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INFORMAL LOGIC 

XI.1, Winter 1989 

Favorable Relevance and Arguments 

GEORGE BOWLES The George Washington University 

Since an argument consists of at least 
two propositions so related to each other that 
one (or more) is a premise and the other 
a conclusion, the definition of an argument 
consists of one or more conditions that are 
singly necessary and jointly sufficient for 
one proposition to be a conclusion and one 
or more others premises. Concerning these 
conditions we may ask the following 
questions: 

1. Do they include the actual or attributed 
favorable relevance 1 of one or more of 
the propositions to another? 

2. Do they include the assertion of some or 
all of the propositions? 

3. Do they include the actual or attributed 
verification, as distinguished from ex-
planation, of one proposition by the 
remainder? 

4. Do they include the expression of the 
propositions in a dialogue? 

The purpose of this paper is to answer on-
ly the first of these questions. 

I. Is the actual or attributed favorable 
relevance of one proposition to another 
a necessary condition for the former to 

be a premise and the latter the 
conclusion in an argument? 

The case for an affirmative answer to 
this question is that at least part of what it 
means for a group of propositions to be an 
argument is that some of those constituents 
are, or at least are said to be, (good) reasons 
for another; and whatever is a (good) reason 
for something else is favorably relevant to 

it. This proves, or at least suggests, that the 
actual or attributed favorable relevance of 
one or more propositions to another is a 
necessary condition for the former to be a 
premise and the latter the conclusion in an 
argument. 

On the other side, it might be urged, 
first, that there can be an argument against 
as well as for a proposition. When there is, 
the proposition that the argument is against 
is the conclusion; and the premises have, 
or at least are said to have, unfavorable 
relevance to it. So, here we have an argu-
ment whose premises are, or at least are said 
to be, not favorably but unfavorably rele-
vant to its conclusion. Consequently, one 
or more propositions' actual or attributed 
favorable relevance to another is not a 
necessary condition for the former to be 
premises and the latter the conclusion in an 
argument. 

But this argument is unsound because 
it claims that, in the case of an argument 
against something, the proposition that the 
argument is against is the same as its con-
clusion. This is false, since when we argue 
against something, our conclusion is not the 
proposition against which we are arguing 
but rather the claim that that proposition is 
false, wrong, or something similar. Our 
premises are, or at least are said to be, 
favorably relevant to that claim-i.e., to our 
conclusion-while at the same time they are, 
or are said to be, unfavorably relevant to 
the proposition against which we are argu-
ing. For instance, if against the possibility 
of unaided human flight we argue from 
premises about the inability of an unaided 
human being to generate enough lift to over-
come gravity, our premises are, or are said 
to be, unfavorably relevant to the propos i-



12 George Bowles 

tion against which we are arguing-namely, 
that human beings can fly without 
assistance. But at the same time they are, 
or are said to be, favorably relevant to our 
conclusion-namely, that it is false that 
human beings can fly without assistance. 

A second argument for the negative 
answer is this. When we deliberate among 
alternatives, we construct an argument some 
of whose premises are, or at least are said 
to be, favorably, others unfavorably, rele-
vant to the conclusion that one alternative 
is best. Depending on the relative strength 
of the premises for and against the conclu-
sion, we accept or reject the conclusion, 
thereby deciding for or against that alter-
native. This shows that it is possible for 
premises to have actual or attributed un-
favorable relevance to a conclusion. 2 

The reply to this second argument is that 
there is a more plausible account of how 
we reason when we deliberate, according 
to which we distinguish the alternatives 
from each other and ascertain all their possi-
ble consequences; we note how desirable 
or undesirable and how probable or im-
probable are all those consequences; we 
compare those data about the consequences; 
and from that comparison we conclude that 
one alternative is better, or at least not 
worse, than the remainder. 3 In this account, 
no premise is, or is said to be, unfavorably 
relevant to its conclusion. Deliberation, 
then, provides no instance of either actual 
or attributed unfavorable relevance of 
premises to a conclusion. 

