In the previous section we saw that every argument involves an inferential claim -- the claim that the conclusion is supposed to follow from the premises. The question we now address has to do with the strength of this claim. Just how strongly is the conclusion claimed to follow from the premises? If the conclusion is claimed to follow with strict certainty or necessity, the argument is said to be deductive; but if it is claimed to follow only probably, the argument is inductive.

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. Deductive arguments are those that involve necessary reasoning. 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. Inductive arguments involve probabilistic reasoning. Here are two examples:

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." (Note that the phrase "it must be the case that" is simply a conclusion indicator that can occur in either deductive or inductive argments.)

Inductive and deductive indicator words often suggest the correct interpretation. However, if they conflict with one of the other criteria (discussed 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:

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 up the need for the third factor to be taken into account, which is the character or form of argumentation the arguer uses.

Deductive Argument Forms

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. A noteworthy exception, however, is arguments that depend on statistics. 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. Categorical syllogisms will be treated in greater depth in Chapter 5, but for now we will say that a categorical syllogism is a syllogism in which each statement begins with one of the words "all," "no," or "some." Example:

A hypothetical syllogism is a syllogism having a conditional statement for one or both of its premises. Examples:

A disjunctive syllogism is a syllogism having a disjunctive statement (i.e., an "either ... or ..." statement) for one of its premises. Example:

Inductive Argument Forms

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 Missouri, 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 Christina's Porsche is a great handling car, it follows that Angela'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.

Further Considerations

It should be noted that the various subspecies of inductive arguments listed here are not intended to be mutually exclusive. Overlaps can and do occur. For example, many causal inferences that proceed from cause to effect also qualify as predictions. The purpose of this survey is not to demarcate in precise terms the various forms of induction but rather to provide guidelines for distinguishing induction from deduction.

Keeping this in mind, we should take care not to confuse arguments in geometry, which are always deductive, with arguments from analogy or inductive generalizations. For example, an argument concluding that a triangle has a certain attribute (such as a right angle) because another triangle, with which it is congruent, also has that attribute might be mistaken for an argument from analogy. Similarly, an argument that concludes that all triangles have a certain attribute (such as angles totaling two right angles) because any particular triangle has that attribute might be mistaken for an inductive generalization. Arguments such as these, however, are always deductive, because the conclusion follows necessarily and with complete certainty from the premises.

One broad classification of arguments not listed in this survey is scientific arguments. Arguments that occur in science can be either inductive or deductive, depending on the circumstances. In general, arguments aimed at the discovery of a law of nature are usually considered inductive. Suppose, for example, that we want to discover a law that governs the time required for a falling body to strike the earth. We drop bodies of various weights from various heights and measure the time it takes them to fall. Comparing our measurements, we notice that the time is approximately proportional to the square root of the distance. From this we conclude that the time required for any body to fall is proportional to the square root of the distance through which it falls. Such an argument is best interpreted as an inductive generalization.

Another type of argument that occurs in science has to do with the application of known laws to specific circumstances. Arguments of this sort are often considered to be deductive -- but only with certain reservations. Suppose, for example, that we want to apply Boyle's law for ideal gases to a container of gas in our laboratory. Boyle's law states that the pressure exerted by a gas on the walls of its container is inversely proportional to the volume. Applying this law, we conclude that when we reduce the volume of our laboratory sample by half, the pressure will double. Considered purely as a mathematical computation, this argument is deductive. But if we acknowledge the fact that the conclusion pertains to the future and the possibility that Boyle's law may not work in the future, then the argument is best considered inductive.

