Critical thinking is the art of reasoning well. Since good reasonong involves arguments, we start with them.

An argument is a series of statements consisting of premises and a conclusion.
A statement is a sentence which has a truth value, that is, in a two-valued logic, is true or false (Hence, questions, exhortations, or commands are not statements)
A statement is a premise in an argument A if its truth is assumed, at least hypothetically, and not established by A.
A conclusion in an argument A is a claim whose truth is supposed to be established by A.
The premises are supposed to provide support for the conclusion so that if one grants their truth, then one should grant that the conclusion is true or, depending on the nature of the argument, likely to be true.

1.All men are mortal (premise)
2.Bob is a man. (premise)
3.Therefore, Bob is mortal. (conclusion)

1. If it snows, then it’s cold (premise)
2. It snows (premise)
3. Therefore, it is cold (conclusion)

Often some of the premises of an argument support as a conclusion a statement serving itself as a premise in the argument for the final conclusion. Such a statement is a sub-conclusion of the argument. Arguments can have any number of premises (even just one) and sub-conclusions.

1. If it snows, then it’s cold (premise)
2. It isn't cold (premise)
3. Therefore, it doesn't snow (sub-conclusion)
4. Either it snows, or Bob is out playing football (premise)
5. Hence, Bob is out playing football (final conclusion)

Unstated premises
Often arguments have unstated premise(s), that is, premise(s) that need to be added for the premises to support the conclusion. It's always instructive to try to state all the premises necessary to support one’s conclusion.
1. If it snows, then it’s cold
2. If it’s cold, Jim is at home
3. Hence, Jim is at home.

Here, there is an unstated premise (it snows) and an unstated sub-conclusion (it’s cold)

Types of arguments: deductive and non-deductive

A. Deductive arguments:
The support the premises provide to the conclusion in a deductive argument is an all or nothing affair.  A valid deductive argument is an argument such that it is impossible for the premises to be true and the conclusion false, i.e., such that if the premises were true (whether or not they actually are), then the conclusion would be true.
1. If it snows, then it's cold
2. It snows
3. Hence, it's cold.
An argument is valid/invalid because of its form (in the example, "if A, then B; A; hence, B).
An argument can be valid even if its premises and conclusion are false.
An argument can be invalid even if its premises and/or conclusion are true.

Informal testing for deductive validity: If you can describe circumstances, even fictional ones, in which the premises are true and the conclusion false, then the argument is invalid. In other words, if you can consistently deny the conclusion while affirming the premises, the argument is invalid.


1. Brown’s fingerprints were on the murder weapon

2.  100 seemingly reliable witnesses claim they saw Brown commit the murder

3.  Brown confessed to the murder

4. Hence, Brown is the murderer


While (4) is most likely true if the premises are true, the argument is nevertheless not valid.  In fact, imagine the following.  The real murder, Brown’s cousin George, managed to put Brown’s fingerprints on the murder weapon.  The witnesses have been bought off by George with the promise of free trips to Florida.  Brown has been drugged by George with a chemical that convinced Brown he is the murderer.  That’s a scenario that makes the premises true but the conclusion false.


B. Non-deductive arguments
Non-deductive arguments are deductively invalid because the truth of the premises does not guarantee the truth of the conclusion.  The support provided for the conclusion in a non-deductive argument is a matter of degree: the truth of the premises makes the truth of the conclusion more (or less) probable. Thus, non-deductive arguments are either strong or weak. The premises of a strong non-deductive argument make it probable that the conclusion is true.
There are two types of non-deductive arguments: inductive and abductive

Examples of inductive arguments:
1.All observed emeralds have been found to be green
2.Therefore, the next observed emerald will be green.

1.In the past, sugar cubes have dissolved in water
2.Thus, this sugar cube will dissolve in water.

1. Most SIUE students are from Illinois
2. Jim is a SIUE student

3. Therefore, Jim is from Illinois

Examples of abductive arguments

Argument by analogy:
1.Lungs are similar to machines in that they are adapted to a particular purpose.
2.Machines are the product of intelligent design.
3.Therefore, lungs are the product of intelligent design.
Argument to the best explanation:
1.Laboratory animals given water flowing from the new chemical plant get sick.

2. The river people got sick after the plant was opened.
3.Therefore, the current sickness among the river people is caused by the new chemical plant.

How to analyze arguments:
1.Find the conclusion.  This is generally what the proponent of the argument is trying to get you to believe.
2.Find the premises, that is, the statements the argument assumes.
3.Eliminate any unnecessary rhetorical fluff.
4.Are there any implicit (unstated) premises?
5.What kind of argument is the author trying to make (i.e., deductive, inductive, abductive)?
Once you have reconstructed the argument, evaluate it by investigating two things:
1.Is the argument valid or non-deductively strong?
2.Are the premises true, or plausible?

NOTE: Suppose you analyze an argument and find out that it is unsatisfactory.  It does not follow that its conclusion is false.

What next?
If the argument is formally incorrect (i.e., invalid or inductively/abductively weak) and/or the premises are false or questionable, it does not follow that it is worthless.  It is a good practice to try to fix the argument by supplying needed premises, and see whether the new argument is satisfactory.