Identifying and Formulating Arguments

© Richard Lee, 1999

Arguments and Non-Arguments

        An argument is a piece of discourse in which some claim is supported by other claims. The conclusion is the claim supported. The premises are the supporting claims.

        It is important in understanding and critiquing someone's position (whether that person be a philosopher, a roommate, a scientist, or a sales representative) to examine and evaluate the arguments the person offers in support of the position. Arguments, then, must be distinguished from other pieces of discourse.

        Here, for example, is an argument:

The exercise of authority requires willing compliance by those subject to it. If those subject to authority do not respect and trust the authorities, the system will break down. Given the importance of the subjects with which professionals are concerned--health care, legal justice, accurate financial reporting, safe buildings and equipment--the proper performance of their activities is important for the public good. Consequently, the public respect and confidence necessary for the professional role are also important. (Michael D. Bayles Professional Ethics)

Bayles is defending the claim he makes in the last sentence, namely that public respect and confidence in members of the professions is important. Each of the first three sentences provides a premise for the argument.

        Here is another example of an argument:

It is admitted that the mind has nothing to do with the causation of purely reflex actions. But the nervous structure and the nervous processes involved in deliberate action do not differ in kind from those involved in reflex action; they differ only in degree of complexity. The variability which characterizes deliberate action is fully explained by the variety of alternative paths and the variable resistances of the synapses. So it is unreasonable to suppose that the mind has any more to do with causing deliberate actions than it has to do with causing reflex actions (C. D. Broad Mind and Its Place in Nature)

        Once again a claim is being supported by various considerations. (I should mention that Broad goes on to deny that this is a good argument.)

        This is not an argument; it is simply a conditional (or "if ..., then ...") statement:

If you were merely a live human body--as the Kleenex box is merely cardboard and glue in a certain arrangement--then the death of your body would be the end of you. (John Perry A Dialogue on Personal Identity and Immortality)

Now clearly this statement may figure in as a part of some argument. Indeed, it could be part of an argument that the death of the human body is the end of that person, since a person is simply a live human body, or--and it is important that there is this alternative--this conditional statement could figure as a premise of an argument that a person is not merely a live human body, because, after all, the death of a person's body is not the end of that person. So this statement might occur in various arguments, but by itself it is not an argument since nothing here is offered in support of some other assertion.

        Finally, here is a passage from William James' article "The Moral Equivalent of War," which, as it stands, consists of unsupported belief or opinion:

There is nothing to make one indignant in the mere fact that life is hard, that men should toil and suffer pain. ... But that so many men, by mere accidents of birth and opportunity, should have a life of nothing else but toil and pain and hardness and inferiority imposed upon them, should have no vacation, while others natively no more deserving never get any taste of this campaigning life at all,--this is capable of arousing indignation in reflective minds.

James claims this, but he does not (in the quoted passage at least) support these claims with any reasons, so this passage does not contain an argument.

Finding Conclusion and Premises

        Arguments may be as short as a single sentence or as long as a book. Every argument, however, must (by definition) have a conclusion. The conclusion is the claim that is argued for.

        Both premises and conclusion must be statements, that is claims that are either true or false (whether or not we know which). Questions, in particular, cannot be premises or conclusions. In the sense of "argument" and "arguing" (offering an argument) we are using here we would not say "John was arguing whether God exists"--or at least if we did say this we would not be identifying the conclusion of his argument. "Who caused the world?" is not going to be a premise or conclusion of any argument, because it is not a statement. Nor is a question of the form "Who is to say that ...?" Premises are claims that support the conclusion. Questions may be used to suggest claims, of course. Indeed this is so often done for effect in debate that such questions are known as "rhetorical questions." Thus a debater might say "Would you want to live under communism? Well, then you should support a strong defense." But insofar as there is an argument here, the premise is not the question "Would you want to live under communism?" but the answer that the debater is presuming you would offer (silently) in reply to the question, namely that you would not want to live under communism.

        Conclusions are sometimes announced by phrases we call conclusion indicators, which are words and phrases which typically indicate a conclusion is to follow. Here are some conclusion indicators:

therefore
consequently
so
hence
thus
it follows that
I conclude that
we may infer that

Notice that the samples of argument offered above have conclusions which are introduced in this way.

