-
Critical Reasoning for beginners
by Marianne Talbot Oxford
Lesson
1
How
to
recognize
arguments
and
What
is
the
nature of arguments
Arguments are a set of
sentences such that one of them (the conclusion)
is being said to be
true, and the
other(s) (the premises) are being offered as
reasons for believing the truth of the
one.
An argument
isn't a set of contradictions.
Part
of
the
point
of
an
argument
is
to
move
us
on
from
where
we
are
to
somewhere
a
bit
further.
Arguments lead to deeper
thoughts. (from where we are to where we want)
An Argument:
(one or more) Premises
Conclusion
(Function)
[to prove---
reasons]
[suppose true]
relationship among sentences
e.g. It's Friday.
Marianne always wears jeans on Friday.
Therefore Marianne will wear jeans
today.
Play attention to
suppressed premises
（隐藏前提）
.
context
——
all
sentences may be argument.
implication
（实质蕴涵）
entailment
（逻辑蕴涵）
Distinguish arguments from
(a) sets of sentences not related as
arguments
(1) aren't related at all
e.g. The sea is salt.
Sydney is in
Australia.
(2) related but not an
argument
e.g. Towards lunchtime clouds formed
and the sky blackened. Then the storm broke.
(b) sentences (assertions)
'if...then...'
e.g.
If it is
snowing, the mail will be late.
(implication
not entailment)
An
argument
is a set of
sentences, one of which is being asserted.
An
assertion
is a
single sentence (possibly complex) ,that is being
expressed in assertive mode.
'because' may be causal or rational.
reason and
cause
causal
relations
（因果关系）
and rational
relations
（推理关系）
A
and B entail C doesn't mean A and B cause C.
e.g. It's Friday. (A)
Marianne always
wears jeans on Friday. (B)
Therefore Marianne will
wear jeans today. (C)
explanation:
(1) causal
explanation
（因果性解释）
:
e.g. Pawl fell down because he wanted
to amuse children.
(2) rational
explanation
（推理性解释）
:
e.g. Pawl fell down because Jelly
pushed him.
Facts
are what makes
sentences true or false. They are not
true or false, they just exist or
don't exist.
Only
beliefs
or
sentences that
express beliefs
are true or false.
Belief
(e.g. concept)..............the concept
'chair'
Language.......................
...........the language 'c-h-a-i-r'
Rea
lity.......................................the
object 'chair'
Arguments
can only be
good or bad
,they can only be
valid or invalid
,they can't be true or
false
because the only thing that can be true or false
is beliefs or the sentences that express
beliefs.
A good argument
is one in which:
(1)the conclusion must follow the
premises
(2)
the
premises must all be true
.
The conclusion must be true. (truth
preserving)
逻辑学并不关心前提正确与否，而只关心前提与结论的关系。
Lesson 2
Different sorts of
arguments
two basic types
of arguments: deduction and induction
Deductive argument :
the
truth of their premises guarantees the truth of
their conclusion.
e.g. It's Friday.
Marianne always wears jeans on Friday.
Therefore Marianne will wear jeans
today.
If the premises are
true, the conclusion would be true.
'truth guaranteeing'
'truth preserving'
Deduction is an 'either or' thing:
a good deductive argument
gives us conditional certainty.
a bad
one tells us nothing.
Inductive arguments are such that the
truth of their premises makes the conclusion more
or
less probable. (don't guarantee)
Inductive arguments can be either weak
or strong.
[strong]:The sun has risen
every day in the history of the universe.
Therefore the sun will rise
tomorrow.
[weak]:Every time I met Mary, she wore
a necklace.
Therefore the next time I
meet her, she will wear a necklace.
逻辑学是中立性的，逻辑的形式可以适用于任何的内容。
Logicians study deduction by studying
valid arguments forms
Arguments that
are valid is in virtue of their forms as opposed
to their contents.
the
forms of deduction:
1
、
Modus
Ponens
肯定前件取拒式
If
P then Q, P, therefore Q.
(P
,Q sentences)
wrong: If P then Q, Q, therefore
P
.
(Affirming
consequent
肯定后件式
)
2
、
Modus
tollens
否定后件式
If P
then Q, not-Q, therefore not-P
.
3
、
Disjunctive
syllogism
选言三段论
P
or Q, not-P
, therefore Q.
（<
/p>
P
或
Q
成立，<
/p>
P
不成立，因此
Q
成立）
4
、
Leibniz's Law
莱布尼兹律（相同者不可辨识）
a
is F, a=b, therefore b is F.
e.g. Jane is(predication) tall.
Jane is(identity) the bank manager.
Therefore the bank manager
is(predication) tall.
Note:
'is' can serve as a
predication
（论断）
or identity
（同等）
.
The 'is's above serve as predications.
And the '=' above serves as identity.
5
、
Syl
logism
三段论
all Fs
are G.
a is an F.
Therefore
a is a G.
6
、
Deontic
Logic
道义逻辑
e.g.
Lying is wrong.
Therefore we shouldn't
lie.
7
、
Modal
Logic
模态逻辑
（
a logic about necessity and
possibility)
e.g. It is necessarily the
case that there are no square circles.
Therefore it is not possible that there
are square circles.
8
、
Temporal
Logic
时序逻辑（时态逻辑）
e.g. It is raining today.
Therefore tomorrow it will have been
raining yesterday.
