L3 Ch 3 Deductive arguments & logic

Question 1

What frustrating part of critical thinking is addressed by argument-reconstruction

Answer 1

When confronted with an argument, we find it hard to hold the whole thing clearly before us, we find it hard to say exactly what the argument is
Representation of arguments in standard form, gives us a clear and comprehensive view of them

Question 2

What frustrating part of critical thinking is addressed by argument-assessment

Answer 2

Even when we do succeed in laying the argument out before us clearly, we find it hard to describe what is wrong with it

Question 3

What is motivated reasoning? What is important factor in this?

Answer 3

More elaboration with high motivation and capacity.
The kind of motivation is important

Question 4

What are three kinds of motivation?

Answer 4

• Accuracy motivation
• Defense motivation - defending our beliefs
• Impression motivation - impressing others is important

It doesn’t come naturally, we need the right attitude

Question 5

What would be the reason for reasoning if we’re so bad at it? What theory answers this question?

Answer 5

The argumentative theory of reason
- The primary function of human reasoning is not necessarily to seek objective truth but to serve a social function
- A tool for argumentation and communication, helping people justify their actions, convince others, and evaluate social interactions.
- People are better in assessing other people’s reasons than in constructing their own

Even if individual reasoning is biased, people scrutinise weaker arguments, selecting for the better ones and collectively they reach more efficient and better reasoning and decision-making

Question 6

What are the steps of critical thinking?

Answer 6

1. Develop a critical disposition
2. Learn to recognise (the elements of arguments)
3. Learn to reconstruct arguments
4. Logical assessment - determine whether or not the premises support the conclusion
5. Factual assessment - determine whether all of the premises are true

Question 7

principle of charity

What is an argument and what are the tasks when trying to understand others’ argument?

Answer 7

• An argument is a system of propositions – a set of premises advanced in support of a conclusion
• Part of the task – clarify what the arguer actually said and to supplement what the arguer actually meant (to make explicit what was merely implicit)

Question 8

Principle of charity

What are the following two consequences from this?

Answer 8

• The sentences we use in a reconstruction of the argument need not be the very same sentences used by the arguer
• Our reconstructed version may contain premises that weren’t previously expressed

Question 9

The principle of charity

What do we have to do when reconstructing other people’s arguments?

Answer 9

Argument-reconstruction = task of interpretation
To reconstruct what the arguer was trying to express, we have to look at context and circumstances

Question 10

Principle of charity

What if we look at context and circumstances and it is still not clear what the arguer meant?

Answer 10

We look at purpose
- Hoping to convince others that the person is wrong, a common tactic is to represent the weakest version of the person’s argument
- What matters is whether or not the conclusion of the person’s argument is true – choose the best and fair representation of the argument – principle of charity

Question 11

Principle of charity

What is principle of charity

Answer 11

Encourages interpreting another person’s argument in the most reasonable and favorable way before criticizing or evaluating it. It involves understanding their statements as logically sound and consistent, even if the language or phrasing is unclear or appears flawed.

Question 12

Principle of charity

What do we have to be careful about when applying principle of charity?

Answer 12

If our task is to reconstruct the argument then we must not go beyond what we may reasonably expect the arguer to have had in mind

Question 13

What is truth in logic?

Answer 13

Truth in logic is very straigthforward - represents the way things are

Question 14

What is truth-value of a proposition

Answer 14

Whether proposition is true or false
- proposition corresponds to reality = true
- Proposition doesn’t correspond to reality = false

Question 15

The diagram how to decide whether argument is valid/sound/forceful

Answer 15

Picture 1

Question 16

What is the critical thinker’s two-step?

Answer 16

Step 1 - Logical assessment - determine whether or not the premises support the conclusion
Step 2 - Factual assessment - determine whether all of the premises are true

Question 17

Through what two processesses can we support logical assessment?

