Science in Christian Perspective



Thorson and Barfield: A Philosophical Analysis

David F. Siemens, Jr.

2703 E. Kenwood Street
Mesa, AZ 85203-2340

From: PSCF 39  (December 1987): 227-230.


Walter R. Thorson, in his article (JASA, June 1986), makes use of Owen Barfield's Saving the Appearances: A Study in Idolatry.1 Barfield distinguishes alpha-thinking, thinking about things. from beta-thinking, thinking about thinking. This is an important distinction. A similar distinction was used by Adler in 1965.2 A related presentation, more sharply drawn and more fruitful, was developed by Broad more than three decades earlier.3 Both of these writers avoid anything like Barfield's "original participation," a problematic notion discussed uncritically by Thorson. Thorson then illustrates beta-thinking in science by matters that are either not quite scientific or involve distinctions other than those between alpha- and beta-thinking. Finally, he phrases some matters in ways that are likely to produce misunderstanding.

To illustrate the problem with "original participation" let us consider someone caught in a storm at sea. The winds and the waves are the same for the "primitive" as for the "modern" individual. The interpretation may be in terms of the wrath of Poseidon and the rapid passage of Argestes, Boreas, Notus, Zephyrus and their brothers, or in terms of an intense cyclone; that is, as "original participation" or as alpha-thinking, respectively. But does singing "dark is His path on the wings of the storms"' transform the latter into "participation"?

As I see it, Barfield saw a genuine difference in the frameworks for understanding the world and transformed them into different logics. Recognizing that the "primitive" world is full of gods and the "scientific" world does "not need that hypothesis," he might have concluded that the scientific world is atheistic-but he makes it idolatrous instead. However, neither conclusion is necessary. The world of science is atheistic only if one claims that there is nothing but what science studies, and idolatrous only if one substitutes a feeling of total human competence for a recognition of our dependence on the Almighty. What is not recognized by Barfield is that both "primitive" and "modern" are faced with the same events; describable, despite the differences in the natural languages, in essentially similar words. The logic by which conclusions are drawn is usually the same, for the sophistication available in contemporary logic is seldom applied by most of us. However, the nearly identical descriptions of the observed events are interpreted within very different sets of categories. This difference of interpretation is not restricted to cultural differences. The same item or event may be described in terms of different scientific disciplines and also in nonscientific language. For example, a controlled substance may be described as a psychotomimetic or hallucinogen, as binding to a specific neural receptor, as having a specific structure and formula, etc. Terminology was drawn from psychology, physiology and chemistry, and could have been expanded to include other sciences. But "controlled substance" belongs to no particular science.

The above examples are some of the reasons why I do not find Barfield's categories very useful. I would have preferred the use of either Adler's or Broad's approach. Adler presented a different pair of categories-first-order questions and answers-in contrast to those of second-order. A first-order question has to do with direct applications to the world, such as:

What is the right thing to do in these circumstances? 
Is that picture beautiful? 
How will this object behave in this field?

First-order answers respond to such questions.

Second-order questions are questions about first-order questions and answers, about language, or about second-order questions. Thus, there can be no third-order questions or answers. Some second-order questions are:

On what basis does one evaluate an action as right or wrong?

What does "beautiful" mean?

What is the relationship between the criteria for beauty, goodness and truth? What is assumed in talking about matter?

It is obvious that Adler's distinctions are related to Barfield's alpha- and beta-thinking. Certainly beta-thinking is asking and answering second-order questions, but there is no place in Adler's systematization for Barfield's "original participation." For Adler, the answer to a first-order question about how to produce rain may be equally:

Offer a sacrifice with appropriate rites.
Repeat this magical incantation. 
Seed the clouds.

Participatory magic and scientific manipulation are equal answers to first-order questions. Thus, Adler avoids the cultural or ethnic snobbery of Barfield.

