My review of The Logical Leap

[merjet]

Here is my first draft review of the book. I plan to put it on Amazon later, perhaps somewhat revised. Comments invited.

Like the subtitle indicates, this book is about induction. When and why is the inference from "some" to "all" legitimate? The narratives about how some famous scientists arrived at their inductive generalizations are interesting and illuminating. There are ones about Benjamin Franklin, Kepler, Galileo, Newton, atomic theory, and chemistry. Harriman's emphasis on integration and conceptual hierarchy are excellent. Integration in physics and science generally involves coherence testing a hypothesis with controlled experiments. New and fundamental generalizations have consequences that extend well beyond what the generalization was specifically made about. Examples are the "inverse square law" and atomic structure. Some reviewers have disagreed with parts of the specific histories. I am not a physicist and don't know the specifics that well, so I will confine my review to the philosophical aspects.

The book starts with an overview of Ayn Rand's theory of concept formation, which I believe is generally sound. Integration is a significant element. I think Harriman, like Rand, over-generalizes on the role of measurement. Harriman gives a very good account of the use of mathematics and measurement in physics, so it seems he should know that physicists use man-made physical instruments to perform all those measurements. Similar measurements are not made when forming all kinds of other concepts to the extent Ayn Rand described, at least until she got to some concepts of consciousness. Harriman says the measurement-omission process is subconscious and automatic (p. 67). What is his alleged "preconceptual measurement" (p. 230)? Do we allegedly have something akin to little man-made, physical, measuring instruments in our heads? Is it "perceptual measurement"? Do other animal species have this capacity, too? If not, why not? Concept-formation involves "omitting" qualitative differences, too. Near the end of the book, Harriman sometimes seems to forget what he said earlier. There he says such things as "consciousness is not numerable" and "numbers are applicable only to entities and their attributes, but conscious states are not entities."

Like the reviewer Todd Becker said, I think Harriman tries to carry quantification too far. An example of such over-generalization is "A generalization is the conceptualization of cause and effect; i.e. induction may be described as measurement-omission applied to causal connections" (p.28). It is true for some, but is it true of every generalization and every induction? I think not. Consider the toddler throwing a ball and watching it roll. That a physicist could understand the action in terms of measurable force and measurable velocity does not imply the toddler does.

Another feature of Ayn Rand's theory of concepts is that they are hierarchical. Some concepts are more basic than others and higher level concepts rest on lower level ones. Harriman often applies this idea in his analysis, speaking of first-level and higher level concepts. Isn't measurement a higher level concept? It uses real numbers, including ratios and fractions. Counting and integers are lower level.

"The human intellect is a faculty for grasping quantities" (p.228). I agree, but it is also a faculty for grasping qualities (attributes), relations, and causes. They aren't all reducible to quantity. "Human consciousness is inherently a quantitative mechanism. It grasps reality--i.e., the attributes of entities and their causal relationships to one another--only through grasping quantitative data. In this sense, quantity has epistemological primacy over quality" (p. 231). Primacy how? Grasping of quantity surely adds to the efficacy of human consciousness, but it is only part of the whole. Harriman is careful to say that his quantitative view is not like that of Pythagoras. However, it does lead him to make some conflicting claims, like on p. 231. He first says that *if* we could know qualities simply by perception, without quantitative processing, then we could know causal relationships by direct perception, without numerical measurements. Yet in the same paragraph, he says to know that fire burns, we simply touch it and yell "Ouch!" -- no numerical measurements are required.

The over-generalization about measurement is not crucial for the book as a whole, however, since measuring and mathematics are a huge part in physics.

I believe a little more comparing his view of induction to Mill's Methods would have been nice. He says quite a bit about two of Mill's Methods. Guessing, he thinks the diversity of contexts and integration by ignoring the differences adds to the strength of an induction using the method of agreement. That is at least implicit in his narratives of Galileo and Newton, but it could have been more explicit. He said he makes no distinction between the method of agreement and method of [concomitant] variations, but what about the other two Mill's Methods?

What is new about this account of induction? The obvious one is the focus on physics. Others are the emphasis on integration and hierarchy. Another is the similarity between induction and concept-formation in general. It's well worth reading.

Edited September 21, 2010 by Merlin Jetton

[merjet]

My review is now on Amazon (link). It is a little different from the draft above.

[merjet]

A generalization is the conceptualization of cause and effect; i.e., induction may be described as measurement-omission applied to causal connections. It is nothing more (or less) than an essential form of the method of concept-formation. Just as a concept, through measurement-omission, integrates an unlimited number of particular existents of a certain kind into a single word, so does a certain union of concepts integrate through measurement-omission an unlimited number of particular causal sequences of a certain kind into a single proposition that subsumes them all: a generalization.(p. 28)

So Peikoff is trying to put measurement-omission as the centerpiece of induction. The word mantra comes to mind.

The quote is from Chapter 1, which Harriman says in the preface is "nearly verbatim" from Peikoff's lecture series "Induction in Physics and Philosophy". Oddly enough, I don't recall even one narrative in Harriman's book showing how measurement-omission was a part of an inductive generalization. Indeed, in my view it is nearly the exact opposite.

It's one thing to say that different particular lengths, e.g. of a pencil, of a rope, and the distance to grandma's house are not esential to the concept length. Each length is independent of the others. It's quite a different matter to say that Tycho Brahe's and other's measurements were not essential to Kepler concluding that planets move in elliptical orbits. The measurements were essential to concluding the orbits were ellipses.

A concept is based on similarities of the things grouped. "Similar" does not mean identical, and so there are differences between the similarities. Harriman on page 10 says such differences are only measurements. Rand originated this idea.

An algebraic formula of an ellipse does not omit, but summarizes or unites the measurements. There are measurable differences between the ellipses of the different planets to omit, but omitting all measurements would do away with the similarity.

Speaking of mantra, not long ago I read somebody saying "logical transitions, individual actions, relationships with others, etc." were all "measurements omitted."

Edited September 27, 2010 by Merlin Jetton

[BaalChatzaf]

A concept is based on similarities of the things grouped. "Similar" does not mean identical, and so there are differences between the similarities. Harriman on page 10 says such differences are only measurements. Rand originated this idea.

Which is nonsense. What about non-quantitative similarities. Where there is no quantity there is no measurement.

Measurement omission, which has a limited application has been carried a furlong too far.

Ba'al Chatzaf