Transcript lesson on logic and arguments

Learning Objective:
To explore what a Philosopher means by “argument”
and “proof”.
Philosophy of language and logic....
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Argument
Proof
Premise
Conclusion
A Priori
analytic
Deductive
A posteriori
synthetic
inductive
Tip: start a glossary or
keyword list to help you
as you are reading and
to make sure you
include them in your
written and verbal
responses.
Philosophers use arguments to prove things.
So we have two questions:
• What is an argument?
• What is proof?
• In philosophy when we talk about an
argument we don’t mean a row between two
people
• It’s means the same as when we say you
“argue” your point of view.
• An alternative word for argument is a proof.
• Lets look at some proofs.
Quotes linked with proofs...
a proof is that which results from a valid argument
constructed from a set of true premises.
an argument which starts from one or more
premises which are propositions taken for granted
for the purpose of the argument, and argues to a
conclusion. (Swinburne)
Or to put more simply....
Proof: Any effort, process, or operation
designed to establish or discover a fact or
truth.
A proof is made up of P + P = C
P = a premise. A premise is a statement about
something, e.g “Mary is a wife”.
C = a conclusion.
So…
Mary is a wife
+
P + P = C
A wife is a
married woman
Mary is a
married woman.
=
Beware!
Based on incorrect premise
• Premise 1: Mary is a wife
• Premise 2: all wives are good at ironing
• Conclusion: so Mary is good at ironing
Beware!
Incorrect conclusion
• Premise 1: Mary is a wife
• Premise 2: all wives are female
• Conclusion: so females are called Mary
Come up with three proofs using the
formula “P + P = C”.
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Premise 1: all his friends are rap fans
Premise 2: all rap fans are word-lovers
Conclusion: so all his friends are…
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Premise 1: all squares are rectangles
Premise 2 all ….. Are quadrilaterals
Conclusion: so all…. Are quadrilaterals
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Premise 1: all ostriches are…
Premise 2: all birds are egg layers
Conclusion : so all …. Are egg layers
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Premise 1: all…. Are bops
Premise 2: all bops are…
Conclusion: so are bips are bups
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Premise 1: all films shown before 9pm are supposed to be suitable for
family viewing
Premise 2: all films that are supposed to be suitable for family
viewing are films without violence
Conclusion: so…..
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• Look at this proof and explain how it is
different from the first example with Mary
• Mary wears a ring
• Married women wear rings
• Mary is a married woman
Mary is a wife
A wife is a married woman
Mary is a married woman
• A Priori, analytic
• A posteriori,
or deductive
synthetic or
Which means.....
inductive
• These arguments are
Which means....
not dependant on
• These arguments are
experience, but have a
based on experience.
logically necessary
They come to a conclusion
conclusion. The
that is probable, but has a
conclusion offers no
chance of not being true.
new information.
Here are two a posteriori arguments.
What is the difference between them?
• Mary wears a ring
• Married women wear
rings
• Mary is a married
woman
They could both be
true, but one is more
PROBABLE than the
other. It is more likely
to be true.
• Mary wears a ring on
the third finger of her
left hand
• Married women wear
rings on this finger
• Mary is a married
woman
Tasks
• In groups write four a priori arguments, and
four a posteriori arguments.
• When you have finished number your a
posteriori aruguments in order of probability.
No 1 is the most likely and No 4 the least
likely.
Logica card sort game
Inductive or deductive????
Strong or weak inductive?
Sound or unsound deductive?
Deductive proof
Can the existence
of God be a
logically
necessary
conclusion?
A set of premises that move towards a
logically necessary conclusion.
Does not conclude anything
that is not already contained
in the original premises
(analytic).
a priori because the conclusion is
not dependent on external
evidence or experience (no
verification necessary)
Do we not need
external verification?
Is God’s existence
self-defining?
Inductive proof
A set of premises that move towards a
conclusion that is not logically necessary,
but is only probable.
Should we rely on
our experience to
verify our
assumptions?
The conclusion of the
proof is not contained
within the premises
(synthetic).
a posteriori because the premises
and conclusion are dependent on
external evidence or experience
(they require verification).
Is a probable conclusion
strong enough evidence
to base faith?
Is it reasonable?
• One of the most famous Greek philosophers Aristotle
(384-322 BC) actually published some rules of logic
that were part of formal education up till the 19th
century.
• Edward Venn, an English clergyman devised a way of
picturing them that made it much easier to
understand. (the VENN diagram!)
How would you draw the
following...
• Premise 1: all As are Bs
premise 2: no Bs are Cs
conclusion: so no As are Cs
• Premise 1: some Fs are Gs
premise 2: all Gs are Hs
conclusion: so some Fs are Hs
Premise 1: all As are Bs
premise 2: no Bs are Cs
conclusion: so no As are Cs
c
b
a
Premise 1: some Fs are Gs
premise 2: all Gs are Hs
conclusion: so some Fs are Hs
g
f
There are 13 different possible 3 circle
combinations in pairs make up a new one and
try to bring the diagram to life with an
example to fit it
Deductive
• Leads to apparently
necessary conclusions –
why is this a weakness?
• Depends on acceptance of
the premises being
analytically true.
Inductive
• Depends on our acceptance of
the nature of the evidence.
• Demands overwhelmingly good
reasons for accepting that the
conclusion is the most
probable.
• Alternative conclusion may be
just as likely.
Problems of proofs
You must
develop
these ideas
further!
• They are dependent on limited
experience and resources.
• Believers do not allow anything
to count against proofs.
• An atheist can legitimately reach
different conclusions from those
of the theist.
• If the existence of God were self
evident, there would be no need
for proof.
Consider……
• What does it mean to say that God exists?
• How would you establish whether it is true to say “Thou shalt not steal”?
Do you think the truth of this statement depends on the society in which
one lives?
• If all the possible checks have been carried out to ensure that a statement
is true, is it still possible that the statement could nevertheless be false?
• Where did you learn about God? How big an influence do you think
parents and background have on the religious beliefs an individual may
have.