Lecture 7: Reasoning Flashcards
Inductive reasoning
aimed at the discovery or construction of a generalized principle by making use of particular cases
-increases semantic information
o The burglary was committed at 8 - 8.30
o Adam was seen running from the house at 8.15
• We may conclude that Adam was involved in the burglary - but it is not necessarily the case
• We add our knowledge of burglaries to the information presented
• Induction often yields plausible conclusions, but they are not necessarily true
Deductive reasoning
It is the ability to draw some logical conclusions from known statement or evidences. Here one starts with already known or established generalized statement or principle and applies it to specific cases. For example, all human beings are mortal you are a human being, therefore, you are mortal.
Syllogisms
• A syllogism consists of two premises and a conclusion and uses quantity terms like all, some, none etc.
• For example:
o All artists are beekeepers
o All beekeepers are chemists
All artists are chemists
• This is a valid argument form – it is truth preserving. This means that if the premises are true then the conclusion will also be true
Propositional reasoning
=the ability to draw conclusions on the basis of sentence connectives such as “and,” “if,” “or,” and “not.”
Conditional reasoning
Conditional reasoning is based on an ‘if A then B’ construct that posits B to be true if A is true.
Note that this leaves open the question of what happens when A is false, which means that in this case, B can logically be either true or false.
Belief Bias
- We are seduced by the believability of conclusions rather than their validity
- Truth and validity are not the same thing, people make snap judgements about whether they believe the conclusion or not without looking at whether it follows or not
Modus ponens
This is a valid inference form – it is truth preserving and will always yield true conclusions from true premises
Modus tollens
a valid argument form and is truth preserving
Affirmation of the consequent
This is not a valid argument form as it will not necessarily always give true conclusions from true premises
Denial of the antecedent
invalid argument form as it will not necessarily always give true conclusions from true premises
Are humans logical?
Marcus and Rips (1979)
o The modus ponens inference (MP) is drawn almost universally
o The modus tollens inference (MT) is drawn less frequently
o Both the affirmation of the consequent (AC) and denial of the antecedent inferences are drawn between c. 30-40% of the time
Abstract rule theories
• Numerous versions of mental logic and they are not all the same (although they share some basic principles)
• People are rational - we have some rules of logic or specialised processes for logical thinking
• We make mistakes because:
o we misunderstand or misrepresent the task (Henle, 1962)
o we lack the necessary rules of logic
o resource limitations
Braine’s abstract rule theory
• Comprehension component
o In the first stage of the theory the premises must be converted into a mental representation that can be held in working memory
• Application of rule schemas (rules of logic like modus ponens)
o core and feeder schemas (feeder schemas provide intermediate conclusions to which core schemas can be applied)
• Incompatibility rules
o check for inconsistent or contradictory reasoning (such as concluding both p and not-p)
Braine’s abstract rule theory: Limitations
- The theory is incomplete - it states little about the comprehension component
- Propositional reasoning is only one type of reasoning - it is unclear whether abstract rules can account for other types
- Context and content have a dramatic effect on reasoning and this is difficult to reconcile with a theory that proposes abstract, content free rules of reasoning
- There is ultimately no compelling evidence that people use any type of logic when attempting to solve deductive problems
- Numerous alternative explanations – mental models, information gain, pragmatic reasoning schemas
