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Inductive & Deductive Reasoning


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Define inductive reasoning.
Forming generalisations from examples or sample phenomena (which may be probable but not certain)
Define deductive reasoning.
Reasoning to a conclusion from a set of premises or statements, where the conclusion follows necessarily from the assumption that the premises are true.
What is affirmation of the consequent?
Belief that when a consequence is true, so to must be its antecedent.
What is modus ponens?
If A, then B - When A is true, so must B
What is modus tollens?
If A, then B - When B is false, so must A
What is denial of the antecedent?
If A, then B - When A is false, so must B (invalid)
- Context / background knowledge
What is a major factor for the acceptance of conditional reasoning?
Describe system 1?
Rapid, automatic response to problems
Describe system 2?
Slower, more reasoned and demanding response to problems.
- Pragmatic Strategy 1
What are Bonnefon's 4 major processing strategies?
Describe the pragmatic strategy
Rapid (as during a conversation) processing - high error rate
Describe the Semantic Strategy
Making use of background knowledge (though not as part of a coordinated argument) - moderate perfoemance
Describe the Inhibitory Strategy
Inhibition of pragmatic and semantic strategies. Focus only on the current
Describe the Generative Strategy
Combining the inhibitory strategy and abstract analytic processing. Best results
What is matching bias
The tendency for participants to select card (etc) matching the those named in the rule - regardless of whether the matched items are correct (eg Watson Selection Task)
What is a syllogism?
A logical argument consisting of two premises
What is belief bias?
In Syllogistic reasoning, the tendency to accept invalid conclusions that are believable or reject valid conclusions that are not.
What is a mental model?
In deductive reasoning, a representation of a possible state of affairs in the world
Define the principle of truth.
The notion that we represent assertions by constructing mental models concerning what is true BUT not what is false.
Permission rules:
What is a pragmatic Rule?
Social Contract Theory
Why do most people do better in pragmatic rule tasks than in Wason Selection Task?
What 4 4 reasons reasoning tasks are considered difficult?
- Need to disregard problem content and prior beliefs
Describe the Mood Heuristic.
When asking about mood, a preceding question may have direct influence of the answer
What is the Availability Heuristic?
Estimation of probability based on how easy it is a generate / think of instances.
What was Ross & Sicoly's (1979) finding, based on married couples, of the availability heuristic?
That division of labour (household chores) summed to well over 100% as both could more easily find instances of their own labour
What was Schwartz's finding, based on asking for instances of self-assertiveness, of the availability heuristic?
When asked to recall 6 events (rather than 12), people saw themselves as much more assertive (than those with more instances) - due to difficulty with recall of 12 instances
What is the Representativeness Heuristic?
Estimating the probability on the basis of similarity
What is the Base Rate Neglect
Ignoring that the probability of something belonging to a class depends on how common that class is.
What is the Conjunction Rule
The probability of a proposition cannot be less than the probability of the proposition conjoined with another proposition.
What is the Halo Effect
The tendency to use global evaluations to make judgments about specific traits. In other words, we use a global characteristic (such as attractive or likable) to determine specific personality traits (such as outgoing or kind).
What is the Narrative Fallacy?
The tendency to construct narratives based on flimsy evidence.
What is Hindsight Bias?
- Difficulty in remebering what we used to believe (Fischoff)
Self - evident :P
Define seeing patterns in random events.
Define Regression to the Mean
Whether we like it or not, extremes in performance etc are likely to be anomalous (self-evident)
- Appeal to popularity
What are Ricco's 6 Common Informal Fallacies?
Inductive reasoning
logic that is based on patterns and observations
Conjecture
An educated guess
conditional statement
a logical statement containing two parts: hypothesis and conclusion.
if/then form
when the hypothesis is contained by "if" and the conclusion by "then" in a conditional statement
Converse
(noun) A statement that switches the hypothesis and conclusion
Inverse
a + (-a) = 0 = (-a) + a OR a * 1/a = 1 = 1/a * a; a cant be 0
Contrapositive
when the hypothesis and the conclusion of a converse of a conditional statement are negated
p-->q
conditional statement
q-->p
converse
~p--.>~q
inverse
~q-->~p
contrapositive
~
not
p
hypothesis
q
conclusion
Law of Detachment
is p-->q is true, then p is true, and q is true
Law of Syllogism
if p-->q and q-->r are true, then p-->r is true
Counter example
Specific case for which the conjecture is false
Contra positive
Formed by negating the converse
hypothesis
an educated guess
Conclusion
Tells if your hypothesis was correct; supported or not supported
Negation
Adding "not" or removing it
Biconditional
Conditional statement where both the converse and inverse are true and uses the phrase "if and only if"
Deductive Reasoning
Reasoning from cause to effect, if this happens then this will happen.
Truth value
Truth or falsity of a statement
Postulate
A statement that does not have to be proven true
Proof
Numbered Logical argument that shows a statement is true
Theorem
A statement that is proved by reasoning deductively from already accepted statements.
inductive reasoning `
type of reasoning use to draw a general conclusion based of observations and patterns in a specific example
point
an exact location in space
Line
A straight path that goes without end in two directions.
line segment
Part of a line with two end points.
plane
A flat surface.
collinear
Points that lie on the same line
coplaner
points that lie on the same plane
opposite rays
2 rays that have the same endpoint and go in opposite directions forming a line
rays
An endpoint with a never ending line extending off one side