changes.diff

diff --git a/alt/conventional-truth.markdown b/alt/conventional-truth.markdown
index b0f7256..9121d97 100644
--- a/alt/conventional-truth.markdown
+++ b/alt/conventional-truth.markdown
@@ -1,15 +1,14 @@
 ---
-title: "There’s nothing special about conventional truths"
+title: "Containing Conventionalism"
 author: "Alex Dunn"
 ---
 
 # Introduction
 
-Quine's attack on the idea of truth by convention [-@quine1966] is
-specifically an attack on the idea that *logical truths* are true by
-convention.  He accepted that there might be conventional truths, and
-merely tried to show that mathematical and logical truths are not
-among them.  Quine's argument is that if the infinity of mathematical
+The doctrine of truth by convention has been in decline for over half
+a century.  The most important early objections came from Quine, but
+they were limited to is the idea that *logical truths* are true by
+convention [-@quine1966].  In brief: if the infinity of mathematical
 and logical truths are all conventional, there has to be some *general
 rules* to generate them all [@quine1966].  One rule might be "for any
 $P$ and $Q$, if '$P$' is true and 'if $P$, then $Q$' is true, then
@@ -23,13 +22,34 @@ which is *not* conventional.  And since the "if" and "then" of that
 pre-existing language are not conventional, logical truths expressed
 using *them* will not be conventional truths.
 
-But Quine concedes more than he needs to.  I'm going to present a
-*general* objection to the notion of conventional truth.  Instead of
-arguing that a particular class of truths (like those of logic) aren't
-conventional, I'm going to argue that there just *are no conventional
-truths.*
-
-## What is conventional truth, and why do we want it?
+This was a major blow, because the whole reason philosophers were
+drawn to conventional truth in the first place was to explain how we
+can know logical truths, mathematical truths, and conceptual truths *a
+priori*.
+
+Some conventionalists were content to retreat to the far more modest
+claim that conventional *versions* of the non-conventional logical
+truths can be introduced *using* them; someone who introduced an
+artificial language could know *its* truths *a priori*.
+
+But there is a further, general objection to the notion of
+conventional truth which has become widely accepted in recent years.
+If a sentence $S$ is *stipulated to be true,* what does it mean?  What
+proposition does someone sincerely uttering it express?  If $S$ is
+introduced to be true no matter what the world is like, then how can
+it be used to say anything at all?
+
+There is one possible definition of conventional truth that avoids
+these objections, but it is a further weakening of the doctrine.  The
+last refuge of the conventionalist is to define "conventional truth"
+as "something the truth of which is explained by convention(s)."  The
+weakness is because, I'll argue, whether something explains something
+else is relative to an audience and a context.  If such conventional
+truths can be known *a priori,* therefore, it will only be by *some*
+people at *some* times.  It's not clear that this is still a doctrine
+worth defending.
+
+# What is conventional truth, and why do we want it?
 
 There are a few different things people mean by "conventional truth":
 something that's *made true* by a convention, something that's true
@@ -58,11 +78,14 @@ Minaj is a musician?
 This is an epistemological problem, so the solution will start and end
 in epistemology.  One epistemological solution is to suggest that we
 "perceive" the truth of mathematical and logical facts by means of
-some faculty of "intuition".
+some faculty of "intuition".  But, arguably, "no one has succeeded in
+saying what this faculty really is nor how it manages to yield the
+relevant knowledge. 'Intuition' seems like a name for the mystery we
+are addressing, rather than a solution to it" [@boghossian2000 231].
 
-The notion of conventional truth was developed as an
-alternative to that solution.  This alternative is what Paul
-Boghossian calls the "analytic explanation":
+The notion of conventional truth was developed in response to the
+shortcomings of "intuition".  The doctrine of conventional is part of
+what Paul Boghossian calls the "analytic explanation":
 
 > The central impetus behind the *analytic* explanation of the a
 > priori is a desire to explain the possibility of a priori knowledge
@@ -89,7 +112,8 @@ does grasping the meaning of "$2 + 2 = 4$" suffice to justify our
 belief?  Why is that enough?
 
 It's at this stage that certain metaphysical theses have been added to
-the solution to fill this explanatory gap.
+the solution to fill this explanatory gap, most notably the doctrine
+of conventional truth.
 
 One such metaphysical thesis is that the truth of mathematical and
 logical sentences (or the truth of the propositions expressed by
@@ -111,12 +135,7 @@ the oddness well:
 >
 > How could the mere fact that $S$ means that $p$ make it the case that
 > $S$ is true? Doesn't it also have to be the case that $p$
-> [-@boghossian1960 364]?
-
-Boghossian also cites Gilbert Harman, who points out that even
-"tautologies" such as that *I am myself* depend for their truth on
-facts about the world—in this case, the fact that all things are
-self-identical.
+> [-@boghossian1996 364]?
 
