Logic As a Philosophical Tool
This is an outline of the contents of this article; topics link to entries below.
- Philosophy and Logic
- Identifying Premises and Conclusions
- Deductive Arguments: Validity and Soundness
- IV. Non-deductive Arguments
I Philosophy and Logic
Philosophy is the quest for truth about the most basic questions of human existence: "What is truth?" "What is knowledge?" "What is the good ?" "What are our duties?" "Does God exist?" "Are we free or determined?" "What is our personal identity?" When putting foreword answers to these and other questions, philosophers do not simply state their views and allow a reader to agree or disagree, rather they attempt to persuade readers by providing reasons why their view should be accepted. When a view is put forward with reasons why it should be accepted, this is called an "argument." Simply put, an argument is a collection of statements where one or more are put forward as reasons why we should believe one or more of the other statements. The statements put forward as reasons are called "premises" and the statement(s) being supported is called the "conclusion." An argument can be short and simple or it can be long and complex . An example of a short argument:
All men are mortal. Socrates is a man. Therefore, Socrates is mortal.
Philosophical writing usually contains long and complex arguments. A philosopher may write a chapter of a book , or the entire book, presenting arguments for the claim that God exists.
A student of philosophy can plunge into reading and hope to follow the arguments presented, and to sort out the strong arguments from the weak arguments, i.e. those that persuade us that we should agree with the view being defended, and perhaps alter our previously held views, from those that do not so persuade us. Students will be better prepared to identify, understand and evaluate arguments of philosophers if they have a basic understanding of the methods for evaluating arguments. Logic is a sub-discipline of philosophy and is the study of arguments. It can also be described as the theory of critical reasoning: "critical" because it seeks standards, or methods of evaluation; "reasoning" because it is concerned with reasons given for our views.
An understanding of logic, or critical reasoning, is not valuable only for the study of philosophy. In most areas of human endeavor, people give reasons why we should accept certain views and reject others. To give just one example. Some scientists and environmentalists present reasons why we should accept the view that the earth is warming and that we must reduce the emission of carbon dioxide or face disastrous consequences. Some persons respond to this with reasons why the consequences of warming will not be disastrous for the environment and that the policies called for to reduce carbon dioxide emission would have disastrous consequences for our economy. A concerned person will have to evaluate the arguments of both sides in this dispute to know which view to believe. Competency in logic will assist a person to do this. Logic alone won't decide the matter, but it will enable one to identify the arguments that are put forward and point in the direction of what one would have to know or decide in order to take a position on the issue.
II Identifying Premises and Conclusions
Philosophy and other areas of inquiry abound with arguments. But not all written and spoken communications contains arguments. Consider the following two sets of statements:
There is a God. Those who believe in him will have everlasting life.
God exists, for the world is an organized system and all organized systems must have a creator. The creator of the world is God.
Both sets state that God exists. The first set makes additional claims about God, but does not supply reasons why one should believe that God exists. The second set provides reasons why God exists. The argument of the second set of statements can be organized into premises and a conclusion.
Premise 1. The world is an organized system.
Premise 2. Every organized system must have a creator.
Conclusion. The creator of the world is God.
The structure of the argument can be recognized because the word "for" follows the statement "God exists." and precedes the statements that are Premises 1 and 2. This tells us that the statements are premises for the conclusion, There are many words that function as premise indicators and conclusion indicators.
Premise indicators:
for, since, because, for the reason that, granted that
Conclusion indicators:
thus, therefore, so, hence, consequently, it is shown that
Other expressions function as indicators of premises and conclusions:
.....(premise).... shows that ....(conclusion) ....
...................... proves that ...........
.......................implies that ............
......................entails that ...............
..................... are the reasons for .........
.....(conclusion)...is established by ......(premise)........
..........................is shown by ...............................
.........................is implied by ..........................
.........................is proven by ...........................
.........................supported by ..................
This is not a exhaustive list of those words and expressions that function as indictors of premises and conclusions. Nor does every use of these words and expressions function as a premise or conclusion indicator. In most cases, the context will tell us how the words are being used. To further complicate matters, not all writers and speakers provide these indicators for their arguments. The reader must determine whether the writer intends to present an argument and, if so, which statements are the premises and which the conclusions.
Examples.
(1) Since all humans have the capacity for creative thought and all capacities should be developed and used, it follows that all humans should think creatively.
This is obviously an argument. The occurrence of "since" tells us that the first statements in the sentence are premises and "it follows that" tells us that the last statement is a conclusion. The standard form for representing an argument is to list the premises first and then the conclusion with a line drawn under the list of premises.
P1. All humans have the capacity for creative thought.
P2. All capacities should be developed and used
C. All humans should think creatively .
If the statements in this example were reversed, it would be the same argument.
All humans should think creatively because all humans have the capacity for creative thought and all capacities should be developed and used.
The premises and conclusion are the same in this version. The use of "because" tells us that the statements following it are premises, and the statement preceding it is the conclusion. The standard form is identical to the above.
(2) That Michelangelo's David is a truth is shown by the view that beauty is truth and truth is beauty and by the beauty of Michelangelo's David.
The expression "is shown by" informs us that the conclusion is "Michelangelos's David is a truth." and the premises are the two statements which follow.
The standard form for the argument is:
P1. Beauty is truth and truth is beauty
P2. Michelangelo's David is beautiful
C. Michelangelo's David is a truth.
Note that when writing the standard form of the argument, some words may be deleted. We need not write P1. as "The view that beauty is truth and truth beauty." When writing out an argument in standard form you only need to write out the central information of the statements and not the words that characterize the statement is some way and lend to the style of the writing rather than the content.
(3) Given that many persons are sentenced to death due to mistakes or careless work by police or prosecutors, the death penalty should be abolished.
This is an argument. The words "Given that" reveal that the first part of the sentence is a reason for the second part of the sentence. In standard form it is:
P1. Many persons are sentenced to death due to mistakes or careless work by police or prosecutors.
C. The death penalty should be abolished.
In addition to the explicit premise that many persons are sentenced to death by mistake or careless work by police or prosecutors, there is an obvious implicit (unstated) premise of the argument This implicit premise can take many forms; one way to put it is: "It is wrong for persons who do not receive a proper trail to be found guilty and sentenced to death."
The structure of the argument with the implicit premise is:
P1. Many persons are sentenced to death due to mistake or careless work by police or prosecutors.
