The Principle of Verifiability says that the meaning of a proposition is its method of verification, or, as I (and Karl Popper) prefer, its method of falsification.
Here's an example. Suppose I say "the Lockheed SR-71 Blackbird is the fastest aircraft in the world." I could mean several different things. I could mean that it accelerates faster than any other airplane. I could mean that it flies in a straight line faster than any other plane. Or, I could mean that it climbs fastest, etc. I can tell you precisely what I mean by telling you the conditions of the experiment that falsifies my statement, e.g., "In level flight, no other airplane that can take off under its own power and is powered by air-breathing engines, can sustain a higher speed than the SR-71 over a 500 mile course."
Okay, that was an easy one.
Look at this proposition: "All Carbon 14 nuclei will eventually decay." Thanks to Nicolas for presenting me with this puzzler. At first glance, scientists will agree with this proposition. The problem is that, as written, we can never falsify it. We would have to wait for all time and observe all C14 nuclei in the universe decay before we were satisfied. This isn't even possible in principle, let alone in practice. This means that, as a logical positivist, I can assign no meaning to this proposition.
This is typical of the kind of challenge philosophers have put forward in opposition to logical positivism. By carefully wording accepted scientific knowledge, opponents of logical philosophy hope to find places where science and logical positivism cannot be reconciled. Poor them - it's a hopeless cause.
The actual law of radioactive decay for C14 says this: "the mean lifetime of C14 nuclei is 8,000 years." Of course, this proposition is perfectly falsifiable. Indeed, the law of radioactive decay does not say that a given nucleus must ever decay. It just says that it will last on average 8,000 years before decaying.
Given a proposition, I can generally reword that proposition in some equivalent form. Instead of saying "I am soaked," I could say "I am covered in water," or "I am drenched." There are a very large number of ways of saying the same thing, though many of these ways become more and more verbose. How do we know whether our alternately-worded propositions are equivalent or not?
Certainly, two propositions cannot be equivalent if an experiment will falsify one proposition, but not the other. That is, verification is one (and, in my opinion, the only) arbiter of equivalency. (Note: I include rigorous mathematical proof as a form of verification of mathematical propositions, so the principle applies to mathematics also.)
This might be called the "Principle of Verifiable Equivalence" (okay, so I'm not good at naming principles). It's weaker than the Principle of Verifiability for two reasons. First, it can be used to compare two similar propositions that don't have identical meaning, but which have overlapping meaning. If I say that "George is lying to me," I am also satisfying the condition that "George is being dishonest towards me." If I falsify the latter proposition (dishonesty), I must falsify the former proposition (lying).
Second, the Principle of Verifiable Equivalence is weaker because it does not say anything about propositions that cannot be verified or falsified. It merely says that any two such propositions can never be shown to be equivalent.
Thanks again to Nicolas for this proposition:
"Homosexuality is unnatural."
This type of proposition is confusing to people because they make the mistake of thinking that it is a proposition about the world. It isn't. Those who utter this proposition are not talking about social convention - they generally do not mean that "homosexuality is practiced by less than 10% of humans." If they did, their utterance would be no more controversial than saying "private aviation is practiced by less than 10% of humans."
What is controversial is what they are really saying, namely: "I consider homosexuality to be wrong." This isn't about the world, per se. It is about how the speaker feels about the issue.
Similarly, if I say "eating fast food is bad," I really mean either "I don't like fast food," or "do not eat fast food!" Of course, this proposition is either an expression of opinion/strategy, or else it is a directive. Neither one can be true or false at all.
So, before you get too deep trying to analyze the proposition "God is good," just remember that this proposition is, at best, not about the world, and, most likely, utter nonsense.