Monday, June 1, 2015

The Role of Errors in the History of Loglans 1A

The Role of Errors in the History of Loglans

Disclaimer: This is my personal account, from my point of view. The events involved are described as I remember them and interpreted them. The science involved is as I understand it and extrapolate from it. I have tried not to assign blame here; I think most of the errors were inevitable in the situations involved and were probably seen as errors only in corrected hindsight (if at all). Others may have different memories or interpretations, read the science differently, and disagree about what was an error, but this is my story. Bring your own salt.

I am dividing this essay into sections headed by various claims that were made for Loglan (and Lojban). Most of the errors discussed here attach more or less well to one of these claims, a few others can be sandwiched in. These claims have played a major role in the spread of interest in Loglans and have, in various ways, guided developments over the decades, so they may an informative and useful guide for presenting the problems.

Maxim One: Loglan is spoken Formal Logic (or Symbolic Logic or First Order Predicate Logic)

In many ways, this is the root error, from which the others derive. Most of the features later claimed for Loglans or sought for them derive from similar feature had by or claimed for FOPL (and it predecessors into the 19th century and successors into the 21st). The formulae of FOPL are syntactically unambiguous; there is only one way to analyze one. Translating an argument into such formulae provides a definitive way to demonstrate the validity of the argument (or its invalidity and where it goes wrong). Such translations also reveal misleading features of ordinary language, which give rise to many needless confusions and disagreements (and much metaphysics, some would say). Thus, FOPL is a valuable tool for rational discussion and for promoting understanding among people of different views, since it can be used to reveal the structures of any language.

Of course, the claim that some set of formulae was translation of a given argument is open to some disagreement; there is no automatic procedure for such translations as there is for judging validity of the translated set. Thus, the validity of many historic arguments (the Ontological, as a prime example) are still undecided. Of course, if the argument was given in FOPL – or an appropriately fleshed-out version of it – to begin with, this problem would disappear. So, the construction and use of such a language (partially realized for present purposes in careful ordinary German or English) became the goal of some logicians/philosophers from the '20s on. James Cooke Brown, the creator of Loglan, studied with Broadbeck at Minnesota and was at least thoroughly exposed to this Logical Positivist tradition. So, whether consciously or not, the “logically perfect language” played a role in his choices when he came to create an experimental language.

Another major factor was simplicity. FOPL does away with the many parts of speech and with the variety of tenses, moods and modes, and cases of familiar languages. Among content words there are only two parts of speech, terms and predicates, and, while there are a variety of subtypes (more as logic developed beyond the '50s) they all behave in the same way. Terms are divided into names, which stand for individuals (however that may be defined), and variables, which play a role in forming compound formulae, together, eventually, with compounded terms. Eventually there came to be terms of various sort, depending upon what was being counted as an individual, but this did not change the basic grammar. Predicates were divided according to the number of terms they required to make a formula (and, eventually, what types of terms). A(n atomic) formula, then, was just a predicate with the appropriate number of terms (of the right sorts) in order: Faxb, for example. No cases or sentential roles, no prepositions, no tenses, etc. Beyond this were the recursive steps involving -makers: a maker took a specified number of variables and formulae and returned a term or a formula, depending on its type (this gets somewhat more complicated later, but the basic pattern remains the same). Thus, &, a typical formula maker, takes two formulae and returns a new formula, their conjunctions: from Faxb and Gxc to (Faxb & Gxc). A, a variable binding predicate maker (quantifier), takes a variable and a formula to give a new formula, the universal generalization of the original formula: so from x and the previous formula we get Ax(Faxb & Gxc). The occurrence of x in this formula are now said to be bound by this quantifier, whereas before they were free. Similarly, @, an illustrative term maker, takes one variable and one formula and produces a new term, in which the variable is now bound: from x and Fx to @xFx, the salient F, say. The formulae used by a maker may be of any degree of complexity and the so may be the terms used in formulae. But the history of their construction and so their ultimate structure is always apparent: there is never any doubt about what formulae and variables (and whatever else) is involved at any level. At any stage in the development of to and beyond FOPL, the set of akers is closed and introducing new ones (beyond mere abbreviations) takes a rather dramatic effort, even though the pattern for defining them is clear throughout.