P2. It is wrong for persons who do not receive a proper trial to be found guilty and sentenced to death. (implicit)
C. The death penalty should be abolished.
It is common in ordinary writing and speaking, i.e. when not doing so as an illustration in logic, for premises, and sometimes conclusions, to be implicit. The writer may be aware of this and not make the statements because it is assumed that every reader will know what they are, or it may be that the writer is unaware. Further, the implicit premise may be non-controversial, as is the above, or it may be the most controversial and doubtful premise of the argument. Writing arguments in standard form and supplying implicit premises allows us to identify all the reasons needed to support the conclusion, and thus reach a better evaluation of the argument.
(4) All restrictions on pornography violate the First Amendment. All restrictions on pornography are restrictions of free speech. All restrictions on freedom of speech violate the First Amendment.
There are no premise and conclusion indicators in this set of statements. We could interpret it as simply a collection of three related statements and not as an argument. However, we can recognize a pattern that is a form of an argument. The pattern is:
P1. All A are B
P2. All B are C
C. All A are B
In this case the standard form of the argument is:
P1. All restrictions on pornography are restrictions of free speech.
P2. All restrictions of free speech violate the First Amendment.
C. All restrictions on pornography violate the First Amendment.
In this example:
A = restrictions on pornography
B = restrictions of free speech
C = violates the First Amendment
So far we have dealt with single arguments, those with one conclusion and two premises. Arguments in philosophy and in everyday discourse are seldom single arguments. Rather they are extended multiple arguments in which several distinct arguments may be made for the same conclusion or in which the conclusion of one or more arguments may function as premises for a further argument.
III Deductive Arguments: Validity and Soundness
When evaluating arguments, i.e. determining whether they are good or bad, strong or weak, persuasive or not persuasive, there are two questions we should ask (1) whether the premises provided appropriate support for the conclusion; (2) whether the premises are, in fact, true. These are the steps taken when evaluating a single argument. When evaluating a complex argument each of the single arguments of which it is composed must be evaluated and then an overall evaluation of how the single arguments fit together must be made.
III-1. Logical Correctness
The first question is a matter of "logical correctness."
An argument is considered to be "logically correct" when it satisfies the following condition:
If the premises were true, this fact would constitute good grounds for accepting the conclusion as true.
Notice that this condition presupposes that one is dealing with statements that are capable of being true or false. Nevertheless this condition is not concerned with whether the premises are in fact true. In evaluating arguments for logical correctness one is concerned with the relation between the premises and the conclusion not with the question of whether the premises are in fact true.
III-2. Deductive Validity
To make this condition more specific we have to specify what we take to be "good grounds". Certainly the truth of the premises guaranteeing the truth of the conclusion would mean the truth of the premises provided good grounds for accepting the conclusion as true. The criterion of logical correctness that requires the guarantee is called "the deductive criterion" of logical correctness
An argument form is deductively valid if and only if it is impossible that its conclusion is false given its premises are true.
Notice that this criterion for deductive validity does not require that the premises are true, nor that the conclusion is true, rather it says that IF the premises are true, the conclusion must be true. Deductive validity is a function of the form, or structure, of the statements in the argument and not a function of whether the statements are in fact true.
Consider the following two examples:
| Argument 1 | Argument 2 |
|---|---|
|
P1. All mammals are four-legged |
|
P2. You (the reader) are a mammal |
|
C. You (the reader) are four-legged |
In Argument 1, both premises and the conclusion are true. In Argument 2, P1 and the conclusion are false. Notice that the arguments have the same form or structure:
P1. All A are B
P2. x is an A
C. x is a B
It is because of this form that we can say that the truth of the premises guarantees the truth of the conclusion. IF it were true that all mammals are four-legged, then it must be true that you, as a mammal, are four-legged. The argument form in these examples is one of many deductively valid argument forms. Other deductively valid arguments will be presented later. If an argument in ordinary discourse fits into a deductively valid argument form, then we can say that if the premises are true the conclusion must be true even though we don't know whether the premises are true. We can know that an argument is valid and not know the meaning of the terms in the premises and conclusion. For example:
P1. All pirons are elactical.
P2. All elacticals are verdish.
C. All pirons are verdish.
The terms in this argument may be from a highly specialized science in which they can be determined true or false or they may be nonsense. But that makes no difference to the validity of the argument. It is a deductively valid argument because of the form. IF the premises turn out to be true, they guarantee the truth of the conclusion.
III-3. Some Deductively Valid Argument Forms
It is useful for understanding and evaluating arguments to have knowledge of a relatively small number of deductively valid argument forms. Much of what you read in philosophy can be analyzed with them.
a. Universal Syllogism
| Form | Example |
|---|---|
|
P1. All dogs are mammals |
|
P2. All mammals are warm-blooded |
|
C. All dogs are warm-blooded |
b. Predicate Instantiation
| Form | Example |
|---|---|
|
P1. All dogs are warm-blooded |
|
P2. Fido is a dog |
|
C. Fido is warm-blooded |
These two argument forms are deductively valid. This means that whatever is substituted for A, B, C and x, the truth of the premises guarantees the truth of the conclusion, provided the substitution is uniform, e.g. whatever is substituted for "A" in one premises must be substituted for "A" in all occurrences of "A" in other premises or conclusion. These two argument forms are part of predicate logic. " is a dog" and "is warm-blooded" are predicates, i.e. the properties of being a dog or being warm-blooded can be applied to individuals, e.g. Fido. Also, it can be asserted that everything that has one property also has an additional property, e.g. all things that are dogs are also things that are warm-blooded. These two argument forms are only a small part of predicate logic, still they are useful when critically reading a text.
Propositional logic is the logic of propositions, or statements. In this logic, the variables in the valid argument forms are place holders for complete statements. In propositional logic statements are connected by logical connectives: "and", "or", "if ... then," and "not." The following are a few of the useful deductively valid argument forms in propositional logic.
c. Affirming the Antecedent (also called Modus Ponens)
| Form | Example |
|---|---|
|
P1. If John is a freshman then he can't enroll in Physics |
|
P2. John is a freshman. |
|
C. John can't enroll in Physics |
d. Denying the Consequent (also called Modus Tollens)
| Form | Example |
|---|---|
| P1. If p then q | P1. If Mary is a freshman then she lives on campus |
|
P2. Mary does not live on campus |
|
C. Mary is not a freshman |
e. Disjunctive Argument
| Form | Example |
|---|---|
| P1. p or q | P1. Either John loves Mary or he loves Susan |
| P2. not p | P2. John does not love Mary |
| C. q | C. John loves Susan |
f. Hypothetical Argument
|
|
|
P1. If Mary loves John then she loves a loser. |
|
P2. If Mary loves a loser then she will be unhappy |
|
C. If Mary loves John then she will be unhappy |
g. Chain Argument
|
|
|
P1. If John is a loser then he will make Mary unhappy |
|
P2. If John makes Mary unhappy Susan will hate him |
|
P3. John is a loser |
|
C. Susan will hate John |
You know, Susan will wind up hating John. I'll tell you why. He's a loser, and if so, he will make Mary unhappy. And if that makes Mary unhappy, then Susan will hate him.
