Normally we classify all arguments into one of two types: deductive and inductive.  Deductive arguments are those meant to work because of their pattern alone, so that if the premises are true the conclusion could not be false.  All other arguments are considered to be inductive (or just non-deductive), and these are meant to work because of the actual information in the premises so that if the premises are true the conclusion is not likely to be false.  The difference is between certainty (we can be sure the conclusion is correct) and probability (we can bet on the conclusion being correct).

We now go one step further.  A deductive argument with the right form is considered to be valid, regardless of the truth of the premises.  When the premises are in fact true and the argument is valid, then we call it sound.

Inductive arguments can be seen as strong (the conclusion is more likely to be true because of support provided by the premises) or as weak.  When an inductively strong argument does have true premises, we call it cogent

How strong does an argument have to be to be acceptable?  A good rule to start with is that the more is at risk, the more likely you want the conclusion to be correct.  For instance, in a civil case (the kind that occurs when one person sues another) a jury is asked to decide between two sides based simply on the preponderance of the evidence, and typically there can be a split decision among the jurors.  However, in a criminal case there is obviously more at stake (it could be a person's freedom or possibly his life), and so the jury is asked to decide unanimously on the basis of there not being a reasonable doubt about their verdict.  In everyday life, you would expect a stronger argument about where to transfer for the last two years of college than you would about what movie to see next weekend.

All arguments then can be classified as valid or invalid.  If valid, they are sound or unsound.  If invalid, they are strong or weak and then, depending on the premises, cogent or not cogent.  Note that a strong argument by definition cannot be valid, and a valid argument by definition cannot be strong.

Some additional notes:  an argument that misuses a form (what we will call a formal fallacy) may not be valid but then we need to look at it in terms of inductive strength.  Also, an argument may be technically sound (valid with acceptable premises) but still not a "good" argument because of some informal fallacy (another kind of mistake in the reasoning but one not related to the pattern).  Most typically this could be a problem of what we call begging the question, when the premises would be acceptable only if someone already accepted the conclusion as true.  (We'll see more about this later on.)

In the first part of the course we are going to look more closely at the form taken by deductive arguments that involve complete statements with a premise expressed as a conditional relationship (one that can be restated with the phrases "if" or "only if"). 

Inductive arguments can be seen as involving reasoning based on the similarities of things or events (reasoning by analogy), reasoning based on inferences from a limited group to a much larger one (inductive generalizations and statistical arguments), reasoning about what is likely to take place in the future or have taken place in the past (think of explanations such as those a jury is called up to make in a trial), and especially reasoning that sets out to decide cause and effect relationships.  We will be looking at all this in more detail in the second half of the course. 

A final point to be considered is how strong is a claim (the type of statement that might become a conclusion in an argument).  Saying that Jack will get a perfect score on his exam is a stronger claim than saying he will do well on it.  A good working rule for evaluating arguments intended to prove such claims is that the stronger the claim, the better the evidence should be.  For instance, knowing that Jack is a good student and is studying hard might be enough to justify saying he will do well on his exam, but we would need more evidence before we can say he will get a perfect score.  We would have a much stronger case for this if we also knew the test was comparatively easy.

Prepared by Professor Doug McFerran of Los Angeles Mission College. Professor Doug's text for symbolic logic is available at This page is part of a new text for courses in critical thinking.