What does Logical Language mean (Lojban course in English)

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What does "logical language" mean?

The book "The Complete Lojban Language" or "the Lojban Reference Grammar", called CLL, is the only source of the official information about Lojban by the creators of Lojban.

There is a lot more information about Lojban on the Internet, and there are a few people who speak Lojban, sometimes self-styled "fluent", but they sometimes or often give inaccurate information by mixing official ideas with their own ones. So, I advise you to read the CLL by yourself first.

However, it sometimes or often contains logical failures. That is a major obstacle to reading. I'm not a spokesperson of any Lojban group, but I would like to help you understand the contents of the book, by pointing out failures, because I think that Lojban itself is beautiful and usable even though the information about it is chaotic.

The editor of the book CLL is the Logical Language Group. It is a non-profit charitable educational scientific association. We find the phrase "logical language" a few times in the book CLL. What does it mean? Is it a language that is logical?

First, let's look up the word "logical" in the dictionary. There are three definitions in Harper-Collins COBUILD Advanced English dictionary.

  1. In a logical argument or method of reasoning, each step must be true if the step before it is true.
  2. The logical conclusion or result of a series of facts or events is the only one which can come from it according to the rules of logic.
  3. Something that is logical seems reasonable or sensible in the circumstances.

Now, I'd like to draw the attention to the nouns that are qualified by the adjective "logical" in the definitions. The word "argument" in definition #1 signifies the meaning of a sentence. A sentence is a series of symbols, formed out of voices, spots on a surface, and so on, while an argument is not a series of symbols, but the meaning of it.

As for the word "logical", it concerns the truth value of the meaning of a series of symbols. Similarly, method of reasoning is a method of deducing the meaning of a sentence from the meaning of another. In definition 2 also, the words "conclusion" and "result" mean "the meaning of sentences". In definition #3, the word "logical" does not qualify nouns, but it is expressed ein other words "reasonable or sensible". Both signify the property of a meaning of symbols. After all, the word "logical" does not qualify the words that mean "a series of symbols", but those that mean "the meaning of it".

While highlighting this point, we will quote the definition of the word "language" in the dictionary. There are six definitions of the word "language" in Harper-Collins COBUILD Advanced English Dictionary.

  1. A language is a system of communication which consists of a set of sounds and written symbols which are used by the people of a particular country origin for talking or writing.
  2. Language is the use of a sys of comm which consists of a set of sounds or written symbols.
  3. You can refer to the words used in connection with a particular subject as the language of that subject. For example, the language of business.
  4. You can refer to someone's use of rude words or swearing as "bad language" when you find it offensive.
  5. The language of a piece of writing or speech is the style in which it is written or spoken.
  6. You can use language to refer to various means of comm involving recognizable symbols nonverbal sounds or actions. I emphasize that all recognizable symbols can be considered as language. Verbal sounds or not, letters, gestures and so on.

According to these definitions, language means symbols, a set of symbols or the use of symbols. So we have three options for the meaning of logical language.

Option 1: symbols that are logical. Option 2: a set of symbols that is logical. Option 3: the use of symbols that is logical.

Among them, Option 1 and 2 are not possible, because the word "logical" does not qualify the words that signify "a series of symbols", but those that signify the meaning of it. As for Option 3, is it poss that the use of symbols is logical? The use of symbols consists of use(r?)s, series of symbols, and meaning of them. According to the definition, the word "logical" may qualify the words that signify the meaning of series of symbols. And "the meaning of series of symbols" belongs to the use of symbols. Option 3 is therefore possible.

So, is Lojban not a series of symbols, but the use of some series of symbols? Okay, let's see the book CLL. In section 1 of chapter 1 of the CLL, version 1.1, which is titled "what is Lojban?", the history of the creation and the main features of Lojban are described. The third among 11 features is: "Lojban grammar is based on the principles of predicate logic."

No, it's impossible. Lojban grammar is a group of rules for arranging symbols, while the principles of predicate logic are rules fore defining the truth value of the meaning of symbols. Since the object of grammar and that of logic are different, they can not be based on the same principles. From the beginning of the book, the description thus gives the impression of words of a swindler who disguises himself as a scientist.

Well, then, perhaps in the text about Loglan, is there a reasonable definition of the phrase "logical language"? It is likely to be, because Loglan is previous versions of Lojban, according to the CLL. Indeed, the definition of "logical language" is found in section 1.2 of the book "Loglan 1: a logical language, 4th edition, 1989" by James Cooke Brown. "Loglan is logical only in the sense of purporting to facilitate certain kinds of thought, namely those kinds which proceed by the transformation of sentences into other sentences in such a way that if the first are true, so also are the second."

So, Loglan language is considered logical not in the sense defined in the dictionary for general purpose, but in the original sense, that it facilitates the logical process of thought, that is to say, the logical operation.

This definition is quite reasonable, and it gives two pieces of info about Loglan.

  1. Loglan is not language, but "a" language. In other words, Loglan is not the use of symbols, but symbols themselves, or a set of symbols.
  2. Loglan facilitates the logical operation.

Since Lojban is the next version of Loglan, this definition of logical language may be valid for Lojban even if it conflicts with that unreasonable description in section 1 of chapter 1 of the CLL.

