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\title{A new route to the necessity of origin}

\author{Guy Rohrbaugh and Louis deRosset}
\begin{document}
\maketitle
\begin{abstract}
  Saul Kripke has claimed that there are necessary connections between
  material things and their material origins.  The usual defenses of
  such necessity of origin theses appeal to either a sufficiency of
  origin principle or a branching-times modal of necessity.  In this
  paper we offer a different defense.  Our argument proceeds from more
  modest `independence principles,’ which govern the processes by
  which material objects are produced. Independence principles are
  motivated, in turn, by appeal to a plausible metaphysical principle
  governing such processes, their invulnerability to non-local
  prevention.  We outline the new argument, and distinguish it from
  both of the usual defenses.
\end{abstract}
\section{Introduction}
Saul Kripke \citeyearpar[112--4]{Kripke:1980} has claimed that there
are necessary connections between material things and their material
origins. His presentation of such necessity of origin theses included
two paradigmatic examples: that it is impossible for a particular
table to have been constructed from any hunk of matter other than that
from which it was actually constructed, or for a particular human
being to have originated in gametes other than those in which he or
she actually did.  Necessity of origin theses (henceforth, simply
`origin theses') are now standard examples of so-called metaphysical
necessities, though unlike many other examples, they posit necessary
connections between distinct individuals.  Despite their familiarity,
the conceptual grounds of origin theses are less clear than is usually
supposed. Kripke's influential discussion provides only the briefest
sketch of an argument. More explicit treatments have since been
offered, but all of these turn out to be variations of just two
strategies. J. L.  Mackie and Penelope Mackie suggest that origin
theses are grounded in a branching times model of necessity. Nathan
Salmon, Colin McGinn, Graeme Forbes, and others suggest that such
theses are grounded in a further principle, the sufficiency of
origin.\footnote{
  \label{fn:interp} For the claim that origin theses are an upshot of
  the branching framework, see J. L. \citet{JLMackie:1974} and
  P. \citet{PMackie:1998}. Accounts that ground origin theses in the
  sufficiency of origin include \citet{McGinn:1976, Johnston:1977,
  Salmon:1979, Noonan:1983}; and \citet[ch. 6]{Forbes:1981, Forbes:1985}. Forbes
  also makes use of a branching-worlds framework, but it plays no
  direct role in his argument for the origin thesis. Rather, it serves
  to support Forbes' sufficiency of origin thesis by restricting the
  range of worlds to which it applies. Both approaches develop
  suggestions found in footnotes 56 and 57 to Kripke's original
  discussion.  The independence approach offered in this paper may
  constitute an interpretation of Kripke's argument in footnote 56,
  but the textual evidence is unclear.}  
Both approaches depend on stronger assumptions than Kripke's original
presentation appeared to call for, assumptions strong enough to
engender a measure of skepticism in the philosophical community.

In this paper, we identify a third,
overlooked approach to such theses, an argument from what we call {\em
independence principles}. On this approach, origin theses are
by-products of a more fundamental feature of the processes by which
material objects are produced, their mutual independence. Independence
principles are motivated, in turn, as a consequence of a plausible
metaphysical principle governing such processes: their invulnerability
to non-local prevention.  We explain this approach and argue that
it yields valid arguments for origin theses, is distinct from the two
orthodox approaches, and proceeds from more plausible assumptions.

\section{The Locality of Prevention}
  Origin theses express restrictions on possible processes of
  creation.  They claim that certain logically possible productions,
  e.g., that of Elizabeth Windsor from the Trumans, are not in fact
  possible. But why shouldn't this be possible? Finding a principled
  answer to this question requires consideration of a broader one:
  What does it take to prevent the production of a particular material
  object from a particular hunk of raw material?  Consider Kripke's
  example of a table, \Tone{}, and the hunk of wood, \Hone{}, from
  which it was actually produced. It is a contingent fact that $H_{1}$
  gives rise to \Tone{}. There are many ways it might not have come to
  pass. We might have made \Hone{} into a chair; we might have burned
  \Hone{} for warmth; we might have seized the means of table
  production; we might just have decided to leave \Hone{} alone. In
  all of these cases, some factor prevents the production of \Tone{}
  from \Hone{}.
  The factors that prevent \Tone{}'s production in each case are those
  divergences from the actual circumstances responsible for \Tone{}'s
  not coming from \Hone{} in that case.\footnote{
    Although causing an effect is a sufficient condition for a factor
    to be responsible for that effect, it is not a necessary
    condition.  Many cases of prevention cannot be thought of as
    strictly causal, as we are often contemplating the absence of a
    certain event being responsible for the absence of another.
    Consider the following case.  \Tone{} fails to eventuate because
    life failed to evolve and there are no trees and, thus, no
    \Hone{}.  Here there is no identifiable causal process involving
    \Hone{} or the production process, but `because' expresses a
    relation of responsibility nontheless.}