The premises and conclusion can be labeled as follows:
You know, (C) Susan will wind up hating John. I'll tell you why.(P3) He's a loser, and (P1) if so, he will make Mary unhappy. And (P2) if that makes Mary unhappy, then Susan will hate him.
h. Reductio Ad Absurdum
Deductive arguments can be used to refute a view, as well as to prove a view. A form of refutation commonly used in Philosophy and other fields of inquiry is "Reductio ad absurdum "(literally "reducing to absurdity".) The reductio method identifies a premise that is not obviously false, combines it with other premises that are clearly true and then deduces by a valid argument a conclusion that is a contradiction or absurd (clearly known to be false.)
The basic structure of a reductio argument is:
P1. Q (the premise in doubt)
P2. (known to be true)
P3. (known to be true)
C. R (absurd, clearly known to be false)
For a successful reductio argument the argument form must be valid. For it if is, the premises cannot all be true and the conclusion false. Given the false conclusion, P1 must be false, since P2 and P3 are known to be true.
Suppose someone argues that we ought to have the death penalty for first degree murder on the ground that the alternative - life in prison without parole - is a more severe penalty than death. This argument for the death penalty has been rejected by the following reductio ad absurdum argument. It reduces the premise that life in prison without parole is more sever than the death penalty to an absurdity. Abbreviating somewhat, the argument is as follows:
|
In doubt |
|
Obviously true |
|
Obviously true |
|
Absurd |
P1 is the key premise in the argument for the death penalty. By showing that it leads to an absurdity in a valid argument, it is shown that the premise must be rejected and so also the argument for the death penalty.
A reductio argument is evaluated by asking:
- does the premise in doubt really imply the absurdity, i.e. is the reductio argument valid;
- is the conclusion really absurd;
- can the premise in doubt be altered in a minor way so it does not imply the absurdity? Which of these approaches would be the best response by an advocate of the death penalty to the reductio argument?
Examples of reductio ad absurdum arguments can be found in the dialogues of Plato. Socrates asks a question and the proceeds to refute the answer by showing that it leads to a clearly false conclusion.
"Well said Cephalus, I replied, but as concerns your answer that justice is speaking the truth and keeping promises, are there not exceptions? Suppose that a friend when in his right mind has deposited weapons with me and he asks for them when he is not in his right mind, ought I to give them back to him? No one would say that I should or that I should be right in doing so, no more than they would say that I ought to always speak the truth to one in his condition."
"You are quite right he replied."
"But then, speaking the truth and keeping promises is not a correct account of justice."
The structure of the argument is as follows:
P1. It is just to tell the truth and keep promises |
In Doubt |
P2. A madman asks for the return of weapons I have promised to return. |
True |
C. I should return the weapons to him or tell him where they are. |
Absurd |
Since the conclusion is absurd, P1 cannot be a correct account of justice.
Philosophers, and other thinkers, frequently use the method of reductio ad absurdum. A student of philosophy can use them to assess the views of the philosopher he or she is reading. There is no mechanical way to generate reductio arguments. You must be imaginative and sometimes have knowledge about the subject matter of the view you wish to challenge. If you are not able to think of a reductio argument, that does not entail that the premises of the argument under consideration are true; it may be that you are not knowledgeable enough or clever enough.
III-4. Examples
Example a.
Many of the examples above are simple and not what you would encounter in real discourse of everyday and in the arguments of philosophers. They were used to most clearly show the validity of the argument forms. Here's an example from philosophy.
If we can cause animals to suffer, then what we do to them not only hurts them, it can harm them: and if it can harm them, then it can detract from the experiential quality of their life, considered over time; and if it can do that, then we must view these animals as retaining their identify over time and as having a good or ill of their own.
Tom Regan, The Case for Animal Rights
The first step in reconstructing this argument into its logical form is to label or pull-out the statements that can be the premises and conclusion of the argument. In this process we can remove what is redundant and those words not necessary to the structure of the argument.
(1) If we cause suffering to animals then we harm them.
(2) If we harm animals then we detract from the experiential quality of their life
(3) If we detract from the experiential quality of their life, then animals must be viewed as having an identity and a good or ill of their own.
Now that we have simplified the argument into these three statements, we can see that this is an extended version of Hypothetical Argument, without the obvious conclusion . It is an extended version of Hypothetical Argument because it has three premises rather than two. Abbreviating in order to see the structure:
|
Logical Form |
P1. If cause suffering then cause harm |
P1. If p then q |
P2. If cause harm then detract from quality of life |
P2. If q then r |
P3. If detract from quality of life then an identity |
P3. If r then s |
C. If cause suffering then an identity |
C. If p then s |
It may be that Regan only means to present this hypothetical argument, but since we know that the title of the book is The Case for Animal Rights, it is reasonable to draw the conclusion that Regan will reach, namely that animals have an identity over time and a good or ill of their own. This is "s" in the formal reconstruction. To reach this conclusion we only need add the premise that we can cause animals suffering. The logical form of the argument is:
P1. If p then q
P2. If q then r
P3. If r then s
P4. p
C. s
This is an extended version of Chain Argument; it has three "if... then..." premises rather than two.
Example b.
Ralph will become a better student. He is studying logic and anyone who studies logic will be a better student.
|
|
P1. Anyone who studies logic will become a better student |
|
P2. Ralph is studying logic |
|
C. Ralph will become a better student. |
|
Notice that "anyone" is being used in the same way as "all." The premise could be written, "All those who study logic will become a better student." The word "every" can function in the same way, e.g. "Every student who studies logic will become a better student."
Example c.
Bloogs does not wish to be an accountant for if he wished to be an accountant he would be enrolled in the Business College, and he is not.
|
|
P1. If Bloogs wished to be an accountant, then he would be enrolled in the Business College. |
|
P2. Bloogs is not enrolled in the Business College |
|
C. Bloogs does not wish to be an accountant |
|
Example d.
