Formal Analysis of Arguments
The Ideal of Logic
If the premises are true, then the conclusion must be true. Example:
"Plato"
All triangles are closed three-sided figures.
That object is a triangle.
_______________________________________
Therefore, that object is a closed three-sided figure.
"Aristotle"
All men are mortal.
Socrates is a man.
______________________
Therefore, Socrates is mortal.
"All men are mortal," is known from experience. The movement from individual experiences or facts like "Sophories is mortal" and "Creon is mortal" to the general truth, "All men are mortal" is called induction, but the movement from the general truth "All men are mortal" to "Socrates is mortal" is called deduction.
The ideal of logic has always been a deductive argument that begins with some general truth of the form "All Xs are Ys." The Western mind has subsequently constructed and reconstructed all arguments as deductive arguments, which begin with some alleged general truth or even a general norm.
Example:
We should never negotiate with blackmailers.
Terrorist are blackmailers.
________________________________________
Therefore, we should never negotiate with terrorists.
Questions of form aside, the controversial issues are whether (a) we have identified the right generalizaion (whether it is a general definition, fact, norm, or whatever), and (b) the case we are dealing with at present is an example of that generalization. While formal logic is focused on the form or structure of an argument, informal logic is concerned with disputes about (a) and (b). Before we can launch into informal logic though, we must keep in mind the structural elements. Once we know the correct form (rules of validity) we can always reconstruct an argument, our own or someone else's, in order to make it valid.
In the reconstruction process we articulate the previously unexpressed premises needed to make an argument formally valid. At the same time we thereby isolate the premises that might be controversial and serve as the subject matter of informal logic. Knowing which of our premises are controversial is important so that we may provide them with extra support or clarification, disguise them in the hope of eluding attack, or perhaps realize that they are indefensible and should be surrendered. Knowing which premises of our enemy's position are most controversial is important so that we can focus our counterattack in the most vulnerable spot.
Syllogisms
Such arguments having two premises are known as syllogisms. All arguments can be reconstructed as syllogisms, that is, as having two premises and a conclusion. Informal logic can be usefully viewed as an exercise in syllogistics reasoning involving some very questionable suppressed premises.
We shall be concerned here with categorical syllogisms. A categorical syllogism is a syllogism in which all of the statements, both premises and the conclusion, are categorical statements. A statement is categorical if it is of the subject-predicate form. That is, it is a statement with four distinguishable parts:
(1) a quantifier, (2) a subject, (3) a copula, and (4) a predicate.
Quantifier Subject Copula Predicate Code
1. All Xs Are Ys A
2. No (-) Xs Are Ys E
3. Some Xs Are Ys I
4. Some Xs Are Not Ys O
We are not concerned here with the truth or falsity of these statements but only their form.
Categorical statements may also be classified as either affirmative or negative. Statements one and three preceding page are affirmative in that they affirm something (namely the predicate) of the subject. Statements two and four are negative in that they deny something of the subject (namely the predicate). When we talk about the statements being affirmative or negative we are speaking of the quality of the statement.
In addition to a quality, statements have quantity. The quantity of a statement refers to the relationship between the quantifier and the subject term. There are three kinds of quantity: (1) universal, (2) particular, and (3) singular. A statement is (1) universal when the subject term refers to the entire class of objects that is names. Thus statements one and two previous page are universal in that they both refer to the entire class of objects that it names. Thus statements one and two previous page are universal in that they both refer to the entire class of Xs.
A statement is (2) particular when the subject term does not refer to the entire class of objects it names; rather it refers only to some part of the class. Thus statements three and four previous page are particular in that they both refer to some part of the class of Xs.
A statement is (3) singular when the subject term is a proper name referring to a single individual. An example would e the following:
"Aristotle was a great logician." Another example is "Bob Dylan is not a logician." By convention, all singular statements are treated as universal statements on the grounds that they refer to the whole of the subject.
(All of Aristotle, all of Bob Dylan).
