intro to arguments

T. Parent

A Brief Intro to Arguments in Philosophy and Logic

An argument is a set of statements one of which (the conclusion) is taken to be supported by the remaining statements (the premises).

Five types of Arguments: Abductive, Inductive, Deductive, Practical, and Other.

An Abductive argument is an argument where the conclusion stands as an explanation of facts given in the premises.

Examples:

(P1) I can't get online from my computer. (P1) I have a headache.
(P2) There's nothing wrong with my hardware or (C) So, my head is shrinking

software.
(C) So, the Unive rsity network must be down.

An argument is a good abductive argument to the degree that the conclusion is likely given the premise(s). If the conclusion of an abductive argument is the most likely explanation out of all the explanations available, then the abductive argument is sometimes called an inference to the best explanation.

An Inductive argument is an argument where the premises register the known cases of a certain phenomenon, and the conclusion suggests that unknown cases will be like the known cases.

Examples :

(P1) The sun rose today. (P1) Everyone in my family has been stung by a bee.
(P2) The sun rose yesterday. (C) So, absolutely everyone has been stung by a bee.
(P3) The sun rose the day before

yesterday.
(P4) The sun rose the day before

the day before yesterday.
[etc.]
(C1) So, the sun will rise tomorrow.

As with abductive arguments, an argument is a good inductive argument to the degree that the conclusion is likely given the premise(s). (In assessing its likelihood, sometimes people talk of the “inductive strength” of the argument.)

A Deductive argument is a specific type of good argument. More often, however, a deductive argument is called (misleadingly) a ‘valid argument’.

An argument is valid (= deductive) if and only if [abbreviation: “iff”] it is not possible for the premise(s) to be true and the conclusion false. Otherwise, the argument is invalid.

Example of a valid/deductive argument:

(P1) Jim likes either Coke or Pepsi.
(P2) Jim does not like Pepsi.
(C) So, Jim likes Coke.

Think of it this way: With a valid argument, if we get you to accept the premises, then you must accept the conclusion too. Why? ‘Cause in a valid argument there’s no way for both the premises to be true and the conclusion false.

Note that ‘validity’ refers to a relationship between premise(s) and conclusion. It is not directly concerned with whether the sentences in the argument are actually true. This is contrary to how we use the word ‘valid’ outside the philosophy classroom, where we often say that someone has made a “valid point” or that someone’s perspective is “valid.” But this is NOT how philosophers use ‘valid’—they only say that arguments are “valid.” (Consequently, philosophers do not speak of a point or a perspective as “valid;” they instead talk of someone making a good point or having a legitimate perspective, etc.)

Of course, not every argument is valid (= deductive). Here’s one example:

(P1) Jim likes either Coke or Pepsi.
(P2) Jim does not like Mountain Dew.
(C) So, Jim likes Coke.

In this, it is possible for the premises to be true, and the conclusion false. That’s not to say the premises are actually true or the conclusion is actually false. Rather, it’s just to say that this combination of truth and falsity is possible. N.B., An invalid argument is also sometimes called a non-sequitur—it is an argument where the conclusion “does not follow” from the premise(s).

Notably, all abductive and inductive arguments are invalid, technically speaking. Still, as we saw, there can be good abductive and inductive arguments. Thus, if you say that an argument is invalid, you’re not automatically saying it is a bad argument full stop. You’re only saying that the premises do not guarantee the conclusion (though the premises may still make the conclusion very likely for all that.)

Some valid arguments are also SOUND: An argument is sound iff it is valid AND every premise is true. Thus, an argument is unsound iff it is invalid or some premise is false.

So, to check that an argument is sound, you have to check the validity of the argument and the truth of every premise.

Example of a sound argument:

(P1) If a thing is a rectangle, then it’s not a circle.
(P2) This page is a rectangle.
(C) So, this page is not a circle.

This argument is sound, since it is valid, and all of its premises are true.

Example of an unsound argument:

(P1) If Bill Gates is poor, then I’m a monkey’s uncle.
(P2) Bill Gates is poor.
(C) So I’m a monkey’s uncle.

This argument is unsound: Although it is valid, it is not true that Bill Gates is poor.

NOTE: Truth and Falsity are NOT properties of arguments, but of premises and conclusions. Thus, we do not say that a deductive argument is ‘true;’ rather, we say that it is valid or sound. Or, if we want to talk of ‘true’ and ‘false,’ we evaluate the statements in the argument as true or false.

A Practical argument is an argument where the conclusion is a statement of what should or ought to be done, yet the argument is not deductive, not inductive, and not abductive. Examples:

(P1) Stocks are low right now (P1) I need to make money.

(P2) The economy will recover soon. (P2) Kidnapping children makes money.

As should be clear, these two arguments are not deductive. Considering the first argument, even if stocks are low and the economy is expected to recover, it is still possible that I should NOT buy stocks right now. After all, I might have barely enough money to feed my family.

Still, the first example can be a good practical argument, e.g., if we’re talking about someone who has expendable income. But even in that case, it remains possible for the premise to be true and the conclusion false. So the argument remains invalid.

When is a practical argument a good practical argument? NOBODY KNOWS. That is still debated vigorously among ethicists. However, there is a sub-type of practical argument, called a decision-theoretic argument, and it is known what makes these arguments good or bad. (Briefly, you have a good decision-theoretic argument when the conclusion recommends an action that is expected to “maximize profit” among the available options. But you needn’t worry about that now.)

Note: Some arguments with a “should” or “ought to” conclusion are NOT practical arguments. Consider the following inductive and deductive arguments (respectively):

(P1) I should have jogged today. (P1) Thou shalt not steal.

(P2) I should have jogged yesterday. (C) I should not steal this ipod.

(P3) I should have jogged the day before that.

[etc.]

(There are also abductive arguments with “should” or “ought to” conclusions as well.) Thus the term ‘practical argument’ is reserved for an argument that is NOT any of the previous three types of argument—and also has a “should” or “ought to” conclusion.

Other arguments exist besides the previous four types. Some of these other arguments are just plain awful, such as:

(P1) I have ten toes.

(P2) Penguins live in Antarctica.

Note that out of context, these three sentences would not seem to be an argument at all. But here, they indeed constitute an argument since one statement is marked as the conclusion, and other statements are marked as premises. So in this case, the three statements here are an argument; it’s just that it’s a really bad argument.

However, some arguments in the “other” category are not obviously bad. Consider, for instance, the following argument by analogy:

(P1) A watch has a designer.

(P2) The universe is like a watch.

The truth of the premises would not guarantee the conclusion, so the argument is not deductive. And the conclusion is not meant to explain the premises (or at least, it isn’t clear how the conclusion would explain the first premise). So it isn’t abductive either.

Some logic books classify arguments by analogy a type of inductive argument. I myself think this is backwards: Inductive arguments are a type of argument by analogy, if induction assumes that the unknown cases will be like the known cases. But normally when philosophers speak of induction, they do not have analogical reasoning in mind. (And they are not normally thinking of induction when they talk of analogical reasoning.)

Consequently, I’ve put arguments by analogy in the “other” category. But unlike the just-plain-awful arguments, it is not obvious whether the design argument (for example) is a bad argument. Its worth would depend on how appropriate the analogy is in (P2)—and specifically, whether the universe is similar in the right way to a watch. I’ll let the theologians among you decide that one. But generally, an argument by analogy is a good argument to the extent that the analogy is a “tight” one (to put it roughly).