Look Bloogs, can't you see that this sample is verigated? Let me convince you. All the pirons we have found so far have been elactic. And all the elactic samples we have are verigated. This sample is a piron, so it has to be verigated.
The conclusion of this argument is "This sample is verigated." The argument uses "all," so the approach to reconstructing the argument is to use the two predicate logic argument forms.
|
|
P1. All pirons so far are elactic. |
|
P2. All elactics are verigated |
|
P3. This sample is a piron |
|
C. This sample is verigated |
|
This argument does not fit one of the two valid argument forms in predicate logic. It is a combination of Universal Syllogism and Predicate Instantiation.
P1. All pirons are elactics
P2. All elactics are verigated
C. All pirons are verigated
P3. This sample is a piron
C. This sample is verigated
Only the most simple arguments in ordinary language can be reconstructed as one of the basic valid argument forms listed above. More often, arguments will have to reconstructed as a combination of basic valid argument forms.
Example e.
The universal right to health care will be enacted if those who have adequate health care vote for liberal democrats. They will vote for liberal democrats if they are concerned about the lack of access to health care of those who are poor and do not have adequate health care. Those who have adequate health care are concerned about those who do not. So, the universal right to health care will be enacted.
Standard Form
P1. If those who have adequate health care vote for liberal democrats then universal right to health care will be enacted.
P2. If those who have adequate health care are concerned about the lack of access to health care of those who are poor and do not have adequate health care then they will vote for liberal democrats.
P3. Those who have adequate health care are concerned about those who are poor and do not have adequate health care.
C. Universal health care will be enacted
Notice that in the original statement of the argument, the "if" clause of the conditional statements came after the "then" clause. This is common in ordinary discourse. The order is reversed in the standard form. If we rewrite the standard from using the notation of propositional logic, we have the following:
P1. If p then q
P2. If r then p
P3. r
C. q
This is an instance of the valid argument form Chain Argument although the order of the first two premises is not the same. To clearly see this form we can rewrite the argument form as follows:
P2. If r then p
P1. If p then q
P3. r
C. q
III-5. Soundness
So far we have been concerned with the validity of arguments; we have been answering the first question about arguments, viz. whether the premises provide appropriate support for the conclusion. Seven deductively valid argument forms have been presented. The second question about arguments is whether the premises are true. This is just as important as whether an argument is logically correct. If an argument is valid, and its premises are false, then the argument for the conclusion is not persuasive, for validity of an argument only tells us that IF the premises are true the conclusion is guaranteed to be true. If the premises are false, the conclusion of the valid argument may in fact be true, but the valid argument hasn't shown this. Consider the following argument:
P1. If Detroit is on the east coast then is it in Michigan
P2. Detroit is on the east coast.
C. Detroit is in Michigan
This is a valid argument, an instance of Affirming the Consequent. The conclusion is true, and both premises are false. If the geography of the U.S. were different than it is, then the premises could be true and would thereby guarantee the truth of the conclusion.
An argument that is valid and has true premises is a sound argument.
Validity + true premises = soundness
Both conditions are required for soundness. An argument with true premises that is not valid is not a sound argument. Assume that Bill lives in Michigan
P1. If Bill lives in Michigan then he lives in the mid west
P2. Bill lives in the mid west
C. Bill lives in Michigan
The premises and conclusion of this argument are true, but it is not a valid argument and hence it is not a sound argument. The argument form is not Affirming the Antecedent nor is it Denying the Consequent. Rather it is Affirming the Consequent.
P1. If p then q
P2. q
C. p
The invalidity of Affirming the Consequent can be shown as follows: in a valid argument the truth of the premises guarantees the truth of the conclusion; so if an argument form can be constructed with true premises and a false conclusion it cannot be valid.
P1. If Brenda's large ring is a real diamond then it is valuable
P2. Brenda's ring is valuable
C. Brenda's ring is a large real diamond.
This argument is not valid because the premises can be true and the conclusion false. P1. is true; large real diamonds are valuable. Suppose Brenda's ring is a real ruby, then it is valuable and hence P2 is true. But if her ring is a real ruby, then the conclusion is false. So this is not a valid argument, and therefore it is not sound, even though the premises are true.
III-6. Determining Truth of Premises.
In the examples above the premises used were known true or false by common knowledge or by stipulation. This will not be so in the case of arguments commonly encountered in the real world.
To determine the truth or falsity of premises, we have to know relevant information about the subject matter in the premises. This is unlike validity. To determine validity, we have to be competent speakers of the natural language used in the argument so we can sort out premises and conclusions, and we have to know deductively valid forms of argument. Whether the premises are true is irrelevant to validity.
The truth or falsity of premises is not a subject matter of logic, but of all the other areas of human knowledge and inquiry. Determining whether a valid argument about environmental hazards is also sound, i.e. its premises are true, depends on our knowledge of environmental science. However, there are some matters of logic that clarify inquiry into the truth of premises.
Propositions, i.e. declarative statements, can be divided into three types: empirical, normative and conceptual. Empirical statements are statements of fact; they say something about how the world is. The following are empirical statements:
1. The moon is X miles from the earth.
2. Humans are descended from non-human primates
3. The Amazon River is the largest river in the world.
4. The disagreement over the morality of slavery was a cause of the Civil War.
5. The rate of acceleration due to gravity on earth is 32 feet per second per second.
6. The costs of health care are increasing faster than the rate of inflation.
Normative statements are statements about how things ought to be in the world, or about how things in the world are good, bad, right, wrong, evil, our duty, our right. Examples are:
1. Killing an innocent human being is immoral.
2. Love they neighbor.
3. Every American should have access to adequate health care.
4. We must stop polluting the environment with toxic waste from industrial plants.
5. We have a duty to tell the truth even when doing so would be to our disadvantage.
6. Physician assisted suicide ought to be legally permissible.
Conceptual statements are statements about what the concepts expressed by words mean. Examples are:
1. A bachelor is an unmarried male.
2. An electron is a negatively charged particle circling the nucleus of an atom.
3. A legal right is an enforceable claim that a person may do or not do some act without interference from others.
4. First degree murder in the law is the killing of one person by another with the premeditated intent to kill.
5. A bicep is the contractor muscle in the upper arm.
6. A touchdown is scored whenever an offensive player has possession of the football in the end zone.
When these kinds of statements appear in argument we determine their truth in different ways. The truth of conceptual statements can often be determined by our personal knowledge of how we use the terms. In the event that we are not sure of how terms are used, we can consult a dictionary. In most cases a standard collegiate dictionary will suffice, but sometimes the terms are from a technical field and do not appear in a standard dictionary, or the author is using the term in a technical way that does not match the definition in a dictionary. Or, the dictionary may give us more than one definition. In that case we will have to discern what an author means by a term by noting how it is used, unless of course the author provides a definition of the term. One of the things to watch for in an argument is clarity of use of terms and consistent use of terms in the premises and conclusion.