The final argument for the negative 
answer says that some arguments (a species 
of what are called 'conductive arguments ') 
have conclusions drawn from premises 
some of which are, or at least are said to 
be, unfavorably relevant to them. For in-
stance, the text-

Although your lawn needs cutting, you 
ought to take your son to the movies because 
the picture is ideal for children and will be 
gone by tomorrow. 

-expresses the argument-

PI. Your lawn needs cutting. 
P2. The picture is ideal for children. 
P3. The picture will be gone by tomorrow. 
C. You ought to take your son to the 

movies. 

-in which the first premise is, or at least 
is said to be, unfavorably relevant to the 
conclusion. 4 

The reply to this is that though 'because' 
in the text tells us that 'You ought to take 
your son to the movies' is a conclusion, and 
'This picture is ideal for children' and 'The 
picture will be gone by tomorrow' 
premises, in an argument, 'although' tells 
us that between 'Your lawn needs cutting' 
and 'You ought to take your son to the 
movies' there is an opposition that is incom-
patible with their being premise and con-
clusion in the same argument. This incom-
patibility may be better appreciated if we 
remove from the text both 'because' and the 
premises it indicates: 

Although your lawn needs cutting, you 
ought to take your son to the movies. 

This makes it apparent that 'Your lawn 
needs cutting' and 'You ought to take your 
son to the movies' are not related as pre!llise 
to conclusion. Nor do they become so upon 
the restoration of the removed material. 

So, an accurate analysis of the reason-
ing expressed in the first text would yield 
two arguments-

AI. 

P. Your lawn needs cutting. 
(C. You ought not to take your son to the 

movies.) 

A2. 

PI. The picture is ideal for children. 
P2. The picture will be gone by tomorrow. 
C. You ought to take your son to the 

movies. 

-in neither of which the premises are, or 
are said to be, unfavorably relevant to the 
conclusion. 

Having now seen that the case for the 



negative answer fails, 5 we may conclude 
that one or more propositions must be, or 
at least be said to be, favorably relevant to 
another in order for the former to be 
premises and the latter a conclusion in an 
argument. 

II. Is the favorable relevance that is a 
necessary condition for one proposition 

to be a premise and another the 
conclusion in an argument actual, 

or is it attributed?6 

Supposing that actual or attributed 
favorable relevance is a necessary condi-
tion for one proposition to be a premise and 
another the conclusion in an argument, the 
question remains which kind of favorable 
relevance is required-actual or attributed. 
To this question there seem to be just these 
two answers: either an argument's premises 
must actually be favorably relevant to its 
conclusion, or else they must at least be said 
to be so. If the first of these answers were 
correct, then a group of propositions would 
constitute an argument only if some of them 
(namely, the premises) actually were 
favorably relevant to another (namely, the 
conclusion); but if the second answer were 
correct, then the premises of an argument 
could fail actually to be favorably relevant 
to its conclusion-i.e., they could fail ac-
tually to make the conclusion either prob-
able or certain-and still be parts of an 
argument. 

Two points of clarification of the second 
answer are in order. First, it is deliberate 
that the agent of attribution-i.e., who or 
what says that some of the propositions are 
favorably relevant to another-is 
unspecified. Usually, the most conspicuous 
such agent would be the arguer-i.e., the 
person or other rational being who offers 
the argument. But it need not always be so. 
Someone may have an argument in mind 
without accepting or offering it himself, in 
which-case he would not attribute to the 
premises favorable relevance to the conclu-