Answer 17

1. Logical necessity (deductive reasoning) - if the premises are true, the conclusion must be true as well; the conclusion is guaranteed by the premises
2. Probability (inductive reasoning) - conclusion is not guaranteed but is likely or probable given the premises

Question 18

What is validity?

Answer 18

It would be impossible for all the premises of the argument to be true, but the conclusion false
- To say that an argument is valid is to say: if the premises are (or were) true, the conclusion would also have to be true
- It’s about the logical connection between conclusion and premises - the conclusion must logically follow from the premises
- It’s about the structure of the argument not the truth in reality

Question 19

What different forms of true/false premises/conclusions can a valid argument contain?

Answer 19

A valid argument can contain premises that are not true & conclusions that are not true. What it cannot contain are premises that are in fact true but a conclusion that is false.
1 The premises are all (actually) true, and the conclusion is (actually) true.
2 The premises are all (actually) false, and the conclusion is (actually) false.
3 The premises are all (actually) false, and the conclusion is (actually) true.
4 Some of the premises are (actually) true, some are (actually) false and the conclusion is (actually) true.
5 Some of the premises are (actually) true, some are (actually) false and the conclusion is (actually) false.

All of these arguments are valid.

Question 20

What does it mean for an argument to not be valid?

Answer 20

The conclusion is not logically connected with the premises
- If an argument is not valid, it doesn’t matter how true the premises are

Argument cannot be valid when the premises are all (actually) true, but the conclusion is (actually) false

Question 21

How do we determine validity?

Answer 21

1. Ignore the actual truth-values of the premises and the actual truth-value of the conclusion
2. Suppose that the premises were all true – could the conclusion be completely false
3. If it couldn’t be false, then the argument is valid, if it could be false, then the argument is invalid

Always ask: Must the conclusion be true, if the premises are true?
Look at the logic behind it - can the conclusion be false even if we assume that all the premises are true?

Question 22

What are the types of valid-argument forms?

Answer 22

1. Argument by cases
2. Disjunctive syllogism
3. Hypothethical syllogism/chain
4. Modus Ponens
5. Modus Tollens

Question 23

Argument by cases

Answer 23

P1) P or Q
P2) P→Y (If P holds then Y is the case)
P3) Q→Y (If Q holds then Y is the case)
C) Y

P or Q is true - they cannot both be false so Y has to be true
Consider multiple cases, show that conclusion follows from each case, so the conclusion must be true regardless of which case holds.

Question 24

Example of argument by cases

Answer 24

P1) Bobby is either married (P) or not married (Q)
P2) If Bobby is married (P), then a married person is looking at an unmarried person (Y)
P3) If Bobby is unmarried (Q), then a married person is looking at an unmarried person (Y)
C) A married person is looking at an unmarried person (Y)

Question 25

Chain/hypothetical syllogism

Answer 25

P1) If P, then Q
P2) If Q, then R
C) If P, then R
The beginning of the chain is P, the end is R and the connecting part is Q
E.g.
P1) When it rains (P), it’s cloudy (Q)
P2) When it’s cloudy (Q), it’s dark (R)
C) It rains (P), so it’s dark (R)

Question 26

Dysjunctive syllogism

Answer 26

P1) P or Q
P2) -Q (not Q so it must be P)
C) P
Only P or Q is true
C is only false if both P&Q are true

E.g.
P1) I dance (P), or everyone dance (Q)
P2) Not everyone dances (-Q)
C) So I dance (P)

Question 27

Modus Ponens

Answer 27

P1) If P, then Q
P2) P
C) Q
If we confirm P, Q must be true

E.g.
P1) When it rains (P), it’s cloudy (Q)
P2) It rains (P)
C) So it’s cloudy (Q)

Question 28

Modus Tollens

Answer 28

P1) If P, then Q
P2) -Q (denying the second part of the ‘if P then Q’ argument)
C) -P
If Q is false then P has to be false as well
If you deny the consequent of the conditional, you also have to deny the antecedent

E.g.
P1) When it rains (P), it’s cloudy (Q)
P2) It’s not cloudy (-Q)
C) So it doesn’t rain (-P)

Question 29

We have a stack of cards with Pokemon on the front and singers on the back
- If there is a squirtle on the front, Rapper Sjors is on the other side
- Which two cards should we turn to see whether this rule holds?

