Argument Analysis.

UNIVERSITY OF THE WEST INDIES
DISTANCE TEACHING EXPERIMENT
(UWIDITE)
CERTIFICATE IN EDUCATION
ED402: INTRODUCTION TO ARGUMENT IN EDUCATION
ARGUMENT ANALYSIS
Ed Brandon
Faculty of Education
U.W.I.
Mona
© University of the West Indies, Mona, October 1983
Revised February 1985, November 1988
CONTENTS
Preface
Introduction
1. Preliminaries
2. The Elementary Structures of Argument
3. Interlude - Confronting Arguments
4. Entertained Arguments
5. Discussions, Explicit and Implicit
6. Varieties of Support
7. Testing for Validity
8. A Note on Non-deductive Arguments
9. Criticism and Cognitive Change
10. Truth, Falsehood, and Evasion
11. Ellipsis
12. Verbs and Abstract Nouns
13. What does it Mean?
14. Facts and Values
15. Some Uses of Argument
16. Reflective Equilibria
17. Standards
Appendix 1: Philosophical and Conceptual Analysis
Appendix 2: Some Precautionary Measures
Argument Analysis, by Ed Brandon ﬁle:///Users/edbrandon/Documents/critthinkinﬂogic/aacomplete...
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Sources of Examples
Recommended Further Reading
PREFACE
This little book is intended to help people deal with arguments. In particular, it is intended to help
people see more clearly what is going on when a person gives reasons for believing something or
doing something, and to see some of the pitfalls in the way of clear reasoning. The foundations of
the approach I have adopted are to be found in logic; the matters I discuss are, for the most part,
well-known and generally agreed upon by students of logic. You should therefore beware of finding
anything original in these pages.
I have learnt most about the questions discussed in this book from the teaching and writings of the
late J.L. Mackie. I am pleased to acknowledge a particular debt in this work to some lecture notes
by Mackie on the structure of arguments and discussions from which I have borrowed liberally in
the earlier portion of this booklet. In my own teaching I have also relied heavily on Anthony Flew,
Thinking about Thinking, P.T. Geach, Reason and Argument, and Michael Scriven, Reasoning. There
are, I hope, echoes of these writers in this book; any distortion is, of course, my responsibility.
This material is being published at the behest of the U.W.I. Distance Teaching Experiment, and I
am grateful to the project team for asking me to participate. I am also grateful to Paul Ernest,
Christine Marrett, Jacquie Moriah, Kay Morrish, Velma Pollard, and Kathryn Shields for their
comments on earlier versions of some of the following.
The first version of this booklet was prepared in 1983. A second version, with several new
examples and some minor additional remarks, was prepared early in 1985. I should like to thank
Kay Morrish for her concern for that version to be as polished in appearance as it could be. This
third version was prepared by the author from a Wordstar text produced by Kay (with a little help
from Island Microsystems) so I can now take the blame not only for the style and content but also
the appearance of the text.
INTRODUCTION
You are being asked to work through this booklet as part of a course in the philosophy of
education, itself part of your course in education. Why? In the first place, I hope it will be useful for
you, not just in coping with your education courses, but also more widely in your everyday life. In
the second place, it is, I think, a reasonable, if somewhat unusual, component of a course in the
philosophy of education, especially when you won't be getting any other kind of input from
philosophy.
The word "philosophy" may well suggest something abstruse and unpractical, and indeed a lot that
goes on in philosophy is pretty obscure and practically useless, but not perhaps everything. On the
one hand, there is the original motive for doing philosophy - a drive for a general understanding of
the world and our place in it and for a reasoned view of what that world ought to be like; on the
other, there are the more detailed studies philosophers have undertaken of the nature of
knowledge and of the workings, and especially the logical structure, of meaningful language (which
is the medium in which much of our knowledge gets expressed). These two aspects of philosophy
can, I believe, offer us something of value. The original motive can spill over into education - we
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can try to see more clearly what we are doing and what we should be trying to achieve - and I
hope that it will in the other part of your philosophy of education course. But for now we are going
to try to learn from the narrower studies of knowledge, language, and logic.
We are going to start by looking at some simple features of the sort of argument in which someone
offers you reasons for believing something or for doing something. We shall go on to dig a little
deeper and so see the different things that are happening - the idea being that if you begin to see
how arguments work you should be better able to judge them and perhaps better able to construct
them yourself. People often try to justify the study of mathematics or Latin or history by saying
that they will help you to reason better. There is evidence that studying history helps you to reason
better about history, studying mathematics helps you to reason better about mathematics, but that
studying these subjects does little for your reasoning outside of the subject, in everyday life or in
other subjects. In this course we shall take the bull by the horns and simply study reasoning.
Reasoning has to be about something, but I hope you won't be distracted by the subject-matter
from the general points being made. (On the other hand, I hope you will find some of the subject-
matter interesting; I have tried to avoid invented examples as much as possible, because the aim
is for you to deal better with real examples.)
After looking briefly at arguments, we shall look at a few of the things that can go wrong with the
statements that make them up. We shall then look at some of the general aims people have in
putting forward an argument, in offering reasons. As before, the idea is that if you know what to
look out for and can draw some subtle distinctions you are better placed to detect flaws in
arguments, your own and other people's.
In this course you are only taking the very first steps towards the study of argument and into the
issues that arise in that study - first steps are, however, among the most important. At the end I
indicate a few of the further issues that arise and suggest a few of the many books you might use
to travel further.
As you will soon discover, there are frequent exercises throughout the text. I suspect you won't
learn very much from reading the text unless you also try to do these exercises. I have given my
answers, with some supporting remarks, at the end [in this Web version, in pop-up boxes which
are also endnotes to each file for those unable to use the pop-up windows]; but please try to do
the exercises for yourself first and then try to work out why my answer is different (if it is). I
should say now that there is often room for alternative answers. I should be glad to know of any
such alternatives, and also of any errors or gross inadequacies in my own suggestions.
I have tried as much as I can to use arguments actually put forward by other people. Such
arguments are followed by a number in square brackets and the source can be found by looking up
the number in the list of sources at the back.
1. PRELIMINARIES
Some arguments simply consist of people shouting at each other, war pursued by other means; but
these are not our concern. We shall be looking at arguments in which someone offers reasons for
what she claims. Indeed it might be better to say that we are concerned with reasoning, since we
very often offer reasons without pretending to be arguing a point. Consider the following remark:
(1) By the look of those clouds, it'll rain today.
If I said that to you, it is hardly natural to say that I have argued for the conclusion that it will rain
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today; I have indicated a reason for believing that conclusion true, but we wouldn't normally call
my remark an argument. But still, we could make a few changes to transform it into what is
obviously an argument for the conclusion. Perhaps we could rewrite it thus:
(2) Those clouds are very dark and heavy, so it is likely that it will rain today.
That is not so natural (nor, perhaps, so persuasive) but it makes explicit what was going on in the
first remark; we could say that it is an explicit argument corresponding to remark (1). What is
important for us is to see, on the surface of (2) but hidden within (1), a movement from reasons to
a conclusion. Whenever we can find such a movement I shall say that we have an argument.
In our example what is at stake is a fact, that it will rain at a certain place and time; since it is a
fact in the future we would normally call it a prediction, but people argue for factual claims of all
sorts and that is all I am concerned with now. But besides offering reasons for believing that
something is, was, or will be so, people also argue for what we can call practical conclusions; they
offer you reasons for doing one thing rather than another. "They will have to raise taxes, but we
won't, so vote for us!" Here the speaker is trying to get you to vote for her; she might have said
"so you ought to vote for us" or "so you should vote for us", but however she expresses herself you
can see again the movement we have noted above from reasons (here possibly dubious claims
about different parties' future decisions about taxes) to a conclusion.
So then, an argument involves three things: reasons for something, the something itself, and the
movement from the reasons to the something. In my first example, the clouds being dark and
menacing; the rain I predict; and the movement I want you to make from the first to the second,
from the clouds to the rain. Let us agree on some terminology. When we have an explicit
argument, we shall be able to distinguish on the one hand one or more premises (some people
spell this "premisses") and on the other, one or more conclusions (for convenience we shall usually
assume there is only one conclusion to each argument), and we shall say that the premises are
intended to support the conclusions.
It is worth noting explicitly that not every connected discourse involves reasoning. A description of
something or some event may involve a lot of statements connected together in various ways, but
it won't usually involve some of those statements supporting others in the way we are concerned
with. Similarly a typical narrative will contain many statements, often with very close connections
between them, but while in a narrative the earlier statements may make the later ones intelligible,
they won't usually be giving them the sort of argumentative support we are focussing on. Very
roughly, a narrative may help you see that the events described by certain claims are intelligible,
an argument will give you reasons for thinking those claims to be true or acceptable.
If you read an explicit argument, or listen to one, the premises and the conclusion will be
statements, the support will be mainly between the statements, as one might say; it will be
indicated as much by how the statements are strung together as by anything else. We shall come
back soon to the claim that the premises and the conclusion are statements; for the time being you
can regard it as one of our attempts at simplifying our subject-matter. The premises will express
the reasons that are being offered for the conclusion. The premises are the starting-points for this
argument; the arguer simply asserts them or takes them for granted, in this argument. (Indeed,
they may be so taken for granted that they are not actually expressed - we shall come back also to
this point later on.) She might argue for them elsewhere, but we must take things one step, one
argument, at a time. The conclusion is what the arguer is getting at, what she is trying to prove or
establish or defend. And the arguer claims that the premises do support the conclusion, that the
conclusion follows from them or is in some other way supported or made more likely by them.
