reasoning top-down biases symbolic distance effects semantic congruity effects formal logic...

Reasoning

Top-down biasessymbolic distance effectssemantic congruity effects

Formal logicsyllogismsconditional reasoning

Reasoning

Top-down biases effects of knowledge on judgements/decisions

symbolic distance effectssemantic congruity effects

Reasoning

Symbolic distance (e.g., Banks, Clark, & Lucy, 1975) Task: Two numbers are presented on each trial.

Identify the smaller number.

3 7 6 8 4 5

Reasoning

Symbolic distance (e.g., Banks, Clark, & Lucy, 1975) Task: Two numbers are presented on each trial.

Identify the smaller number.

3 7 6 8 4 5

Result: Faster RT for pairings with the biggest difference; in the example, RT would be lowest for the 3 7 pair (7 – 3 = 4 vs. 8 – 6 = 2 vs. 5 – 4 = 1)

Reasoning

Semantic congruity effect(e.g., Banks, Clark, & Lucy, 1975) Task: Two numbers are presented on each trial.

Identify the smaller number. Or Identify the bigger number.

34 35 98 99

Semantic congruity effect(e.g., Banks, Clark, & Lucy, 1975) Task: Two numbers are presented on each trial.

Identify the smaller number. Or Identify the bigger number.

34 35 98 99

Results: For smaller number identification, faster RT for pairs of smaller numbers (34 35) relative to larger numbers (98 99)

For larger number identification, faster RT for pairs of larger numbers (98 99) relative to smaller (34 35) numbers.

Reasoning

Additional distance effects and semantic congruity effects

Judgements of object size (e.g., animals)form an image of object

Judgements on semantic orderingstime (e.g., seconds, days)performance (e.g., poor, excellent)temperature (e.g., cold, hot)

Judgements on geographical distance

Reasoning

Formal logicsyllogismsconditional reasoning

Reasoning

Syllogisms

three statementsstatements 1 and 2: premisesstatement 3: conclusion

The premises and conclusion may or may not be true in the real world.

Reasoning

Syllogismsthree statements

statements 1 and 2: premisesstatement 3: conclusion

Example in Abstract Form

All X are Y (1st premis)All Y are Z (2nd premis)Therefore, all X are Z

Note: means “therefore”; means “not”

Example in Abstract FormAll X are Y (1st premis)All Y are Z (2nd premis)Therefore, all X are Z

Substitute real words for letters

All orchids are flowers.All flowers are plants. All orchids are plants.

Check with Venn diagrams (circles representing concepts)

Substitute real words for letters

All Orchids are Flowers.All Flowers are Plants. All Orchids are Plants.

Check with Venn diagrams.

Substitute real words for letters

All Orchids are Flowers.All Flowers are Plants. All Orchids are Plants.

Check with Venn diagrams.

O

Substitute real words for letters

All Orchids are Flowers.All Flowers are Plants. All Orchids are Plants.

Check with Venn diagrams.

O

F

Substitute real words for letters

All Orchids are Flowers.All Flowers are Plants. All Orchids are Plants.

Check with Venn diagrams.

O

FP

All Orchids are Flowers.All Flowers are Plants. All Orchids are Plants.

Logically valid conclusion(also happens to be true in the real world)

O

FP

All Orchids are Cats.All Cats are Plants. All Orchids are Plants.

All Orchids are Cats.All Cats are Plants. All Orchids are Plants.

O

CP

All Orchids are Cats.All Cats are Plants. All Orchids are Plants.

Logically valid conclusion(premises not true in the real world; conclusion true in the real world)

O

CP

All Orchids are Flowers.All Flowers are Domesticated (things). All Orchids are Domesticated (things).

O

FD

All Orchids are Flowers.All Flowers are Domesticated (things). All Orchids are Domesticated (things).

Logically valid conclusion(2nd premis and conclusion not true in the real world)

O

FD

A logically valid conclusion may not represent an empirical truth (i.e., be true in the real world)

So, a conclusion may be logically valid, but the syllogism as a whole may be false.

If one part of the syllogism is false

(e.g., All orchids are cats), then the whole

syllogism is false.

Trouble spot: Confirmation bias

All X are Y.

Some Y are Z.

Some X are Z.

Trouble spot: Confirmation bias

All X are Y.

Some Y are Z.

Some X are Z.

People make errors on whether the conclusion is valid.

Trouble spot: Confirmation bias

All Dalmations are Dogs.

Some Dogs are Smart.

Some Dalmations are Smart.

People make errors on whether the conclusion is valid.

Trouble spot: Confirmation bias

All Dalmations are Dogs.

Some Dogs are Smart.

Some Dalmations are Smart.

People make errors on whether the conclusion is valid.