We should notice an important feature of these examples. Each factor
which prevents \Tone{} from eventuating makes a difference to \Hone{}
or the people and tools involved in the productive effort. In this
sense, the preventions are \emph{local}. What makes no difference to the 
existence of \Hone{} or the process by which \Tone{} actually came
from \Hone{} is irrelevant to \Tone{}'s production and cannot
interfere. These reflections suggest that processes of table-creation
are governed by a principle of \emph{locality of prevention}: any case
in which some factor prevents the production of \Tone{} from
\Hone{} must differ from actual circumstances with respect to
properties of either \Hone{} or other elements of the process by which
\Tone{} actually emerged.\footnote{
  This claim states only a necessary condition for preventing the
  production of \Tone{} from \Hone{}.  No implication of the converse,
  a sufficient condition for preventing that production, is intended.
  A productive effort using \Hone{} as raw material may result in
  \Tone{} even though there are significant differences from the
  actual circumstances in the locale of the production.  The locality
  of prevention allows that there is more than one way to produce a
  table.}

 The locality of prevention is a thesis about dependencies.\footnote{
 Thanks are due to an anonymous referee for bringing the necessity of
 this clarification to our attention.}  It limits the factors on which
 the success of a productive effort may depend to those which make for
 local differences.  No restriction on how those local differences may
 be made is involved.  For instance, it is consistent with the
 locality of prevention that there be action at a distance, whereby a
 distant event is directly causally responsible for some effect, e.g.,
 on \Hone{}, precipitating the failure of \Tone{} to emerge.  The
 question of the truth of the locality of prevention is orthogonal to
 questions about the possibility of action at a distance, and more
 generally about the nature of causal connections.

The locality of prevention lies at the heart of the present
approach. It expresses what looks like a general truth about processes
of table-creation: they are essentially local phenomena. The
causal-historical path leading to this desk runs through quite
specific materials and processes of assembly which are distinct from
those leading to your desk, or, indeed, to anything constructed from
completely different materials, at other times, or in other
places. Because the actual production of this desk from its source
hunk is solely a matter of what happens along the causal-historical
path, any factor which prevents that production must make a difference
along this path. Factors that fail to influence it do not prevent the
desk from coming into existence just as it actually does. Running the
process which actually leads from \Hone{} to \Tone{} in the presence
of factors which do not locally infringe can still lead to
\Tone{}. 

It is important to distinguish two claims at this point.\footnote{
 We are again indebted to that same anonymous referee for pointing out
the need to highlight this distinction.}
The claim we defend is that, in the absence of any factor which
affects \Hone{} or some other element of the production of \Tone{},
that production \emph{may} result in the production of \Tone{}.
Nothing prevents \Tone{} from being produced, and its emergence is
possible.  A stronger claim, with which it might easily be confused,
is that in the absence of such factors the process \emph{must} result
in the production of \Tone{}.  Nothing prevents \Tone{} from being
produced, so its emergence is inevitable.  The stronger claim, unlike
the weaker, articulates a sufficient condition for being \Tone{}: any
table which is produced from \Hone{} under precisely the actual
conditions is, as a matter of necessity, \Tone{}.  The present
approach eschews such sufficient conditions for being \Tone{}.  All
that is promised by the locality of prevention is that \Tone{} might
still be the product in such a case.  But, for all that the principle
tells us, it also might not.\footnote{
There is a delicate question here about the force of the `might' in
`\Tone{} \emph{might} still be the product.' Although we find the ordinary
English locution expresses our thought tolerably well, those who are
overly used to hearing `could' as `there exists a possible world in
which' may be left puzzled. In the locution of possible worlds, our
claim amounts to this: 
any condition or factor $F$ not affecting the locale of the
\Hone{}-\Tone{} production, but otherwise compossible with it, is such
that there is a possible world in which $F$ obtains, and \Tone{} is a
table produced from \Hone{}.  In that sense the production \emph{can}
still succeed, even though $F$ takes place.  Of course this is
consistent with there being another possible world in which $F$
obtains and \Tone{} is not produced from \Hone{}.}