In addition, the example about Aristotle is affirmative and the example about Bob Dylan is negative. Using the code from the chart above, the statement about Aristotle is an A statement, like "All Xs are Ys," and the statement about Bob Dylan is an E statement, like "No Xs are Ys."
Again, using the code letters, A, E, I, O, we summarize our discussion so far in the following;
A: Universal Affirmative
E: Universal Negative
I: Particular Affirmative
O: Particular Negative
The concept of quanity refers primarily to the relationship of subject term and quantifier. Quantity overlaps with another concept, distribution, which refers to the predicate term as well as to the subject term. A term (either subject or predicate) is distriuted if it refers to the whole class it names. A term is undistriuted if it refers not to the whole class it names, but to only part of the class. As is obvious from our discussion of quantity, the subject of an A statement (All Xs) and the subject of an E statement (No Xs) are both distributed. Moreover, the subject of an I statement (Some Xs) and an O stateent (Some Xs) are both undistributed.
Now let us examine the predicates.
The predicate of an A statement ("All Xs are Ys") is undistributed since we are not referring to all Ys. The predicate of an E statement ("No Xs are Ys") is distributed since we are saying that nowhere in the entire class of Ys we will find an X. The predicate of an I statement ("Some Xs are Ys") is undistibuted since, again, we are not referring to all Ys. The predicate of an O statement ("Some Xs are not Ys") is distributed since we can only say that some Xs are excluded from the class of Ys if we have excluded them from the entire class o Ys.
The discussion of distribution now looks like this:
Statement Subject Predicate
A Distributed Undistributed
E Distributed Distributed
I Undistributed Undistributed
O Undistributed Distributed
There is one other set of relationships among statements that should be noted. A contradiction exists between two statements if they both cannot be false at the same time. A and O are contradictions. If "All Xs are Ys" is true, then "Some Xs are not Ys" must be falase, and vice versa. Two statements are said to be contraries if it is possible for both to be true at the same time.
A and E are contraties since it is possible for "All Xs are Ys" and "No Xs are Ys" both to be false if it is the case that only some Xs are Ys. At the same time, if "All Xs are Ys" is true, then "No Xs are Ys" cannot be true.
*One could embarrass an opponent by attacking the contrary of an argument rather than its contradictory. Take the following example:
You wish to argue the A statement that "All Communists are bad" and your opponent wishes to argue that "Some Communists are not bad," which is an O statement. In attacking him you pretend that his position is an E and not an O and attack with case E proposition "No Communists are bad."
While both of you cannot be right - that is, one of you must be wrong either way - the attack on E allows for both of you to be wrong. This is a safety value in case you find yourself trapped.
The traditional square of opposition brings out the foregoing relationships.
A Contraries E
I Contradictories O
Now we examine categorical syllogisms. Each statement has two terms, a subject term and a predicate term. Since a syllogism has two premises and a conclustion (a total of three statements), there isa grand total of six terms. However, in a syllogism each of those terms appears twice. Thus a categorical syllogism has three terms each of which appears twice.
Example:
All carp are fish.
All fish are found in water.
_______________________________
Therefore, all carp are found in water.
As you can see, "fish" appears twice, "carp" appears twice, and "found in water" appears twice.
We may next distinguish among the (1) major, (2) minor, and (3) middle terms.
The (1) major term is that term which appears as the predicate of the conclusion. In our example above, "found in water" is a major term. The premise, and in our example "All fish are found in water" is the major premise. The minor term is that term which appears as the subject of the conclusion. In our example above, "carp" is the minor term. The premise that contan the other appearnace of the minor term is called the minor premise, and in our example "All carp are fish" is the minor premise. Thus ever categorical syllogism consists of a (1) major premise, (2) a minor premise, and a (3) conclusion. The middle term is the term that appears in both premises. In our example above, "fish" is the middle term.