        While these words and phrases may help you to spot an argument, you should be advised that not all conclusions are preceded by these conclusion indicators, and not all statements preceded by these words and phrases are conclusions. So, for example, the word "thus" in the above excerpt from Tolstoy does not introduce a conclusion--and neither does the word "so" in this sentence. Also, a conclusion does not always come at the end of the passage containing the argument. Sometimes it is expressed first and the premises follow.

        Premises are the reasons which are offered in support of a conclusion. There are sometimes telltale signs of premises, as there are of conclusions. Words and phrases that commonly indicate that the statement following is a premise are called premise indicators. Here are some premise indicators:

since
because
for
given that

        Again, not all premises are introduced by premise indicators, and these same words and phrases sometimes serve functions other that introducing premises. "Because" frequently appears in explanations, and there is a use of "for" as a preposition, a use more common than its use as a premise indicator. Similarly, "since" commonly functions as a preposition concerning duration of time rather than as a premise indicator. Notice also that "for" not only indicates that a premise is coming, but that what has just been stated (before the word "for") is the conclusion (whether intermediate or final).

        As an example of an argument that uses indicators let us consider an argument offered by Rene Descartes in the third of his famous Meditations. In this meditation Descartes develops an argument that God exists, a God, he insists,

who possesses all those supreme perfections of which our mind may indeed have some idea but without understanding them all, who is liable to no errors or defect and who has none of all those marks which denote imperfection.

        Immediately after saying this Descartes goes on to write:

From this it is manifest that He cannot be a deceiver, since the light of nature teaches us that fraud and deception necessarily proceed from some defect.

        This is an important, but likewise brief, argument. There are two phrases in this sentence which indicate parts of an argument. The word "since," of course, indicates a premise here. As a first approximation we might suppose that the premise is the clause that follows the premise indicator, namely "the light of nature teaches us that fraud and deception necessarily proceed from some defect." But one might then consider that the substance of this claim is more simply that fraud and deception necessarily proceed from some defect. The phrase "the light of nature teaches us that" appears, then, to be Descartes' way of telling us how we know that premise to be true.

        The phrase "from this it is manifest that" was not on our list of conclusions indicators, but it seems to indicate that a conclusion is coming, just as "it follows that" does. The conclusion of Descartes' argument here, therefore, is "God cannot be a deceiver." (Sometimes figuring out what pronouns are intended to refer to can present a problem, but there is no difficulty in this case.) But the "from this" also suggests that what has preceded this remark is support for this conclusion, that a premise appears earlier. What the "this" refers to, presumably, is what Descartes claimed about God, namely that he "is liable to no errors or defect."

        We can therefore formulate Descartes' little argument as follows:

1.God is liable to no errors or defect.
2.Fraud and deception necessarily proceed from some defect.
:.3. God cannot be a deceiver.

        Some of these "indicators," like "so" and "for" help us identify both a conclusion and a premise. Consider the word "therefore." This introduces a conclusion. But this word would not be used unless some reason (or premise or piece of argumentation) preceded the word "therefore." The same applies to most conclusion indicators. (But not to all. A writer may say "My conclusion is ...," and thus indicate a conclusion, and may do so before any argumentation is given.)

        The premise indicators "since," "because," and "given that" may introduce a premise whether or not a conclusion has been stated. The word "for," however, indicates not only that what follows is a premise (or reason, or piece of argumentation), but that what precedes is the conclusion that is drawn from that premise (possibly together with other premises, of course). So, when you see a passage of the form "..., for ___," you can be pretty sure that "___" indicates some premise used to support conclusion "..." This structure of writing is found very often in Thomas Aquinas, but it is common in other philosophers as well.

        For example, Descartes in his proof of the existence of God in Meditation III ends one paragraph by saying "hence, from what has been already said, we must conclude that God necessarily exists." Obviously this states a conclusion and indicates that there is argument for this conclusion prior to this sentence. And it might be felt that his entire argument precedes this statement of the conclusion. But Descartes begins the next paragraph with the word "for," saying:

For although the idea of substance is within me owing to the fact that I am substance, nevertheless I should not have the idea of an infinite substance--since I am finite--if it had not proceeded from some substance which was veritably infinite.

