Idea: Truth Projection
Let us start wth an example:
- You have 2 apples and 3 pears
- Someone asks you "How many apples do you have?"
- You are only allowed to give a number in your answer.
- What will you respond?
My answer here would be "3 apples"
I think. Why?
Let us first agree on some things. If
the rule in 3 wasn't there, you'd say "I have only 2 apples, but
I do have 3 pears also". Perhaps someone is hungry, baking an
apple cake, making apple juice or something else. Here it would be
interesting to know about the pears.
The other thing we should easily agree
on is that some answers are plain wrong: If you answer "1"
or "0" that is (for all possible intents) wrong. If you
answer "6 apples", "7 apples", or more, that is
also wrong (for all possible intents of the question).
So why "3 apples"? I can
picture a range of different scenarios (intents of the question). If
the person asking only could eat apples and was hungry (think Death
Note), then you would be slightly wrong. The same goes if the one
posing the question was in the store and could easily have bought 1
more apple.
What if the one who asked wanted to
make apple juice, and he thinks that pears are good too. Well, then 2
apples and 3 pears would make a lot more apple/pear juice than would
2 apples (150% more). On the other hand, 2 apples and 3 pears would
make a bit more juice than 3 apples (67%).
In day-to-day life, this doesn't happen
with apples and pears, as it is simple to give all the information.
But you can never give all possible information, so we try to say
what's relevant, and to not say stuff we think is irrelevant
This phenomenon appears clearly in the teaching of mathematics and physics.
Mathematics example: We normally teach
that all (positive) functions can be integrated. Some teachers tell
the students that there are some (positive) functions that cannot be
integrated, but you would never teach what kind of functions these
are, so in essence you say "Any function you will ever encounter
is integrable". Then when you study some more you learn that
there are lots of functions that cannot be integrated. Then you learn
that these can actually be integrated, we just have to expand our
method of integration a bit. Then you learn that even with this new
kind of integration there are some super-strange functions that
cannot be integrated.
Physics example: When you learn about
electrons on a small scale (quantum mechanics), you learn that they
work the way waves on the water works. You can have one big "up"
wave meeting a big "down" wards wave, and cancel out. When
a wave hits a small opening, it expands out after this opening. But
electrons do not work as waves on the ocean; they can be collapsed,
they have more directions than just "up" and "down"
(they have a kind of imaginary "left" and "right"
also).
Often the whole point of being pedagogical is to be able to give the best possible Projection of what
you considers to be True, down onto the 'plane' of the listeners
understanding.
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