Philosophy in Practice

Lecture 2: Introduction to Critical Reasoning

Outline of the lecture

• Recap: last lecture• Continue learning some basic concepts of critical reasoning• Practice identifying arguments• Practice reconstructing arguments

Arguments

• In philosophy we pay attention to the structure and value of an argument. An argument is the attempt to persuade by giving reasons. • And interrogating this is the task of the critical

thinker, which breaks down into two tasks:

1. Being able to distinguish argumentative from non-argumentative attempts to persuade.

2. Being able to assess whether arguments do in fact succeed in providing you with good reasons for believing something or taking action.

Critical reasoning

Learning to

IdentifyReconstructEvaluate

Arguments

Premises and conclusion

Arguments have two components:

1. The supporting claims (or what we should call ‘premises’)

2. And the claim for which the supporting claims are being given (the ‘conclusion’)

The premises are intended to support the conclusion.

Standard form

This is the clearest expression of an argument. It’s made up of premises, the bar (which signifies ‘therefore’) and the conclusion.

P1: If backwards time travel were possible, then people would have come back from the future to visit us.P2: People haven’t come back from the future to visit us._________________________C: Backwards time travel is impossible.

Deductive validityThere are two ways in which an argument might succeed:• Either: the premises are in fact true• Or there’s a particularly tight connection

between the supposed truth of the premises and the truth of the conclusion.

Critical reasoning focuses on the second way. By paying attention to the internal relations of the argument, we can see that the premises support the conclusion.Just assume that the premises are true, no matter how ridiculous they might seem. Based on these premises, is the conclusion false?

Deductively valid argument

P1: If Diet Sprite is the greatest drink in the world then the Queen drinks it.P2: Diet Sprite is the greatest drink in the world._________________________ C: The Queen drinks Diet Sprite.

Supposing that P1 and P2 are true, the conclusion must be true. Or, to put it another way, assuming the truth of P1 and P2, C could not possibly be false.

Antecedent and consequent

A conditional statement is one that is structured like this: “if…then…”. So a conditional statement is composed of two parts:

• The first part is called the antecedent (and follows ‘if’)• The second part is called the consequent

(and follows ‘then’)

If antecedent, then consequent

Necessary and sufficient• The antecedent is supposed to be sufficient

(enough) for the consequent.• The consequent is supposed to be necessary (required) for the antecedent.

If you were born in London, then you were born in England.• Being born in London is sufficient but not necessary for being born in England.• Being born in England is necessary but not sufficient for being born in London.

Valid or invalid?P1: If the mind and body are distinct then we may survive our bodily deaths.P2: The mind and body are distinct._________________________C: We may survive our bodily deaths.

The conditional statement (P1) is true.The antecedent statement (P2) is true.Therefore the argument (C) can be validly inferred.

Therefore, the argument is valid

Affirming the antecedentP1: If the mind and body are distinct then we may survive our bodily deaths.

P2: The mind and body are distinct.

_________________________

C: We may survive our bodily deaths.

If P, then QPTherefore Q

This is also known as ‘modus ponens’.

Valid or invalid?P1: If backwards time travel were possible, then people would have come back from the future to visit us.

P2: People haven’t come back from the future to visit us.

_________________________

C: Backwards time travel is not possible.

The conditional statement is true

The negation of the consequent is true

We can validly infer the negation of the antecedent

Therefore, the argument is valid

Denying the consequentP1: If backwards time travel were possible, then people would have come back from the future to visit us.

P2: People haven’t come back from the future to visit us.

_________________________

C: Backwards time travel is not possible.

If P, then QNot-QTherefore, not-P

This is also known as ‘modus tollens’

Valid or invalid?P1: Either the giant duck is the biggest bird or the giant sparrow is the biggest bird.

P2: The giant sparrow is not the biggest bird.

________________________

C: The giant duck is the biggest bird.

• The first premise is an either/or (either P or Q) P and Q are known as disjuncts.• The second premise eliminates one of them.• This leaves us with the other.

