Reasoning

1
Reasoning Top-down biases symbolic distance
effects semantic congruity effects Formal
logic syllogisms conditional reasoning
2
Reasoning Top-down biases effects of
knowledge on judgements/decisions symbolic
distance effects semantic congruity effects
3
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
4
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)
5
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
6
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 Re
sults 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.
7
Reasoning Additional distance effects and
semantic congruity effects Judgements of
object size (e.g., animals) form an image of
object Judgements on semantic
orderings time (e.g., seconds,
days) performance (e.g., poor,
excellent) temperature (e.g., cold,
hot) Judgements on geographical distance
8
Reasoning Formal logic syllogisms conditiona
l reasoning
9
Reasoning Syllogisms three statements stateme
nts 1 and 2 premises statement 3
conclusion The premises and conclusion may or
may not be true in the real world.
10
Reasoning Syllogisms three statements statemen
ts 1 and 2 premises statement 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
11
Example in Abstract Form All 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)
12

• Substitute real words for letters
• All Orchids are Flowers.
• All Flowers are Plants.
• All Orchids are Plants.
• Check with Venn diagrams.

13

• Substitute real words for letters
• All Orchids are Flowers.
• All Flowers are Plants.
• All Orchids are Plants.
• Check with Venn diagrams.

O
14

• Substitute real words for letters
• All Orchids are Flowers.
• All Flowers are Plants.
• All Orchids are Plants.
• Check with Venn diagrams.

F
O
15

• Substitute real words for letters
• All Orchids are Flowers.
• All Flowers are Plants.
• All Orchids are Plants.
• Check with Venn diagrams.

P
F
O
16

• All Orchids are Flowers.
• All Flowers are Plants.
• All Orchids are Plants.
• Logically valid conclusion
• (also happens to be true in the real world)

P
F
O
17

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

18

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

P
C
O
19

• 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)

P
C
O
20

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

D
F
O
21

• 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)

D
F
O
22
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.
         
23
Trouble spot Confirmation bias All X are
Y. Some Y are Z. ? Some X are Z.  
         
24
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.
         
25
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.
         
26
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)
         
27
All Dalmations are Dogs. Some Dogs are Smart. ?
Some Dalmations are Smart.  check using Venn
diagram
         
DOG
DALM
28
All Dalmations are Dogs. Some Dogs are Smart. ?
Some Dalmations are Smart.  check using Venn
diagram
         
SMART THINGS
DOG
DALM
29
All Dalmations are Dogs. Some Dogs are Smart. ?
Some Dalmations are Smart.  check using Venn
diagram
         
Logically, dalmations may not be smart
SMART THINGS
DOG
DALM
30
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 conclusionthey end up judging that the
conlusion is valid. The conclusion is
invalid. This error reflects a confirmation bias.
         
Logically, dalmations may not be smart
31
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.
         
32
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
33
Reasoning Top-down biases symbolic distance
effects semantic congruity effects Formal
logic syllogisms conditional reasoning
34
Conditional reasoning three parts 1)
conditional statement (if thing 1 occurs, then
thing 2 will occur) thing 1 antecedent thing
2 consequent 2) evidence 3) inference In the
abstract 1) Statement If p, then q 2)
Evidence p 3) Inference ? q
35

• Conditional reasoning
• In the abstract
• 1) Statement If p, then q
• 2) Evidence p
• 3) Inference ? q
• 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)

36

• Conditional reasoning
• 1) Statement If p, then q
• 2) Evidence p
• 3) Inference ? q
• 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 assignments
• 3) 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)

37

• Other possibilities (other arguments)
• 1) Statement If p, then q
• 2) Evidence ? p (not p)
• 3) Inference ? ? q (not q)
• 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.

38

• Other possibilities
• 1) Statement If p, then q
• 2) Evidence q
• 3) Inference ? p
• 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.

39

• Other possibilities
• 1) Statement If p, then q
• 2) Evidence q
• 3) Inference ? p
• 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
  Latin
• name modus tollens) is valid.

40

• Importance of modus tollens
• 1) Statement If p, then q
• 2) Evidence q
• 3) Inference ? p
• Hypothesis testing Test the Null Hypothesis
• 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 )

41
(No Transcript)
42
B
U
3
6
43
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
44
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?
B
U
3
6
People do pretty well applying modus ponens but
have trouble applying modus tollens. (The
problem is easier when real world examples are
used.)
45
Reasoning Top-down biases symbolic distance
effects semantic congruity effects Formal
logic syllogisms conditional reasoning
46
End Have a good day!