(A page from the Loglan web site.)

(From Lognet 93/4. Used with the permission of The Loglan Institute, Inc.)

Sau La Lodtua
(From the Logic-Worker = Logician)

by M. Randall Holmes

This time, I'm going to argue with myself. Briefly, I will give a counterargument to one I advanced in a previous column (LN93/2:10ff) in which I questioned whether learning Loglan is likely to have effects confirming the Sapir-Whorf hypothesis.

This is the thesis of my previous column: "I do not think that Loglan is capable of expressing essentially more than a natural language like English. This means, obviously, that I expect negative results from tests of a strong version of the Sapir-Whorf hypothesis using Loglan! While Loglan might facilitate certain kinds of thinking to some degree, I do not believe that it implements any basically new kind of thinking, or even improves existing kinds of thinking to the point where qualitative improvement in thought can be expected."

I continued, "One of my sources for evidence for this claim is Quine's 1961 book Word and Object, in which he gives an analysis of the logical structure of natural language (using English, of course) which looks like an engineering blueprint for Loglan! This seems to indicate (as I will claim explicitly below) that, far from being basically different from existing natural languages (at least some of them), Loglan is a refinement of natural language."

Against this I will argue that the first-order logic features of natural language are largely implicit rather than explicit, potential rather than actual. Evidence for this is found in mathematics teaching, for example: it is very hard for students to understand a sentence, stated in what seems to be plain English, of the form "for each positive real number epsilon, there is a positive number delta such that..." (as in the definition of limit in the calculus). Another source of evidence is the testimony of philosophers (trespassing on Gaynor's turf): they, if anyone, should know how to express what can be expressed in their language, and philosophers had uniformly serious difficulties with any use of quantifiers more complex than that found in the Aristotelian syllogism, and especially with reasoning about relations, until modern times. The counterargument is that the full power of first-order logic has been potentially present in the natural languages since relative clauses were introduced, but this did not mean that this power was actually available to any speaker. The fact that relative clause constructions are extremely ambiguous strengthens the case for this position; an attempt to make a truly sophisticated logical argument in a natural language could (and, as with the Sophists of ancient Greece, often (sometimes intentionally) did) founder on natural language ambiguities. (In Loglan, I suppose I could actually say the last sentence, nested parentheses and all!)

I went on: "The next step (which, as I will explain, is the last step, in my opinion) is the expression of higher-order logic, or, equivalently, of type theory or set theory. Loglan is more capable in this direction than I originally thought, but not ideal. It does have the ability to construct sets by abstraction ("the set of all x such that...") and it has just been augmented with finite sets and sequences (I think), the need for which was not originally anticipated. However, these features were implemented as afterthoughts. Loglan is at the point where it is no longer possible to add major new features; it is running out of little words!"

I agree (in my role as devil's advocate) that the next step after full first order logic is correctly described here. Of course, I do not agree that natural languages have been at this level for very long, and I maintain that in fact only a minority of speakers of natural languages can bring out the potential in their language for full first-order reasoning, which requires careful attention to making things unambiguous. Again, drawing from teaching experience, I find that calculus (and other mathematics) students often find instructions on my exams most confusing when I take the most care to be absolutely clear and "logical".

The potential in natural language for higher-order reasoning is much more limited. It consists mainly in devices for forming abstractions similar to those found in Loglan. In principle, the same device of forming relative clauses that assists quantification should allow the definition of sets or attributes/properties. Just as in first-order logic, it is easier to define sets or properties of single objects than relations in natural language. The claim that higher order logic (essentially the theory of types of Bertrand Russell) is actually rather than potentially implemented in natural language can be countered, as above, by exhibiting the total confusion of philosophers (presumably keen thinkers and users of their native natural languages) on the subject of properties, "universals", or sets until modern times.

A general summary of this position is that the natural languages themselves have had to be engineered and re-engineered in order to express the full first-order logic and partial higher-order logic which they may now be used to express in the speech and writing of careful, highly educated speakers. Most speakers of a natural language do not speak such "engineered" versions of their language, or at least speak a much earlier "release" of the engineered version than the vanguard uses. Ambiguities and limitations of natural language make this achievement a precarious one, even for the vanguard of educated speakers.

"I believe that this was the most recent Whorfian revolution, but it occurred (for us, at least) in recent prehistory when the implicit capabilities were implemented in natural language, not when propositional and first-order logic were explicitly laid out."

On my alternate view, I would say that the most recent Whorfian revolution occurred between the seventeenth and nineteenth centuries (and may not be over); it is certainly not over (may not even have begun) for the general population of natural language speakers.

After discussing the higher-order logic features of Loglan (abstractions, sets, and sequences) I closed with "Actually, my prediction is that these [higher order] features of the language will be widely misused!" This is a remark which I second from this alternate standpoint; all features of Loglan which express logical concepts not correctly understood by speakers will be misused (usually by analogy with usage of their native language). It is important that it be understood that there is more to making Loglan a logical language than giving it an unambiguous syntax; the semantics (the meaning or logical interpretation) of the constructions and usages provided by its gurus have to be clearly communicated. This is a reason for Loglan to have been designed to be even more radically different from natural languages than it has turned out to be; misuse of the language by analogy with natural languages might have been made more difficult than it is, that is, made somehow less likely to occur by the very design of the language. To some extent, unambiguous syntax will help the learner to keep the meanings of logical constructions straight, but the semantics remains a separate issue.

In the following passage, I was actually intimating the alternate view I am now expressing here: "Quine, in Word and Object, gives some grounds for the belief that natural language already supports this level higher-order logic; he handles class abstraction [the construction of sets] using relative clauses. But issues related to sets or classes have caused logical and philosophical errors on the part of great thinkers right up to modern times; an engineered language which encouraged the correct use of these concepts might indeed cause Whorfian effects."

From either standpoint, I maintain that "my experience as a mathematician leads me to believe that in any event the Whorfian revolution which fully implements higher-order logic will be the absolute last" for reasons explained in the previous column. But the view expounded here is that we are farther from that goal than we thought, and that different segments of the linguistic community, either in those using natural languages or in a potential community using an engineered one, are and will be functioning at widely different levels.

For Loglan, the message is similar. A distinction has to be drawn between the potential and the actual. Use of an unambiguous syntax is a valuable step toward correct use of sophisticated logical concepts, but the logical concepts themselves must be communicated over and above the teaching of the syntax. My experience in teaching thinking at this level to students in college is that the syntax will help, but that we should not believe that the syntax (likely to be easier to learn) will automatically carry the semantics (likely to be harder to learn) with it. That the Academy is defining a construction or usage to have a certain meaning will not necessarily prevent the community from using it in some different, less logically acceptable sense. From the standpoint of Whorfian effects, we might end up with more than one Loglan speech community: some exhibiting effects that might dazzle Whorf, some exhibiting none at all.

Copyright 1993 by The Loglan Institute, Inc. All rights reserved.

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