Introduction

    To begin thinking about the nature of arguments, try to evaluate the following arguments. Do this by asking yourself, Does the conclusion (the statement following "therefore") logically follow from the other statements (the premises)? Or in other words, ask yourself, Ifthe premises were true, would the conclusion have to be true? Notice that it is not necessary to agree that the premises are true to decide that the conclusion logically follows from them. If the conclusion does not follow (it is a bad argument), imagine how you would explain to someone else why it is a bad argument

 1 .If the universe shows evidence of design, then there is a God. The universe shows evidence of design. Therefore, there is a God.

 2. If Jones is a mother, then Jones is a parent. But Jones is not a mother. Therefore, Jones is not a parent.

 3. If Thomas Aquinas's arguments for God are good ones, then there is a God. But Thomas Aquinas's arguments for God are not good ones. Therefore, there is not a God.

 4. After a lifetime of proclaiming the death of God, Friedrich Nietzsche died completely insane. Therefore, his arguments for atheism must be worthless.

 5. No one has proven that there is not a God. Therefore, God must exist.

 6. If there was not a God, I could not bear to live my life. Therefore, there is a God.

    Do not feel stressed if you had problems figuring these arguments out, because such analysis is what this section is all about. These same examples will be repeated again in our discussion of arguments, so the answers to these exercises will appear later on.
 

     In order to evaluate and choose between competing philosophical claims and theories, philosophers have agreed on a number of criteria, or tests. We will consider the six most common ones. I have formulated each criterion so that it contains a keyword that begins with the letter c in order to make the points easy to remember. The criteria are (1) conceptual clarity, (2) consistency, (3) rational coherence, (4) comprehensiveness, (5) compatibility with well- established facts and theories, and (6) having the support -of compelling arguments. We will briefly look at each one in turn.

 Clarity

 Conceptual clarity is the first test that a philosophy must pass. If the terms or concepts in which the philosophy is expressed are not clear, then we don~t know precisely what claim is being put forth. Suppose someone says, "The only thing in life that has value is pleasure." We need to ask, What does the author mean by "pleasure"? Is the term referring only to physical sensations, or do intellectual pleasures count? If it makes me feel good to sacrifice my own needs for those of others, am I really pursuing pleasure?

 Consistency

 Consistency is the second test that a philosophy must pass. A philosophy cannot contain any contradictions. One way a philosophy flunks this test is through logical inconsistency, which consists in making two assertions that could not both be true under any possible circumstances. The most obvious case of this inconsistency would be any claim of the form, "A is true and not-A is true." For example, if I claim that God determines everything that happens in the world at the same time that I claim that humans have free will, I appear to have an inconsistency. The first claim implies that God determines what choices we make, but this claim seems to conflict with the claim that we freely make our own choices. The terms determines and ftee will would have to be defined differently than they normally are to avoid the inconsistency. A second kind of inconsistency is more subtle. It is called self-referential inconsistency, and it occurs if an assertion implies that it itself cannot be true, or cannot be known to be true, or should not be believed. My statement that "All opinions are false" implies that the opinion I just expressed is false. Similarly, my claim that "Only statements that can be scientifically proven should be believed" is a statement that cannot be scientifically proven.

 Coherence

 Rational coherence is a criterion that considers how well the various parts of a philosophy "hang together." The elements of a philosophy may not be explicitly contradictory, but they can still fail to fit together very well. A philosopher who believes that God acts in the world but who fails to explain how that belief fits together with the belief that nature runs according to universal physical laws has articulated a philosophy that lacks coherence. Similarly, philosopher Ren6 Descartes argued that humans are made up of a physical body and a nonextended, nonphysical mind. Although he believed that the two interacted, he failed to make clear how such different types of substances could causally influence one another. This gap in his theory earned him low points on the coherence criteria in the minds of many critics.

 Comprehensiveness

 We evaluate a philosophy positively if it makes sense out of a wide range of phenomena; we evaluate it negatively if it ignores significant areas of human experience or raises more questions than it answers. A philosophy that illuminates humanitys scientific, moral, aesthetic, and religious experience is better than one that explains only science but ignores the rest of human experience. To take a more specific example, a philosopher who claims that all knowledge is based on sensory data but who fails to explain how we can have mathematical knowledge or moral knowledge falls short on this criterion. Similarly, a philosopher who claims that all morality is derived from the Ten Commandments but who fails to explain how some cultures have developed similar moral principles even if they never heard of these commandments fails in terms of comprehensiveness.

logical inconsistency two assertions that could not both be true under any possible circumstances

self-referential inconsistency an assumption that implies that it itself cannot be true, cannot be known to be true, or should not be believed
 

Compatibility

 Compatibility with well-established facts and theories is important because a good theory (in philosophy or science) is one that increases our understanding by unifying our knowledge. Hence, a theory that flies in the face of the rest of our understanding of the world may require us to lose more than we gain. For example, a philosophical theory about the mind should fit with the well-established findings of biology and psychology. There are, however, exceptions to this rule. Throughout history, well-argued theories in philosophy and science have sometimes required us to violate common sense and abandon centuries-old beliefs, resulting in new knowledge. Nevertheless, we should do so only when the new theory is better than its competitors and promises to replace our current beliefs with an increase in understanding.
 

Compelling Arguments

 Before I discuss the sixth criterion, I think it will be worthwhile to discuss a special type of reasoning that is commonly used in philosophy (as well as science). This form of reasoning is known as an inference to the best explanation. (This sort of reasoning is sometimes called abduction.) Unlike the sorts of arguments we will be discussing shortly, an inference to the best explanation does not try to directly prove the truth of a theory; it tries to show that the theory is superior to all its competitors and that it is therefore the one most likely to be true. This way of showing that a particular theory is the best one makes use of the five criteria discussed thus far. An inference to the best explanation has the following form:

 1.There is a collection of data that needs an explanation.

