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article 

IGNORATIO 
ELENCHI: The 
Red Herring 
Fallacy 
Dougias N. Walton 
University of Winnipeg 

It is a longstanding presumption of the 
tradition of logic that several major infor-
mal fallacies essentially involve failure 
of topical appropriatene~s or relevance. The 
~ baculum! the ad ~opulum, and th7 ad 
m~ser~cord~am each ~nvolve an emot~onal 
appeal.! But there need be nothing wrong 
with appeals to emotion as such, nor need an 
appeal to emotion even involve argument, let 
alone fallacious argument. Indeed, many an 
emotional appeal is deceitful as a complete 
abandonment of argument covered up by the 
distraction of a naked appeal to emotion. 
~fuat can be fallacious in emotional appeals 
however, where there is argument, is that the 
proposition that appeals to emotion turns out 
to be, in some important sense, irrelevant to 
the conclusion to be argued for. Thus if an 
advertiser tries to communicate the idea that 
his product is popular, there may be nothing 
fallacious in that. But if popularity is a 
premiss for the conclusion that his product 
is a good buy, or technically or nutrition-
ally sound, an ad POtUlum may be in the of-
fing. Reason: :popu ar~ty is not an appro-
priate or relevant basis for establishing 
technical performance or nutritional ade-
quacy of a product. One has simply strayed 
off topic altogether. 

The ad hominem is another case in point. 
PersonaT characteristics or circumstantial 
factors may often fail to be argumentatively 
connected in any serious way to the conclusion 
at issue. Perhaps it's true that our physi-
cian who cites evidence of the dangers of 
smoking cannot herself give up the habit. 
Yet to dwell on this interesting circumstan-
tial inconsistency may commit an irrelevant 
appeal by masking the fact that the evidence 
cited by the physician is reasonable and good 
evidence, not to be overlooked. 2 Similarly, 
ad verecundiam 3 may dwell on an appeal to the 
sayso of some glamorous "expert" in lieu of 
evaluating serious evidence for or against 
some proposition. 

The term ignoratio elenchi (misconception 
of refutation)~ften used, following in 
the Aristotelian tradition, to refer to fail-
ure of relevance in argument. But as Hamblin 

3 

comments, until we have some firm idea of 
what is meant by "relevance" in this context, 
just calling failure of relevance a fallacy 
is not any help.S And indeed, historically 
the ignoratio elenchi has tended to become 
a rag-bag category to cover any argument where 
the author is uncertain why it is fallacious. 
What has happened is that the ad gorulum, ad 
hominem, and other major fallaCIes, have ~ 
stayed in the textbooks, but with the lame 
~xplanation that they are somehow failures of 
an argument to be relevant, The problem is 
that until we know what Qrelevant" means" we 
have no clear guidelines for showing clearly 
what really is fallacious about these argu~ 
ments that so strongly seem to go wrong by 
being off topic, 

Formal logic does not seem to be any help 
in resolving the problem. It is well known 
that classical logic has theorems like 
p :::> (q :>p) and -p::) (p ::>q), which suggests that 
classical logic is simply neutral on the 
issue of whether p and q are in any way topi-
cally related to each other. The classical 
material 'If, •• then' or 0, only assures 
us that p::> q never takes us from a true p to 
a false q, never mind whether p and q are 
connected in any way, 

The branch or formal logic called relevance 
logic is specifically designed to deal with 
"fallacies of relevance" like the two clas-
sical tautologies above. But the problem 
with it is that although it offers a variety 
of formal logics based on the idea of rele-
vance, somehow--at least so far--it has not 
provided us with a clear basic idea of what 
"relevance" means in one or more of these 
formal logics. We need a concept of rele-
vance that can be applied to fallacies like 
the ad baculum and ad verecundiam so that we 
can see spec~ficallY-how these arguments are, 
at least sometimes, dramatic failures of a 
proposition to be relevant to a given argu-
ment or conclusion. "Relevant", that is, in 
a sense which shows us why such arguments can 
correctly be said to be fallacious. The prob-
lem is that the philosophical task of showing 
the relevance of relevance logics to the major 
fallacies of relevance remains unsolved, or 
perhaps even unaddressed. It is by no means 
clear that "relevance" in the technical sense 
of relevance logic is the same concept of 
relevance that is meant when we say that the 
ad misericordiam is a fallacy of relevance. 
Part of the problem, as we will see, is that 
quite a variety of notions of the connections 
between the antecedent and consequent of a 
conditional proposition could be involved. 

