1.4 (old) Strength, Truth, Cogency

An argument that proceeds from the knowledge of a certain sign to a knowledge of the thing or situation that the sign symbolizes. 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

Argument based on signs

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, Because Christina's Porsche is a great handling car, it follows that Angela's Porsche must also be a great handling car is an example of _________________________. The argument depends on the existence of a similarity, or analogy, between the two cars. The certitude attending such an inference is obviously probabilistic at best.

Argument from analogy

an argument in which the conclusion rests upon a statement made by some presumed authority or witness. 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

Argument from authority

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 only necessary 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, they must also not ignore some important piece of evidence that outweighs the given evidence and entails a quite different conclusion. As an illustration of this point, 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, then obviously the argument is not cogent. Thus, for cogency the premises must not only be true but also not overlook some important important factor that outweighs the given evidence and requires a different conclusion.

Cogent argument

a claim that something is true; a claim that evidence or reasons are being presented. Not all passages contain arguments. Because logic deals with arguments, it is important to be able to distinguish passages that contain arguments from those that do not. In general, a passage contains an argument if it purports to prove something; if it does not do so, it does not contain an argument. Two conditions must be fulfilled for a passage to purport to prove something: (1) At least one of the statements must claim to present evidence or reasons. (2) There must be a claim that the alleged evidence or reasons supports or implies something—that is, a claim that something follows from the alleged evidence. As we have seen, the statements that claim to present the evidence or reasons are the premises, and the statement that the evidence is claimed to support or imply is the conclusion. It is not necessary that the premises present actual evidence or true reasons nor that the premises actually support the conclusion. But at least the premises must claim to present evidence or reasons, and there must be a claim that the evidence or reasons support or imply something. The first condition expresses a ________________, and deciding whether it is fulfilled usually presents few problems. Thus, most of our attention will be concentrated on whether the second condition is fulfilled. This second condition expresses what is called an inferential claim. The inferential claim is simply the claim that the passage expresses a certain kind of reasoning process—that something supports or implies something or that something follows from something. Such a claim can be either explicit or implicit. An explicit inferential claim is usually asserted by premise or conclusion indicator words (''thus,'' ''since,'' ''because,'' ''hence,'' ''therefore,'' and so on). Example: The human eye can see a source of light that is as faint as an ordinary candle from a distance of 27 kilometers, through a nonabsorbing atmosphere. Thus, a powerful searchlight directed from a new moon should be visible on earth with the naked eye. (Diane E. Papilla and Sally Wendkos Olds, Psychology) The word ''thus'' expresses the claim that something is being inferred, so the passage is an argument.

Factual claim

A cogent argument may have a probably false conclusion.

False

An argument may legitimately be spoken of as ''true'' or ''false.''

False

If an argument has true premises and a true conclusion, we know that it is a perfectly good argument

False

True or False? A strong argument may have true premises and a probably false conclusion.

False

True or False? Invalid deductive arguments are basically the same as inductive arguments

False

An argument in which the premises are claimed to support the conclusion in such a way that it is improbable that the premises be true and the conclusion false. Thus, deductive arguments are those that involve necessary reasoning, and _____________________ are those that involve probabilistic reasoning. Examples: "The meerkat is a member of the mongoose family. All members of the mongoose family are carnivores. Therefore, it necessarily follows that the meerkat is a carnivore" is an example of an example of a deductive argument. "The meerkat is closely related to the suricat. The suricat thrives on beetle larvae. Therefore, probably the meerkat thrives on beetle larvae" is an example of an __________________.

Inductive argument

Inductive argument strength test 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 gold. Therefore, probably the next meteorite to be found will contain gold. The premise of this argument is actually false. Few, if any, meteorites contain any gold. 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 will still be considered valid. But if the conclusion of an inductive argument is probably true independently of the premises, the argument will be 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 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. Analogously to 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. 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, 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 70 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.