 2. A theory is proposed that offers an explanation of the data.

 3.This theory offers the best explanation of all known alternatives.

 4.Therefore, until a better explanation is proposed, it is rational to believe this theory.

 This method of reasoning can best be illustrated by an example from science. In the 1930s, scientists were puzzled by a type of event, known as beta decay, in which an atom disintegrates into its parts. The problem was that a measurable sum of energy seemed to disappear into thin air in the process, thus violating the conservation of energy, a sacred principle in physics. Wolfgang Paull, a twenty-year-old physicist, proposed, that the missing energy could be accounted for by supposing that an unobserved particle was included with the other particles that were flung off from the atom. The problem was that to balance the numbers in the equations, this unknown particle had to have no electric charge, its mass had to be nearly zero or equal to zero, and besides being extremely small, it had to travel near the speed of light. In short, the mystery particle (which came to be called the neutrino) had to be completely incapable of being observed.

Inference to the best explanation a form of reasoning that tries to show that a particular theory is superior to all its competitors and that it is therefore the one most likely to be true; sometimes called abduction

 Physicists were reluctant to accept the existence of the neutrino because of the criterion of compatibility. It was incompatible with the long and firmly held belief that all entities accepted by science had to be observed. On the other hand, this theory was not only compatible with the conservation of energy, but it saved this more fundamental principle from being abandoned. Furthermore, in terms of the other criteria, the neutrino theory was clear and consistent, it brought coherence by preserving the closely-knit fabric of physics, and it scored high on comprehensiveness because it eventually explained other events besides beta decay. Almost thirty years later, physicists designed a very elaborate and expensive experiment whose results suggested that they could detect the effects of a neutrino interacting with another particle. However, no matter how useful the neutrino postulate is and how many events it explains, we will never directly observe one. The only reason scientists believe in it is because it makes sense out of so many other events we believe and can observe.

 The evidence and explanations that are offered in science (as in the case of the neutrino) can provide very helpful models for understanding the explanations that are provided by philosophical theories. First, scientists cannot always directly observe the entities or events postulated by their theories (neutrinos, quarks, black holes, the big bang). Similarly, in philosophy we cannot directly observe with our senses the presence or absence of God, free will, moral values, or justice. Second, inferences to the best explanation in science and philosophy are evaluated using the five criteria that we have discussed thus far and can be used to justify belief in either neutrinos or in the claims made by philosophers. For example, various philosophers attempt to justify claims such as the following: there is a God, mental events are really brain events, humans have free will, the morality of an action is determined by the consequences. Even though the defense of such claims cannot take the form of a confirming observation, philosophers can try to show that these theories make the best sense of what we do know and observe.

 In addition to arguing that a philosophical theory provides the best explanation of what we are trying to understand, philosophers also try to Justify their theories more directly. They do this through the support of compelling arguments. This method of justifying a claim attempts to show that from certain true (or plausible) statements, the claim either necessarily follows or is highly probable. The rest of this chapter is a discussion of the nature of arguments and how to decide whether they are compelling.
 
 

 Philosophers attempt to establish the truth of their claims by means of arguments. But the word argument has two different meanings in everyday discourse. Suppose that two students were discussing whether there is a God, and they began shouting at each other, saying, "Yes there is," "No there isn't," "Yes there is, " "No there isn't." If the exchange began to be quite heated, we might say that they were having an argument. In this context, argument would mean "a contentious dispute." However, this definition is not what philosophers mean by argument. In philosophy, an argument is a set of statements in which one or more of the statements attempt to provide reasons or evidence for the truth of another statement. A premise is a statement in an argument that serves to provide evidence for the truth of a claim. A conclusion is the statement in an argument that the premises are claimed to support or imply.

 An important step in analyzing an argument is deciding which statements are the premises and which is the conclusion. Often the conclusion is the last statement in a passage. However, an author may place the conclusion first or even in the middle. Using common sense and grasping the author's intentions are the best ways to figure out the elements of a particular argument. Key terms are often used to indicate which statements are premises and which are conclusions. Premise indicators are terms that usually indicate that a premise will follow. Typical examples of premise indicators are since, because, for, given that. Conclusion indicators are terms that usually indicate that a conclusion will follow. Typical examples of conclusion indicators are therefore, so, hence, thus, consequently.

 When it comes to determining whether an argument is acceptable, we can get some tips from the field of architecture. In the late Middle Ages, cathedral architects were obsessed with the goal of designing each successive cathedral to reach higher into the skies than the previous ones. The crowning glory of the architects' craft was thought to be the Beauvais Cathedral in France, whose ceiling rose to a height of 157 feet. This competition to break architectural records came to a sudden halt in 1284, however, when the main structural arches of Beauvais collapsed, unable to bear the weight that had been imposed on them.

 Recently, I visited a college campus in which the focal point was a six-story administrative building. The outside walls were made from a newly invented composite material containing concrete and stone that had been formed into huge panels. Unfortunately, the new material did not hold up and large chunks of the stone slabs began falling off the building. After pouring hundreds of thousands of dollars into vain attempts to fix the problem, the building finally had to be torn down.

