Deductive Arguments CH : 2 - PHIL 121

Deductive Argument

The conclusion (3) follows necessarily from premises 1 and 2. If those premises are true, they guarantee the truth of the conclusion: It would be impossible for the conclusion to be false.

Inductive Argument

The conclusion is certainly supported by the premises, but it would be possible for the conclusion to be false even if the premises are true

syllogisms

simplest form of a deductive argument

hypothetical syllogism

The premise is a compound statement which, as we saw in Chapter 1, does not assert that either of the component propositions p and q is true, nor that either of them is false; what it asserts is a relationship between p and q.

Example of Hypothetical Syllogism

If robbery were the motive, then the victim’s money would’ve been taken | The victim’s money was not taken | → Therefore robbery was NOT the motive

Example of Hypothetical Syllogism

If the victim died of a gunshot to the back, then he was murdered | the victim died of a gunshot to the back | → the victim was murdered

Disjunctive Syllogism

disjunctive statements do not assert either of the components as true (or false); they assert only that one or the other is true. But if we also know that one of them is not true, we can draw the obvious conclusion in a disjunctive syllogism:

example of disjunctive syllogism

either the motive of the murder was robbery or vengeance | the motive was not robbery| → the motive was vengeance

categorical syllogism

Another type of deductive argument involves noncompound statements, and the conclusion follows because of the repetition of subject and predicate terms in the statements. the premises and conclusion assert something as categorically true.

example of categorical syllogism

all water flows downhill | All rivers in Taiwan are water | → therefore all rivers in Taiwan flow downhill

example of categorical syllogism

No us senator is under the age of 30 | Chuck Shumer is a U.S Senator | → Therefore chuck shumer is not under the age of 30

validity

In each of these deductive arguments, there is no gap between premises and conclusion. If the premises are true, the conclusion must be true as well. If you accept the premises but deny the conclusion, you contradict yourself