"Relevance" could mean all kinds of things, 
but let us go back to the basic idea so often 
expressed that a proposition p is connected 
to (relevant to, related to) another propo-
sition q, if p and q share meaning content. 

Suppose we begin with the idea that an 
argument or discourse is about a set of 
topics, T. Of course, with many arguments, 
the set of topics that the argument can com~ 
prise is not firmly agreed on by the partic~ 
ipants at the outset. But to work towards 
what we want to analyse, let us adopt the 
model of an argument, after Hamblin, as an 
interchange ~etween participants. An argu-
ment, by these lights is then a sort of inter-
change or discourse between arguers, a back 



and forth sequence of moves and countermoves. 
For a given discourse, let us make the as~ 
sumption that the participants can establish 
a set of topics that comprises the legitimate 
subject of that discourse. Given an overall 
set of topics for a given series of inter-
changes, we can then look at any particular 
argument that is part of that series, and 
evaluate whether or not it is "off topic". 

Following a suggestion made by David Lewis, 
we take every proposition p, q, r, ••• , in 
the discourse we are concerned with, and 
assign it its subject-matter, called £, ~, r, 
• • • , which is in each case a subset or T76 
Then we can say that p is related to q if 
there is subject-matter overlap between £ and 
~. For example if 'Bananas are yellow' con-
tains the subject-matters 'bananas' and 'yel-
low', and 'Bananas are nutritious' contains 
the subject-matters 'bananas' and 'nutri-
tious', then the two propositions are related. 
They both contain the topic 'bananas' in 
their subject-matters. This ,is a clear and 
simple idea of "relevance", or relatedness as 
we prefer to call it, that provides a begin-
ning point for exploring fallacies like those 
we have mentioned. 

Clearly 'p is related to q' in the sense of 
overlapping subject-matters is a relation 
that is reflexive and symmetrical, but not 
transitive. The following example will show 
why transitivity fails. 'Bananas are yellow' 
is related to 'There are two bananas on my 
desk'. And the second proposition is related 
to '2+2=4'. But 'Bananas are yellow' is not 
related to '2+2=4'. 

Here at any rate is one clear conception of 
relatedness of propositions--that of subject-
matter overlap7_-that offers a place to begin 
in analyzing fallacies of relevance. 

A typical example of irrelevance in argu-
ment is given by Johnson and Blair (1977, 
p. 54), where then-Senator Paul Martin took 
exception to the slur contained in Arthur 
Hailey's Wheels that Windsor is as grimy and 
ugly as Detro~E. Martin responded: 

When I read this I was incensed • • • 
Those of us who live there know that 
INindsor] is not a grimy city. It is 
a city that has one of the best flower 
parks in Canada. It is a city of fine 
schools, hard-working and tolerant 
people. 

In critically analyzing this argument, John~ 
son and Blair point out that Martin's initial 
point about the flower park does tell against 
Hailey's appraisal. But instead of continuing 
to build his case for the beauty of Windsor, 
the Senator changed the subject, by effecting 
a quick transition to-Dther topics: the hard-
working and tolerant characteristics of the 
people of Windsor. This shift is a red her-
ring or ignoratio elenchi move in the argu-
ment, as Johnson and Bla~r point out. 

The thrust of the argument runs something 
like this, if we break it down into distinct 
premisses. 

Premiss 1: Windsor has one of the best flower 
parks in Canada. 

Premiss 2: Windsor has fine schools. 

4 

Premiss 3: Nindsor has hard-working, toler-
ant citizens. 

Conclusion: Windsor is not a grimy city. 

Now the question is: how could what is fal-
lacious about this argument be shown to be an 
incorrect argument in a relatedness model-
ling? The evidently insuperable initial 
problem is this: the fact is t~t there is 
subject-matter overlap between every premiss 
and the conclusion of the argument. There-
fore, if ignoratio elenchi is failure of 
subject-matter overlap, then the above argu-
ment is definitely not an ignoratio elenchi 
at all! 