 So what does architecture and building construction have to do with philosophy? Think of the ways in which constructing a building and constructing a philosophical position or argument are similar. Consider what is necessary for a building to be solid and well designed. Compare that with what is necessary for an argument to be solid and well designed. Think about the ways that the buildings mentioned in the text failed and the ways in which a philosophical argument can fail. Can you think of any further analogies or connections between buildings and philosophy?

argument:   a set of statements in which one or more of the statements attempt to provide reasons or evidence for the truth of another statement

premise:   a statement in an argument that serves to provide evidence for the truth of a claim

conclusion:   the statement in an argument that the premises are claimed to support or imply premise indicators terms that usually indicate that a premise will follow.

conclusion indicators:   terms that usually indicate that a conclusion will follow
 

The two examples of the failed buildings are not alike. In the case of the Beauvais Cathedral there was nothing wrong with the materials used; they were the solid blocks of stone used in all cathedrals. The problem was a structural one. The arches of the building were not designed to support the weight of the ceiling. Similarly, a philosophical argument can fall because of structural defects. These defects occur when the form of the argument is such that the premises do not provide adequate support for the conclusion. In the case of the contemporary college building, the architect's design of the skeletal structure of the building was okay but the materials that were attached to it were faulty. The concrete slabs cracked, fell apart, and disintegrated. Similarly, an argument can be defective if the premises are known to be false or are, at least, implausible.

 Here is an example of an argument in which the form is structurally flawed even though the premises are true (nothing is wrong with the materials composing the argument):

 1. If Ronald Reagan was a U.S. president, then he was famous.

 2. Ronald Reagan was famous.

 3. Therefore, Ronald Reagan was a U.S. president.

 I think that your logical intuitions will tell you that even though both premises are true and the conclusion is true, the conclusion does not logically follow from the premises. This lack of logic can be shown by the fact that in 1960 both premises were true but the conclusion was false, because Ronald Reagan was famous for being a movie star and not a president. Hence, even though the conclusion happens to be true, it does not logically follow from the premises.

 In the next example, the form of the argument is a good one, but the premises are false (the materials that fill out the form are faulty):

 1. If President George Washington was a horse, then he had five legs.

 2. President George Washington was a horse.

 3. Therefore, President George Washington had five legs.

 In this case, if the premises were true, the conclusion would have to be true. In other words, the conclusion logically follows from the premises. The problem, of course, is that this argument starts from false premises.

 These examples provide us with two basic questions to ask about an argument: (1) If the premises were true, would they provide adequate logical support for the conclusion? and (2) Are the premises true (or at least plausible)? The answer to the first question concerns logic, the study of methods for evaluating arguments and reasoning. Any standard textbook in logic will provide many techniques for determining how strongly the premises support the conclusion, but in this chapter I can only provide a few guidelines. A rather simple way to approach the question is to ask yourself, How easy would it be to imagine that all the premises were true at the same time the conclusion was false? If there are many ways to imagine that the premises were true and the conclusion false, this finding may indicate that the truth of  logic the study of methods for evaluating arguments and reasoning  sometimes in Latin. In each case, I represent the skeletal structure of the argument in terms of various letters, such as P and Q The letters are variables that stand for propositions. To the right of each argument form, I add flesh to the skeleton by replacing the letter variables with actual propositions. To make this discussion of logic relevant to our philosophical journey, I then provide a simple philosophical argument that makes use of the form in question. While examining these examples of valid or invalid arguments for a philosophical conclusion, do not suppose that the example is the last word on the particular issue or that the arguments are the best ones available for the conclusion. In each case, if the argument is valid and you disagree with the conclusion (e.g., "there is a God" or "there is not a God"), then try to figure out a basis for questioning one or more of the premises.

 Before discussing the first set of argument forms, we need to examine the nature of conditional statements (also known as hypothetical statements). A conditional statement contains two simpler statements that are connected with the words ifthen. For example:

 If it is raining, then the ground is wet.

 If you study, then you will get good grades.

 If Jones is pregnant, then Jones is a female.

 The first part of a conditional statement (which follows the "if") is called the antecedent. The second part (which follows the "then") is called the consequent. In the examples the antecedents are "it is raining, 11 11 you study", and "Jones is pregnant." The consequents are "the ground is wet," "you will get good grade," and "Jones is a female."

 A conditional statement claims that the truth of the antecedent is a sufficient condition for the truth of the consequent. To say that A is a sufficient condition for B means that if A is true, then B is true. Sometimes the conditions that would make the antecedent true would cause conditions that would make the consequent true (as in the first two of the previous examples). However, Jones being pregnant does not cause Jones to be a female. So the notion of a sufficient condition has to do with the relationship between the truth of each statement and does not always express a causal relationship. A conditional statement also claims that the consequent is a necessary condition for the antecedent to be true. To say that A is a necessary condition for B means that for B to be true, A must be true. For example, being a female is a necessary condition for being pregnant. However, being a female is not a sufficient condition for being pregnant. These remarks about conditional statements are illustrated by the first five argument forms, which all contain conditional statements.

 Modus Ponens

1. If P, then Q         1. If Spot is a dog, then Spot is a mammal.
2. P.                        2.    Spot is a dog.
3. Therefore, Q       3. Therefore, Spot is a mammal.

 conditional statement-- two simpler statements that are connected with the words ifand then

 antecedent-- the first part of a conditional statement (the if clause)

 consequent-- the second part of a conditional statement (the then clause)

 sufficient condition-- statement A is a sufficient condition for statement B if the truth of A guarantees the truth of B

 necessary condition-- statement A is a necessary condition for statement B if the truth of B requires the truth of A
 

Philosophical Example of Modus Ponens

 1. If the universe shows evidence of design, then there is a God.

 2. The universe shows evidence of design.

 3. Therefore, there is a God.

 Modus ponens is also known as affirming the antecedent.
 
 

 Modus Tollens

 1. If P, then Q                   1. If John is eligible for the award, then he is a junior.

 2. Not-Q.                           2. John is not a junior.

 3.Therefore, not-P           3. Therefore, John is not eligible for the award.

