### Reasoning

```Reasoning
Lindsay Anderson
The Papers
“The probabilistic approach to human
reasoning”- Oaksford, M., & Chater, N.
“Two kinds of Reasoning” – Rips, L. J.
“Deductive Reasoning” – Johnson-Laird, P. N.
What is reasoning?
• A systematic process of thought that yields a
conclusion from percepts, thoughts, or
assertions
• Reminder:
Deduction: general -> specific
Induction: specific -> general
“The probabilistic approach to human reasoning”
Oaksford & Chater
People have successful reasoning in everyday
life, but they perform poorly on laboratory
WHY ?!?!?
First: Other Approaches to Reasoning
• Mental logic & Mental Model approaches:
- argue that systematic deviations from logic represent unavoidable
performance errors
- working memory limitations restrict reasoning ability
According to both: people rational in principle but err in
practice
______________________________________________
To resolve conflict, Other theorists propose that there are 2
types of rationality:
• Everyday rationality- does not depend on formal system like logic
• Formal rationality- is error prone
Still, how is everyday success explained?
Problem with Standard Logic
Allow “strengthening of antecedent”
-
“if something is a bird it flys”
If tweety is a bird, then can infer that tweety flies
Strengthening antecedent means that when given further info, like “tweety is
an ostrich” you still infer that “tweey flies”
Do this in standard logic because ostrich still a bird
This new info about ostrich should defeat the previous conclusion that tweety
flies
• Probabilistic handles this problem by using conditional
probability:
-
If tweety a bird, then probability of flying is high
If tweety an ostrich, probability of flying is 0
Probabilistic approach’s Solution…
• Errors on lab tasks because importing everyday,
uncertain, reasoning strategies into laboratory
• This seemingly “irrational behavior” is a result of the
behavior being compared to an inappropriate logical
standard
• When compare behavior to probability theory
instead of logic, reasoning seen more positively
Probabilistic Models applied in 3 main
areas of human reasoning research:
• Conditional Inference
• Syllogistic Reasoning
Applying probability approach to these areas explains
ppl’s lab performance as rational attempt to make
coping with everyday uncertainty
“Two kinds of reasoning”
Rips
• View 1: People can evaluate arguments in at least
2 qualitatively different ways:
- In terms of deductive correctness
- In terms of inductive strength
• View 2: Single Psychological continuum;
argument strength and correctness are functions
of arguments position on this continuum
- Deductively correct- max value on continuum
- Strong argument- high value on continuum
Unitary View of Reasoning
Implies only assess argument in terms of strength
But, maybe other ways people assess arguments (e.g.,
plausibility)?
Testing Unitary View
• If the Unitary View correct, then argument
evaluation one dimensional
• If Unitary does not hold true, then must
accept that there are other ways people
assess goodness of arguments
What they did (the experiment)
Participants evaluated arguments in terms of
correctness and strength
Deduction Condition: valid/not valid, then rated
condifence
Induction Condition: strong/not strong, then rated
degree of strength
Varied, wording of instructions to check whether
results depended on wording (no effect)
Results
For unitary to be correct,
increases in deductive
correctness should mimic
increases in inductive
strength (b/c reflecting
differences on same
underlying one-dimensional
scale)
As can see, this is not happening
Conclusion
• People not using probability as the SOLE basis
for both judgments
• Reasoning is not one-dimensional
“Deductive Reasoning”
Johnson-Laird
3 Principle Approaches to Deductive Performance:
1. Deduction as process based on Factual Knowledge
* 2. Deduction as formal, syntactic process
* 3. Deduction as semantic process based on mental
models
Deduction controversial: may rely on 1 of the above, or
some combination
Deduction as process based on factual
knowledge:
• Reasoning has nothing to do with logic
• Instead, reasoning based on memories of
previous inferences
• Come to conclusions based on our current factual
knowledge base
Problem: This theory does not explain why we can
Deduction as formal, syntactic process:
• Deduction relies on formal rules of inference
Rip’s Theory (& others)- proposes reasoners
extract logical forms of premises and use rules
to derive conclusions
- Rules for sentential connectives like “if” and
“or” and for quantifiers like “all” and “some”
- Based on natural deduction, so have rules for
introducing and eliminating sentential
connectives
• With rules, complications arise:
Ex: introducing “And”
A
B
Therefore A and B
Therefore A and (A and B)
Therefore A and [A and (A and B)]
As you can see, this gets very messy
Deduction as semantic process based
on mental models:
• Mental models are not based on arrangement
of words (syntax), rather they are based on
meaning
• Each mental model represents a possibility
- its structure and content capture what is
common about all the ways the possibility can
occur
Example
• “there are a circle and a triangle”
• Model captures whats common in any situation where
circle and triangle exist
• Given that premise is true, a conclusion is possible if in
at least 1 mental model
• If in all mental models, conclusion necessary
The Phenomena of Deductive
Reasoning
•
•
•
•
•
•
•
Reasoning with sentential connectives
Conditional reasoning