 I think this objection is ultimately correct, but it's worth
 describing the situation in a bit more detail.  Rudolf Carnap and
@@ -160,6 +179,20 @@ sentence without reference to the world and then use it to express
 something---a proposition---which necessarily says something about the
 world.
 
+This is true even for "tautologies" such as "I am myself" and "all
+cats are cats."  These also depend for their truth on facts about the
+world—in the first case, the fact that all things are self-identical,
+and in the second the fact that for all $x$, if $Fx$ then $Fx$.  It's
+true that "all cats are cats" is true in part because of language
+conventions governing the meanings of the constituent terms---it
+wouldn't have been true if "all" meant "no"---but once the meaning is
+fixed there's the further question of whether the proposition an
+utterance of it, meant literally, expresses.  If it's not also true
+that *all cats are cats,* then "all cats are cats" isn't true.  And
+whether all cats are cats has nothing to do with convention.  All cats
+are cats because of the general logical truth that for all $x$, if
+$Fx$ then $Fx$.  (And that's not true by convention either.)
+
 If one replies that not all propositions say things about the world,
 and so need not depend on facts for their truth; I think then we would
 be disagreeing over what a proposition is.  A "conventional truth" the
@@ -178,7 +211,7 @@ $A$ is sometimes sufficient to know that you will do or even are doing
 $A$, having an intention to use a sentence $S$ in such a way that it's
 true may be sufficient to know that $S$ is true: "in intending to use
 my terms in such a way that $S$ is true, given the way I am using my
-temrs, I know directly that $S$ is true, given the way I am using my
+terms, I know directly that $S$ is true, given the way I am using my
 terms" [@harman1996 393].
 
 There are some things that we can know we are doing (or are going to
@@ -213,7 +246,7 @@ something true without knowing whether the world is as I say it is.
 These considerations, expressed so well by Boghossian, in fact
 undermine his own notion of "implicit definition" with which he tries
 to develop a non-conventional explanation of how we know logical
-truths *a priori.* I believe that it is simply conventionalism in
+truths *a priori.* I believe that it is simply Conventionalism in
 disguise:
 
 Implicit definition
@@ -232,7 +265,7 @@ the world is like.
 
 Boghossian appeals to Kripke's example of the meter-stick in order to
 claim that his "implicit definition" is legitimate in a way that
-conventionalism is not:
+Conventionalism is not:
 
 > To help us think about this, consider Kripke's example of the
 > introduction of the term "meter". As Kripke imagines it, someone
@@ -242,7 +275,7 @@ conventionalism is not:
 > 1. Stick $S$ is a meter long at $t$.
 >
 > Suppose that stick $S$ exists and is a certain length at t. Then it
-> follows that "meter" namees that length and hence that (1) says that
+> follows that "meter" names that length and hence that (1) says that
 > stick $S$ is that length at $t$, and since it is that length at $t$,
 > (1) is true.
 >
@@ -264,7 +297,7 @@ priori* truth if introduced this way.  And to instead say something
 like "'Stick $S$ is a meter long at $t$' is true at this world and all
 those where $S$ is a meter long" would be to presuppose a meaning for
 "meter" in the process of defining it---the same mistake Quine found
-in the original conventionalism.
+in the original Conventionalism.
 
 Only certain sentences seem to work as "implicit definitions" of
 constituent terms.  In Boghossian's word, only some are
@@ -274,13 +307,15 @@ implicit definition at all, but the use of a sentence *non-literally*
 to perform an *explicit* definition.  Suppose I want to introduce the
 term "floop".  I say to you "this book is one floop thick."  I am not
 using the sentence literally because "floop" is not yet part of your
-ideolect, and I know that.  Nor do I mean to stipulate that the
-sentence I uttered is true.  What I mean is instead something like
+ideolect, and I know that (it surely violates some conversation maxim
+to use a term that I know my audience doesn't understand, without
+first providing them a definition). Nor do I mean to stipulate that
+the sentence I uttered is true.  What I mean is instead something like
 "let 'floop' designate the thickness of this book."
 