The truth or falsity of empirical statements is determined in the first place by observation. The distance of the moon from the earth has been accurately determined by the observations of astronomers. The increase in the cost of health care is determined by economists and others carefully tracking the records of cost of various health care procedures over a period of several years. We commonly know the truth of empirical statements without making our own observations. For example, we know how far it is from New York to Los Angeles not because we have made our own measurements, but because we can look it up somewhere or ask someone we believe has more knowledge then we do. Many of our most important beliefs about the world are like this. None of us can make direct observations to confirm all the beliefs we rely on in our life. We have to trust the expertise and honesty of others. If the premises in an argument are not common knowledge, we ought to be sure that the sources of the facts stated are experts, honest and not biased. If we cannot determine that immediately, we have to set aside accepting or rejecting the conclusion of a valid argument until we are able to ascertain this.
Students frequently hold the view that normative statements are not true or false but simply a matter of opinion. They sometimes add that this means that one person's view is just as "true" as any others'. There is a correct intuition behind this, namely that normative statements cannot be determined true or false by observation, i.e. they are not empirical statements. Many philosophers share the view that we cannot say that normative statements are true or false. But this does not imply that one normative statement is just as acceptable as its contrary. One example is the statement that "It is wrong to kill an innocent human being." Would anyone of us seriously entertain the view that it is morally permissible to kill an innocent human being? The view that all normative statements are equally acceptable may stem from an unbalanced diet of examples. The morality of abortion is controversial, so also the question of whether the death penalty is a just form of punishment. But these controversial cases should not lead us to regard all normative statements as controversial and the debates about them irreconcilable. If an argument has normative premises, we need to ask ourselves whether they are acceptable. If we find the normative premises acceptable and the empirical premises true, and the argument is valid, then we must accept the conclusion.
Arguments with normative conclusions frequently do not state a normative premise. An earlier example was:
Given that many persons are sentenced to death due to mistakes or careless work by police or prosecutors, the death penalty should be abolished.
This argument was constructed into premises and conclusion are follows:
P1. Many persons are sentenced to death due to mistake or careless work by police or prosecutors.
P2. It is wrong for persons who do not receive a proper trial to be found guilty and be sentenced to death.
C. The death penalty should be abolished
P2. is an implicit premise. Without it the argument is not valid. P1. is an empirical statement and C. is a normative statement. Validity is sometimes characterized as an argument where the conclusion is contained in the premises, or it is said that there can't be anything in the conclusion that is not already contained in the premises. So, for C to be a valid conclusion, there must be a normative statement in the premises. P1 states a matter of fact; assuming it is true, it does not alone support the conclusion. It is good reason for abolishing the death penalty, only when we also state that what it describes ought not to happen, that it is wrong that it happens. Philosophers summarize this by stating that you cannot infer a normative conclusion from only empirical premises.
III-7. Counter Examples
One way to cast doubt on the truth of a premises is to find a counter example. This technique is used to show that one or more of an arguments premises are false. It is most effective against premises that make universal statements.
P1. All poodles are white or black
P2. Sara's dog is a poodle
C. Sara's dog is white or black.
This is a valid argument; if the premises are true the conclusion must be true. But P1 can be shown false by pointing out a poodle that is brown. You may be able to do this because you or someone you know has a brown poodle. Whenever there is a universal claim in the premises of an argument, trying to think of a counter example is a good way to cast doubt on its truth.
An example from philosophy is St. Augustine's refutation of the claim of astrology that a person's future can be predicted by the position of the stars at the time of the person's birth. This view is committed to the following:
1. The positions of the stars at the time of a person's birth can be used to predict the person's future.
What follows from this is:
2. If two persons are born at the same time, then the predictions of their future will be the same.
Augustine observed that in the case of twins, they are born at the same time and under nearly identical circumstances. So, astrology would predict the same future for them. Augustine further noted that twins do not have the same future. The major events in their lives are not the same. The difference in the lives of twins is a counter example to the astrologers claim that the position of the stars at the time of birth can be used to predict a person's future.
The method of counter example can be used to show that the conclusion of a valid argument is false and therefore one or more premises must be false. For, if an argument is valid then the premises can't be true and the conclusion false. We can apply the astrologer's claim to a particular case.
P1. All persons born when the stars are in arrangement C will have futures F1
P2. Bill and Bob are twins both born when the stars were in arrangement C
C. Bill and Bob will both have futures F1.
Counter Example: Bill had future F1 and Bob had a different future, F2. This shows that C is false and therefore that either P1 or P2 is false. P2 is an easily confirmed fact, so P1 is the false premise.
Counter examples are effective against universal claims. So one way they can be avoided is to not make universal claims. An astrologer might modify P1 to something like, "It is highly likely that all persons born under the same arrangement of stars will have the same future, but they will not when their futures are influenced by things in the heavens we cannot know."
IV Non-Deductive Arguments
IV-1. Distinguishing Deductive and Non-deductive Argument Forms
In the section on deductive arguments, the general concept of "logical correctness" was defined as follows:
If the premises were true, this would constitute good grounds for accepting the conclusion as true.
Deductive logical correctness (validity) was defined as:
An argument form is deductively valid if and only if it is impossible that its conclusion is false given its premises are true.
Not all arguments encountered in philosophy and other areas of inquiry can be formulated as deductive arguments. Non-deductive arguments are those argument forms in which the truth of the premises does not guarantee the truth of the conclusion, and yet they can be strong arguments. Compare the following two arguments:
P1. All freshmen are between 18 and 22 years of age
P2. John is a freshman
C1. John is between 18 and 22 years of age
P3 90% of freshmen surveyed have been between 18 and 22 years of age
P4. John is a freshman
C2. John is between 18 and 22 years of age.
The first argument is deductively valid, but we would certainly question the truth of P1. So we would be reluctant to consider it sound. The second argument is a more plausible way of constructing what a speaker would report. It is a strong argument, but the truth of the premises does not guarantee the truth of the conclusion. We are aware of freshman who are younger than 18 and older than 22.
Deductive validity is only one criterion for the logical correctness of arguments. When an argument does not fit a deductively valid form then the criterion for logical correctness is:
If the premises were true, the conclusion is likely to be true.
