How Arguments Work

Deductive arguments

 A deductive argument is a structured set of premises from which a conclusion is drawn.

Examples:

Premise 1: All men are mortal.

Premise 2: Socrates is a man.

Conclusion: Socrates is mortal.

Premise 1: P or Q

Premise 2: Not P

Conclusion: Q

Premise 1: Giraffes are animals

Conclusion: Giraffes are animals

In these arguments, it is impossible for the conclusion to be false if the premises are true.

Rules of Deductive Arguments

Valid vs Invalid

If a deductive argument is valid, then its conclusion follows from the premises. In other words, if all the premises are true, then the conclusion must also be true.

An argument can be valid, but still false. Take the following argument for example:

Premise 1: Horses can fly

Premise 2: Jodie is a horse

Conclusion: Jodie can fly

This argument is false, because the first premise is false. However, this argument is valid, because if premise 1 and premise 2 were both true, then the conclusion must be true.

An invalid argument is one that can have all true premises and a false conclusion. For an argument to be invalid, it does not matter whether the premises or conclusion is true; it only matters that if the premises were all true, then it would be possible for the conclusion to be false.

Here is an example of an invalid argument:

Premise 1: Kangaroos live in Australia.

Premise 2: Circles are round.

Conclusion: Water is made of hydrogen and oxygen.

Even though all the premises and the conclusion are true, it is not a valid argument because it is possible that the conclusion could be false even with all the premises being true.

Sound vs Not Sound

For a deductive argument to be sound, it must be valid AND it must have all true premises.

Example:

Premise 1: The ocean is saltwater

Premise 2: Swordfish live in the ocean

Conclusion: Swordfish live in saltwater

Notice how if premise 1 and 2 are both true, the conclusion follows necessarily, and premise 1 and 2 are actually true.

Inductive arguments

An inductive argument is a structured set of statements in which the premises are taken to provide evidence for the conclusion.

Example:

Premise 1: Most people who play cards have fun

Premise 2: John is playing cards

Conclusion: John is having fun

*Note that in this argument, it is possible for the conclusion to be false even if the premises are true.

Inductive arguments are used in science to draw conclusions about the way the world works. We think that ravens are black, because the ravens we have observed have been black.

Abductive Arguments

An abductive argument is reasoning to the best explanation from a set of facts.

Example:

Fact 1: A cookie is missing
Fact 2: John has cookie crumbs on his shirt and chin
Fact 3: No one except John has been near the cookies.

Conclusion: John ate a cookie.

Abductive reasoning is the kind of argument that Sherlock Holmes uses to draw conclusions about crimes. This is also the kind of argument that is frequently used in courtrooms.