Logic 103: Deductive vs Inductive Arguments

Hey everybody, Marcus here.

In the last video in this series we discussed how an argument is composed. In this video, we will discuss the difference between inductive and deductive arguments. However, first let us review what we had learned in the last video.

An argument is composed of at least one or more premises. An argument has exactly one conclusion though you can construct many arguments with the same premises to derive multiple conclusions from them. The premises and the conclusion of an argument are always propositions. Pretty much no arguments you will encounter in the real world will be presented in the formal argument structure. As such, you will be tasked to extract the arguments from the various passages you encounter in the real world.

To help you extract argument you can use premise indicator words as well as conclusion indicator words. However, you will also encounter a great number of passages that in themselves do not contain an argument. There are broadly 5 types of passages which do not contain arguments. These are simple noninferential passages which can further be broken down to warnings, pieces of advice, statements about beliefs or opinions, loosely associates statements, and report. The other type of non-argumentative passages are expository passages, illustration passages, explanations, and conditional statements.

Now, let us turn our attention to the subject of this video.

The idea that arguments come in two forms, deductive and inductive, was first asserted by Aristotle. In the intervening centuries, deduction and induction have become a settled fixture not only in logic but in our intellectual culture. Countless books, both fiction and nonfiction, have referred to it. Einstein wrote a paper on it. And a huge number of textbooks ranging from philosophy to education, business to psychology, and chemistry to anthropology explore the subject. So, what is the difference between a deductive and an inductive argument? Briefly we can say that deductive arguments are those that rest on necessary reasoning, while inductive arguments are those that rest on probabilistic reasoning.

Stated more precisely, a deductive argument is an argument incorporating the claim that it is impossible for the conclusion to be false given that the premises are true. On the other hand, an inductive argument is an argument incorporating the claim that it is improbable that the conclusion be false given that the premises are true. Two examples:

The noob gamer is closely related to the filthy casual.
The filthy casual usually plays on consoles.
Therefore, probably the noob gamer plays on a console.

The noob gamer is a gamer.
All gamers own a device they can play games on.
Therefore, it necessarily follows that the noob gamer owns a device he can play games on.
The first of these arguments is inductive, the second deductive.
In deciding whether an argument is inductive or deductive, we look to certain objective features of the argument. These features include (1) the occurrence of special indicator words, (2) the actual strength of the inferential link between premises and conclusion, and (3) the form or style of argumentation. However, we must acknowledge at the outset that many arguments in ordinary language are incomplete, and because
of this, deciding whether the argument should best be interpreted as deductive or inductive may be impossible.

The occurrence of special indicator words is illustrated in the examples we just considered. The word “probably” in the conclusion of the first argument suggests that the argument should be taken as inductive, and the word “necessarily” in the conclusion of the second suggests that the second argument be taken as deductive. Additional inductive indicators are “improbable,” “plausible,” “implausible,” “likely,” “unlikely,” and “reasonable to conclude.” Additional deductive indicators are “certainly,” “absolutely,” and “definitely.”

Inductive and deductive indicator words often suggest the correct interpretation. However, if they conflict with one of the other criteria which we will discuss shortly, we should probably ignore them. Arguers often use phrases such as “it certainly follows that” for rhetorical purposes to add impact to their conclusion and not to suggest that the argument be taken as deductive. Similarly, some arguers, not knowing the distinction
between inductive and deductive, will claim to “deduce” a conclusion when their argument is more correctly interpreted as inductive.

The second factor that bears on our interpretation of an argument as inductive or deductive is the actual strength of the inferential link between premises and conclusion. If the conclusion actually does follow with strict necessity from the premises, the argument is clearly deductive. In such an argument, it is impossible for the premises to be true and the conclusion false. On the other hand, if the conclusion does not follow with strict necessity but does follow probably, it is often best to consider the argument inductive. Examples:

All alpha males are extroverts.
Billy is an alpha male.
Therefore, Billy is an extrovert.

