logic definitions and concepts

philo 1000

logic

science of arguments

arguments

a group of statements in which some statements are given as evidence for a specific statement

statement

a declaritive sentence that must be true of false

specific statement

conclussion

conditional statement

if ____, then ____ statement

• if antecedant, then consequent

• antededant = sufficient condition

• consequent = necessary condition

sufficient condition

a guarentee

• A is a sufficient condition for B when the occurence of A is all that is needed for the occurence of B

necessary condition

B is a necessary condition for A when A cannot occur without the occurence of B

inductive arguments

arguments in which the conclusion follows probably from the premisis

deductive arguments

arguments in which the conclusion follows necessarily from the premisis

validity

deductive arguments only

• the truth preserving quality of an argument

validity cont

in a valid argument

• if the premises are true, the conclusion must be true

• concerns the form of an argument

soundness

deductive arguments only

• applies to the truth of the premises

  • asks whether the premises are true

soundness cont.

premises = concerns the content of a valid argument

• only applies to valid arguments

  • the argument and its content are invalid

modus ponens

valid argument form

affirms the antecedent

• P1: if p, then q

• P2: P

• C: Q

modus ponens cont

P1: socrates is human, socrates is mortal

P2: socrates is human

C: socrates is motal

modus ponens (affirming the consequent, don’t do!)

P1: if p, then q

P2: Q

C: P

affirming the consequent

P1: if, socrates is human, socrates is mortal

P2: socrates is mortal

C: socrates is human

modus tollens

valid (denying the consequent)

P1: if P, then Q

P2: ~ Q

C: ~ P

modus tollens cont

P1: if socrates is human, socrates is moral

P2: S is not mortal

C: S is not human

denying the antecedent (don’t do)

P1: if P, then Q

P2: ~ P

C: ~ Q

denying the antecedent (don’t do)

P1: if s is human, s is mortal

P2: ~ s is human

C: ~ s is mortal

correlation = cause confusion

correlation = cause

• the mistake of treating a correlation as conclusive evidence of a direct casual connection

casual connection

might result from a common cause of the two events

correlation = cause confusion cont

• from coincidence

• may provide evidence of an alternative hypothesis

  • just as much as it provides evidence for the one you favor

strawman fallacy

a caricature of your opponents view which weakens theirs position and makes it easy to disprove

• literally from a straw figure that is easy to push down

  • Bishop Berkeley

begging the question

assuming the very point as issue

• involves circularity (circular argument)

begging the question cont.

subtler form of circularity/circular argument

• BTQ says it will inform you of X, but they assume the answer as part of their evidence

  • descartes = “I think, therefore I am”