Deductive logic

1
Deductive logic
All generalizations are false, including this one
You do not reason a man out something that he was
not reasoned into

• What is it?
• How does it work?
• Why does it matter?

Critical reason is the only alternative to
violence so far discovered.
Logic is the beginning of wisdom, not the end
2
An example..
Sherlock Holmes (the master of deductive logic)
speaking to a police officer about the theft of
an expensive racehorse Police Officer Holmes,
does any one aspect of the crime strike you as
significant? Holmes Yes, the curious incident
of the dog in the night time Police Officer
But the dog did nothing in the night
time! Holmes That was the curious incident!

3
The deductive reasoning..

• Watchdogs bark at strangers
• The Watchdog did not bark at the thief
• Therefore the thief was not a stranger

4
More examples..

• You know that you left your mobile phone either
  in your pocket or on your desk
• Your mobile isnt in your pocket
• Therefore it must be on your desk

5

• You know that The West Lake in Hangzhou is a
  fresh water lake
• You know that sharks cannot live in fresh water
• Therefore there cannot be any sharks in the West
  Lake

6
The benefits?

• You dont have to check every single fresh water
  lake to know that there arent any sharks in it
  deductive logic tells you that there are no
  sharks in any freshwater lakes.

7
So what is deductive reasoning?

• Any form of reasoning that moves from the general
  to the particular e.g.
• All dogs are mammals
• Fido is a dog
• Therefore Fido.

Is a mammal
8
Syllogisms

• The kind of deductive argument that we just
  looked at is known as a syllogism
• A syllogism consists of
• Two premises and a conclusion
• Three terms, each of which occurs twice (dogs,
  mammals, fido)
• Quantifiers such as all, some or no

9
Truth Vs Valid which is this?

• All rocket scientists are stupid
• Bill Gates is a rocket scientist
• Therefore Bill Gates is stupid

10
It is Valid!

• Both the PREMISES are false
• The CONCLUSION is false
• Yet the ARGUMENT ITSELF IS VALID!

11
WHAT ABOUT THIS ONE..

• All tacos are teachers
• Mr. Wright is a taco
• Therefore Mr. Wright is a Teacher

12
Valid

• Both the premises are false
• But the conclusion is true
• However the argument is still VALID

13
This one?...

• All projectors require electricity
• This classroom has a projector
• Therefore this this classroom does not have a
  projector

14
INVALID

• The premises are both true
• The conclusion is false
• This is the one combination where the argument
  MUST be invalid

15
DIY make your own valid syllogisms

• Two true premises and a true conclusion
• One true premise, one false premise and a true
  conclusion
• One true premise, one false premise and a false
  conclusion
• Two false premises and a true conclusion
• Two false premises and a false conclusion

16
Pure logic

• Concerned merely with the structure of arguments,
  it doesnt matter if the premises are false, or
  even meaningless!
• All that matters is does the conclusion follow
  logically from the premises.
• E.g.
• All blims are blams
• Some blims are bloms
• Therefore some blams are bloms

17
Aghhhh my head hurts! Algebra in TOK!

• All As are Bs
• Some As are Cs
• Therefore some Bs are Cs

18
Whats the point?

• Removes belief bias
• Sometimes we tend to believe an argument is valid
  because we already agree with the conclusion
• E.g. Democrats are in favour of free speech
• Dictators are not Democrats
• Therefore all dictators are opposed to free
  speech
• This is NOT a valid argument

19
Using Venn diagrams

• Refer to the photocopied information Venn
  diagrams can be useful way of picturing a
  Syllogism and determining whether an argument if
  valid

20
Enthymemes

• Incomplete arguments that exclude a premise
  because it is considered obvious/assumed.

21
Supply the missing premise for these enthymemes

• Jenny goes to Oxford University, so she must be
  very intelligent
• Drugs should be legalised because they only harm
  the addict
• Graham is a politician, so he is probably lying.
• Cheerleading should be an olympic event becauses
  cheerleaders compete, train and have a high level
  of physical fitness
• Since it is natural to eat meat, there is nothing
  morally wrong with it

22
But where do our premises come from?

• INDUCTIVE REASONING!
• To be continued.

23
Bibliography

• Much of this presentation is shamelessly based
  upon material from the excellent TOK book by
  Richard van de Lagemaat thanks go to him!