Rules for Valid Syllogisms
In a valid categorical syllogism, if both premises are true then the conclusion must be true. Logicians have been able to work out a few rules such that any syllogism that violates these rules is invalid, and any syllogism that does not violate the rules is automatically valid. Thus we might speak of the rules for invalidating the syllogism.
These are three rules, the violation of any of which automatically shows the categorical syllogism to be invalid.
First Rule: The middle term must be distributed at least once. This rule is the only rule that is seriously and frequently violated in everyday reasoning. For example:
All Communists are in favor of reform.
All liberals are in favor of reform.
_____________________________
All liberals are Communists.
In the above argument, the middle term is "in favor of reform." Both premises, in which the middle term occurs, are A statements and the middle term is the predicate in both premises. We know from our chart above on distiution that the predicate of an A statement is never distributed. Therefore, the middle term is not distributed at least once and the argument is invalid. The fallacy of quilt by association is a form of this kind of invalidity.
Second Rule: A term that is distributed in the conclusion must be distributed in one of the premises. For example:
All radicals are in favor of reform.
No conservatives are radicals.
_____________________________
No conservatives are in favor of refom.
In the above statement, we have an E statement for the conclusion. "No conservatives are in favor of reform." Thus both the subject and the predicate are distributed. However, in the major premise "All radicals are in favor of reform," which is an A statement, the predicate "in fovor of reform" cannot be distributed. Thus there is a term "in favor of reform" that is distributed in the conclusion but not one of the premises are the argument is invalid.
Knowing this rule is especially important when your opponent employs an argument with a suppressed premise. Suppose your opponent uses the following argument:
"Since no concservatives are radicals they cannot be in favor of reform" your reply is twofold. First, you reconstruct your opponent's argument in order to make it valid; supply the missing premise that would make it valid ("All those in favor of reform are radicals"), and ask him if this is what he means. If he says yes, then obviously he is making a false statement and he is embarrassed in front of the audience. Presumably everyone knows that radicals are not the only people in favor of reform. Second, you reconstruct your opponent's argument to make it invalid and supply the missing premise that would make it invalid and your opponent as a logical ignoramus.
Third Rule: The number of negative premise must be the same as the number of negative conclusions. This rule sounds odd but just think of the possibilities. Since the one conclusion (a) if the conclusion is negative then there must be one, and only one, negative premise. As soon as there are two negative premises the argument is automatically invalid; (b) if the conclusion is affirmative there can be no negative premises. If there is a negative premise there must be a negative conclusion.
For example: Suppose your opponent argues that "Country X is not a capitalist country, therefore, Country X respects the working man." There is no possible way of making this a valid argument.
All (or No) countries that respect the working man are capitalist countries.
Country X is not a capitalist country.
_________________________________________________________
Conclusion: Country X is a country that repects the working man.
Either way the above arguent is invalid. The only way to get to the affirmative conclusion desired is to present the affirmative argument:
All noncaptialist countries are countries that respect the working man.
Country X is a noncapitalist country.
______________________________________________________
Conclusion: Country X is a country that respects the working man.
However, by making the argument valid we expose its Achilles heel or its most questionable point. Why should we accept the statement that "All noncapitalist countries are countries that respect the working man?" Not only is this sentence not intuitively obvious, it is downright false. Once again, knowing the rules helps us to expose the implicit generalizations of your opponent's case.
The point behind those three rules can be put more intuitively. The first rule about the undistributed middle tells us that things which are alike in one respect may not be alike in other or all other respects. The second rule about distribution tells us that the strength of the conclusion cannot exceed the strength of the premises. The conclusion cannot be more general (have a greater distribution) or go beyond what is implicit in the premises. The third rule shows that we cannot reach a positive conclusion from purely negative premises. To show that a thing lacks one quality does not by itself prove that it has another. To reach a positive or affirmative conclusion we must at some point introduce one or more affirmative premises. However, negative conclusions can be arrived at by a combination of both positive and negative information. Even a negative conclusion requires some positive backing.