Answer 29

If there is a squirtle on the front (P), Rapper Sjors is on the other side (Q)
1. We turn the squirtle to see whether Rapper is there. If he isn’t, but Justin Bieber is then the rule doesn’t hold
P1) P→Q
P2) P
C) Q
2. Then, we turn Justin bieber, to see whether Pikachu is on the other side. If the squirtle is there, then the rule doesn’t hold
P1) P→Q
P2) -Q
C) -P

Turning anything else, we would not get to the conclusion because they would be the formal fallacies of confirming the consequent (If Q then P) and denying the antecedent (If not P then not Q)

Question 30

What are argument trees?

Answer 30

Devices used for representing arguments in the form of a diagram
- helpful when reconstructing arguments = means of showing the ways in which the different parts of an argument are related to each other

Question 31

How can we represent different argument structures with an argument tree?

Answer 31

Look at picture 2 in pdf
1. In argument A, each premise supprts the conclusion individually
2. In argument B, neither premise supports C by itself, they work together to support C

This is represented in the argument tree by the arrows - argument A doesn’t explicitly include its ‘connecting’ premise (it was left implicit)
There are arguments that can have multiple intermediate conclusion - picture 3

Question 32

What are prescriptive claims?

Answer 32

Claims which state or express desires, norms or moral rules
E.g.
It is wrong to keep Rover on a chain all day.
You ought to allow John to attend the party.
Freedom is a basic value.
The US needs a different health care system.

Question 33

What are descriptive claims?

Answer 33

Fact-stating claims
E.g.
The cat is on the mat.
Jupiter is larger than Saturn.
2+2=4.
If Susie is late, then she will miss dinner.
There are some otters in the river.

Question 34

The connection to formal logic

Why do we use ‘‘dummy’’ letters intead of premises?

Answer 34

The point of the argument doesn’t depend on the declarative sentence but on the logical properties of the sentence (unless, if-then…)
Enables us to generalise about arguments on the basis of their forms
P1) If P then Q1
P2) P
C) Q

Question 35

What are the symbols of the surrogates for the logical expressions of english that join sentences?

‘if-then’, inclusive or, and, not, use of paranthesis

Answer 35

‘→’ for ‘if-then’
‘∨’ for inclusive ‘or’
‘&’ (or ‘∧’) for ‘and’
‘¬’ for ‘not’ or ‘It is not the case that’
‘∀’ (universal qualifier) = ‘every … is such that’
‘∃’ (existential qualifier) = ‘There is/are…’

Parantheses:
¬ P & Q = says that P is false and Q is true
¬ (P & Q) = it’s false that both P&Q are true

All of these are required for truth-functional logic

Question 36

What letters can we use further to truth-functional logic? Which meaning do they have and why are they useful?

Answer 36

‘F’ and ‘G’ stand for general terms (volcano, piano…)
‘P’ and ‘Q’ stand for whole sentences
Lower case letters are used in place of names (Vienna, Mount Fuji, Justin Bieber)
x stands for ‘thing’ or ‘it’

It’s useful because the validity of the argument is independent of the particular meaning.

