M3S1 Flashcards
The essence of reasoning is a search for X
truth.
involves drawing conclusions from
facts, using logic.
Inductive reasoning
— Draws a conclusion from a generalization. For example, “All
the swans I have seen are white; therefore, all swans are probably white.”
Generalized
Draws a conclusion based on statistics. For example, “95
percent of swans are white” (an arbitrary figure, of course); “therefore, a
randomly selected swan will probably be white.”
Statistica
— Draws a conclusion about one group based on a different, sample
group. For example, “There are ten swans in this pond and all are white;
therefore, the swans in my neighbor’s pond are probably also white.”
Sample
Draws a conclusion based on shared properties of two groups.
For example, “All Aylesbury ducks are white. Swans are similar to Aylesbury
ducks. Therefore, all swans are probably white.”
Analogous
Draws a conclusion based on a prediction made using a past
sample. For example, “I visited this pond last year and all the swans were
white. Therefore, when I visit again, all the swans will probably be white.”
Predictive —
Draws a conclusion based on a causal connection. For
example, “All the swans in this pond are white. I just saw a white bird in the
pond. The bird was probably a swan.”
Causal inference —
begins with a broad truth (the major premise),
followed by the minor premise, (a more specific
statement), then the conclusion.
deductive
is black and white; a conclusion is
either true or false and cannot be partly true or partly
false.
Deductive reasoning
comes from general premises to
specific conclusions
Deductive reasoning
often
comes from specific examples to general conclusions.
inductive reasoning
is a representation, an explanation or an interpretation directly
accepted by us as something normal, self-evident, intrinsically
meaningful, like a simple, given fact.
Intuition
is an inferential argument for a mathematical statement. In the
argument, other previously established statements, such as theorems, can
be used
Proof
is perfect knowledge that has total security from error, or the
mental state of being without doubt.
Certainty