What I think this shows is that subject-
matter overlap between premisses and conclu-
sion does not constitute a sufficient condi-
tion of correct argument. Perhaps another 
illustration will make this point more clear-
ly. The thirteenth century logician l'lilliam 
of Sherwood cites the two arguments oelow as 
incorrect. They are cited as instances of 
Ignorance Regarding Refutation (Ignoratio 
Elenchij--see the translation of Kretzmann 
(1966, p. 156). (1) Socrates is naturally 
pious, but he is not absolutely pious; there-
fore he is both pious and not pious. (2) 
Socrates is running at time a (currit in al 
and he is not·running at time bi thererore he 
is ooth running and not running. Now notice 
that in both these arguments there is subject-
matter overlap between premisses and conclu-
sion, yet botA arguments are clearly incor-
rect. Indeed, both are sophismatical or 
fallacious arguments from premisses that are 
possibly true to a conclusion that can't be 
true. 

So subject-matter overlap is not enough to 
rule out fallaciousness. To be a correct 
argument meeting reasonable standards that 
will avoid i~noratio elenchi, not only must 
there be subJect-matter overlap but also the 
argument must not allmoT us to go from true 
premisses to a false conclusion. Hence the 
relatedness conditional, p ~q, must incor-
porate both requirements that (1) it is not 
the case that p is true and q is false, and 
(2) p is related to q. 

In short, the reason why Senator Hartin's 
argument fails is not failure of subject-
matter overlap, but by virtue of the fact 
that the second two premisses simply fail to 
imply the conclusion, either deductively or 
inductively. It is neither impossible nor 
improbable that a grimy city might have hard-
working and tolerant citizens. 

Still, one might persist, isn't the red 
herring really explained by the evident pre-
sumption that 'has hard-working tolerant 
citizens' as a property of some city x, fails 
to have subject-matter overlap with 'is not a 
grimy city' for any x. The suggestion is 
that the following argument fails by reason 
of lack of subject-matter overlap, where x is 
any city. 

Premiss 1: For all x, x has fine schools. 

Premiss 2: For all x, has hard-working, 
tolerant citizens. 

Conclusion: For all x, x is not a grimy city. 

And to be sure, this argument does fail to 
have significant subject-matter overlap, and 
is a bad argument. 

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So perhaps there is a second explanation of 
what is fallacious about Senator ~~rtin's 
argument. It is, by these lights, really a 
true red herring after all and not merely a 
failure of implication not specifically due 
to subject-matter disjointedness. Still, 
even if this second analysis is acceptable, 
our general point remains that subject-matter 
connectedness by itself is not enough to as-
sure correctness of an argument, as the ex-
amples from William of Sherwood show, For we 
cannot analogously reconstruct the liilliam.s 
arguments as failures of subject matter over ... 
lap. For example the reconstruction of (ll 
as follows remains incorrect: for some indi ... 
vidual x, x is naturally pious but x is not 
absolutely pious; therefore x is both pious 
and not pious. This argument is incorrect, 
but it still has subject-matter overlap be ... 
tween premisses and conclusion. Therefore 
generally we must conclude that ignorance of 
refutation involves more than just failure of 
subject-matter overlap. TOpics are involved 
essentially, but they are not the whole story 
about ignoratio elenchi. 

As can be seen by the examples cited above 
from William of Sherwood, the traditional 
Aristotelian fallacy of ignorance of refuta-
tion was not restricted merely to instances 
of failure of subject-matter overlap. In-
deed, the Aristotelian tradition of the 
"topics", so influential in medieval logic, 
distinguished numerous different kinds of 
connections or "topics" that could relate the 
premisses and conclusion of a correct argu~ 
ment. Boethius followed Cicero's conception 
of a topic as sedes argumenti (a seat of argu-
ment), and described it as "that from which a 
fitting argument may be drawn for a proposed 
question" (De Differentiis Topicis). For 
these earlier authorities, a topic functions 
primarily as a way of finding new arguments, 
but for later writers like Abelard and Ockham 
the topic became the inferential basis of a 
conditional proposition. 

Abelard claims that the topics show the in-
ferential force (vis inferentiae) of all con-
ditionals. According to Bird (1960) Abelard 
uses the topic as an "inference-warrant" that 
can accommodate formal as well as non-formal 
inferences. An example of Abelard's is that 
'If it is man, it is animal' is a correct 
(good and necessary) inference whereas 'If it 
is stone, it is animal' is not, because the 
second lacks the relation of the Topical 
Difference of Species. 

