Is the statement "These letters are black." true or false?
If the letters are black, then the statement is true.
If the letters are not black, then the statement is false.
In this example we have a subject (These letters) and a proposed description of that subject (black). In the same way, we have the Liar Paradox:
Is the statement "This sentence is false." true or false?
If the sentence is true, then the statement is false.
If the sentence is false, then the statement is true.
Here we have a subject (This sentence) and a proposed description of that subject (false).
The questions is, how do we determine if the description is correct?
To start, we have to realize that in this context the statement itself cannot tell us that the sentence is false as it might appear to. This is because when asking "Is the statement 'This sentence is false.' true or false?" we are implying that the description of the subject may be either true or false. This means that the description (false) of the subject (This sentence) is solely a proposed description as stated above.
Therefore, the word "false" is not defining the truth value of the sentence as it might first appear, but only proposing a truth value for it. It is our job to determine whether this proposed truth value is correct or incorrect.
To do that, we need to understand what the proposed description (false) is actually proposing. What does it mean to describe something as "false"?
True and false are names for relationships between a subject and some proposed description of that subject. If the proposed description matches the subject, then the relationship is named true. If the proposed description does not match the subject, then the relationship is named false.
If true and false are only names given to relationships between a subject and a proposed description of that subject, then you need both a subject and a proposed description of that subject before you can determine which relationship exists.
In the statement 'This sentence is false,' we have a subject (This sentence) and a proposed relationship that subject has with some proposed description of it (false). The proposed description of it is not stated, therefore it is impossible to determine whether or not the proposed relationship is correct or incorrect.
This means that the statement "This sentence is false" cannot hold a truth value because there is nothing to attach one to; in the same way that you cannot attach a truth value to the statement "Water is not made of things." until you know what the term "things" is referring to.
To put it another way, "This sentence is false" refers to a proposed relationship between "This sentence" and conditions for truth and falsity. We are not shown which of these conditions exist, so the truth value of the proposed relationship cannot be determined.
To be clear, I did not contradict my terminology when stating that "false" is both a proposed description, and a proposed relationship between the subject and a proposed description of that subject. I am considering the word "description" as a variable for any proposition made about the subject.
Feedback and critiques on my reasoning would be greatly appreciated. I apologize for any elementary mistakes and unconventional terminology that may have been used. I have never taken a course in logic so I am relying almost entirely on intuition. I am also unable to read symbolic logic easily, so I would appreciate it if replies could avoid using it.