Relevance and Arguments 13 

sion. Moreover, an argument might be ex-
pressed independently of any rational 
agency-e.g., by unusual erosion on a 
hillside or an improbable arrangement of 
colored pebbles on a beach-so that no one 
would attribute favorable relevance to the 
premises. In such admittedly atypical but 
possible cases as these, although no arguer 
attributes to the premises favorable 
relevance to the conclusion, something else 
does. In the first case the attribution is done 
not by the argument's uncommitted con-
templator but by a proposition he has in 
mind (but does not accept) that sums up the 
whole argument-viz., a proposition that 
says that the premises are favorably rele-
vant to the conclusion. Similarly, in the sec-
ond case the attribution is done not by any 
rational being but again by the proposition 
that sums up the whole argument and is ex-
pressed by the entire text. In fact, even 
when an arguer is involved, he attributes 
to the premises favorable relevance to the 
conclusion only insofar as he believes or ex-
presses a proposition that attributes to the 
premises favorable relevance to the conclu-
sion. So, in all arguments, one agent of at-
tribution is such a proposition; in most, an 
additional agent is the arguer. 

The second point of clarification is that, 
even if an arguer attributes to the premises 
some degree of favorable relevance to the 
conclusion, he need not say so: his enter-
tainment of the argument may be private, 
or he may express it without saying just how 
favorably relevant he thinks the premises 
are to the conclusion. Where a rational agent 
of attribution is involved, attributing is one 
thing and expressing that attribution is 
another. 

So, the second answer claims that an 
essential feature of an argument is that, 
whether by rational agency or not, and in 
the former case whether expressed or not, 
favorable relevance to the conclusion is at-
tributed to the premises. 

Having now clarified the second answer, 
let us proceed to the arguments that com-
pose the case for the first answer-namely, 



14 George Bowles 

that a group of propositions constitutes an 
argument only if some of them actually are 
favorably relevant to another. That case 
seems to consist wholly in the case against 
the second answer-namely, that a group 
of propositions makes up an argument on-
ly if some of them are said to be favorably 
relevant to another. One such argument is 
that it is sometimes possible to ascertain that 
someone is arguing from premises to a con-
clusion but impossible to ascertain whether 
he thinks that his premises are favorably 
relevant to his conclusion. For example, if 
someone had said-

Socrates is mortal. He is a man, and all men 
are mortal. 

-his text would express an argument. But 
there is no evidence that the author at-
tributed to the premises favorable relevance 
to the conclusion, since he used no illatives 
like 'proves' or 'suggests' and no 
probability-indicators like 'certainly' or 
'probably'. It seems, then, that here is an 
argument whose premises lack attributed 
favorable relevance to the conclusion. If so, 
attributed favorable relevance cannot be an 
essential feature of an argument. 

This argument assumes that the only 
evidence we can have about attributed 
favorable relevance must consist of verbal 
clues like illatives or probability-indicators. 
But this is false: other sources of evidence 
are possible. For instance, people do not 
usually neglect or reject the apparent logical 
relations among the propositions they ex-
press by means of sentences that are near 
each other. So, a person would be unlikely 
to express together several propositions, 
some of which would plausibly be reasons 
for another, unless he thought some of the 
propositions favorably relevant to the re-
mainder. If so, then we have a source of 
evidence about attributed favorable 
relevance beyond verbal clues like illatives 
and probability-indicators. And this refutes 
the preceding argument. 

A second argument against the second 
answer is that it is incompatible with for-

mal logic. If attributed favorable relevance 
were a necessary condition for an argument, 
then in order to ascertain whether a group 
of propositions constitutes an argument we 
would usually have to ascertain whether 
someone attributed to some of them 
favorable relevance to another. But this is 
a psychological question and is, as such, 
alien to formal logic, which is independent 
of all psychological considerations. So, a 
definition of an argument in terms of 
attributed favorable relevance would be 
incompatible with formal logic. 

The reply is that if the second answer 
is to be rejected because it is incompatible 
with formal logic, then what makes a group 
of propositions an argument must be ascer-
tainable on formal grounds alone. Now, on 
formal grounds alone it is possible to ascer-
tain actual, not attributed, relevance. But 
whether actual, rather than attributed, 
favorable relevance is a necessary condi-
tion for an argument is the very thing in 
question. Hence, the argument begs the 
question by assuming what is to be proved. 