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Let us see if we can pick out premises and conclusions from a couple of real arguments. Here is
part of a chapter by Bertrand Russell:
(3) The instincts and reflexes with which a child is born can be developed by the
environment into the most diverse habits, and therefore into the most diverse
characters. Most of this happens in very early childhood; consequently it is at this
period that we can most hopefully attempt to form character. [1]
When we want to distinguish premises from conclusions it is often easiest to start by looking for the
conclusion. What is Russell getting at? What would he want us to take away from this passage?
Russell has in fact set out his argument very clearly and he has given us our answer by his use of
the word "consequently". Putting it explicitly, his conclusion is that we can most hopefully attempt
to form character in very early childhood. (Note that to make it absolutely explicit we had to look
back to see what "at this period" referred to.) What reasons does Russell offer? He makes two
points. The first is contained in the first sentence: "The instincts and reflexes with which a child is
born can be developed by the environment into the most diverse habits, and therefore into the
most diverse characters." The second is the claim of the second sentence that most of this
environmental moulding happens in very early childhood. These two points join together to support
his conclusion. If we want to formulate Russell's argument absolutely explicitly we would have to
do a little rewriting, expanding the word "this" a couple of times, but in this case there is very little
such manipulation to be done. Regimented in text-book fashion, with premises in a column,
followed by the conclusion, Russell's argument might appear thus:
(4) The instincts and reflexes with which a child is born can be developed by the
environment into the most diverse habits, and therefore into the most diverse
characters.
Most of this development happens in very early childhood.
So, we can most hopefully attempt to form character in very early childhood.
Let us move on to a less straightforward example, taken from Dr. Johnson (with spelling
modernized):
(5) Many of the books which now crowd the world, may be justly suspected to be
written for the sake of some invisible order of beings, for surely they are of no use to
any of the corporeal inhabitants of the world. [2]
This is less straightforward partly because Dr. Johnson does not exactly mean what he says; he is
being sarcastic. But let us take him at his word (which is a necessary part of appreciating his
sarcasm) and try to sort out his reasoning. We can rephrase his points in the interest of brevity and
clarity. What is the conclusion of the literal argument? Many of the books that now crowd the world
are written for some invisible order of beings. Why? They are of no use to us. The explicit argument
is then:
(6) Many present-day books are of no use to us.
So, those books are written for some invisible beings.
Note that in Johnson's argument the conclusion comes first. He begins with what he is getting at,
and then tells us why we should accept it. Notice also that he indicates the conclusion by using the
phrase "may be justly suspected to be" which I have changed to "are". This phrase is really part of
the scaffolding of the argument and is not really part of the content of the conclusion itself; it is
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Johnson's way of telling us that we may reasonably move from the fact that many books are of no
use to us to the conclusion that they are written for an invisible order of beings. In less literary
English there are other words, e.g. "must", which often play a similar role. Just now I could well
have said "the conclusion that they must be written for an invisible order of beings". But really the
"must" is not a part of what is concluded; it indicates that it is the conclusion.
In general it is worth noting explicitly that you will often be able to rephrase and usually simplify
what a person writes. But be careful; some apparently minor parts of what is written can be of the
utmost significance.
In looking at our examples I have relied on your ability to recognize the major components of each
piece of reasoning. In learning how to describe arguments you must be able to do this well, so it
might be useful to stand back to see how you do it, or at least how you might go about doing it
when the going gets rougher. What we need to know is how to pick out the various statements that
make up an argument. The first step is easy, at least if you have to contend with a written
argument: pick out the sentences. But several of the examples we have already looked at show
you that you will often need to do more, since sometimes (as with (2) and (5)) what is
grammatically one sentence may contain a whole argument and in many other cases what is
grammatically one sentence will contain more than one of the component parts of an argument (as
with the second sentence of (3)). The second step is then to pick out some of what in grammar are
known as the clauses in each sentence. Very roughly this is a matter of picking out finite (inflected)
verbs; each such verb belongs to a different clause. So if we are faced with the sentence "OPEC is
in disarray, so oil prices will fall" we can find two finite verbs, "is" and "will" (or "will fall" if you
want to include the whole of the verbal phrase). The first gives you one component, "OPEC is in
disarray," the second the other, "Oil prices will fall." Note that equally helpful in parcelling out the
sentence are the conjunction "so" and the punctuation mark.
Unfortunately when you start looking at what you have been doing without a care in the world, it
often turns out to be frightfully complicated. It is in this case. I said the second step is to pick out
some of the clauses in each sentence, because we have been ignoring some of them in our
preceding discussions. Look, for instance, at the second sentence of (3). Here we find three finite
verbs, "happens", "is", and "can...(attempt)", but we only counted two important components. In
this case we ignored the way Russell had focussed on the period of time and rewrote it making "can
attempt" the only finite verb in the conclusion. Once again our division of the sentence is supported
by the punctuation and the conjunction "consequently". Nor have we made any separate mention
of clauses which simply describe things talked about in other clauses, such as "with which a child is
born" in (3), or "which now crowd the world" in (5). (But note that in one case we kept the clause
in our reformulation while leaving it out in the other, though Johnson's clause certainly contributes
to what he says, but not to the content of the reasoning contained therein.)
I have already alluded to another kind of complexity in the analysis of the sentences used to
convey an argument when we looked at Johnson's phrase "may be justly suspected to be". To
connect this to our suggested second step of counting clauses, let us suppose Johnson had written
"We may suspect that many books have been written..."; here we would count two finite verbs,
"may (suspect)" and "have (been written)" but I have suggested that we ignore the first as merely
an ornamental comment on the content of the second, which is the real meat of the argument.
Sometimes similar comments are more important and should not be ignored in reformulating the
argument, as in (2) where "it is likely" makes a difference to the reasoning. (For our purposes we
can regard the conclusion of (2) either as "It will rain today" with "It is likely" qualifying the
amount of support given that conclusion or as "It is likely that it will rain today", though for other
purposes the former approach is preferable. But many such comments will have to be treated in
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the second way.)
The moral of all this is that we don't have automatic procedures for picking out the crucial parts of
an argument. Isolating the clauses can be useful, but don't do it uncritically.
So far I have suggested two steps: pick out the sentences, then pick out their component clauses.
We shall see in some later examples that it may be useful to go on even further, in particular to
reconstruct some of the clauses that might underlie phrases in your statements. Suppose someone
said "The present disarray in OPEC strongly suggests a fall in the price of oil." This has only one
finite verb "suggests", but it is arguably a close paraphrase of the reasoning we looked at earlier,
so in analysing it we would translate "the present disarray in OPEC", a noun phrase, into the
sentence "OPEC is now in disarray", and similarly treat the other noun phrase, "a fall in the price of
oil". More generally still, paraphrases in terms of clauses (and clause connectives) can often be
illuminating - so one might suggest translating "All bald men are discontented" into something like
"If any man is bald then he is discontented."
One last suggestion for sorting out the appropriate components of an argument: look to see
whether what you have listed as distinct components cannot be merged, either because they are
simply stylistic variants, different ways of saying the same thing, or because one is the opposite of
another, i.e. what you have listed as "p" and "q" are really "p" and "not p", to use the conventions
we shall adopt. Considering these two possibilities can often do a lot for the clarity of your
description of an argument, but be careful! What may seem slight differences may be crucially
important, and you need to make sure that you have real opposites - "No men are selfish" is not
the opposite of "All men are selfish."
On the basis of examples (3) and (5) we can also see that the two functionally different
components of an argument, premises and conclusion, can be arranged in various ways. You can't
automatically write down the structurally significant parts of the argument from the sequence of
sentences in front of you, just as we have seen the bare sentences do not necessarily yield all the
significant statements within the argument. You have to ask: "What is the arguer getting at?" and
then "What is she offering in support of this conclusion?" And as we have seen, the order alone
can't decide these questions. But we have also seen that some words can act as clues to the
answers to these questions. Words like "and so", "consequently", "implies", or "therefore" usually
join premises to a conclusion in that order. On the other hand, words like "because", "for", "since",
or "may be inferred from the fact that" tend to link a conclusion to its premises in that order. Again
we noticed that the conclusion of an argument may be marked by the presence in it of a word like
"must". All these clues can help you discover what is going on in any particular argument; but in
the final analysis, you have to use your total grasp of the language to arrive at the most likely
structure of argument in a passage.
While it's not automatic, I've suggested you use the following strategies to reveal what is going on
in an argument:
(a) pick out the grammatical sentences;
(b) pick out the conclusion;
(c) pick out salient clauses;
(d) paraphrase to release other salient clauses;
(e) let conjunctions, punctuation reveal structure.