Question 37

An example of truth-functional logic

Very long flashcard but no need to memorise, just understand the logic

Answer 37

• Everything is such that if it is a soprano then it is Italian

Replace ‘thing’ and ‘it’ with x
- Every x is such that if x is a soprano then x is Italian

Replace ‘ … is a soprano’ with ‘F’, and ‘ is Italian’ with ‘G’
We swap the order, turning ‘x is a soprano’ into ‘Fx’
- Every x is such that if Fx then Gx

Replace ‘if-then’ with the arrow and put in parentheses for clarity
- Every x is such that (Fx→Gx)

Invoke the universal quantifier ‘∀’ for the phrase ‘Every is such that …’
- ∀x(Fx → Gx)

This is quantificational logic

We can add existential qualifier
- ∃x(Fx & Gx)

This means: ‘There is an object which is both
F and G’

Question 38

What is practical logic and why is it useful?

Answer 38

Learn to identify the reasoning in commonly encountered attemptd to persuade us and to assess it as good or bad
- We need the concept of validity but we don’t need artificial symbols or elaborate technical procedures for detecting validity

Question 39

What is syllogism

Answer 39

Logical form with three statements of fact

• two premises followed by a conclusion

Question 40

How do we evaluate the truth of syllogisms?

Answer 40

Using Venn diagrams - picture 5

• The syllogism must be true under all conditions to be considered true
• It’s important to try to falsify the syllogism - If the first two premises are true, can we conclude that the conclusion must be true?

Question 41

What are the three types of errors people make when faced with a syllogism?

Answer 41

The errors are systematic - people aren’t guessing

1. Conversion error
2. Conversational implicature
3. The effect of atmosphere

Question 42

Errors - syllogism

Conversion error

Answer 42

People reverse terms that should not be reversed

• Some terms (no and some) can be reversed
  ↪ e.g. No dogs are cats. No cats are dogs
• Some terms however (all and some…not) cannot be reversed
  ↪ e.g. All canaries are birds. All birds are cannaries. → not true
  ↪ e.g. Some mammals are not cows. Some cows are not mammals. → not true

Question 43

What is conversational implicature?

Answer 43

Some terms are used more casually, with different meaning in conversational language than in logicians’ language
E.g. Some in logic means ‘at least one, and possibly all’. In conversational language, ‘more than one, but not all’. (Look at the example in previous flashcards 42 and try to apply those rules and you’ll see the meaning changes with what is actually meant by some)

Question 44

How does the atmosphere created by the syllogisms affect people’s judgment of the truth of the syllogism?

Answer 44

When both of the premises in a syllogism are both either positive, negative or use the same quantifiers (e.g. all, none)
No As are Bs
No Bs are Cs
No As are Cs
↪ the conclusions seems appropriate because of the athmosphere created but it doesn’t logically follow the premises
- nothing is said directly about the relationship between A and C. Just because A and B are mutually exclusive, and B and C are mutually exclusive, it doesn’t guarantee that A and C are mutually exclusive

Question 45

What is a conditional proposition?

Answer 45

A conditional is a compound proposition consisting of two parts
- Each of these two parts are itself a proposition
- The two parts are joined by some connectinh words such as ‘if-then’, ‘either-or’, ‘unless’, ‘only-if’…
- ‘‘If it’s raining, it’s cloudy.’’

Question 46

What is the difference between a conditional and an argument?

Answer 46

• Conditional is said to be true or false rather than valid or invalid like an argument
• Conditional is not an argument but one proposition that comprises two propositions as parts
• Whereas argument has to have at least two propositions
• Many arguments have conclusion which themselves are conditionals

Question 47

Does the order of the propositions matter in a conditional?

Answer 47

It doesn’t matter in what order the two smaller sentences occur, what matters is the logical relationship asserted by the sentence

Question 48

What are the two parts of a conditional?

Answer 48

P→Q
1. Antecedent - the part in front of the arrow
2. Consequent - the part after the arrow

Question 49

What relationship do an antecendent and a consequence have in terms of necessity and sufficiency?

Answer 49

The antecendent is sufficient (but not necessary) for the consequent
The consequent is necessary (but not sufficient) for the antecendent
- in the P→Q example, P is sufficient for Q but Q is necessary for P

Question 50

Why is the consequent necessary for the antecedent?

