How We Know #6: Concept-Formation

Binswanger says, "Things that are similar differ quantitatively" (HWK, 110). Then noting that a young child may not see a pig and a collie as similar, he says in all cases similar concretes possess varying degrees of the distinguishing characteristic, and those degrees fall within “specified categories of measurement” – which is why they appear as similar. Ayn Rand called this “measurement omission.” (HWK, 115).

In effect he denies that similar things or attributes can have only qualitative differences. Similarly, in the Appendix of ITOE2 Rand assented to “establish the similarity by showing the characteristic is the same and only [emphasis mine] the measurements vary” (ITOE2, p. 221).

Is it true that all differences between units that fall under the same concept are only quantitative? Both Rand and Binswanger say yes. I say absolutely not. There are many, many exceptions. It takes only one to disprove their claim, but I will offer more anyway.

Consider boats. Having some means of locomotion is essential to being a boat. There are oars, sails, outboard motors, water jets, paddle-wheels, air fans, and inboard engines of various kinds – steam, gas, diesel, nuclear, electric, coal. These are qualitative differences, not quantitative ones. One attribute – speed – of locomotion and even other differences being measurable does not imply that every attribute is measurable.

Consider animals. Some live on land, some in water, some both. Some are carnivores, some herbivores, some omnivores. For some respiration uses lungs, others gills, still others skin. Some have fur, some have scales, and some have feathers. I could go with many other kinds, not simply degrees, of differences. These are qualitative differences, not quantitative ones.

Consider different tools -- hammer, screwdriver, wrench, pliers, file, saw, etc. Each has a different purpose, which is qualitative, not quantitative.

I will defer qualitative, non-quantitative, differences of motion to a future post.

Binswanger says nothing about it, but later in ITOE Rand undercut her prior claim of omitting only measurements when she addressed concepts of consciousness.

“For instance, the concept “thought” is formed by retaining the distinguishing characteristics of the psychological action (a purposely directed process of cognition) and by omitting the particular contents as well as the degree of the intellectual effort’s intensity. The concept “emotion” is formed by retaining the distinguishing characteristics of the psychological action (an automatic response proceeding from an evaluation of an existent) and by omitting the particular contents (the existents) as well as the degree of emotional intensity” (ITOE, 32).

“These concepts [knowledge, science, idea, etc.] are formed by retaining their distinguishing characteristics and omitting their content. For instance, the concept “knowledge” is formed by retaining its distinguishing characteristics (a mental grasp of a fact(s) of reality, reached either by perceptual observation or by a process of reason based on perceptual observation) and omitting the particular fact(s) involved” (ibid., 35).

Why did she say omitting particular “contents” and “facts”? What happened to omitting only measurements?

Binswanger also confuses counting, e.g. the number of sides of a polygon and atomic numbers, with measurement. “An interesting case of measurement is that of measuring materials qua materials, such as wood, copper, water. Obviously, one can measure the attributes of the objects formed out of various materials, but in what sense is the difference between copper and lead a difference in measurement? On the sensory level, one uses difference in perceptible qualities—the colors differ, the densities differ, the hardness differs, etc. … Modern chemistry, however, goes to a deeper level: copper and lead differ in “atomic number.” Atomic number is a measurement. It refers to the number of protons in the nucleus of the atom: copper has 29 protons, lead has 82” (p. 121).

However, counting and measurement are quite different. Both use numbers, but counting uses only integers and measuring uses both integers and fractions. Authentic measuring as done by scientists, engineers, and others uses a measuring instrument – a ruler, weight scale, thermometer, voltmeter, pressure gauge, etc. Counting does not rely on such instruments.

By the way, what is the atomic number of wood? 😊

Note: Some of the above is repeated from my article 'Omissions and Measurement' in The Journal of Ayn Rand Studies, Vol. 7, No. 2 (Spring 2006). Link. Another related article is my 'The Sim-Dif Model and Comparison' that appeared in The Journal of Ayn Rand Studies, Vol. 11, No. 2 in December, 2011. Link. Either can be read on-line for no money with a free JSTOR account.