 ## One last try
 
-The major issue for conventionalism was the idea that a sentence could
+The major issue for Conventionalism was the idea that a sentence could
 be declared true, without reference to the world that makes it so.
 This, however, suggests a way forward---though it is a bit desperate.
 The problem for conventional truth as I've presented it is that it
@@ -298,17 +333,18 @@ corresponding convention exists; and how could that be known *a
 priori?*
 
 Maybe it's possible for someone to know a conventional truth *a
-priori* if they themselves institute the convention.  If *I* stipulate
-that *S* is true, then how can I fail to know that I've done so?  On
-this line of thought, conventional truths are contingent *a priori*
-truths.  They arise by stipulation, just as do the contingent *a
-priori* truths discussed by Kripke in *Naming and Necessity*.
-
-This explaination of why conventional truths are *a priori* has an
-obvious problem: only the person who stipulates a conventional truth
-can know it *a priori*.  Just as it's only *a priori* for whoever
-performs the "dubbing" that this bar is a meter long, so it's only *a
-priori* for whoever makes the stipulation that some *S* is
+priori* if they themselves institute the convention.  If *I* introduce
+the convention that makes *S* true, then how can I fail to know that
+I've done so, and therefore also that $S$ is true?  On this line of
+thought, conventional truths are contingent *a priori* truths.  They
+arise by stipulation, just as do the contingent *a priori* truths
+discussed by Kripke in *Naming and Necessity*.
+
+This explanation of why conventional truths are *a priori* has an
+obvious problem: only the person who performs the stipulation can know
+the corresponding truth *a priori*.  Just as it's only *a priori* for
+whoever performs the "dubbing" that this bar is a meter long, so it's
+only *a priori* for whoever performs the stipulation that *S* is
 (conventionally) true.
 
 This is unfortunate, but it's not unique to my version of
@@ -365,9 +401,6 @@ priority.  Let's assume, then, that *if* there are truths that are
 true because of, or in virtue of, a convention, then they can be known
 *a priori*.
 
-The rest of this paper will be arguing that the antecedent of that
-conditional is false.  There aren't any truths of that sort.
-
 # Three proposed definitions
 
 1. Conventional truths are *made true by* conventions;
@@ -397,9 +430,10 @@ If this division is correct, then we have two questions to answer:
 2. Is a conventional truth something the truth of which is *explained*
    by (the existence of) a convention?
 
-My answer to both will be "no"; and if there are no better candidate
-definitions for "conventional truth", then the upshot is that there
-probably aren't any.
+My answer to the first will be "no".  My answer to the second will be
+"only in some contexts".  If there are no better candidate definitions
+for "conventional truth", then the upshot is that whether something is
+a conventional truth is a relative affair.
 
 # Entailment relations
 
@@ -413,7 +447,7 @@ In this section I need to do two things:
    is entailed by (the existence of) a convention" can't work as a
    definition of "conventional truth."
 
-### *is made true by* $=$ *is entailed by*
+## *is made true by* $=$ *is entailed by*
 
 This section won't be entirely conclusive; the best I can do is
 explain why I think that these relations are identical, and address
@@ -532,9 +566,9 @@ difference between conventional and other truths.  The problem was
 that it boils down to nothing more than first-order logical
 entailment; we need something more robust.  The relation of *is true
 because of,* or, equivalently, *is true in virtue of,* might better
-serve our purpose.  (Spoiler: I don't think it will.)
+serve our purpose.
 
-Again I've got two tasks:
+I'll be doing two things in this section:
 
 1. Justify my claim that the *is true because of* and *is true in
    virtue of* relations are the same explanatory relation; and
@@ -542,8 +576,10 @@ Again I've got two tasks:
 2. Show the following: being explained by (the existence of) a
    convention is not what makes conventional truths special, and so
    why "truth which is explained by (the existence of) a convention"
-   can't work as a definition of "conventional truth," at least not if
-   we want there do be conventional truths *full stop.*
+   can't work as a definition of "conventional truth"---at least not
+   if we want there do be conventional truths *full stop*.  But it may
+   be the conventionalist's only option to accept a notion of
+   conventional truth that's relative.
 
 ## "because of" and "in virtue of"
 
@@ -588,7 +624,7 @@ explain why a given conventional truth is true.
 But whether or not this proposal is true depends on what an
 explanation is.
 
-## What's an explanation?
+## What explanation isn't
 
 The classic deductive-nomological theory treats explanations as a
 subset of entailments. A deductive-nomological "explanation" as to why
@@ -611,10 +647,13 @@ Carla has not become pregnant:
 4. Therefore, Carla has not become pregnant.
 
 Carla has failed to become pregnant not because she's taking birth
-control, but because she doesn't have a womb.  *That's* the relevant,
-explanatory bit of information, but the deductive-nomological model
-treats all laws as (equally) explanatory, at least with regard to
-deductions that they're essential to.
+control, but because she doesn't have a womb.  "Nobody without a womb
+becomes pregnant" is a more explanatory law on account of its
+increased generality and lack of irrelevant information, but the
+deductive-nomological model treats (3) as equally explanatory.  Indeed
+it treats *all* laws that are essential to these deductive-nomological
+"explanations" as explanatory to the same degree, ignoring the role
+that relevance plays in determining explanatoriness.
 
