St. Patrick's Day Note a Month Late

 

Consider the following axiomatic system:

1. Leprechauns exist.

2. Leprechauns are non-human humanoids all of whom are three feet tall or less.

3. Leprechauns occur only in Ireland.

4. Leprechauns’ clothing and possessions consist only of things producible by the technology of the late Middle Ages.

5..Some leprechauns have hair and beards.

These axioms seem consistent. Their consistency is as nearly obvious as that of axioms in some other well known systems.

One can use these axioms to prove meaningful theorems such as

1. Every humanoid over five feet tall is not a leprechaun.

2. Leprechauns do not have cell phones.

3. The clothing of leprechauns is made from natural materials.

One can elaborate the system by adding another axiom such as

“6. A red unicorn lives in the same part of Ireland as the leprechauns do”,

and argue that both it and its denial likely are consistent with the first five. This axiom would be useful in proving theorems not provable by the first five alone.

Of course the system and its conclusions are false and have nothing to do with reality. There are not any leprechauns. One can create a very similar system by replacing the original axiom 1 with “Leprechauns are fictitious creatures of stories and legends.” The new system would be demonstrably consistent and also true, since one easily could display a storybook containing leprechauns satisfying all five axioms.

This fairly silly example illustrates the fact that in considering systems of axioms, one has to look at each axiom and decide whether it is really axiomatic, that is .whether it should be accepted as true about something. One cannot escape from the need to consider meaning. The same thing holds in cases that are not silly.

Trump's Tariffs

 

People have known all along that Trump’s ideas on trade were bad. Now we are getting to see how bad. His tariffs will create more price inflation for Americans, annoy America’s allies (and perhaps alienate some of them), damage American exporters, harm innocent people around the world dependent on trade for their livelihoods, and probably cause a recession and a bad stock market. Other than that, they are just a massive tax increase on Americans delivered by the party that claims to believe in keeping taxes low. (His people are claiming between six hundred and eight hundred billion dollars a year, none paid by the man behind the tree.) I hope his sycophants are right in claiming that they are a ploy to get other nations to cut their tariffs, but I doubt it. Besides being deeply economically ignorant, I think he and his supporters are also motivated in this by a general crude nativism that shows up in some of their other policies and desires. If this goes on, we all may be paying a big price for showing them durn furriners who the big dog is.

There is a useful aspect to all this though. With Republican politicians suddenly turning back flips over a tax increase, it can be a useful lesson to people on just how phony and unprincipled these public servants are.

There is an exception. Nations should not engage in free trade with a hostile foreign power, and particularly should not have a hostile foreign power as a source of any important products. The only hostile foreign power with whom there is much trade is China. It would have made sense for Trump to act to restrict that trade, but that trade alone.