Definitions of loglanghood
This article contains opinions that may not necessarily reflect the views of the LLWiki or larger loglanger community.
When the term loglang first came into being, in the 1990s, it meant language 'based' on formal logic, the then prototypical examples being Loglan and Lojban. This wiki does not presuppose any particular definition of loglanghood, but nevertheless some loglangers have proposed more precise definitions (at least in their own loglangologizing).
And Rosta: predicate-argument structures
And Rosta has for many years defined loglang as a language that unambiguously encodes a limitless range of predicate-argument structures
- In other words, a language that unambiguously encodes the syntax of Propositional Thought.
- 'unambiguously' = what John Clifford has termed monoparsing. At minimum this requires that, where sentences are pairings of phonological form and logical form, no two sentences share the same phonological form.
Maiku: syntax-semantics isomorphism
Some crude thoughts to be developed:
My view of the definition of loglang is heavily influenced by Richard Montague's work, which in my opinion was a product of pure loglanging, albeit carried out in the opposite direction of usual loglanging: rather than starting with a grammar and adding a phonology and building up a speakable language, Montague started with an already existing natural language (namely English), focused on a "fragment" of that language, and attempted to demonstrate the formal properties of various elements of that fragment, including quantifiers, articles, and conjunctions. Open-class English content-words such as "fish", "walk", "tall" etc. were treated as predicates as might be found in any loglang, and Montague uses category theory to develop a syntactic schema to explain the allowed combinations of English's various parts of speech.
Montague's program contains a lot of important concepts, but one I'll touch on here is the idea of syntax-semantics isomorphism, which can also be called model-theoretic semantics, which embodies the idea of a loglang not merely having a formal grammar but having an interpreted formal grammar. What this means is that every syntactic unit from sentence down to word or morpheme has an interpretation in the "model", i.e. something that the syntactic unit points to in the domain of discourse. So a sentence like "le mlatu cu xekri" expresses the proposition that the cat is black. This sentence can be decomposed into "le mlatu", which expresses a first-order entity, namely the cat, and "cu xekri" which is roughly a mapping from first-order entities to truth values, or to propositions (i.e., a predicate). "Le mlatu" can be further decomposed into the choice operation "le" and another predicate "mlatu". Thus, the overall structure of the sentence observes Frege's principle of compositionality from top to bottom. In constructing loglangs, the loglanger carries this principle to the furthest limit -- ideally, there is one formal rule of semantic interpretation for each formal rule of grammar (morphology and above). This one-for-one ideal is one that has been all too often neglected in the history of loglanging, but in my humble opinion it's the ultimate goal, without which formal grammars amount to rather pointless string rewriting rules.
Toaq Blog article: “Logical Language Misconceptions”.
Velt: eliminating ambiguity or vagueness
Seems that it's commonly agreed that a loglang should eliminate ambiguity or vagueness. So the problem left here is: what is ambiguity/vagueness?
In fact, we are often talking about several different concepts. They cause different phenomena:
1. Polysemy. There're several different ways of understanding a sentence, and the impossible branches will be discarded automatically until a acceptable understanding is obtained.
- e.g. a bat can be an animal, or a sports instrument
- Intuitive test by conjunction
- "The colors are light." (normal)
- "The feathers are light." (normal)
- "The colors and the feathers are light." (strange)
- Intuitive test by quantifier
- "Each thing exists on the ground is a crane." (Assume that here's a crane as a bird and a crane as a machine on the ground.)
- Intuitive test by contradiction
- "That bank isn’t a bank." (possible)
- "That dog isn't a dog." (impossible)
2. Unstable meaning. It's possible for various people to have inconsistent understandings or for someone to have different understandings at different times.
- When do we say "somebody is tall", "A are similar to B"?
- (Sorites paradox) How do we tell "that's a pile of sand"/"that's not a pile of sand"? Where's the boundary?
- How do we tell "two physical objects have contacted each other"? Is it OK to say true here if the distance of atoms is less than 10 micrometers? Furthermore, what's a physical object?
- Definition of "understanding"
- truth value of propositions
- epistemic structure/progress
- mental state(emotion, moral preference, etc.)
- Consistency (this is the one mentioned above)
- e.g. understandings of different people should be the same
- Correspondence test for the truth value: there is a truth table for a predicate and everyone always gives judgments that are correspondent to the truth table
- Consistency (this is the one mentioned above)
3. Uncertainty. Have doubts on determining or be unable to determine a truth value.
- This is commonly explained as the lack of some knowledge.
- Sorites paradox is also an example for here.
- However, you can be confident to assert something is true, while it's truth value is unstable.
- When a fat boy is passing a narrow gap, we may say "he is too fat".
- Two paradigms of such vagueness in predicate logic
- Vague predicate
- In the sorites paradox, if we can't tell whether something is a pile, we can say we don't understand "pile" completely. An alternative description is: we understand piles vaguely.
- Vague symbol
- In a reference, we can use "a book" to refer to an substantially existing book on the shelf, without knowing its title, author, content etc..
- Vague predicate
4. Generality. It has a large range of denotation. It's truth value can only make a small distinction.
- We hate the generality while we're trying to denote/refer to something, and we often have no problem for abstract concepts.
- "I'm being." is too general to be useful.
- "There's a pig" is less general than "there's an animal".
- "A bird" is more general than "the only bird in the room"
For some examples of the phenomena above, it's possible to avoid them. But this may be impossible for the others. I will talk about this topic later, by listing the methods of eliminating ambiguity/vagueness.
Furthermore, ambiguity/vagueness is sometimes acceptable or even required.
Required for a lower cost of expressing and understanding
If a precise true statement entails the vague one, why not use the precise one?
For example, "he is 198 centimeters tall" entails "he is tall (under some standard)", but we usually cannot determine that numerics value in our daily life. If we ask the users to use the precise expression only, we can only obtain it by an estimation.
This not only improves the cost of expression, but also is an indirect way of expressing, which does not reflect our real epistemic process. It may be better for an expression to have a precision that matches our capacity of knowing.
Required for the lack of knowledge itself: mystery, art or surprise
e.g. A boy said "buy a surprising gift for me" (and might have narrowed the range of acceptable gifts by "expect toys"). If you bought a hat for him, you can say "this hat is that surprising gift". But this is impossible for the boy to know this sentence while he was expressing his demand, otherwise it won't be surprising.
Here, the vagueness is deliberately wanted. And the more specific the claim is, the less likely it is to be true.
Velt: clarify the distinction between analytic/synthetic propositions
I've also observed that some loglangers try to promote the analytic way of thinking. This is also a bit related to vagueness. And it can be expressed by the old philosophical issue: analytic/synthetic distinction.