 Another problem for the deductive-nomological theory is that the
 "explanations" it produces are symmetric.  For example, both of the
@@ -719,18 +758,20 @@ says that something is explanatory just to the extent that it's
 indicative of the content of an ideal text.  That's not what
 "explanatory" actually means, and we can see this when we see that
 this is a perfectly sensible question: *what if the ideal text is not
-explanatory?*  Railton is committed to the answer to this question
-always being "no," *by definition*.  But it's not, because
-"explanatory" does not mean what he thinks it means, and an
-explanation is not what he thinks it is.
+explanatory?* Railton is committed to the answer to this question
+always being "no," *by definition*.  But it's not, because as we've
+seen *relevancy* is an essential part of the meaning of
+"explanation"---and Railton's ideal text might not be relevant in all
+situations.  Ultimately, "explanatory" does not mean what he thinks it
+means, and an explanation is not what he thinks it is.
 
 *Explanations are aids to understanding*.  If what I say does not help
- you understand why $p$, I have not explained $p$ to you.  Railton
- abstracts away from the fact that explanations are *offered* from one
- person to another.  By treating them as abstract objects that could
- theoretically exist in a world with no people at all, he loses sight
- of what is constitutive of explanations: their role in aiding *our*
- understanding.
+you understand why $p$, I have not explained $p$ to you.  Railton
+abstracts away from the fact that explanations are *offered* from one
+person to another.  By treating them as abstract objects that could
+theoretically exist in a world with no people at all, he loses sight
+of what is constitutive of explanations: their role in aiding *our*
+understanding.
 
 ## Explanations are aids to understanding
 
@@ -748,7 +789,7 @@ because it doesn't help you understand why cats have tails.
 
 *****
 
-Jeb Lund recently proposed a revisionary definition of "sandwich" in
+Last year Jeb Lund proposed a revisionary definition of "sandwich" in
 the *Guardian* such that when he says "a hot dog is a sandwich," what
 he says (or at least what he means) is true.  His definition of
 "sandwich" is "a portable, relatively tidy meal inside a bread
@@ -847,13 +888,13 @@ people's interests, *nothing* is an explanation *full stop*.
 
 ## An objection
 
-We may have gone slightly astray, however, because "a hot dog is a
-sandwich" is not actually a conventional truth in the sense we're
-interested in.  It's what Quine would call a "truth definitionally
-abbreviated" [-@quine1966 72].  Lund, by defining "sandwich" as
-"portable, relatively tidy meal inside a bread conveyance," has
-introduced a convention of abbreviation: "sandwich" simply
-*abbreviates* "portable, relatively tidy meal inside a bread
+I used the hot dog example because it is nice and straightforward, but
+of course "a hot dog is a sandwich" is not actually a conventional
+truth in the sense we're interested in.  It's what Quine would call a
+"truth definitionally abbreviated" [-@quine1966 72].  Lund, by
+defining "sandwich" as "portable, relatively tidy meal inside a bread
+conveyance," has introduced a convention of abbreviation: "sandwich"
+simply *abbreviates* "portable, relatively tidy meal inside a bread
 conveyance" as a result of this definition.  And all a definition
 does, as Quine pointed out, is to *transmit* truth [-@quine1966 71].
 If "a hot dog is a portable bread meal" is not (already) true, then "a
@@ -924,8 +965,8 @@ not involve any particular convention.  Therefore $\ulcorner$If $P$
 and $P \rightarrow Q$, then $Q\urcorner$ is *not* a conventional truth
 *full stop*.  And it seems to me that there is no such thing.
 
-Corey McGrath offers one last-ditch attempt to salvage the notion of
-conventional truth:
+Corey McGrath offers one last-ditch attempt to salvage a notion of
+conventional truth (full stop) in terms of explanation:
 
 - $\ulcorner P$ is a conventional truth$\urcorner$ $=_{df}$
   $\ulcorner$it is impossible to explain to someone *who does not know
@@ -939,19 +980,87 @@ definitionally abbreviated.  Adopting definitional abbreviations (even
 if that is a conventional process) does *not* produce conventional
 truths.
 