However, it is clear that genus-species was 
not the only topical relation recognized by 
the medievals, and in fact the diversity of 
the dialectical topics subdivided the kinds 
of correct conditionals they recognized into 
many classifications. For example we find in 
Peter of Spain an enumeration of some twenty-
one topics including part-whole relations, 
attributions of place and time, causation, 
similarity, authority, adverbial modification. 
and so forth. ~'Jhat is corranon to them is that 
a topic is always a relation that warrants an 
inference. 

This tradition of the topics suggests that 
the application of formal theories of the 
conditional to the wide' varieties of failure 
of correct inference that are involved in 
many informal fallacies and practical argu~ 

5 

ments is no simple matter. It appears to 
involve many different kinds of relations 
that link the antecedent to the consequent in 
conditionals, Subject-matter overlap is one 
such relation that helps to clarify one sense 
of "failure of relevance" central to under-
standing the modern conceptions of the ad 
~pUlurn, ad hominem and related fallacies. 
crearly however, other kinds of relatedness 
relations are involved as well, if the many 
different varieties of conditional used in 
practical arguments are to be studied. 

Let us turn to seeing how a general theory 
of relatedness could be formulated to accom-
modate the above requirements and still allo,,, 
for a good deal of flexibility in application 
to specific arguments. \'le will see that it 
can be done by modifying the usual proposi-
tional calculus and requiring the relatedness 
of antecedent and consequent in order for a 
conditional to obtain. Could such a formal 
approach be useful? 

Uany of those who are drawn to informal 
logic see it as a subject that shows pedagog-
ical promise in teaching students how to han-
dle the practicalities of evaluation of argu-
mentation in pragmatic situations like the 
consumer marketplace. Because they see it as 
a practical discipline they are skeptical 
that formal logic can be meaningfully appli-
cable to realistic argumentation. After all, 
doesn't formal logic rest on a propositional 
calculus that certifies as valid argument 
forms schemata like ...,p::> (p ::> q) ? How could 
a logic that allows conditionals to obtain 
between ostensibly unrelated proposition be 
applicab17 to fallacies like the ad populum or ad hom1nem? 

Yet on the other hand, if formal guidelines 
on what constitutes correct versus incorrect 
forms of argument are not ava11able, how coul& 
practical logic of the informal sort ever 
offer clear and precise guidelines for eval-
uating arguments? 

perhaps the dilerrana can be ameliorated by 
clarifying more precisely what is meant by 
"formal logic" in this context. True, clas-
sical PC is not a model of argument that 
suits the fallacies of subject-matter related-
ness, but perhaps other formal approaches 
that deviate from classical logic in order 
to capture the relevant sense of proposi-
tional connectedness could be more useful. 

One formal approach that shows great promise 
in studying fallacies associated with failure 
of subject-matter overlap is the relatedness 
logic of Epstein (1979). In relatedness 
logic, the conditional p ~ q is defined as 
incorporating the classical requirement that 
it not be the case that p is true and q false 
with the additional requireMent that p be 
related to q. R(p,q) is read as 'p is 
related to q', a relation that is ref17xive 
and non-transitive. It may be syrranetr1cal 
or not, as you wish, but if relatedness is 
interpreted as meaning 'subject~matter over-
lap of p with q' t~en clearly it is also a 
symmetrical relation. Negation is defined in 
the classical way. Conjunction and disjunc-
tion may be defined either as classical or as 
requiring relatedness, as you wish. However, 
it is proposed in Walton (1979) that for 
purposes of subject-matter relatedness, it is 
natural to think of disjunction as requiring 



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relatedness, but to think of conjunction as 
classical, i.e. not requiring relatedness. 
The final building block that yields a formal 
logic of relatedness is to show how the com-
plex formulas are related to the simple for-
mulas. The key ruling is this: p is related 
to q ~ r if, and only if, p is related to q 
or p is related to r. This ruling seems 
reasonable for subject-matter relatedness 
because it is natural to say that 'Socrates 
is snub-nosed' is related to 'If Socrates 
sprints then some man is running' because the 
simple proposition is related to one of the 
propositions in the conditional, namely the 
antecedent. 