A final point needs to be made about the distinction between inductive and deductive arguments. There is a tradition extending back to the time of Aristotle that holds that inductive arguments are those that proceed from the particular to the general, while deductive arguments are those that proceed from the general to the particular. (A particular statement is one that makes a claim about one or more particular members of a class, while a general statement makes a claim about all the members of a class.) It is true, of course, that many inductive and deductive arguments do work in this way; but this fact should not be used as a criterion for distinguishing induction from deduction. As a matter of fact, there are deductive arguments that proceed from the general to the general, from the particular to the particular, and from the particular to the general, as well as from the general to the particular; and there are inductive arguments that do the same. For example, here is a deductive argument that proceeds from the particular to the general:

Summary

To distinguish deductive arguments from inductive arguments, we attempt to evaluate the strength of the argument's inferential claim -- how strongly the conclusion is claimed to follow from the premises. This claim is an objective feature of an argument, and it may or may not be related to the subjective intentions of the arguer.

To interpret an argument's inferential claim we look at three factors: special indicator words, the actual strength of the inferential link between premises and conclusion, and the character or form of argumentation. Given that we have more than one factor to look at, it is possible in a single argument for the occurrence of two of these factors to conflict with each other, leading to opposite interpretations. For example, in drawing a conclusion to a categorical syllogism (which is clearly deductive), an arguer might say "It probably follows that..." (which suggests induction). To help alleviate this conflict we can list the factors in order of importance:

Unfortunately, many arguments in ordinary language are incomplete, so it often happens that none of these factors are clearly present. Determining the inductive or deductive character of such arguments may be impossible.

1.4 Validity, Truth, Soundness, Strength, Cogency

This section introduces the central ideas and terminology required to evaluate arguments. We have seen that every argument makes two basic claims: a claim that evidence or reasons exist and a claim that the alleged evidence or reasons support something (or that something follows from the alleged evidence or reasons). The first is a factual claim, the second an inferential claim. The evaluation of every argument centers on the evaluation of these two claims. The more important of the two is the inferential claim, because if the premises fail to support the conclusion (that is, if the reasoning is bad), an argument is worthless. Thus we will always test the inferential claim first, and only if the premises do support the conclusion will we test the factual claim (that is, the claim that the premises present genuine evidence, or are true). The material that follows considers first deductive arguments and then inductive.

Deductive Arguments

The previous section defined a deductive argument as one incorporating the claim that it is impossible for the conclusion to be false given that the premises are true. If this claim is true, the argument is said to be valid. Thus, a valid deductive argument is an argument in which it is impossible for the conclusion to be false given that the premises are true. In these arguments the conclusion follows with strict necessity from the premises. Conversely, an invalid deductive argument is a deductive argument in which it is possible for the conclusion to be false given that the premises are true. In these arguments the conclusion does not follow with strict necessity from the premises, even though it is claimed to.

An immediate consequence of these definitions is that there is no middle ground between valid and invalid. There are no arguments that are "almost" valid and "almost" invalid. If the conclusion follows with strict necessity from the premises, the argument is valid; if not, it is invalid.

To test an argument for validity we begin by assuming that all the premises are true, and then we determine if it is possible, in light of that assumption, for the conclusion to be false. Here is an example:

All television networks are media companies.
NBC is a television network.
Therefore, NBC is a media company.

In this argument both premises are actually true, so it is easy to assume that they are true. Next we determine, in light of this assumption, if it is possible for the conclusion to be false. Clearly this is not possible. If NBC is included in the group of television networks (second premise) and if the group of television networks is included in the group of media companies (first premise), it necessarily follows that NBC is included in the group of media companies (conclusion). In other words, assuming the premises to be true and the conclusion false entails a strict contradiction. Thus, the argument is valid.

Here is another example:

All automakers are computer manufacturers.
United Airlines is an automaker.
Therefore, United Airlines is a computer manufacturer.

In this argument, both premises are actually false, but it is easy to assume that they are true. Every automaker could have a corporate division that manufactures computers. Also, in addition to flying airplanes, United Airlines could make cars. Next, in light of these assumptions, we determine if it is possible for the conclusion to be false. Again, we see that this is not possible, by the same reasoning as the previous example. Assuming the premises to be true and the conclusion false entails a contradiction. Thus, the argument is valid.

Another example:

All banks are financial institutions.
Wells Fargo is a financial institution.
Therefore, Wells Fargo is a bank.

