At the beginning of each class I teach, I lay down the ground rules: raise your hand if you want to ask a question, turn off your smart phones, try to pay attention. My students are often surprised to learn that it’s OK to stuff their faces with donuts if they can’t answer a question. I get it… that’s what the donuts are for.
Here’s one thing my students are not allowed to do: call an argument “false,” “wrong,” or “stupid.” I am a stickler for rules. Language matters.
In logic, we don’t speak of arguments as being “true” or “false,” nor do we speak of statements as being “valid” or “invalid.” We assume that the premises upon which the author’s conclusion is based are all true. There are very, very few instances in which test makers would ever let us question the veracity, or the truth value, of a premise. Assuming that all the premises are true, there are two categorically different types of arguments you’ll come across on the test: deductive and inductive. How we evaluate their conclusions, and the labels we use in our assessment, will depend on the type of argument we’re dealing with.
In a deductive argument, the conclusion is supposed to necessarily follow from the premises. If it does, then the argument is considered valid. However, if it is possible for the conclusion to be false despite the truth of the premises, then the argument is invalid. There is no middle ground here: deductive arguments are either valid or invalid. For instance:
Paris is the capital of France. I live in Paris. Therefore, I live in France.
This argument is valid, because the conclusion necessarily follows from the premises.
Paris is the capital of France. I live in France. Therefore, I live in Paris.
This argument is invalid (it commits a Mistaken Reversal). The conclusion could be false, because I could live outside of Paris and still live in France. Note that the conclusion in invalid arguments can still be “true”: validity only refers to the extent to which the premises support, or do not support, the conclusion. Validity has nothing to do with whether the premises are true or false; we assume that they are true. Rather, validity is determined by the relationship between the premises and the conclusion. The only question you need to ask yourself when evaluating deductive arguments is this:
Do the premises fully support the conclusion?
Argument forms associated with deductive arguments include:
- Conditional Reasoning
- Formal Logic
- Arguments based on mathematics (where the conclusion depends on purely mathematical computation)
(Note: people sometimes speak of “sound” and “unsound” deductive arguments. “Soundness” is not synonymous with “validity.” A sound deductive argument is a deductive argument that is valid and has all true premises. Since the premises on LSAT arguments are assumed to be true by default, the distinction between “soundness” and “validity” is a moot point. On the LSAT, all valid arguments are sound arguments).
An inductive argument rests on probabilistic reasoning: the author must argue that the conclusion probably, or likely, follows from the premises. The conclusion of an inductive argument often goes beyond the scope of the premises, which is fine, as long as the language of the conclusion is carefully qualified (by words such as “probably” and “likely”).
Depending on the actual strength of the inferential link between the premises and the conclusion, such arguments are classified as either “strong” or “weak.” A strong inductive argument is an argument where the conclusion is probably true, given that the premises are true. Conversely, a weak inductive argument is an argument in which the conclusion does not probably follow from the premises. Evaluating the strength of these arguments depends on a number of considerations, such as the strength of the evidence presented, the availability of alternative causes (in causal arguments), etc. This is a much more complicated (and holistic) task than evaluating the validity of a deductive argument. Unlike our assessment of deductive arguments, there is middle ground here: arguments can be strong, weak, or anything in-between. When evaluating the strength of inductive arguments, here’s the question you should keep in mind:
Do the premises probably support for the conclusion?
Argument forms associated with inductive arguments include:
- Causal reasoning
- Arguments from analogy
- Generalizations, incl. arguments using statistical samples
(Note: people sometimes speak of “cogent” and “uncogent” deductive arguments. “Cogency” is is the inductive equivalent of “validity.” A cogent inductive argument is an inductive argument that is strong and has all true premises. Since the premises on LSAT arguments are assumed to be true by default, the distinction between “cogency” and “strength” is a moot point. On the LSAT, all strong inductive arguments are cogent).
To help you differentiate between deductive and inductive arguments, take a look at the indicator words we expect to see in the conclusions of either type of argument:
|necessarily||it is reasonable to conclude that…|
Compare the following two arguments:
All prospective law students must take the LSAT before applying to law school. Gina has not yet taken the LSAT. Therefore, she cannot apply to law school.
All prospective law students must take the LSAT before applying to law school. Nikki has no plans to take the LSAT anytime soon. Therefore, Nikki will probably not apply to law school.
The first argument is deductive (and is also valid), as it takes the form of the contrapositive. The second argument is inductive (and is also quite strong), because if the premises are true, then it the conclusion is probably true as well.
On the LSAT, most deductive arguments will be invalid. Why? Because the premises would provide some support for the conclusion, whereas the conclusion will be argued to necessarily follow them. Most invalid deductive arguments will be flawed because of a strictly formal type of a logical fallacy, such as the MR or the MN, or else because of an error in the use of evidence. Likewise, most inductive arguments will be quite weak: they could be using an unrepresentative sample to draw a probabilistic conclusion, commit a causal fallacy, make an appeal to authority, contain an error of equivocation, composition or division, etc. There are many types of logical fallacies out there. Depending on the type of argument we are dealing with, such fallacies would either make a deductive conclusion invalid, or else they would make an inductive conclusion weak.
Contrary to popular belief, knowing proper terminology is important: it cultivates a certain analytical rigor that helps you think precisely and clearly.
If you don’t do that, you get penalized by eating donuts. Not the worst thing in the world 🙂
Image courtesy of Dave Crosby.