Given the requirements set out above, what 
forms of inferences come out valid or invalid? 
The usual truth-table decision procedure en-
ables us to determine tautologies. Consider 
modus ponens. 

p q R(p,q) p-q (p-q)-q p -[ (p-q) -q] 

T T : T T T T 

T T F F T T 

T F T F T T 

T F F F T T 

F T T T T T 

F T F F T T 

F F T T F T 

F F F F T T 

As you can see, the truth-tables are similar 
to classical logic except that we must take 
relatedness into account, in addition to the 
truth-values of ~~e propositions. 

As an example of a classical tautology that 
fails in relatedness logic, consider 
[(p 1\ q) ... r] ... [Cp .... r) v (q ... r)]. This 
schema can fail as follows. Let q be true 
and r false, then the q ~ r in the consequent 
is false. Let p be unrelated to r, then 
p ... r in the consequent is false. Hence, on 
this interpretation the consequent is false. 
But assume p is false. Then p 1\ q in the 
antecedent is false, hence (p 1\ q) ... r must 
be true, assuming that q is related to r, an 
assumption that is consistent with the as-
signments given to the consequent. In short, 
there is a consistent assignment of truth-
values and relatedness relations that makes 
the antecedent of the schema in question come 
out true and the consequent come out false. 
Hence the schema fails to be a tautology. In 
general, truth-tables always enable us to tell 
whether an argument is correct or not in re-
latedness logic. 

To see how rejection of the schema above 
applies to practical arguments, consider a 
syllogism like this: All men are mortal (p), 
Socrates is a man (q), therefore Socrates is 
mortal (r). It is true that (p A q) ~ r 
applies, but it is false that (p ~ r) V 
(q ~ r) applies. Hence it is "paradoxical" 
indeed that [(p A q) :> r] :> [ (p ::> r) V 
(q'~ r)] is a tautology in classical PC. 
More usual "paradoxes" cited are _p ':) (p ::> q) 
and q:> (p :>q), but these too fail to be 
relatedness tautologies. In short, related-

6 

ness logic turns out to be a subsystem of 
classical PC. All relatedness tautologies 
are classical tautologies, but there are 
some classical tautologies that fail in re-
latedness logic. 

We can summarize our findings as follows. 
Many traditional major informal fallacies can 
be and often are categorized as involving a 
failure of'propositions to be related to each 
other. Particularly, what seems to be upper-
most in mind is failure of subject-matter 
overlap. But the traditional study of the 
logic of the topics suggests that there can 
be many different kinds of relatedness in-
volved in studying sophismata that reflect 
fallacies important to practical reasoning by 
conditionals. However, we can focus on 
subject-matter overlap as one particularly 
central and clearly definable species of 
relatedness, 

If we are to construct a general theory of 
conditionals based on relatedness that is 
useful in studying the underlying fallacy of 
ifinoratio elenchi that is common to fallacies 
t at go wrong by failure of relatedness, we 
must be clear that subject-matter connected-
ness is not by itself sufficient to assure 
correctness of an argument. In addition, we 
must requir~ that a correct argument does not 
go from true premisses to a false conclusion. 

Ianoratio elenchi, whether it be character-
ize as failure of subject-matter overlap in 
conditionals, or as failure of any kind of 
relatedness, is a general kind of fallacy 
that helps to explain, at least partly, what 
has often thought to be fallaciOUS about 
arguments like the ad POtUlum or ad hominem. 
But it is only part-of t e story of these 
other fallacies, and specific studies of 
these various individual fallacies help to 
bring out other important aspects of them. 

Notes 

lSee Walton (1980). 

2see Woods and Walton (19771. 

3see Woods and Walton (19741. 

4But sometimes also translated as Uignorance 
of refutation If , 

SActually, as Hamblin indicates, and as will 
be pointed out below, the Aristotelian con~ 
ception of ignoratio elenchi may be somewhat 
different from inferences that many modern 
writers might tend to classify as fallacies 
of relevance. 

6see also Epstein (1979, p. 156 f.). 

7Another notion of related is that of 
temporal adjacency in an act-sequence. R (p,q) 
in this context has this meaning: what makes 
p true can affect what makes q true. 

80ther classical tautologies that obtain in 
relatedness logic are modus tollens, contra~ 
position, disjunctive syllogism, and 
reductio ad absurdum, i.e., (p _ q) -+ [(p -+ 
-q) - -p]-:-

9Some other principles that fail are ex-
portation, hypothetical syllogism and addi~ 



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References 

Otto Bird, "The Formalizing of the Topics in 
Mediaeval Logic," Notre Dame Journal of 
Formal Logic, 1, 1~38 .. 149. -

Richard L. Epstein. "Relatedness and Implica-
tion," Philosophical Studies, 36, 1979, 
137-173. 