Soundness and Informal Logic
We have defined a valid argument as one that does not violate the rules so that of its premises are true then its conclusion must be true. However, this does not mean that a vali argument automatically has true premises. Arguments can be valid and still have false premises. However, when an argument is valid (i.e., it does not violate the rules) and its premises are know to be true, then we say it is a sound argument.
One finds a incredible number of unsound arguments. By reconstructing your opponent's arguments to make them invali, and thereby bringing out the implicit premise (usually the major premise), you can put your finger on some generalization that might be weak enough to be attacked.
We have seen this in the second and third rules above. When you attack that premise as untrue you are accusing your opponent of having an unsound argument. Further, most, if not all, of the traditional fallacies of informal logic may be viewed as valid arguments but with an unacceptable major premise, and therefore an unsound arguments. For example, the fallacy of composition is the fallacy of believing that what is true of all the parts is true of the whole:
All that is true of the parts is true of the whole.
All of the parts of a locomotive are light.
____________________________________
Therefore, a (whole) locomotive is light.
Since the argument is valid but the conclusion is false (or unacceptable), one of the premises must be false (or unacceptable).
The fallacions use the ad populum is an appeal to the major premise that what most people like is good. Consider the following argument:
Whatever book most people like is great literature.
Most people like Love Story.
________________________________________
Therefore, Love Story is great literature.
The second premise is true if one judges by best seller lists. The conclusion is considered false by many literary experts. At the same time, the argument is logically valid. The only way of challenging the conclusion is to argue that the major premise ("Whatever book most people likeis great literature") is false, and therefore, that the argument is unsound.
The ad baculum, or the appeal to force, can also be viewed as an instance of an unsound argument. Consider the following argument:
Whenever I threaten you is a time when you must do as I say.
Now is a time I threaten to raise your taxes if you do not vote for Smith.
_____________________________________________________
Now is a time that you must do as I say (vote for Smith).
The argument is valid but unsound if you reject as false the premise that you must do as I say whenever I threaten you. Knowing syllogistic logic thus helps to analyze the weak points in your opponent's argument.
If the premises are true, then the conclusion must be true. Example:
"Plato"
All triangles are closed three-sided figures.
That object is a triangle.
_______________________________________
Therefore, that object is a closed three-sided figure.
"Aristotle"
All men are mortal.
Socrates is a man.
______________________
Therefore, Socrates is mortal.
"All men are mortal," is known from experience. The movement from individual experiences or facts like "Sophories is mortal" and "Creon is mortal" to the general truth, "All men are mortal" is called induction, but the movement from the general truth "All men are mortal" to "Socrates is mortal" is called deduction.
The ideal of logic has always been a deductive argument that begins with some general truth of the form "All Xs are Ys." The Western mind has subsequently constructed and reconstructed all arguments as deductive arguments, which begin with some alleged general truth or even a general norm.
Example:
We should never negotiate with blackmailers.
Terrorist are blackmailers.
________________________________________
Therefore, we should never negotiate with terrorists.
Questions of form aside, the controversial issues are whether (a) we have identified the right generalizaion (whether it is a general definition, fact, norm, or whatever), and (b) the case we are dealing with at present is an example of that generalization. While formal logic is focused on the form or structure of an argument, informal logic is concerned with disputes about (a) and (b). Before we can launch into informal logic though, we must keep in mind the structural elements. Once we know the correct form (rules of validity) we can always reconstruct an argument, our own or someone else's, in order to make it valid.
In the reconstruction process we articulate the previously unexpressed premises needed to make an argument formally valid. At the same time we thereby isolate the premises that might be controversial and serve as the subject matter of informal logic. Knowing which of our premises are controversial is important so that we may provide them with extra support or clarification, disguise them in the hope of eluding attack, or perhaps realize that they are indefensible and should be surrendered. Knowing which premises of our enemy's position are most controversial is important so that we can focus our counterattack in the most vulnerable spot.
