=Paper=
{{Paper
|id=None
|storemode=property
|title=Conditionals, inference, and evidentiality
|pdfUrl=https://ceur-ws.org/Vol-883/paper4.pdf
|volume=Vol-883
|dblpUrl=https://dblp.org/rec/conf/esslli/KrzyzanowskaWDV12
}}
==Conditionals, inference, and evidentiality==
https://ceur-ws.org/Vol-883/paper4.pdf
Conditionals, Inference, and Evidentiality
Karolina Krzyżanowska1 , Sylvia Wenmackers1 , Igor Douven1 , and Sara
Verbrugge2
1
Faculty of Philosophy, University of Groningen, Oude Boteringestraat 52, 9712 GL
Groningen, The Netherlands
2
Department of Psychology, University of Leuven, Tiensestraat 102, 3000 Leuven,
Belgium
Abstract. At least many conditionals seem to convey the existence of
a link between their antecedent and consequent. We draw on a recently
proposed typology of conditionals to revive an old philosophical idea
according to which the link is inferential in nature. We show that the
proposal has explanatory force by presenting empirical results on two
Dutch linguistic markers.
1 Introduction
Although various theories of conditional sentences have been proposed, none of
them seems to account for all the empirical data concerning how people use
and interpret such sentences.3 It is almost universally agreed that no theory of
conditionals counts as empirically adequate if it validates sentences like these:
(1) a. If badgers are cute, then 2 + 2 = 4.
b. If weasels are vegetables, then unicorns hold Frege in particularly high
esteem.
It is easy to understand why people are reluctant to accept conditionals like
(1a) and (1b): the antecedents of those conditionals have nothing to do with
their consequents. And it seems that using a conditional construction is meant
to convey the existence of some sort of link between the content of the if-clause
and the content of the main clause.
But what kind of link might this be? According to an old philosophical idea,
the link is inferential in nature. If this idea is currently unpopular, at least in
philosophy, that may be due to the fact that theorists have failed to recognize
that the inferential connection need not be of one and the same type. We draw
on a recently proposed typology of conditionals to reinstate the old idea, at
least for a large class of conditionals that linguists have aptly termed “inferen-
tial conditionals.” We buttress our proposal by presenting experimental results
concerning two Dutch linguistic markers.
3
For a survey of various accounts of conditionals and problems they are facing see,
for instance, Edgington [1] or Bennett [2].
39
2 Inferential Conditionals
Probably the most general distinction to be made when it comes to conditionals
is that between indicative and subjunctive conditionals. In this paper, we will
only be concerned with indicative conditionals.4 For many theorists this is only
the beginning of a typology, though there is little unanimity as to what the ty-
pology should further look like. What has become common in linguistics, but is
rarely encountered in the philosophical literature, is to classify indicative condi-
tionals as inferential and content conditionals.5 The class of content conditionals
is not particularly well defined—its members are sometimes loosely said to de-
scribe relations between states of affairs or events as they happen in reality—but
those will not concern us here. We are going to limit our attention to inferen-
tial conditionals, that is conditional expressing a reasoning process, having the
conditional’s antecedent as a premise and its consequent as the conclusion, for
example: “If she has not had much sleep recently, she will perform poorly on her
exams” or “If he owns a Bentley, he must be rich.” Arguably, these constitute a
common, if not the most common, type among the conditionals we encounter in
natural language.
That a conditional sentence can be considered as a kind of “condensed argu-
ment” [8, p. 15] is not altogether new to philosophy; it can be traced back at
least to Chrysippus, a stoic logician from the third century BC. He is believed
to have held the view that a conditional is true if it corresponds to a valid ar-
gument [9]. Obviously, if we limit our understanding of a valid argument only
to the classical deductive inference, we can easily find counterexamples to the
above claim. Yet deduction is not the only type of reasoning people employ, and
a plausible theory of inferential conditionals should not neglect this fact.
Although linguists have proposed various finer-grained typologies of infer-
ential conditionals (see, e.g., Declerck and Reed [6]), most of these stem from
grammatical distinctions. However, we are interested in a specific typology re-
cently presented in Douven and Verbrugge [10] who acknowledge the variety of
inferential relations between a conditional’s antecedent and its consequent. A
first distinction these authors make is that between certain and uncertain infer-
ences, where certain inferences guarantee the truth of the conclusion given the
truth of the premises while uncertain inferences only tend to make the truth of
the conclusion likely given the truth of the premises; the former are standardly
referred to as “deductive inferences.” Douven and Verbrugge further follow stan-
dard philosophical usage in grouping uncertain inferences into abductive and
inductive ones, where the former are inferences based on explanatory considera-
tions and the latter are inferences based on statistical information. More exactly,
in an abductive inference we infer a conclusion from a set of premises because
4
The distinction between indicative and subjunctive conditionals is not as clear-cut as
one might wish, but the conditionals we used in our materials were all uncontroversial
cases of indicative conditionals. Henceforth, indicative conditionals will be referred
to simply as “conditionals.”