As in the first example, both premises of this argument are true, so it is easy to assume they are true. Next we determine, in light of this assumption, if it is possible for the conclusion to be false. In this case it is possible. If banks were included in one part of the group of financial institutions and Wells Fargo were included in another part, then Wells Fargo would not be a bank. In other words, assuming the premises to be true and the conclusion false does not involve any contradiction, and so the argument is invalid.

In addition to illustrating the basic idea of validity, these examples suggest an important point about validity and truth. In general, validity is not something that is uniformly determined by the actual truth or falsity of the premises and conclusion. Both the NBC example and the Wells Fargo example have actually true premises and an actually true conclusion, yet one is valid and the other invalid. The United Airlines example has actually false premises and an actually false conclusion, yet the argument is valid. Rather, validity is something that is determined by the relationship between premises and conclusion. The question is not whether the premises and conclusion are true or false, but whether the premises support the conclusion. In the examples of valid arguments the premises do support the conclusion, and in the invalid case they do not.

Nevertheless, there is one arrangement of truth and falsity in the premises and conclusion that does determine the issue of validity. Any deductive argument having actually true premises and an actually false conclusion is invalid. The reasoning behind this fact is fairly obvious. If the premises are actually true and the conclusion is actually false, then it certainly is possible for the premises to be true arid the conclusion false. Thus, by the definition of invalidity, the argument is invalid. . "

The idea that any deductive argument having actually true premises and a false conclusion is invalid may be the most important point in all of deductive logic. The entire system of deductive logic would be quite useless if it accepted as valid any inferential process by which a person could start with truth in the premises and arrive at falsity in the conclusion. _v"

Table 1.1 presents examples of deductive arguments that illustrate the various combinations of truth and falsity in the premises and conclusion. In the examples having false premises, both premises are false, but it is easy to construct other examples having only one false premise. When examining this table, note that the only combination of truth and falsity that does not allow for both valid and invalid arguments is true premises and false conclusion. As we have just seen, any argument having this combination is necessarily invalid.

Table 1.1 Deductive Arguments

	Valid	Invalid
True premises True conclusion	All wines are beverages. Chardonnay is a wine. Therefore, chardonnay is a beverage. [sound]	All wines are beverages. Chardonnay is a beverage. Therefore, chardonnay is a wine. [unsound]
True premises False conclusion	None exist.	All wines are beverages. Ginger ale is a beverage. Therefore, ginger ale is a wine. [unsound]
False premises True conclusion	All wines are soft drinks. Ginger ale is a wine. Therefore, ginger ale is a soft drink. [unsound]	All wines are whiskeys. Chardonnay is a whiskey. Therefore, chardonnay is a wine. [unsound]
False premises False conclusion	All wines are whiskeys. Ginger ale is a wine. Therefore, ginger ale is a whiskey. [unsound]	All wines are whiskeys. Ginger ale is a whiskey. Therefore, ginger ale is a wine. [unsound]

The relationship between the validity of a deductive argument and the truth or falsity of its premises and conclusion, as illustrated in Table 1.1, is summarized as follows:

Premises	Conclusion	Validity
T	T	?
T	F	Invalid
F	T	?
F	F	?

A sound argument is a deductive argument that is valid and has all true premises. Both conditions must be met for an argument to be sound; if either is missing the argument is unsound. Thus, an unsound argument is a deductive argument that is invalid, has one or more false premises, or both. Because a valid argument is one such that it is impossible for the premises to be true and the conclusion false, and because a sound argument does in fact have true premises, it follows that every sound argument, by definition, will have a true conclusion as well. A sound argument, therefore, is what is meant by a "good" deductive argument in the fullest sense of the term.

In connection with this definition of soundness, a single proviso is required: For an argument to be unsound, the false premise or premises must actually be needed to support the conclusion. An argument with a conclusion that is validly supported by true premises but with a superfluous false premise would still be sound. By similar, reasoning, no addition of a false premise to an originally sound argument can make the argument unsound. Such a premise would be superfluous and should not be considered part of the argument. Analogous remarks, incidentally, extend to induction.