The difference between the two claims can be illustrated by appeal to
a metaphysical view which accepts the weaker, but denies the stronger.
Consider a view according to which there are no non-trivial sufficient
conditions for being \Tone{}.  \Tone{}'s identity is `bare' in the
sense that it depends on no further facts about either \Tone{} 
or anything else.  A proponent of this view holds that \Hone{}'s being
in the place that it actually was, being manipulated and shaped as it
actually was, with the tools, by the workers, and under the
circumstances it actually was, provides no guarantee that \Tone{},
rather than some other table, is the product.  The product of their
labors might simply have been a different table. The proponent of bare
identities, then, denies the stronger claim that \Tone{} must
emerge in those circumstances.  But she will find nothing to quarrel
with in the locality of prevention: it is the inevitability of
\Tone{}'s emergence she finds repugnant.  Its possibility is no
problem for her.\footnote{
 We are not endorsing the position according to which there are no
non-trivial sufficient conditions for being \Tone{}.  We broach the
position only for the purposes of illustration.  It does serve to
underscore, however, the broad appeal that the locality of prevention
has.  Some of the literature on the necessity of origin rests the case
for origin theses on the rejection of this position,
e.g. \citep[ch. 6] {Forbes:1985}. \citet{Noonan:1983} thinks the case
for origin theses rests on the rejection of `bare' identities (see
esp. p. 3), but argues against the ultimate coherence of such a
position.  Obviously, the route we are sketching here does not rest
on its rejection.}


This distinction will also help to contrast our claim with another,
more familiar thought for which it may be taken. It is sometimes
claimed that identity is an `intrinsic' relation. Expressions of this
view vary widely, but the basic thought is that relations of identity
hold only in virtue of the (other) intrinsic properties of the relata
and cannot be determined by the existence or non-existence of some
other thing or the obtaining of some extrinsic fact.\footnote{
  We should distinguish three claims that may march under the banner
  `the intrinsicness of identity': (1) If $x = y$, then the identity
  of $x$ and $y$ is an intrinsic feature of $x$ (i.e. $y$). (2)
  Whether $x = y$ is not determined by any merely extrinsic feature of
  $x$ or $y$. (3) Not only is (2) true, but whether $x = y$ is
  determined by other intrinsic features of $x$ and $y$.  (2) implies
  (1), for if the identity of $x$ and $y$ were an extrinsic feature of
  $x$, then an extrinsic feature of $x$, namely its identity with $y$,
  would determine whether $x$ is identical to $y$.  If the existence
  of a `best candidate' $z$ for identity with $x$ is held to be an
  extrinsic feature of $x$ or $y$, then (2) will also yield the `only
  $x$ and $y$ principle' mentioned below.  A proponent of the `bare
  identities' view will find nothing to quarrel with in either claim.
  Since, according to this view, nothing other than the fact that $x =
  y$ settles the question of whether $x = y$, its proponent can
  embrace both (1) and (2).  But the third claim is simply
  inconsistent with the `bare identities' view.  Since proponents of
  the intrinsicness of identity are so often motivated by a distaste
  for bare identities, we shall assume throughout that the strongest
  claim (3) is intended.} 
One version of this thought, the `only $x$ and $y$ principle,' claims
that the identity of a thing with itself over time cannot depend on
whether some other individual is or is not present and rules out, for
instance, `best candidate' theories of identity over time.\footnote{
  For the intrinsicness thesis and the only $x$ and $y$ principle, see,
  e.g., \citet[94--99]{Wiggins:1980} and \citet{Noonan:1985a}. For the
  closest continuer theory, see \citet[29--70]{Nozick:1981} and
  \citet{Noonan:1985b}.}
Although we have formulated our idea in terms of a factor's locality
--- its making a difference to those objects, events, and agents in
the locale of a production process --- and not the intrinsic
properties of a certain object or region, there are clear affinities
between the two ideas. One who accepts the intrinsicness of identity
should also accept the locality of prevention, as a world with no
local differences in the production process may also be
one with no intrinsic differences, and an intrinsic duplicate of that
production process will have a product which is intrinsically just
like \Tone{}.

Even so, it should be clear that the claim of intrinsicness goes
beyond ours in a number of ways. First, the intrinsicness claim,
especially in its `only $x$ and $y$' guise, is usually applied to
questions of identity over time. We make no claims about what form a
correct account of identity over time must take. Our concern is only
with what it takes to prevent a given object from coming to be and not
with its continued survival after that point. The locality of
prevention is compatible with a variety of accounts of identity over
time, including `best candidate' or even a counterpart-theoretic
accounts, whether or not such theories are advisable.

This leaves `cross-world' applications of the intrinsicness claim,
which bring us to a second, more important difference. The
intrinsicness claim is typically taken to imply a sufficiency
principle for cross-world identity: given that \Tone{} eventuates from
\Hone{} in a region $R$ in $w$, any world which is an intrinsic
duplicate of $w$ in $R$ (and contains \Hone{} in $R$) will be a world
in which \Tone{} eventuates from \Hone{} in $R$. \citep[82]
{Noonan:1985a} This is precisely the sort of consequence to which we
deny that the locality of prevention need be committed. As should be
clear from the example of bare identities, the locality of prevention
only requires that \Tone{} may eventuate in such a similar situation,
not that it must. We emphasize the distinction between `may' and
`must' here both because weaker premises make stronger arguments and
because keeping the distinction firmly in mind will help distinguish
the present approach from those based on sufficiency principles when
we come to them.