Broad, though earlier, presents a more sophisticated analysis. He separates science from mathematics, and both from philosophy, further distinguishing critical philosophy from speculative philosophy. Science, he notes, requires observation. It tells us, for example, what happens when gold is put in aqua regia. In this, it assumes that nature obeys uniform laws of causation. That is, science generally assumes and works with commonsense beliefs, although it is not restricted to them. Mathematics, like philosophy, is not observational. Like science, it begins with assumptions, though it calls them axioms. Unlike both science and philosophy, its logic is restricted to deduction. Critical philosophy, on the other hand, asks what we mean by "cause" and "uniform," and what is involved in claiming that there are uniform laws of causation. That is, it looks into the meanings of the words
used and the basis of the beliefs assumed by members of the human race, including scientists. This is critical philosophy. But it is not Adler's second-order or critical philosophy, although it includes it along with the first-order philosophy.

Broad's critical philosophy is a requirement for relevant speculative philosophy, since a clear understanding of what one is claiming is a necessary foundation for a more abstract superstructure. Without this clarity, polysyllabic drivel will mislead, or produce nonsense. Speculative philosophy involves the widest possible overview of all human thought and experience, in the hope that "we may be able to reach some general conclusions as to the nature of the Universe, and as to our position and prospects in it.5 This area includes the systems of thought, such as Platonism and Thomism, materialism and idealism, realism and instrumentalism, etc. It includes, for the most part, the matters Thorson considers in his study.

Thorson's first illustration of beta-thinking in science comes from mathematics; Godel's 1931 theorem.6 This involves two kinds of distinctions. The first of these, between first and second intention, goes back in principle to Averroes in the eleventh century. The alternate descriptions of linguistic usage from medieval times, de re and de dicto, are clearer to us. The former, "of the thing," is now called object language. It is the normal use of language to talk about entities in the world, as in the following three sentences:

The cat is on the mat.
Some swans are white
All men are mortal.

The latter, "of the saying," is the use of language to talk about language. It is now usually termed metalanguage.

It is important to note that one does not have to be clear about what is going on to use metalinguistic constructions. For example, grammarians talk about nouns and adjectives, verbs and adverbs, clauses and phrases, usually without noting de dicto. But this is all talk about language. So are the discussions about the logical validity of arguments, and about what philosophers classify as semantics or metaethics, for example. Some examples of metalinguistic sentences are:

A period ends declarative sentences.
'Pepe' means 'Joe'. 
All dogs are canines
is true.

Note that in the latter two sentences I am using a convention common among philosophers: single quotes form the name of written linguistic entities.

Although this is all that is necessary to follow Godel's theorem, it is not the end. If one needs to speak of metalinguistic entities, one does so in the metametalanguage, as in:

'Pepe' means 'Joe'.' is true.

In this case, 'true' is not the same as in the earlier instance, but is another level up. In other words, 'true' is not one word, but represents a hierarchy of terms with no ultimate element.

These distinctions seem excessive to those not familiar with the paradoxes produced by their neglect. One version of the most ancient one I know. the Liar, is given in Titus 1: 12. Such paradoxes, unless avoided, bring an end to rational analysis and communication.

The second distinction involved in the theorem is in the levels of logic. introduced by Frege.7 The simplest logic, the sentential or propositional calculus. operates on complete sentences or clauses. -More complex than the sentential calculus is the lower functional calculus. which involves functions or predicates. names and individual variables, with quantification over variables. The next step up involves predicate variables in addition to individual variables, with quantification over both. This level is necessary to formulate Godel's proof. Neither of these distinctions is a matter of beta-thinking, although the theorem has consequences for the logic needed for both levels of thinking.

A consequence closely connected to Godel's theorem is that there is no effective proof procedure, no set of rules or techniques that can be followed mechanically that will guarantee that a proof will be found for any theorem in the functional calculi8 There is an indication in Thorson's section (2), in the reference to "mechanistic logic," that this has not been appreciated. Logic, except in its simplest forms, cannot be mechanical. Perhaps what Thorson had in mind is that the nature of intelligence is not simply deducible a priori from first principles.

