(I understand this post may seem difficult to understand what I'm getting at, at first, but the "Possible counter arguments" section near the bottom, I believe explains enough [especially the first one])

Introduction:

The Liar’s Paradox can be understood by the following statement “This statement is false”. This is a self-referential statement that leads to a logical contradiction when we try to assign a truth value to it. The paradox happens because the statement refers to itself in a way that creates an infinite loop of reference. If we assume the statement is true, then it must be false, but if it is false, then it must be true, leading to a paradox where it is neither true nor false.

To understand this paradox, we can consider words and statements as mirrors that reflect our attempts to understand them (by themselves). Just as a mirror reflects our image but does not contain the actual image, words and statements reflect meaning but do not inherently contain meaning. When we try to understand the statement “This statement is false” by thinking that the statement itself contains meaning, we fall into a trap of trying to find meaning where there is none. Therefore, the Liar’s Paradox can only be considered valid from a “logical seeming” standpoint if we ignore all of the true values and give into the illusion that the mirror is a window and not a mirror by oversimplifying things.

Implications for Language and Truth:

The perspective that words and letters are like mirrors has great implications for our understanding of language and truth. Firstly, it challenges the traditional view that words and sentences have inherent truth values. Instead, it suggests that truth is a product of our interpretation of language, rather than an inherent value of language itself.

This view also highlights the subjective nature of truth. Since truth is dependent on our interpretation of language, different individuals may interpret the same statement differently, leading to different truths. This challenges the notion of objective truth and emphasizes the importance of context and perspective in determining what is true.

Furthermore, viewing words as mirrors suggests that our understanding of the world is limited by our own understanding, not the words we use. Words and symbols can only reflect our understanding up to a certain point, beyond which they will fail to accurately represent reality (due to our own lack of understanding), thus the reason why the Liar Paradox forms in our minds because we're trying to use words for things they can't be used for.

Application to the Sorites Paradox:

Applying this perspective to the Sorites Paradox helps us understand our struggle with defining a heap. In this paradox, the term “heap” seems simple on the surface, but as we examine it more closely, we realize that our understanding of what constitutes a heap is vague and subjective.

The word “heap” is merely a linguistic construct, a symbol that represents a concept. This symbol acts as a mirror, reflecting our attempt to understand the concept of a heap through the word alone. Our inability to define the boundaries of a heap is not a limitation of the concept itself, but rather a reflection of our limited understanding. Just as a mirror can only reflect what is placed in front of it, our understanding of a heap can only reflect our current level of knowledge and perception. As our understanding grows and becomes clearer, the reflection in the mirror becomes sharper, allowing us to better grasp the concept of a heap.

In this light, the Sorites Paradox is not a flaw in the concept of a heap, but rather a reflection of our own limitations in understanding and defining abstract concepts. It serves as a reminder of the complexity and subjectivity of language and our ongoing quest to understand the world around us.

Application to Russel's Paradox:

The Russel's paradox, "a set that contains all sets that do not contain themselves" is only a paradox to those who think that the word "set" is not a mirror. Those that understand it is a mirror understand that "a set that contains all sets that do not contain themselves" is a set that cannot exist, but instead relies on the assumption that words are absolute, and not mirrors, thus you can arrange them all in a way which creates a paradox that must seem to exist to someone who doesn't understand that words are mirrors.

Conclusion:

In reconsidering the Liar’s Paradox through the lens of words as mirrors of understanding, we uncover a shift in our perception of language/truth. This perspective challenges us to see that words and letters are not carriers of truth or falsehood, but symbols that reflect our own understanding in a way that others can understand. This realization leads us to question the traditional view of truth as an objective and fixed concept, highlighting instead its subjective nature, dependent on our interpretations.

Ultimately, we must acknowledge that our logical frameworks are constructed upon the foundation of our subjective interpretations and agreements about the meanings of words and statements. In this sense, logic requires a certain degree of faith in the validity and consistency of our interpretations. Yes, faith, meaning that even logic is a faith-based system of reasoning.

Note:

While I do not deny the existence of objective truths, the nature of truth itself raises questions about our ability to definitively prove or disprove the existence of such truths. Objective truths, if they exist, are independent of individual beliefs or interpretations. However, our access to and understanding of these truths are understood through our subjective perceptions and interpretations of the world. Therefore, while we may have faith in the existence of objective truths, our understanding and certainty regarding these truths require our subjective experiences and interpretations.

Possible Counter Arguments:

1 - "To understand this paradox, we can consider words and statements as mirrors that reflect our attempts to understand them (by themselves)."

Argument: It's not clear what this means.

Counter argument: A word itself doesn't have meaning, we just pick words to reflect meaning (hence a mirror). But where did that meaning first come from? It didn't come from words, it came from thoughts in our mind. A basic example of this is a tree. At first, we only thought of a tree via images from our memories/senses, not words. We drew images of trees to express to someone what we were talking about (poorly drawn images usually), and then we changed images to words to save time and effort.

The origin of a statement was our own senses. We saw the form of a statement after arranging words a certain way, and created a word to [reflect] what we saw. But when have we ever truly sensed the liar's paradox? "This statement is false" This statement has two aspects to it, first, it's a statement, and second, it conveys a specific meaning. So let's break it down:

The statement, "This statement is false" doesn't have meaning in the same way the statement, "The sky is blue" has meaning. This is because the statement, "The sky is blue" reflects knowledge of the blue sky, but the statement, "This statement is false" reflects knowledge of words which are "mirrors". When you place two mirrors facing each other, it creates an image of infinity, of the reflections reflecting the reflections back and forth forever (if the light aspect in that situation were able to continue on forever, but it doesn't, so eventually the image gets darker and darker until you can't see it anymore. Still, the image is in a state where it would continue forever if the source of light were endless). So, in this context, the Liar's paradox doesn't actually go on forever, because its value is a reflection of our own thoughts, and we can't keep thinking about the Liar's paradox forever (just like how a source of light doesn't go on forever).

So, the real value of, "This statement is false" is the "image" of a statement, set up to reflect the meaning of a normal statement for as long as we can keep thinking about it. In other words, the statement, "This statement is false" is just an illusion of a greater than normal statement due to where the "mirrors" are set up, for those who understand that words are indeed mirrors.

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2 - Argument: This is much more of a philosophy of language problem. Logic is the study of correct reasoning.

Counter Argument: In the case of the Liar's Paradox, the assumption that creates it is that language inherently contains meaning and that statements can be categorized as true or false in a more straightforward manner. Through my solution that words are mirrors reflecting our understanding rather than carriers of inherent meaning, I'm offering a solution that requires a shift in how people think about language, truth, and logic. So yes, the solution to this paradox cannot be solved through just traditional logic due to the need to re-frame things.

However, logic requires awareness of the full scope of a situation to be accurate. Take this for example:

The Paradox of the Literal and Figurative

Imagine someone says, "I'm so hungry I could eat a horse." In traditional logic, if we take this statement literally, we might analyze it as follows:

A. Premise 1: The person claims they could eat a horse.

B. Premise 2: Eating an entire horse is humanly impossible due to its size and the limitations of human appetite and digestion.

C. Logical Conclusion: The statement is false or absurd.

However, this analysis falls apart when we recognize that the statement is not meant to be taken literally. It's a hyperbolic way of expressing extreme hunger. The real meaning isn't about eating a horse but conveying the intensity of hunger. Traditional logic, without considering the non-literal use of language, leads to a misinterpretation. Hence the reason why awareness of how things are is required for logic to be useful. And so, by gaining awareness of what causes the Liar Paradox to form, a solution can take form due to the pieces of information then available to work from.