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 ${1+1=2}$.

Amazing.

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

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 ${1+1=2}$ takes 100’s of pages; it may or may not increase your confidence. Here is a short “proof” that ${2=1}$:

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 ${0}$ which is the source of the error that ${2=1}$. 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 ${\dots}$

## 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. This is the 900th post on this blog; it like everything else is a continuing story.

1. June 4, 2020 11:30 am

Just a random forkful of thoughts from a pragmatic peircepective …

Pragmatic Theory Of Truth

June 4, 2020 2:18 pm

Dear Jon:

Thanks for the pointer. I will take a look. Thanks for this.

Best and be safe

Dick

June 4, 2020 12:30 pm

I’m also eager to read your next post on the matter of truth. 🙂
All the best, Jacob.

3. June 4, 2020 9:41 pm

This is a super fascinating post. One of the strange qualities of mathematical truth is that it can’t be “falsified” in the Popperian sense of the word.

June 5, 2020 12:37 am

This is an interesting post, but I do not agree with the conclusion. The current corona virus comes from a well-studied family of viruses, and there are people who spent their entire career studying this family of viruses. Surely their opinion carries more weight than the opinion of a layman.

There are also two inaccuracies in the post. First, many children were diagnosed with the virus, so the question whether they can get it is not open at all. Second, the last pandemic was not 100 years ago. Even if one ignore the recent Swine flu pandemic that was less lethal than the average seasonal flu, the last pandemic was the Hong Kong flu in 1968 which was estimated to kill one to four million people world wide.

June 5, 2020 7:45 am

Dear Moran:

Thanks for the comment. Here is a pointer to that flu. I do agree that I am just a layman. But I do still wonder how much the expertise from the past extends to the current. Its like the story about the one-sided cows.

Best and stay safe.

Dick

• June 6, 2020 5:18 am

It is also a question of what exactly is the expertise of someone. To take a policy-decision or a decision for your own individual safety or the safety of your family, you do not necessarily have to be an expert in coronaviruses or in aerosol transmission. If your goal is to minimize risk, you can get away with a very coarse understanding and focus on worst case. We are all absolute experts in survival, as per our evolutionary past.

5. June 5, 2020 7:26 am

Thanks for this post! In times like these, it feels good to read such unbiased thoughts.

June 5, 2020 7:47 am

Dear gentzen:

Thanks for your support. I think that we must even in these tough times stay unbiased.

Best and stay safe

Dick

6. June 5, 2020 11:37 am

I would enjoy getting feedback on this piece on platonism and pluralism in mathematics (and in society): http://tuvalu.santafe.edu/~moore/Feature.Moore.Kaag.pdf

• June 6, 2020 7:00 am

The “irritation of doubt”, a state of uncertainty or surprise, marks the beginning of inquiry according to pragmatic thinkers like Peirce and Dewey, so it’s critical to acknowledge and value such states when they occur.

According to John Dewey, it is because of the human quest for perfect certainty that philosophy has inherited three problematic viewpoints:

“the first, that certainty, security, can be found only in the fixed and unchanging;
the second, that knowledge is the only road to that which is intrinsically stable and certain;
the third, that practical activity is an inferior sort of thing, necessary simply because of man’s animal nature and the necessity for winning subsistence from the environment.”

— John Dewey • The Quest for Certainty

June 6, 2020 7:22 am

“Mathematical truth is the one absolute we can count on—right?”

Well, if one could define the notion of truth in mathematics, then this would be very helpful. However, there is a big problem with defining this notion, and Tarski’s Theorem on undefinability of truth in (Peano) Arithmetic System, says just about it.

September 2, 2020 7:24 am

Reblogged this on Pink Iguana.

September 5, 2020 10:56 pm

Dear Wisty:

Thanks for doing this. WE now link to JSS there.

Best

Dick