Given this, spoken FOPL would seem to be an easy thing to achieve. We need an open class of expressions for names and another for variables and another for predicates, perhaps with some special markers for different types of each sort. Then we get some special expressions for the various makers in use. Then we just rattle the formulae off as they are written, using the recommended expressions for the various symbols. Every logic teacher does this every day to talk about the formulae on the board:”For all ex both eff ay ex be and gee ex see”, for the sentence above. Clearly, this ad hoc technique is not quite good enough for our purposes, even leaving aside the fact that we don't have any meaningful expressions here yet. The three classes of expressions are not separated; they are all just letters and the capital/lower case distinction does ot come across in speech. Then there are the parentheses, the left one here pronounced “both”, looking ahead to the connective to follow, and the right one omitted altogether. With a different connective, the left parenthesis would have been differently pronounced, as “if” or “either” or “as”, say, so we need either to deal with them all the same (as “paren”, say) or make the nature of the enclosed compound sentence clearer at the beginning. (This is the way this problem arises in parenthesized infix – or Principia – notation; in other version the problem arises in different way, either by complexities on the connective to show how deeply it is buried in the compound, in labeled infix, or , in prefix – Polish – notation, by the need to mark the division between component sentences.). The right parenthesis can, in fact always be dropped in sentence compounding (though it is often a kindness not to), but needs to be reintroduced (and, indeed, extended) in the case of compounded terms with in a simple sentence: is Fa@xGxcb, composed of the predicate F and the terms a and @xGxcb or of that predicate and the terms a , @xGxc and b, or, indeed, of the terms a, @xGx, c, and b with predicate F? We must either enclose the formula in the composition in parentheses, if they are not already there, or else enclose the terms which follow a predicate in some sort of parentheses as well (F, say) and in either case, take care to pronounce both of these parentheses. (There are other, even more tiresome ways to deal with this problem, by always marking the number of places of each predicate, for example). But these can all be done rather cheaply: a few more words for constant characters, like right parentheses of various sorts (or, actually, for right parentheses, one sort is enough, if we put all of them in – but would we want to?).

The thought of a string of “end”s (say) at the end of every sentence is enough to show that spoken FOPL needs to be different from the written form, where adding a few right parentheses is a minor matter. So you need rules about when you can drop parentheses and when you can't and (probably) when you can but shouldn't, for clarity's sake. Or find another way around the problem. This is the first stage of the Loglans' adoption of FOPL.
Step A. Atomic sentences

Loglan took as its basic sentence type, before any frills, a predicate with a fixed number of places (given in the glossary but not marked in the word anywhere, despite regular suggestions to do so). Predicates had a definite (though increasingly complex as the years went by) phonemic structure, so were distinctive. Names also were distinctive in a variety of ways, while term variables were given by a finite list and rules for extending by subscripts. Composite terms were formed by replacing the first term (which Loglan had moved in front of the predicate – an insignificant change, to aFxb and xGc) by an operator which did the work of a 1-variable, 1-formula term maker and by attaching the arguments of the predicates the formula by explicit connectives, @G+c, for instance. This solved the first level of possible term misalliance, but for deeper ones, a right hand end marker for these term makers was used as needed (i.e., when more terms for a higher component followed). The problem about only using the first term of a predicate was solved a device creating new predicates in which the original first term and another term were swapped, from aFxb to xF'ab, for example, giving rise then to a term @F'+a-b, say. The situation calling for RHE markers is then something like H@xF' b>, which would first appear as H@F'+@G+c-b, where the predicate to which b is attached is unclear, hence H@F'+@G+c]-b, however pronounced. These and other changes created a new problem, when the predicate of a term might come directly before the predicate of a sentence, creating a potential ambiguity (predicate strings having been made legal – see later). One could make this a case where the RHE parenthesis of the term was used, but, since that could trigger a string of such parentheses, a separate divider was introduced. H@xFx becomes @F/H (or, still legal but riskier, @F]H). Since this automatically closes all the terms that went before, it suggests similar RHEs to close several terms, but not all without stringing out the term closers. This turns out to not help a lot, since learning different words for closing two, three, … terms is less efficient that just using two or three or … closers (having that many open terms at any point is probably bad style, but grammar has to apply to bad style as well as good).

