Transcript Document 7318450

LOGO
Reasoning and Logic
Week 02
In today’s lecture…
recap of last week’s lecture
deductive and inductive
reasoning
truth and truth-value
basic principles of logic
problem cases
Before we start…
Students who missed the first
lecture may go to the course
website to download the course
outline, lecture notes
(PowerPoint) and other reading
materials. The address is:
filmandphilosophy.weebly.com
Before we start…
If you have any questions about
lectures, tutorials or coursework,
you can contact me at:
[email protected]
Before we start…
During lectures, every time you
see a question or some questions
in red, you will be given 2
minutes to think about them.
Don’t sit passively doing nothing.
Try to write down some thoughts
and ideas of your own. Ask for
help if there are things that you
don’t understand.
Before we start…
Please make sure you have
signed up for tutorials.
Tutorial dates, times and
classroom numbers can be found
on the course website under
‘Announcement’.
Recap
In last week’s lecture, we looked
at the following:
what is philosophy
how to study philosophy
critical thinking skills
the course outline
Recap
Basically, philosophy is
concerned with:
[1] questions that may not have
ultimate answers
[2] issues that cannot be
adequately understood through
common sense
Recap
We study philosophy by:
[1] asking questions
[2] analyzing concepts and ideas
[3] comparing and evaluating
various viewpoints
[4] developing arguments
through critical thinking
Recap
To develop the skills of critical
thinking, you should:
[1] consider issues from a
variety of perspectives (觀點)
[2] examine relevant facts and
arguments
[3] be ready to support your own
views with reasoned arguments
Reasoning and arguments
Critical thinking requires the use
of reasoned arguments (合理的論
據) to support one’s views.
Reasoned arguments are
relevant (切題的), valid (有效的),
and supported by evidence
(facts, observations, statistics
and examples).
Reasoning and arguments
An argument consists of one or
more ‘premises’ 前提 (facts or
reasons) and a ‘conclusion’ (a
claim, a judgment or an
assertion).
Premises are statements that
support a conclusion. They are
supposed to provide the reason,
evidence or justification for a
conclusion.
Reasoning and arguments
Reasoning is the act of drawing
(or deriving) a conclusion from a
premise or a set of premises.
An argument is unsound (無效的)
or fallacious (錯誤的) if the
premise or premises do not
support the conclusion. A
‘fallacy’ (謬誤) is an error in
reasoning.
Evaluating arguments
An important part of philosophy is
the evaluation (評估) of
arguments. When we evaluate
arguments, we should always ask:
Is the evidence/data relevant?
Are the facts correct?
Is the reasoning logical and valid?
Are there other possibilities?
Are there any counterarguments?
Evaluating arguments
“The power is out. You must
have forgotten to pay the
electricity bill.”
What is the problem with this
line of reasoning?
Evaluating arguments
The question we should ask is:
“Are there other possibilities that
may lead to power failure?” (e.g.
Maybe the fuse is damaged.)
If there are other possibilities,
the conclusion does not
necessarily follow from the
premise (i.e. the reasoning may
be incorrect).
Deductive reasoning
A deductive (演繹的) argument is
made up of premises (facts and
reasons) and a conclusion.
All children love pets. [premise 1]
Sue is a child. [premise 2]
Sue loves pets. [conclusion]
Deductive reasoning
A deductive argument is valid if
the conclusion follows
necessarily from the premises.
All men are mortal (會死的).
Socrates is a man.
Therefore, Socrates is mortal.
Deductive reasoning
A deductive argument is sound if
and only if [1] it is valid, and [2]
all of its premises are true.
Otherwise, a deductive argument
is unsound or fallacious.
We can say that the truth of the
conclusion is contained within
the truth of the premises.
Deductive reasoning
All children are afraid of the dark.
Dorothy is afraid of the dark.
Dorothy is a child.
Is this an example of a valid
deductive argument? Why or why
not?
Inductive reasoning
Inductive (歸納) reasoning is an
act of drawing a general (普遍的)
conclusion from particular (個別的)
facts or observations. Example:
My cat is lazy.
