Our language (human language) is not a formal system because its axioms share a property called active meaning. Active meaning is somewhat related with the idea that two differently posed elements might achieve equal paradigms.
These so called fundamental elements are, for instance, letters like “a” or “c”. Besides the fundamental elements, we’re also concerned with how these elements are related; so, in conjunction with symbols we argue that there is a set of proper rules R dictating the possible relative relationships between those elements. Therefore, the analogy between the fundamental elements (symbols) plus the set of rules (R), and the general definition of Axioms is comprehensible.
In math, shortly, axioms are starting points. We ought to prove the existence of larger structures (theorems) through the axioms we built.
In human language we construct phrases out of those Axioms. Phrases are complex structures relative to the underpins (smaller elements + R) it possesses by necessity (you can’t write phrases without acknowledging both the existence of letters and the existence of rules). So, basically, one might argue that to prove the existence of a phrase is equivalent to determining whether it makes sense relative to the Axioms. For example, in the english language writing Monty Python is diverse is fundamentally different from writing Monty Python si diverse. The latter is not a theorem because it doesn’t make sense from an axiomatic perspective. However, even if you hadn’t read the first form (Monty Python is diverse) you would’ve been able to estimate what the phrase (false theorem) was saying. Therefore, is such a phrase still a theorem, even though it happened to violate our major rule ? Does the phrase Monty Python si diverse happens to be a theorem just because it conveys some general form of thought that we all mechanically perceive ?
Let’s argue that it does not.
If the former phrase is not a theorem then it’s meaningless, because it violates the logical paradigm on which it is brought. Even though the phrase did not mean a thing we were able, to some extent, to decipher what it possibly could’ve meant, but chances are, following a more drastic example, you wouldn’t get it right. What does your intuition tells you about this non-theorem: a goodmortyteveryrweeko ?
You were probably able to come up with something like: a good morning to every week. However, what I really meant was: a good morty to every rick. The latter exercise proves, to some extent, that there is a set P’ of phrases which are both non-theorems and whose source meaning is counter-intuitive or even impossible to determine.
At some level, language ceases to engage with reality. We say x even though we meant y or expected a person to get it as z. The lack of honesty in language is somewhat fuelled by its unformalaty. Therefore, how can we guarantee that at least one debate, or exchange of verbal thoughts, does not merge with inconsistency or even mutual delusion ?
Let P be the set of all phrases which are both theorems and whose source meaning is counter-intuitive or even impossible to determine.
Then I argue that virtually any question, whose form happens to be verified as belonging to P, is irrelevant partially due to its second nature.
At what point is the question What is Consciousness ? a derivation of some element in P ?
At some level, language ceases to engage with reality.
There are some people that would say that it is language that creates meaningful reality.
Some would even say that the onset and use of language by humans is what led to human consciousness.
I think that natural language can enfold and transmit propositions. It’s not an efficient notation but it has other strengths. I think think that ambiguity and imprecision of (some) language is a strength as well as a weakness.
I think we are still emerging from our natural history. We still express ourselves with violence and coercion on a regular basis. A language of pure fact and concept lacks the tools of negotiation. The fact that ordinary sentences are open to interpretation and relative to subtext gives them pliability. It gives people who are motivated but insufficiently confident a degree of permission to use diplomacy.
Further, some concepts are intrinsically poetic. Or intrinsically moral. Or in some other way difficult to capture with mathematical symbols. We need a code that is adaptable and fluid for many tasks.
Consciousness in particular, I think is probably a concept that hovers at the perimeter of our creative imagination. We can loosely define it in negative terms. We can have an array of intuitions about it. We can, perhaps identify some necessary causes. Still, it’s not a property that we can concretely measure. It could be that we are better off, at least for the time being dealing some issues in a more poetic or philosophical way. At least while we develop better tools.
This reminds me of the concept of “Papanca”. But what is left once all of this is hypothetically removed? I don’t claim to know.
I think you are confusing the idea of a formal system and the idea of a model of a formal system. Thus, the things you want to call “axioms” are really assignments of meanings. If language were a formal system then any grammatical string of primitive symbols that could be deduced from purely syntactic axioms (no assignment of meanings) would be a theorem of the system. But a meaningful sentence in English is not a theorem of English. But perhaps I miscomprehended what you were trying to say.
If language were a formal system then any grammatical string of primitive symbols that could be deduced from purely syntactic axioms (no assignment of meanings) would be a theorem of the system. But a meaningful sentence in English is not a theorem of English. But perhaps I miscomprehended what you were trying to say.
I’m inferring the existence of two different qualities for the word meaning.
Let m be the first qualaty for meaning:
(1) A phrase has m if, and only if, it’s an extension of the axioms (symbols + R)
(2) If a phrase is an extension of the axioms, then the phrase is a theorem of language
phrase 1. I am sleepy. -> has m because it does not violate the axioms
phrase 2. Tomorrow there is a soccer game. -> has m because it does not violate the axioms
phrase 3. I great person constipated but in a horse. -> has m because it does not violate the axioms (note that 3. makes no sense)
Let M be the second qualaty for meaning:
(1) A phrase has M if, and only if, without any major doubt, the globalaty of the phrase conveys objectivity
(2) There are phrases M which are not theorems
phrase 1. I am hungry. -> happens to have both m and M.
phrase 2. A great person exists somewhere. -> happens to have m but not M
phrase 3. His knii does hurt. -> has M but not m. (His knee does hurts)
I’m basically arguing that the phrase What is Consciousness is of the form m but not M.
I would have to disagree with the idea that the question is invalid. It’s one of my favorite things to think about. My favorite thought so far was consciousness being inevitable. All of the elements that can be found in the human body, each having no choice but to react to radiation, consciousness is forced into existence, and the things that are conscious can’t figure it out because they think of it as a choice. But that’s just my favorite.