Therefore, the argument is valid

Disjunctive syllogismP1: Either the giant duck is the biggest bird or the giant sparrow is the biggest bird.

P2: The giant sparrow is not the biggest bird.

---------------------------------------------------------------------

C: The giant duck is the biggest bird.

Either P or Q Not-QTherefore, P

Valid or invalid?P1: If there is a God then there is an objective morality.P2: There is an objective morality.----------------------------------------------------------------------------C: There is a God.

Even if the conditional statement is trueAnd the consequent is affirmedThe conclusion doesn’t follow from the premises

This is an invalid argument

Affirming the consequent

P1: If there is a God then there is an objective morality.P2: There is an objective morality.___________________C: There is a God.

If P, then QQTherefore, P

Valid or invalid?P1: If the Democrats win the election, then Western civilisation is doomed.P2: The Democrats won’t win the election.______________________C: Western civilisation is not doomed.

Even if the conditional statement and the antecedent are both true, it doesn’t give us a good reason to establish the conclusion. There are other reasons why civilisation is doomed.

This is an invalid argument.

Denying the antecedent

P1: If the Democrats win the election, then Western civilisation is doomed.P2: The Democrats won’t win the election.______________________

C: Western civilisation is not doomed.

If P then QNot-PTherefore, not-Q

Valid or invalid?

P1: If I have the flu, then I have a sore throat.P2: I have a sore throat._________________________C: I have the flu.

Invalid argument (affirming the consequent)

Valid or invalid?

P1: If it's raining, then the streets are wet. P2: It isn't raining. _________________________C: The streets aren't wet.

Invalid argument (denying the antecedent)

Valid or invalid?

P1: If I want to go to the concert I have to get hold of some tickets.P2: I want to go to the concert._________________________C: I have to get hold of some tickets.

Valid argument (affirming the antecedent)

Valid or invalid?

P1: If you give a man a knife, he may kill someone.P2: He doesn’t have a knife._________________________C: He won’t kill anyone.

Invalid argument (denying the antecedent)

Valid or invalid?

P1: If human beings have moral obligations then human beings have free will.P2: Human beings do not have free will._________________________C: It is not the case that human beings have moral obligations.

Valid argument (denying the consequent)

Conditionals vs. arguments

Note the key difference between conditionals and arguments.

• Conditionals can be true or false• Arguments can be valid or invalid 

Identifying arguments

Capital punishment is wrong. The main reason for thinking this is that capital punishment involves deliberately killing a human being, and it’s always wrong to deliberately kill a human being.

Q: is this an argument? If so, what is the conclusion and what are the premises?

Identifying argumentsCapital punishment is wrong. The main reason for thinking this is that capital punishment involves deliberately killing a human being, and it’s always wrong to deliberately kill a human being.

Conclusion: Capital punishment is wrong.Premises: • Capital punishment involves deliberately killing

a human being. • It is always wrong to deliberately kill a human

being.

Reconstructing argumentsCapital punishment is wrong. The main reason for thinking this is that capital punishment involves deliberately killing a human being, and it’s always wrong to deliberately kill a human being.

P1: Capital punishment involves deliberately killing a human being.P2: It is always wrong to deliberately kill a human being.______________________C: Capital Punishment is wrong.

Conclusion indicators

Therefore...Hence...Thus...It can be concluded that...So...It follows from this that...... is established by the fact that ...

(see Bowell and Kemp: 2nd Edition – Ch.1, pp. 12-16; 3rd Edition - Ch. 1, pp. 15-16)

Premise indicators

The reason for thinking this is...The evidence for believing this is...... follows from the fact that...This is true because...

(see Bowell and Kemp: 2nd Edition – Ch.1, pp. 16-18; 3rd Edition - Ch. 1, pp. 17-19)

Note: looking out for conclusion and premise indicators is by no means a fool proof method for their identification. Often, you will need to use your interpretative skills to identify conclusions and premises…