In statistics, we draw conclusions from data. But to get data, we need to be able to measure the variable(s) that we are interested in. Measuring can be very crude (say, a trait is absent or present) or rather sophisticated (the expression levels of large numbers of genes). In the social sciences or in medicine, in order to reach uniformity in measuring a particular condition and make results more comparable, a standard scale is often developed that everyone is using. But can we measure everything? Here is an unusual example of trying to measure the immeasurable:
Irritable bowel syndrome (IBS) is a disorder that leads to abdominal pain and cramping, changes in bowel movements, and other symptoms (PubMed). When trying to develop a drug for combating IBS, one way to measure its success is to look at stool consistency. You think that is immeasurable? In fact, there is a scale for measuring just that, called the Bristol stool scale, which classifies stool into seven categories. The following (graphic) picture explains the scale:
So, it seems, everything is measurable!