Name: Lec 1 | 麻省理工學院 6.042J 計算機科學數學，2010年秋季。 (Lec 1 | MIT 6.042J Mathematics for Computer Science, Fall 2010)
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PROFESSOR: Who can tell
me what a proof is?

AUDIENCE: It's a chain of
statements, each logically

That's very close to what
we're going to do here, yeah.

Now, that's a special
kind of proof, though.

That's correct, what
you said, but there's

a higher meta level notion of
what a proof is beyond that.

It may have no logical
deductions potentially.

Now, by ascertaining, I mean
establishing truth, verifying

And there's lots of
ways to ascertain truth

AUDIENCE: Observations, like
seeing that piece of chalk

I mean, who really knows if
there's gravity out there?

And so we then conclude
that's the truth.

There's gravity, and
we have laws about it.

across scientific disciplines,
or beyond science, just

AUDIENCE: Well,
establishing what's false,

Then that helps you
narrow down what is true.

PROFESSOR: Yes, truth--
yeah, that's great.

How you decide something is
not true in every day-- yeah?

PROFESSOR: Find counterexamples,
yeah, that's good.

So in fact, even a step
more general, sampling.

If you do something, an
experiment, ten times,

and every time, it comes out
one way, that's truth, maybe.

But there's fields where
that becomes truth.

How are we going to
decide if Roger Clemens is

guilty of perjury for lying
about steroids to Congress?

How is that truth going
to be ascertained?

AUDIENCE: Would it be by
examining the evidence

Truth is established
by juries or judges.

his name, the Illinois governor,
Blagojevick-- he's guilty.

but of lying to the authorities
about campaign financing.

but of breaking into an
apartment to steal back

So judges and juries
make decisions on truth.

What are other truths-- bigger
truths, even, than judges

There's one really big one
that causes a lot of issues.

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Lec 1 | 麻省理工學院 6.042J 計算機科學數學，2010年秋季。 (Lec 1 | MIT 6.042J Mathematics for Computer Science, Fall 2010)

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