Answer 50

The consequent envelops the antecedent
- Q is necessary but not sufficient for P to be true since P is inside Q and Q can be true without P but P can’t be true without Q

The clouds are necessary but not sufficient for the rain
The rain is sufficient but not necessary for the clouds

Question 51

What does necessity and sufficiency mean for the truth of the premises in relation to each other?

Answer 51

Not sufficiency = as soon as we know that the conseqent is true, it doesn’t mean that the antecedent is true as well
Sufficiency = If the antecedent is true, the consequent is true as well
Not necessity - the consequent can also be true if the antecedent is false
Necessity - the antecedent cannot be true without the consequent also being true

Question 52

What does it mean for an argument to be deductively sound?

Answer 52

Knowing that the argument is valid is not enough to show that the conclusion is true so we must determine the truth-value of the premises
When an argument is valid there are two possibilities:
1. One or more of the premises are false = we can’t conclude the truth-value of the conclusion
2. All of the premises are actually true = a valid argument with true premises cannot have a false conclusion, so the conclusion must be true = deductively sound

Question 53

What does it mean for an argument to be deductively unsound?

Answer 53

One or more premises are false, or the argument is invalid, or both
Because deductive soundness, like validity, pertains to whole arguments, not to a single propositions

Question 54

What is logical equivalence?

Answer 54

Two statements are logically equivalent if they always have the same truth value in every possible situation or interpretation

Question 55

What is an example of logical equivalence?

Answer 55

“If it’s 11:00, the tutorial starts.”

Is logically equivalent to:

1. The tutorial starts, if it’s 11:00.
2. If the tutorial doesn’t start, it’s not 11:00.
3. It’s 11:00, only if the tutorial starts.
4. It’s not 11.00 unless the tutorial starts
5. The tutorial starts, or it’s not 11:00

Question 56

Why is ‘the tutorial starts, if it’s 11:00’ equivalent to ‘It it’s 11:00, the tutorial starts’?

Answer 56

The if travels with the antecedent so the two sentences have the same meaning. It’s about the logical relations, not about the place of the words in the sentence

Question 57

Why ‘If the tutorial doesn’t start, it’s not 11:00’ is logically equivalen to ‘It it’s 11:00, the tutorial starts’?

Answer 57

It’s called contraposition
If P then Q
We can switch P and Q and deny them both and it will logically have the same meaning since Q is necessary for P
If not Q, then not P

Question 58

Why is ‘It’s 11:00, only if the tutorial starts’ logically equivalent to ‘It it’s 11:00, the tutorial starts’?

Answer 58

The ‘only if’ represents necessary condition of the consequent for the antecedent

Question 59

Why is ‘It’s not 11.00 unless the tutorial starts’ equivalent to ‘If it’s 11.00, the tutorial starts.’?

Answer 59

Unless = if not
So we can turn it into: ‘It’s not 11:00, if the tutorial doesn’t start.’
Basically like contraposition but the position is switched since the if travels with the ‘the tutorial doesn’t start’

Question 60

Why is ‘The tutorial starts, or it’s not 11:00’ equivalent to ‘If it’s 11:00, the tutorial starts.’?

Answer 60

Q, or not P
Unless, explicitly stated that the or is exclusive, we can assume that the or is inclusive = either Q is true, or P is true, or they are both true
If P is denies and we say that’s false, it’s basically saying P is true so Q must be true as well.

(exclusive = both Q and P cannot be true at the same time)

Question 61

Why do we strive for our theory to be falsifiable through deductive reasoning?

Answer 61

For a theory to be scientific, it must be testable; if a theory can’t be tested, it remains speculative
↪ Falsification ensures that the theory generates predictions that can be observed and tested in the real world
- Also avoiding confirmation bias

Karl Popper - argued strongly for falsicification in science

Question 62

How can we demonstrate that falsification is the only way that’s definitive?

Answer 62

Picture 4