5
See, among others, Dancygier [3,4], Dancygier and Sweetser [5], Declerck and Reed
[6], and Haegeman [7].
40
the conclusion provides the best explanation for those premises; for example, we
may infer that Sally failed her exam from the premises that Sally had an exam
this morning and that she was just seen crying and apparently deeply unhappy:
that she failed the exam is the best explanation for her apparent unhappiness.
Inductive inferences rely on information about frequencies (which may be more
or less precisely specified); for instance, we infer that Jim is rich from the premise
that he owns a Bentley because we know that by far the most Bentley owners
are rich. The validity of both abductive and inductive inferences is a matter of
controversy and ongoing debate. It is largely uncontested, however, that people
do engage in these types of inferences on a routine basis.
Douven and Verbrugge’s typology of inferential conditionals follows the afore-
said typology of inference. That is to say, they distinguish between certain (or
deductive) and uncertain inferential conditionals, and then divide the latter class
further into abductive and inductive inferential conditionals. More specifically,
they propose the following:
Definition 1. “If p, then q” is a deductive inferential (DI, for short) / inductive
inferential (I I) / abductive inferential (AI) conditional if and only if q is a de-
ductive / inductive / abductive consequence of p.
(Various formalizations of the inductive and abductive consequence relations
have been offered in the literature, though, like Douven and Verbrugge in their
paper, we refrain from committing to any in particular.) Douven and Verbrugge
note also that, often, the inference may rely on the antecedent p together with
background assumptions that are salient in the context in which the conditional
is asserted or evaluated. Such conditionals are called contextual DI, AI, or I I
conditionals, depending on the type of inference involved.6
Definition 2. “If p, then q” is a contextual DI / I I / AI conditional if and only
if q is a deductive / inductive / abductive consequence of {p, p1 , . . . , pn }, with
p1 , . . . , pn being background premises salient in the context in which “If p, then
q” is asserted or evaluated.
Douven and Verbrugge do not claim that their typology is correct and the
ones that so far have been propounded by other theorists are incorrect. Indeed,
it might even be odd to think that there are natural kinds of conditionals that
a typology should try to chart. What they do claim is that their typology is
exceedingly simple and that it is non-ad hoc in that it relies on a time-tested
distinction between types of inference. More importantly still, they show in their
2010 paper that the typology has considerable explanatory force by recruiting it
in service of testing a thesis, first proposed by Adams [11] and championed by
many since, according to which the acceptability of a conditional is measured by
the probability of its consequent conditional on its antecedent.
6
As Douven and Verbrugge [10, p. 304] note, in contextual AI conditionals, the con-
sequent need not always be the best explanation of the antecedent. It may also be
that the consequent is, in light of the antecedent, the best explanation of one of the
background assumptions.
41
We expand here on the main experiment of Douven and Verbrugge’s paper,
because it served as the starting point for our own empirical work. In their exper-
iment, Douven and Verbrugge divided the participants into two groups, asking
one group to judge the acceptability of ten DI, ten AI, and ten I I conditionals
and the other group to judge the corresponding conditional probabilities. This
is an example of a question asking for the acceptability of an AI conditional:7
Context: Judy is waiting for a train. She is looking for her iPod. It is not in
her coat. She suddenly sees that the zipper of her bag is open. She cannot
remember having opened it. It is announced that there are pickpockets
active in the train station.
Conditional: If Judy’s iPod is not in her bag, then someone has stolen it.
Indicate how acceptable you find this conditional in the given context:
Highly unacceptable 1 2 3 4 5 6 7 Highly acceptable
The corresponding question asking for the conditional probability is this:
Context: Judy is waiting for a train. She is looking for her iPod. It is
not ain her coat. She suddenly sees that the zipper of her bag is open.
She cannot remember having opened it. It is announced that there are
pickpockets active in the train station. Suppose that Judy’s iPod is not in
her bag.
Sentence: Someone has stolen Judy’s iPod.