Inductive argument validity test

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, 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

Inductive generalization

A claim that alleged evidence or reasons support or imply something Not all passages contain arguments. Because logic deals with arguments, it is important to be able to distinguish passages that contain arguments from those that do not. In general, a passage contains an argument if it purports to prove something; if it does not do so, it does not contain an argument. Two conditions must be fulfilled for a passage to purport to prove something: (1) At least one of the statements must claim to present evidence or reasons. (2) There must be a claim that the alleged evidence or reasons supports or implies something—that is, a claim that something follows from the alleged evidence. As we have seen, the statements that claim to present the evidence or reasons are the premises, and the statement that the evidence is claimed to support or imply is the conclusion. It is not necessary that the premises present actual evidence or true reasons nor that the premises actually support the conclusion. But at least the premises must claim to present evidence or reasons, and there must be a claim that the evidence or reasons support or imply something. The first condition expresses a factual statement, and deciding whether it is fulfilled usually presents few problems. Thus, most of our attention will be concentrated on whether the second condition is fulfilled. This second condition expresses what is called an _______________ ______________, which is simply the claim that the passage expresses a certain kind of reasoning process—that something supports or implies something or that something follows from something. Such a claim can be either explicit or implicit. The human eye can see a source of light that is as faint as an ordinary candle from a distance of 27 kilometers, through a nonabsorbing atmosphere. Thus, a powerful searchlight directed from a new moon should be visible on earth with the naked eye. (Diane E. Papilla and Sally Wendkos Olds, Psychology) The word ''thus'' expresses the claim that something is being inferred, so the passage is an argument.

Inferential claim

the premises deal with some known event in the present or past, and the conclusion moves beyond this event to some event in the relative 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" are examples of a ___________________ 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.

Prediction

The following arguments are inductive. Determine whether each is strong or weak, and note the relationship between your answer and the truth or falsity of the premise(s) and conclusion. Then determine whether each argument is cogent or uncogent. All previous American presidents were women. Therefore, probably the next American president will be a woman.

Strong - false premise, probably false conclusion (uncogent)

None Exist

Strong - true premises, probably false conclusion

The following arguments are inductive. Determine whether each is strong or weak, and note the relationship between your answer and the truth or falsity of the premise(s) and conclusion. Then determine whether each argument is cogent or uncogent. All previous American presidents were television debaters. Therefore, probably the next American president will be a television debater.

Strong - true premises, probably true conclusion (uncogent)

The following arguments are inductive. Determine whether each is strong or weak, and note the relationship between your answer and the truth or falsity of the premise(s) and conclusion. Then determine whether each argument is cogent or uncogent. All previous American presidents were men. Therefore, probably the next American president will be a man.

Strong - true premises, true conclusion (cogent)

An inductive argument such that if the premises are assumed true, then the conclusion is probably true.

Strong inductive argument

A cogent argument must be inductively strong.

True

True or False? A strong argument may have false premises and a probably false conclusion.

True

True or False? Inductive arguments admit of varying degrees of strength and weakness

True

The following arguments are inductive. Determine whether each is strong or weak, and note the relationship between your answer and the truth or falsity of the premise(s) and conclusion. Then determine whether each argument is cogent or uncogent. A few American presidents were Libertarians. Therefore, probably the next American president will be a Libertarian.

Weak - false premise, probably false conclusion (uncogent)

The following arguments are inductive. Determine whether each is strong or weak, and note the relationship between your answer and the truth or falsity of the premise(s) and conclusion. Then determine whether each argument is cogent or uncogent. A few American presidents were Libertarians. Therefore, probably the next American president will be a television debater.

Weak - false premise, probably true conclusion (unsound)

The following arguments are inductive. Determine whether each is strong or weak, and note the relationship between your answer and the truth or falsity of the premise(s) and conclusion. Then determine whether each argument is cogent or uncogent. A few American presidents were Federalists. Therefore, probably the next American president will be a Federalist.

Weak - true premise, probably false conclusion (uncogent)

The following arguments are inductive. Determine whether each is strong or weak, and note the relationship between your answer and the truth or falsity of the premise(s) and conclusion. Then determine whether each argument is cogent or uncogent. A few American presidents were Federalists. Therefore, probably the next American president will be a man.

Weak - true premise, probably true conclusion (uncogent)

An inductive argument such that if the premises are assumed true the conclusion does not follow probably from the premises, even though it is claimed to.

Weak inductive argument

A sentence that is either true or false. Argentina is located in North America. Rembrandt was a painter. The first ______________ is true, the second false.

statement

the truth or falsity of a statement The ________ __________ of the statement "Rembrandt was a painter" is true, the truth value of the statement "Argentina is in North America" is false.

truth value

an inductive argument that is weak, has one or more false premises, or both.

uncogent argument

The following arguments are inductive. Determine whether each is strong or weak, and note the relationship between your answer and the truth or falsity of the premise(s) and conclusion. Then determine whether each argument is cogent or uncogent. A few American presidents were Federalists. Therefore, probably the next American president will be a man

weak - true premise, probably true conclusion (uncogent)