The applicability of the locality of prevention is no less general
than its appeal.  Nothing about the locality of prevention is really
specific to tables. Analogous restrictions on prevention seem to
govern the production of most kinds of material objects, many kinds of
events, and perhaps even some kinds of nonmaterial objects.\footnote{
  Although the independence approach to origin theses offered here
  applies most obviously to material objects, considerations of
  constitution play no essential role in the reasoning. What matters
  is rather creatibility and the invulnerability of such creation
  processes to non-local prevention. Where events and nonmaterial
  things fit this profile, as, for example, symphonies and species of
  animal arguably do, similar reasoning will apply.  This would appear
  to vindicate J. L. Mackie's suggestion,
  \citeyearpar[360]{JLMackie:1974}, that `the contrast between the
  necessity of origin and the contingency of development is not
  essentially connected with constitution,' while offering a rather
  different explanation of the contrast.}
Despite their generality, the restrictions imposed by the locality of
prevention are not trivial. There are kinds for which these
restrictions do not hold. Call something a {\em prototypical table} if
it is the first table ever made in the universe.  We may prevent the
production of a prototypical table from a source hunk simply by
constructing another prototypical table at some earlier point in
time. Such prevention need not be local.\footnote{
  The interference is not just with the existence of, say, \PTone{},
  nor with its creation from some hunk or other, but with the {\em
  production} of \PTone{} from, say, \Hone{}.  We are thinking of
  productions as individuated in part by the kind of thing the product
  is.  So, supposing \PTone{} to be a prototypical table constructed
  from \Hone{}, the production of that very table from \Hone{} may
  fail in some other world, even though the right table is produced
  from \Hone{} in that world. The prototypical table production fails
  because the product is not a {\em prototypical} table.}
It is also easy to find examples of kinds for which interference might
occur `after the fact.' Call something a {\em
super-prototypical-table} if it is the only table ever to exist in the
universe. What produces a super-prototypical-table in one circumstance
may fail to do so in another. The construction of a second table, even
after the first is completed, spoils it.  Productions of
prototypical- and super-prototypical-tables are vulnerable to forms of
competitive interference. What prevents their production is our
running the very same sort of process on another hunk somewhere else.

\section{Independence Principles}
The contrast with ordinary tables is instructive, for ordinary tables
do not seem vulnerable to the same sort of non-local, competitive
interference. As far as making \Tone{} from \Hone{} goes, it just
doesn't matter what you do with some other hunk of wood somewhere else
in the universe. Make it into a table or don't. As long as the second
process doesn't infringe on the process which actually makes \Hone{}
into \Tone{}, this process may well run as it actually did, resulting
in \Tone{}. The reasoning is symmetric. Suppose we do make that second
hunk into a table. Whether we make \Hone{} into \Tone{} or not is
irrelevant to the success of our new endeavor, unless the two
processes locally interfere with one another.

The locality of prevention has the following consequence: if one table
production need not have effects in the locale of another and
\emph{vice versa}, then it is possible for both productions to
succeed.  Table productions can be isolated from the effects of other
table productions in most cases.  The upshot is that processes that
turn hunks into tables seem to enjoy a form of {\em independence} from
one another. A process that turns one hunk into a table \emph{need
not} interfere with any other, though there are cases in which they
do, in fact, interfere. Suppose we burn one of the hunks in order to
power the machine which makes the other hunk into a table.  In this
situation, we can no longer make any of the tables we might otherwise
have made from the burned hunk. But this connection between the
processes is contingent. Had we found another source of power, the
second hunk would have remained available for table-manufacture. The
relevant form of independence is one which rules out only necessary
interference between table-making processes.

If this reasoning is correct, we seem to have the following
situation. Given any two distinct hunks, a table constructed from the
first hunk can, in principle, also be constructed in the presence of
the production of any of the tables which can be constructed from the
second hunk. This is what we call an \emph{independence
principle}.\footnote{
  Independence principles, and the availability of valid arguments
  from them to origin theses, appear to have been first noticed by Kit
  Fine and Robert Stalnaker. In footnote 11 of \citep{Salmon:1979},
  Salmon attributes a similar idea to Fine and Stalnaker, but does not
  there recognize that it represents an approach to origin theses
  fully distinct from his own. Later writers appear either to have
  overlooked the suggestion or to have accepted Salmon's assimilation
  of the suggestion to the sufficiency approach. If the interpretive
  suggestion of note \ref{fn:interp} is correct, the idea is
  originally Kripke's.}
It expresses the compossibility of table-productions from distinct
hunks. Independence is the ineluctable result of the locality of
prevention. Because making a table is just a matter of what happens
locally along the casual-historical path, the paths are compossible
when nothing requires one to affect the other as a matter of
necessity.  Whenever processes of production are invulnerable to
non-local prevention, there will be an analogous principle of
independence.  So, independence principles seem to hold no less
generally than does the locality of prevention.\footnote{
  The `seem to' should be taken seriously.  We will meet examples
  where independence principles fail even though locality holds when
  we discuss productions whose source-hunks overlap below.  Such cases
  are very much the exception rather than the norm.}

