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## To revolutionize both math and physics by the grassroots popularization of a new quantitative tool which is introduced below.

We start with the Law of the Excluded Middle. Consider it's complement and call this new law the Law of the Exclusive Middle. Let these two laws be equivalent. You now have something similar to Fuzzy Math, but it is very different. These two laws are connected by equivalence which is very different than Fuzzy Math.

Next consider Descartes "I think therefore I am". We reverse engineer this into a statement which reflects our foundation (above), to derive "Maybe I think therefore maybe I am". We keep both of these statements and set them as equivalent.

We then proceed to all of the standard tools of mathematics which are used for the analytic quantification of magnitudes. In math, things are said to exist. In our new system things are regarded as "maybe existing". We keep both of these tools and regard them as being equivalent. We will call one of them Mathematics, and the other should be called something like Conjectural Modeling to reflect that it is based entirely on absolute indeterminacy.

We now have a quantitative tool which is split down the middle, essentially a kind of mirror image. On one side, absolute determinacy. On the other side, absolute indeterminacy. Both sides held together by equivalence.

We now have a tool which is capable of addressing both the equivalence inherent to relativity, and the indeterminacy which is inherent to Quantum Mechanics.

We can write correct and accurate quantitative models using either system. In fact, for every possible question there should be two solutions. One based on determinacy, and the other based on randomness. These two answers are equivalent. As an example, whether I know with absolute certainty that I have 10 dollars, this is quantitatively identical to not knowing but "expecting" that I have 10 dollars where 10 is an expected value instead of a value known with absolute certainty.

I have many examples and a lot of math to reinforce these views. I am convinced that this solution is extremely important.

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## William Kuch

Another example might be helpful. Bob has an apple, and Mary has an apple. Bob is 100% certain that his apple exists and he assigns a truth value T=1 to this magnitude of existence. Mary is not certain that her apple exists at all, she is permanently uncertain whether it exists or not. But it is very, very convincing that it does, however she remains uncertain of it. She says that her apple exists with truth value T= .999... to reflect the inherent existential uncertainty of this apple.

Bob is certain, Mary is uncertain. However, quantitatively these are identical views to hold because .999... = 1. Qualitatively they are different. But quantitatively, they are in fact quite the same.

We have proven that these two approaches to the existence of apple are quantitatively equivalent.

This has very little to do with epistemology, or the study of words and language. I am doing philosophy of math & physics, definitely not epistemology.

## Gail . 50+

1 minus .000000000000000000001 = .999999999999999999999.

One cannot equal .999999999999999999999

I can be 99.99999% certain that something is right and still be wrong. 99.99999 =/= 1. The probability that I am wrong can be slim, but it still exists. Therefore, knowledge =/= faith.

## William Kuch

I cannot debate this topic here, it is off topic. This thread is about equivalenve and applying it to the Law of the Excluded Middle. Please read the Wikipedia article I cited or check with a mathematician. I cant use this space to debate something which is considered to be an elementary fact of mathematics, this is why calculus works, I wont debate that here. Again, it is universally accepted that 0.999... = 1 identically, it is not an approximation.

Thanks for the feedback but Im trying to stay on topic.

## Gail . 50+

The law of excluded middle can be expressed by the propositional formula x=x. It means that a statement is either true or false. Think of it as claiming that there is NO middle ground between being true and being false. Every statement has to be one or the other. That’s why it’s called the law of excluded middle, because it excludes ANY middle ground between truth and falsity. So while the law of non-contradiction tells us that no statement can be both true and false, the law of excluded middle tells us that they must ALL be one or the other.

If x = something other than x, then it is necessary to declare the conclusion false.

The Law of the Excluded Middle does not take infinity into consideration. It deals with finite things only, therefore, .999 does not equal 1. 1 only = .999 if you take it into the realm of infinity.

If you do not take it into the realm of infinity, then if you say 1=.999, you are violating the law of non-contradiction.

Or do I misunderstand the law of the excluded middle?

If I can't speak of the math, how can I speak of the law of the excluded middle? It's founded on mathematical principles.