The second illustration, namely problems associated with describing and modeling intelligence, should primarily involve Broad's critical philosophy, although it may be entered under beta-thinking. However, much of the time Hofstadter sees the problem as one of presenting a scientific model, which is alpha-thinking even though it is, in a sense, about thinking. It seems to me that Thorson has intuitively recognized this and rightly objects to the implicit nothingbuttery that sometimes intrudes. There are, however, other aspects to the problem that are passed over. First, for example, is the necessity of human intelligence to understand any scientific model or theory, whether Einstein's theory of Brownian motion or Schrodinger's wave theory, as well as any theory of intelligence. Second is the incompleteness of all scientific theory. For example, to say that gravity is universal, affecting every material body, and to present the full set of equations that describe gravitational attraction (ignoring the difficulties with the inclusion of three or more bodies), is not to explain why matter involves gravity. Science describes how things interact, but does not explain why nor define what they are.

There is an analogy between the study of computers and the study of intelligence. One may "explain" a computer in terms of power input and heat dissipation, but this has no more to do with the usual view of its function than describing the thermal parameters of the brain has to do with intelligence. One may also view a computer in terms of circuits or machine language, much as one can talk of neurons, synapses and trains of nerve impulses. To some extent, one can think in terms of software, although neural programs have not been deciphered.9 All of these are legitimate ways to describe both computers and the brain that are involved in every physically measurable aspect of mental activity. But none of these approaches involve the reason we have computers at home and in the laboratory or office; namely, that a computer can manipulate input and output in a more useful pattern. Psychological studies may observe mental inputs and outputs, and gain some insight into cerebral hardware and software, but this is as far as science can go. To understand the science, as well as to understand understanding, is not the province of science. It will not do to chide the scientist for not providing what science cannot provide, unless he has moved from scientific description to scientism. However, then he is functioning not as a scientist but as a naive philosopher.

The matter of logical indeterminacy taken from MacKay is extended by Thorson. who seems to add a tacit assumption as he develops his argument. As I understand him, we can imagine an entity, E. which understands me totally. E recognizes that I am strictly determined and that my world is strictly determined. Thus. E can predict my every action. But I cannot accept these predictions. On the assumption that E is self-conscious, and therefore must be at least as complex as 1; if there be an entitv N' that similarly understands E, E cannot accept N's predictions any more than I can accept E's. On the other hand, if E is more simple, so that it is not self-conscious, the problem of accepting or rejecting N's predictions does not arise. But if E is so simple, how can it be assumed to understand? The discussion seems to involve contradictory, or at least contrary, assumptions.

I pass by the raft of problems connected with the interpretation of quantum physics where Thorson notes, "I admit the connection to the previous instance of beta-thinking is fuzzy." He seems here implicitly aware that scientific modeling or theory-construction is not the same as doing critical philosophy.

The fifth illustration, regarding the recognition of order, seems to me to confuse pattern with communication, especially as the pattern has the linear sequence that we associate with language. Physical scientists find an order, a pattern, in the phenomena they study just as surely as molecular geneticists do. But none of the patterns mean, as human communication means, any more than the punch cards controlling a Jacquard loom. Granted, one may remark that a certain hole in one of the cards controlling the loom means that a specific harness is raised or lowered, This parallels the statement that a messenger RNA triplet means that a definite amino acid will be inserted into a protein at this point. However, this is a different sense of 'means' than that associated with language. There is talk of the translation of genes into proteins. Were this language, the protein would have to mean the same as the DNA or RNA sequence that produced it; but I have nowhere encountered this claim. When proteins fold into the complex pattern of an enzyme, they function rather than mean or communicate. It is certain that there is an analogy between DNA and language. The analogy aids our understanding, but we must never identify the entities we have put side by side.

Another aspect of the analogy may be noted. If we can imagine a culture which developed science in the total absence of writing, one in which all verbal communication was aural, it is unlikely that they would develop the analogy. It seems to spring from the letters-words-sentences pattern that partially parallels the base-triplet-protein pattern. It is plain that sentences are still linguistic whereas proteins are not DNA. It does not help to make the patterns more complex: letters-words-sentences-meanings and base-tripletgene-protein, respectively. Meanings are the abstract entities that are translated, strictly speaking, so the analogy cannot be made perfect. Restricted to communication by sound, one might begin by phonemes; however, phonemes seem to have been suggested by the association between the sounds of the letters forming written words.

