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Re-examining the Givens: Testing Our Theories of the World

Marshall Specter

Boundaries and Barriers: On the Limits to Scientific Knowledge. John L. Casti and Anders Karlqvist, eds. 250 pp. Addison-Wesley, 1996. $37.61.

Are there limits to what we can know through science? This question formed the basis for an interesting collection of 10 papers, mainly by physicists and biologists, which came out of a 1995 conference held in Abisko, Sweden. Twentieth-century science and mathematics seem to be riddled with limitative results. Some frequently cited examples are Kurt Gödel's incompleteness theorem in mathematical logic, Alan Turing's results about uncomputability, Werner Heisenberg's uncertainty principle in quantum physics, and Albert Einstein's speed-of-light limit to signal transmissions. These all seem to express or imply cases of scientific problems that cannot be solved—questions that are statable within a theory, but that the theory itself tells us cannot be answered.

As John Hartle says in his paper "Scientific Knowledge from the Perspective of Quantum Cosmology," we must first be quite clear about what kinds of limits are at issue here. For example, the deep limitative results cited above should not be confused with more mundane (but perhaps practically serious) limitations to what we can know about the universe—limits imposed by economics, engineering or political will, for example. Thus the cancellation of the Superconducting Supercollider by Congress because of its high cost was a blow to the study of the behavior of matter at ultrahigh energies and may therefore impose a practical limit to our knowledge of the very early universe; but this does not constitute a logical limit of the kind intended by the conveners of this conference.

Nor are we interested in what Hartle calls "false limits." Heisenberg's result, for example, does not say that the question, "What is the exact position and velocity of this elementary particle at a given time?" is a question statable within quantum theory that we cannot answer. Rather, according to quantum mechanics, particles have no such state in the first place, despite what classical mechanics says in this regard. Classical mechanics, which does posit such states, is just a false theory. This common misreading of Heisenberg's result as a limit on our knowledge of "what is really out there" arises from an incorrectly understood comparison of two theories: classical mechanics and quantum mechanics.

I would argue that Einstein's signal-velocity law is also nonlimitative, or, put another way, all laws of physics can be considered as limitative. For as Karl Popper pointed out decades ago, any physical law can be equivalently stated either as a universal or as a limitative statement—a "principle of impotence." Statements of the form 'all A are B' are equivalent to statements of the form 'no A are non B'. So Einstein's law 'There are no signals faster than light' can be restated as 'all signals are slower than light'. Is the statement 'all crows are black' a "limitative principle" just because it can be rewritten as 'no crows are non black'? Perhaps Einstein's signal-velocity law seems to stand out as particularly limitative only because it was such a shock to the mind trained in classical physics.

Hartle's analysis of the Heisenberg case is interesting because of what it tells us about the proper approach to the issue of limits to science. This example should make us realize that the issue of "limits to scientific knowledge" is not simply a set of empirical questions that can be posed within current theories. Rather, the issue is one of the relation between the world and our theories of the world. It also involves the relations among our theories, both at a given time and as our accepted theories change over time. Indeed, the key theoretically significant philosophical thread that is woven throughout the collection is this realization, stated or implicit in different ways by different contributors. It is vital to distinguish between characteristics of (some aspect of) the world, and characteristics of some particular theory of, or methodology for dealing with (that aspect of) the world. Obviously these are related, but not in any simple way. Thus a fast and loose blurring of this distinction can only get us into trouble, as the Heisenberg case illustrates so well.

At bottom, what we really need here is a comprehensive and articulated understanding (a meta-theory, if you will) of the relationship between the world and our scientific theories of the world. We also need a similar understanding of our theories about how to appropriately investigate the world (our methodologies). The question of limits to scientific knowledge is a question within this (as yet unfinished) meta-theory, namely: Are there facts or laws about the world that we can never know, or never know through science or scientific method? The distinction in question is referred to in about half of the papers in the collection and examined with some degree of care in some of them—most deeply, in my opinion, in Robert Rosen's contribution, "On the Limitations of Scientific Knowledge." A common result of ignoring this distinction is to impute to the world (and to science, scientific knowledge and scientific method) limits that may well only be artifacts of the particular theories (or models) we currently accept, or the current methods of investigation we employ, or of our current views as to what scientific knowledge is.