A third argument against the second 
answer is that the attributed favorable 
relevance of one or more propositions to 
another is not necessary for the former to 
be premises and the latter the conclusion in 
an argument, because there can be an argu-
ment in the absence of such attributed 
favorable relevance. Let A be a Chinese 
peasant in 932 B.C., let B be a Roman mer-
chant in 106 A.D., and let C be a South 
African geographer in 1935 A.D. Suppose 
that A thinks to himself, "All men are mor-
tal". Several centuries later, in ignorance 
of what A thought, B thinks to himself, 
, 'Socrates is a man". And after the lapse 
of many more centuries, C, in ignorance 
of what A and B thought, thinks to himself, 
"Socrates is mortal". This example exhibits 
none of the attributed favorable relevance 
required by the second answer, yet it does 
contain an argument, because the proposi-
tions that A and B have in mind are actual-
ly favorably relevant to the proposition that 
C has in mind. 7 



The reply to this is that, despite the fact 
that the propositions that A and B have in 
mind are actually favorably relevant to that 
which C has in mind, these propositions do 
not in this case constitute an argument. The 
contrary impression may arise from the fact 
that some fourth person, such as the reader, 
has all three propositions in mind and at-
tributes to some of them favorable relevance 
to the remainder. 8 The second answer, then, 
is not overthrown by this alleged 
counterexample. 9 

So much for the evidence against the se-
cond answer-namely, that a group of prop-
ositions constitutes an argument only if 
some of them are said to be favorably rele-
vant to another-and in favor of the first-
namely, that a group of propositions con-
stitutes an argument only if some of them 
actually are favorably relevant to another. 
Now, what is to be said against the first and 
in favor of the second? 

The argument against the first, and in 
favor of the second, answer goes like this. 
If the first answer were correct, then the 
actual favorable relevance of one or more 
propositions to another would be necessary 
to make the former premises, and the lat-
ter a conclusion, in an argument. But this 
leads to false consequences. For instance, 
suppose that someone says, "All men are 
mortal, and Socrates is mortal; therefore, 
all men are Socrates". It seems clear that 
his use of the illative 'therefore' tells us that 
he has in mind an argument whose premises 
are 'All men are mortal' and 'Socrates is 
mortal' and whose conclusion is 'All men 
are Socrates'. This is consistent with the 
second answer, which would say that there 
is an argument only where there is attributed 
favorable relevance, and the speaker's use 
of the illative 'therefore' shows that in this 
case there is attributed favorable relevance. 
But it is inconsistent with the first answer, 
which would say that, because the first two 
propositions are not actually favorably rele-
vant to the third; and because the actual 
favorable relevance of one or more propos i-

Relevance and Arguments 15 

tions to another is necessary in order for 
the former to be premises, and the latter a 
conclusion, in an argument; they do not 
constitute even a bad argument. 10 Accord-
ing to this answer, the person's use of the 
illative 'therefore' shows, not that an argu-
ment is present (since it does not show that 
one or more propositions actually are 
favorably relevant to another), but at 
most that he is trying to argue. The first 
answer, then, entails a false, while the 
second is compatible with a true, 
conclusion. 11 

This argument, then, concludes that the 
first answer is false because it entails a false 
consequence: contrary to what it asserts, 
actual favorable relevance is not a necessary 
condition for an argument. So, assuming 
that the second is the only other answer, 
it is true: a group of propositions 
constitutes an argument only if to some of 
them is attributed favorable relevance to 
another. 

This last argument, I think, settles the 
question: attributed, rather than actual, 
favorable relevance is a necessary condi-
tion for an argument. 