Inductive Arguments

Section 1.3 defined an inductive argument as one incorporating the claim that it is improbable that the conclusion be false given that the premises are true. If this claim is true, the argument is said to be strong. Thus, a strong inductive argument is an inductive argument in which it is improbable that the conclusion be false given that the premises are true. In such arguments, the conclusion does in fact follow probably from the premises. Conversely, a weak inductive argument is an argument in which the conclusion does not follow probably from the premises, even though it is claimed to.

The procedure for testing the strength of inductive arguments runs parallel to the procedure for deduction. First we assume the premises are true, and then we determine whether, based on that assumption, the conclusion is probably true. Example:

All dinosaur bones discovered to this day have been at least 50 million years old.
Therefore, probably the next dinosaur bone to be found will be at least 50 million years old.

In this argument the premise is actually true, so it is easy to assume that it is true. Based on that assumption, the conclusion is probably true, so the argument is strong. Here is another example:

All meteorites found to this day have contained sugar.
Therefore, probably the next meteorite to be found will contain sugar.

The premise of this argument is obviously false. But if we assume the premise is true, then based on that assumption, the conclusion would probably be true. Thus, the argument is strong.

The next example is an argument from analogy:

When a lighted match is slowly dunked into water, the flame is snuffed out.
But gasoline is a liquid, just like water.
Therefore, when a lighted match is slowly dunked into gasoline, the flame will be snuffed out.

In this argument the premises are actually true and the conclusion is probably false. Thus, if we assume the premises are true, then, based on that assumption, it is not probable that the conclusion is true. Thus, the argument is weak.

Another example:

During the past fifty years, inflation has consistently reduced the value of the American dollar.
Therefore, industrial productivity will probably increase in the years ahead.

In this argument, the premise is actually true and the conclusion is probably true in the actual world, but the probability of the conclusion is in no way based on the assumption that the premise is true. Because there is no direct connection between inflation and increased industrial productivity, the premise is irrelevant to the conclusion and it provides no probabilistic support for it. The conclusion is probably true independently of the premise. As a result, the argument is weak.

This last example illustrates an important distinction between strong inductive arguments and valid deductive arguments. As we will see in later chapters, if the conclusion of a deductive argument is necessarily true independently of the premises, the argument is still considered valid. But if the conclusion of an inductive argument is probably true independently of the premises, the argument is weak.

These four examples show that in general the strength or weakness of an inductive argument results not from the actual truth or falsity of the premises and conclusion, but from the probabilistic support the premises give to the conclusion. The dinosaur argument has a true premise and a probably true conclusion, and the meteorite argument has a false premise and a probably false conclusion; yet both are strong because the premise of each provides probabilistic support for the conclusion. The industrial productivity argument has a true premise and a probably true conclusion, but the argument is weak because the premise provides no probabilistic support for the conclusion. As in the evaluation of deductive arguments, the only arrangement of truth and falsity that establishes anything is true premises and probably false conclusion (as in the lighted match argument). Any inductive argument having true premises and a probably false conclusion is weak.

Table 1.2 Inductive Arguments

	Strong	Weak
True premise Probably true conclusion	All previous U.S. presidents were older than 40. Therefore, probably the next U.S. president will be older than 40. [cogent]	A few U.S. presidents were lawyers. Therefore, probably the next U.S. president will be older than 40. [uncogent]
True premise Probably false conclusion	None exist	A few U.S. presidents were unmarried. Therefore, probably the next U.S. president will be unmarried [uncogent]
False premise Probably true conclusion	All previous U.S. presidents were TV debaters. Therefore, probably the next U.S. president will be a TV debater. [uncogent]	A few U.S. presidents were dentists. Therefore, probably the next U.S. president will be a TV debater. [uncogent]
False premise Probably false conclusion	All previous U.S. presidents died in office. Therefore, probably the next U.S. president will die in office. [uncogent]	A few U.S. presidents were dentists. Therefore, probably the next U.S. president will be a dentist. [uncogent]

Table 1.2 presents the various possibilities of truth and falsity in the premises and conclusion of inductive arguments. Note that the only arrangement of truth and falsity that is missing for strong arguments is true premises and probably false conclusion.

