On 11 Feb 2014, at 04:27, LizR wrote:
On 10 February 2014 01:49, Bruno Marchal <[email protected]> wrote:
So with "->" and "f" we can define all connectors.
Is there a connector (like "&", "V", "->", ...) such that all
connectors can be defined from it?
You just said that ... oh do you mean without using 'f' ?
This is a facultative exercise. Only for possible raining sundays.
We will not use this in the sequel.
OK. I don't know. It doesn't seem intuitively obvious, but if you
can use ~ then we have already used & and (I think) V that way... I
think.
Well, even though I did it, the result still looks rather strange
to me!
Cantor said "I see but don't believe it". it is normal. von Neuman
said "nobody understand math", mathematicians get only used to it.
I seem to be in good company. They laughed at Archimedes. The
laughed at Einstein. The laughed at Bozo the clown...
Understanding is good.
Understanding and memorizing, even with the help of a well
presented diary, is better, as it saves the future possible works.
I agree. I'm sure I started one, too, but I can't find it now. (So
sometimes I have to treat you as my diary...)
Well, I hope you will not lost me too!
Likewise.
Gosh!
Well, I lost myself myself, if I can say, and that as many times as
they are numbers ...
Memorizing is good, but only if you manage to keep the memory
accessible. 'course.
Yes....
OK.
I hope you will not forget that.
Some would disagree...
I guess that they met the bad math teacher who kicks the student
before math kick them, making it impossible for them to understand
the real kicking back of math, and develop the appreciation.
That's bad for the slow student, which sometimes are slow because
they are more demanding in understanding, and it is good for the
quick student, who can learn to solve problem by no more than
pattern matching, without any understanding. Consumerist societies
favour quick students, which aggravate the situation for slow
students, and long term project.
As a math teacher, I try to help the two kinds of student, but it is
not always easy, and to be honest, I favor the slow one.
For me, a valid reasoning with a false answer is better than a false
reasoning with a correct answer. I know that in real life, the
contrary is true.
Wise words.
Some others seems interested in the thread too, but might be less
courageous for participating, as you need some courage to do a sort
of persistent "exam" online. I can understand. But I know that if I
explain everything ex-cathedra, everyone will be lost somewhere,
and nobody will know where. I do hope some others will participate
to make things lighter on your shoulders.
It takes a bit of courage for me, certainly. Especially since it's
all stuff that seems to melt away, even though I understood it at
the time. But then I *can* switch back and understand it again. But
I find popularised physics and biology easier to follow than
popularised logic, even though we have most of Raymond Smullyan's
books.
Physics, biology, natural science are aristotelian, and use the
natural intuitive (1p) conception of reality. Logicians and Classical
logicians, well, first they insist not doing physics, nor philosophy,
but mathematics, and this (most of the time unconsciously) makes them,
with comp, exploring the highly counter-intuitive mindscape of the
universal machine.
Logicians like the counter-intuitive surprises, and they delight in
invalidating prejudices.
Smullyan's brother, if I remember well, told to the little Raymond
--'tonight, I will surprise you, I promise!'
Little Raymond waited all the night, but got nothing, so at morning he
complained to his brother "I thought you would surprise me!".
The brother replied: "If you thought that, are you not surprised by
the fact that nothing happened". "You got me!", Smullyan said, and he
was very pleased, and surprised.
Bruno
Thank god he is still alive! I had to go and check - last time I
checked on someone, he'd died. It was John Galbraith Graham, my hero
of the crossword world. I never knew him .... yet I did in a way,
just like Mr Smullyan and Ursula le Guin.
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