The Truth

What is the truth?

Alfred Whitehead was a logician and philosopher, who had a student of some note. The student was Bertrand Russell and together they wrote the famous three-volume Principia Mathematica. It took several hundred pages to get to the result that .

Amazing.

Today I thought that discussing truth might be an interesting topic.

Whitehead said:

There are no whole truths; all truths are half-truths. It is trying to treat them as whole truths that plays the devil.

I like this quote. Whitehead was not the best lecturer, however. He gave the prestigious Gifford lectures a year after the astronomer Arthur Eddington. As Wikipedia relates quoting Victor Lowe:

Eddington was a marvellous popular lecturer who had enthralled an audience of 600 for his entire course. The same audience turned up to Whitehead’s first lecture but it was completely unintelligible, not merely to the world at large but to the elect. My father remarked to me afterwards that if he had not known Whitehead well he would have suspected that it was an imposter making it up as he went along … The audience at subsequent lectures was only about half a dozen in all.

Between the pandemic and the unrest in our cities there is debate about what is the “truth”. On cable news—CNN, MSNBC, FOX—one hears statements about the truth. You can also hear statements like “the experts know” or the “model” shows that this is true. Can math shed light on these discussions? What would Whitehead say?

What is the Truth?

Mathematical truth is the one absolute we can count on—right? Math is precise in its own way, but does it yield truth? Not so clear.

Whitehead’s proof that takes 100’s of pages; it may or may not increase your confidence. Here is a short “proof” that :

Math proofs are only as safe as two elements that are unavoidably social:

1. The care we use in applying our reasoning; and

2. The care we use in choosing our assumptions.

In the above proof snippet, one step divided by which is the source of the error that . A more worrisome issue is reasoning from assumptions. Wrong assumptions are a problem.

Who are the Experts?

One definition of expert is: An expert is somebody who has a broad and deep competence in terms of knowledge, skill and experience through practice and education in a particular field.

More amusing definitions are:

Mark Twain defined an expert as “an ordinary fellow from another town.” Will Rogers described an expert as “A man fifty miles from home with a briefcase.” Danish scientist and Nobel laureate Niels Bohr defined an expert as “A person that has made every possible mistake within his or her field.”

I find the use of the term expert in regard to the pandemic at best puzzling. How can anyone be an expert when the current situation is unique? The last pandemic happened over a hundred years ago. Unfortunately Twain, Rogers, and Bohr are closer to being correct. The situation we find ourselves in today does not lend itself to being an expert. At least in my non-expert opinion.

Yes there are people, for example, who are experts on various viral agents. But there is more we do not know about this agent that we do know.

• Can you get the virus twice?

• Can children get the virus?

• Will a vaccine be possible?

• Are there long-term affects even for those who survive?

• And so on

Where are the Models?

Models are created by experts, so you probably guess that I am not bullish on models. There are lots of models, for example, on the projection of how many will be infected, and how many will get seriously sick, and sadly how many will succumb. These models are based on various assumptions about how the virus works. Most of these assumptions are not proved in any sense.

Open Problems

I plan on saying more about truth in the future. Take care.