This is a matter of degree. In the second argument if only 10 freshmen at a large college were surveyed and 9 of them are 18 -22 the argument is not strong. But, if 500 freshmen were surveyed and 450 were 18 -22, this is a stronger argument. Yet it is possible that the premise is true and the conclusion false.
Common types of non-deductive arguments are inductive arguments (both general to specific and specific to general), analogical arguments, and explanations. NOTE. Do not make the mistake that deductive arguments are general to specific and inductive arguments specific to general. The arguments examined above are inductive arguments and they go from general premises to specific conclusions. Universal Generalization is a deductively valid argument form and it goes from general to general. A deductively valid argument can go from specific premises to a specific conclusion. For example:
The man who shot the duke in 1923 was killed later that year. Kraznakov was alive in 1924. Therefore, Kraznakov is not the man who shot the duke.
IV2. Specific to General Arguments.
Arguments of this sort are commonly called empirical generalizations because they start with premises reporting specific observations of the world and infer a general statement about the world, i.e. from a sample of a population to the entire population. The schematic form of empirical generalization is:
P1. X% of a sample of F are G
C. Most likely, X% of all F are G
Examples
P1. 33% of Midvale College students surveyed said they are Republicans
C. 33% of Midvale College students are Republicans
P1. 51% of a sample of registered voters said that they will vote for Senator Bloogs.
C1. 51% of all registered voters will vote for Bloogs.
C2. Bloogs will most likely win the election.
These arguments do not guarantee the truth of their conclusions when the premises are true. So, the criteria for logical correctness must be different than that for deductive arguments. The strong making characteristics of empirical generalizations are: 1) the evidence in the premises are true; 2) the sample size is large enough; 3) the sample is representative; 4) no counter evidence to the conclusion .
A person reading or hearing the argument about Republicans at Midvale College may doubt the truth of the premises because she does a quick survey of students and finds that 20% say they are Republicans. This would also be counter evidence to the conclusion. Neither of the examples above state how many individuals out of the total population were sampled. If Midvale has 5000 students and only 9 were surveyed, that would not be as strong evidence for the conclusion as sampling 900 students. Nor does either example tell us how the sample was selected. If the students selected were only those living on campus and excluded those living off campus, the sample would not be representative of the entire Midvale College population. If the voters surveyed were those living in one part of the state, then they may not be representative of the entire voting population. In order to avoid a non-representative sample, survey researchers commonly select the sample at random so that each member of the total population has an equal probability of being selected.
IV-3. General to Specific Arguments
These arguments will have statistical premises (statements with "most", "many" "few", "a certain percentage.") As in the case of specific to general arguments, counter evidence to the premises or conclusion will weaken the argument. Another method of evaluating the strength of these arguments depends on background knowledge and knowledge of the specifics in the argument. Two general to specific arguments can have true premises and yield incompatible conclusions.
Examples
P1. Men who eat a diet high in fat are a high risk for a heart attack.
P2. Jones eats a diet high in fat.
C1. Jones is at high risk for a heart attack
P3 Men who are not overweight, who do not smoke and who exercise regularly are at low risk for a heart attack.
P4. Jones is not overweight, does not smoke and exercises regularly
C2. Jones is at low risk for a heart attack.
The problem with both arguments is that neither of them consider all of the factors relevant to a heart attack. A stronger argument would be one that considers all four of the above factors and compares the rate of heart attacks for those men who have none of the four factors with those who have one, two, three and four of the factors. If Jones has two of the risk factors, then the important information for Jones would be his comparison to those who have one and those who have none of the risk factors.
IV-4. Analogical Arguments
This is a common type of non-deductive argument. Two things are analogous if they share one or more properties, i.e. they are similar in some respects. Hockey and soccer are analogous because in both a player has to put the ball into a net to score. An argument by analogy is an argument that because two or more things share a specific set of properties they will also share a further property. The general schema for arguments by analogy is:
P1. x has properties A, B, and C
P2. y has properties A, B and C
P3. x has property D
C. y has property D
Arguments by analogy are not limited to comparing single entities.
P1. t, v and x have properties A, B and C
P2. y has properties A, B, and C
P3. t, v, and x have the property D
C. y has property D
Arguments by analogy, like empirical generalizations and general to specific arguments, do not guarantee the truth of the conclusion when the premises are true. They are strong or weak depending on features of the argument.
Examples
A weak analogical argument:
P1. Bob has red hair, is from San Francisco and majors in Philosophy
P2. Bill has red hair and is from San Francisco
C. Bill is a major in Philosophy
A criterion for a strong analogical argument is that the similarities are relevant to the inferred property. In this case hair color and city of origin are not relevant to what a student's major is. A stronger argument would be:
P1. Bob is reflective, likes to discuss deep subjects , reads a lot and is a Philosophy major
P2. Bill is reflective, likes to discuss deep subjects, and reads a lot
C. Bill is a major in Philosophy
The premises of this argument could be true and the conclusion false, but the premises provide more support for the conclusion than those in the previous argument because the properties Bob and Bill share are more relevant to being interested in Philosophy.
Another criterion for strong analogical arguments is that there are no relevant dissimilarities. If Bob is tall and Bill is short, that dissimilarity does not weaken the analogical argument. However, if Bill's parents are physicians and Bill does volunteer work in hospitals and takes biological science courses, while Bob does not share any of these characteristics, then this dissimilarity weakens the argument. Note again, that to make these evaluations of the logical strength of analogical arguments we have to have knowledge of the subject matter of the argument. This is unlike deductive arguments where we can determine validity simply by the structure of the argument. Evaluating the above arguments we had to appeal to our beliefs about sorts of activities a Philosophy major is likely to engage in, and we assumed some particular facts about Bob and Bill to show a dissimilarity that weakened the argument. If the subject matter of an analogical argument is in a area about which we are ignorant, we will not be able to do much to evaluate the strength of the argument. If we are not familiar with the persons or objects specified in the argument, we will not be able to find specific dissimilarities. However, we will be able to say in some cases that if the objects in question were dissimilar in a particular relevant respect, that this would weaken the argument.
Example
P1. Jones is a Republican, owns a small business, and supports tax cuts
P2. Smith is a Republican and owns a small business
C. Most likely, Smith will support a tax cut.
Based on our general knowledge we can say that the similarities between Jones and Smith are relevant to support of tax breaks. We don't know Jones and Smith so we can't identify a relevant dissimilarity. However, we may believe that a person's age and wealth are relevant to support for tax cuts, e.g. a person who is a senior citizen and not wealthy is less likely to support tax breaks, If that is so, and if we know that Jones is rich and young and Smith is old and not rich, then that would be a relevant dissimilarity.
