Recall that an arguer claims two things:

1. That the premises are all true (or reasonable to believe);

   AND

2. That the premises, if true, support the conclusion.

The first claim is the FACTUAL claim; the second is the INFERENTIAL claim.

An argument has good logic when the inferential claim is true. In other words, an argument has good logic when its premises, if true, support its conclusion. When an argument has good logic, we say its conclusion follows from its premises.

Bad or incorrect logic occurs when the inferential claim is false: the premises if true fail to support the conclusion. The conclusion does not follow from the premises.

It is extremely important that you understand exactly what we mean by “support.” We said an argument has good logic when its premises support its conclusion. By this we mean either:

1.     That the premises if true guarantee the truth of the conclusion.

OR

2.     That the premises if true make the conclusion likely.

If an arguer claims support in the first way above, she is said to be arguing deductively. That is, when an arguer argues deductively, she is claiming that the premises guarantee the truth of the conclusion, i.e., she is claiming the conclusion can’t be false if the premises are true.

Typical kinds of deductive arguments include

• Argument based on mathematics
• Argument from definition
• Categorical syllogism
• Hypothetical syllogism (argument containing one or more conditional premises)
• Disjunctive syllogism

If an arguer claims support in the second way above, she is said to be arguing non-deductively, or inductively. That is, when an arguer argues inductively, she is claiming that the premises make the conclusion likely, i.e., the conclusion might be false if the premises are true, but it’s not likely to be false if these premises are true.

Typical kinds of inductive arguments include

• Predictions
• Argument from analogy
• Generalization from a sample
• Argument from authority
• Argument based on signs
• Causal inferences

To sum up so far, an argument has good logic if the inferential claim is true: i.e., the premises support the conclusion. There are two senses of "support": the deductive and inductive senses. Deductive arguments with good logic are those in which the conclusion really is supported by the premises in the deductive sense, i.e., the conclusion really must be true (it cannot be false) if the premises are true. We call deductive arguments with good logic valid arguments.

By contrast, deductive arguments with bad logic are those in which the arguer claims the premises guarantee the conclusion, but the arguer is mistaken: it is possible after all for the premises to be true and the conclusion false. Such arguments are called invalid.

Likewise, inductive arguments with good logic are those in which the conclusion really is supported by the premises in the inductive sense, i.e., the conclusion really is likely if the premises are true. Such arguments are usually called strong . Inductive arguments with bad logic are called weak. Weak arguments are those in which the arguer claims the premises make the conclusion likely, but the arguer is mistaken: the conclusion isn’t really likely.

Notice that in all this discussion of good and bad logic, we have said NOTHING about whether the premises are in fact true. That’s because an argument can have good logic — the inferential claim can be true (the premises can support the conclusion) — even if its premises are false. This is because false statements have logical consequences just like true ones. I am not saying you should accept arguments with false premises. Such arguments are defective, of course, and should be rejected. You want arguments to have both good logic and true premises. I am saying that good logic and true premises are two different things. An argument can have good logic — its premises can support its conclusion in the sense of “support” described above — even if its premises are in fact false.

Here’s an example.

All bears fly.

Lassie is a bear,

Therefore, Lassie flies.

Do you see how this argument is logically correct, in the sense that its premises if true support its conclusion? I.e., its conclusion must be true if its premises are true? I.e., it follows from these premises that Lassie flies? The premises of this argument are not true, but the conclusion would have to be true if the premises were true.

An argument like this is logically correct but factually incorrect. It passes step 3 of the Critical Thinking Checklist, but fails Step 4. You’d certainly reject it – but not because it has any logical error. Its logic is perfect; what’s wrong here is that the premises are false.

If a deductive argument is valid AND has all true premises, the argument is said to be sound.

If an inductive argument is strong AND has all true premises, the argument is said to be cogent.

Typical logical mistakes are called fallacies. 

Formal fallacies occur only in deductive arguments, since validity is a matter of form. (See notes on “Refutation by Logical Analogy.”) Formal fallacies result from mistaking an invalid form for a valid one, because of a resemblance between the valid and invalid forms.

Informal fallacies comprise all the other common logical errors.