III. Conclusions 

This paper has reached two conclusions. 
The first is that the actual or attributed 
favorable relevance of one proposition to 
another is a necessary condition of the 
former's being a premise and the latter the 
conclusion of an argument, because a group 
of propositions constitutes an argument only 
if some of them are, or at least are said to 
be, (good) reasons for another; and 
something is a (good) reason for something 
else only if it is favorably relevant to it. The 
second conclusion is that attributed, rather 
than actual, favorable relevance is a 
necessary condition for an argument. 
For only thus can we avoid a prohibition 
against calling some arguments 
'arguments' . 



16 George Bowles 

Notes 

1 Any two propositions are such that one is either 
relevant or irrelevant to the other. If relevant, 
it is either favorably relevant (in which case it 
makes the other probable or certain) or un-
favorably relevant (in which case it makes the 
other improbable or impossible). There may be 
degrees of favorable or unfavorable relevance: 
one proposition may be more or less favorably 
or unfavorably relevant to another than a third. 
Favorable relevance which is said to obtain be-
tween the propositions may either actually ob-
tain or not. 

2 See the argument -diagrams in Stephen N. 
Thomas, Practical Reasoning in Natural 
Language, Third Edition (Englewood Cliffs, 
New Jersey: Prentice-Hall, Inc., 1986), p. 306. 

3 See, for instance, Patrick Suppes, "Decision 
Theory", in The Encyclopedia of Philosophy, 
ed. Paul Edwards (New York: Macmillan 
Publishing Co., Inc., & The Free Press, 1967), 
Vol. 2, p. 311. 

4 Carl Wellman, Challenge and Response: 
Justification in Ethics (Carbondale: Southern Il-
linois University Press, 1971), p. 57. See also 
Trudy Govier, Problems in Argument Analysis 
and Evaluation (Dordrecht, Holland: Foris 
Publications, 1987), pp. 69, 72. 

5 William H. Halverson (A Concise Logic [New 
York: Random House, 1984)) defines an induc-
tive argument as "an argument whose conclu-
sion follows from its premises with a probability 
greater than 0 percent but less than 100 
percent-or, as it is more commonly express-
ed, an argument whose conclusion follows from 
its premises with a probability greater than 0 
but less than 1" (p. 254). If this were the cor-
rect definition of an inductive argument, then 
such an argument would not involve favorable 
relevance. But it is questionable whether this 
is really what Professor Halverson meant to say, 
since it leads to such unacceptable consequences 
as that 'Few dogs have fleas' and 'My dog has 
fleas' are the premise and conclusion of an in-
ductivc argument, since the first of these prop-
ositions confers on the second a probability 
grcater than 0 but Icss than I-in fact, less than 
V2. Perhaps Professor Halverson meant to say 
'degree of favorable relevance' instead of 
'probability' . 

6 Although the majority opinion on this question 
seems to be that the favorable relevance that 

is a necessary condition for an argument is at-
tributed, some logicians say otherwise. For 
instance: 

[In a proof, or argument,] "each prop-
osition is a premise (which provides 
grounds or basis for the reasoning) or a 
conclusion (which follows from, or is 
logically derived from) the premise(s). 
The premises of an argument provide the 
evidence on the basis of which a conclu-
sion is derived. "-Henry Ehlers, Logic 
by Way of Set Theory (New York: Holt, 
Rinehart and Winston, Inc., 1968),p.147. 

"An argument in logic is a set of 
statements. Some of the statements serve 
as premises, or statements of evidence, 
and others serve as the conclusions that 
can be drawn from the premises."-
Louis O. Kattsoff, "Logic", in The 
World Book Encyclopedia, (Chicago: 
Field Enterprises Educational Corpora-
tion, 1967), Vol. 12, pp. 381-2. 

" ... a statement is called a conclusion 
when it is justified by other statements, 
which in turn are called evidence or 
reasons. " - Peter T. Manicas and Arthur 
N. Kruger, Essentials of Logic (New York: 
American Book Co., 1968), p. 4. Quoted 
in Kenton F. Machina, Basic Applied 
Logic (Glenview, Illinois: Scott, Foresman 
and Company, 1978, 1982), p. 66. 

