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The Logical Leap by David Harriman|
|Like the subtitle indicates, this book is about induction. When and why is the inference from "some" to "all" legitimate? The narratives about some famous scientists arriving 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, conceptual hierarchy, and the role of mathematics are excellent. Integration in physics and science generally involves coherence testing a hypothesis with controlled experiments. A new and fundamental generalization has consequences extending well beyond what the generalization was specifically made about. Examples are the "inverse square law" and discoveries of atomic structure having important implications for chemistry. He explains how the chemical revolution that began in the late 18th century was to a large extent a quantitative one. "With the foundation provided by a quantitative method and an objective language, the chemists who followed Lavoisier made rapid progress in understanding how elements combine to form compounds" (p. 153). Some reviewers have disagreed with parts of the specific histories. I am not a physicist and don't know the specifics that well, so my review will mainly be on the philosophical part. |
His narrative on Galileo includes the following: "Integration is the process of uniting a complexity of elements into a whole. Cognitive integration is the very essence of human thought, from concept-formation ... to induction ... to deduction. An item of knowledge is acquired and validated by means of grasping its relation to the whole of one's knowledge. A thinker always seeks to relate, grasp hidden similarities, discover connections, unify. A conceptual consciousness is an integrating mechanism, and its product--knowledge--is an inter-connected system, not a heap of isolated propositions" (p. 53).
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. He 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 or infer those measurements. Similar measurements are not made when forming all kinds of other concepts to the extent Ayn Rand described, at least until she considered 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 like little man-made, physical, measuring instruments in our heads? Does "preconceptual measurement" translate to "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." If consciousness is an attribute, these claims seem to conflict.
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). This seems fine for physics and chemistry, but in general? Grasping of quantity surely enhances the efficacy of human consciousness, but it is only part of the whole. Harriman says his quantitative view is not like that of Pythagoras. However, it does lead him to make some conflicting claims, e.g. p. 231. He first says *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 and gave several examples of Galileo and Newton using them. 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. 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? Some comparison of his view of induction to those of Francis Bacon and William Whewell would have been nice, too. Both wrote extensively about induction. Harriman's idea of integration seems to have a good deal in common with Whewell's ideas of colligation and consilience. Colligation is the mental operation of bringing together a number of empirical facts to form a general law. Consilience occurs when the evidence in favor of an induction is much stronger when it enables us to explain and predict cases of a kind different from those which were contemplated in the formation of our hypothesis.
What is new about this account of induction? The obvious one is the focus on physics. Others are the emphasis on integration, hierarchy, and the role of mathematics. Another is the similarity between induction and concept-formation in general. It's well worth reading.