Download 1. Backhanded Sentences We are attending a modern art exhibit

CLS 49: April 18, 2013
That’s Not Art: Backhanded Sentences and Distant Worlds
Patrick Munoz
1. Backhanded Sentences
We are attending a modern art exhibit, and you are singing exhortations to a particularly
amorphous work on display. Incredulous, I say:
(1) If that’s art, then I’m a sperm whale.1
I call sentences like (1) backhanded sentences. Some variants:
(2) If that’s art, then my pet dinosaur can fly.
Or, if I wish to voice my approval:
(3) Either that’s art, or I’m a sperm whale.
(4) Either that’s art, or my pet dinosaur can fly.
Their asserted content is irrelevant to their meaning; this is all shouldered by what they imply.
• They need not be, and are almost always not, believed by the speaker or interlocutor.
(5) I changed my mind–that is art! So I’m a sperm whale, then.
• They can’t be denied by negating their asserted content.
(6) No, if that’s art, then you’re a whale shark, not a sperm whale.
How do these implications arise?
2. Features
• Logically complex: consist of two proposition-denoting clauses, whose propositions I
label p and q.
• Can be either conditional (1-2), or disjunctive (3-4).
• Imply something about p, the first clause:
Conditional (1-2): “That’s not art.”
(1) If [that’s art]p, then [I’m a sperm whale]q.
(2) If [that’s art]p, then [my pet dinosaur can fly]q.
Disjunctive (3-4): “That is art.”
(3) Either [that’s art]p, or [I’m a sperm whale]q.
(4) Either [that’s art]p, or [my pet dinosaur can fly]q.
• Engender the appropriate implication by the presence of q.
• q is agreed by the speaker and interlcutor not to be true in the actual world.
(1, 3): Empirical falsehood: I am not a sperm whale.
(2, 4): Presupposition failure: my pet dinosaur is a definite description denoting a nonexistent entity.
3. Outlandishness and Hyberbolical Implication
Two crucial characteristics of backhanded sentences are as follows.
Outlandishness: q must not only not be true in the actual world, but somehow “egregiously” so; a
“slight” falsity (8), or a “plausible” existential presupposition failure (9) causes the implication to
falter.
1
A common variant is the “Queen of England” sentence: “If that’s art, then I’m the Queen of England.” These
conventionalized examples tend to be somewhat easier to interpret, but I have avoided them so as to make clear that
the meaning of backhanded sentences is productive. Likewise, (3) commonly appears with variants like, “or I’ll eat
my hat,” and “or my name isn’t [name].”
CLS 49: April 18, 2013
That’s Not Art: Backhanded Sentences and Distant Worlds
Patrick Munoz
(8) If [that’s art]p, then [I’m wearing a light gray shirt]q. [where I’m wearing a dark gray
shirt]
(9) If [that’s art]p, then [my pet canary can fly]q. [where I own a parrot and not a
canary]
I term this “egregious” untruth outlandishness. (8) and (9) show that outlandishness, and not
mere untruth in the actual world, is required for the implications of backhanded sentences to be
effective.
Hyperbolical Implication: While (10) and (11) below both mean “that’s not art,” this meaning
stated explicitly in (10), and implied in (11). The implied meaning in (11) is intuitively
“stronger” than the stated meaning in (10); that is, the implications of backhanded sentences are
hyperbolical.
(10) That’s not art.
(11) If that’s art, then I’m a sperm whale.
These two features are crucially related, as will be shown.
4. Desiderata
An account of backhanded sentences should explain:
(a) Why they require a complex logical structure
(b) Why their conditional and disjunctive forms have opposite implications
(c) Why q licenses existential presupposition failures w.r.t. the actual world
(d) In what sense “egregious” existential presupposition failures and falsities can be
commonly considered outlandish, and both engender the implications
(e) Why mere untruth is insufficient for the implication, and outlandishness is required
(f) Why backhanded sentences result in hyperbolical implications
5. A Gricean Approach
Perhaps these implications can be treated as the result of syllogistic reasoning, derivable from the
logical structure of backhanded sentences and some simple Gricean assumptions, evaluated with
respect to the actual world.2 For instance, let us say that (12) is a material conditional, of the
form p → q.
(12) If [that’s art]p, then [I’m a sperm whale]q.
p→q
(i) p → q is true. [Maxim of Quality; the speaker tells the truth]
(ii) q is false. [Agreed by speaker and interlocutor]
(iii) Therefore, p is false. [From (i), (ii), by Modus Tollens]
This is a propositional inference of classical logic; the consequent is false, so the antecedent must
be rejected in order to preserve the truth of the conditional.
Similar pragmatic-logical reasoning applies for the disjunctive cases, but in the form of a
Disjunctive Syllogism; one disjunct is false, and so the remaining one must be true.
