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Review of  Real Conditionals

Reviewer: Anne Reboul
Book Title: Real Conditionals
Book Author: William G. Lycan
Publisher: Oxford University Press
Linguistic Field(s): Linguistic Theories
Philosophy of Language
Issue Number: 13.1632

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Lycan, William G. (2001) Real Conditionals. Oxford University
Press, 223pp, hardback ISBN 0-19-924207-0

Anne Reboul, Institute for Cognitive Sciences, CNRS, France

This very interesting book is a must for anyone, whether a
linguist or a philosopher, interested in conditionals and
conditional reasoning. However, it is a very compact book,
suitable only for well-informed readers. It should on no
account be taken for a text book or introductory work.

The book is made of eight fairly homogeneous chapters with an
appendix on ''non-conditional conditionals''. Its aim is to give
a truth-conditional account of conditionals avoiding the
(mainly linguistic and syntactic) pitfalls in which most
''logical'' accounts of conditionals fall and keeping some of
the virtues of the non-truth-conditional account known as the
Ramsay Test.

It thus opens, unsurprisingly, with a chapter devoted to ''The
Syntax of Conditional Sentences''. This begins with an attack
against the general logical view of conditionals, according to
which a conditional involves a ''syntactically unstructured
binary sentence operator'' (1), i.e. ''if... then''. This is true
whether ''if...then'' is taken as equivalent to the material
implication or to the intensional or modal operator. This lead
logicians to treat ''If A, then B'', ''B if A'' and ''A only if B''
as equivalent. This, Lycan claims, is wrong, for syntactic
considerations. Though conditionals are generally defined as
sentences with the connective ''if'', other adverbials such as
''in case'', ''in the event that'', etc. are semantically very
similar and any theory of conditionals should take them into
account. Other sentences, generally considered as logically
equivalent to conditionals (e.g. some disjunctions) are
syntactically quite different from them. Lycan proposes to
consider as conditional any sentence in which ''if'' occurs and
any sentence which is synonymous with, not merely logically
equivalent with, such sentences. Finally, Lycan rejects the
idea that conditionals are unstructured conjunctions, showing
that conditional sentences exhibit syntactic properties
radically different from conjunctions (e.g. neither
conjunction reduction, gapping, across-the-board principle
apply to conditionals). Neither are conditionals unstructured
subordinating conjunction: they can be modified by ''even'' and
''only''. Indeed, the proximity of ''if'' with ''when'' and ''where''
seems to indicate that conditional clauses are adverbial,
making ''tacit reference to events and circumstances'' (11).
Finally, Lycan rejects, for syntactic reasons, the idea that
''unless'' is equivalent to ''if not''. Again, a Relative-Clause
account should apply to ''unless'', as it applies to ''if'',
though in the case of ''unless'', it undergoes a twist: the
negation applies indeed, but not in the scope of ''unless'';
rather it applies on the quantification over the events
described in the clause.

The second chapter, ''Truth Conditions: The Event Theory'', is
devoted to a description of Lycan's theory of conditionals. It
is the longest chapter in the book and is indeed pivotal. The
theory is a semantic theory in the sense that it intends to
propose a systematic assignment of truth-conditions to
sentences with ''if'', ''unless'', ''only if'' and ''even if''. This
is supposed to account for the implications of such sentences,
to explain the dependence of their truth-values on context and
to agree with their syntactic properties. Lycan proposes the
following paraphrases of such sentences: ''P if Q -- P in any
event in which Q''; ''P only if Q -- P in no event other than one
in which Q''; ''P even if Q -- P in any event including any in
which Q''; ''P unless Q -- P in any event other than one in which
Q''. All of these formulas involve universal quantification
over a domain of events in which Q. Event is here to be taken
as situation, in a sense similar to that of situation theory.

Formalizations of the paraphrases express the truth-conditions
of the corresponding sentences. The universal quantifiers
should be restricted to a reference class of ''real
possibilities'', i.e. possibilities which ''the utterer must
have (...) at least tacitly in mind as a live prospect'' (19).
The reference class, however, should contain only ''relevant''
properties, which leads Lycan to a discussion of semifactuals
and ''weak'' conditionals. A second problem is that the utterer
might be wrong about possibilities. A solution to the first
problem (the relevance of events) is to restrict the reference
class to events where either P, non-P, Q or non-Q is true
(Moderate Relevance Restriction) or to restrict it to events
where either P or non-P is true (Strict Relevance
Restriction). Both of these conditions probably apply to
different classes of conditionals. The reference class is thus
''a hidden parameter that will vary with context'' (23). The
second difficulty is more serious. A way out is to see that
''with the inclusion or non-inclusion of all actual relevant
event in R [the reference class], stands or falls the validity
of Modus Ponens'' (24). Lycan postpones the issue till chapter
3. Lycan's theory (henceafter the ''Event theory'') does not
meet with the syntactic objections outlined in the first
chapter against the unstructured-sentential-operator theory
and has quite a few semantic benefits, among which avoidance
of the paradoxes of material implication, accomodation (with
some suplementation) of Stalnaker invalidities (antecedent-
strengthening and transitivity), contraposition, semi-factuals
and weak conditionals, explanation of the direction of
conditionship, parametric differences between apparent
equivalents, simplification of disjunctive antecedents and
impossible antecedents.

