Reason

Continued…

Recap types of logic:Deductive Logic

• Reasoning from the general to particular

• Example: – all metals expand when heated.– A is a metal– Therefore A expands when heated

• Its more certain but less informative than induction

Inductive logic• Reasoning from the particular to

the general• Example:

– Metal A expands when heated– Metal B expands when heated– Metal C expands when heated– Therefore all metals expand when

heated

• Its more informative, but less certain than deduction

The relationship between reasoning and certainty

• What percentage of the metal existing on our planet would you guess scientists have tested to see if it expands when heated?

• What does this tell you about the certainty or otherwise of scientific laws?

What distinguishes good and bad generalisations?

• Number – you should look at a reasonable amount of instances

• Variety - You should look at a variety of instances

• Exceptions – You should actively look for counter examples. This will help to guard against a confirmation bias.

• Coherence – you should demand more evidence to support surprising claims than to support unsurprising ones.

• It would take more to convince me that there is life on Mars than to convince me that there is life in the school pond.

• Subject Area – generalisations are more reliable in some subjects than in others

Logic as a pathway to truth• We have seen that reason

provides a way of laying out information, in a way that sometimes helps us get closer to truth.

• When using deductive reasoning one must be able to answer ‘yes’ to both of the following questions:

1) Are the premises true?

2) Is the argument valid?

Logic as a pathway to truthPremise 1) some Monks are

TibetansPremise 2) All Tibetans are

good at yogaTherefore,Conclusion: some monks are

good at Yoga

1) Are the premises true?

2) Is the argument valid?

• ..some evidence of Tibetans who are good at Yoga

• So Premise 2) is possibly true

Preserving truth

• So, although we can’t be 100% certain of the truth of the 2nd premise, unless we find evidence from every Tibetan,

• And unless we have reason to believe that Tibetan monks generally shun yoga,

• Although the argument is not strictly valid,• We can tentatively accept the truth of the conclusion.• This is because the scope of the claim could be fairly

small. • We don’t need to find many Tibetan Monks who are

good at Yoga for the conclusion to be true.

Filling in the premises to an argument

• When people argue in everyday life, they rarely set their arguments out in a formal way.

• If the speaker regards one of the premises as obvious, they may simply imply or assume that these are true, without stating them explicitly as a premises.

• Therefore, you will sometimes have to fill in the premises to someone else’s argument, if you want it to make logical sense.

Fill in the missing premise:

• 1) Lucy goes to Oxford University

• 2) Oxford only takes very intelligent students

• Therefore: Lucy must be very intelligent.

• 1) Graham is a politician• 2) All politicians are

probably lying.• Therefore: Graham is

probably lying

Fill in the missing premise:

• 1) Cheerleaders compete, train, and have a high level of physical fitness.

• 2) All Olympic events involve competing, training and having a high level of physical fitness.

• Therefore: Cheerleading should be an Olympic event

• 1)it is natural to eat meat

• 2) There is never anything morally wrong with anything natural

• Therefore: There is nothing morally wrong with eating meat.

Using Venn diagrams

Venn diagrams help you work out if a syllogism or argument is valid• It is sometimes difficult to work out if a syllogism is

true or false.• One way of working out what is going on is to draw a

Venn diagram. Consider the following syllogism:– 1) all As are Bs.– 2) some As are Cs.– Therefore: some Bs are Cs.

• To work out if this is valid or not, represent the groups of things which are As inside the group of things which are Bs ...

Using Venn diagrams

...and to represent ‘some As are Cs’ have the circle of Cs intersect the circle of As.

So it follows that ‘somes Bs are Cs’

the argument is valid.

B

A

C

Task:

• Can you use the following venn diagram to make a syllogism?

Fallacies

Types of invalid reasoning

Types of Fallacy

The types of Fallacy we’ll focus on:

• Post hoc ergo propter hoc• Ad Hominem Fallacy• Circular reasoning• Equivocation• False Dilemma

Fallacies

Post hoc ergo propter hoc• Meaning: ‘after this, therefore

on account of this’• consists of assuming that

because one thing, B, follows from another thing, A, then A must be the cause of B. eg:– 1) at 6pm the girls ate tomato soup– 2) at 7pm the girls committed

murdersTherefore: tomato soup causes girls

to murder

Fallacies

Ad Hominem • Meaning: ‘against the man’• consists of attacking or

supporting a person rather than the argument itself. eg:– Raffles told me to vote

conservative at the next election– Raffles would say that because

he is a conservative counsellor

• Although the ad hominem fallacy is committed mostly by criticising someone, it can also be committed by supporting them.

• If I said ‘Martin Luther King jr was a Christian, so Christianity must be true’

• Then I am again focusing on the speaker rather than the argument.

fallacies

Circular reasoning• Aka ‘begging the question’• Consists in assuming the truth

of the thing you are supposed to be proving. Eg:– “I know that Jesus was the Son of

God because he said he was, and the Son of God would not lie.”

• this is not an argument, but a reassertion of original position, with no appeal to reasons.

Anthony Flew’s example:‘Three thieves are arguing about

how to divide up 7 pearls they have stolen.

One picks up the pearls and gives two to each of the other two, keeping three for himself.

“I get more because I’m the leader”

“how come your the leader?”“because I’ve got more pearls.”

fallacies

Equivocation• This occurs when a word is

used in two different senses in an argument.– 1) a hamburger is better than

nothing– 2) Nothing is better than good

heath– Therefore: a hamburger is

better than good health.

• This appears formally valid, because the premises follow from the conclusion.

• But there is something wrong with it.

• The problem lies with the word ‘nothing’ because it has a different meaning in each of the premises.

• In the 1st premise it means ‘not having anything’

• In the 2nd it means ‘there is not anything’

• Maybe this is why many argument s end up being about the meanings of words.

Fallacies

False Dilemma• This is the fallacy of assuming

that there are only two alternatives, when there are in fact a wider range of options. Eg:

• ‘Do those who advocate an increase in military expenditure want to see schools and hospitals close?’

• They imply that we only have two choices:

• Either we increase military expenditure

• Or we keep our schools and hospitals open.

• But in fact there may be more than two choices. Eg

• If taxes are raised we can have both options.

Keep schools

and hospitals

open Increase military expenditure