One thing you will soon realize is that your total grasp of the language often reveals how
complicated even the simplest arguments are. For one thing, as we have already noted, an
enormous amount is left out - you may well have felt that in both (1) and (5) the arguers were
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relying on connections that they didn't state. For another, there may be hints of complexities both
inside the argument and in its external relations to the rest of what someone is saying. For
instance, when we looked at Russell's argument (3), I said nothing about the occurrence of "and
therefore" in the middle of what I called the first point. But I went on to say that words like
"therefore" usually link premises to conclusions, so you might well ask what it is doing here. If we
were to look closely at Russell's argument, I think we could say that what I called the first point
itself contains a little argument - from the premise that instincts and reflexes can be developed by
the environment into the most diverse habits, to the conclusion that instincts and reflexes can be
developed by the environment into the most diverse characters; or perhaps we should say that the
people whose habits they are will, therefore, exhibit the most diverse characters. Russell certainly
relies on some such connection between habits and character. In the passage I quoted, he may be
relying on some earlier, more detailed presentation of this connection; in this argument (3) it is
almost a single claim, but for completeness' sake there is nothing to stop us recognizing this
complexity in his first premise. We can analyse arguments with different degrees of detail; the
appropriate amount depends on our purposes.
A different sort of complexity is displayed by (5), since in its context this is not seriously meant as
an argument for the conclusion that many books are written for some invisible order of beings, but
simply as an exaggerated way of saying that many books are of no use to us. But if we want to see
exactly how Johnson makes his point, then we can isolate it from its context as we did above. But
our final verdict on the argument must wait upon our examination of the wider context. I do not
apologize for starting with examples that are not completely clear or cut and dried. Just as physical
science uses simplifications and idealizations to help us understand the tremendous complexity of
the actual world, so we are beginning to use some simple tools for dealing with the tremendous
complexity of actual thought and argument. Understanding usually requires simplification.
One simplification, or perhaps regimentation, of actual arguments that we shall adopt has been
mentioned already. We shall regard all arguments as made up of statements. Statements are the
sorts of thing you use declarative or indicative sentences to express. The test for a declarative or
indicative sentence is: can you grammatically put "Is it true that....?" around it? If you can, it is
declarative; if you can't, it isn't. So if someone answers a question by saying "Rain" or "Stop asking
me such silly questions" he is not using declarative or indicative sentences, so we could not use
them, as they stand, as parts of an argument. But if instead he had said "It is raining" or "I wish
you would stop asking such silly questions" or "You are to stop asking such silly questions", then he
is using declarative sentences, and so, on our terms, making statements that could appear in an
argument. These examples may also suggest how many actual cases can be handled to fit our
requirement. In particular, facts are often not stated (as in our very first example (1)) - we require
them to be set out explicitly; and often the conclusion of an argument or piece of reasoning is a
command or an action - we can find ourselves a statement that the action is to be done. (You could
handle commands directly, but in this course there is a very great deal we shall have to omit or
approximate.)
To sum up what we have covered so far, when we tidy up a piece of reasoning it consists of a
sequence of statements, with one or more premises supporting one or, occasionally, more
conclusions.
EXERCISE A
(I) Which of the following are indicative or declarative sentences?
1. Can you lend me five dollars?
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2. You will lend me five dollars.
3. Cloud, and scattered showers over the hills.
4. If only John would come!
5. If India wins the test in Antigua they will still lose the series.
6. Breaking promises is wrong.
7. I wonder what became of Rimbaud.
[Answers.]
(II) Rewrite the following passages as explicit arguments:
1. The two strongest determinants of completed family size are education and
occupation. So, achieving the goal of replacement fertility must encompass
improvements in education and increased job opportunities for women to be effective.
[3] [Answer.]
2. Time spent on dialogue should not be considered wasted time. It presents problems
and criticizes, and in criticizing, gives human beings their place within their own reality
as the true transforming Subjects of reality. Even when we regard the work of the
agronomist-educator as limited to no more than the teaching of new techniques, there
is no comparison between dialogue and anti-dialogue. Any delay caused by dialogue
means time saved in firmness, in self-confidence, and confidence in others, which
anti-dialogue cannot offer. [4] [Answer.]
3. If the French Revolution were to recur eternally, French historians would be less
proud of Robespierre. But because they deal with something that will not return, the
bloody years of the Revolution have turned into mere words, theories, and discussions,
have become lighter than feathers, frightening no one. [40] [Answer.]
2. THE ELEMENTARY STRUCTURES OF ARGUMENT
Now that we have agreed how to talk about arguments, let us move on to examine how they are
constructed. Actual arguments exemplify an unlimited number of structures, shapes, or forms; but
all these variations are built up out of a few simple patterns, and it is with these that we shall be
concerned. To make life easier, and to save space, we shall use some simple notation: little letters,
a, b, c,... to stand for the statements that make up the premises and conclusion, and an arrow
--->, to stand for the support the premises are meant to give the conclusion. It doesn't matter
which little letters we use, just so long as in each argument the same little letter means the same
statement each time. We shall also allow ourselves to write "not a" for the statement that is the
opposite of "a". We shall occasionally modify our simple little letters by other words such as "never"
and "it is possible that" to convey meanings that should be obvious from the context. We shall also
use brackets and asterisks to help make the structure clearer. When we draw a picture of an
argument using our little letters (with their interpretation) and arrows, we shall call it a labelled
structure diagram.
To illustrate our way of displaying the structure of an argument, consider the following piece of
reasoning:
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(7) Mary must be at home because there's a light in the kitchen.
The premise here is "There's a light in the kitchen" which we can symbolize "a", the conclusion is
"Mary is at home" (note again our change of "must be" to "is") which we'll write "b". So the labelled
structure diagram for example (7) is:
(8) a = There's a light in the kitchen.
b = Mary is at home.
a -----> b
That is an example of the simplest structure of all: one premise supporting a conclusion.
Not merely is it simple, it is not very persuasive. Suppose the arguer offers an expanded version:
(9) Mary must be at home because there's a light in the kitchen and she never leaves
the kitchen light on when she goes out.
This time we have a third statement, which we can label "c", "Mary never leaves the kitchen light
on when she goes out." What is this extra statement doing? Surely, it is working with the
statement we have labelled "a" to support the conclusion; it's joining together with the statement
"a" to help reach the conclusion. We need to show the way "c" is joined to "a"; to do this we shall
use brackets, as in diagram (10):
(10) a )
) -------> b
c )
Here you can see that "a" and "c" are joined by the brackets, and the arrow goes from the
bracketed pair of statements to the conclusion, telling us that the two premises together support
the conclusion.
Suppose instead of (9) the arguer had offered a differently expanded version:
(11) Mary must be at home because there's a light in the kitchen and her car's in the
garage.
This time our new statement is "Mary's car is in the garage" which we shall label "d". Do you notice
any important difference in the way they contribute to the argument between "c" in (9) and "d" in
(11)? What I think is important is that in (9) "c" only contributes in conjunction with "a" whereas in
(11) "d" makes its contribution quite independently. The statement "d" could stand alone as a
reason for "b", and in terms of the argument structure it does stand alone. What (11) offers are in
fact two separate arguments for the conclusion, and so we show that in our diagram:
(12) a ---
--- >
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b
/--- >
d ---/
We don't bracket the premises this time, but instead we have two arrows to show two separate
lines of support. (They are meant to be straight just as in (10) but running diagonally to "b".)
Let us see this distinction in a couple of real arguments. Consider this:
(13) Most of the rocks at the surface in the southern Appalachians are highly deformed
metamorphic ones. Furthermore, they are older than or contemporaneous with the
horizontal sedimentary strata that were discovered under them. This fact suggests that
roughly 475 million years ago the surface rocks began to be transported as a thin
sheet for at least 260 kilometers over the eastern continental margin of the land mass
that was to become North America. [5]
There's a lot of information here, but see if you can come up with anything like the following
analysis:
(14) a = Most of the rocks at the surface in the southern Appalachians are highly
deformed metamorphic rocks.
b = The rocks at the surface in the southern Appalachians are older than or
contemporaneous with the horizontal sedimentary strata under them.
c = Roughly 475 million years ago the surface rocks began to be transported as a thin
sheet for at least 260 kilometers over the eastern continental margin of the land mass
that was to become North America.
a )
) -----> c
b )
What does this pattern indicate? As in (10) the important point is that in such an argument it is the
premises taken together that support the conclusion. I don't know any geology, but I take it that
the mere fact that surface rocks are highly deformed metamorphic ones doesn't give you any
reason to think that they have been transported over some other strata; nor, perhaps, does the
simple fact that the surface strata are older or contemporaneous with strata below them. But the
claim is that taken together (and note that this is not quite what the author says) these two facts
do support the conclusion given.
Now consider the following argument:
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(15) The clerk is a nobody, not merely because he is not a scientist, but also because
in the developed societies everyone is now a clerk. [6]
I think that here we are being offered two separate reasons for the conclusion, so the structure
diagram needs two arrows, thus:
(16) a = The clerk is a nobody.
b = The clerk is not a scientist.
c = In the developed societies everyone is now a clerk.
b ---
---->
a
/---->
c ---/
This diagram tells us that each premise supports the conclusion independently; the author is
offering us two independent reasons for thinking that, in developed societies, being literate (and a
student of the "humanities") is of no worth.