 Philosophical Examples of Modus Tollens

 1.  If we are morally responsible for our actions, then we have freedom of the will.

 2.  We do not have freedom of the will.

 3.  Therefore, we are not morally responsible for our actions.
 

1.  If God exists, there would be no unnecessary evil in the world.

2.  There is unnecessary evil in the world.

3.  Therefore, God does not exist.

 Since modus tollens (also known as denying the consequent) is a valid argument form, it is clear that this argument about God's existence is valid. That is, if the premises are true, then the conclusion logically follows. Consequently, a theist who rejects the conclusion would have to find reasons for rejecting at least one of the premises. The first premise seems consistent with the traditional concept of God. So a theist would probably want to question the truth of the second premise by asking, Do we really know that there is unnecessary evil in the world? and Isn't it possible that all apparent evil is justified in terms of some greater good that the evil achieves? I explore these issues further in the section on the problem of evil in chapter 4 (section 4.5).

 Fallacy of Denying the Antecedent

 A fallacy is an argument form that is logically defective because the premises provide little or no support for the conclusion. Two invalid arguments (deductive fallacies) can be confused with either modus ponens or modus tollens. The first is the fallacy of denying the antecedent, which has this form:

 1. If P, then Q               1.  If Jones is a mother, then Jones is a parent.

 2. Not-P.                      2. Jones is not a mother.

 3. Therefore, not-Q     3. Therefore, Jones is not a parent.

 modus ponens - a valid argument form that has this pattern: If P then Q, P, therefore Q.

 modus tollens - a valid argument form that has this pattern: If P then Q, not-Q, therefore not-P.

 fallacy - an argument form that is logically defective because the premises provide little or no support for the conclusion
 

As the example illustrates, this argument form is invalid because we can imagine a situation in which the premises are true and the conclusion false. If Jones is a father, then it is true that Jones is not a mother but false that Jones is not a parent.

 Philosophical Example of the Fallacy of Denying the Antecedent

 1. If Thomas Aquinas's arguments for God are valid, then there is a God.

 2. Thomas Aquinas's arguments for God are not valid.

 3. Therefore, there is not a God.

 This example is an argument about arguments, and it illustrates an important point. If you refute a philosopher's argument, you have not shown that his or her conclusion is false, you have merely shown that this particular proof for the conclusion fails. A theist could agree with both premises of the previous argument but still not accept the conclusion, for other arguments besides those of Aquinas could prove God's existence. Furthermore, some theists, such as Blaise Pascal and Soren Merkegaard (see section 4.4), would claim that from a lack of rational arguments for God's existence it does not follow that God does not exist, but merely that reason is not the correct means to find God.

 Fallacy of Affirming the Consequent

 The fallacy of affirming the consequent is another invalid argument form that is also a counterfeit version of the valid forms of modus ponens and modus tollens.

 1. If P, then Q                1. If George Washington was assassinated, then he is dead.

 2. Q                                 2. George Washington is dead.

 3.Therefore, R               3. Therefore, George Washington was assassinated.
 

Philosophical Example of the Fallacy of Affirming the Consequent

 1.If morality is completely subjective, then people will differ in their moral beliefs.

 2.People do differ in their moral beliefs.

 3.Therefore, morality is completely subjective. (There are no objective truths about what is morally right or wrong.)

 One way to show that an argument is invalid is to construct another argument that has the same form as the original but goes from true premises to a false conclusion. This argument would be an invalid argument because a valid argument will always carry us from true information to a true conclusion. However, if the form of reasoning is the same as the original argument, the counterexample will show that the original argument is invalid also. Because the following argument is the same as the argument about morality except for the subject matter, it shows that the previous argument is invalid.
 

I .   If medical science is completely subjective, then people will differ in their medical beliefs.

2.   People do differ in their medical beliefs. (Some people believe that sacrificing twin babies will cure the community of a plague; on the other hand, our society doestA believe this.)

3.  Therefore, medical science is completely subjective. (There are no objective truths about what will or won't cure disease-a false conclusion.)

 Hypothetical Syllogism

 A syllogism is a deductive argument with two premises and a conclusion. Some syllogism a deduclogic books call the following type of syllogism a pure hypothetical syllogism to tive argument with distinguish it from arguments such as modus ponens and modus tollens, which two premises and a are partially hypothetical in that they contain one hypothetical (or conditional) conclusion premise.

1. If P, then Q                               1.If I learn logic, then I will write better essays.

2. If Q, then R.                               2.If I write better essays, then I will get better grades.

3. Therefore, if P, then R.           3.Therefore, if I learn logic, then I will get better
     grades.

 Philosophical Example of a Valid Hypothetical Syllogism

 I .If the methods of science give us only information about physical reality, then science cannot tell us whether a nonphysical reality exists.

 2.If science cannot tell us whether a nonphysical reality exists, then science cannot tell us whether we have a soul.

 3.Therefore, if the methods of science give us only information about physical reality, then science cannot tell us whether we have a soul.

 Notice that the key to a hypothetical syllogism is that the consequent (Q) of one premise is the antecedent (Q) of the other premise such that the premises could be linked up like a chain if they were laid end to end. This connection would be true even if the order of the premises were reversed. Furthermore, the antecedent of the conclusion (P) is the beginning of the chain formed by the premises, and the consequent of the conclusion (R) is the end of the chain. Any other arrangement will be invalid, as in the following examples.

 Counterfeit (Invalid) Hypothetical Syllogisms

 1. If P, then Q                                 1. If P, then Q

 2. If R, then Q                                 2. If Q, then R.

 3. Therefore, if P, then R.             3. Therefore, if R, then P.
 

See if you can substitute statements for the letter variables in the previous invalid hypothetical syllogisms. Try to construct arguments that follow the given forms but in which true premises lead to a false conclusion in order to show that something is wrong with  these types of arguments.
 