Conclusion is Invalid (but the syllogism is true)

All Dalmations are Dogs.

Some Dogs are Smart.

Some Dalmations are Smart.

 check using Venn diagram

DALM

DOG

All Dalmations are Dogs.

Some Dogs are Smart.

Some Dalmations are Smart.

 check using Venn diagram

DALM

DOG

SMART THINGS

All Dalmations are Dogs.

Some Dogs are Smart.

Some Dalmations are Smart.

 check using Venn diagram

DALM

DOG

SMART THINGS

Logically, dalmations may not be smart

All Dalmations are Dogs.

Some Dogs are Smart.

Some Dalmations are Smart.

 check using Venn diagrams

The problem is that some Dalamations in the real world may, in fact, be smart.

People misapply this empirical truth to the validity of the conclusion—they end up judging that the conlusion is valid. The conclusion is invalid.

This error reflects a confirmation bias.

Logically, dalmations may not be smart

All Dalmations are Dogs.

Some Dogs are Smart.

Some Dalmations are Smart.

To help avoid an error, make substitutions (e.g., Marsupials for Smart)

All Dalmations are Dogs.

Some Dogs are Marsupials.

Some Dalmations are Marsupials.

All Dalmations are Dogs.

Some Dogs are Smart.

Some Dalmations are Smart.

To help avoid an error, make substitutions (e.g., Marsupials for Smart)

All Dalmations are Animals.

Some Dogs are Marsupials.

Some Dalmations are Marsupials.

Logically, dalmations may not be smart

Logically, dalmations may not be marsupials

Reasoning

Top-down biasessymbolic distance effectssemantic congruity effects

Formal logicsyllogismsconditional reasoning

Conditional reasoning

three parts1) conditional statement

(if thing 1 occurs, then thing 2 will occur)thing 1: antecedent; thing 2: consequent

2) evidence3) inference

In the abstract

1) Statement: If p, then q2) Evidence: p3) Inference: q

Conditional reasoningIn the abstract

1) Statement: If p, then q2) Evidence: p3) Inference: q

1) If you have As on all of your PSYC231 assignments (p), then you will get an A as your final mark (q).

2) Evidence: Have As on all assignments (p)

3) Inference: Get an A as final mark (q)

Conditional reasoning1) Statement: If p, then q2) Evidence: p3) Inference: q

1) If you have As on all of your PSYC231 assignments (p), then you will get an A as your final mark.2) Evidence: Have As on all assignments3) Inference: Get an A as final mark

Given the conditional statement and evidence, this inference (3) must be true; the argument as a whole is valid. This type of argument is referred to as affirming the antecedent (Latin name: modus ponens)

Other possibilities (other arguments)1) Statement: If p, then q2) Evidence: p (not p)3) Inference: q (not q)

1) If you have As on all of your PSYC231assignments (p), then you will get an A as your final mark (q).

2) Evidence: Do not have As on all assignments (~ p)

3) Inference: Do not get an A as final mark (~ q)

This conclusion (inference) is not logically true; the argument (called denying the antecedent)is invalid.

Other possibilities1) Statement: If p, then q2) Evidence: q 3) Inference: p

1) If you have As on all of your PSYC231 assignments (p), then you will get an A as your final mark (q).

2) Evidence: Get an A as final mark. (q)

3) Inference: Have As on all assignments (p)

This conclusion (inference) is not logically true; the argument (called affirming the consequent) is invalid.

Other possibilities1) Statement: If p, then q2) Evidence: ~ q 3) Inference: ~ p

1) If you have As on all of your PSYC231 assignments (p), then you will get an A as your final mark (q).

2) Evidence: Do not get an A as final mark. (~ q)

3) Inference: Do not have As on all assignments (~ p)

This conclusion (inference) must be true; the argument (called denying the consequent: Latinname: modus tollens) is valid.

Importance of modus tollens 1) Statement: If p, then q2) Evidence: ~ q 3) Inference: ~ p

Hypothesis testing: Test the Null Hypothesis

1) If conditions of some variable are similar (unimportant), then the variable should have no effect on performance.

2) Evidence: There is a an effect (a difference between conditions). (~ q)

3) Inference: The conditions are not similar. (~ p) (Rejection of the Null Hypothesis )

B U 3 6

B U 3 6

Rule: A card with a vowel will have an even number on the other side. Which card or cards should be turned over to test the rule?

B U 3 6

Rule: A card with a vowel with have an even number on the other side. Which card or cards should be turned over to test the rule?

People do pretty well applying modus ponens but have trouble applying modus tollens. (The problem is easier when real world examples are used.)

Reasoning

Top-down biasessymbolic distance effectssemantic congruity effects

Formal logicsyllogismsconditional reasoning

End

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