DEDUCTIVE & INDUCTIVE ARGUMENTS

Deductive Arguments

Deductive Arguments For a deductive argument, if all its premises are true, its conclusion is necessarily true (or it is logically impossible for the conclusion to be false.) I.e., the truth of premises guarantees the truth of conclusion. E.g.: Either you work hard or you will fail the test. You do not work hard. Therefore, you will fail the test.

3 Types of Possibility Technological possibility Physical possibility e.g., Going to the moon is technological possible, but going to Mercury is not. Physical possibility e.g., Going to Mercury is physical possible, but making water boil at 95 C under one atmospheric pressure is not. Logical possibility e.g. Making water boil at 95 C under one atmospheric pressure is logical possible, but drawing a triangle with 4 angles is not.

Deductive Arguments When we talk about deductive arguments, we have already presupposed that the arguments are successful or valid deductive arguments. The conclusion of a valid argument is called a valid conclusion.

Deductive Arguments For an unsuccessful deductive argument (the premises are intended to guarantee the conclusion but fail to do so), we call it an invalid argument. A deductive argument may be valid or invalid, there is nothing in between.

Deductive Arguments Whether a deductive argument is valid or invalid depends on its form or structure, not on its content. The above argument is valid because it has this valid form: p or q. Not-p. Therefore, q. p and q are statement variables. A letter represents a term.

Deductive Arguments Any argument having that form will also be a valid argument. There are infinite possible valid structures. Here are some common examples: If p, then q p____  q Not-q____  Not-p

Here are more examples: If p, then q If q, then r  If p, then r If p and q, then r p_____________  If q, then r

Deductive Arguments A valid argument may have false conclusion if it has false premises. E.g.: CY Leung is either a genius or an idiot. He is not an idiot. Therefore, He is a genius.

Deductive Arguments In order to guarantee the truth of conclusion, we have to make sure all the premises are true. When all the premises of a valid argument are true, the argument is called a “sound argument”. And the conclusion of a sound argument is called a sound conclusion. If an argument is invalid or has false premises, it is unsound.

Deductive Arguments On the other hand, the fact that an argument is invalid does not entail that its conclusion is false. It just means that its conclusion does not follow from its premises. You can consider a valid argument structure as a truth-keeping machine: When you input T information into it, it will output T information. When you input F information into it, it will output T or F information.

Inductive Arguments

A typical example of inductive argument: Swan1 is white. Swan2 is white. Swan3 is white. … Swann is white. ________________ All swans are white.

Another typical example: An event of type B follows an event of type A at time t1. An event of type B follows an event of type A at time t2. … An event of type B follows an event of type A at time tn. ___________________________ A causes B.

Many people think that the characteristic of inductive arguments is arguing from particular to general. However, deductive arguments may also argue from particular to general, e.g.: I have two cats, Fluffy and Garfield. Fluffy does not eat fish. Garfield does not eat fish either._____ Therefore, All of my cats do not eat fish.

Some inductive arguments may argue from general to particular, e.g.: Most of our students are born in HK. Jim is one of our students. Therefore, Jim is born in HK.

Inductive Argument The main difference between deductive arguments and inductive arguments is that, for the latter, if all its premises are true, its conclusion is likely to be true but still possible to be false I.e., The truth of its premises makes it reasonable to hold that the conclusion is true but the content of the premises does not include (imply) the content of the conclusion.

Inductive Argument We call a good inductive argument a strong argument, a bad inductive argument a weak argument. Whether an inductive argument is strong or weak depends on its content, not on its structure.

Inductive Argument These 2 arguments have the same structure but one is strong and the other is weak: HK is a wealthy society. Therefore, most of HK people are wealthy. HK is a Chinese society. Therefore, most of HK people are Chinese.

Inductive Argument Even for a strong argument, if its premises are false, we still have no reasons to believe in the conclusion. If all the premises of a strong argument are true, the argument is called a “cogent argument.” The conclusion is called a “cogent conclusion.” If an argument is weak or has false premises, it is uncogent.

Composite Arguments

If an argument is made up of two deductive sub-arguments, the whole argument is still a deductive argument.

Example: Either you work hard or you will fail the exam. You do not work hard. So, you will fail the exam. (Sub-conclusion) If you fail the exam, you need to retake the course. Therefore, you need to retake the course.

If an argument consists of a deductive sub-argument and an inductive sub-argument, the whole argument is an inductive argument.

Example: Either you have enough sleep or you will feel sleepy in class. You do not have enough sleep. So, you will feel sleepy in class. (Sub-conclusion) Most students who feel sleepy in class have poor grades. Therefore, you will have poor grades.