Inductive arguments
All
inductive arguments rely on the assumption of
the uniformity of nature
(the idea that the
future will be like
the past)
哲学中的一个基本问题是，
我们对未来的
假设，
会不会和过去的经验相一致？
Uniformity
一致性
，
uniformity of nature (David
Hume)
自然界是否具有一致性？
Within the category of
inductive arguments
there
are many different sub-types:
1
、
arguments from
analogy
类比推理
a is
like b, a is F, therefore b is F.
（小写字母：
particular
thing
特定的事物
大写字母：性质或句子）
2
、
arguments from
authority
诉诸权威的论证
e.g. Einstein is a brilliant physicist.
Einstein says relativism is true.
Therefore relativism is true.
Causal
arguments
因果论证
Causal arguments can be
deductive
or
inductive
, depending on
whether we are arguing
from a
causal claim
or
to a causal claim.
deductive: As cause Bs.
There was an A.
Therefore
there will have been a B.
inductive: Every observed A has been
followed by a B.
Therefore As cause Bs.
negative
existential
否定存在判断句
e.g.
飞马不存在。
We can know that
arguments that are deductively valid
——
in virtue of their forms
——
in virtue of their content
e.g.
Deontic
Logic ,Temporal Logic
arguments that
are inductively valid
——
the
uniformity of nature
Lesson
3
'logic-book-
style'
逻辑书
the point:
(a)it
enables us to add suppressed
premises
隐含前提
(b)it enables us to eliminate cross
references, irrelevancies and inconsistent terms
排除交叉引
用、无关和不一致词语
(c)it makes it easier to evaluate
arguments.
A set of steps
for analyzing arguments:
1. identify
the conclusion of the argument
Look for the argument indicators (so,
therefore, then, if...then..., accordingly, hence,
since,
for, because, from which we see
that, it follows that, which establishes that...)
2. identify each of the premises
3. add suppressed premises
4. remove irrelevancies
5.
remove inconsistent terms
6. remove
cross-references
Example 1:
Socialism did not provide
the incentives need for a prosperous economy.
Therefore socialism
was doomed to
failure.
Premise 1:
Incentives are needed for a prosperous economy.
Premise 2: Socialism did not provide
incentives.
Conclusion: Socialism was
doomed to failure.
Premises
and conclusion must be sentences.
P
, unless Q.
If
Q, then R.
P
But not R.
Example 2:
Since
many newly emerging nations do not have the
capital resources necessary for sustained
growth, they will continue to need help
from industrial nations.
Premise 1: Many newly emerging nations
do not have capital resources
Premise
2: Capital resources are necessary for sustained
growth.
Premise
3:
If
a
newly
emerging
nation
is
to
sustain
its
growth,
and
it
does
not
have
capital
resources, it will need help from
industrial nations.
Conclusion: Many
newly emerging nations will need help from
industrial nations.
Example
3:
Well perhaps she didn't want you to
tickle her tummy, or she didn't realize that was
what you
were going to do. If she
didn't realize , then you obviously went about it
in the wrong way. In
that case you
deserved to get scratched unless you ready thought
she was such a perceptive
cat that
she'd understand 'woof-woof' meant 'roll over '.
If you thought that you're an idiot.
But
you're
not
an
idiot
you're
just
twisted.
So
if
the
poor
thing
did
want
you
to
tickle
her
tummy you deserve to get
scratched.
1
Identify premises and conclusion
Premise1: Well perhaps she didn't want
you to tickle her tummy, or she didn't realize
that was
what you were going to do
Premise2: If she didn't realize , then
you obviously went about it in the wrong way.
Premise3: In that case you deserved to
get scratched unless you ready thought she was
such a
perceptive cat that she'd
understand 'woof-woof' meant 'roll over '.
Premise4: If you thought that , you're
an idiot. But you're not an idiot you're just
twisted.
Conclusion:
So
if
the
poor
thing
did
want
you
to
tickle
her
tummy
you
deserve
to
get
scratched.
2
Add suppressed premises
(None)
3
Remove irrelevancies
draft:
Premise1:
Well perhaps
she didn't want
you to tickle her
tummy
, or
she didn't realize that was
what you
were going to do
Premise2: If she
didn't realize , then you
obviously
went about it in
the wrong way.
Premise3: In that case
you deserved to get scratched
unless
you ready thought she was such a
perceptive cat that she'd understand
'woof-woof' meant 'roll over '
.
Premise4:
If you thought
that , you're an idiot. But you're not an idiot
you're just twisted.
Conclusion:
So
if
the
poor
thing
did
want
you
to
tickle
her
tummy
you
deserve
to
get
scratched.
Premise1: She didn't want you to tickle
her, or she didn't realize that was what you were
going
to do
Premise2: If she
didn't realize , then you went about it in the
wrong way.
Premise3: In that case you
deserved to get scratched.
Conclusion:
So if the poor thing did want you to tickle her
you deserve to get scratched.
4
Remove
inconsistent terms and cross references
(simplify)
Premise1: She didn't want you to tickle
her, or she didn't realize
you were
going to tickle her
Premise2: If she didn't
realize
you were going to tickle
her
, then
you were going to
tickle her
in the wrong way.
Premise3:
If you were going
to tickle her in the wrong way
, you
deserved to get scratched.
Conclusion:
So if
she
did want you to
tickle her, you deserve to get scratched.
To show you how easy it is
to reveal the structure of this argument , let's
formalize it.
Premise1: She
didn't want you to tickle her, or she didn't
realize you were going to tickle her
Premise2: If she didn't realize you
were going to tickle her , then you were going to
tickle her
in the wrong way.
Premise3: If you were going to tickle
her in the wrong way, you deserved to get
scratched.
Conclusion: So if she did
want you to tickle her, you deserve to get
scratched.
interpreter: