Representational measurement of temperature

As indicated in the previous post, I plan to use the measurement of temperature to illustrate some ideas about perception.  This post will give a representationalist account of measurement, as an illustration of indirect perception.

The apparatus to be used is very similar to a mercury thermometer.  I shall assume that the reader is reasonably familiar with traditional analog thermometers, and how they are used.

The design of the instrument

The thermometer uses a glass tube.  At the bottom of the tube, there is a largish bulb which can be filled with mercury.  Above the bulb, the glass tube contains only a very narrow tube of small diameter, sometimes called a capillary.

The bulb is initially filled with mercury, and the mercury extends to part way up the capillary tube.  Above the mercury, the tube is empty.  The air is pumped out, though it need not be a perfect vacuum.

How it works

As the temperature of the mercury in the bulb rises, the mercury expands.  This causes the height of the mercury column in the capillary tube to increase.  To measure the temperature increase, we measure the increase in height of the mercury column.

From that increase in height, we can compute the increase in the volume of mercury.  Then, using our knowledge of thermal expansion, and the coefficient of expansion for mercury, we can compute how much the temperature had to increase in order for the mercury column to rise to that height.  That gives us the temperature.

In summary, the height of the column represents the temperature.  By using a computation with that height, we can compute what the actual temperature must be.

Knowledge and truth requirements

There is some prerequisite knowledge, in order for us to use this method.

1. We must know the physics of thermal expansion.
2. We must know the coefficient of expansion of mercury.
3. We must know the coefficient of expansion for glass.  The mercury expands, but so does the glass.  It is because the mercury expands more than the glass, that the mercury column rises.  We need the coefficient of expansion for the type of glass used, so that we can compute the difference.
4. We must know the volume of mercury in the bulb.  We need a fairly accurate value for this, to compute expansion as a function of temperature (or, actually, temperature as a function of expansion).
5. We must know the diameter of the capillary tube.  We need this, so that from the increase in height of the mercury column, we can compute the increase in volume.
6. We must be able to accurately measure the increase in height of the mercury column

Plantinga’s EAAN

Alvin Plantinga has offered what he calls “the evolutionary argument against naturalism“.  His argument is that if cognitive systems are the result of evolution, then it is unlikely that they could be reliable.  He is using “reliable” to refer to the knowledge and truth requirements, such as I have outlined above.

In the case of the thermometer, there is no issue.  We all agree that the thermometer is the result of human intelligent design.  Plantinga argues that there’s a problem with the idea that perception evolved, because of the difficulty of meeting those knowledge and truth requirements (or reliability requirements).

I mention this, mostly to compare representational measurement with direct measurement (in a future post).

Tags: measurement, perception