+# The last hope for Conventionalism: relativity
+
+As unappealing as the idea will be to many, it may be possible to
+salvage the notion of conventional truth as a relative thing.  $S$
+might then be a conventional truth for me, but not for someone else.
+
+This is not as disastrous as it seems, when we take into consideration
+how much the conventionalist has already given up.  Remember that
+Geoffrey Hellman was already compelled, by the force of Quine's
+criticisms, to limit conventional truths to the domain of artificial
+language.  It was already true, then, that the *a priori* knowledge
+provided by apprehension of conventional truths was limited to those
+engaged in explicit stipulation.
+
+I admit that it's not yet clear to me what truths could be explained
+by (the existence of) a convention and also known *a priori.* We
+*want,* of course to be able to include (artificially stipulated)
+logical truths in this group.  However, that will first require
+stipulating conventional versions of the logical connectives, and I'm
+not sure how that is possible in the case of some, including $=$.  How
+do we define a "$=^{*}$" such that our justification for believing
+propositions involving it does not ultimately trace back to our
+knowledge of $=$?  For example, I cannot see how Hellman's attempt is
+satisfactory:
+
+> Self-identity is a paradigm example of what I would call a
+> "stipulated universal trait": we introduce "$=$" (or can: if anyone
+> insists that the symbol "$=$" already has another use, we choose a
+> new symbol, "$=^{*}$") by stipulating that, in any context whatever,
+> including all modal and counterfactual contexts, "$=$" ("$=^{*}$")
+> holds just between any object and itself [-@hellman1998 194].
+
+When it comes time to evaluate whether $x =^{*} y$, what do we do?
+The instruction provided by our definition of "$=^{*}$" is more or
+less "are they *really* identical?"  The buck gets passed back to the
+original, non-conventional $=$: we're only justified in believing that
+$x =^{*} y$ if we're also justified in believing that $x = y$.
+
+This is not to deny Hellman's point from earlier, that the
+conventionalist can be satisfied with defining the conventional in
+terms of the non-conventional:
+
+> Here what is at stake is whether knowledge of language suffices for
+> knowledge of the soundness of logical rules. (Since the rules govern
+> the logician’s regimented language, that is the one that is
+> relevant, of course.) It is quite irrelevant that the satisfaction
+> conditions cannot serve the purposes of first language acquisition
+> [-@hellman1998 199].
+
+As he admits, it's not enough to define "$=^{*}$" in terms of "$=$".  Our
+knowledge of the soundness of "$=^{*}$" must be based in knowledge of
+language.  But as far as I can tell, using his definition, it's not.
+Rather, it's based in metaphysical facts about identity.
+
 # Conclusion
 
-The claims I've made, and tried to defend, are these:
+This, then, is the corner we've driven Conventionalism into:
+
+- Quine showed that the justification for our beliefs about logic,
+  math, etc., is not based in convention unless we introduce
+  artificial versions of the logical and mathematical terms "on top
+  of" the original, non-conventional ones.
+
+- To simply stipulate that some sentence $S$ is true does not yield
+  anything that can be used to express a proposition.  "Conventional
+  truths" as commonly conceived are incapable of being really true
+  *or* false because (by design) they say nothing about the world.
+
+Our novel solution of defining "conventional truth" as something
+made true by or true in virtue of a convention is a poor alternative:
 
 - We cannot identify what's special about conventional truths by
   appealing to the entities (states of affairs, or facts, or tropes)
   that entail them.
 
-- We can't appeal to the facts that *explain* them either, because
-  there are no explanations in isolation---something is an explanation
-  only in a context, which includes individuals and their interests.
-  "A hot dog is a sandwich" is true because of a conventional fact in
-  one context (when the explanation refers to the convention of using
+- We can't motivate a non-relative notion of conventional truth by
+  appealing to the facts that *explain* them either, because there
+  are no explanations in isolation---something is an explanation only
+  in a context, which includes individuals and their interests.  "A
+  hot dog is a sandwich" is true because of a conventional fact in one
+  context (when the explanation refers to the convention of using
   "sandwich" with a stipulative meaning), but is true because of
   non-conventional facts in other contexts (when the explanation
   refers to the physical properties of a hot dog).  Even
@@ -963,10 +1072,11 @@ The upshot seems to be that the closest thing we can do is define
 "conventional truth" as "truth explained by (the existence of) a
 convention," a definition which results in truths being convention in
 some contexts and not in others.  "Conventional truths" in this sense
-cannot solve the epistemological problem that they were introduced to
-solve.
+may be able to ground *a priori* knowledge in a limited way, but there
+are immediate obstacles to this approach as well.  It may be finally
+time to give up on conventional truth.
 
 \section*{Acknowledgments}\label{acknowledgments}
 
-Many thanks to Corey McGrath for conversation and references on this
-topic.
+Many thanks to Corey McGrath and Juliana Lima for conversation and
+references on this topic.