Never mind now what this means and what it specifically has to do with Descartes's argument. What is important to notice is that this is meant to be part of the argument whose conclusion he has already stated.

        So when you see the word "for," you should look not only for a premise which follows, but look directly before the word "for" for the statement that that premise is supposed to be supporting.

Hints on Formulating Premises

        Each statement in the argument, whether a premise or a conclusion, should be expressed as a single statement--not as a question, and not as an inference. So in formulating premises and conclusions be sure you don't list "Who is to say that lying to dying people is wrong?" as a premise. Whenever you are tempted to list a question as a premise, think instead of what point you are trying to make. Often it is the answer to the question that is the real premise. I know I have mentioned this before (above), but since students so frequently ignore this point, it is worth mentioning again.

        So if Socrates says

What subject of difference would make us angry and hostile to each other if we were unable to come to a decision? Perhaps you do not have an answer ready, but examine as I tell you whether these subjects are the just and the unjust, the beautiful and the ugly, the good and the bad. Are these not the subjects of difference about which, when we are unable to come to a satisfactory decision, you and I and other men become hostile to each other whenever we do? (Euthyphro 7c-d)

the premise (once Euthyphro nods his head in agreement) is something like this:

The subjects of difference about which men, when they are unable to come to a satisfactory decision, become hostile to each other are the just and the unjust, the beautiful and the ugly, and the good and the bad.

        Other times the real premise is not the answer to the question so much as the claim that there is no answer. So when someone is tempted to write "Who can say ...?" as a premise, what they really mean is something like "No one is in a position to say ..." And if they try to argue against the existence of a first mover by saying "so, who moved the first mover?" what they really may mean could be something more like "If there was a first mover, that first mover would have to have been moved by something else. Yet a first mover is something that is not moved by something else." Notice that that single question here is spelled out more clearly as two premises. Part of making an argument clear sometimes involves spelling out the argument more fully (as part sometimes involves eliminating superfluous wording).

        Another thing to watch out for in formulating premises is to formulate an inference as though it were simply a premise. So some students will write something like "..., therefore ___" as a premise. But this is really a little argument. The "..." part is, of course, the premise, and the "___" is the conclusion. (This little argument may simply be part of a larger argument. See below "Layers of Argumentation.") Beware of premises that involve premise or conclusion indicator words. Usually you will find that such "premises" instead express inferences that can be broken down into premise and conclusion.

        Other times people just try to put too much into a premise. Make each premise a single statement. Some statements are fairly complex . They can be conditional statements or disjunctive ("either ... or ___") statements (see below for an example), but they should be able to be expressed as a single sentence.

Links

        Premises are supposed to provide support for the conclusion. To do so they must relate to the conclusion. In looking for premises of an argument, therefore, you should (as well as looking for premise indicators) look at the terms (words or phrases) that appear in the conclusion, and see where else the author uses those phrases (or synonyms). So, if a conclusion states that abortion is wrong, some premise ought to mention abortion (e.g. "abortion is the killing of a fetus") and some ought to say something about what is wrong (e.g. "killing is wrong.").

        Once you have located one premise of an argument and have located the conclusion, you can often find other premises by looking for a link between the premise and the conclusion. A link is a premise stating some connection between something mentioned in one premise and something mentioned in the conclusion.

        So, for example, consider an argument with this conclusion: "Morality is all relative." (A good philosopher would say this only if she explained carefully what it meant, but let us bypass that step here.) Suppose you find a premise "Morality is all a matter of feelings." So far, so good: Obviously this premise relates the conclusion, in that it says something about morality (which is a term in the conclusion). Now you should look for a link. What need to be linked together are the "all a matter of feelings" mentioned in the identified premise with the "all relative" mentioned in the conclusion. A link of the form "whatever is all a matter of feelings is all relative" would do the job.

        Often a link between a premise and a conclusion will be a conditional statement.

        When formulating an argument, list all linking claims as premises in the argument.