So, how does Lojban or Loglan facilitate the logical operation? If we continue reading of the CLL, we will recognize the following points that can facilitate the logical operation, compared to other languages. Some rules in Lojban grammar are similar to the grammar of the language used for composing formulas of predicate logic.

In this regard, let's discuss a little more about formulas in predicate logic. Predicate logic is a domain of symbolic logic. The idea of origin appeared in the 17th or 18th century, at the latest in a text written by Gottfried Wilhelm von Leibniz, who lived from 1646 to 1716. A collection of posthumous works by Leibniz titled Die philosophischen Schriften, is published in the 19th century in Berlin. This is the 2nd edition of the 7th volume published in 1890. There are many descriptions of "characteristica universalis", universal characteristic. For example, let's read some of the sections in the category of "Vorarbeiten zu Algemeinen Characteristik", preparing for the universal characteristic.

Sed ut redeam ad expressionem cogitationum per characteres, ita sentio nunquam controversias finiri neque sectis silentium imponi posse, nisi a ratiocinationibus complicatis ad calculos simplices, a vocabulis vagae incertaeque significationis ad characteres determinatos revocemur.

Id scilicet efficiendum est, ut omnis paralogismus nihil aliud sit quam error calculi, et ut sophisma, in hoc novae scripturae genere expres- sum, revera nihil aliud sit quam soloecismus vel barbarismus, ex ipsis grammatices hujus philosophicae legibus facile revincendus.

Quo facto, quando orientur controversiae. non magis disputatione opus erit inter duos philosophos, quam inter duos Computistas. Sufficiet enim calamos in manus sumere sedereque ad abacos, et sibi mutuo (accito si placet amico) dicere: calculemus.

But in coming back to the subject of expressing thought with symbols, I think we will never be forced to end the debate in silence, if we only replace complicated reasoning with simple calculation, words of vague and uncertain meaning by symbols of definite meaning.

As a result, of course, all paralogisms are nothing but errors in calculation, and any sophism is nothing but errors in copying, it's really nothing but solicism or barbarism, by themselves, philosophical laws are easily convinced by the grammar.

If this happens, when we start talking, there will be no disputes between two philosophers, that is to say between two calculators. Just take pens in your hand, sit in front of an abacus, and say to each other (please address yourself friendly): let's calculate.

Yes, it is most important: "please address yourselves friendly". This is the ideal that Leibniz thought feasible with "characteristica universalis", the universal characteristic. It was not realized until the 19th century that particular symbols were used to represent logic.

Here are the particularities of predicate logic.

  1. A finite set of symbols, including predicates, are created.
  2. By arranging the symbols according to a defined grammar, finite series of symbols are formed, which are called formulas.
  3. Rules for transforming a formula into another are called "rules of inference".
  4. Not always, but in some systems, some formulas are called "logical axioms".

Axioms are considered to mean something true, that can be premises in a logical deduction. Logical axioms are some of them that substitute for rules of inference. The axioms themselves are series of symbols, which cannot be logical according to the definition of logical in dictionaries for general purpose. The phrase "logical axiom" has thus the particular definition in some systems of predicate logic.

If we properly define the rules of inference and the logical axioms in some cases, we can transform a formula that means something true into another that is also considered to mean something true by following a formal procedure. Thus as Leibniz thought ideal, philosophical discussions also can be deduced by formal procedure, which is similar to mathematical calculation. If the premises of a philosophical discussion are true, the conclusion are also true. Which are premises which are true? That's another problem.

In my opinion, all these things are principles of predicate logic. The rules of inference and the logical axioms define the use of a set of symbols such that formulas derived from formulas that mean something true cannot mean something false. They do not define a language, that is a set of symbols.

Now, let's go back to the subject of Lojban. I told you about some rules in Lojban grammar are similar to the rules of grammar used for composing formulas in predicate logic. So, what are the points of similarity? I have two points to emphasize.

  1. By aligning a predicate and 0 or more terms, an atomic formula is formed.
  2. By connecting two formulas with a logical connector, a complex formula is formed.

The words "predicate" and "term" mean symbols that are used to represent pred logic. I will explain it to you at another time.

To conclude, in the context of the description of Loglan or Lojban, the phrase "logical language" does not conform to the definition in the dictionary for general purpose. There is an original definition that, "logical language is a language that facilitates logical operation". Judging by this simple fact, I must challenge the description in 1.1 of CLL. The following correction may represent the reality of Lojban:

"Lojban is a language, and the grammar is based on the grammar of the language that is used for representing predicate logic."

In addition, I oppose the use of the phrase "logical language" in the general context, without giving a reasonable definition. A language cannot be logical. When we use the word language, in the sense of "our language", not in the sense of the use of a language, it cannot be qualified by the word "logical" in the proper sense. Hence, the phrase "logical language" without reasonable definition produces an atmosphere of pseudo-science, or at least it can deceive people.

By the way, we will find in the book CLL a lot of discussion about semantics, some of which concern logic. Among them however, we will find several defects from a logical point of view. In this sense, Lojban has latter illogical use of language, in the semantics of the CLL. I will talk about each defect of semantics in the CLL when I discuss a related topic.