Tuesday, November 23, 2004

The Principle of Verifiable Equivalence

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.

Equivalence
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.

Directives
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.

4 comments:

Nevin ":-)" said...

How does one falsify "the mean lifetime of C14 nuclei is 8,000 years" without having to "wait for all time and observe all C14 nuclei in the universe decay?"

Is logical positivism really "In the absence of being able to show x is false, assume x is true?"

Doctor Logic said...

Hi Nevin,

You're not the only one who found my posting confusing, so I'll have to write another posting to clear up my first one. I'll comment on your questions here though...

Logical positivism really says that the only meaningful propositions are either scientific propositions or mathematical propositions. Whether a scientific proposition is actually true or not isn't the concern of logical positivism. Logical positivism is concerned with the meaning and method of proof of the proposition, not with its actual truth.

So your paraphrase ("in the absence of being able to show x is false, assume x is true") should really be the following:

"x is a meaningful proposition which may happen to be true or false, if and only if we can prove that x is false when x happens to be false. Otherwise, x is meaningless."

Of course, we can substitute y = ~x into this and get:

"y is a meaningful proposition which may happen to be false or true, if and only if we can prove that y is true when y happens to be true. Otherwise, y is meaningless."

Why do I use the term falsification? Scientific theories generally predict values to a certain precision over a certain domain. Such theories can almost never be perfectly verified over the entire domain, but they can only be proven false at points within the domain. This is not to say that verification never works: Newton's laws of motion have been verified over a large domain (classical physics), even though they do not apply universally.

Back to the proposition about C14 nuclei. A proposition about the statistical decay rate of C14 is finitely testable (we can test the mean lifetime of C14 in a few minutes in the lab), whereas a proposition about all C14 nuclei in the universe is not testable.

doctor(logic)

Nevin ":-)" said...

Scientific proposition is used to predict various aspects of the future. However, many of the examples you picked are merely facts, not propositions.

Take the SR-71 example. What is the predictive value of this proposition? I don't see any beyond the trivial (ie, if I see a really fast plane, it might be an SR-71).

And much of what you have presented seems more like language lawyer semantic games than a way to gain true insight. While "lying" may be stronger than being "dishonest" (since the latter can be satisfied by withholding the truth), at times many of those details are irrelevant and drowning in a sea of details can keep us from making higher level connections and abstractions. On the other hand, our theories can be mistaken when we throw away relevant details. It is just a balancing act.

As for the C14 example, I don't see how you can "prove" or "falsify" it in a lab, since that is at best only taking a statistical sample on the third rock from the sun in the 21st century. Why should I believe this is generalizable? That is an article of faith, not logical positivism.

Finally, I'm not really sure why you keep bringing up a Supreme Being. You give an awful lot of attention for something you believe is "most likely, utter nonsense".

Doctor Logic said...

Nevin,

Scientific propositions are theories that can be refuted by experiment. The more evidence we have, the more experimental data we accumulate, the more fact-like these theories become. Philosphically, I would say that an actual fact is the statement of an observation or the outcome of a particular experiment. For example, that the temperature gauge in my experiment read 100 degrees isn't in dispute, though the actual temperature may not have been exactly 100 degrees.

My proposition about the SR-71 predicts the outcome of a race between the SR-71 and any other aircraft currently in production.

The Carbon 14 example is certainly falsifiable. Technically, scientific propositions make claims:

1) Subject to the implicit claim that the universe is causal and follows physical laws.
2) Over a certain domain and to a certain precision.
3) Accurate in isolation, where other effects are negligible (e.g., acceleration due to gravity is independent of mass, neglecting air resistance).

Implicit Claim #1: Causality. Of course, if the universe did not follow physical laws, it would be impossible to have scientific theories at all. Is trust in causality a form of faith? I don't think so. Causality is a heuristic. Either the universe is causal and science works, or the universe is acausal and there is no possibility of knowledge of any kind. I cannot prove that the universe will be causal tomorrow. However, in an acausal universe, there is no knowledge and no possible survival strategy. Therefore, the assumption of causality is necessary if we are to influence our own survival.

Implicit Claim #2: Domain. It often happens that there are parts of the claimed domain where our scientific theory breaks down. Relativity and quantum mechanics are used in domains once claimed by classical Newtonian physics, e.g., the ability of electrons to tunnel through a potential wall falsifies pure classical physics on small scales. Classical physics is still used in the vast majority of today's engineering projects because it is a superb approximation to the quantum result on large scales. Our previously successful tests of classical physics are still valid, they just didn't test parts of the domain where classical physics breaks down.

Implicit Claim #3: Isolation. No one claims that the law of radioactive decay applies everywhere and cannot be affected by other physical factors such as intense gravitational fields. The theory says that neglecting other effects, the half-life of C14 will be 5,700 years. This cannot be proven true everywhere in every circumstance, but it can be proven false in the lab!


I certainly do not advocate using "language lawyer semantic games" in everyday discourse. As you say, it would be quite inefficient. 95% of our speech concerns intention, directive, fact or scientific theory. One might ask "is the other 5% so much of a problem that we need to invoke logical positivism?" Yes. I believe that the number one cause of bigotry and violence on this planet is religion. The fact that 90% of the world's population suffers from some sort of language-induced mass-delusion is a serious concern. This is why I continue to bring up religious propositions as examples of the nonsensical.

doctor(logic)