Formulation of Premises and Conclusion: An Example

        Let us, as an extended example, consider an argument somewhat more complex than any we have looked at so far. Consider the following passage from the end Plato's Apology after Socrates has been condemned to death and is reflecting upon his fate:

... there is good hope that death is a blessing, for it is one of two things: either the dead are nothing and have no perception of anything, or it is, as we are told, a change and a relocating for the soul from here to another place. If it is complete lack of perception, like a dreamless sleep, then death would be a great advantage. For I think that if one had to pick out that night during which a man slept soundly and did not dream, put beside it the other nights and days of his life, and then see how many days and nights had been better and more pleasant than that night, not only a private person but a great king would find them easy to count compared with the other days and nights. If death is like this I say it is an advantage, for all eternity would then seem to be no more than a single night. If, on the other hand, death is a change from here to another place, and what we are told is true and all who have died are there, what greater blessing could there be, gentleman of the jury?

Socrates then goes on to speak of how much he would enjoy talking with the other people he would meet in this other "place."

        Let us first find the conclusion of this argument. What Socrates is attempting to defend here is clearly the claim that death is a blessing (or less decisively, that "there is good hope that death is a blessing"). And right after that clause there appears the word "for," which in this context functions as a premise indicator suggesting that what follows is a premise supporting this claim. The first premise, then, is this: "Death is one of two things: either the dead are nothing and have no perception of anything, or death is a change and relocating for the soul from here to another place." Notice how I have kept close to the wording of the original, but have replaced the pronoun "it" with "death" where appropriate and have cut out some unnecessary words. But before continuing I would like to restructure this premise even further. It is claiming that there are two possibilities. We can express this clearly, and slightly simplify the premise (without, I think, losing anything essential to the argument), by writing it as:

1.Either dead people have no perception of anything or death is the relocating of the soul to another place.

        This is a fine start, but there are other premises as well. Indeed, another premise is stated quite succinctly in the very next sentence of the passage: "If it is complete lack of perception, like a dreamless sleep, then death would be a great advantage." A few things should be noted about this. First, obviously "it" here refers to death. Second, the phrase "death would be a great advantage" is roughly synonymous with "death is a blessing." (I don't think Socrates is making a distinction between something being advantageous and it being a blessing here, and the subjective ("would be") is just used because of the grammatical place of the clause in the sentence.) Third, the sentence here, in spite of lacking the word "then" is a conditional statement which is practically in standard "if ... then ..." form. Finally, the antecedent part of this conditional, "death is complete lack of perception," is intended to express the same thing as the first part of premise 1. It is best, then, to standardize on one way of expressing this idea and stick with it in the formulation of each premise. Taking all those points into account we can express this second premise as:

2.If dead people have no perception of anything, then death is a blessing.

        Notice that this premise (2) serves as a link between premise 1 (which mentions the thought that dead people have no perception of anything) and the conclusion (that death is a blessing).

        Most of the remainder of the quoted passage--indeed all but the final sentence--consists of a defense of this second premise. While that is important for evaluating Socrates' entire line of argumentation, we will skip over it here and look for some additional premise which is appealed to, together with 1 and 2, in support of the conclusion. We find that premise in the final sentence quoted: "If, on the other hand, death is a change from here to another place, and what we are told is true and all who have died are there, what greater blessing could there be ...?" Now this is a question, and I have emphasized that questions cannot be premises, but clearly Socrates is intending to make a positive statement here and is using a rhetorical question to make it. Once again the statement suggested is a conditional statement. If we eliminate unnecessary wording and express his meaning in the words and phrases we have already used, we can see that Socrates' claim here is:

3.If death is the relocating of the soul to another place, then death is a blessing.

        This is another linking premise. It, like premise 2, links the first premise with the conclusion. It is not, however, simply a restatement of premise 2.

        This completes the core argument. What Socrates goes on to do for a couple of paragraphs following the quotation is to defend premise 3 by talking about whom he would expect to meet and how wonderful this would be.

        But let us stop for a moment here and put together the argument we have extracted from the passage:

1.Either dead people have no perception of anything or death is the relocating of the soul to another place.
2.If dead people have no perception of anything, then death is a blessing.
3. If death is the relocating of the soul to another place, then death is a blessing.
:.4.Death is a blessing.