Indicate how probable you find this sentence in the given context:
Highly improbable 1 2 3 4 5 6 7 Highly probable
The results obtained in this experiment show that Adams’ thesis holds for DI
conditionals at best, and that for AI conditionals the most that can be said
is that acceptability and conditional probability are highly correlated; for I I
conditionals not even that much is true.
This already shows that the typology of inferential conditionals proposed
by Douven and Verbrugge has considerable explanatory force. Here, we aim
to extend the case for this typology by relating it to two putative evidential
markers. Before we move on to report our experimental results on these markers
(in section 4), we briefly discuss the concept of an evidential marker.
3 Evidential Markers
In some languages, it is common for speakers to communicate information about
the evidential grounds for the contents of their assertions. Some languages also
possess a rich arsenal of prefixes, suffixes, particles, and other linguistic items for
7
See Appendix A of Douven and Verbrugge [10] for the full materials used in this
experiment.
42
this purpose.8 European languages do not encode evidentiality grammatically,
but this is not to say that speakers of European languages do not have the
resources to indicate evidential grounds, or that they never use those resources.
Sentences like:
(2) Adam works hard.
do not indicate the speaker’s source of information at all—the speaker can actu-
ally share an office with Adam and see him working hard on an everyday basis,
but she could also have inferred (2) from Adam’s work output or simply heard
someone else say so.
But other sentences do suggest the speaker’s evidential grounds. For instance,
when we are wondering about the translation of a phrase in Latin and we know
that Susan studied classical languages for a number of years, we might say
(3) Susan should be able to translate this phrase.
This assertion would seem odd if we knew that (say) the phrase is from a text
which Susan recently published in English translation. Similarly, when an English
speaker tries to call her friend but does not get an answer, she may infer that
her friend is out and express the resulting belief by saying:
(4) She must be out.
Were she to see her friend walking on the street, her assertion of (4) would again
seem odd or even inappropriate.
Some authors have argued that the modal auxiliary verb “must” makes the
assertion weaker than the one without it.9 But this is not generally true. For
sometimes “must” seems to indicate the necessity of what has been asserted: if
one knows that Mary has put a bottle of wine either in the fridge or in the
cupboard, and one has checked that it is not in the cupboard, it seems natural
for one to conclude:
(5) It must be in the fridge.
As noticed by von Fintel and Gillies [17,18], what (4) and (5) have in common
in the first place is that they signal the presence of an inference. Specifically,
the verb “must” indicates that the speakers’ grounds for their assertions are
inferential, and hence indirect, but as they also argue, this need not mean that
8
On the basis of data from 32 languages, Willett [12] proposed a taxonomy of markers
encoding main types of sources of information. The main distinction is between di-
rect (perceptual) and indirect access, and the latter can be further divided into other
speaker’s reports and inference. Since then, various aspects of evidentiality in lan-
guage have been investigated, like for instance a developmental study by Papafragou
and colleagues [13] on Korean speaking children’s learning of evidential morphology
and their ability to reason about sources of information.
9
See e.g. Karttunen [14, p. 12], Groenendijk and Stokhof [15, p. 69] or Kratzer [16,
p. 645]
43
these grounds are weak or inconclusive. Again, some confusion could have been
avoided if the variety of inference relations had been attended to.
Of course, sometimes we convey information about our evidential grounds
in more direct ways, as when we say that we saw that John crossed the street,
or that it seems to us that Harriet is worried, or by the use of such words
as “probably,” “presumably,” “possibly,” “apparently,” “allegedly,” “putatively,”
and so on. But in this paper we focus on “must” and “should” in their roles
as evidential markers, or rather, we focus on their Dutch counterparts “moet
wel” (“must” 10 ) and “zal wel” (“will,” “should”). Evidential markers can serve
a number of purposes. For instance, they may be used to indicate the source
of the speaker’s evidence: whether it is perceptual evidence, or evidence from
testimony, or evidence from some third type of source still. They may also be
used to indicate the quality of the evidence (e.g., indicate how reliable the source
was). We will be mainly interested in the question of whether “moet wel” and “zal
wel” play any distinctive role in signaling the kind of inference that is involved in
making whatever evidence the speaker has bear on the content of her assertion.
Can anything systematic be said about whether these markers go better with
some type or types of inference than with others?
To clarify this question, note that the inference underlying the assertion of
(4) in our example is most plausibly thought of as being abductive, that is, as an
inference to the best explanation: that the friend is out is the best explanation
for the evidence that the speaker has, to wit, that her friend does not answer the
phone. In the example of Susan, it rather seems to be some form of inductive
reasoning that warrants the assertion of (3): the people we met in our lives
who had studied classical languages for a number of years were typically able
to translate Latin phrases; given that Susan studied classical languages for a
number of years, we expect her to be able to translate the designated phrase.
