On Logic

Observation and Abstraction

Logic

Consider these statements:

“All swans are white”.

“Of all the swans I’ve observed, all swans are white”.

The latter statement is a fact. The former statement is a generalisation of that fact; a “theory”.

We can “falsify” the theory, by demonstrating that there are swans that are not white; black swans, for example.

But what about facts? Can we falsify facts?

Observation

Suppose only white swans live in my country, and only black swans live in your country. And suppose we meet in a country with no swans.

For you, “Of all the swans I’ve observed, all swans are black” would be correct. And you would, reasonably, believe in the theory “All swans are black”.

If I were unable to understand your “perspective”, or that your country was a “black swan” country (and vice versa), we would never be able to agree. You would insist that swans are black; and I, white.

But there are even deeper problems.

Abstraction

Suppose the swans in your country were precisely the same as the swans in my country. And they were neither black nor white, but some shade of grey.

The swans in your country live in sunny woods surrounded by bushes with bright white flowers. The swans in my country live in dark ebony forests with tall trees with the darkest barks.

Hence, because of their white background, the grey swans in your country appear black. And similarly, the grey swans in my country appear white.

Now despite the swans being identical, we disagree on two abstractions: “Whiteness” and “Blackness”. Your “blackness” is the same shade as my “whiteness”. But we can’t agree that they are the same thing.

The Problem

Logic depends on set theory.

Set theory, in turn, depends on two things:

1. Our ability to observe. To assign something to a “white swan” set, we need to see a “thing” which exhibits both “swan-ness” and “whiteness”.
2. Our ability to assign things to sets, through abstractions. For example, to assign a swan to the “white swan” set, we need to define “swan-ness” and “whiteness”.

Unfortunately, we have a flawed ability for both abstraction and observation. As long as these flaws exist, our the ability to reason with logic is also imperfect.

We might think we are logical. But we are not.

Simultaneous Contrast Illusion. The background is a color gradient and progresses from dark grey to light grey. The horizontal bar appears to progress from light grey to dark grey, but is in fact just one colour (Source: Wikipedia)