In the next to last section, Thorson notes that the scientific paradigm has been the machine, and suggests that the future paradigm may be the organism. Historically, the biological paradigm antedated the mechanical one. For example, it was once believed that minerals grew in the womb of the earth. And while philosophers, such as Descartes in the seventeenth century and Kant in the eighteenth, argued that animals are no more than complex mechanisms, vitalism-with its insistence on purposiveness-had a tight hold on biology. Harvey, Stahl, Buffon, Oken, von Baer and Driesch advocated it. But it was a dead end in science, more compatible with Lamarckianism than with modern views. My feeling, which I offer without being able to present a proof, is that life is so complex a collection of phenomena that it presents broad opportunities to those who have axes to grind. This kind of pattern seems to me to turn up in the use of quantum physics to support Eastern mysticism, and of entropy to support recent creationism.

I am not accusing Thorson of advocating such obfuscation. He may well be right that biology will furnish the new paradigm that we need. A recent study of ethnology pairs an organismic analogy with natural science in contrast to a language analogy." Whatever analogies are helpful, to individuals or to groups, may be used freely. Yet I feel that, however useful such analogies may be heuristically, science will do better to extend the use of the logico-mathematical models that have served physicists so well. They have the virtue, essential when human beings are involved, of preventing the inadvertent insertion of unrecognized presuppositions into scientific formulations. Rigorously deriving formulas quite effectively excludes bootlegged assumptions. As I understand the historical development, the earlier physical theories were interpreted mechanistically. But contemporary theories resist mechanical interpretations. I wonder if it is even possible to think of an orbital in a mechanistic, deterministic manner.

Thorson has much to contribute. However, I find that his insights, as presented in his paper, do not have a handle that I can solidly grasp. Had he focused his formidable intellect precisely and then communicated his perceptions with accuracy and clarity, we would jointly profit to a much greater degree.


1Thorson makes reference to the 1965 paperback edition. The work was first published in 1957.

2M.J. Adler, Condition of Philosophy (New York: Atheneum, 1965), pp. 44 ff. 

3C.D. Broad, Scientific Thought (1923), pp. 11-25. The same pagination is found in its numerous reprints.

4Robert Grant, "0 Worship the King," v. 2 in Edward Bickersteth, ed., Christian Psalmody (London: Seeley, 1833).

5Broad, op. cit., p. 20.

6The original paper in Monatshefte ffir Mathernatik und Physik, 38:173-198 (1931), is translated in jean van Heijenoort (not Heignenoort as in Thorson's note 22), From Frege to G&del, Source Book on Mathematical Logic, 1879-1931 (1967), pp. 596-616. Also in Kurt Godel (B. Meltzer, trans.), On Forrnally Undecidable Propositions of Principia Mathematica and Related Systems (1962 and reprints). The translation in Martin Davis, The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems, and Computable Functions (1965), pp. 5-38, is not as good.

7See Gottlob Frege, Begriffischrift (1879, reprint 1964). [Note that the full title is very seldom used.] Translations are in van Heijenoort, op. cit., and, in part, in Peter Geach and Max Black, Translations from the Philosophical Writings of Gottlob Frege (1952). Although Frege pioneered, his notation is too cumbrous for use and has been superseded.

8See Alonzo Church, "A Note on the Entscheidungsproblem," Journal of Symbolic Logic, 1:40 ff (1936). With corrections, ibid., 101 ff.

9See, for example, James P.C. Dumont and R. Meldrum Robertson, "Neuronal Circuits: An Evolutionary Perspective," Science, 233:849-853 (22 August 1986); especially pp. 849, 852.

10 May Ebihara, review of Elman R. Service, "A Century of Controversy: Ethnological Issues from 1860 to 1960," in Science, 233:371 (18 July 1986).