[Daniel Terhorst]

Originally Posted by november

Why would we assume that "Today is Tuesday" implies "Today is raining"? It's my understanding that in order to have an implication like that, we'd first have to have the supposed logical arguments that verified "Today is Tuesday" and/or "Today is raining".

It's no different from saying (→ means imply): Let A → B. When we happen to observe A, then we know B must also be true.

The example of Tuesday/raining is misleading, because it is easy to confuse our observations of the real world (where it is definitely false that it always rains on Tuesday), with the purely logical structure of the example.

Originally Posted by november

The implication comes into play when we say, "Since it is raining today, it must be Tuesday." or vice versa.

A → B does not necessarily mean that B → A. That is, if we observe A, we know B is true, but if we observe B, we have no idea whether or not A is true. To use the words of the example, knowing that it's true in our environment that "If today is Tuesday, then it is raining" (it is an example, and does not have to reflect the real world), then if we know it is Tuesday, we can also conclude that it is raining. However, if all we know is that it happens to be raining today, we cannot conclude whether or not today is also Tuesday. We simply don't know whether or not it rains on other days.

Originally Posted by november

One or the other must be established as fact before there can be any implications.

And it was when it was stated, "then if today is Tuesday."

This statement says that we are about to consider the situation (and only the situation) where this is true. Therefore, in the environment we have established, it is true by definition. In other environments, it may or may not always be so, and might even never be the case.

Originally Posted by november

What you wrote is like saying, "The apple is red, so the apple is red." True? Maybe. Redundant? Yes. And, redundancy doesn't prove anything.

Not quite. It's more like, "All apples are red; since this is an apple, it must also be red." That is: (Apple → Red), and Apple... therefore Red.

To say, "The apple is red, so the apple is red," one would state, Red Apple → Red Apple, which is, as you said, pretty meaningless.

Originally Posted by Andreas

Back that train up, Conductor. Previously we've been unable to measure the mass of an electron. Does that mean the electron didn't exist previously? You don't even need other realities when talking about this. Just because something cannot currently be measure does not negate it's existence.

I made this same misinterpretation myself at first because of the wording. If one looks closely, it says:

Observable is hereby defined as being capable of affecting the structure of our universe.

(emphasis mine)

Thus, the electron, being demonstrably capable of measurably affecting more than one observer existed, was never imaginary, regardless of our inability to previously witness it. The provided definition, then, still handles this example.

-- Daniel Terhorst