Completion

Here are some examples of complete propositions.

Scientific propositions are the easiest:

The mass of the proton at rest is 0.938 +/- 0.001 GeV.

Two objects with different masses will accelerate at the same rate in a uniform gravitational field in which external forces are negligible. Link

In these scientific examples, an experimentalist knows enough to devise an experiment that will falsify the proposition.

Let's move on to less scientific propositions.

I paid my taxes for fiscal year 2003.

Volkswagen makes the cheapest car in each category of automobile, with categories defined as groups of vehicles with comparable performance and luxury appointments.

I think that tartar sauce smells repellent.

In each case, we can test the proposition and potentially prove it false. The last proposition is the most difficult to argue as complete, but I think that there are very few people who could lie on this subject and still evade all of the potential falsification tests. To the extent that it is an empirical proposition about personal feelings, it may not need to be falsifiable. I'll discuss this more below.

The following natural language statements are incomplete, but are completable (--> indicates completion):

Unemployment is bad. --> Unemployment in contemporary American society is bad for economic growth, tends to increase crime and depresses morale.

Tartar sauce smells repellent. --> I think that tartar sauce smells repellent.

There is no bread at the supermarket. --> There were no salable packages of bread in edible condition on the bread shelves at the supermarket when I was there 15 minutes ago.

Again, an incomplete statement is completable if we can agree that it is equivalent to a complete statement.

Let's now look at statements that are generally intended as non-completable:

God exists.

God is good.

God created the universe.

Killing is absolutely wrong.

Each of these statements suffers from the problem that the person who speaks these things generally does not intend them to be equivalent to falsifiable propositions.

For example, most people would not be willing to translate "God is good" as "I think of my wife is a goddess, and she makes me feel good," or translate "God exists" as "There is an extraterrestrial life form that possesses technology vastly superior to our own."

Most statements that are "incomplete by intention" are the result of confusion. For example, they may be attempts to explain the unknown ("the universe") in terms of the more unknown ("god").

Empirical facts are not themselves falsifiable. If my photodetector records two events between 1pm and 2pm, this is an empirical fact: "Photodetector #12 detected two events between 00:13:00 GMT and 00:14:00 GMT with the time measured by clock #27". Note that this does not necessarily mean that there were no other photons passing through detector #12 during that same time period. Other detectors may see the events differently. Sometimes, you only have one detector, and it may give you an inaccurate result.

The scientific view of the universe as a machine that follows physical laws is perfectly consistent with imperfect measurement.

We humans are also detectors. If you see something that no one else could have seen, that empirical fact may not be falsifiable. However, this does not mean that your measurements correctly reflect physical events. You may have imagined the events. Furthermore, humans are more than just detectors. Humans are theorizers as well as detectors. To make a measurement directly, a human must fit the observation into his or her neural model of reality. This means we may express a measurement in terms that are not reliable or consistent. We are also gamers, so we can lie about what we observe (consciously or subconsciously).

Empirical propositions are readouts from scientific equipment, or expressions of sense observations by humans:

I saw a large bird of prey soaring over my home town this afternoon.

The electrical potential across the terminals of this battery reads 5.25 volts.

Due to known flaws in human perception, we must rely on methods that minimize these flaws. Double-blind experiments are one such method.

doctor(logic)