But this does not account for:
2
See, e.g. Sadock (1977) for an account of similar sentences as a conventionalized Modus Brevis.
CLS 49: April 18, 2013
That’s Not Art: Backhanded Sentences and Distant Worlds
Patrick Munoz
•
•
•
The presence of existential presupposition failures, which should render the sentences
incalculable w.r.t. the actual world
The impotence of non-“egregious” untruth; mere falsity should function here, with no
requirement of outlandishness
The hyperbolical implication of backhanded sentences; what is implies here is merely
that p or that ¬p, which does not encode any emphasis
6. Distant Worlds
As a crude appropriation of Lewis (1973: 13-16)’s “system of spheres” approach to
characterizing possible worlds, we can rank possible worlds against one another according to
how similar or dissimilar they are to some world w (the actual world, etc.). We can characterize
increasing dissimilarity to this world in terms of distance. We can then further create a
distinction between worlds close to w, and worlds distant from it.
Using this schema, we can provide a characterization of outlandishness:
A proposition is outlandish iff it is neither true in the actual world, nor in any worlds
close to the actual world.
We thus characterize backhanded sentences requiring that the speaker and interlocutor agree that
q is outlandish in this sense; and this subsumes the “egregiousness” of the falsity and
presupposition failures seen above.
7. Asserted Content
We can treat conditional and disjunctive backhanded sentences as universal quantifications over
possible worlds.
Conditional
For all worlds of evaluation w: if p is true in w, then q is true in w.
∀w[p(w) → q(w)]
Disjunctive
For all worlds of evaluation w: either p is true in w, or q is true in w.
∀w[p(w) ∨ q(w)]3
8. Deriving the Implied Meaning
Conditional: ∀w[p(w) → q(w)]
(i)
q is neither true in the actual world, nor in any world close to it (q is outlandish).
[Definition of outlandishness; speaker and interlocutor agree that q is outnlandish]
3
Inclusive disjunction is assumed, but the reasoning in §8 where it is put to use follows equally with an exclusive
interpretation.
CLS 49: April 18, 2013
That’s Not Art: Backhanded Sentences and Distant Worlds
Patrick Munoz
(ii)
Any world in which p is true is one in which q is true. [Literal content of
conditional]
(iii)
p is neither true in the actual world, nor in any world close to it (p is outlandish).
[From (i), (ii)]
Crucially, the implication is that p is outlandish, not merely false.
The same derivation can be carried out for disjunctive sentences, but with the antecedent flipped,
since [∀w[p(w) ∨ q(w)]] ⟷ [∀w[¬p(w) → q(w)]]. The result will be the same, but with the
antecedent negated; the disjunctive sentences imply that ¬p is outlandish.
9. So What?
(a) Why do they require a complex logical structure?
Two propositions are required for the above derivation of the implication. What is
achieved is not possible by means of a single proposition; the roundabout mechanism is
needed because the goal is to imply outlandishness.
(b) Why do their conditional and disjunctive forms have opposite implications?
Their logical structure differs only with respect to the negation of the antecedent; thus,
one implication is the negation of the other.
(c) Why does q license existential presupposition failures w.r.t. the actual world?
The sentences are not evaluated w.r.t. the actual world, but w.r.t. all worlds w, and the
“egregious” presuppositions need not be satisfied anywhere for the conditional to hold;
but they might be in distant worlds, where pet dinosaurs exist!
(d) In what sense are “egregious” existential presupposition failures and falsities considered
outlandish, and both engender the appropriate implications?
Both are neither true in the actual world, nor in any worlds close to it, and so behave the
same way with respect to the derivation.
(e) Why is mere untruth insufficient for the implications, and outlandishness required?
The purpose of backhanded sentences is to imply outlandishness of p or ¬p, not their
mere untruth, and this can only be implied if q is outlandish.
(f) Why do backhanded sentences result in hyperbolical implications?
They imply that p or ¬p is outlandish, meaning that one would have to be far from
actuality to attain the opposite; they are in effect “very false” or “very true.”
•
•
•
Backhanded sentences round out the theoretical notion of distance between possible
worlds, by focusing on distant rather than close worlds, as is done e.g. with
counterfactuals.
They give us further reason to suppose that the consideration of possible worlds is
structured according to similarity, and not flatly organized; and that speakers exploit this
knowledge.
They provide an example of a rhetorical phenomenon having a principled logical and
semantic grounding.4
4
References
Lewis, David (1973). Counterfactuals. Oxford, UK: Blackwell.
Sadock, Jerrold (1977). “Modus Brevis: The Truncated Argument.” In W. Beach, S. Fox, and S. Philosoph, eds,
Papers from the 13th Regional Meeting of the Chicago Linguistics Society, 545-554. Chicago, IL: Chicago
Linguistics Society.