Syllogisms
Such arguments having two premises are known as syllogisms. All arguments can be reconstructed as syllogisms, that is, as having two premises and a conclusion. Informal logic can be usefully viewed as an exercise in syllogistics reasoning involving some very questionable suppressed premises.
We shall be concerned here with categorical syllogisms. A categorical syllogism is a syllogism in which all of the statements, both premises and the conclusion, are categorical statements. A statement is categorical if it is of the subject-predicate form. That is, it is a statement with four distinguishable parts:
(1) a quantifier, (2) a subject, (3) a copula, and (4) a predicate.
Quantifier Subject Copula Predicate Code
1. All Xs Are Ys A
2. No (-) Xs Are Ys E
3. Some Xs Are Ys I
4. Some Xs Are Not Ys O
We are not concerned here with the truth or falsity of these statements but only their form.
Categorical statements may also be classified as either affirmative or negative. Statements one and three preceding page are affirmative in that they affirm something (namely the predicate) of the subject. Statements two and four are negative in that they deny something of the subject (namely the predicate). When we talk about the statements being affirmative or negative we are speaking of the quality of the statement.
In addition to a quality, statements have quantity. The quantity of a statement refers to the relationship between the quantifier and the subject term. There are three kinds of quantity: (1) universal, (2) particular, and (3) singular. A statement is (1) universal when the subject term refers to the entire class of objects that is names. Thus statements one and two previous page are universal in that they both refer to the entire class of objects that it names. Thus statements one and two previous page are universal in that they both refer to the entire class of Xs.
A statement is (2) particular when the subject term does not refer to the entire class of objects it names; rather it refers only to some part of the class. Thus statements three and four previous page are particular in that they both refer to some part of the class of Xs.
A statement is (3) singular when the subject term is a proper name referring to a single individual. An example would e the following:
"Aristotle was a great logician." Another example is "Bob Dylan is not a logician." By convention, all singular statements are treated as universal statements on the grounds that they refer to the whole of the subject.
(All of Aristotle, all of Bob Dylan).
In addition, the example about Aristotle is affirmative and the example about Bob Dylan is negative. Using the code from the chart above, the statement about Aristotle is an A statement, like "All Xs are Ys," and the statement about Bob Dylan is an E statement, like "No Xs are Ys."
Again, using the code letters, A, E, I, O, we summarize our discussion so far in the following;
A: Universal Affirmative
E: Universal Negative
I: Particular Affirmative
O: Particular Negative
The concept of quanity refers primarily to the relationship of subject term and quantifier. Quantity overlaps with another concept, distribution, which refers to the predicate term as well as to the subject term. A term (either subject or predicate) is distriuted if it refers to the whole class it names. A term is undistriuted if it refers not to the whole class it names, but to only part of the class. As is obvious from our discussion of quantity, the subject of an A statement (All Xs) and the subject of an E statement (No Xs) are both distributed. Moreover, the subject of an I statement (Some Xs) and an O stateent (Some Xs) are both undistributed.
Now let us examine the predicates.
The predicate of an A statement ("All Xs are Ys") is undistributed since we are not referring to all Ys. The predicate of an E statement ("No Xs are Ys") is distributed since we are saying that nowhere in the entire class of Ys we will find an X. The predicate of an I statement ("Some Xs are Ys") is undistibuted since, again, we are not referring to all Ys. The predicate of an O statement ("Some Xs are not Ys") is distributed since we can only say that some Xs are excluded from the class of Ys if we have excluded them from the entire class o Ys.
The discussion of distribution now looks like this:
Statement Subject Predicate
A Distributed Undistributed
E Distributed Distributed
I Undistributed Undistributed
O Undistributed Distributed
There is one other set of relationships among statements that should be noted. A contradiction exists between two statements if they both cannot be false at the same time. A and O are contradictions. If "All Xs are Ys" is true, then "Some Xs are not Ys" must be falase, and vice versa. Two statements are said to be contraries if it is possible for both to be true at the same time.