        We can see that there is a pattern here, one which arguments having nothing to do with death might also share. If we symbolize each clause by a letter, we can uncover the form of Socrates' argument as:

1.Either p or q.
2.If p, then r.
3.If q, then r.
:.4.r.

        Here I have simply taken clauses and consistently substituted letters for them. That is, I have taken the clause "dead people have no perception of anything" and have replaced this with "p" not only in (1) but also in (2), and have replaced the clause "death is the relocating of the soul to another place" with "q" not only in (1), but in (3) as well. The clause "death is blessing" is symbolized by "r" in (2), (3), and (4). I have done this to allow us to see more clearly how the argument is connecting these clauses with one another. This is analogous to looking at the skeleton of an animal to see its anatomical structure better.

        Incidentally, this particular argument form is called "simple dilemma".

Layers of Argumentation

        What I have outlined here is only, as I said, the main structure of the argument Socrates presents (as it was reported by Plato). Some of the passage quoted consists of a defense of what I have listed as line 2, and the material in the Apology following the quoted passage consists of a defense of line 3 of this argument. These two lines are thus not unsupported premises, but intermediate conclusions. That is to say, they are each a conclusion of one little argument and then a premise for another. Argumentation can often be dissected in this way.

        Let us look briefly at how Socrates attempts to defend (3). He writes:

... what would one of you give to keep company with ... Hesiod and Homer? I am willing to die many times if that is true. It would be a wonderful way for me to spend my time whenever I met [certain others who have died] ... to compare my experience with theirs. I think it would be pleasant. Most important, I could spend my time testing and examining people there, as I do here ...

        This together with the final sentence of the longer passage quoted suggests that Socrates thinks that if death involves relocation of the soul, then he would have an opportunity to talk with Homer and others, and that this would be a blessing.

        So he is arguing:

5.If death is the relocating of the soul to another place, then when one is dead one can converse with Homer and others.
6.If when one is dead one can converse with Homer and others, then death is a blessing.
:.3.If death is the relocating of the soul to another place, then death is a blessing.

        Notice how the conclusion of this argument serves then as a premise of the previous argument, the one from (1), (2), and (3) to conclusion (4).

        By the way, the form of this argument is:

5.If p, then q.
6.If q, then r.
:.3.If p, then r.

(I have reassigned the correlations between letters and clauses from the previous example, just as mathematicians use "x" in one problem and then again in another where it refers to something completely different.)

        Incidentally, this form is called "hypothetical syllogism" and is discussed in "Some Common Valid Argument Forms--with Examples."

        Such complexity as we find here in Socrates' argument is not rare. Indeed, as far as complexity of argument goes, this sample is extraordinarily mild for philosophical argument. It is common, particularly in philosophy, for arguments to involve premises which are themselves argued for. A conclusion may rest on premises which in turn rest on other premises. Graphically an argument may thus look like this (the numbering here is arbitrary):

unsupp.prem.1      unsupp.prem.2      unsupp.prem.3
                                              
        +-------------------+                   
                                               
    Intermediateconclusion1   intermediateconclusion2
                                          
                +--------------------------+
                              
                      Finalconclusion

The outside "layer" of argumentation (closer to the bottom here) is from "intermediate conclusion 1" and "intermediate conclusion 2" to the "final conclusion." But since the premises of this argument might be called into question, they are defended in another layer of argument, from "unsupported premise 1" and "unsupported premise 2" to "intermediate conclusion 1" and the separate argument from "unsupported premise 3" to "intermediate conclusion 2." And of course this is simply a sample of such layering. There may be several layers and each intermediate conclusion may be supported by more than one or two premises.

        Here's how the layers (so far uncovered) of Socrates' argument would look when laid out in this fashion:

                           5         6
                                    
                           +---------+
                                
                1       2       3
                              
                +-------+-------+
                        
                        4

        If we were developing the layers of this argument more fully, we would find premises which support 2 (which would then be taken to be an intermediate conclusion instead of an unsupported premise).