The vast majority of alpha males are extroverts.
Billy is an alpha male.
Therefore, Billy is an extrovert.
In the first example, the conclusion follows with strict necessity from the premises. If we assume that all alpha males are extroverts and that Billy is an alpha male, then it is impossible that Billy not be an extrovert. Thus, we should interpret this argument as deductive. In the second example, the conclusion does not follow from the premises with strict necessity, but it does follow with some degree of probability. If we assume that the premises are true, then based on that assumption it is probable that the conclusion is true. Thus, it is best to interpret the second argument as inductive.

Occasionally, an argument contains no special indicator words, and the conclusion does not follow either necessarily or probably from the premises; in other words, it does not follow at all. This situation points to the need for the third factor to be taken into account, which is the character or form of argumentation the arguer uses.

Deductive Argument Form
Let us not talk in a little bit more detail about deductive arguments.
Many arguments have a distinctive character or form that indicates that the premises are supposed to provide absolute support for the conclusion. Five examples of such forms or kinds of argumentation are arguments based on mathematics, arguments from definition, and categorical, hypothetical, and disjunctive syllogisms.

An argument based on mathematics is an argument in which the conclusion depends on some purely arithmetic or geometric computation or measurement.

For example, a shopper might place two apples and three oranges into a paper bag and then conclude that the bag contains five pieces of fruit. Or a surveyor might measure a square piece of land and, after determining that it is 100 feet on each side, conclude that it contains 10,000 square feet. Since all arguments in pure mathematics are deductive, we can usually consider arguments that depend on mathematics to be deductive as well. However, arguments that depend on statistics are a noteworthy exception. As we will
see shortly, such arguments are usually best interpreted as inductive.

An argument from definition is an argument in which the conclusion is claimed to depend merely on the definition of some word or phrase used in the premise or conclusion. For example, someone might argue that because Claudia is mendacious, it follows that she tells lies, or that because a certain paragraph is prolix, it follows that it is excessively wordy. These arguments are deductive because their conclusions follow with necessity from the definitions of “mendacious” and “prolix.”

A syllogism, in general, is an argument consisting of exactly two premises and one conclusion. A categorical syllogism is a syllogism in which each statement begins with one of the words “all,” “no,” or “some.” For Example:

All neckbeards are sources of cringe.
Some neckbeards are targets of ridicule.
Therefore, some sources of cringe are targets of ridicule.
Arguments such as these are nearly always best treated as deductive. A hypothetical syllogism is a syllogism having a conditional (“if . . . then”) statement for one or both of its premises. For Examples:

If furries are abolished, then sources of lulz will diminish greatly.
If lulz diminish greatly, then we will all end up as sad pandas.
Therefore, if furries are abolished, then we will all end up as sad pandas.

A disjunctive syllogism is a syllogism having a disjunctive (“either . . . or . . .”)
statement. Example:
Either the vote is taken away from women, or we will end up with a mad max style post-apocalyptic world.
The vote will not be taken away from women.
Therefore, we will end up with a mad max style post-apocalyptic world.
As with hypothetical syllogisms, such arguments are usually best taken as deductive.

Inductive Argument Form

Now, let us talk in a little bit more detail about inductive arguments.

In general, inductive arguments are such that the content of the conclusion is in some way intended to “go beyond” the content of the premises. The premises of such an argument typically deal with some subject that is relatively familiar, and the conclusion then moves beyond this to a subject that is less familiar or that little is known about. Such an argument may take any of several forms: predictions about the future, arguments from analogy, inductive generalizations, arguments from authority, arguments based on signs, and causal inferences, to name just a few.

A prediction is an argument that proceeds from our knowledge of the past to a claim about the future. For example, someone might argue that because certain meteorological phenomena have been observed to develop over a certain region of central America, a storm will occur there in six hours.
Or again, one might argue that because certain fluctuations occurred in the prime interest rate on Friday, the value of the dollar will decrease against foreign currencies on Monday. Nearly everyone realizes that the future cannot be known with certainty; thus, whenever an argument makes a prediction about the future, one is usually justified in considering the argument inductive.