Before moving on, let us note that there is no magic in the number two. The patterns would be
relevantly the same, however many premises were added: someone might offer us more
independent reasons for the insignificance of humane studies, or the geologists might require
additional pieces of evidence to produce a good case for their conclusion about the Appalachians.
Patterns (10) and (12) are importantly different. Why? Remember the point of arguments. They
are meant to give you good reasons for a conclusion; and good reasons need to be true or
acceptable. As we shall see in more detail later, if you want to challenge an argument there are two
different things you can do: you can argue that really these premises do not support this
conclusion, or you can attack the premises by arguing that they are mistaken, false, or otherwise
unacceptable. Now if you choose this second strategy, it matters a lot whether you are confronting
a pattern (10) argument or a pattern (12) one. If the argument is pattern (10), then, as we have
seen, it needs all the premises together to reach its conclusion. If any of the premises give way,
support for the conclusion falls. So with pattern (10) you need only rebut one of the premises to
undermine the argument. Suppose you were able to show that the arguer was mistaking the light
in the hall for the kitchen light or, in (14), that the geologists had got the surface rocks wrong,
then you can ignore claims about Mary's never leaving the kitchen light on or the relative ages of
rock strata. These claims may be true, but they no longer help the argument. Equally, of course,
you could focus on these claims and rebut them - if the top strata are not older or
contemporaneous with the lower strata then the argument in (13) fails, whether or not the top
strata are highly deformed metamorphic rocks. Pattern (10) arguments are vulnerable at each
premise.
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But now consider pattern (12). Here the conclusion is supported independently by each premise.
So to undermine this sort of argument you would have to knock out every independent premise.
Knocking one of them out merely removes that support for the conclusion; but there are still the
others, independently supporting the conclusion. To deprive the conclusion of all the support
offered by the argument you have to knock out all the premises. You can in fact say that pattern
(12) consists really of two separate arguments for the conclusion rolled into one.
(And analogously, when you have an argument with more than one conclusion you could see it as
really several arguments with the same premises leading to each of the different conclusions.)
We have trespassed into the question of how to evaluate an argument, of how to reply to it, when
our present job is simply to learn how to describe what is going on. But I wanted you to see that
the subtleties of our descriptions have a useful point. It matters whether an arguer is asserting that
all these premises together yield a conclusion, or whether she is saying that each one on its own
can do the job.
Two final comments before we move on. The distinction between pattern (10) and pattern (12) is
very close to the distinction between the words "and" and "or". In pattern (10) we have a structure
in which premise 1 and premise 2 support the conclusion, while in pattern (12) we could say that
premise 1 or premise 2 support the conclusion, leaving it open that they both do. So one might
paraphrase (15) as "if the clerk is not a scientist or if everyone is a clerk then the clerk is a
nobody", whereas paraphrasing (13) in a similar way you would have to join the conditions with
"and".
The second point is that it is not always clear what an arguer intends. When you diagram an
argument you may have to clarify, not merely describe, what the arguer has put forward. In
general, when it is not clear what was intended it is best to ask yourself what is the more plausible
structure and so give the most charitable interpretation to your author's text.
So far we have looked at the simplest structures which involve only some premises and a
conclusion. But arguments in real life often involve what I shall call intermediate steps, conclusions
reached on the way to the main conclusion, stepping stones to the final conclusion. We have
already met an example of this sort in the argument from Russell (3), where a premise about
diverse characters was itself derived from a claim about diverse habits. Here is another example,
with several small steps to its conclusion:
(17) The course of human history is strongly influenced by the growth of human
knowledge. We cannot predict, by rational or scientific methods, the future growth of
our scientific knowledge. We cannot, therefore, predict the future course of human
history. This means that we must reject the possibility of a theoretical history; that is
to say, of a historical social science that would correspond to theoretical physics. There
can be no scientific theory of historical development serving as a basis for historical
prediction. The fundamental aim of historicist methods is therefore misconceived; and
historicism collapses. [7]
Here, I suggest, we may discern at least the following structure (check to see whether you
understand and agree with the simplifications I have made):
(18) a = The course of human history is strongly influenced by the growth of human
knowledge.
b = We cannot predict, by rational or scientific methods, the future growth of our
scientific knowledge.
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c = We cannot predict the future course of human history.
d = There can be no scientific theory of historical development.
e = Historicism collapses.
a )
) --> c --> d --> e
b )
Whether or not there is more to this argument, it certainly involves the passage through
intermediate conclusions from what I have called "c" to "e".
Real arguments are full of items that are strictly speaking irrelevant to the bare bones of the
reasoning. The arguer may repeat herself or give further illustrations or analogies that are not
intended to do much for the final conclusion. She may bring in other issues. But some of the items
that occur in the middle of an argument do play genuine roles. We have already met intermediate
steps; we can also find additional premises that are invoked as the argument moves towards its
final conclusion. Let us look at this imaginary argument (due to J.L. Mackie) to illustrate both
intermediate steps and the appeal to additional premises:
(19) A witness claims to have seen Smith at the scene of the crime near the time it
was committed, and Smith has no alibi, so we can take it that he was there then; an
innocent man would not lie about where he was, but Smith denied being there at the
time; so Smith must be guilty.
As the following structure diagram shows, we first have an argument to the intermediate
conclusion that Smith was at the scene of the crime; to this we add the new premises about
Smith's denying having been there, and the behaviour of innocent people, to conclude that Smith is
guilty:
(20) a = A witness claims to have seen Smith at the scene of the crime near the time it
was committed.
b = Smith has no alibi.
c = Smith was at the scene of the crime.
d = An innocent man would not lie about where he was.
e = Smith denied being at the scene of the crime.
f = Smith is guilty.
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a )
) ---> c )
b ) )
d ) ---> f
)
e )
I have said that in real life we tend to clutter up our arguments with unnecessary matter. The
opposite happens as well: we leave out crucial parts of the argument and we expect our hearers or
readers to be able to supply them, or at least to be able to appreciate the force of the argument,
which depends upon the unstated parts just as much as it does upon those that actually get
expressed. Look at (19) again. You might find something like it in a court of law, but it wouldn't do
in "Perry Mason". In a television series perhaps the lawyer would say no more than:
(21) A witness claims to have seen Smith at the scene of the crime, and he has no
alibi. Would an innocent man have lied about where he was?
All that is explicitly stated is what I called "a" and "b". The intermediate conclusion and the
additional premises are all squashed up into the rhetorical question, "Would an innocent man have
lied about where he was?", and the final and major conclusion is left unstated.
Filling these gaps is a difficult but important job; we shall come back to it later. For the present, it
is worth noting that in real life arguments must often be reconstructed, rather than simply
diagrammed, as we have been doing. But to build up your confidence for tackling any sort of
argument, you will only need to rephrase the examples in Exercise B to get a reasonable structure
diagram.
EXERCISE B
(I) Look back at example (16); would it have made any difference if I had drawn the structure
diagram like this?
a = The clerk is a nobody.
b = The clerk is a scientist.
c = In the developed societies everyone is now a clerk.
not b --
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---->
a
/---->
c --/
[Answer.]
(II) Draw a labelled structure diagram for each of the following arguments:
1. Cast thy bread upon the waters: for thou shalt find it after many days. [41]
[Answer.]
2. Another argument for determinism about actions is that all physical states and
events are causally determined, including states of the brain, that brain states are
correlated with mental states in such a way that, given a certain brain state, just such
a mental state must occur, and that actions are causally determined by mental states.
[8] [Answer.]
3. The classical spirit belongs to all eras and all countries, because it is the cult of pure
Reason, of the disinterested search for Beauty. [42] [Answer.]
4. Theory and practice need not be separated completely from one another. Theory,
therefore, need not be impractical. One of the criteria of a good theory is that it is
capable of being tested, and thereby supported or discredited. The theory that has
been supported by strong evidence may then become of practical value in a variety of
situations. [9] [Answer.]
5. In any case there is no lack of evidence of the increase in road traffic in the Balkans.
To take Ragusa, commercial papers for 1590-1591 on the eve of Spalato's rise to
fortune reveal the extent of her traffic with the interior; as does the construction of a
new bazaar near the town for Turkish merchants. In 1628 a more spacious quarantine
building was set up at the end of the port. This detail, insignificant in itself, suggests,
when taken together with others, that these overland communications must have
eliminated or at least reduced the halts in Syria and Egypt and the long sea voyages
from the East to Italy; they furthered the movement westwards of merchants and
merchandise from the Levant. The Fontico dei Turchi in Venice at San Giovanni
Decolato dated from 1621. Ragusa also witnessed the arrival of large numbers of
Jewish and Turkish merchants. [10] [Answer.]
6. Death be not proud, though some have called thee
Mighty and dreadful, for, thou art not so,
For, those, whom thou think'st, thou does overthrow,
Die not, poor death, nor yet can'st thou kill me;
From rest and sleep, which but thy pictures be,
Much pleasure, then from thee, much more must flow,
And soonest our best men with thee do go,
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Rest of their bones, and soul's delivery. [11] [Answer.]
3. INTERLUDE - CONFRONTING ARGUMENTS
We are looking at arguments, or in other words, at reasoning offered for a conclusion or proposal.
