Challenging the Boundaries

How many of us just accept what we are told, or read? Like myself, I guess most of us most of the time. When I was about seven my father told me one of the wisest things I have ever heard from anyone, it was 'never trust what you read in the newspapers.'

Which leads to the general question, how do we know what is true and what is false? Clearly direct knowledge is the only guarantee. But the world is too large to research every fact or piece of evidence that affects our lives. We have to make value judgements based on trusted sources of information.

Common experience has taught us that certain things are incontrovertible, we call these axioms. Mostly these are formulated as propositions, if a=6 then 6=a. Or a straight line is the shortest distance between two points. Or if a>b and b>c, then a>c.

That last one looks similar to deductive logic, also called common reasoning, in that three entities are compared. Consider
All Welsh people eat steak. John eats Steak. Therefore, John is Welsh.

The argument is valid as a weak deduction from the first two statements. However, it is false because the first statement is false, not all Welsh people eat steak. The argument is weak because others than the Welsh also eat steak, ie John might be Scottish. Series of deductive reasoning can be used to trick some people who are too lazy, trusting or whatever, to check the accuracy of individual statements.

We are too used to accepting certain axioms or statements as true. To challenge accepted facts requires imagination, creativity and a certain amount of stubbornness. Einstein’s General Theory of Relativity required decades to be verified by scientific experiment. But in the mean time, a whole branch of mathematics has arisen dealing with the theories of curved space, whereby the shortest distance between two lines is curved.

I am not sure it is possible to teach creativity, but it is possible to encourage thinking. Let us challenge the axiom a>b and b>c, so that c>a !!
How would that look?
It would have to be some kind of circular argument.
If I were to raise my eyes above this monitor screen, I could see the perfect example.

A graduated progression whereby the end circles into the beginning, but the beginning is greater than the end.
It’s a clock! Three O'clock is greater than Two, but One is greater than Twelve.

That was not intended as a riddle, rather an illustration of how we can think about common things in different ways. I leave it to the reader to examine the proposition for flaws :-)