Unseen

Strega wrote:
Genghis Khan unified all the Mongolian tribes with his brutality.

The British created the modern state of India out of a gaggle of minor local kingdoms with theirs. And the modern state of Germany wouldn’t have the national treasure of Schloss Neuschwannstein without the brutality of The Mad King Ludwig of Bavaria, either.

Strange…[Read more]

Here’s another weird number from mathematics. It’s called “i” (the letter between h and j in the standard alphabet). I wasn’t absolutely sure mathematicians consider it a number, so I asked the Gemini AI “is i considered to be a number in mathematics?” and got this reply:

Yes, i is considered a number in mathematics.

While it might seem unusual…[Read more]

Strega wrote:
For me, numbers and letters all carry specific colours, shades and textures. Z is dark blue and velvety. No idea why, but it is.

If I give you the number Pi, what color comes to mind?

Simon Paynton wrote:
It looks hard. Does it have any practical applications?

I seem to remember something related to the Riemann hypothesis.

Reg the Fronkey Farmer wrote:
@unseen – The Law of Forms is a very interesting idea. I had never heard of it before. It is like applying an “Occam’s Razor” to algebra.

Many years ago, when I was in college, I was obsessed with logic, so I studied Russel, Carnap, the early Wittgenstein, and others. However, when I stumbled onto Laws of Form, i…[Read more]

_Robert_ wrote:
Not much programming you can’t do using only AND, OR, NOT, IF (x) THEN (y) logical. statements

Yeah, there are many ways of writing functionally identical logical forms.

BTW, you might be interested in G. Spencer Brown’s logical calculus as presented in his classic book, Laws of Form. His logic is notable for not having four b…[Read more]

_Robert_ wrote:
Actually, even the logical construction of the premise is incorrect because of the use of ‘OR’. This implies that a migrant can’t be a mental patient AND a criminal AND a rapist. This first statement needs to be proven true before any rational inferences may be made about it.

“Or” is the oddball logical operator because it comes…[Read more]

Simon Paynton wrote:

Unseen wrote:
True premises used in an argument with a valid form must imply a true conclusion.

This is what I’m saying. Sometimes the premises given aren’t true, but a logically-formed argument can be made out of them. E.g. Donald Trump – “All migrants are rapists, criminals or mental patients.” “X is a migrant.” C…

[Read more]

@ Simon

No. True premises used in an argument with a valid form must imply a true conclusion. If it doesn’t, there is a disturbance in the force.

If you disagree, provide an example.

Simon Paynton wrote:
I think reason is the problem half the time.  There is something in propositional logic, that states that a set of propositions can have internal validity – they are logical – they follow reason – without being true overall.

C.S. Peirce brilliantly realized that people don’t reason with propositional deduction or even with i…[Read more]