The third chapter, ''Truth Conditions: Reality and Modus
Ponens'', returns to the problem left aside in chapter 2. It
critically examines the three major essays in the refoundation
of conditional investigation, i.e. Adams (1965), Stalnaker
(1968) and Lewis (1973). As Lycan points out, two different
major paradigms emerged from these essays: the first one (from
Adams) in terms of an epistemic assertibility semantics (non-
truth-conditional); the second one (Stalnaker and Lewis) in
terms of a possible worlds truth-conditional semantics. Both
Adams' and Stalnaker's accounts stem from Ramsey's test.
Ramsey's test consists in adding the antecedent hypothetically
to one's present set of beliefs, revising this set where
necessary, and checking whether the consequent is part of the
revised set of belief. If it is, the conditional is
assertible, if not, it is not. Adams translated it in terms of
conditional probability relative to one's belief set,
considering that indicative conditionals are restricted to
epistemic assertibility and do not have truth-values. He said
nothing of subjunctive conditionals. Stalnaker recasted Ramsey
Test in terms of alternative possible worls with a selection
function based on similarity. Conditionals would be evaluated
by checking whether C holds in the world most similar to ours
where A holds. Notably, Stalnaker defends this as a truth-
conditional account of conditionals which he afterward adapted
for subjunctive conditionals. Lewis rejected the notion of a
uniquely nearest world with the accompanying acceptance of
Conditional Excluded Middle. He replaced it with the notion of
comparative similarity. Lewis' account was criticized for its
reliance on an intuitive notion of overall similarity, through
a number of counterexamples. He responded by discarding the
everyday notion of similarity and advocating a brand of
similarity specific to counterfactuals, though he was not
specific about it. This is deeply unsatisfactory as noted by
Lycan. The Ramsey Test is not immune from counterexamples
either, though they mostly center on the relativity to
epistemic situations it introduces. There are also
counterexamples to the proximity between the Ramsey Test
(taken to establish truth-value and not mere assertibility)
and Similarity Theory, based on the fact that the two accounts
do not always yield the same results. Notably, some exemples
examined through the Ramsey Test will contradict Modus Ponens.
This might be taken as an indication of the worthlessness of
the Ramsey Test in establishing truth-value. This would lead
to the choice of restricting the Reference class to ALL actual
relevant events, whether or not they are envisaged or not (the
Reality Requirement). However, Lycan points out that Modus
Ponens does raise more problems than it solves, notably
relative to Sobel sequences (i.e. ''if A then C'' may be false
eventhough ''If A and B then C'' and ''A and B'' are true). This
problem does not arise for Similarity accounts. However, it
does for Ramsey Test accounts. In the Event Theory, which can
be seen as a ''mixed view'', ''If A then C'' and ''If A and B then
C'' can be true. Lycan, after discussing a few objections,
turns to further counterexemples against Modus Ponens. One
question which the Event Theory has to face is whether the
reference class shifts when iteration or Sobel sequences are
involved in the antecedent. Lycan's answer is clearly
positive: this entails given up Modus Ponens as valid because
of its FORM.

In the previous two chapters, Lycan had described the two
great trends in approaching conditionals: the non-truth-valued
(NTV) view and the truth-valued (TV) view. Though his approach
tries to keep some of the advantages of the Ramsey Test, it is
clearly TV. The fourth chapter, ''In defense of Truth Value'',
offers some arguments for TV and counter-arguments for NTV.
Lycan begins by listing arguments against NTV: its
philosophical peculiarity; its linguistic bizareness; the fact
that conditional speech acts suppose sincerity and truth; the
many parallels between indicatives and subjunctives which make
it hard to claim that, for instance, only indicatives would
have truth-values; the possibility of embedding conditionals
in longer sentences, where assertibility can play no role;
their dependence on nomologicals, which goes against NTV; the
problem of deductive validity for deduction involving
conditionals; the problem of modals; and, finally, the problem
with deflationism (which implies that conditionals should have
truth-values). Lycan then shows that the Event Theory can
answer all the problems which NTV answers without giving up
truth-values. He now turns to what he calls the new horseshoe
theory (NHT), which tries to make conditionals equivalent to
material implication and to answers the numerous problems this
raises. His criticisms of NHT are based on the claims that
indicative conditionals are not restricted to the actual, that
the material implication leads to a clearly invalid inference
pattern (from ''not(if A then b)'' to ''A'', ''not-C''), and that it
cannot explain the validity of some clearly valid entailments.