In fact, there is reason to think that independence principles can
hold even in the presence of certain failures of the locality of
prevention. The only failures of locality which undermine independence
principles are those in which non-local \emph{competitive} prevention
is possible, as in the case of the prototypical-tables. While we
believe that the case for independence is clearest for the broad array
of processes which are plausibly thought immune to all forms of
non-local prevention, it is logically possible for a pair of
production processes to be independent in the required sense even
though each is vulnerable to some forms of non-local prevention. This
means that the independence approach to origin theses may remain
available in some difficult cases, though at the cost of additional
philosophical work. Although it is our purpose here to illustrate the
core of the approach, a brief discussion of an example may indicate
the direction one might take here.

Our example is inspired by the literature on personal identity.  Our
focus, however, will be on the production of human beings rather than
persons.  Suppose a human being, \Hone{}, actually develops from
gametes $G$.  Suppose also that it is possible for the process which
actually led to \Hone{} to have led to a human being \Htwo{}, who
later `split,' resulting in identical twins.  Consider a view which
maintains, ``It is essential to \Hone{} that she not split.  Because
of the split, \Htwo{} and \Hone{} are distinct; in general it is
impossible for a human being to split like this if she does not
actually do so.  In effect, \Htwo{}'s split prevents the productive
process involving $G$ from yielding \Hone{}.''  If we accept this
view, we seem to have a case of non-local prevention \emph{par
excellence}.  An event in the subsequent history of the product
\Htwo{} prevents the production from yielding \Hone{}, but not by any
effect on $G$ or other elements of the process.\footnote{
  This view is broached for purposes of illustration only.  We do not
  endorse the view, and will make no attempt to motivate or defend it.
  The philosophical literature on personal identity is replete with
  views regarding the metaphysics of the fission of persons.  Perhaps
  a good place to start is \citep{Parfit:1986}.}

Even granting this view, it remains clear that the production processes
display the relevant form of independence from production processes
involving other gametes.  The splitting of an individual coming from a
set of gametes is not required by the coming of an individual from
distinct origins. \Htwo{}'s production from $G$ is as compossible with
the production of individuals from other origins as \Hone{}'s
is.\footnote{
  We bypass for now issues involving the entanglement of productive
  processes that lurk in the wings here.  Consider, for instance,
  cases of productions from overlapping source-hunks, a possibility
  for gametes.  It is doubtful that the production of \Hone{} from $G$
  is compossible with the production of another human being from
  overlapping origins.  These issues do not affect the paradigm cases
  for origin theses, where there is no such entanglement, and will be
  discussed in detail later.}

 Independence principles imply that, even if one thinks that a given
origin could have given rise to a variety of different individuals ---
distinct solo alternatives, twins, or what have you --- all the
processes starting with that material origin are independent of those
starting with distinct material origins; any of the individuals
obtainable from one are compossible with any of the individuals
obtainable from another. Perhaps \Hone{} can only appear when there is
no splitting, but it may appear alongside any individual from another
origin.  Independence principles govern relations between productions
from distinct source hunks.  Since the splitting cases do not involve
other source hunks, they do not touch independence principles, even if
they threaten the locality of prevention.\footnote{
  Another issue on which independence does not pronounce is whether
  the twins resulting from the split of \Htwo{} are separately
  producible. Independence only maintains that individuals having
  distinct material origins are compossible, but the twins share a
  material origin. Furthermore, independence principles only license
  inferences from claims about what is separately producible to what
  is jointly producible, never the reverse.}

