Question

So I have been pondering about language. By language L I just mean a series of symbols. The upper limit of this series of symbols is Aleph-zero. Yet somehow using these symbols the human is able to understand the meaning of phenomena of cardinality Aleph-one. Let us denote the meaning of phenomena as M. How is this happening (what is the possible mappings)? The cardinality of L is Aleph-zero, that of the phenomena Aleph-one and M(Aleph-one) must be Aleph-zero?

So this seems to have interesting possibilities:

M is not a well defined operation and cannot be expressed in mathematics (rather should be taken for granted)
There is no one to one mapping between L and M(Aleph-one). We humans do not understand meaning (solely) through language
There is no one to one mapping between M(Aleph-one) and Aleph-one. Certain meanings are redundant.
There can be truths about the phenomena of Aleph-one which cannot be captured in L.
Here's an example:

I have a friend Bob who speaks only in morse code. After a long time I explain him to him what rational numbers are. He understands he concept. A natural question comes does my friend understand this concept in it's entirety. Perhaps there are things he doesn't get. But I can talk more morse and he (perhaps) will get it. How do a countable set of symbols make Bob understand phenomena which is uncountable.

Mathematics cannot ever formally describe meaning*
Well maybe Bob used innate knowledge and was inspired by speech to bring it forth.
While the phenomena of rational numbers can be of cardinality aleph-one the meaning behind the rational numbers reduces to phenomena of cardinality to aleph-zero.
There are truths about the rational numbers that no amount of symbols will ever make sense on why it is so.
Question
Are there any possibilities I have missed? What answer(s) are correct?

*Please do not ask me to formally describe meaning since I kind of subscribe to this line of attack.

Answer 1

The question explores the relationship between language and understanding of phenomena. Language, as a series of symbols, has a finite upper limit, while the meaning of phenomena can have a larger cardinality.

Step-by-step explanation:

The question explores the relationship between language and understanding of phenomena. Language, as a series of symbols, has a finite upper limit, while the meaning of phenomena can have a larger cardinality. One possibility is that there is no one-to-one mapping between language and the meaning of phenomena, suggesting that humans do not solely rely on language for understanding. Another possibility is that certain meanings are redundant, indicating that some aspects of phenomena may not be fully captured in language.

It is also proposed that there can be truths about phenomena that cannot be expressed in language, suggesting that language is limited in its ability to capture all aspects of reality. An example is given with a person communicating in Morse code, demonstrating that a countable set of symbols can convey understanding of an uncountable phenomenon.