Our aim is to be able to handle such things better, and that is largely a matter of being able to
judge whether they are good or bad arguments. To begin with, we are looking at ways of
describing arguments, but the point of it all is that we should eventually be able to evaluate them.
While we shall fill in some details later, it is worthwhile noting some very basic points about
criticizing arguments early on.
I said in the previous section that an argument has three things: premises, conclusions, and the
link between them. My premise might be that there is a light on in the kitchen, my conclusion that
Mary is at home, and my argument supposes there is some connection between the premise and
the conclusion, the premise is supposed to support the conclusion. In another context, I might
conclude that we shouldn't take any drink to the picnic and my reason might be that Graham said
he would bring a crate of beer; again I would be supposing that my reason did support my
conclusion somehow.
Now given that there are these three components in any argument, any or all of them can go
wrong. The premises may be wrong - false or otherwise unacceptable; the conclusion may be
wrong in the same ways; and finally the premises may not support the conclusion. As we shall see,
this last possibility is itself somewhat complicated - what appears to the ordinary person as
premises supporting a conclusion is an amalgam of at least two different issues: the detailed
structure of the argument, and the truth or falsehood of its component statements. But for the
present, we need only note that it is a separate question whether the premises do support the
conclusion - separate, that is, from whether the premises and the conclusion are true or
acceptable.
A further important issue is that being supported by an argument is not the same as being true. My
argument for Mary being at home might be awfully bad - my premise might not support that
conclusion at all - and yet it might be true that Mary is at home. You may be able to rebut my
argument for the claim, but that doesn't amount to showing that the claim is false. Again, in
general, my argument might be a good one - it might support the conclusion - and yet that
conclusion may be false, either because my premises turn out to be mistaken themselves or
because they are not quite good enough.
So when an arguer offers you "reason-therefore-conclusion" you can object to any of the three. But
note that there is a difference between your mere counter-assertion and your producing an
argument of your own to defend what you are saying. People too easily confuse denying what
someone has said (i.e. just saying the opposite) and refuting what they have said (i.e. showing by
argument that the opposite is true). Serious and constructive criticism of what someone has said
involves several moves, in particular, it involves pointing out where the person's argument has
gone wrong, showing where necessary that this is the case, and indicating reasons for some other
position. Merely asserting that someone is wrong, without doing these other things, is often of little
use in arriving at the truth or at sensible decisions.
Suggested Answers to Exercises
A. I. You have to decide whether the sentences are declarative, that is, can you grammatically
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wrap "Is it true that...?" around each of them. The answer should be obvious.
1. No. It is already a question.
2. Declarative.
3. No. It lacks a finite verb. If you add something like "There will be" in front of it, it becomes a
declarative sentence, but as it stands it isn't.
4. No. It may mean pretty much the same as "I wish John would come" which is a declarative
sentence, but again, as it stands, it isn't one.
5. Declarative. I shall later (in Section 4) be suggesting a way of handling such sentences that
treats them differently, but as they stand they are declarative.
6. Declarative. Whatever you might think about the status of such evaluations, the form in which
they are standardly expressed in English is that of a declarative sentence.
7. Declarative. It may only be a stylistic variant for asking the question "What became of
Rimbaud?" which is not a declarative sentence, but as it stands it is one.
One point to note is that we can often find almost equivalent sentences one of which is declarative
the other not. The other way of seeing this point is that some rather subtle grammatical differences
are very important for logical analysis.
II. You are asked to tidy up the passages so the arguments are clearly revealed.
1. At one level of analysis you hardly need to rewrite this argument. Its premise is the first
sentence, its conclusion everything in the second sentence after the "so". But the second sentence
is obviously rather complicated and it tells us what we must do, if we want to achieve something; I
would suggest rewriting the argument to bring this out:
The two strongest determinants of completed family size are education and occupation;
so,
if you want to achieve replacement fertility, you must improve education and increase
job opportunities for women.
It may be that instead of "if" we should write "given that" since the author may be
accepting that we already have the aim of achieving replacement fertility - the main
thing is to see how the second sentence can be broken up into two separate claims.
2. This passage is somewhat more involved. Its main contention, however, is stated first (time
spent on dialogue is not wasted time), and reiterated later in different terms (there is no
comparison between dialogue and anti-dialogue). It may be easier to see the passage as containing
two arguments to these differently stated but basically identical conclusions:
Dialogue presents problems and criticizes; in criticizing, dialogue gives human beings
their place within their own reality as the true transforming Subjects of reality;
so,
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time spent on dialogue is not wasted time.
This is then followed by explicit consideration of the stock response (dialogue doesn't give you time
to teach the syllabus):
Suppose you only want to teach new techniques; any delay caused by dialogue means
time saved in firmness, in self-confidence, and confidence in others;
so,
time spent on dialogue is not wasted time.
(I have here rewritten the supposition very considerably.) Notice that I have changed "should not
be considered" to "is not" - this is just like the change in Dr. Johnson's passage. Perhaps as a way
of exalting in our self-consciousness we very often make points in a way which talks about the
point (what has been called "meta-communication") rather than simply making it. Here the literal
conclusion is that we should not consider that time spent on dialogue is wasted time, but the point
is not really about what we should think but rather about the truth about dialogue. This is one very
common example of how we can ignore some of the clauses in a passage when we wish to uncover
its line of argument.
Later in the course (Section 5) I shall suggest a way of looking at some arguments whereby you
could analyse this passage as itself an implicit dialogue (I have almost presented it that way
already). The first part remains as it is; you then imagine an anti-dialogue objector replying that
dialogue delays the teaching of techniques so that it is a waste of time; then the author replies that
it may delay the teaching of techniques but it makes up by giving confidence etc. so that it is not
wasted time.
3. Here we have an argument in a work of literature; my rewrite will ignore the niceties of
expression. The basic line of argument is:
If the French Revolution were to recur eternally, French historians would be less proud
of Robespierre.
The Revolution does not recur.
so,
It is no longer frightening.
To illustrate the point in the text about merging separate statements, you can see that "French
historians would be less proud of Robespierre" actually amounts, for the argument, to "The French
Revolution would be frightening," a denial of the argument's conclusion. So underlying the various
sentences there are only two statements and their negations.
EXERCISE B
I. No, it wouldn't make any difference. If "b" stands for "The clerk is a scientist" then "not b" stands
for "The clerk is not a scientist", and it doesn't matter what letter we use for each sentence. Notice,
however, that just putting "not" in front of a little letter standing for a sentence is a much less
complicated procedure than that used in English to negate a sentence, so sometimes you will have
to be careful in moving from one to the other.
II. 1. Here the conclusion is an instruction to do something, which we must rewrite as an indicative
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sentence. Notice that the word "for" tells you which part is premise and which conclusion.
a = You should cast your bread upon the waters.
b = You will find your bread after many days.
b -----------> a
Since the passage is not meant to be taken literally you may, if you wish, paraphrase its
components to indicate what you take them actually to be conveying; but it may be better to leave
such questions of interpretation for a later stage of dealing with a piece of reasoning.
2. Note here that the conclusion is named but not explicitly stated (you should make both the
premises and conclusion into proper sentences so it becomes "All actions are determined").
a = All actions are determined.
b = All physical states and events, including brain states, are causally determined.
c = Brain states are correlated with mental states in such a way that, given a certain
brain state just such a mental state must occur.
d = Actions are causally determined by mental states.
b )
)
c ) ------> a
)
d )
3.
a = The classical spirit belongs to all eras and all countries.
b = The classical spirit is the cult of pure Reason.
c = The classical spirit is the disinterested search for Beauty.
b )
) ------> a
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c )
This is an example where it is not clear to me whether we have a pattern 10 or a pattern 12
argument. I have drawn it as pattern 10, since the author might have thought that the cult of pure
Reason was identical with the disinterested search for Beauty. You might also have decided to split
my "a" into the two claims about all eras and all countries. The original is hardly a piece of
reasoning, and this is brought out by the uncertainties about its logical structure.
4.
a = Theory and practice need not be completely separated.
b = Theory need not be impractical.
c = A good theory is capable of being tested.
d = A good theory can be supported or discredited.
e = A well supported theory can be of practical value.
c ---> d )
) ---> a ---> b
e )
5. Here both the conclusion and some of the premises are indicated rather than fully set out, and
some are left unmentioned, though we are given to believe the author could quote them if
necessary. The passage begins with an intermediate conclusion, that there was an increase in road
traffic, gives evidence for this, and then argues that the overland routes furthered the westward
movement of merchants and merchandise from the Levant. A structure diagram might look like
this:
a = Road traffic increased in the Balkans in the late 16th, early 17th century.
b = Commercial papers for 1590-1591 for Ragusa reveal considerable traffic with the
interior.
c = A new bazaar was built in Ragusa for Turkish merchants.
d = In 1628 a larger quarantine building was set up in Ragusa.
e = ?? (unstated claims).
f = These overland routes eliminated or at least reduced the halts in Syria and Egypt
and the long sea voyage from the East to Italy.
g = The overland routes furthered the movement westwards of merchants and
merchandise from the Levant.