        In order to solidify our ability to uncover layers of argumentation and graphically display them in this manner, let us consider another example of layered argumentation. Consider this fairly straightforward argument by the twentieth century British philosopher, C. D. Broad:

Thus there is both need and room for a science which shall try to analyze and define the concepts which are used in daily life and in the special sciences. There is need for it, because these concepts really are obscure, and because their obscurity does lead to difficulties. And there is room for it, because, whilst all the special sciences use these concepts, none of them is about these concepts as such. ("Critical and Speculative Philosophy")

        While some of the argument appears prior to the quoted passage, we will restrict our attention to these few sentences. Notice that the first sentence is the conclusion (and in this context, at least, the "final" conclusion, although Broad could go on to argue for something else using this as a premise). Conveniently it starts with the conclusion indicator word "thus." The remaining two sentences express the argument for this conclusion. And their doing so can be displayed by exposing two layers to the argument.

        The conclusion again is: "There is both a need and room for a science which shall try to analyze and define the concepts which are used in daily life and in the special sciences." To avoid a lot of repetition here let us use "Concepts" temporarily as an abbreviation for "the concepts which are used in daily life and in the special sciences." (By the "special sciences" Broad means those sciences such as chemistry and physics, or psychology, for that matter, which have some particular subject matter.) So the final conclusion is: There is both a need and room for a science which shall try to analyze and define Concepts.

        This is argued from two main (intermediate) premises (or intermediate conclusions, since they are in turn the conclusions of other argumentation):

C1:There is a need for a science which shall try to analyze and define Concepts.
C2: There is room for a science which shall try to analyze and define Concepts.

        This part of the argument is clear enough. To defend some claim of the form "p and q" one needs to establish p and to establish q. But to see how Broad attempts to establish each of these takes us to a further layer of the argument in the passage.

        C1 is supported by:

P1:Concepts really are obscure.

and

P2:The obscurity of Concepts really does lead to difficulties.

C2 in turn is supported by:

P3:None of the special sciences is about Concepts as such.

        Seen this way the argument Broad has given exactly fits the pattern above:

 P1                 P2             P3
                                 
 +------------------+              
                                  
            C1                     C2
                                  
            +----------------------+
                       
               Final conclusion

Finding Implicit Premises

        Sometimes there is more to an argument than meets the eye--or than is printed on a page. In particular, sometimes certain premises are left unstated. This is often done only when what is left out is felt to be so obviously true that it would be superfluous to state it.

        Consider this passage from John Stuart Mill's Utilitarianism:

... happiness is the sole end of human action, and the promotion of it the test by which to judge all human conduct; from whence it necessarily follows that it must be the criterion of morality, since a part is included in the whole.

        The conclusion indicator "it ... follows that" identifies "the promotion of happiness is the criterion of morality" as the conclusion of this argument. The word "since" in that same sentence introduces the premise "a part is included in the whole." The first sentence quoted is also a premise, as suggested by the phrase "from which it follows ..."

        Recognizing that "criterion of" and "test by which to judge" are probably being used synonymously, on a first attempt to formulate this as a carefully stated argument we produce:

The promotion of happiness is the criterion of human conduct.
A part is included in the whole.
Thus, the promotion of happiness is the criterion of morality.

        So far, so good, but there are some problems here: the sense of the second premise is vague, and it is not clear what role it plays in the argument.

        Instead of thinking what "a part is included in the whole" might mean (and apart from the argument, we may have a fairly good sense of what it means), let us first think of how more fully to explicate this argument. In particular, let us look for links.

        Obviously the first premise relates to the conclusion: it mentions happiness and speaks of a criterion, both of which are mentioned in the conclusion.

        But what links the second premise to the conclusion? There is no other stated premise in the passage which says anything about parts or wholes. But statement 2 is obviously intended by Mill as a premise in the argument. So something is obviously missing here. Mill is leaving something unstated. Any premise to an argument that is left unstated in a passage is called an "implicit premise." (Sometimes this "implicitness" is a matter of degree. Some premises are stated outright. Others are left completely unstated. But there is a middle ground in which premises are alluded to but not fully stated.)