A and E are contraties since it is possible for "All Xs are Ys" and "No Xs are Ys" both to be false if it is the case that only some Xs are Ys. At the same time, if "All Xs are Ys" is true, then "No Xs are Ys" cannot be true.
*One could embarrass an opponent by attacking the contrary of an argument rather than its contradictory. Take the following example:
You wish to argue the A statement that "All Communists are bad" and your opponent wishes to argue that "Some Communists are not bad," which is an O statement. In attacking him you pretend that his position is an E and not an O and attack with case E proposition "No Communists are bad."
While both of you cannot be right - that is, one of you must be wrong either way - the attack on E allows for both of you to be wrong. This is a safety value in case you find yourself trapped.
The traditional square of opposition brings out the foregoing relationships.
A Contraries E
I Contradictories O
Now we examine categorical syllogisms. Each statement has two terms, a subject term and a predicate term. Since a syllogism has two premises and a conclustion (a total of three statements), there isa grand total of six terms. However, in a syllogism each of those terms appears twice. Thus a categorical syllogism has three terms each of which appears twice.
Example:
All carp are fish.
All fish are found in water.
_______________________________
Therefore, all carp are found in water.
As you can see, "fish" appears twice, "carp" appears twice, and "found in water" appears twice.
We may next distinguish among the (1) major, (2) minor, and (3) middle terms.
The (1) major term is that term which appears as the predicate of the conclusion. In our example above, "found in water" is a major term. The premise, and in our example "All fish are found in water" is the major premise. The minor term is that term which appears as the subject of the conclusion. In our example above, "carp" is the minor term. The premise that contan the other appearnace of the minor term is called the minor premise, and in our example "All carp are fish" is the minor premise. Thus ever categorical syllogism consists of a (1) major premise, (2) a minor premise, and a (3) conclusion. The middle term is the term that appears in both premises. In our example above, "fish" is the middle term.
Rules for Valid Syllogisms
In a valid categorical syllogism, if both premises are true then the conclusion must be true. Logicians have been able to work out a few rules such that any syllogism that violates these rules is invalid, and any syllogism that does not violate the rules is automatically valid. Thus we might speak of the rules for invalidating the syllogism.
These are three rules, the violation of any of which automatically shows the categorical syllogism to be invalid.
First Rule: The middle term must be distributed at least once. This rule is the only rule that is seriously and frequently violated in everyday reasoning. For example:
All Communists are in favor of reform.
All liberals are in favor of reform.
_____________________________
All liberals are Communists.
In the above argument, the middle term is "in favor of reform." Both premises, in which the middle term occurs, are A statements and the middle term is the predicate in both premises. We know from our chart above on distiution that the predicate of an A statement is never distributed. Therefore, the middle term is not distributed at least once and the argument is invalid. The fallacy of quilt by association is a form of this kind of invalidity.
Second Rule: A term that is distributed in the conclusion must be distributed in one of the premises. For example:
All radicals are in favor of reform.
No conservatives are radicals.
_____________________________
No conservatives are in favor of refom.
In the above statement, we have an E statement for the conclusion. "No conservatives are in favor of reform." Thus both the subject and the predicate are distributed. However, in the major premise "All radicals are in favor of reform," which is an A statement, the predicate "in fovor of reform" cannot be distributed. Thus there is a term "in favor of reform" that is distributed in the conclusion but not one of the premises are the argument is invalid.
Knowing this rule is especially important when your opponent employs an argument with a suppressed premise. Suppose your opponent uses the following argument:
"Since no concservatives are radicals they cannot be in favor of reform" your reply is twofold. First, you reconstruct your opponent's argument in order to make it valid; supply the missing premise that would make it valid ("All those in favor of reform are radicals"), and ask him if this is what he means. If he says yes, then obviously he is making a false statement and he is embarrassed in front of the audience. Presumably everyone knows that radicals are not the only people in favor of reform. Second, you reconstruct your opponent's argument to make it invalid and supply the missing premise that would make it invalid and your opponent as a logical ignoramus.
