Exploring the Concept of Right and Wrong on the Infinite Number Axis

[dovil]

Let's say, hypothetically, there exists an infinite number axis, with 0 located at the center. On one side, the numbers increase to the positive values of (1, 2, 3, ...), while on the other side they decrease to the negative values of (-1, -2, -3, ...).

First, let's clarify the concept of 0. It represents the lack of a numerical value and is not a tangible entity with physical form or substance.

Now, let's assume that each point on the number axis (1, 2, 3, ...) represents a universe, similar to Earth, for simplicity. There is a statement, which can be either true or false, such as "chickens can't fly". On the positive side of the axis, if the statement is true, there is a corresponding Earth. On the negative side, if the statement is false, there is a corresponding Earth with the opposite number. For example, the statement "humans can fly". On the axis at number 56, there is a world where this statement is true. On the opposite side, at number -56, there is a world where this statement is false.

Given this hypothetical situation, does 0 represent anything at all? And if so, what does it represent?

Regardless of your decision to answer, I would be grateful for your opinions and thoughts on the hypothetical situation presented.

[Summer48]

Thank you for presenting this interesting hypothetical situation.

In this scenario, if we consider each point on the number axis to represent a separate universe with its own set of facts and realities, it would seem that 0 does not represent a universe. Instead, it is the point from which the axis originates, indicating the starting point for the positive and negative values.

However, it's worth noting that this interpretation is based on the assumption that each point on the axis represents a separate universe. It's also possible to interpret the axis differently, where 0 represents a universe in its own right. In this case, the statement "chickens can't fly" would correspond to the universe at 0, which represents the absence of any particular fact or reality.

Ultimately, the interpretation of 0 in this hypothetical scenario depends on the framework and assumptions we make. Regardless, it's a fascinating thought experiment that highlights the complexity of concepts like zero and infinity, and how they interact with our understanding of the universe

[Eckhart Aurelius Hughes]

Hi, dovil,

Interesting question and exploration!

let's assume that each point on the number axis (1, 2, 3, ...) represents a universe, similar to Earth, for simplicity. There is a statement, which can be either true or false, such as "chickens can't fly". On the positive side of the axis, if the statement is true, there is a corresponding Earth. On the negative side, if the statement is false, there is a corresponding Earth with the opposite number. For example, the statement "humans can fly". On the axis at number 56, there is a world where this statement is true. On the opposite side, at number -56, there is a world where this statement is false.

Given this hypothetical situation, does 0 represent anything at all? And if so, what does it represent?

If I am understanding your model, then I think the following can be said about it:

The sides of the two number lines would be mirror images of each other, in a sense, meaning that all universes would be duplicated on both sides of 0. This is because any proposition (i.e. meaningful statement) has an opposite. For example, if "chickens can't fly" is 75 then "chickens can fly" could be 76, which would mean -76 is actually a copy of 75, and -75 is actually a copy of 76.

0 would correspond to a universe in which no propositions at all are true (or false), which would be a violation of the Law of Excluded Middle which is of course utterly illogical, and thus logically must be considered impossible. For example, in the would-be universe represented by 0 it would have to both the case that the proposition "Chickens can fly" is neither true nor false.

Granted, the interesting thing about the Law of the Excluded Middle is that it is itself based in a way on circular reasoning (i.e. a Begging the Question Fallacy). This is because if the Law of the Excluded Middle is not true then it can also be true, since it is only via the Law of Excluded Middle that we would logically have to choose between the Law of the Excluded Middle being either true or false. No matter how much it seems that the Law of Excluded Middle is true or must be true, we cannot possibly exclude the possibility that it is also untrue without committing a Begging the Question Fallacy.

There is a poetic beauty in your construction in that it has 0 represent the seemingly logically impossible universe where the Law of the Excluded Middle is violated, since 0 is in the middle of the number line.

However, even ignoring 0, your construction appears to become nonsense when analytic and/or a priori truths are considered, such as the common example of the proposition "All bachelors are unmarried" or the statement "2 + 2 = 4". So you would presumably want to address that by modifying your construction.

An interesting effect would be that 0 would then also presumably represent a universe in which only analytic and/or a priori propositions are true. Those would be statements that are true in all universes, positively number, negative numbered, and the one at 0. 0 is then perhaps some of form of Plato's Platonic Realm, so to speak.

While your construction is very particular, it seems to scratch at an age-old philosophical collection of various broad questions along the lines of "Can pure nothingness exist?" or "Is the would-be concept of pure nothingness self-contradictory nonsense?" or (to quote Einstein) "Did God have a choice when he created the universe?"

It comes up in questions like, "Why is there something rather than nothing?" or "Why does anything exist at all?"

One response is that the very would-be thing/idea/concept referred to by "nothing" in the question above is nonsense. It couldn't exist. It's self-contradictory and illogical. It's not an option. Thus, the question "Why is there something rather than nothing?" is as nonsensical and unanswerable and meaningless a question as asking "Why is there ketchup in my fridge instead of an married bachelor?" Or "why is it that there is mustard in my fridge instead of 2 + 2 equaling 5?"

Logically, it would seem "nothing" isn't an option, can't be an option, and never was an option. Because, logically speaking, it's illogical nonsense.

[Alan Masterman]

I'm afraid I lost the focus when the chickens entered. And the "negative infinities" only clinched it.