Disjunctive Syllogism

 A disjunctive argument contains a disjunctive statement in a premise. A disjunctive statement asserts that at least one of two alternatives is true. It typically is expressed as an either-or statement. Normally a disjunctive statement asserts that at least one alternative is true and possibly both. For example, if Sherlock Holmes determines that the murder was an inside job, he might state, "Either the butler is guilty or the maid is guilty." Obviously, the fact that one of them must be guilty also includes the possibility that both of them are guilty. Here is what a disjunctive syllogism looks like:
 

1. Either P or Q                          1.   Either the bulb is burnt out or it is not receiving electricity.

2. Not-P.                                     2.   The bulb is not burnt out.

3. Therefore, Q                            3.   It is not receiving electricity

PhilosophicalExample of a Disjunctive Syllogism

1.Either the universe contains in itself a sufficient reason for its existence or it was caused to exist.

2.The universe does not contain in itself a sufficient reason for its existence.

3.Therefore, the universe was caused to exist.
 

Fallacy of Affirming the Disjunct

 1. Either P or Q                     1.Either the bulb is burnt out or it is not receiving electricity.

 2. P.                                       2. The bulb is burnt out.

 3. Therefore, not-Q               3. Therefore, it is not receiving electricity.

The fallacy of affirming the disjunct is an invalid argument form that is a counterfeit of the dis)unctive syllogism. In the example just given, the fact that the bulb is burnt out does not exclude the possibility that there are problems with the electricity as well. Since both alternatives could be true in a normal disjunction, simply affirming one alternative does not prove that the other is false. However, if the disjunction contained two contradictories (two statements that could not both be true), then this type of argument would be valid. For example, if the first premise
disjunctive statement a statement that asserts that at least one of two alternatives is true was  "Either Howard is married or he is single," then the truth of one statement would imply the falsity of the other.

 Philosophical Example of the Fallacy of Affirming the Disjunct

 1.Either reason is the source of moral principles or divine revelation is.

 2.Reason is the source of moral principles.

 3.Therefore, divine revelation is not the source of moral principles.

 In this case, the conclusion does not follow because the two statements in the disjunction could both be true. (Some philosophers, such as Thomas Aquinas, believed that both reason and revelation could provide us with moral principles.)

 Reductio ad Absurdum Arguments

 The label of the reductio ad absurdum argument, a valid argument form, means "reducing to an absurdity." To use this technique, you begin by assuming that your opponent's position is true and then you show that it logically implies either an absurd conclusion or one that contradicts itself or that it contradicts other conclusions held by your opponent. Deducing a clearly false statement from a proposition is definitive proof that the original assumption was false and is a way of exposing an inconsistency that is lurking in an opponent's position. When the reductio ad absurdum argument is done well, it is an effective way to refute a position.

Typically, the argument follows this form:

 1.   Suppose the truth of A (the position that you wish to refute).

 2.   If A, then B.

 3.   If B, then C.

 4.   if C, then not-A.

 5.   Therefore, both A and not-A.

 6.   But 5 is a contradiction, so the original assumption must be false and not-A must be true.

A variation of the reductio ad absurdum argument is one in which the conclusion is something that is obviously false, even though it does not contradict one of the premises.

Philosophical Example of a Reductio Ad Absurdum.

As I mentioned in the previous section, Socrates' philosophical opponents, the Sophists, believed that all truth was subjective and relative. Protagoras, one of the most famous Sophists, argued that one opinion is just as true as another opinion. The following is a summary of the argument that Socrates used to refute this position.

 I.   One opinion is just as true as another opinion. (Socrates assumes the truth of Protagoras's position.)

 2.  Protagoras's critics have the following opinion: "Protagoras's opinion is false and that of his critics is true."

 3.  Since Protagoras believes premise 1, he believes that the opinion of his critics in premise 2 is true.

 reductio ad absurdum argument argument form that begins with an assumption that the opponent's position is true and then proceeds to show that that position logically implies an absurd conclusion, a conclusion that contradicts itself, or a conclusion that contradicts other conclusions held by the opponent, or a conclusion that is obviously false.

4.  Hence, Protagoras also believes it is true that: "Protagoras's opinion is false and that of his critics is true."

5.  Since individual opinion determines what is true and everyone (both Protagoras and his critics) believe the statement "Protagoras's opinion is false," it follows that

6.  Protagoras's opinion is false.
 
 

 Unlike deductive arguments, inductive arguments do not show that the conclusion necessarily follows from the premises. Instead, these arguments. try to demonstrate that if the premises are true, then it is highly probable that the conclusion is true. One common form of inductive argument starts from the observation that a number of similar cases have a certain property in common and concludes that all other cases of this type will also have that property. For example, a medical researcher finds that everyone who has a rare form of cancer was exposed to a certain toxic chemical; when she encounters a new patient with this disease, she will suspect that this person has been exposed to the same chemical. Here are two examples of philosophical arguments based on inductive reasoning. Since different philosophers will evaluate these arguments differently, I leave it up to you to decide how strong you think these arguments are.

1.  Every event that we have observed has had a cause.

2.  Therefore, it is rational to presume that all events have a cause.

1.  In the past, when something seemed mysterious and unexplainable (such as solar eclipses), eventually it was found that it could be scientifically explained as the result of physical causes.

 2.  Consciousness seems mysterious and unexplainable.

 3.  Therefore it is probable that someday consciousness will be scientifically explained as the result of physical
      causes.

Although a large part of our everyday lives and the scientific method is based on inductive reasoning, inductive arguments do not have the simple techniques that deductive arguments do for deciding whether the arguments are strong or weak. There are, however, a few rules to keep in mind when watching out for fallacious inductive arguments. I discuss three such fallacious inductive arguments here.

