I. 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 “Michelangelo’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.
II. 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.
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.
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 humans are mortal
P1. All mammals are four-legged
P2. You (the reader) are human
P2. You (the reader) are a mammal
C. You (the reader) are mortal
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.
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 A are B
P1. All dogs are mammals
P2. All B are C
P2. All mammals are warm-blooded
C. All A are C
C. All dogs are warm-blooded
b. Predicate Instantiation
Form Example
P1. All A are B
P1. All dogs are warm-blooded
P2. x is an A
P2. Fido is a dog
C. x is a B
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 p then q.
P1. If John is a freshman then he can’t enroll in Physics
P2. p
P2. John is a freshman.
C. q
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. not q
P2. Mary does not live on campus
C. not p
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
Form
Example
P1. If p then q
P1. If Mary loves John then she loves a loser.
P2. If q then r
P2. If Mary loves a loser then she will be unhappy
C. If p then r
C. If Mary loves John then she will be unhappy
g. Chain Argument
Form
Example
P1. If p then q
P1. If John is a loser then he will make Mary unhappy
P2. If q then r
P2. If John makes Mary unhappy Susan will hate him
P3. p
P3. John is a loser
C. r
C. Susan will hate John
The order of the premises in the above argument forms is the order for which most people intuitively see the validity of the arguments. In everyday discourse, the premises and conclusions won’t always be presented in this order. Consider a “real life” version of the example of Chain Argument.
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:
P1. Life is a more severe penalty than death
In doubt
P2. Lesser crimes should receive less severe penalties
Obviously true
P3. 2nd degree murder is a lesser crime than 1st degree murder.
Obviously true
C. Life for 1st degree murder & death for 2nd degree murder.
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.