The relationship between the strength of an inductive argument and the truth or falsity of its premises and conclusion, as illustrated in Table 1.2, is summarized as follows:

Premises	Conclusion	Strength
T	prob.T	?
T	prob. F	Weak
F	prob.T	?
F	prob. F	?

Unlike the validity and invalidity of deductive arguments, the strength and weakness of inductive arguments admit of degrees. To be considered strong, an inductive argument must have a conclusion that is more probable than improbable. In other words, given that the premises are true, the likelihood that the conclusion is true must be more than 50 percent, and as the probability increases, the argument becomes stronger. For this purpose, consider the following pair of arguments:

This barrel contains 100 apples.
Three apples selected at random were found to be ripe.
Therefore, probably all 100 apples are ripe.
This barrel contains 100 apples.
Eighty apples selected at random were found to be ripe.
Therefore, probably all 100 apples are ripe.

The first argument is weak and the second is strong. However, the first is not absolutely weak nor the second absolutely strong. Both arguments would be strengthened or weakened by the random selection of a larger or smaller sample. For example, if the size of the sample in the second argument were reduced to seventy apples, the argument would be weakened. The incorporation of additional premises into an inductive argument will also generally tend to strengthen or weaken it. For example, if the premise "One unripe apple that had been found earlier was removed" were added to either argument, the argument would be weakened.

A cogent argument is an inductive argument that is strong and has all true premises; if either condition is missing, the argument is uncogent. Thus, an uncogent argument is an inductive argument that is weak, has one or more false premises, or both. A cogent argument is the inductive analogue of a sound deductive argument and is what is meant by a "good" inductive argument without qualification. Because the conclusion of a cogent argument is genuinely supported by true premises, it follows that the conclusion of every cogent argument is probably true.

There is a difference, however, between sound and cogent arguments in regard to the true premise requirement. In a sound argument it is necessary only that the premises be true and nothing more. Given such premises and good reasoning, a true conclusion is guaranteed. In a cogent argument, on the other hand, the premises must not only be true, but they must also not ignore some important piece of evidence that entails a quite different conclusion. This is called the total evidence requirement. As an illustration of the need for it, consider the following argument:

Swimming in the Caribbean is usually lots of fun.
Today the water is warm, the surf is gentle, and on this beach there are no dangerous currents.
Therefore, it would be fun to go swimming here now.

If the premises reflect all the important factors, then the argument is cogent. But if they ignore the fact that several large dorsal fins are cutting through the water (sug-gesting sharks), then obviously the argument is not cogent. Thus, for cogency the premises must not only be true but also not overlook some important fact that requires a different conclusion.

Summary

For both deductive and inductive arguments, two separate questions need to be answered: (1) Do the premises support the conclusion? (2) Are all the premises true?

To answer the first question we begin by assuming the premises to be true. Then, for deductive arguments we determine whether, in light of this assumption, it necessarily follows that the conclusion is true. If it does, the argument is valid; if not, it is invalid. For inductive arguments we determine whether it probably follows that the conclusion is true. If it does, the argument is strong; if not, it is weak. For inductive arguments we keep in mind the requirements that the premises actually support the conclusion and that they not ignore important evidence. Finally, if the argument is either valid or strong, we turn to the second question and determine whether the premises are actually true. If all the premises are true, the argument is sound (in the case of deduction) or cogent (in the case of induction). All invalid deductive arguments are unsound, and all weak inductive arguments are uncogent.

Note that in logic one never speaks of an argument as being "true" or "false," and one never speaks of a statement as being "valid," "invalid," "strong," or "weak."

1.3 Deduction and Induction

Deductive Argument Forms

Inductive Argument Forms

Further Considerations

Summary

1.4 Validity, Truth, Soundness, Strength, Cogency

Deductive Arguments

Inductive Arguments

Summary