My friends’ cats are lazy too.
Therefore, all cats are lazy.
Inductive reasoning
“I have read 100 comic books.
They are all very interesting. Joe
just gave me a new comics. I
haven’t read it, but I know it
must be very interesting.”
Do you think this is a valid
argument? Why or why not?
Inductive reasoning
Here, the argument can be
broken down into 2 parts: [1]
The 100 comic books I have read
are interesting; therefore, all
comic books are interesting.
(inductive reasoning); [2] If all
comic books are interesting, the
one that Joe gave me must be
interesting. (deductive
reasoning)
Inductive reasoning
Part [1] of the argument
(induction) is invalid because the
premise about particulars (I
have read 100 interesting comic
books.) does not necessarily
support the general conclusion
(All comic books are interesting.)
Part [2] is a valid deductive
argument.
Inductive reasoning
An inference (推論) from a number
of particular facts and
observations to a general rule is
called ‘generalization’.
Generalizing from a limited set of
facts or observations, however, is
not always reliable. This is called
‘the problem of induction’ or ‘the
problem of the black swan’.
Inductive reasoning
In the past, people of the West
thought that all swans (天鵝)
were white.
The 17th century discovery of
black swans in Australia showed
that the premise ‘All swans are
white’ was mistaken.
Inductive reasoning
The existence of ‘black swans’
illustrates the problem of
induction.
It draws attention to the
limitation of inductive reasoning
based on limited experiences (i.e.
generalizing from a limited set of
facts and observations).
Truth and truth-value
Good reasoning and logic is
especially important in the study
of philosophy.
The subject matter of logic is the
correct connection between
ideas. In other words, logic is
concerned with the rules or
principles (原理) of correct
reasoning.
Truth and truth-value
In logic and philosophy, the term
‘truth-value’ means ‘truth or
falsehood’. To ask for the truthvalue of a proposition p is to ask
whether p is true or false.
The concept of truth-value can
be applied to propositions (命題),
beliefs, theories, etc.
Truth and truth-value
A proposition is a statement.
For example, to ask “What is the
truth-value of the proposition
‘Steve is Bob’s brother’?” is the
same as asking whether the
statement ‘Steve is Bob’s
brother’ is true or false.
Truth and truth-value
Beliefs and propositions are ways
we make sense of the world.
Merely believing in something,
however, does not automatically
make it true. A man may firmly
believe that he is Jesus Christ or
Napoleon, but his belief still
cannot possibly be regarded as
true.
Truth and truth-value
Beliefs are mental entities – they
only exists in people’s minds.
Propositions (statements), on
the other hand, can exist
independently of the mind as the
meaning or content of spoken or
written words.
Truth and truth-value
A proposition, however, is
different from a sentence
(spoken or written words); it is
the meaning expressed by a
(spoken or written) sentence.
Whenever you say something
about something (through
speech or writing), the sentence
you say or write expresses a
proposition.
Truth and truth-value
Two sentences (spoken or
written) express the same
proposition if they have the same
meaning.
For example, “Snow is white” (in
English) and “Schnee ist weiß”
(in German) are different
sentences, but they express the
same proposition.
Truth and truth-value
Not everything we say or write
or think is a proposition.
Questions (e.g. What time is it?)
and requests (e.g. Please keep
quiet.), for example, are not
propositions.
3 logical principles
Now, let us consider some of the
most basic principles of logic:
1. The law of bivalence
2. The law of the excluded middle
3. The law of non-contradiction
3 logical principles
The law of bivalence:
‘For any proposition p, p is either
true or false.’
e.g. The statement ‘Craig is an
artist’ is either true or false.
3 logical principles
The law of the excluded middle:
‘For any proposition p, either p is
true or not-p is true.’
e.g. Either the statement ‘Craig is
an artist’ is true, or the
statement ‘Craig is not an artist’
is true.