\section{The Argument from Independence}
We are now in a position to understand origin theses, not as bottom
level metaphysical principles or mere intuitions, but instead as
byproducts of independence principles. Let us start with an explicit
characterization of independence for tables. Here and throughout the
paper, we use `made from' as short for the relation \emph{made
entirely and exclusively from}, i.e. that relation which holds between
tables and hunks of material that contain all and only the material
from which the table is made.\footnote{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Revised the following to carry through ``all and only''
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  It is natural in English to speak of tables being made from hunks
  containing only a portion of their original material, as in `this
  table was originally made from that leg.'  If we allowed such a
  colloquial understanding of the expression `made from', then the
  resulting origin theses would have actual counter-examples.  For
  instance, this table was not only ``made from'' that leg, but also
  from other, distinct legs.  It is not only possible for this table
  to have been ``made from'' a hunk distinct from this leg, it
  actually was ``made from'' a distinct hunk, e.g. that other leg.  We
  adopt the stipulation of the main text as a way of avoiding such
  uninteresting counter-examples.  One could, alternatively, avoid the
  irrelevancies by taking the relation indicated colloquially by
  ``made from'' as one's starting point in formulating our principles.
  One could then specify the more artificial relation we intend as one
  that holds between a table and a hunk iff all and only parts of the
  hunk are things the table is ``made from'', in the colloquial sense.
  (Really, an even more complicated specification is required, given
  that it is also natural in English to speak of a table's being made
  from a hunk which is only partially used up in the manufacture, as
  in `this table was originally made from a certain block of wood,
  half of which was left over'.)  Because substituting this
  specification for `made from' would overcomplicate the formulation
  of our principles, we reserve the expression `made from' for the
  relation \emph{made entirely and exclusively from}, as we explain in
  the main text.}

\begin{description} 
    \item[(T-IND)]Necessarily, given a table, \Tone{}, made from a
      hunk, \Hone{}, for any table, \Ttwo{} which might be made from a
      hunk, \Htwo{}, distinct from \Hone{}, it is also possible that
      both \Tone{} is a table made from \Hone{} and \Ttwo{} is a table
      made from \Htwo{}.
\end{description}

In line with our reasoning, this expresses a compossibility claim
about processes of table production. As promised, it is no logical
truth, for the inference from `Actually P' and `Possibly Q' to
`Possibly P and Q' is invalid. Furthermore, we believe that (T-IND),
as it stands, is susceptible to counter-example. Because our purpose
here is to demonstrate a valid argument schema from independence-style 
principles to origin theses and not a full investigation of the
truth of such principles, it is simplest to consider an unrestricted
version of independence. Later, we will suggest how the principle
might be restricted in order to restore its plausibility.

The argument requires two other premises. The first is a familiar 
logical principle, the (necessary) necessity of distinctness. 
\begin{description} 
  \item[(ND)]Necessarily, if $x \neq y$, then necessarily $x \neq y$. 
\end{description} 
The second is another metaphysical principle. Call it origin uniqueness. 
\begin{description} 
  \item[(OU)]Necessarily, if \Tone{} is a table made from \Hone{} and 
    \Ttwo{} is a table made from \Htwo{} and $H_{1} \neq H_{2}$, then 
    $T_{1} \neq T_{2}$. 
\end{description} 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% spelling out the reasoning somewhat pedantically here
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Keeping in mind our stipulative use of `made from,' this principle
says that a single table cannot \emph{entirely and exclusively}
originate from each of two distinct hunks within a \emph{single}
possible world. Suppose that there is a world in which \Tone{} is made
from both \Hone{} and \Htwo{}.  Our stipulation regarding the use of
`made from' requires that \Hone{} and \Htwo{} contain exactly the same
material.  Barring the possibility of distinct but exactly coincident
hunks, \Hone{} and \Htwo{} are identical, as (OU) says.  The principle
is no logical truth, since the impossibility of distinct but exactly
coincident hunks is no logical truth.  Nevertheless, (OU) is still a
trivial truth about material objects like tables: tables with distinct
origins (in a world) are also distinct. The conclusion is a necessity
of origin thesis for tables.
\begin{description} 
  \item [(T-NO)]Necessarily, given a table, \Tone{}, made from a hunk,
    \Hone{}, any table, \Ttwo{}, which might be made from a hunk,
    \Htwo{}, distinct from \Hone{}, is distinct from \Tone{}.
\end{description} 