The nature of life is Rosen's particular scientific interest in this philosophically astute paper. A form of reductionism is his example of the sort of error that can result from failure to distinguish characteristics of the world from characteristics of our changing theories of it. In particular, the rejection of function as an unacceptable concept in biology is the result of a self-imposed methodological limitation wherein apparently "finalist" (teleological) ideas are not to be used in doing biological science—perhaps because they are not needed in physics? Rosen states that, "It is astounding to watch adult physiologists twisting themselves into bizarre shapes to avoid saying things such as 'the function of the heart is to pump blood.'"

Rosen pushes his point even into the realm of mathematics and mathematical logic. Mathematics too has a history of expanding what is considered methodologically acceptable, so that what was once viewed as some property of the mathematical entities themselves later comes to be seen as an artifact of one (narrow) way of viewing them. What we call mathematics changes! (The extension of arithmetic from finite to infinite domains is his example.)

Indeed, in this regard we must be careful about computability as well—a concept at the heart of many of the papers in this collection. (Roughly, what we can know scientifically is what we can compute.) For what is or is not computable depends on our concept (theory) of computability. Must it be Turing-computability, which is usually taken for granted? As John Casti points out in his paper, "The Outer Limits: In Search of the 'Unknowable' in Science," there are other possible models of computability. Moreover, Rosen reminds us that Turing machines are finite-state machines—classical devices (albeit with infinite, or at least unbounded tapes). Is this a limitation we should continue to accept in our understanding of what computability is—and thus in what limits there are to our understanding of nature? This decision about our methodology will affect our view of what we can know scientifically about the world, and hence our view of what limits the world imposes on our knowledge of it.

Did the conferees reach any consensus about limits to scientific knowledge? Most of the contributors agree that there are no barriers to scientific knowledge that cannot be overcome. The editors put it this way in their introduction: "The provisional message coming out of these disparate efforts is that, unlike mathematics, there is no knock-down, airtight argument to believe that there are questions about the real world that we cannot answer—in principle."

But this consensus does not reach unanimity. John D. Barrow, in his paper "Limits of Science," calls attention to a number of particular questions that appear to be unanswerable in principle given current theories and methodologies. For example, it is now believed to be impossible in principle to ever know any particular facts about distant parts of the universe that are beyond our event-horizon because of the finite velocity of light and the expansion of the universe. Barrow uses this and other examples to reach a more pessimistic conclusion than his colleagues at the conference.

But I would point out that there have been similar situations throughout the history of science—clearly impossible-to-answer questions, for which we now have the answers! I will mention just one example: In the mid-19th century it was believed to be impossible in principle to ever know the chemical constitution of the stars. Just consider what theories of matter and light we use today to do this routinely, and what theories were available then, and the following should become obvious: It was indeed impossible in principle then. Anyone who had suggested otherwise would have been viewed as one who did not understand current science, or even what science is—or worse. But science changes, and will continue to change—unless John Horgan is right in his recent book The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age. Moreover, the changes—and hence the breaking of limits—typically take place in wholly unexpected ways. (See Piet Hut's paper "Structuring Reality: The Role Limit.") Indeed I would say unexpectable ways, for our specific expectations must be formulated on the basis of our currently accepted theories.

We should therefore be extremely cautious about drawing any conclusions from the existence of some particular limits to knowledge that we now face, such as the limits related to the event-horizon cited by Barrow. Our view of the stars (and the world in general) is of course largely determined by our theories of the stars, but it is not wholly determined by any particular such theory. The same is now true of distant parts of the universe. The history of science is a history of the breaking of limits, the breaching of barriers. The epigraph from Les Liaisons Dangereuses with which Rosen begins his paper is exactly to the point: "There are no impregnable fortresses. There are only fortresses that are badly attacked."

There are a number of other issues related to the notion of limits to science that are discussed in this excellent collection, but they must be omitted in a brief review. Just to mention three: the distinction between objectivity and subjectivity, the concept of complexity and the related concept of emergent properties. Finally, the editors are to be commended for supplying a useful index.—Marshall Spector, Philosophy, State University of New York at Stony Brook

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