Reasoning Flashcards
reasoning
the cognitive process of deriving new information from old information
deductive reasoning
general –> specific
starts with general premises and draws specific conclusions, like “All humans are mortal, and John is a human, so John must be mortal.”
- logically true, but also realistically true
Inductive reasoning
specific –> general
infers general principles from specific observations, such as “Every swan we’ve seen is white, so we conclude that all swans are white.”
- logically true, but may not realistically be true
abductive reasoning
suggests the most plausible explanation for observed phenomena, like “The grass is wet, so it might have rained.”
premises
statements assumed to be true, from which conclusions are drawn
valid
arguments in which the conclusion must be true if the premises are true
Two types of deductive reasoning
propositional and syllogistic reasoning
propositional reasoning
reasoning about statements connected by logical relations such as “and”, “or”, “not”, “if”
evaluates logical relationships between statements, such as “If it’s raining, then the ground is wet.”
syllogistic reasoning
reasoning about groups/sets using statements connected by logical relations of “some”, “none”, “all”, and “some not”
involves deducing conclusions from two premises, like “All mammals are warm-blooded, and whales are mammals, so whales are warm-blooded.”
inference rules
guide logical deductions from premises to conclusions. Valid deductive reasoning patterns used to draw conclusions from premises in a logical and consistent manner.
Three types: modus ponens, modus tollens and hypothetical syllogism
modus ponens
Affirming the antecedent; if A implies B, and A is true, then B must be true.
Example: If it is raining (A), then the ground is wet (B). It is raining (A is true). Therefore, the ground is wet (B is true).
modus tollens
Denying the consequent; if A implies B, and B is false, then A must be false.
Example: If it is raining (A), then the ground is wet (B). The ground is not wet (B is false). Therefore, it is not raining (A is false).
hypothetical syllogism
is like connecting two “if-then” statements to reach a conclusion
Example: If it is raining (A), then the ground is wet (B). If the ground is wet (B), then people might slip (C). Therefore, if it is raining (A), then people might slip (C).
double negation
Asserting a positive statement by denying its negation.
“It is not untrue that John is happy” implies “John is happy.”
Two main logical fallacies
- Affirming the consequent
- Denying the antecedent
They represent errors in reasoning rather than valid forms of logical inference.
affirming the consequent
Assuming that because something happens (the consequent), something else must have happened before it (the antecedent).
For example, “If it’s raining (A), the ground gets wet (B). The ground is wet (B), so it must have rained. (A)”
denying the antecedent
Assuming that because something didn’t happen (the antecedent), something else couldn’t have happened afterward (the consequent).
For example, “If it’s raining (A), the ground gets wet (B). It’s not raining (A is false), so the ground must not be wet. (B is false)”
mental models approach
the view that people tackle logical reasoning problems by forming mental representations of possible states of the world and draw inferences from those representations
categorical syllogisms
simple deductions using categories. They involve three parts:
1. general statement (major premise)
2. specific statement (minor premise)
3. conclusion.
For example, “All humans are mortal (major premise), Socrates is a human (minor premise), so Socrates is mortal (conclusion).”
atmosphere effect
a tendency to draw conclusions in syllogisms that are over influenced by the form of the premises rather than the logic of the argument
mental model approaches to syllogisms
people create mental pictures to understand logical statements. They build these mental models based on the information given and check if they fit the conclusion. By simplifying and adjusting these mental images, individuals figure out whether the conclusion makes sense. It’s about how our minds naturally visualize and reason through logic puzzles.
belief bias
when our existing beliefs influence how we evaluate arguments, sometimes leading us to accept invalid reasoning because it aligns with what we already believe
dual system theory by Kahneman & Tversky
suggests that human thinking operates through two distinct systems: System 1 and System 2.
System 1: intuitive and automatic
System 2: analytical and slower
Helps explain how humans process information and make decisions, highlighting the interplay between intuitive and analytical thinking processes.
hypothetico-deductive reasoning
a form of inductive reasoning which is a problem-solving approach where hypotheses are formed and then tested through deductive reasoning to confirm or reject them.