An argument from analogy is an argument that depends on the existence of an analogy, or similarity, between two things or states of affairs. Because of the existence of this analogy, a certain condition that affects the better-known thing or situation is concluded to affect the similar, lesser-known thing or situation. For example, someone might argue that because Steve’s Porsche is a great-handling car, it follows that
Roger’s Porsche must also be a great-handling car. The argument depends on the existence of a similarity, or analogy, between the two cars. The certitude attending such an inference is probabilistic at best.

A generalization is an argument that proceeds from the knowledge of a selected sample to some claim about the whole group. Because the members of the sample have a certain characteristic, it is argued that all the members of the group have that same characteristic. For example, one might argue that because three oranges selected from a certain crate were especially tasty and juicy, all the oranges from that crate are especially tasty and juicy. Or again, one might argue that because six out of a total of nine members sampled from a certain labor union intend to vote for Johnson for union president, two-thirds of the entire membership intend to vote for Johnson. These examples illustrate the use of statistics in inductive argumentation.

An argument from authority is an argument that concludes something is true because a presumed expert or witness has said that it is. For example, a person might argue that earnings for Hewlett-Packard Corporation will be up in the coming quarter because of a statement to that effect by an investment counselor. Or a lawyer might argue that Mack the Knife committed the murder because an eyewitness testified to that effect under oath. Because the investment counselor and the eyewitness could be either mistaken or lying, such arguments are essentially probabilistic.

An argument based on signs is an argument that proceeds from the knowledge of a sign to a claim about the thing or situation that the sign symbolizes. The word “sign,” as it is used here, means any kind of message (usually visual) produced by an intelligent being. For example, when driving on an unfamiliar highway one might see a sign indicating that the road makes several sharp turns one mile ahead. Based on this information, one might argue that the road does indeed make several sharp turns one mile ahead. Because the sign might be misplaced or in error about the turns, the conclusion is only probable.

A causal inference is an argument that proceeds from knowledge of a cause to a claim about an effect, or, conversely, from knowledge of an effect to a claim about a cause. For example, from the knowledge that a bottle of wine had been accidentally left in the freezer overnight, someone might conclude that it had frozen (cause to effect). Conversely, after tasting a piece of chicken and finding it dry and tough, one might conclude that it had been overcooked (effect to cause). Because specific instances of cause and effect can never be known with absolute certainty, one may usually interpret such arguments as inductive.

Okay. Let us now summarize everything we have learned in this video. Briefly we can say that deductive arguments are those that rest on necessary reasoning, while inductive arguments are those that rest on probabilistic reasoning. A deductive argument is an argument incorporating the claim that it is impossible for the conclusion to be false given that the premises are true. On the other hand, an inductive argument is an argument incorporating the claim that it is improbable that the conclusion be false given that the premises are true.

Broadly speaking, we can categorize common types of inductive and deductive arguments. Common inductive arguments are predictions about the future, arguments from analogy, inductive generalizations, arguments from authority, arguments based on signs, and causal inferences.
Common deductive arguments are arguments based on mathematics, arguments from definition, categorical, hypothetical, and disjunctive syllogisms.

Now, based on what we have learned today, if we look at the Sherlock Holmes stories written by Sir. Arthur Conan Doyle, we would have to conclude that Sherlock Holmes never deduced shit. The reasoning that Sherlock Holmes used to solve the various mysteries present in those stories was almost exclusively inductive and not deductive. Most of the day to day reasoning we apply is inductive and most of our decision making is inductive as well. However, deductive arguments are much stronger than inductive arguments as the conclusion of a deductive argument is certain.

In the next, and hopefully last video in this series, we will go over how to evaluate arguments. More specifically, we will look at the validity and soundness of arguments.

But for now, thanks for listening.

Go team!

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