Reasoning
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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?.

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Reasoning

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Reasoning

Reasoning

Lindsay Anderson


The papers

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

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

“The probabilistic approach to human reasoning” Oaksford & Chater

PARADOX

People have successful reasoning in everyday life, but they perform poorly on laboratory reasoning tasks

WHY ?!?!?


First other approaches to reasoning

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

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

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

Probabilistic Models applied in 3 main areas of human reasoning research:

  • Conditional Inference

  • Wason’s selection task

  • Syllogistic Reasoning

    Applying probability approach to these areas explains ppl’s lab performance as rational attempt to make sense of the lab tasks by using strategies adapted for coping with everyday uncertainty


Two kinds of reasoning rips

“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

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

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

What they did (the experiment)

Participantsevaluated arguments in terms of correctness and strength

DeductionCondition: valid/not valid, then rated condifence

InductionCondition: strong/not strong, then rated degree of strength

Varied, wording of instructions to check whether results depended on wording (no effect)


Results

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

Conclusion

  • People not using probability as the SOLE basis for both judgments

  • Reasoning is not one-dimensional


Deductive reasoning johnson laird

“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

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 reason about the unknown


Deduction as formal syntactic process

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


Reasoning

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

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

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

The Phenomena of Deductive Reasoning

  • Reasoning with sentential connectives

  • Conditional reasoning

  • Reasoning about Relations

  • Syllogisms and reasoning with quantifiers

  • The effects of content on deduction

  • The Selection Task

  • Systematic Fallacies in Reasoning

    (in the context of these phenomena, author discusses evidence for/against 3 main theories so you can arrive at your own conclusion)


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