Antenna Guru

RF is not 'black magic' – It's Synthesis, Optimization, Analysis and Realization.

Tag Archives: Critical thinking

Gödel

Kurt Gödel (Wikipedia)

It’s easier to disregard someone when you leave them out. It’s easier to disregard ideas when we don’t think about them. We sometimes do this when faced with inconsistency don’t we?

Haven’t we learned that consistency is absolutely necessary in order to be logical?

To be logical is to be reasonable… Isn’t it therefore unreasonable to be inconsistent?

Although I am not a professional mathematician, I use mathematical concepts daily. Most of us think that mathematics is the epitome of logical thinking. Most of us would think that arithmetic –the “oldest and most elementary” kind of mathematics there is– has to be self-consistent, but this only turns out to be true so long as you assume arithmetic is self-consistent but don’t try to prove its self-consistency using arithmetical statements.

Officially,

[In] any consistent effective formal system that includes enough of the theory of the natural numbers …there are true statements expressible in its language that are unprovable.

Gödel’s first incompleteness theorem

But hang on a second, this is a theorem saying it is mathematically true that there are mathematically true statements that cannot be proven (or disproven) true mathematically!

Doesn’t that wreck mathematics?

Crying in the Wilderness

So they said to him, “Who are you? We need an answer! What do you have to say for yourself?”

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