Like many Daily Post readers, I occasionally get tired of reading (or hearing… or watching…) the news. In my case, it usually happens around 7:30am each morning.
That leaves me plenty of time for reading other things that are not news, and might even have some authentic connection to reality.
Lately, I’ve been amusing myself with a book many of you are no doubt familiar with. It’s a book left over from my short stint in college: Introduction to Logic and to the Methodology of Deductive Sciences by Alfred Tarski. (The fact, that I am just now reading it for the first time, helps explain why my stint in college was so short.)
Tarski’s treatise was first published in 1936 in Polish, as O logice matemattycznej i methodzie dedukcyjnaj. The author intended it to be a friendly scientific introduction of modern logic, and especially, mathematical logic, for the ordinary (but perhaps somewhat educated) layman. This was back in the day when things still seemed logical. But why Tarski would choose to write a book, intended to be popular, in Polish, we will probably never know.
One section of his book that piqued my interest came on page 61, when the author presented a rather simple mathematical theorem:
if x = y and x > z, then y > z.
The truth of this statement seems evident, if you still remember your high school algebra. If a numerical value x is equal to a numerical value y, and if the number x has a value greater than another number, z, then the number y also has a value greater than the number z.
Tarski calls this type of logical statement an example of “sentential calculus” and he’s careful to note that a sentence can follow the rules of sentential calculus, but still be false. Here’s an example of a properly formulated, but false, sentence:
if x = y, then x > y.
Logic, it seems, is pretty straightforward, as long as we remain in the realm of mathematics. Considerable complexity enters the picture, however, if we try to apply the same kind of sentential calculus to non-mathematical elements. Tarski explains that the rules of logic can be applied — not merely to numbers — but also to tangible objects. But things can get messy. For example:
if men = women and men > mice, then women > mice.
To put that in plain English, if men and women are equal, and men are greater than mice, then women are greater than mice.
We all know that men and women are equal, except that (here in the U.S.) employed women earn an average of about 80 percent of what employed men earn — and a few other minor differences, like the ability to dunk a basketball or knit a sweater.
But what does it mean, if a man or woman is ‘greater than’ a mouse? We don’t really have a logical way to assess such a comparison. While we know that the man or woman might be capable of writing a book like Introduction to Logic and to the Methodology of Deductive Sciences, a mouse is capable of things that no man or woman can do, like slip through a tiny hole in the kitchen baseboard and make annoying noises inside the wall while you’re trying to sleep. Late at night, we may not be able to determine which capacity is more consequential.
Things get even more complicated if we try to apply logic to politics. Complicated… maybe even dangerous.
For example:
Certain well-meaning people have recently taken to wearing red hats emblazoned with the phrase “Make America Great Again”. In a logical world, the word, “great” has a certain meaning, similar to the word “good” or “wonderful” — except that the word “great” implies “superiority.”
Two people can both be “good” people. In which case, we can illustrate the relationship mathematically.
Person A = Person B
But if one person is “great”, it suggests that the other person is “not so great.” We have a mathematical inequality implied by the use of the word, “great.”
Person A > Person B
When an entire country is “great”, then, for comparison purposes, we logically need to have a country that is “not so great”. For example:
America > China
Which, logically, brings us to a news report from last summer (on a day when I wasn’t yet feeling tired of reading the news) when the U.S. Trade Representative’s Office revealed a list of $200 billion worth of Chinese imports that would be to subject to 10 percent tariffs – including “hats and headgear”.
For Zhenjiang Kimtex Industrial Company in eastern China’s Jiangsu province, the U.S. accounts for 40 per cent of its sales, about $445,000 a year. While it manufactures mostly winter hats and scarves, in 2016 it also produced hundreds of the “Make America Great Again” baseball hats.
George Jing, a manager at the company, said he was keeping a close eye on the developing dispute. “If the tariffs are placed on our importers in August, then their costs will rise, and the prices of our products will go up.” Sounds logical.
U.S. news outlets reported that sellers of the “Make America Great Again” caps were stockpiling them, while they waited for a decision on the tariffs. David Lassoff, manager of the California-based IncredibleGifts, told ABC News that if he was forced to switch to an American supplier because of the tariffs on Chinese imports, he would have to raise the retail price of the caps he sells to at least $20 – up from the current price of $9.
Which leaves us with one final, logical sentence.
$20 > $9.