Hasty Generalization Fallacy

When generalizing from facts about some cases of a certain type to a conclusion about all cases of that type, you must be sure that the premises are based on a sufficient number of observations and that the sample is representative. Failure to do so is to commit the fallacy of hasty generalization in which a general conclusion is drawn from premises that are not based on a sufficient number of observations or from premises in which the sample is not representative

Philosophical Examples of the Hasty Generalization Fallacy.

The physician and psychologist Sigmund Freud was the founder of the twentieth-century theory of psychoanalysis. In developing his theory he formed conclusions about the nature of religious belief. He speculated that religion was embraced by people who were emotionally weak and who projected the image of their own father onto the cosmos to create a heavenly father who would always be there for them. The problem was that as a therapist, Freud was exposed to multitudes of patients who were emotion ally disturbed. Given the times and the culture, most of them were also religious. So, Freud studied numerous cases of emotionally disturbed religious people and concluded that religion was psychologically dysfunctional. Given the biased sample of religious people he studied, it is likely that he committed the fallacy of hasty generalization. Since then, psychologists of religion have also studied emotionally mature religious people and developed a more balanced view of religious belief.

The citizens of a small, rural town were shocked when a local teenager took a gun to school and massacred many of his classmates. It was discovered that he belonged to a cult of like-minded youths who engaged in satanic practices and read the philosopher Nietzsche. Some ministers used this incident as evidence that people who read "weird stuff" like philosophy are dangerous to society. But this hasty generalization ignores the millions of people who have read and enjoyed Nietzsche but who did not kill their colleagues. It also assumes that reading Nietzsche was the cause of the student's violence. The student may have been psychologically compelled to violence even if he had not read Nietzsche (see the false cause fallacy discussed next).

"There have been a number of financial and sexual scandals involving television evangelists in recent years. Therefore, it is likely that all religious people are frauds." This argument is a hasty generalization because the conclusion is about all religious people but it is based on a small and unrepresentative sample of this group.

 False Cause Fallacy

 Another form of induction reasons to the causes of a given event. The false cause fallacy is committed when we assume that simply because event X occurred before event Y, we may conclude that X caused Y. Causal connections are very difficult to establish; simple priority in time all by itself is usually insufficient to draw these connections.

Philosophical Examples of the False Cause Fallacy.

"Nietzsche spent a lifetime publishing his atheistic philosophy. He died totally insane. Therefore, his own, dismal philosophy drove him mad." This causal reasoning overlooks the fact that some religiously pious people have gone insane and ignores the evidence that Nietzsche had a neurological disease.

"As sexually explicit movies have increased in number over the years, so have the number of sex crimes. Therefore, the movies have caused the crimes." These data show that sexually explicit movies cause sex crimes.

 false cause fallacy-  the assumption that because event X occurred before event Y, X caused Y are insufficient to establish a causal connection. It is also a fact that church attendance has increased over the years. Could we then conclude that the movies have caused church attendance to rise or that the increase in church attendance has caused the increase in crime?

 False Analogy Fallacy

Some inductive arguments are based on an analogy. An argument from analogy is one in which the premises state that two cases share one or more properties in common. It is then concluded that a further property of the first case will also be a property of the second case. Some analogies can be useful, as when we learn about false analogy fallacyhuman physiology by studying that of primates. However, the false analogy fallacy  in which the fallacy is committed when there are more differences between the two situations than there are similarities. For example, if I have a 1980 gas-guzzling car that is blue and two or more cases my friend has a brand new compact car that is blue, the similarity in color is not that contain moresufficient to conclude that my car will get the same gas mileage as hers.
differences than similarities

Philosophical Examples of the False Analogy Fallacy.

"Nobody can be healthful without exercise, neither natural body or politic; and certainly to a kingdom or estate, a just and honourable war is the true exercise. A civil war indeed is like the heat of a fever; but a foreign war is like the heat of exercise, and serveth to keep the body in health."  This defense of war by Fra d nations and that individual exercise,  unlike war, does not kill people.

It was common in the eighteenth century to argue for God's existence from the evidence of design in the world. It was said, for example, that the regular move ments of the planets were like those of a clock. Since a clock had a designer, so the universe must have had a divine designer. The skeptic David Hume countered by saying, in effect, that this argument committed the fallacy of false analogy. It picked out one analogy in preference to many other possible ones. By way of counter  example, he suggested that the universe could more likely be compared to a vegetable than a clock. The particles given off by comets, for example, might function like the seeds given off by trees. After the comet passes through our galaxy, it sprouts new planetary systems in the outer darkness. Hume's point was that the clock analogy of the theists is no more likely than this analogy.
 
 

In this section, I survey several types of defective arguments known as informal type of bad reasoning fallacies. Informal fallacies are types of bad reasoning that can only be detected by that can only be de-examining the content of the argument. In most cases, if you set out the formal tected by examining structure of the arguments using the letters P and Q as we did previously, the the content of theproblem with the reasoning would not be evident. On the surface, the following argumentinvalid argument has the valid form of a modus ponens argument: "If something is a ruler, then it is twelve inches long, and the Queen is a ruler, so the Queen is twelve inches long." Actually, it only superficially has the form of a modus ponens argument because the term ruler shifts its meaning from one premise to the next. The  following selection of informal fallacies is not an exhaustive list, but it contains many of the typical kinds of bad reasoning that you are likely to encounter in philosophical discussions.

 Ad Hominem (Abusive)

 Ad hominem means "against the person." The abusive ad hominem fallacy consists of an attempt to reject someone's conclusion by attacking the person making the claim. The problem is that simply providing negative information about a person does not prove that his or her claims are false.

Philosophical Examples of the Abusive Ad Hominem Fallacy.