Now the argument. Start with a table, \Tone{}, made from a hunk,
\Hone{}. Let \Ttwo{} be some arbitrary table it is possible to make
from a hunk, \Htwo{}, distinct from \Hone{}. Since \Tone{} actually
comes from \Hone{} and it is possible that \Ttwo{} come from \Htwo{},
the independence principle says that both are jointly possible in some
world $w$. Since \Hone{} and \Htwo{} are distinct, they are distinct
in $w$ as well by the necessity of distinctness. By origin uniqueness,
the distinctness of the hunks in $w$ shows that \Tone{} is distinct
from \Ttwo{} in $w$.  An application of the necessity of identity
shows that \Tone{} and \Ttwo{} are actually distinct as well. Since
the choice of \Htwo{} and \Ttwo{} was arbitrary, we conclude that any
table it is possible to make from such an \Htwo{} is distinct from
\Tone{}. Since the choice of starting world was arbitrary, the
conclusion holds for all possible worlds. Q.E.D.\footnote{ The proof
is straightforward and requires only the K and T axioms along with the
rule of necessitation. One could, for elegance, use B and the
necessity of identity in lieu of (ND). The relevant QML symbolizations
are:
  \begin{description} 
    \item[(T-IND)] $\square \forall t_{1}\forall h_{1} (O(h_{1}, t_{1}) 
      \Rightarrow \square \forall t_{2} \forall h_{2} (h_{1} \neq 
      h_{2} \land O(h_{2}, t_{2}) \Rightarrow \lozenge (O(h_{2}, 
      t_{1}) \land O(h_{1}, t_{1}) )))$ 
    \item[(ND)] $\square\forall x\square\forall y\square (x \neq y \Rightarrow \square (x \neq y))$ 
    \item[(OU)] $\square \forall t_{1} \forall h_{1} \square\forall
      t_{2} \forall h_{2}\square [ (h_{1} \neq h_{2} \land  O(h_{1},
      t_{1}) \land O(h_{2}, t_{2})) \Rightarrow t_{2} \neq t_{1}]$ 
    \item[(T-NO)]$\square \forall t_{1} \forall h_{1} (O(h_{1}, t_{1}) 
      \Rightarrow \square \forall t_{2} \forall h_{2} ( h_{1} \neq h_{2} \land 
        O(h_{2}, t_{2}) \Rightarrow t_{2} \neq t_{1} ))$ 
  \end{description}
} 

\section{Circularity Worries}
One natural reaction to the argument is to think that, while valid, it
simply begs the question because the independence principle just is
the necessity of origin in disguise. What difference is there, one
might ask, between being told that a table could have come from no
other hunk and being told that the production of any table from
another hunk is compossible with the first table? Strictly speaking,
the charge is false.  Independence and the necessity of origin do not
imply one another.  First, independence, by itself, does not imply any
origin thesis in the absence of the necessity of distinctness and
origin uniqueness. For instance, if distinctness were contingent,
then \Tone{} could be made from \Htwo{} in a world in which that hunk
is identical to \Hone{}.  While neither the necessity of distinctness
nor origin uniqueness is open to much doubt, our reasons for
accepting them come from quarters far removed from those which support
the origin thesis. Second, the necessity of origin does not imply
independence.  Even if no table could ever come from other matter, it
might still be the case that independence fails because some distinct
table-productions are not compossible. The necessity of origin only
denies the existence of certain possibilities, while independence
principles make a positive claim that a certain situation, that
containing both table-productions, is possible.

Such logical niceties aside, one might still think there is something
to the spirit of the charge. After all, if independence is true, it
rules out any form of necessary interference between the making of
\Tone{} from \Hone{} and the making of any table at all from
\Htwo{}. Haven't we just stipulated away the apparent counter-example
to the origin thesis, that in which the interference comes from our
making \Htwo{} into \Tone{}? To see why the answer is `no,' we need to
go back to the justification of independence. Where \Hone{} and
\Htwo{} are distinct hunks and we have a way making \Hone{} into a
particular table, if we also have a way of making \Htwo{} into a
particular table, then it seems that we could, in principle, run both
of these processes together. The distinctness of the hunks seems to
guarantee that there is no necessary interference between the
processes; in at least one world, we can run them both and get the
very tables we produced separately. Someone who wants to claim that we
can make \Htwo{} into \Tone{} needs to explain either why we could not 
also run the process which in fact turned \Hone{} into \Tone{} or why
that process could not result in \Tone{}. Either sort of explanation
would appear to violate the locality of prevention. It won't do simply
to say, `We've already made \Tone{}, so \Tone{} can no longer be
made,' without also telling us what factor necessarily affects \Hone{}
or some other element needed to produce \Tone{} from it. Without some
explanation of why the two processes \emph{must} interfere with each
other, the objector is left baldly claiming some unspecified form of
interference. One may object to independence, but the assertion of
independence is not just the bald assertion of the origin
thesis. Independence has its own grounds of support, and one who
objects to the origin thesis must find some flaw in these independent
grounds.

\section{Independence and Branching Times}
It will be worthwhile at this point to distinguish the independence
approach to the origin theses from the two other dominant approaches,
the branching account and the sufficiency account. The former grounds
origin theses in the so-called branching times model of necessity.
Questions about possibility are settled
according to this model by asking whether the history of the universe
could have gone as it actually has, up to a point, and then diverged
in a way that brought about the possibility in question. On one simple
version of this framework, the {\em de re} possibilities for \Tone{}
are given in all the ways the universe could have gone on after the
advent of \Tone{}. None of these histories, however, include \Tone{}'s
coming from another hunk. By the time of the divergence, it is too
late for \Tone{} to have had a different origin. There are
possibilities for tables included in earlier divergences, but none of
these, according to the framework, are possibilities for \Tone{};
these divergences are too early to represent possibilities for it.