The complexity of speaking even a relatively simple sentence makes one wonder if there is not some other way organize terms without loss of crucial information (what term occupies what place with which predicate). The answer so far is “No”. There are ways of reducing the reliance on order and devices for tagging terms according to what predicate they go with, but these all introduce yet more essentially empty and repetitive items, which the present complexities sought to reduce. A case system, meant both to relieve the requirements for a fixed order and to give some meaning to the various positions – which now have meaning only if you remember the definition of the predicate correctly – does not simplify the need to shift order to make a term nor does it help enough with the problem of dropped places (upcoming) to be worth the cost. It is not clear that the Loglans' solution to making this structure speakable is the simplest or shortest or clearest one, but alternate proposals so far have offered no obvious advantages and have often had clear downsides. So let us call this a success: it keeps all the essential information but gets rid of as much superfluous verbiage as possible. That it is often notoriously easy to get wrong, whether by (unstylishly) leaving in unnecessary RHEs or by (disastrously) leaving out needed ones, is a problem for eventual textbooks. And one that gets worse as we get deeper into the language.

In making a language based in this way on FOPL, another inelegance arises. When using FOPL to transcribe arguments from another language, we naturally pick predicates that exactly fit the situation we are dealing with. But, in a Loglan, we have fixed predicates with fixed places. So, to deal with a particular situation, we may not need all places that the predicate supplies (or we may need one not supplied, but that is a later problem). For instance, the predicate briefly rendered “go” is actually a five-place predicate “1 goes to 2 from 3 along route 4 using mode of travel 5”, so to say just “Sam goes to San Francisco” leaves three places unfilled. Since we don't at the moment care about what goes in there in fact (from here on Southwest by airplane, say), we don't want to say anything more (as we don't in English). The stock logical move in this case would be to bind each of these unused places with a particular quantifier, “some” (and, so, a number of at least implicit parentheses) Sx*Sy*Sz*sGfxyz***. The Loglans can do that, of course, but that seems to be defeating the purpose of making this as much like other spoken languages as possible while keeping it as rigorous as FOPL. So, the Loglans have three responses, each ultimately going back to the official form. One is to introduce a new predicate based on the original but having on the interesting places (it holds of the mentioned things just in case there are things for the other places so that the original predicate holds for all of them together). The second is to insert a dummy term in the unfilled slots. And finally, and most pleasingly, the slots are just left empty. This last is the standard when the empty slots are all at the end, with no intervening filled slots. The dummies (there are several, for some reason) are used when a filled slot comes after an unfilled slot, though other devices can also be used with just the blanks. So “Sam is going by Southwest”, officially SxSySzsGxywz, might be sG- -w- (- for a dummy insert) or sG- -w or sG4w (where 4 is a marker that the next term is, in fact, the fourth one for the predicate) or, modifying the predicate, sG[1,4]w (dropping the other terms) or sG<2>w (rearranging the terms by exchanging the 2nd and 4th), dropping the unused final terms in each case. Of course, restoring the FOPL original requires knowing the places of the original predicate so that the quantifiers can be properly placed, as close to the predicate as possible. These unmentioned quantifiers will come to raise questions in going beyond atomic sentences. 

In the opposite direction, predicates may be extended by adding terms. Although the general idea of prepositions (or cases) to give overt meaning to predicate places was rejected, it is retained for situations where a predicate needs to be extended beyond its usual sense. So a new term is introduced by a marker that says what its role is to be. It can be inserted into the physical string of arguments at almost any place, though traditionally goes at the end. Similarly, the possibility, briefly mentioned above, of a “preposition” to indicate which place of a predicate an argument fills is fully realized in the Loglans, though rarely used. The prefixes to the predicate that exchange the first place and another can be combined to create any order of arguments we want. However, these combinations are often long and not transparent for some rearrangements, so the prepositions are a better choice in speakability terms. Both these prepositional structures behave just like the regular arguments. In particular, they attach to the predicate of a term with the same ties as other arguments. They can even, with some adjustments be made the term replaced by a term-maker. And they are closed off just like other terms.At this point is is fairly clear, if not rigorously demonstrated, that the Loglans' reading of atomic sentences does represent the structure completely and accurately.   

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