Example
In the nineteenth century it was frequently argued by analogy that there must be life on Mars.
The planet Mars posses an atmosphere with clouds and mists resembling our own; it has seas distinguished from the land by a greenish color, and polar regions covered with snow. the red color of the planet seems to be due to the atmosphere, like the red color of our sunrises and sunsets. So much is similar in the surface of Mars and the surface of the earth, that we readily agree that there must be inhabitants there as well.
Prior to twentieth century astronomical instruments and exploration of Mars via satellites and landings, knowledge of Mars was limited to what could be seen by the naked eye and by telescope. So this argument was persuasive. Today we know that the atmosphere of Mars will not support inhabitants that are any thing like us. We have discovered relevant dissimilarities.
IV-5. Non Argument Uses of Analogy.
The best way to explain something to a person who has yet to understand it is to make a comparison with something that the person is familiar with. Explanatory analogies are frequently used to explain science to lay persons.
Carbon is gregarious stuff; the carbon atom has an outer shell with four electrons available for making shared electron pairs - or covalent bonds - four hands so to speak, to clasp its neighbor - where oxygen, say, has but two and hydrogen only one.
It it not always easy to determine whether an analogy is an explanation or an argument.
For the average user, trying to understand the workings of a computer is like trying to understand what your nerves and muscles are doing while you run.
This could be seen as an explanation of why it is difficult, if not impossible, to use a computer and simultaneously try to understand its workings, or taken as an argument that just as it is ridiculous for us to try to understand what our nerves and muscles are doing while we are running, it is ridiculous for us to try to understand what a computer is doing while we use it.
IV-6. Explanation and Abduction
An argument is an attempt to justify a statement, i.e. show that it is true. Suppose Jones says to Smith that Smith was late for work, and Smith protests that he was not. Jones might then say, "I was in my office at 8:00 and didn't see you in your office, further, when I looked out my window at 8:30 I saw you coming in the door." Jones is providing reasons why it is true that Smith was late for work. Jones is presenting premises to support the conclusion that Smith was late.
P1. Smith was not in his office at 8:00
P2. Smith came in the door at 8:30
P3. Starting time is 8:00
C. Smith was late
Now suppose that Smith says. "OK. I was late, but it wasn't my fault. There was an accident on Vine Street and it held up traffic for 20 minutes." Smith is not giving an argument to prove that he was not late, he admits that he was. He is now giving an an explanation of why he was late.
Smith's explanation has the following form:
P4. There was an accident on Vine Street
P5. Traffic was not moving
P6. I was held up for 20 minutes
C. I was late for work
Both inferences support the truth of the same conclusion, viz, that Smith was late for work. There is an important difference: Jones's argument is an inference from premises to conclusion. Jones's argument is designed to prove a matter on which he and Smith disagreed. When Smith's finally agrees that he was late he is providing an explanation of a matter not in dispute. An explanation begins with a statement known to be true, and provides statements to show why is it true. To give an explanation is to reason from the fact to be explained to some statements that provide the explanation. Jones' initial argument is a deduction; it reasons from premises to a conclusion. Smith's explanation is an abduction, it reasons from the conclusion to the premises. It is called an abduction because it is reasoning "up" to premises rather than "down" to a conclusion.
There can be alternative explanations for a particular fact. Suppose again that Smith is late for work. Jones wonders why, for Smith is nearly always on time. Jones could come up with several explanations: a traffic accident held him up; his car broke down; his alarm clock failed; he is sick, etc. Each one of these explanations can be constructed as an argument in which the premises support the conclusion. This shows that the logical strength of the argument from the statements that explain to the statement of the fact that needs explaining is not the only criterion for a good explanation.
Another criterion is that the statements offered as an explanation are true. Jones could call the police and find out if there was an accident on the streets Smith drives to work. If there was not, this explanation can be rejected. Jones might also cast doubt on the truth of this explanation by observing that other workers drive to work on the same route as Smith, and they weren't late. Another criterion for a good explanation is that is complete, i.e. that it explain all aspects of what needs explanation. Smith's explanation was that the accident held up traffic for 20 minutes and suppose that this confirmed by the police. This explains why Smith was late, but it doesn't explain why he was 30 minutes late.
Explaining why things in the world are the way they are is one of the tasks of science. Scientists collect facts about the world; in addition they formulate general laws and theories to explain why things are the way they are. Suppose we put an ice cube in a glass and then fill the glass to the brim with water; the ice cube floats on the water and part of it will stick above the water level. When the ice melts, will the water level rise and overflow, will it remain the same, or will it go down? Suppose we try this a few times and each time the water level stays the same. Why does this happen. We want an explanation. The explanation is given by the law of buoyancy.
An object in water is buoyed up by a force equal to the weight of the water it displaces.
This implies that if we put an object in water it will sink until it displaces a volume of water that is equal in weight to the weight of the object. The ice cube is frozen water; when it melts it will fill in the volume it displaced and the level will remain the same because the volume of water in the glass does not increase.
The structure of a common type of scientific explanation is this:
General laws
Initial conditions
Fact explained
In the case of the ice cube the pattern is:
General law of buoyancy
Ice cube floating in a filled glass of water
The level of water remains the same when cube melts
Among the reasons this is a good explanation is that the general law of buoyancy can be used to predict other phenomena. It will explain why a one cubic foot block of Styrofoam floats higher in the water than a one cubic foot block of wood. One cubic foot of Styrofoam weighs one pound; one cubic foot of wood weighs, say, 25 pounds. The Styrofoam will sink until it displaces an amount of water equal to one pound. The wood block will sink until is displace an amount of water equal to 25 pounds. The volume of water for 25 pounds is greater than the volume for one pound, so the Styrofoam will float higher in the water.
Another criterion for a good explanation it that the statements that explain a fact do not imply something that is not true. For example, suppose a student receives a poor grade on an essay and the student knows that her view disagrees with that of the professor. The student explains the poor grade with the claim that the professor give poor grades to students who disagree with his view. The structure of the explanation is:
P1. If an essay disagrees with Professor Bloogs' views then he will give it a poor grade
P2. Susan's essay disagrees with Professor Bloogs' views
C. Susan received a poor grade
The explanation in P1 can be tested by predicting the grades of other students. If James' essay disagrees with Professor Bloogs views then it should have received a poor grade.