Naturally, the inferential connection between evidence and grounds for assertion
may also be deductive, as in the case of (5). The question we are interested in is
whether the use of “moet wel” and “zal wel” gives us any indication as to what
kind of inference (if any at all) led the speaker to feel warranted in making the
assertion she did on the basis of the evidence she had.
4 Experiment: Linguistic Markers
Our experiment makes use of the typology of inferential conditionals discussed
above. We look at a number of instances of the various types whose degrees of
acceptability have been ascertained in previous research and we look whether
these degrees are affected by inserting “moet wel” or “zal wel” into the sentences.
We encountered the putative English counterparts of these markers already in
our examples involving (4) and (3). “Must” and “zal wel” have also been de-
scribed as inferential markers in the literature. As for the latter, Verbrugge [20]
established a close connection between “zal wel” and inferential conditionals.
10
“Wel” is a positive polar marker which has no counterpart in English; see Nuyts and
Vonk [19, p. 701]. In German, “bestimmt” comes close.
44
Specifically, in an elicitation task in which they were requested to complete con-
ditionals whose antecedents were given, participants tended to come up with
a significantly higher number of inferential conditionals (as opposed to content
conditionals) when they were in addition requested to use “zal wel” in the conse-
quents than when they were not. As for “must,” Dietz [21, p. 246] notes that in
“It must be raining,” the auxiliary indicates that the speaker only has (what he
calls) “inferential evidence,” and no direct observational evidence, that it is rain-
ing; see also the papers by von Fintel and Gillies cited earlier as well as Anderson
[22], Papafragou [23], and Nuyts and Vonk [19]. However, so far researchers have
not considered differentiating between the various types of inference by means of
the said markers. Might not one marker go better with the expression of one type
of inference and the other with the expression of another type of inference? Even
more fundamentally, is “must” really an inferential marker? We are not aware
of any empirical evidence that warrants a positive answer. Philosophers may be
convinced that “must” can serve as an evidential marker, but philosophers were
also convinced that the acceptability of a conditional is equal to the correspond-
ing conditional probability, and—as Douven and Verbrugge showed—empirical
evidence gives the lie to that thought.
To investigate the aforementioned questions, we used the materials of the ex-
periment described in the previous section. We inserted “moet wel” and “zal wel”
into the consequents of the conditionals used in Douven and Verbrugge’s main
experiment and checked whether this made a difference to acceptability ratings
and their correlations with probability ratings. We were particularly interested
in the effect the presence of the auxiliaries has on these correlations for different
types of conditionals.
4.1 Method
Participants
Fifty seven students of the University of Leuven took part in the experiment.
Design
The type of conditional (DI / AI / I I) was manipulated within subjects. The dif-
ferent lexical markers were manipulated between subjects.
Materials and Procedure
All materials were in Dutch, the participants’ mother tongue. Thirty items were
presented in a booklet. Every participant had to evaluate ten abductive, ten
inductive, and ten deductive items. Items were randomized per booklet and the
booklets were randomly distributed in the lecture hall. The items consisted of the
same context–sentence pairs that were presented to the participants in the main
experiment of Douven and Verbrugge [2010] who were asked to judge the accept-
ability of conditionals, except that the conditionals now contained the markers
“moet wel” and, respectively, “zal wel.” For instance, to the AI conditional “Als
Judy’s iPod niet in haar tas zit, dan heeft iemand die gestolen” (“If Judy’s iPod
is not in her bag, then someone has stolen it”), whose acceptability participants
in Douven and Verbrugge’s experiment had been asked to grade, corresponded
45
in our experiment the AI conditionals “Als Judy’s iPod niet in haar tas zit, dan
moet iemand die wel gestolen hebben” (“If Judy’s iPod is not in her bag, then
someone must have stolen it”) and “Als Judy’s iPod niet in haar tas zit, dan zal
iemand die wel gestolen” (“If Judy’s iPod is not in her bag, then someone will
have stolen it”).
Participants (N = 30) in the condition “moet wel” were asked to judge the
acceptability of the conditionals containing “moet wel.” Participants (N = 27) in
the condition “zal wel” were asked to judge the acceptability of the conditionals
containing “zal wel.” The instructions were the same as the ones used in the
acceptability condition of Douven and Verbrugge’s experiment.
