LOGIC AND REASONING Deductive Reasoning (Ex. All dogs are
animals, so my dog is an animal.)
MATHEMATICAL LOGIC Inductive Reasoning
-study of valid reasoning (Ex. Every object that I release from my hand
-deals with methods of reasoning falls to the ground. Therefore, the next object I
-provides rules/techniques whether an release from my hand will fall to the ground.
argument is valid
Every swan I have seen so far has been white,
PROPOSITION (STATEMENT) so the next swan I see will be white.)
-complete declarative sentence; a truth value
(T or F) Main Differences: Structure Strength
Negation of a Proposition Remarks:
-“negation connective” uses the symbol ~ or 1. The premises of a valid argument need not
(to mean not). have to be true. In fact, a valid argument may
have a false conclusion. (ROMY, COFFEE, BEER)
Argument (Mathematical Reasoning)
-a series of statements made in support of an 2. Inductive argument is never valid!
assertion together with the assertion drawn
from these supporting statements 3. Only valid arguments can be sound or
unsound.
Parts of an Argument:
premises – supporting statements 4. An invalid argument is never sound!
conclusion – assertion drawn from these
premises 5. If the argument form is valid, it is impossible
to find a counter-example.
ARGUMENT CAN BE CLASSIFIED according to Soundness of an Argument
how strong the relation of support between the -valid, and premises are true.
premises and the conclusion
Test of Validity
Types of Argument (Mathematical Reasoning): 1. the form of the argument
2. whether it is possible for that form to have
Structure Strength true premises and a false conclusion
DEDUCTIVE General (all, VALID if
REASONING always, never) premises are
to specific truth Euler Diagram -visually evaluate the validity of a
(strong) deductive argument (VENN DIAGRAM)
INDUCTIVE General MORE LIKELY
Invalid: if there is a way to draw the diagram
REASONING conclusion true (but
from specific could be that makes the conclusion false.
premises(some, false) If the premises are insufficient to determine the
most, %, often, -opinionated location of an element or a set mentioned in
usually)
the conclusion, then the argument is invalid.
Premise: If you bought bread, then you went to
the store. b → s
animals, so my dog is an animal.)
MATHEMATICAL LOGIC Inductive Reasoning
-study of valid reasoning (Ex. Every object that I release from my hand
-deals with methods of reasoning falls to the ground. Therefore, the next object I
-provides rules/techniques whether an release from my hand will fall to the ground.
argument is valid
Every swan I have seen so far has been white,
PROPOSITION (STATEMENT) so the next swan I see will be white.)
-complete declarative sentence; a truth value
(T or F) Main Differences: Structure Strength
Negation of a Proposition Remarks:
-“negation connective” uses the symbol ~ or 1. The premises of a valid argument need not
(to mean not). have to be true. In fact, a valid argument may
have a false conclusion. (ROMY, COFFEE, BEER)
Argument (Mathematical Reasoning)
-a series of statements made in support of an 2. Inductive argument is never valid!
assertion together with the assertion drawn
from these supporting statements 3. Only valid arguments can be sound or
unsound.
Parts of an Argument:
premises – supporting statements 4. An invalid argument is never sound!
conclusion – assertion drawn from these
premises 5. If the argument form is valid, it is impossible
to find a counter-example.
ARGUMENT CAN BE CLASSIFIED according to Soundness of an Argument
how strong the relation of support between the -valid, and premises are true.
premises and the conclusion
Test of Validity
Types of Argument (Mathematical Reasoning): 1. the form of the argument
2. whether it is possible for that form to have
Structure Strength true premises and a false conclusion
DEDUCTIVE General (all, VALID if
REASONING always, never) premises are
to specific truth Euler Diagram -visually evaluate the validity of a
(strong) deductive argument (VENN DIAGRAM)
INDUCTIVE General MORE LIKELY
Invalid: if there is a way to draw the diagram
REASONING conclusion true (but
from specific could be that makes the conclusion false.
premises(some, false) If the premises are insufficient to determine the
most, %, often, -opinionated location of an element or a set mentioned in
usually)
the conclusion, then the argument is invalid.
Premise: If you bought bread, then you went to
the store. b → s