3 logical principles
The law of non-contradiction:
‘For any proposition p, it is not
the case that both p is true and
not-p is true.’
e.g. The statement ‘Craig is an
artist and Craig is not an artist’ is
false.
3 logical principles
Note that some ideas or concepts
are self-contradictory (自相矛盾的).
We know, for example, that there
are no round squares, no living
dead people, and no largest
number because such things
violate the law of noncontradiction.
3 logical principles
To summarize: the basic logical
principles require that [1] every
proposition has exactly one
truth-value; [2] a proposition
must be either true or false; and
[3] no proposition can be both
true and false.
Truth and truth-value
In logic and philosophy, it is
often assumed that a proposition
(statement) must have a truthvalue; it must be either true or
false.
A sentence that is neither true
nor false (i.e. a sentence that
does not have a truth-value)
does not express a proposition.
Think!
Suppose Craig is a computer
programmer. He writes songs
and draws pictures in his spare
time. Some people think that he
is an artist, but others do not.
Does the statement ‘Craig is an
artist’ have a truth-value?
Think!
Can you think of any statements
that are neither true nor false?
In what follows, we will consider
some counterexamples (反例) to
the logical principle that ‘every
proposition must be either true
or false’.
5 problem cases
1. sentences containing nonreferring expressions
2. predictions of future events
3. liar sentences
4. sentences containing indexicals
5. sentences about moral, ethical,
or aesthetic (美學) values
Non-referring expressions
e.g. ‘The present king of France
is bald (秃頭的).’
Because France has no king in
present times, philosopher P. F.
Strawson argues that the
statement has no truth-value – it
is neither true nor false.
Non-referring expressions
In a famous dispute (爭論),
Bertrand Russell disagreed with
Strawson, arguing that the
statement ‘The present king of
France is bald’ has a truth-value
– it is a false proposition.
Who is right? Strawson or
Russell? Why?
Non-referring expressions
Do the following sentences have
truth-values?
“A unicorn is a horse-like
creature with a horn in its
forehead.”
“Santa Claus keeps reindeers.”
“A crocodile ate my homework.”
Future events
Some philosophers think that the
sentence ‘It will rain tomorrow’
is neither true nor false at
present.
They argue that because the
future is not fixed or determined
(注定), predictions about the
future has no truth-value.
Liar sentences
Examples of liar sentences:
‘I’m lying.’
‘This sentence is false.’
By referring to itself, a liar
sentence generates a paradox (悖
論) when we consider what truthvalue to assign to it.
Indexicality
Indexicals (e.g. this, that, here,
now, etc.) are words whose
meanings may change under
different circumstances.
The truth-values of sentences
with indexicals must be
determined with reference to
their specific contexts (語境).
Indexicality
The sentence “Yesterday was
Wednesday” expresses different
propositions on different days of
the week.
For example, the sentence
expresses a true proposition if
today is Thursday, but the same
sentence expresses a false
proposition if today is Saturday.
Indexicality
The sentence “Jess is hungry”
expresses the same proposition
whenever it is used. However,
the truth-value of the proposition
varies (改變) with time – it may
be true before Jess had lunch
and not true after she had lunch.
Ethics and aesthetics
Some philosophers believe that
statements such as ‘Lying is
wrong.’ (an assertion of moral
principle) and ‘Paris is beautiful.’
(an aesthetic judgment) are
neither true nor false.
Ethics and aesthetics
In their view, judgments in
ethics and aesthetics do not have
truth-values because they only
show the speakers’ subjective
preferences (what they like or
dislike).
These sentences do not tell us
any facts about objective reality.
Ethics and aesthetics
Is the statement ‘Paris is
beautiful’ merely an expression
of the speaker’s subjective
opinion?
Or is it possible to draw attention
to some objective facts to
support the claim that ‘Paris is
beautiful’?
Ethics and aesthetics
Questions about art, ethics or
politics are often regarded as
‘matters of opinion’ (見仁見智).
Judgments on such matters are
likely to be subjective rather
than objective because different
people may have very different
views.