Results
Comparisons with the condition investigating the probability were set up. We
computed the mean per sentence (ten abductive sentences, ten inductive sen-
tences, and ten deductive sentences) over the participants. We thus obtained
a mean for each of the thirty sentences. Then we computed the correlations
between the condition with marker (“zal wel” / “moet wel”) and the mean prob-
abilities per item obtained on the basis of Douven and Verbrugge’s experiment.
For the thirty sentences in the experiment, probabilities as obtained in Dou-
ven and Verbrugge’s experiment and acceptability of the sentences with “zal wel”
were highly correlated: N = 30, Spearman R = .837712, t(N − 2) = 8.116914,
p < .0001. For the thirty sentences in the experiment, probabilities as ob-
tained in Douven and Verbrugge’s experiment and acceptability of the sen-
tences with “moet wel” were highly correlated: N = 30, Spearman R = .855871,
t(N − 2) = 8.756641, p < .0001.
We next considered different types of conditionals. For the abductive sen-
tences, probability and “moet wel” were highly correlated: N = 10, Spearman
R = .993902, t(N − 2) = 25.49522, p < .00001. We obtained similar results for
“zal wel”: N = 10, Spearman R = .936175, t(N − 2) = 7.532386, p = .0001. For
the inductive sentences, correlations did not reach significance level; for “moet
wel” and “zal wel”: N = 10, Spearman R = .612121, t(N − 2) = 2.189453,
p = .059972. For the deductive sentences, probability was highly correlated with
“moet wel”: N = 10, Spearman R = .814593, t(N − 2) = 3.972223, p < .01.
For probability and “zal wel,” the correlation did not reach significance level:
N = 10, Spearman R = .613985, t(N − 2) = 2.200141, p = .058981.
Comparison with the results from Douven and Verbrugge’s experiment showed
that, overall, the markers had little effect on the perceived acceptability of the
conditionals as well as, correspondingly, on the correlation between acceptabil-
ity and probability (see Table 1). However, splitting the results for the various
types of conditionals was more revealing. It appeared that, while for I I condition-
als, adding either of our two markers had virtually no effect on the correlation
between acceptability and probability, adding them to the AI conditionals did
increase the said correlation, even to the extent of yielding a near-to-perfect cor-
relation for the AI conditionals containing “moet wel” (for no marker, R = .8997;
for “zal wel,” R = .936175; and for “moet wel,” R = .993902). For DI conditionals,
46
Table 1. Correlations with and without markers (* = marginally significant; for all
other results p < .01)
All DI II AI
No marker .851102 .818182 .620064* .899700
“zal wel” .837712 .613985 .612121* .936175
“moet wel” .855871 .814593 .612121* .993902
adding “moet wel” had almost no effect, but adding “zal wel” led to a considerable
decrease of the correlation between acceptability and probability.
4.2 Discussion
These results confirm that “moet wel” and “zal wel” are inferential markers, given
that (i) inserting either of them in the AI conditionals has the effect of increasing
the correlation between acceptability and probability, and (ii) inserting “zal wel”
in the DI conditionals has the effect of decreasing that correlation. It is no
surprise that inserting “moet wel” in the DI conditionals does not have a similar
effect: like “must” in English, “moet wel” can also serve as an alethic modality,
and may thus be naturally interpreted in a DI conditional as underlining the
necessity of the inference.
5 Concluding Remarks
The typology proposed in Douven and Verbrugge [10] helps to explain why
adding inferential markers to conditionals makes the systematic kind of differ-
ence that we found in our experiment. That is further support for the thought
that this typology is of theoretical significance. The experimental work reported
here is part of a larger project. Experiments concerning the English “must,”
“should,” and “will” are currently being undertaken, and the results are to be
compared to the results of the experiment reported above. A further avenue
for future research concerns applications of these markers. For instance, if some
markers can be used as a kind of litmus test for distinguishing between various
types of conditionals, then testing for the effect that adding these markers to
conditionals has may help us in classifying conditionals whose type is controver-
sial. Perhaps the most important part of the project is to see whether the current
typology of conditionals can serve to ground a new semantics and/or pragmatics
of conditionals. Once it is recognized that various types of inferential connection
may be involved, it becomes quite plausible to claim that at least many condi-
tionals require for their acceptability the existence of an inferential link between
antecedent and consequent. Whether this is then to be taken as a brute prag-
matic fact, or whether it has a deeper explanation in terms of truth conditions,
is the question we ultimately hope to answer. The investigations reported here
are meant as a first step toward that answer.
47
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