        Obviously, what is being assumed in this argument without being stated is that morality is a part of human conduct. Otherwise there is no connection between the first premise and the conclusion, and the second "premise" contributes nothing to the argument. This is the unstated assumption that links premise 2 (which talks about parts) with the conclusion (which talks of morality). Notice that this also links premise two with premise one. Suddenly the argument is becoming more coherent (i.e. its premises and conclusion are fitting together well).

        If we add this missing claim to the argument, it becomes:

1.The promotion of happiness is the criterion of human conduct.
2.A part is included in the whole.
3.Morality is a part of human conduct.
:.4.The promotion of happiness is the criterion of morality.

        Still, premise 2 requires clarification, but now we have a clue to its intended force, since we see that it must hook up with the other two premises. Does premise 2 mean that "whatever is true of the whole is true of all parts of the whole"? If so, the argument would be valid, since "has the promotion of happiness as its criterion" is, by premise 1, true of the whole mentioned in the third premise, and the conclusion states that this is also true of the part mentioned in the third premise. However, so understood, premise 2 would be definitely false. For example, it is true of this sheet of paper that it is larger than fifty square inches in area, but it has parts--the molecules that make it up--of which this is not true.

        If we charitably assume Mill would not make such an obvious error (famous philosophers make mistakes, but they are not stupid, and thus we should interpret their arguments with charity--that is we should assume they are saying something that is not obviously wrong ), it is therefore more plausible to presume that by "a part is included in the whole" in the context of this argument Mill meant the more restricted claim that the criterion of (or "test by which to judge") a whole is the criterion of all its parts. (If we wanted complete understanding of this argument we would, of course, have to ask for a fuller account of what Mill means by "criterion," but I will skip over that here.) This revision of the second premise can be phrased as a generalized conditional statement as: For every x, y, and z, if y is a part of z, and x is the criterion of z, then x is the criterion of y. The idea here is that we want some general claim from which it follow that if morality is a part of human conduct and if the promotion of happiness is the criterion of human conduct, then the promotion of happiness is the criterion of morality. This is not as terse and pithy as Mill's "a part is included in the whole" statement, but it seems to be what his claims must be presumed to mean to make the argument work.

        The entire argument in the brief excerpt from Mill then becomes:

1The promotion of happiness is the criterion of human conduct.
2.For every x, y, and z, if y is a part of z, and x is the criterion of z, then x is the criterion of y.
3.Morality is a part of human conduct.
:.4.The promotion of happiness is the criterion of morality.

        One must make explicit any implicit premises in an argument not only to see the structure of the full argument and determine whether it is valid, but also because sometimes a suppressed (i.e. implicit) premise is in fact objectionable and making it explicit provides an extra line of attack on the soundness of the argument.

The Search For Premises

        It is one thing to follow such analysis of arguments when I lay it all out for you, and another to be able to do it on arguments yourself. You can get practice on arguments by opening any philosophy book (or many an editorial or letter to the editor) and searching for the arguments.

        Let me provide, as a review, a few quick "pointers" to help you in your exploration of arguments. Remember the premise indicators and conclusion indicators. This will help you identify the conclusion and some premises.

        First focus on the conclusion. Look at each term that appears in the conclusion, each important word or phrase. Then make sure that at least one premise makes use of that term. (This is how I found the implicit premise in the example from Mill: no explicit premise mentioned morality, which was mentioned in the conclusion.) If the conclusion says "the soul can survive the death of the body," there had better be at least one premise which mentions the soul, and one which mentions death and one which mentions the body.

        Looking through the passage for claims that involve the terms of the conclusion should turn up some premises. These premises may introduce other terms which do not appear in the conclusion. Look then for further premises which use these terms. The idea here is to find the connections, i.e. links, between the premises and the conclusion. Imagine tying the conclusion direct to a couple of premises by finding common terms in them (e.g. the term phrase "highest degree" in a conclusion and a premise), and tying the premises to other premises. Doing this help bring out not only the premises of the argument, but its layered structure as well.

        Some people get to explore the moon. Some people get to explore far away countries. Some people get to explore the inner workings of the human body. You and I get to explore arguments. Such exploration can be just as fascinating, useful, and enjoyable.


Richard Lee, rlee@uark.edu, last modified: 29 August 2004