"After a lifetime of proclaiming the death of God, Friedrich Nietzsche died completely insane. Therefore, his arguments for atheism must be worthless."

"Immanuel Kant was a rigid neurotic who never traveled more than sixty miles from the place of his birth. How could anyone who was so limited and inexperienced have anything worthwhile to say about morality? Therefore, we do not need to bother looking at Kant's arguments for an objective morality."

 Ad Hominem (Circumstantial)

 Someone using the circumstantial ad hominem argument does not verbally abuse the opponent but dismisses his or her arguments by suggesting that the opponent's circumstances are the sole reason why he or she embraces the conclusion. In other words, this argument is a way of ignoring the opponent's arguments and of refusing to evaluate them on their own terms.

Philosophical Examples of the Circumstantial Ad Hominem Fallacy.

"We do not need to consider Thomas Aquinas's arguments for the existence of God, because he was a Christian monk. Of course he thought belief in God was reasonable. In putting forth his proofs he was simply trying to rationalize a faith he already held."

 "We do not need to consider philosopher Bertrand Russell's arguments against the existence of God. He was raised in a very strict religious home, which turned him against religion. That upbringing is the real reason he was an atheist."

 Appeal to Ignorance

The appeal to ignorance fallacy occurs when lack of evidence against a conclusion is used to prove the conclusion true or when lack of evidence for a conclusion is used to prove a conclusion false. For example, "The president of this university is a spy for a foreign power, because you cannot prove that he isn't." Generally, the person making an extraordinary claim has the burden of proof to provide positive arguments for the conclusion. Lack of evidence against the conclusion is not sufficient. When a person's character is being maligned (as in the previous example), the principle of law that states "innocent until proven guilty~' should prevail.

 Philosophical Examples of the Appeal to Ignorance.

"There must be a God, because no one has ever proven there isn't."

 "Atheism is true, because no one has ever proven there is a God."

With respect to philosophical issues such as the existence of God, if we really believe there is a lack of compelling evidence either way, then we should suspend judgment.

 Begging the Question

 Begging the question also goes by the name of circular reasoning for reasons that will soon be evident. This fallacy is committed when the premises assume the truth of the conclusion instead of providing independent evidence for it. In the simplest version begging the question has the form, V is true, therefore P is true." For example, "The dean is a liar because he never tells the truth." If you did not believe the conclusion, you would not believe the premise either, for they make identical claims.

Philosophical Examples of Begging the Question.

"God exists because the Bible says he does, and we can trust the Bible because the Bible is the inspired word of God, and we know the Bible is the word of God because God has told us in Il Timothy 3:16 that 'All scripture is inspired by God."' This argument contains two pieces of circular reasoning. It assumes the words in the Bible are the words of God and uses this assumption as evidence for the claim that the words in the Bible are the words of God. Furthermore, it assumes that there is a God who inspired the words in the Bible and uses the claims in the Bible as evidence that there is a God.

In one of his arguments against belief in divine miracles, the eighteenth-century philosopher David Hume said that the laws of nature have been established not simply by the majority of human experiences but by their unanimous testimony that collectively forms "a firm and unalterable experience." Furthermore, he claimed that there is "a uniform experience against every miraculous event."   But Hume could know this statement is true only if he knew that all the reports of miracles were false. And he could know this claim only if he knew that miracles never happened. At this point in his essay, it appears he is arguing in this fashion:

 1.  No miracle has ever happened.

 2.  So, all reports of miracles are false.

 3. Human experience universally counts against miracles.

 4. Therefore, no miracle has ever happened.

Composition Fallacy

 In the fallacy of composition a person argues from a property of each part of a whole (or member of a group) taken individually and concludes that this property also may be attributed to the whole (or group). A silly example: "Every member of this I 00-student class weighs less than 500 pounds. Therefore, the class as a whole weighs less than 500 pounds." A more subtle but equally fallacious example: "This essay is well written because every sentence in it is well written." Taken individually, each sentence may be well written, but the essay as a whole may be poorly written because it rambles, is disorganized, and lacks a central theme. Another example: "Because every member of this organization is a veteran, this organization must be a veteran's organization."

Philosophical Examples of the Fallacy of Composition.

In a famous debate with Father Frederick Copleston on the existence of God, Bertrand Russell accused Copleston of committing the fallacy of composition. Copleston had argued that because everything in the universe has a cause, the universe as a whole must have had a cause. Russell responded with this counterexample: "Every man who exists has a mother, and it seems to me that your argument is that therefore the human race must have a mother, but obviously the human race hasn't a mother-that's a different logical sphere."" (Copleston responded by arguing that the notion of cause in his argument differed from that in Russell's counter-example.)

 Early in the twentieth century, physicists discovered that the behavior of subatomic particles was random and not perfectly predictable. This discovery is called Heisenberg's principle of indeterminacy and is part of quantum mechanics. Some philosophers have used this principle as a premise in the following argument: "Because the behavior of subatomic particles is not determined but is unpredictable, and because we are made up of such particles, it follows that our behavior is unpredictable, not determined, and that we have freedom." But, critics respond, this argument is the fallacy of composition. For example, the particles making up my desk may be moving in random ways, but the statistical average of their behavior as exhibited in the desk as a whole is very predictable and determined. The same could be true of our behavior.
 

Division Fallacy

 The fallacy of division is the exact reverse of composition. Here the premise asserts that a whole or a group has some property and the argument concludes that this property applies to each one of the parts or members of the group as well. Example: "Since every third child born in New York is Roman Catholic, Protestant families there should not have more than two children." Even though the population as a whole may be one-third Catholic, it does not follow that a particular, individual family will be one third Catholic.

Philosophical Example of the Fallacy of Division.