R. H. Johnson and J. A. Blair, Logical Self~ 
Defense, Toronto and New York, McGraw=-
Hill Ryerson, 1977. 

Norman Kretzmann .. trans. and ed., William of 
Sherwood's Introduction to L?g~c, 
Hinneapolis, Un~vers~ty of M~nnesota 
Press, 1966. 

Douglas N. Walton, "Philosophical Basis of 
Relatedness Logic,",Philosophical Studies, 
36, 1979. 115-136.' 

Douglas N. Walton, "Why is the Ad POJilulum a 
Fallacy?" Philosophy ~ Rfietor~c, to 
appear, 1980. 

John Woods and Douglas l"lalton, "ARtiumentum ad 
Verecundiarn, " Philosophy and etoric, r, 
1974, 135-153. --

John vloods and Douglas Walton, "Ad Hominem," 
~ Philoso~hical ~, 8, ~77, 1-20. 

responses 

Mare on Deductive 
and Inductive 
Arguments 

Trudy Govier 
Trent UniverSity 

The existence of confusing material in 
textbooks has not been enough to convince 
Samuel Fohr that the distinction between in-
ductive and deductive arguments should be re-
linquished. CSee" The Deducti ve-Inducti ve 
Distinction", Informal 'L09tc Newsletter, 
ii.2.l Fohr proposes, fol owing a definition 
in Olson's Meaning ~ Argument, that the 
distinction between deduct~ve and inductive 

7 

arguments be established on the grounds of 
the intentions of the person putting forward 
the argument. Arguments, he says, are 
people's arguments; they are put forward in 
order to convince other people. People may 
intend either that their arguments provide 
conclusive reasons for what they are trying 
to demonstrate, or that they provide less 
than conclusive reasons. In the first case, 
an arguer's intentions establish his argument 
as deductive. In the second case, they make 
it inductive. A desirable consequence of 
this approach is that it provides for both 
good and bad arguments in each category. 
Most of the time, Fohr thinks, we are able to 
tell what an arguer's intentions are, or were. 
If we cannot, we must judge the argument 
"both ways". 

This proposal does not strike me as very 
satisfactory. I am surprised that Fohr, who 
says that he cannot accept "purportedly valid" 
as a definition of 'deductive argument', can 
rest content with an appeal to intention here. 
I have the following difficulties with his 
proposal: 

1. Either there will be evidence for the 
arguer's intentions regarding conclusiveness 
in the wording of his argument, or there will 
not. In the first case, intentions and 
"purported validity" or "involving a claim to 
validity" (Copi) will amount to much the same 
thing. There are numerous examples, as Fohr 
admits, where wording is not helpful. After 
all, conclusiveness in the sense of logical 
entailment is a philosopher's concept, and 
even such English words as "must", "there-
fore", and "shows conclusively" will not 
provide a reliable basis for inferring that 
the arguer is claiming conclusiveness in the 
sense that the premises are supposed to 
10*ica11Y entia1 the conclusion. If, on the 
ot er hand, we seek to avoid these difficul-
ties with wording--making the author's safso 
and that alone the criterion for determ~n~ng 
his intention--we will find ourselves unable 
to apply the distinction to many cases where 
authors are dead or absent. This is absurd 
if the inductiye/deductive distinction is 
supposed to be a fundamental tool in the 
assessment of argument. We can, of course, 
look at the indeterminate arguments "both 
ways", as Fohr suggests; but the more often 
we do this, the more often we are bound to 
wonder why all of logic should have been 
erected around this fuzzy distinction in the 
first place. 

2. If we really take Fohr seriously on the 
over-riding importance of intention, then we 
will have to accept the peculiar consequence 
that there are inductive arguments which are 
deductively valid, and deductive arguments 
which are inductively strong. For instance, 
suppose someone argues: 

1. Either L€vesque will be defeated at 
the next election, or he will win 
and call another referendum . 

2. Since Quebecers are fond of Levesque, 
he will not be defeated at the next 
election. 

3. Thus, there will in all likelihood 
be another referendum. 

This argument is deductively valid, but the 
conclusion contains the tentative expression 
"in all likelihood". If the arguer is a