P1. If an essay disagrees with Professor Bloogs' views then he will give it a poor grade
P2. James' essay disagrees with Professor Bloogs' views
C. James' received a poor grade
Suppose James essay did disagree with Professor Bloogs' view and it received a good grade. In that case C, above is false, and so P1 must be false. Susan might also explain Professor Bloogs bias by claiming that if an essay agrees with his view it will receive a good grade. This predicts that if Bill received a good grade then his essay must have agreed with Professor Bloogs view. But if Bill has a poor grade and his essay agrees with Bloogs view, then the explanation of bias is not confirmed.
Suppose Simmons has a cold and explains this by stating that he went out of doors on a cold and rainy day without a coat. The general statement explaining Simmons' cold is that exposure to cold and rain causes colds. This explanation could be tested by seeing how well it predicts the occurrence of colds in those who go out in a cold rain without a coat. There is another way to evaluate the explanation - ask whether the general statement is consistent with other beliefs we have about colds. If we believe with modern medicine that a cold is an infection of the upper respiratory system, then we would say that a cold is the result of exposure to germs - to a bacteria or virus. The claim that colds are caused by exposure to cold rain is not consistent with the claim that colds are caused by exposure to germs. We have to give up one or the other of these claims, or we have to combine the two explanations in a consistent way. We might say that germs are necessary for the occurrence of an upper respiratory infection and add that exposure to a cold rain weakens the immune system and makes it more likely that exposure to germs will lead to a cold.
In summary, the criteria for good explanation are:
1) logical strength, i.e. the explanatory statements must strongly support the statement of the fact to be explained;
2) truth of the explanatory statements;
3) breadth of the explanation - it can explain other related phenomena
4) the explanatory statements predictions are not disconfirmed and there are confirming instances beyond the statement initially calling for explanation;
5) the explanatory statements are consistent with our well founded beliefs.
The examples of explanation used so far have been from everyday life and from science. Philosophers also use explanation. It is often claimed that a student of philosophy must identify and evaluate the arguments of philosophy, i.e. find the premises and conclusions and determine if the arguments hare logically strong and if the premises are true. The methods of deductive arguments are then the proper approach to philosophy texts. Many philosophical arguments are best understood as deductive arguments. But philosophers also use abduction. The philosophical theses they put forward are premises in an explanation of a phenomena
IV-7. Abductive Reasoning in Ethics
In scientific explanation a premise is abduced to explain a known phenomena and to then predict other phenomena. Issues in ethics present themselves for justification. "Was it right for Jones to lie to Smith?" "Are experiments on non-human animals ethical?" "Should an American citizen have a goavernment protected right to health care?" Answers to these sorts of questions are frequently presented by arguing from cases where the answer is clear. This is sometimes interpreted as reasoning by analogy.
It is wrong for a doctor to lie to a person about a test result, even if the doctor thinks that lying is in the patient's best interest. We know this because even doctors would agree that it would be wrong for a financial adviser to lie to them about a potential investment, even if the financial adviser thinks that this lie is in the doctor's best interest.
The analogical interpretation would be:
P1. A financial adviser lies to a doctor when he think doing so is in the doctor's best interest.
P2. A doctor lies to a patient when she thinks doing so is in the patient's best interest .
P3. The financial adviser is morally wrong.
C. The doctor is morally wrong.
A better interpretation of the argument is that it abduces a general rule about lying from the example of the financial adviser and then uses this general rule to apply to the case of the doctor. The argument starts from the view that we would all agree that it is wrong for a financial adviser to lie to a doctor, or any customer, on the ground that the financial adviser believes lying is in the interest of the customer. There is an implicit general rule that supports this view - that professionals should tell clients the truth and allow them to determine what is in their best interest. Once this general rule is abduced from the case of the financial adviser, it can be applied to the case of the doctor and show that it is wrong for doctors to lie to patients.
C1. It is wrong for a financial adviser to lie to a client when he believes it is the best interest of the client
P1. Professionals should tell clients the truth and allow them to determine what is in their best interest.
C2. It is wrong for a doctor to lie to a patient when she believes it is in the best interest of the patient.
C1. is written above P1 to show that P1 is abduced from C1, and C2 is written below P1 to show that it is deduced from P1.
This is simple presentation of the issue of professionals lying to clients. Situations involving lying are usually more complicated. One can ask about the competence of the doctor's patient and of the adviser's client. If they are deluded in some significant way, they may choose to do something that they would not choose if they were competent. This does not totally undercut the general rule, rather it requires a more precise formulation.
Professionals should tell clients the truth and allow them to determine what is in their best interest, except when the client is not competent and because of this likely to choose a course of action that they would not choose if competent.
There may be other circumstances where lying to a patient, or a client, is justifiable. Ethical analysis and argument frequently proceeds from the examination of many and divers cases in order to abduce the most plausible general rules of ethical conduct.
Here is an abductive argument that is also a reductio ad absurdum argument.
A full grown cat is capable of much more than a human infant. The cat has a sense of its own interests, and is capable of receiving and displaying affection. Further, it engages in play and activities like hunting that show that its level of intelligence is as great, if not greater than, that of an infant. Hence, if we consider painful, destructive experiments performed on cats to be morally legitimate then we must also accept the legitimacy of similar experiments on human infants.
This argument starts from what the author believes is a widely accepted view - that it is morally permissible to do painful experiments on cats. He abduces a general rule from this and some facts about the behavior and capacities of cats, and then applies it to human infants.
P1. It is morally permissible to do painful experiments on beings who have a sense of their own interests, display affection, and have intelligence.
P2. An human infant is not more capable of these behaviors than a full grown cat.
C. It is morally permissible to do painful experiments on a human infant.
This conclusion is one that nearly everyone would reject as morally outrageous. Since the argument is valid, one or other of the premises must be rejected. The author believes that only P1 can be rejected since P2 is obviously true. But without P1, there is no justification for painful experiments on cats, and we should find it just as outrageous as painful experiments on human infants.
Note the similarity between the structure of this argument and of explanations in science. A particular statement of fact is explained by subsuming it under a general law which explains the statement. The explanation can be rejected if we can deduce from it a prediction that turns out false. In this ethical argument the practice of painful experiments on cats was subsumed under a general ethical rule which justifies the practice. The general rule was rejected by showing that one can deduce from it a statement of what is permissible that we would all reject.
Much more could be said about this argument. For example, there may be alternative general rules that justify painful experiments on cats that would not justify painful experiments on human infants.
