Reasoning Part 1 (Pre-lecture 16)

Question 1

What is logic?

Answer 1

Essentially a set of standards for us to judge how good one’s reasoning is.
Specifies relationship between components (premises and conclusions) of propositions.
Enables us to identify these components.
Allows us to perform some cognitive analysis of inferential reasoning- going beyond what’s presented (what is implied).
Permits decomposition and aids analysis.

2 components of arguments/propositions:

• premises: information that (supposedly) provides support for conclusion- basis.
• conclusion: statement that is claimed to follow (logically) from info contained in premises- usually at the end.

Question 2

Conditional reasoning

Answer 2

“If… then…” reasoning (If P then Q).
How the words in connecting propositions influence inferential reasoning.
- affect drawing correct conclusions based on making inferences (going beyond evidence).
- ‘connective’: words such as ‘if’, ‘or’, ‘not’.
Typically comprise 1 premise (with two parts), 1 statement of (factual) info and 1 conclusion.
Propositions logically-correct (valid) if conclusion follows logically from premise given info statement.

Example:
If it is raining (antecedent), then I take an umbrella with me (consequent).
It is raining (factual info), therefore I take an umbrella with me (conclusion - valid).

Question 3

Conditional reasoning: inferences

Answer 3

4 different types of inference:
2 logically-valid (comply with principles of logic):
- modus ponens (MP)- or ‘affirmation of antecedent’. (Agree with the ‘if’ part)
- modus tollens (MT)- or ‘denial of consequent’. (Counter the ‘then’ part).

2 logically-invalid (non-logical):
Drawing logically-incorrect conclusion from premises.
- affirmation of consequent (AC).
- denial of antecedent (DA).

Question 4

Psychological data

Answer 4

Evans, Handley & Buck (1998): looked at ppts accuracy of four conditional reasonings.
Results:
- DA (non-logical): endorsed by 59% (said it was logical when it was in fact not).
- AC: endorsed by 77%.
- MP: 98% said logical.
MT: 60%.
Why?- presence of negation (“not”) in statement makes it harder to judge logic of arguments when they contain negation words.
Two theoretics accounts: mental rules; mental models.

Question 5

Mental rules theory (Rips, 94)

Answer 5

Principles:
- mind contains ‘mental logic.’
- premises represented in language-like way.
- only have rules for some inferences (rule for MP not MT).
3 stages:
1. represent underlying logical form of argument.
2. access appropriate rules.
3. evaluate argument components (eg. conclusion).

Question 6

‘Mental rules’: modus ponens

Answer 6

Eg. “If Joe goes fishing, then he will have a fish supper. Joe goes fishing.”
1. requite logical form: if P then Q.
2. apply inference rule: P therefore Q- derive conclusion.
2. insert original content: Joe will have a fish supper.
Inference easy because: it involves just one rule; just three steps; its rule is automatically accessed as part of processing IF.

Question 7

‘Mental rules’: modus tollens

Answer 7

Eg. “If Joe goes fishing (P), then he will have a fish supper (Q). Joe does not have a fish supper (not-Q).”
Modus tollens difficult because: it involves 4 rules (supposition rule, modus ponens rule, conjunction introduction rule, reductio ad absurdum rule); involves 6 steps.

Question 8

Mental models theory (Johnson-Laird, 83)

Answer 8

Assumptions:
1. procedures for manipulating mental representations- mind contains no ‘mental logic’ (mental rules).
2. models constructed to interpret/understand premise.
3. errors due to failure to keep track of mental models.
Three stages:
1. comprehension of premise (model construction).
2. draw conclusion based on mental models.
3. search for counter-examples (alternative models where conclusion false).

Need to generate more models for modus tollens than modus ponens.
- modus tollens: need to ‘flesh out’ basic, modus ponens inference mental model to draw conclusion.

Question 9

Summary

Answer 9

Logic: standard for judging reasoning quality.
Conditional reasoning: ‘if… then…’
- drawing conclusions from inferential reasoning.
- performance worse for MT than Mp inference- due to presence of negation in MT inference.
Mental rules and mental models theories- attempts to explain ‘presence of negation’ problem.