Lycan then turns to ''A beautiful but false theory of 'even
if'''. He begins by claiming that ''even'' in ''even if'' means
just... ''even''. He distinguishes three views about ''even'', given
that ''even'' strongly implies a contradiction of contextual
presumptions: the minimal view, according to which ''even''
contributes nothing to the semantics of the sentence; the
conventional view, where the unexpectedness is supposed to be
a conventional (though non-truth-conditional) implicature; the
semantic view, in which ''even'' does have a truth-conditional
contribution to make. The last one is the one favoured by
Lycan, who defends the view that ''even'' expresses ''a
comparison of expectedness with a contextually indicated
reference-class'' (100). The specificity of ''even if'' is that
the meaning of a sentence where it occurs does not seem
conditional anymore. This leaves the role of the antecedent
open. The situation is however slightly more complicated,
given that the consequent may be entailed or not depending on
focus phenomena. Thus some ''even if'' conditionals entail their
consequent, while others do not. In fact, the Event Theory
answers these questions, and also answers the pragmatic
question of why the utterer asserts ''Q even if P'' where ''Q''
might seem sufficient. This leaves two questions unanswered:
the place of focus in the theory and the defence of the
semantic view of ''even''. This leads Lycan back to his begining
assumptions and to show that they can account for focus:
notably the idea that ''even'' adds to conditionals both the
widening of the reference class and a universal quantification
over all its members. There are, however two different
classes, the comparison class of conditions attached to the
''even if'' conditionals and the reference class of real
circumstances attached to the corresponding ''bare''
conditionals. Though the second is often a subclass of the
first, it is not always the case. This leads to a
reformulation of the original formulation for ''C even if A'',
where A is explicitly included in the comparison class. This
leaves Lycan with the defense of the semantic view of ''even
if'', for which he gives three arguments: the rarity of
semantically empty words in natural languages; evidence for
the fact that ''even if'' involves universal quantification; the
linguistic similarity between ''even'' and ''only'', which are
''syntactic soulmates'' (112) and ''logical contraries'' (113).

Lycan then turns to counterexamples to that theory which lead
him to ''An Unbeautiful but less easily refutable theory of
'Even If'''.He begins with four apparent counterexamples to the
theory, which drive him to definetively drop both the Reality
Requirement and Modus Ponens. There is a more serious
objection to the universal quantifier theory of ''even'' and
that is that ''even'' seems to allow of exceptions (e.g. ''I'll
eat anything on pizza, even squid or bull's testicles, but not
a brick or a crowbar''). This is the problem of the contrast
within the reference class. Weakening the quantifier to a less
than universal reading (''many'' for instance) would not however
be satisfying. A way of preserving the universal analysis is
to consider the comparison class as encompassing everything
''within reason''. This however seems rather ad hoc. Another way
of saving the universal hypothesis is to take ''even'' as
meaning not ''every...including...'' but ''every... plus...''. This means
that the Consequent-Entailment problem fades away: on this
analysis, ''Q even if P'' does not entail ''Q'', though the
assertion of ''Q even if P'' does most often amount to an
assertion of ''Q'', notably when the reference class is a
subclass of the comparison class.

Lycan then turns to ''The 'indicative'/'Subjunctive'
distinction''. Despite the great similarities between
indicative and subjunctive conditionals, there are some cases
where the indicatives and the corresponding subjunctives
differ in truth-values. Lycan begins by noting that the
difference is not a matter of grammatical moods and that the
terminology is, therefore, ill-chosen. He substitutes to it
''straight'' and ''boxarrow'' conditionals, noting that some so-
called indicative conditionals are not conditionals at all and
should be treated independently. After a reminder of some
theories of conditionals (Adams, Lewis, Stalnaker, etc.), he
turns to the distinction in the event theory. This turns out
to be, quite simply,a difference in reference classes,
indicated through ''lexical presumption''. This means that a
straight conditional and its boxarrow counterpart share their
logical forms but differ in the the values their parameters
take, and thus in truth-values. More precisely, a conditional
is straight when its utterer holds fixed a salient fact in his
epistemic field, while it is boxarrow if the utterer neglects
contextual facts and considers a wider range of possibilities.
The Law of Conditional Excluded Middle (CEM) fails for
boxarrows and, according to Lycan it also fails for straights.
Finally, the straight/boxarrow distinction does not seem to
apply to future conditionals.