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h = The Fontico dei Turchi in Venice dates from 1621.
i = Ragusa witnessed the arrival of large numbers of Jewish and Turkish merchants.
b)
)
c) ---> a)
) )
d) d) ------> f)
) )
e) h) --> g
)
i)
Note here "d" is repeated - it contributes, I suggest, to support the general claim for an increase in
road traffic, but it also helps support the further claim that the overland routes speeded up
East-West trade. "c" may also be echoing further along the argument - it mentions a bazaar for
Turkish merchants and so could help to support "g" (indeed it is very close to "i"). It may well be
that the diagram should begin thus:
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b -----
--->
c ---------> a
/--->
d -----/
since the different pieces of evidence each suggest an increase in road traffic; but "a", "d" and "e"
have to be taken together, as the passage makes clear. The same question may arise at the end,
with "h" and "i": are these separately supporting the final conclusion, or only together? In fact, "h"
and "i" do not so much support "g", as the weaker claim there were more Eastern merchants in the
West; "g" says the overland route helped bring this state of affairs about. I think the structure is as
I have shown it, but there may be a slight weakness, or hidden complexity, here.
Constructing a structure diagram has made us tighten up this argument somewhat and has forced
us to raise questions that may not have occurred to its author of what exactly is supporting what.
One last point which might arise from this argument is the relation of causal claims to the structure
diagram of an argument. Our author is claiming that it was a causal consequence of the routes'
reducing delays in the East and at sea that they furthered the westward movement of merchants
etc. We can avoid the grave difficulties of analysing causal claims by noting that often when we
claim that A caused B, we may be able to express ourselves in this way: "A, therefore B." When
these As and Bs have been tidied up, we can produce an argument structure which mirrors the
causal structure, and so we may be able to avoid answering the question whether any particular
"therefore" is causal or simply logical. The difference is important in many contexts, but we can
perhaps afford to overlook it if we are simply finding a structure diagram.
One last point that often arises in dealing with causal claims, but has a wider application, is that it
makes structure diagrams more illuminating to break up complex sentences into their component
statements. Suppose someone said "The increase in road traffic led to greater prosperity in
Ragusa." This is one declarative sentence and could be diagrammed with just one letter, but I have
suggested that such causal claims can be more fruitfully handled by uncovering the simpler
sentences hidden within (often by resolving nominalizations back into their original sentences, to
use some technical terminology), so "the increase in road traffic" is translated into a sentence, as
in the preceding diagram, "Road traffic increased," and the effect likewise is rendered "Ragusa
became more prosperous," and finally the link between them is indicated by an arrow.
6. One reason for including this specimen is to remind you that arguments are not only found in
prose. There are, I think, two arguments on the surface, one telling death not to be proud, and the
other suggesting that death is desirable. While we could preserve the personification, and the
imperative mood of the first conclusion, I shall tidy these things up, as I have been asking you to:
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a = Death should not be proud.
b = Death is not mighty and dreadful.
c = Death does not overthrow its victims.
d = Death can not kill me.
e = Much pleasure flows from rest and sleep.
f = Rest and sleep are pictures of death.
g = Much more pleasure flows from death.
h = Soonest our best men with death do go,
Rest of their bones, and soul's delivery.
(My edition of the poem suggests that "h" is ambiguous, but it functions as one
premise in the argument, and does not need unpacking for our very restricted
purpose.)
If we see it as two arguments, the first is:
c )
) --> b --> a
d )
and the second:
e )
) -----
f ) -->
g
/-->
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h -----/
It should be noted, however, that "g" probably functions as a reason for "c" (or "d" as well) and so
the two portions can be put together.
Note that this argument may also be better seen as a genuine dialogue with death, in which death
reminds us that some people have called him mighty and dreadful, so that he rightfully boasts of
his power. The present tidying up can find nothing to do with the remark that "some have
called...thee", whereas this fits into a genuine dialogue. But as I have stressed in the text, analyses
can be more or less complete; what I have offered above is there, and is the basic pattern, even if
we can dig deeper to find some more complexities.
4. ENTERTAINED ARGUMENTS
In section 2 we looked at some of the basic structures of argument. In all the cases we have looked
at, the person putting forward the argument has actually asserted the premises she has been
using; she has been committed to the premises and to the conclusions they are intended to
support. Now while we often are so committed, it is important to see that we can also argue in a
different way: we merely suppose something, or we assume something for the sake of the
argument, or, as philosophers sometimes say, we entertain a thought to see where it may lead.
The general pattern of such arguments involves the arguer in first supposing something and then
asserting something else within the scope of the supposition. We can do this openly, as for
instance, by saying "Let's suppose..." or "Let ABC be a triangle,...". But perhaps more commonly
we begin to disguise what we are doing by using conditional sentences (sentences constructed out
of "if...then...") which sometimes feel like straightforward statements themselves rather than the
more complicated structures I am suggesting.
One important point about all such cases is that we are not asserting what we merely suppose, or
what we say follows from a supposition. If I say, "Suppose Manley had won the last election in
Jamaica, we would have devalued the currency" I am not asserting that Manley did win the last
election (indeed I am in this case giving away the fact that I know he didn't by using the verb
forms "had won...would have") nor am I asserting that we did devalue (although we did). If I say,
"If Mrs. Thatcher wins again, I'll despair of human rationality" I am not asserting that she will, or
that she will not, win again, nor am I making any unconditional predictions about what I will do. In
both cases I only assert something within the scope of a supposition.
To indicate this suspension of commitment, I shall enclose the entertained portion of an argument
within a boundary of asterisks. Let us see how this works by picturing the following argument by
M.K. Bacchus:
(22) If the present situation of extremely wide income differentials between
occupations continues, the process of selection for jobs will become an even more
vexing issue. The assessment of work performance and aptitude, especially since the
validity of aptitude tests has, so far, left much to be desired, will be a matter in which
the subjective impressions of a supervisor will be crucial. [12]
What does Bacchus directly assert here? I think the only clear assertion is that the validity of
aptitude tests has so far left much to be desired; the other claims are made within the supposition
that wide income differentials remain. The main part of the second sentence he says follows from
it; it is what makes job selection that much more vexing an issue. I suggest therefore that we
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should draw its structure diagram thus:
(23) a = The present situation of extremely wide income differentials between
occupations continues.
b = The process of selection for jobs will become an even more vexing issue.
c = The assessment of work performance and aptitude will be a matter in which the
subjective impressions of a supervisor will be crucial.
d = The validity of aptitude tests has so far left much to be desired.
*************************
* a ) *
* ) *
*****)* --> c --> b *
)*******************
d )
As often with real arguments, there may be residual doubts about the structure. In this case
perhaps Bacchus is suggesting that whatever the validity of aptitude tests, still the assessment of
work performance will be a matter in which subjective impressions are crucial, given the present
income differentials; so we should have two arrows, one from "a" and the other from "d" to "c". But
while constructing structure diagrams forces us to consider such possibilities, the main point at
present is to see why most of the argument is within the asterisks - because, in this passage,
Bacchus is not saying income differentials will continue or that job selection will become a more
vexed issue, he is only saying if the first then the second.
There are two points worth noting now. The first is that often a writer only says "if p then q" but
can be understood as tacitly asserting the "p" as well. When that happens she is also to be
understood as asserting the "q" absolutely and not only within the scope of some supposition. In
fact, it is quite likely that this is happening in Bacchus' argument, especially since he would not be
risking much in asserting that extremely wide income differentials will continue, but what he
explicitly says and what forms an essential part of whatever else he might be hinting at is as I have
diagrammed it above. The second point relates to our diagrams. Since we are using arrows inside
asterisks to picture entertained arguments and conditional statements it is worth noting that the
arrows may here have a very weak sense. They show that something is being asserted within the
scope of a supposition, but not necessarily that the supposition gives one the main grounds or even
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a good reason for asserting it.
Since many generalisations can be paraphrased in terms of conditional statements or entertained
arguments, and since it is usually illuminating to break up sentences into smaller sentences for the
purposes of argument analysis, you are likely to find that entertained arguments keep cropping up
in your analyses. Thus a claim like "All acids taste sour" could be treated as one sentence in a
diagram, but it might reveal more if we paraphrase it thus: "If any substance is an acid, then it is
sour" or "Suppose a substance is an acid, then it is sour." These paraphrases would then be
diagrammed as entertained arguments. Notice that we have various ways of expressing general
claims. We could, for instance, equally well have said "An acid tastes sour."
A frequent and important use of entertained arguments is in what we may call indirect or reductio
ad absurdum proofs. In these you argue for a claim by supposing its opposite and showing that this
supposition leads to absurdity, usually self-contradiction. In such cases the point of the supposition
is to be able eventually to assert something fully outside the scope of the supposition. It is an
important form of argument in mathematics, but also in everyday life. For an everyday example,
consider this argument (due to J.L. Mackie):
(24) You think I'm a swindler. But I've had $1,000 of your money for three days, and I
could have walked off with it safely. But I'm still here.
Notice the rephrasing and additions in the structure diagram:
(25) a = I'm a swindler.
b = I've had $1,000 of your money for three days.
c = I could have walked off with your money safely.
d = I did walk off with your money.
