Can the incompleteness theorems of Kurt Gödel be extended to systems other than mathematical systems? If you don't know what I'm blathering about, here's a simplistic one-liner purporting to summarize Gödel's work: the correctness of statements in a system such as arithmetic can only be proved outside of arithmetic.
There are no shades of grey in Arithmetic, only black and white. Arithmetical statements can only be evaluated as true or false, correct or incorrect, by reference to the axioms comprising the foundation of the system.
If arithmetic is discreet, language is continuous. If arithmetic is a particle, language is a wave. Arithmetic digital, language analogue. Arithmetic lumpy, language smooth. While arithmetic deals in black and white, language deals in black, white, grey, and all the colors of the rainbow. Therefore, to evaluate language statements meaningfully, more than just two criteria are required. (Actually, only one criterion is required for Arithmetic, because each of the pairs in yes/no, correct/incorrect and true/false are the absence of the other, eg falsity is the absence of truth.)
It's true that language statements can be evaluated as correct or incorrect. "The Earth revolves around the moon" is an incorrect statement. But the incorrectness is decided by virtue of reference to data and/or axioms that do not belong to language, but rather to such formal systems as astronomy and physics.
Language is not susceptible to Gödelian "incompleteness" in terms of correctness or incorrectness, truth or falsity. Language is susceptible to Gödelian "incompleteness" in terms of MEANING---language's unique and peculiar vulnerability. In the context of language, MEANING is the proxy for those characteristics (eg being-built-upon-axioms) that in mathematically based formal systems enable incompleteness theory validly to be applied to them. It is only by stepping outside of language into a metasystem at a higher level of abstraction that the non-metaphorical meaning of words can definitively be assessed for consistency and completeness, clarity and unambiguity.
Semiotics alerts us to the issues arising from relationships between the SIGN, the SIGNIFIER, the thing that is SIGNIFIED, and the NAME of the thing that is signified. Or in other words, the issues relate to confusion on the part of language users about the thing itself, the attributes of the thing, the word for the thing, and the name of the thing.
Language is a labelling system, and words are labels. Sometimes people use a different label than one previously used to describe the same thing, or a different label to the one that another person applies or would apply to the same thing. It's called "disagreement" but actually it's just different styles of labelling. To paraphrase Humpty Dumpty in Lewis Carroll's "through the looking glass", a word means whatever the utterer of the word means the word to mean, no more and no less. And that is an issue of semantics that cannot be resolved within language.
In English, "dog" is the word for a creature referred to (signified as) "Canis lupus familiaris". But say that I create a new word, "ooga-booga", to refer to Canis lupus familiaris. I'm not wrong. My statement is not wrong. The word "ooga-booga" is not the wrong word in the circumstances. There are no wrong words, there are only words for which new meanings have yet to be established among language users. The word "dog" itself came into usage through the process whereby meaning is allocated to "words" (or words allocated to meanings? (my head hurts!)). The first step in that process is the minting of the word, ie the invention of it in the first place. So re "ooga booga", step one of that process has already taken place.
[There are no wrong names either, as highlighted by the emergence in recent times of a plethora of parentally invented and/or idiosyncratically spelled names, eg Heavenly Hiraani Tiger Lily.]
Consider the following 6 statements: 1. "Neptune is the god of the sea" vs 2. "Poseidon is the god of the sea" vs 3. "There is only one God, named Jehovah" vs 4. "...named Allah" vs 5. "...named Ahura Mazda" vs 6. "there is no God or gods, only matter and energy; fermions and bosons."
In #1 vs #2, there is disagreement about the NAME of the thing, and agreement about the ATTRIBUTE of the thing (being-a-god-of-the-sea).
Statements #3, #4 and #5 disagree amongst themselves as to the NAME of the thing. And each of #3, #4 and #5 disagrees with both #1 and #2 about the ATTRIBUTE of the thing (deity-is-one vs deity-is-many).
The best example arises from a comparison of #3 and #6, as follows:
Statement #3 is the Judeo-Christian monotheistic proposition. Statement #6 is the atheistic proposition, (ideally based on a robust structure of physics, chemistry, cosmology, etc!).
The attributes of the thing in the Judeo-Christian monotheistic proposition are: OMNIPRESENCE*, OMNIPOTENCE and OMNISCIENCE. In other words, the people embracing #3 believe that the thing for which the English word is "god" is everywhere, all-knowing and all-powerful.
Funnily enough, the people embracing #6 believe that the ATTRIBUTES of being everywhere, all-knowing and all-powerful apply to the thing for which the English word is "Universe":
- By definition, there is nothing outside of the Universe, including the Universe itself. Everywhere that there is a place to be, the Universe is there. Therefore the Universe is OMNIPRESENT.
- There are forces and powers within the Universe (eg Gravity, Electromagnetism, etc). There are no forces or powers outside of the Universe. In fact, the Universe includes all of the forces and powers that exist. Therefore the Universe is OMNIPOTENT.
- There is no knowledge outside the Universe; there are no knowers (or believers for that matter) outside the Universe. All the knowledge there is to be known, is known inside the Universe. Therefore the Universe is OMNISCIENT.
The preceding discussion shows that atheists and believers agree about the ATTRIBUTES (the 3 x omni~s) of the thing. They disagree about the word (label) to be used for (applied to) the thing (ie "God" vs "the Universe"). And they disagree about the NAME of the thing. For the believer, the name of the thing is "Jehovah" (or "Allah" or "Brahman" or "Ahura Mazda" or whatever). For the atheist, the thing has no name, but if the thing had to have a name, "ooga booga" would be just as valid as "Jehovah", "Allah", "Brahman", "Fred Bloggs", "Cthulhu" or "Dollar". There's no correctness or incorrectness in assigning names.
Nor is there such a thing as correctness or incorrectness in allocating words to things, or to meanings. The words in English "help" and "assist" are different in spelling and origin, but both may validly be attached to the same thing. Let's not get into examples involving multiple different languages --- that's too complex for my simple brain. (It's language's "hard" problem.)
Recently the English word "cougar" has been adopted to refer to an older woman seeking a relationship with a younger man. Previously, the thing to which the word "cougar" could validly be attached is a large, tawny cat, Felis concolor. Same word, two different meanings, of which the latter has recently been invented by language users.
All of the above examples show (I hope) that from any standpoint inside the formal system of language, there is not and can't ever be endorsement or rejection of the consistency or completeness of the MEANING of language statements.
To validate the non-metaphorical meaning of words, one has to step outside of language. Which reminds me, I need to do a post about the metaphorical vs non-metaphorical nature of language. In the meantime, have a look at mutter, utter and stutter, the incompleteness of language, Buddha's loincloth and the traitor word.
* Omnipresence is a strange one: theologians such as St Augustine and many others hold that the God named Jehovah stands outside of time and space, outside of zir own creation. Strictly speaking, therefore, Jehovah cannot be said to be omnipresent. And yet, monotheists of all stripes say that God is everywhere: in you, in me, in the third rock on the left. And yet, their own experts say that Jehovah is separate from zir creation. If that's not inconsistency, I don't know what is. No wonder many monotheists feel separate from the divine (=the Great Divide)