in the temperature range and therefore some fluid boils out at the high end? Well, we can calibrate in freezing gallium (85.6°F) for a better center range. Other metals would work, like Cesium or Indium. But Gallium is safest for the home tinker, if a bit more expensive. We can now interpolate toward the two ends, either bi-linear or quadratic to compensate our readings.

So, let’s say we finally have a thermometer that we trust. What have we got? A number based on a cultural convention. Sure, there is a theory to connect this essentially arbitrary number to the average molecular velocity that has an absolute meaning. But even this energy measurement is based on units that hinge on how long it takes for our planet to circle the sun (seconds). It can further be connected to quantum energy levels in a particular element. But then we have a completely objective measure that no one understands, without a very solid grounding in physics.

But how do I even know what the instrument says? Back in my pre-verbal youth I developed a theory that the image on my retina is related directly to objects outside of myself. Some I could control, like my fingers. Others I could reach, like my bottle. Still others made no sense until I received training, like how to relate the personal effect (how hot I felt) with the height of a colored column in a glass tube in a metal frame with markings on it. I eventually learned that the markings had meaning that could be expressed as words, proportions, or levels. All these stacked and much tested theories led me to eventually be able to unconsciously convert the image of a colored column in a thermometer adjacent to markings next to it into the idea of a certain level of comfort in my environment. Later I learned to relate this idea of temperature to much of the universe, as in the colors of glowing coals and stars, and PV=nRT, and Bose-Einstein condensates, and degenerate matter in the cores of stars, and rates of chemical and biological reactions, and so on.

So, although one might initially consider a temperature reading a fact, it is really a conclusion based on cultural conventions and a lot of early (and mostly forgotten) learning. It is a personal observation based on a particular instrument. If other people come along and read the same value off the same thermometer at about the same time, and feel that that number is not unduly different from what they expect given their level of comfort, then it gains some weight as a fact. Some might bring other thermometers using different technologies, like a bi-metal or a thermistor, and more solidly corroborate the observation as a fact.

But how do I know that the thermometer will read the same level for the same temperature tomorrow? Some fluid might leak out, or the glass might expand (this latter effect was a problem in early thermometers), or other factors might cause the same level of physical molecular activity (or at this stage you can still pretend it is the discredited fluid caloric) to give a different reading. How can I be sure?

I can’t. It is a matter of faith, compounded by regular corroboration, that the meaning which I derive from seeing this thermometer is reliable. Also that it relates to everything mentioned above in a completely consistent, measurable, and predictable manner. This degree of reinforced certitude is what makes it a fact rather than a (colloquial) theory.

Here is a brief history of thermometry selected largely at random from the web: The Thermometer—From The Feeling To The Instrument. It illustrates some of the (scientific) theory that goes into measuring the fact of temperature.