Finally, Lycan turns to a well-known example, ''The Riverboat
Puzzle'' in which (Simple version) a henchman signals to one of
players what the cards of the other player are, then leaves.
He utters two conditionals, one straight, one boxarrow. In the
anomalous version, a second henchman, better informed (he has
seen the hands of both players), utters conditionals with the
same antecedents but the opposing consequents. Considering
only the straight versions, it is claimed that they are both
true and that it seems that the law of Conditional
Noncontradiction does not hold. This has been used to argue
for NTV. Lycan counterargues that in fact the first henchman's
conditional is a backtracker, evaluated by holding fixed the
present actual fact which is the most jarring relative to the
counterfactual and adjusting other facts to make the
counterfactual true. Backtrackers are not incompatible with
ordinary conditionals and hence the law of conditional
noncontradiction is not violated.

There are two appendixes to the book, the first one conjointly
written by Lycan and Geis and the second one by Lycan alone,
both on Nonconditional Conditionals (NCCs). In the first one,
Geis and Lycan begin by justifying the claim that some
apparently conditional sentences are not, in fact, conditional
(e.g. Austin's example: ''There are biscuits on the sideboard
if you want them'') by showing that they do not satisfy a list
of syntactic, semantic or pragmatic features which are typical
of conditionals. This raises two questions: what is the
function of antecedents of non-conditional conditionals and
how is it that non-conditional conditionals are interpreted as
such, without any need for disambiguation from bona fide
conditionals? A tentative answer to the first question is that
consequents are indeed what is asserted in NCCs, while
antecedents articulate some ''felicity condition'' of the
consequent assertion, though sincerity conditions are
excluded. This raises a new question. Why should this be
expressed through a ''phony antecedent adverbial''? Another
tentative answer to that new question is that the antecedents
of NCCs, as the antecedents of bona fide conditionals, make
explicit possibilities. Geis and Lycan then lists some less
obvious types of NCCs which form a continuum but makes it even
less easy to link NCCs with regular conditionals. In the
second appendix, Lycan comes back to the problem of the
semantics of NCCs, suggesting that NCCs could be accomodated
in the Event Theory if the reference class is taken to include
no non-Q event. This answers the third and fourth of the
queries above, the second one being tackled through pragmatic
considerations. Lycan's pragmatic answer is that NCC
antecedents are metalinguistic and thus clearly not bearing a
conditional relation to the consequent, which excludes NCCs
being perceived as ambiguous.

Lycan began his career as a philosopher of language, has
become best known in the past few years as a philosopher of
mind and this book comes as a reminder that he still is a
foremost philosopher of language. Lycan's book is extremely
interesting and seems quite successful in combining the
insights of both the Ramsey Test and Similarity Theory in a
unified truth-conditional theory of conditionals. It also
seems to take satisfactorily into account the syntactic
features so often neglected by logicians. It does not eschew
the difficulty which non-conditional conditionals have put in
the path of semantic theories of conditionals. The book is
thus well worth reading and indeed should, I think, be read by
anyone interested in the subject.

However, I want to insist on the fact that the book is clearly
not for beginners: extended knowledge of the field is needed.
It should also be said that it is a comparatively short book
(210 pages, including the appendixes) and that it has a high
level of content, making for a rather dense, though quite
clear, book. I think it might have been easier to read of it
had been some fifty pages longer. However, it is a must for
any one interested in conditionals and conditional reasoning.

Adams, E.W. (1965), ''The logic of conditionals'', INQUIRY 8,

Lewis, D. (1973), Counterfactuals, Cambridge, Mass., Harvard
University Press.

Stalnaker, R. (1968), ''A theory of conditionals'', in N.
Rescher (ed.), Studies in Logical Theory, Oxford, Blackwell.
Anne Reboul is a First Class Research Fellow at the French
Center for Scientific Research (CNRS) in France. She has a
Ph.D. in Linguistics (EHESS, Paris) and a Ph.D. in philosophy
(University of Geneva, Switzerland). She has written some
books, among which an Encyclopaedic Dictionary of Pragmatics
and quite a few papers in French and English, on pragmatics
and/or philosophic subjects.

Format: Hardback
ISBN: 0199242070
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Pages: 234
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