"An argument is a series of statements 
arranged in such a way that one state-
ment is a conclusion and at least one 
statement is a premise which supports the 
conclusion." "In every genuine argu-
ment, the premises provide some support 
for the conclusion. " " ... an argument, 
in order to be an argument, must have 
premises which support the conclusion 
.... " -Barrie Wilson, The Anatomy 
of Argument (Washington, D. C.: 
University Press of America, 1980), pp. 
16,247,252. 

"In the context of logic, an argument is 
defined as a set of statements which is 
such that one of them (the conclusion) 
is supported or implied by the others (the 
premises). "-Robert Baum, Logic, Sec-
ond Edition (New York: Holt, Rinehart 
and Winston, 1981), p. 87. 



-
"An argument is a group of statements, 
one or more of which (the premises) 
support or provide evidence for another 
(the conclusion) .... "-T. Edward 
Darner, handout for his workshop 
"Using the Fallacies to Teach Critical 
Thinking", Conference 88 on Critical 
Thinking, Christopher Newport College, 
Newport News, Virginia, April 10, 
1988, p. l. 

7 Cf. Baum, op. cit., p. 87: "An argument is an 
argument if it satisfies the above definition 
[namely, "a set of statements which i~ such that 
one of them (the conclusion) is supported or im-
plied by the others (the premises)"], even if no 
one has ever thought of it, let alone intended 
that it be used to prove something." 

8 Here are two instances of a spectator's becom-
ing an arguer: 

[1] "There is an argument in what they 
say, only they don't see it." (Perry 
Weddle, "Deductive/Inductive", In-
formal Logic Newsletter, Vol. ii, No. 
I [November, 1979], p. 2, col. 2.) It 
is not "they" but the speaking observer 
who is the arguer. 

[2] Suppose I find a piece of paper with 
the sentence 

1) All men are rational. 

written on it. At some other time 
(earlier or later) I hear on the radio 

2) All U.S. presidents are men. 

And at some other time still I read on 
my classroom blackboard 

3) All U.S. presidents are rational. 

Relevance and Arguments 17 

I would be a poor logician not to 
recognize that 1 and 2 jointly entail 3. 
There are no explicit or implicit in-
dicators here. There is no specifiable 
author to claim explicitly or implicitly 
that and how 1 and 2 relate to 3 . Yet 
I judge these sentences to constitute a 
(valid) deductive argument. . . . 
(George Englebretsen, "Freeman on 
Deduction/Induction' " Informal 
Logic, Vol. vi, No.1 [January, 1984], 
p. 27, col. 2.) 

James B. Freeman ("Reply to Englebretsen", 
Informal Logic, Vol. vi, No.2 [December, 
1984], p. 39, col. 2) denies that there is any 
argument here at all. He is right, in that there 
is no argument until the spectator creates one. 
But after the spectator says, "Yet I judge these 
sentences to constitute a (valid) deductive argu-
ment", there is an argument; and the arguer 
is the spectator. 

9 The preceding paragraph of the text is derived 
from an unpublished manuscript by the present 
author and Thomas E. Gilbert, What is an 
Argument? An Inquiry in the Philosophy of 
Logic (1979), pp. 122-126. 

10 Cf. Baum, loco cit.: " ... even if someone in-
tends that a certain set of statements be used 
to prove something, that set of statements does 
not constitute an argument unless it satisfies the 
definition" -i. e., unless some of the statements 
support or imply another. 

11 The preceding paragraph is derived from 
Bowles and Gilbert, loco cit. 

GEORGE BOWLES 
DEPARTMENT OF PHILOSOPHY 
THE GEORGE WASHINGTON UNIVERSITY 
WASHINGTON, D.C. 20052. D