SPRING Reasoning Flashcards
what is deductive reasoning
conclusion that necessarily follows given that the statements are assumed to be true
logic as normative theory
what is inductive reasoning
generalised conclusions that goes beyond the informatino provided
ie scientific reasoning and theories
what are conditionals
deductive reasoning forms
if….then…
if the condition and premise are assumed to be true then the conclusion is logically also true
what are syllogisms
a form of reasoning in which a conclusion is drawn from two given or assumed propositions (premises); a common or middle term is present in the two premises but not in the conclusion, which may be invalid
“some..all..that…are..”
what are relational inferences
making inferences about the relationship between things
ie a>b b>c so a>c
why do we make deductive inferences? (johnson laird and byrne 1991
form plans eval actions interpret and formuate rules/principles pursue arguements weigh evidence compare theories solve problems
what four deductive inferences can be made
valid: modus ponens and modus tollens
invalic: affirmation of the consequence and denial of the antecedent
what is the atecedent
if….. part of the reasoning format
what is the consequent
then…
describe modus ponens
method of affirming the antecedent
logically the consequent follows
90-100% correct
“bob is poisoned”
describe modus tollens
denial of the consequent
logically the antecedent would be false
60% correct
“bob does not die”
describe affirmation of the consequent
logically invalid - should the consequent be true then nothing will follow as may be many causes
40-50%
“bob dies” - any cause
describe denial of the antecedent
logically invalid - should the antecedent be denied, not logically valid to assume the consequent would not still occur - many different factors that also lead to the consequent so stil occur
40-50% correct
“bob is not poisoned” - still die of other causes
what are biconditional arguements
if and only if
following these, all four inferences would be valid
mental models theory (johnson laird and byrne)
when we reason we think about different possibilities - construct based on our understanding of the premise and general knowledge of the world - what is possible, probable and necessary
develop initial model, generate conclsion and look for counter examples to check for validity
BUT dont initially think about all possibilities - MP explicit but MT, DA AND AC implicit and tend to use heuristics
therefore get wrong as dont think further
mental models and MP > MT
MP is explicit “if p then q; p; therefore q) explicitly what is true
but MT requires recognising at least one more model to get the correct answer (if p then q; not-q; therefore not-p)
must flesh out models - do not represent the case ‘not-q’ in their initial model of the conditional
mental models MP > DA, AC
AC AND DA require 2+ counter examples
even more fleshing out of model
‘if p then q; not p - not q BUT ALSO Q’
‘if p then q; q - p BUT ALSO NOT P’
define the principle of truth
minimise working memory load by constructing mental models that represent what is explicitly true but not what is false (pos or neg)
therefore bad at holding information that holds untrue elements
copeland and radvansky 2004 mental models and wm capacity
ability to construcy mental models limited by wm
MP - 1 mental model - 83% correct
MT - 2 models - 39% correct
AC/DA - 3+ models - 31% correct
pos corr between wm capacity and performance on reasoning tasks
legrenzi, girrotto and johnson laird 2003 illusory inferences
more difficult as need to bear in mind true and false information
“only one is true….the following is definitely true….are the assertions consistent with the consequent?” - no, only one can be true but majority say yes
adv of mental models
goood account of general approach to reasoning - prev theories tend to rely on mathematical proof and what seems most likely to occur
describe dual systems theory
apply broadly to rationality judgement, decision making and reasoning
two systems:
1 - universal, automatic, fast heurstic
2 - limited capacity, deliperative, slow, effortful, wim and permits abstract hypothetical thinking
reasoning mostly knowledge and context and deductive reasoning later
define the singularity principle (dual systems heuristic)
only one mental model may be considered at any one time
define the relevance principle (dual systems heurstic)
the most relevant model is based on prior knoweldge and experience and is considered first
define the satisficing principle (dual systems heuristic)
eval of current model to determine if appropriate - if conclusion is probable
if seems likely then accept even if not logically valid
define belief bias
Given things that look like they link
And given conclusions that may or may not be believable
Good evidence that the believability of conclusions impacts whether we accept them or not
- ability to resolve conflict logcally correlates with cog ability ( use of wm sys 2)
evans barston and pollard 1983 validity and belief
validity - tendency to accept valid conclusions and reject invalid - logically competent
belief - tendency to accept believable conclusions- not always logical
validity x belief - can work together or against
believability effects are much stronger for invalid syllogisms/inferences – belief bias acceptance of too many believable, invalid conclusions – if see an invalid conclusion and sounds believable then more likely to accept that – general knowledge/context input
eval dual systems
includes heursitics and can be broadly applied
oversimplifies the distinction between heturistic and analytic procedures
theories of deductive performance
performance based on factual knowledge “cased based”
deduction as a formal syntactic process “sentential”
mental models
dual process
describe performance based on factual knowledge “case based reasoning”
mind uses content specific conditional rules to make inferences from general knowledge
rules - triggered by current content of wm > actions - ass new info to wm developing a chain of inferences
reasoning is based on memory of prev inferences
reasoning not logical - chain of inferences made from contect specific rules developed via experience thar are applied to new situations
new problems solved by finding a similar past case and revising in a new problem situation
problem with cased based knowledge on reasoning
cant explain how people are able to successfully reason about unknown or uncertain situations
do not fully understant the characters or the situations and cannot refer to previouus situations
deduction as a formal syntactic process
“sentential reasoning”
braine 1998
reasoners extract logical forms of premises and use rules to derrive conclusions
reasoning that hinges on
the use of negation and sentential connectives, such as “if,” “or,” and “and.” and quantifiers ie “all” “some”
have an inference system that holds a set of deduction rules which constructs proofs in wm - rules contruct proof of concl from premise
rips 1994 sentential reasoning
attempt to solve deductive problems by generating in wm a set of sentences linking the premise of the prob to the conclusion
each link embodies an inference rule - provides a bridge between the premise and conclusion that explains WHY the conclusion follows
incorrect deductions because not possess/not able to apply inference rule for a proof
disadv mental models
not as good at accounting for specific strategies - use of heuristics ignored
diff between mental models and dual systems
mental models - resoning initially based on internal cog knowledge
THEN deductive reasoning applied - flesh out models to come to the right answer but tend to not
dual systems - 1 and 2 occur in parallel - first to come up with what seems like a reasonable answer is what is acccepted- lead to BELIEF BIAS - accept invalid conclusion if believable because sys 1 faster
