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Summary: logical strength and inductive and deductive arguments

Logical Strength and Weakness

Inductive arguments:

Inductive Strength and Weakness

Deductive arguments

Deductive Validity and invalidity

Deductively Valid Argument Forms

1. Disjunctive Syllogism

A disjunction is a complex proposition that has the form either p or q

Either you had white milk or you had chocolate milk

Either p or q (*note p and q are simple propositions that are combined

to form the complex proposition either p or q

p and q are the disjuncts (simple propositions) of the disjunction

(complex proposition) either p or q

example 1:

Either you had white milk or you had chocolate milk

You did not have white milk

Therefore, you had chocolate milk

Example 2:

One is either a cat person or a dog person

Socrates is not a dog person

Therefore, Socrates is a cat person

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Disjunctive Syllogism form

Either p or q.

Not-p

Therefore, q.

2. Reductio ad Absurdum

One way to show that a proposition is false is to show that a

contradiction follows from it

Socrates is an Olympian godshow this is false

(Note when we write out arguments in standard form, we can, for the

sake of clarity and convenience, label and number the premise(s) and

conclusion(s)

P1: Socrates is a man

P2: All men are mortal

C: Socrates is a man

Example

Demonstrate that the proposition “Socrates is an Olympian God” is

false

Assume P1: Socrates is an Olympian God

P2: Socrates died in 399 BC

C1: Therefore, Socrates is immortal (by P2) and mortal (by P3).

CONTRADICTION

C2: Therefore, the statement “Socrates is an Olympian God’’ is false.

(By Reductio ad Absurdum)

Explanation: the law of Non-Contradiction: contradictions cannot be

true. Therefore, any proposition that implies a contradiction cannot be true

Now we can take this one step farther: if one proposition is false, its

negation must be true

We know this by the law of the excluded Middle /bivalence(in classical

logical, true and false are your only values, there is no value in between)

Therefore, we can demonstrate a certain proposition to be true, by

assuming it to be false, or assuming its negation and then deriving a

contradiction

Socrates is not an Olympian God (~Socrates is an Olympian

God)prove this is true

Assuming its negation:

It is not the case that Socrates is not an Olympian God

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