************************
* a ) *
*****)* *
b )* --> d * )
)****************** ) [ ---> not a ]
c ) not d )
What happens is that the speaker asserts "b" and "c" and claims that these, together with the
27 of 109 1/16/16, 1:14 PM

supposition that he is a swindler, lead to the conclusion that he would have walked off with your
money; but he obviously hasn't walked off, and this, together with the whole previous argument,
leads to a denial of the supposition that the speaker is a swindler (which is left for you to fill in - I
have put the unstated part of the argument within square brackets). The supposition that he is a
swindler has led to the absurdity of believing on the one hand that he has walked off with your
money and on the other that he hasn't, since he is still here; so you must reject the supposition.
One of the reasons, besides simple accuracy, that we need to note when a claim is merely
entertained and when it is genuinely endorsed relates to the kinds of critical response that are
appropriate. If I tell you that Mary is at home, and give as my reason that there is a light on in the
kitchen, then it is very sensible for you to object, "But there isn't a light on in the kitchen." But if I
say "If Manley wins there will be another devaluation" you don't help the discussion by saying that
he won't. Why not? Because here, as in very many such cases of entertained arguments or
conditional statements, what is said is sustained by some other claims that the arguer may or may
not be able to articulate precisely. In fact, the usefulness of these linguistic resources arises out of
the fact that very often we cannot specify very exactly what these sustaining claims might be.
(That is also the usefulness of the device we met long ago, in example (1), of talking about the
look of clouds instead of having to say how they looked.) So, in the example we are using, my
claim about what will happen if Manley wins invokes some connection between political and
economic facts, but not one that I could easily state or defend explicitly. Using a conditional
statement, or offering an entertained argument, is often a way of appealing to some such
connection without having to bring it out explicitly. So disagreeing with such statements or
arguments requires that you criticize the connection rather than pick irrelevantly on the
supposition. Whether Manley wins or loses, the connection I am appealing to may exist, and it is
that that I am in a sense really concerned about; so instead of irrelevantly saying that my
supposition is false, you have to say something like "Even if Manley wins, there still won't be a
devaluation" - that is one way of denying the connection I am appealing to. This feature is more
obvious with the kind of conditional we met earlier where the arguer makes it clear she already
knows the supposition is false, as when she says "If Dukakis had won, then shares would have
fallen." Here objecting that Dukakis didn't win is a total waste of time since it has already been
tacitly admitted. Taking the disucssion further requires us to attend to other factors.
In terms of our structure diagrams, rejecting a conditional statement or an entertained argument
can be indicated simply by writing "not" in front of the whole argument in asterisks. It should be
noted that this is so whenever someone denies that certain premises support a conclusion. Thus in
a debate someone may assert "a" and go on to infer "b"; if you reject the inference you have to
say "It is not the case that if a then b", so that part of the argument is diagrammed with a "not" in
front of an argument in asterisks.
If you accept the conditional statement or the entertained argument there are two main things you
can do next. You could go on to assert the statement that you had merely supposed, and that
would licence you to assert what had previously been asserted only within the supposition. So if I
say "If you have enjoyed reading this booklet so far, you will enjoy doing formal logic" and you
reply "I have enjoyed reading this booklet so far" I am stuck with asserting "You will enjoy doing
formal logic." The other thing you could do, if you accept a conditional statement or an entertained
argument, is to deny what follows from the supposition, and this licences you to go on to deny the
supposition. We met this strategy in the reductio ad absurdum argument, where the arguer
deliberately chooses a supposition so that it can be categorically denied as the conclusion of the
reasoning, but it is a general point - if we agree that something follows from a supposition but that
the something is false, we can argue to the falsity of the supposition. This is a tremendously fruitful
mode of argument - if it was the butler who killed the secretary his shoes would be muddy, but his
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shoes aren't muddy, so it wasn't the butler - and not just in detective stories. It is at the root of
our attempts to understand the world we live in.
Before trying to analyse any arguments yourselves with this new tool, let us work through one
further example. It is taken from a paragraph of advice on running a state, and we shall break it up
to get a better grip on what is going on. Here are the first two sentences:
(26) The best fortress is to be found in the love of the people, for although you may
have fortresses they will not save you if you are hated by the people. When once the
people have taken arms against you, there will never be lacking foreigners to assist
them. [13]
Let us take this sentence by sentence. The first sentence involves four separate ideas that we can
write as separate sentences in the structure diagram:
(27) a = The best fortress is in the love of people.
b = You have fortresses.
c = Your fortresses will not save you.
d = You are hated by the people.
*********************
* b ) *
* ) ---> c * ---> a
* d ) *
*********************
The structure diagram shows that the first sentence asks the reader to make two suppositions
together: you have fortresses and you are hated by your subjects. The author then says that if you
suppose these two conditions your fortresses will not save you ("c"), and that entertained
argument is his reason for his original assertion that the best fortress is to be found in the love of
the people. The second sentence quoted above explains more fully why your fortresses won't help
you - if you suppose the people have taken arms against you, there will always be outsiders
prepared to help them. If we add these ideas to the diagram, we must incorporate the claim about
the people taking arms as a further supposition, so it goes inside the asterisks, but the other claim
is made absolutely so it goes outside thus:
(28) e = The people take arms against you.
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f = There are always foreigners to assist the people.
*********************
* b ) *
* ) *
* d ) ---> c * ---> a
* ) *
* e ) *
****)****************
)
f )
The passage goes on to review contemporary experience to show that it fits in with the claims
already analysed:
(29) In our times we do not see that they have profited any ruler, except the Countess
of Forli on the death of her consort Count Girolamo, for she was enabled to escape the
popular rising and await help from Milan and recover the state; the circumstances
being then such that no foreigner could assist the people. But afterwards they were of
little use to her when Cesare Borgia attacked her and the people being hostile to her
allied themselves with the foreigner. So that then and before it would have been safer
for her not to have been hated by the people than to have had the fortresses. [13]
Here, as is usual when evidence is being presented, there are quite a lot of different claims, but the
pattern of argument should be fairly clear. Having argued for the general claim labelled "a" the
author says that contemporary history supports it with one exception. But he goes on to add that
the exception happened because on that occasion no foreigners could intervene - which we must
take to be a very unusual circumstance. The usual course of events, and his generalization, are
exemplified by the same Countess' later misfortune when attacked by Cesare Borgia. In
diagramming these two arguments I shall use letters that reflect the claims in the original
argument the evidence illustrates:
(30) a'' = The Countess of Forli would have been safer if she had not been hated by
her people.
b' = The Countess of Forli had fortresses.
c' = The Countess' fortresses did not save her, the first time.
c'' = The Countess' fortresses did not save her, the second time.
d' = The Countess was hated by the people.
e' = The Countess was attacked by the people.
f' = There were foreigners to assist the people, the first time.
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f'' = There were foreigners to assist the people, the second time.
On the death of her consort: b' )
)
d' )
) ---> not c' )
e' ) )
) )
not f' ) )
) ---> a''
When Cesare Borgia attacked: b' ) )
) )
d' ) ---> e' ---> c'' )
)
f'')
Note that we don't need asterisks here since all these historical claims are being asserted. You
might note that the claim labelled "a''" is itself a conditional statement and so could have been
further decomposed into an entertained argument. (We might have let "a'" stand for "The Countess
of Forli was safe" and then replaced "a''" in the diagram with:
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(31) **************************
* *
* not d' -----> a' *
* *
**************************
This is closer to the entire text, but our main concern is with the first two sentences. Note that we
have not really done justice to the comparative claims in the last sentence of the original text.) If
we wanted to draw one diagram for the whole passage, one could have all this historical section
pointing towards "a" in (28) since the historical data are meant to be supporting that conclusion;
but there is no need to combine diagrams once you grasp what is going on in the different parts
and how those parts fit together. We have produced a fairly complicated picture (and there are
questions of interpretation that I haven't gone into) for a fairly simple part of a paragraph, but
don't be downheartened: taking things bit by bit should allow you to see the simple connections
that get put together to form these sorts of structure.
EXERCISE C
Draw a labelled structure diagram for each of the following arguments:
1. If Pluto had a diameter of more than 4,200 miles, then an occultation would have
occurred at McDonald Observatory, and the records clearly indicated that it did not.
Thus Pluto must be that size or smaller; it cannot be larger. [14] [Answer.]
2. If we had not rushed into the development of atomic power, we would not be facing
the risk of annihilation today. Would it not be better to learn from experience and
proceed into the field of genetics with more caution instead of discounting all
questioning voices as "alarmists"? [43] [Answer.]
3. One cannot be forced to do what one cannot do, and one cannot do what one is not
free to do. Hence one is free to do what one is forced to do. [15] [Answer.]
4. In truth, there never was any remarkable lawgiver amongst any people who did not
resort to divine authority, as otherwise his laws would not have been accepted by the
people; for there are many good laws, the importance of which is known to the
sagacious lawgiver, but the reasons for which are not sufficiently evident to enable him
to persuade others to submit to them; and therefore do wise men, for the purpose of
removing this difficulty, resort to divine authority. [16] [Answer.]