"If there is no God, then the universe has no purpose. It follows that our individual lives have no purpose." But if the universe as a whole has no purpose, that does not mean that some parts of the universe (such as you and I) cannot find purpose in our own lives.

 Equivocation Fallacy

 The fallacy of equivocation occurs when a word or phrase changes its meaning in the course of the argument. Consider this obvious example of equivocation: "My client, your honor, should not be sent to jail, for by your own admission he is a good burglar. Surely someone who is good does not belong in jail." (In the first statement good means "competent" or "skilled." A "good burglar" is a competent burglar. In the second statement good means morally good.)

 Philosophical Examples of Equivocation.

"I had a legal right to foreclose on this widow's property without giving her a chance to negotiate, so how can you say that what I did is not right?" Here the speaker confuses a legal right with doing what is morally right. Obviously, the two are different.

 The famous nineteenth-century British philosopher John Stuart Mill (see chapter 5, section 5-3) seems to be guilty of equivocation in one of his arguments for hedonistic utilitarian ethics. He claims that happiness (which he defines as the experience of pleasure and the absence of pain) is the only thing desirable in itself His argument is that the only proof capable of being given that an object is visible is that people actually see  it. The only proof that a sound is audible is that people hear it: and so of the other sources of our experience. In like manner, I apprehend, the sole evidence it is possible to produce that anything is desirable is that people actually desire it. 14

 Now it is true that visible means "capable of being seen." But does the same sort of definition apply to desirable? Two meanings of the word desirable seem to be lurking in this passage: (1) It is trivially true that if someone desires something, we can say that for that person the thing is desirable; (2) But in ethics, desirable does not mean simply "desired," it means "worthy of being desired" or "something that ought to be desired." The two meanings of the word that Mill confuses is illustrated by this sentence: "Trixie finds drugs desirable (meaning 1), but compulsive drug addiction is not a very desirable (meaning 2) lifestyle for anyone to pursue."

 "Doctors are saying the new pill that cures baldness is nothing short of miraculous. Therefore, religious people are correct in saying that miracle healings can occur." In the premise, saying the new pill is "miraculous" is a metaphorical exaggeration, but in the conclusion, the word is being used literally.

False Dichotomy

The false dichotomy fallacy is also known as false dilemma, the either-or fallacy, bifurcation, or the black or white fallacy. It is called the black or white fallacy because one of the premises assumes that the only alternatives are the extremes of black or white (figuratively speaking), and it ignores the fine shades of gray in between. A false dichotomy argument begins with a disjunction (P or Q). However, the fallacy is committed when one or more other alternatives, such as R, are not being acknowledged. If there are other possibilities, then both P and Q could be false. Thus, by eliminating P, you have not proven that Q is true. A simple example: "Son, you will either graduate from college and make something of yourself or you will be a bum all your life." Are there other possibilities? Bill Gates, the chairman and CEO of the Microsoft Corporation and one of the richest persons in the world, dropped out of Harvard University.

 On the surface, an argument based on a false dichotomy has the valid form of a disjunctive syllogism, which is the argument on the left in the following example, whereas the real situation, represented in the argument on the right, makes clear the fallacious reasoning.

 (apparent form)            (real situation)

 1. P or Q.                        1. P or Q or R

 2. Not-P.                        2. Not-P,

 3.Therefore, Q.               3. Therefore, Q.

Philosophical Example of a False Dichotomy.

The seventeenth-century mathematician, scientist, theologian, and philosopher Blaise Pascal proposed his famous wager in which he suggested that considering religious belief is like making a bet as to which option had the best possible payoff and the least risk (see section 4.4). Pascal's argument went like this:

 1.We are faced with two choices in life: either to believe in believe in the biblical God.

 2.It is not prudent to believe in atheism. (For if we are wrong lose eternal life.)

 3.Therefore, it is prudent to believe in the biblical God.

 As with all cases of a false dichotomy, the problem is with the disjunction. The only alternatives are not limited to atheism or belief in the biblical God. There are many other religions, some of which have quite different ideas about the afterlife and some in which there is no notion of the afterlife. There is also agnosticism, the decision to believe in neither atheism nor religion until more convincing evidence is found for one view or the other. So, even a rejection of atheism does not automatically prove the wisdom of belief in Pascal's version of the biblical God.

Strawman Fallacy

The strawman fallacy occurs when someone attacks a weak version of an opponent's position or attacks a conclusion that the opponent does not support. This fallacy is like knocking over a strawman and claiming that in doing so you have defeated the world heavyweight boxing champion.

Philosophical Examples of the Strawman Fallacy.

"Thomas Aquinas argues that we should believe in God, but having religious faith requires that we throw our reason out the window. So, Aquinas thinks we should commit intellectual suicide." Because Aquinas thought that reason can show that belief in God is rational, he did not hold that we should "commit intellectual suicide" (see section 4. 1).

 "My opponent claims that we evolved from the lower animals. Therefore, because he believes we are just animals, he must believe that we should live without any civil laws, without any moral rules, and that we should mate in the streets just like dogs." But supporting the theory of evolution obviously does not entail any of the conclusions the speaker attributes to his opponent.

Wishful Thinking

Sometimes we may be tempted to believe a claim because we find the opposite conclusion to be so unpleasant. But whether we find a claim to be subjectively pleasant or not tells us nothing about its truth or falsity. Sometimes the truth about reality may be unpleasant and we simply have to face it. The problem with wishful thinking is illustrated by this example: "If I thought there was no money in my checking account, I could not sleep at night. Therefore, there must be money in my account." Here is another example of the wishful thinking fallacy: "If there was no God, I could not bear to live my life. Therefore, there is a God." A similar example: "If there is a God, then we could not live our lives any way we please. Since human beings must have moral freedom to have dignity, there cannot be a God."