Third Rule: The number of negative premise must be the same as the number of negative conclusions. This rule sounds odd but just think of the possibilities. Since the one conclusion (a) if the conclusion is negative then there must be one, and only one, negative premise. As soon as there are two negative premises the argument is automatically invalid; (b) if the conclusion is affirmative there can be no negative premises. If there is a negative premise there must be a negative conclusion.
For example: Suppose your opponent argues that "Country X is not a capitalist country, therefore, Country X respects the working man." There is no possible way of making this a valid argument.
All (or No) countries that respect the working man are capitalist countries.
Country X is not a capitalist country.
_________________________________________________________
Conclusion: Country X is a country that repects the working man.
Either way the above arguent is invalid. The only way to get to the affirmative conclusion desired is to present the affirmative argument:
All noncaptialist countries are countries that respect the working man.
Country X is a noncapitalist country.
______________________________________________________
Conclusion: Country X is a country that respects the working man.
However, by making the argument valid we expose its Achilles heel or its most questionable point. Why should we accept the statement that "All noncapitalist countries are countries that respect the working man?" Not only is this sentence not intuitively obvious, it is downright false. Once again, knowing the rules helps us to expose the implicit generalizations of your opponent's case.
The point behind those three rules can be put more intuitively. The first rule about the undistributed middle tells us that things which are alike in one respect may not be alike in other or all other respects. The second rule about distribution tells us that the strength of the conclusion cannot exceed the strength of the premises. The conclusion cannot be more general (have a greater distribution) or go beyond what is implicit in the premises. The third rule shows that we cannot reach a positive conclusion from purely negative premises. To show that a thing lacks one quality does not by itself prove that it has another. To reach a positive or affirmative conclusion we must at some point introduce one or more affirmative premises. However, negative conclusions can be arrived at by a combination of both positive and negative information. Even a negative conclusion requires some positive backing.
Soundness and Informal Logic
We have defined a valid argument as one that does not violate the rules so that of its premises are true then its conclusion must be true. However, this does not mean that a vali argument automatically has true premises. Arguments can be valid and still have false premises. However, when an argument is valid (i.e., it does not violate the rules) and its premises are know to be true, then we say it is a sound argument.
One finds a incredible number of unsound arguments. By reconstructing your opponent's arguments to make them invali, and thereby bringing out the implicit premise (usually the major premise), you can put your finger on some generalization that might be weak enough to be attacked.
We have seen this in the second and third rules above. When you attack that premise as untrue you are accusing your opponent of having an unsound argument. Further, most, if not all, of the traditional fallacies of informal logic may be viewed as valid arguments but with an unacceptable major premise, and therefore an unsound arguments. For example, the fallacy of composition is the fallacy of believing that what is true of all the parts is true of the whole:
All that is true of the parts is true of the whole.
All of the parts of a locomotive are light.
____________________________________
Therefore, a (whole) locomotive is light.
Since the argument is valid but the conclusion is false (or unacceptable), one of the premises must be false (or unacceptable).
The fallacions use the ad populum is an appeal to the major premise that what most people like is good. Consider the following argument:
Whatever book most people like is great literature.
Most people like Love Story.
________________________________________
Therefore, Love Story is great literature.
The second premise is true if one judges by best seller lists. The conclusion is considered false by many literary experts. At the same time, the argument is logically valid. The only way of challenging the conclusion is to argue that the major premise ("Whatever book most people likeis great literature") is false, and therefore, that the argument is unsound.
The ad baculum, or the appeal to force, can also be viewed as an instance of an unsound argument. Consider the following argument:
Whenever I threaten you is a time when you must do as I say.
Now is a time I threaten to raise your taxes if you do not vote for Smith.
_____________________________________________________
Now is a time that you must do as I say (vote for Smith).
The argument is valid but unsound if you reject as false the premise that you must do as I say whenever I threaten you. Knowing syllogistic logic thus helps to analyze the weak points in your opponent's argument.
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