5. Redi demonstrated that the worms in putrefying flesh were larvae from the eggs of
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flies. His proofs were as simple as they were decisive, for he showed that surrounding
the putrefying flesh with fine gauze absolutely prevented the appearance of these
larvae. [17] [Answer.]
6. Medical science is steadily increasing the expectation of life and this, combined with
the concentration of industry into larger and larger units, is having the effect that an
ever greater proportion of the final power of decision is being concentrated into the
hands of very old men, which is the worst possible way of facing the problems of a
rapidly changing future. Since those who hold offices of power will never willingly give
them up, I believe there is only one solution to this problem. The young must somehow
or other enforce quite arbitrary rules of early retirement. [18] [Answer.]
7. The relative freedom we enjoy depends on public opinion. The law is no protection.
Governments make laws, but whether they are carried out, and how the police behave,
depends on the general temper of the country. If large numbers of people are
interested in freedom of speech, there will be freedom of speech, even if the law
forbids it; if public opinion is sluggish, inconvenient minorities will be persecuted, even
if laws exist to protect them. [44] [Answer.]
8. Had every man sufficient sagacity to perceive, at all times, the strong interest which
binds him to the observance of justice and equity, and strength of mind sufficient to
persevere in a steady adherence to a general and a distant interest, in opposition to
the allurements of present pleasure and advantage; there had never, in that case,
been any such thing as government or political society, but each man, following his
natural liberty, had lived in entire peace and harmony with all others.... It is evident,
that, if government were totally useless, it never could have place, and that the sole
foundation of the duty of allegiance is the advantage, which it procures to society, by
preserving peace and order among mankind. [19] [Answer.]
9. Let ABC be a triangle having the angle ABC equal to the angle ACB;
I say that the side AB is also equal to the side AC.
For, if AB is unequal to AC, one of them is greater.
Let AB be greater; and from AB the greater let DB be cut off equal to AC the less; let
DC be joined.
Then, since DB is equal to AC, and BC is common, the two sides DB, BC are equal to
the two sides AC, CB respectively;
and the angle DBC is equal to the angle ACB;
therefore the base DC is equal to the base AB, and the triangle DBC will be equal to the
triangle ACB, the less to the greater; which is absurd.
Therefore AB is not unequal to AC; it is therefore equal to it.
Therefore, if in a triangle two angles be equal to one another, the sides which subtend
the equal angles will also be equal to one another. [20] [Answer.]
5. DISCUSSIONS, EXPLICIT AND IMPLICIT
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So far we have considered arguments in monologue. A single speaker or writer is putting forward
her train of reasoning. But we should also consider arguments of the sort that require at least two
protagonists, i.e. discussions or disputes.
The crudest and least profitable kind of dialogue consists merely of counter-assertions: one speaker
says one thing, the other says the opposite, and each merely repeats his own claim. A notorious
intellectual vice is for the interlocutors to say that it is just a matter of individual opinion, and leave
it at that. There are some matters which are indeed merely matters of individual (subjective)
opinion or taste. But in any context in which it is worth discussing or trying to argue a point, there
is usually a lot of ground to be covered and critically examined before one should agree to give up
rational persuasion in this way. Of course, a man, or a woman for that matter, might not consent
to continue the argument, to continue probing the ins and outs of a problem, but obstinacy is no
reason to suppose that there is nothing to be said, nothing for critical thought to achieve. But I am
in danger of digressing from our path; let us return to serious argument.
If a person puts up an argument, there are various rational possibilities open to others. In the first
place, they may simply accept what has been said, premises and conclusion. This is often
eminently sensible, and I hope that you don't get the mistaken impression from this booklet that
you should always be searching for holes in what someone has said. Though on the other hand it
must be admitted that much argument and discussion on matters of general social and political
importance, such as education and schooling, is remarkably feeble.
But if you are not inclined to swallow what someone has put forward, what may you do? In the first
place, you may try to rebut the argument, which requires that you deprive its conclusion of the
support the argument offers it. There are two ways of doing this: either you deny vital premises
(and possibly produce arguments of your own to show that these premises are unacceptable) or
you challenge the strength of the link between premises and conclusion (saying in effect, I can
accept your premises but they don't serve to support your conclusion). We shall look soon at some
of the issues that arise in criticizing the kind of support involved in an argument. In the second
place, however, you may put forward a counter-argument of your own for a different conclusion, a
conclusion in conflict with that of the first speaker. A full reply to the speaker requires that you do
both of these things. If you only rebut her argument, you deprive her conclusion of the support she
offered it (in effect, you deny her right to continue believing the conclusion), but it might yet be
correct, and you have done nothing to show that it isn't. If you only put forward a counter-
argument, we are left with two arguments in the field, but with no guide as to how to decide
between them.
The result of an intelligent reply to an argument is likely to be that new points of disagreement
come to light. The rational thing to do is to carry on the discussion by taking up these new matters
and looking for ways of resolving the issues one way or the other.
People do on occasions discuss matters with one another, and one could analyse their dialogue
along the lines suggested. Sometimes people present their ideas by means of a fictional dialogue -
in philosophy we have the many dialogues written by Plato, as well as some notable examples by
Berkeley and Hume. Here is an extract from a short passage of such imaginary dialogue on a
philosophical topic:
(32) Until recently, debates about materialism have gone something like this:
Hylas: Since science seems to need to talk about nothing save atoms and the void in
order to explain everything that happens, only atoms and the void are really real.
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Philonous: But what is science save a scheme for ordering our experiences? Or, if it is
more than this, how can it possibly deny that it rests upon experiences, and that these
experiences are something different from either the atoms or the void?
H: What you call 'experience' is but another name for bounding atoms in the brain.
P: That is the sort of thing one would only say if one were defending a theory at all
costs. What criterion of 'same' could one possibly use to show that two such different
things were the same?
H: Two things are the same thing if talking about the one serves all the purposes as
talking about the other. [45]
In this fragment (the author continued with four more speeches) we can see several of the points
made above about what can happen in serious debate. But note that several contributions are
either straightforward questions or rhetorical questions which we must translate into the simple
assertion implied. Here is a possible diagram of the argument:
(33) a = Science only needs atoms and the void to explain everything.
b = Only atoms and the void are real.
c = Science explains (or is supported by) experience.
d = Experiences are different from atoms and the void.
e = Experiences are atoms moving in the brain.
f = X is the same as Y.
g = Talk about X serves all the purposes of talk about Y.
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1 H: a --------> b
2 P: c )
) [-----> not b ]
d )
3 H: e [-------> not d ]
4 P: What criterion for f in this case?
5 H: *************************
* *
* g --------> f *
* *
*************************
You can see clearly here how many of the intermediate conclusions are left unstated by each of the
speakers, and I have left out the fairly complicated unstated extras needed for the last remark:
talk of atoms in the brain serves all the purposes of talk of experiences so experiences just are
such atoms in motion. We do not have the tools to deal adequately with the last part of the
dialogue, but you can see that in the earlier part the moves link up with each other in the way we
mentioned above and that P's question in turn 4 is asked in the hope of showing that H's claim in 3,
"e", is false. H in turn 5 assumes that the general principle applies to the case in point, and the
debate then goes on (in the original) by discussing that unstated claim.
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While we can find explicit dialogue in some writings, much more commonly people develop their
ideas through a sort of implicit dialogue. They argue for a position not only by presenting a case for
it, but often more importantly by attacking other positions or by imagining objections to their own
view and replying to them. Writing on controversial topics is very often shot through with such
implicit dialogue, and sometimes it is difficult to disentangle the resulting fabric of thought, to tell
when the author is speaking in her own voice, as it were, and when through the mouth of an
imagined opponent. But, as with structure diagrams in general, it is a worthwhile exercise to try
sometimes to formulate explicitly the backwards and forwards movement of thought in a passage,
or indeed in a whole article or book.
Although it can be difficult to disentangle a passage, in many cases there will be clues in the text to
suggest which parts belong to which voice. Very frequently a speaker or writer will explicitly
attribute some opinion to other people and then tell us her own, usually different view. Jesus is
portrayed as making the contrast: "Ye have heard that it was said by them of old time .... But I say
unto you...." Other writers often tell you what "most people" think, or expound what "is commonly
believed" before launching into their own refinements or opposing views. In the following passage
the author distinguishes two views, one held by the ancients, the other by his contemporaries.
Since he gives reasons for both views it can simplify our task of describing his argumentation to
separate the two bits of reasoning as shown in the diagram:
(34) Tyrannicide, or the assassination of usurpers and oppressive princes, was highly
extolled in ancient times; because it both freed mankind from many of these monsters,
and seemed to keep others in awe, whom the sword or poinard could not reach. But
history and experience have since convinced us, that this practice increases the
jealousy and cruelty of princes; a Timoleon and a Brutus, though treated with
indulgence on account of the prejudices of their time, are now considered as very
improper models for imitiation. [46]
(35) a = Tyrannicide is admirable.
b = Tyrannicide frees us from oppression.
c = Tyrannicide deters some rulers.
d = Tyrannicide increases the cruelty of princes.
Ancients: b )
) -----------> a
c )
Hume: d ----> [ not c ] ---> not a
This diagram may be rather insensitive, but my main point is that any attempt to present the
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Argument Analysis.

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