The branching times and independence approaches differ, most
obviously, in the scope of the claim in which they ground their
arguments. While the independence approach relies on a specific
insight about what it takes to prevent the production of a
material object, the branching times approach relies on an overarching
claim about what, in general, determines the possibilities for things,
in short, a full-fledged interpretation of necessity. The
independence approach, in contrast, requires no particular
interpretation. The two approaches may also conflict directly, for it
is not obvious that independence principles will come out true under a
branching times interpretation of necessity. Consider, for instance,
the simple version of the branching times interpretation broached in
the last paragraph.  Let \Ttwo{} be a merely possible table which
might have been created from \Htwo{} long before \Tone{} was actually
created from \Hone{} and thus resides on a branch which diverges from
actuality prior to the advent of \Tone{}.  Compresence with the
production of \Ttwo{} from \Htwo{} is not a possibility for \Tone{} as
independence claims, since only branches which diverge from actuality
after \Tone's advent represent possibilities for it. 
Perhaps some subtler, more complicated version of the branching times
model is consistent with independence principles.  Even so, the
subtlety and complexity required underscores the differences between
the two approaches.

\section{Independence and the Sufficiency of Origin}
The difference between the independence approach and the sufficiency
approach is more subtle because the forms of argument are
superficially similar. Both use the necessity of distinctness, origin
uniqueness, and some compossibility claim about table productions to
reach the origin thesis. The sufficiency account starts with an
independence-like principle, though one that is weaker and more
obviously true. Call it weak-independence for tables.
  \begin{description}
    \item[(T-WIN)]For any two distinct hunks of matter, \Hone{} and
      \Htwo{}, and any table, \Tone{}, made from \Hone{}, it is
      possible both that \Tone{} is a table made from \Hone{} and that
      \Ttwo{} is a table made from \Htwo{}.
  \end{description} 

Of our usual \Hone{}-\Htwo{}-\Tone{} situation, this says that it is
possible to construct some table or other from \Htwo{} alongside
\Tone{}; call it \Ttwo{}.  \Ttwo{} is, by the necessary distinctness
of the hunks and origin uniqueness, distinct from \Tone{} and
necessarily so. But this leaves open the possibility of another,
special table, $T_{3}{}$, which is constructible from \Htwo{} but is
not compossible with \Tone{}'s production from \Hone{}. Thus, the
logic of the situation so far allows that $T_{3}{}$ might be \Tone{},
and thus a counter-example to the origin thesis. This gap is bridged
by appealing to another principle, the sufficiency of origin for
tables.
  \begin{description}
    \item [(T-SO)]If it is possible for a table, $T$, to originate
      from a hunk, $H$, then necessarily any table originating from $H$
      is $T$.
  \end{description} 
This claims that each hunk has lurking in it at most one possible
table, or, more generally, that having a particular origin is a
sufficient condition for being a particular table. With the
sufficiency principle in hand, one may infer that $T_{3}{}$ is
identical to \Ttwo{} because both share the very same origin, {\em
viz}., \Htwo{}. Since it was shown that \Ttwo{} is necessarily
distinct from \Tone{}, we can conclude the same for $T_{3}{}$ and for
any table coming from a distinct hunk.

We, along with many others, are skeptical about the truth of such
sufficiency principles,\footnote{
For some doubts, see, e.g., \citet{Salmon:1979, Robertson:1998,
Gendler:2000, MacKay:1986, Chihara:1998, DRocca:1996, Sarkar:1982,
Noonan:1983}; and \citet[43, 46]{Kripke:1980}. }
but what is relevant here is that the argument from independence does
not presuppose, and is compatible with the falsity of, the sufficiency
of origin. The independence principle says that the making of \Tone{}
from \Hone{} does not foreclose the possibility of making any table
that might otherwise be made from \Htwo{}, for both may be constructed
in the same world. The truth of this claim is entirely compatible with
our being able to make a number of alternative  tables from a single hunk
of matter, and this is the denial of the sufficiency principle.
Essentially, the sufficiency principle functions in the argument by
ensuring an unusually strong form of independence between
table-makings: no table from \Htwo{} need interfere with \Tone{}'s
coming from \Hone{} because any table from \Htwo{} is \Ttwo{}, which
we already know from (T-WIN) does not interfere. But once one sees how
the argument from independence proceeds, it becomes clear that
sufficiency principles are an unnecessarily strong way of guaranteeing
the independence required to derive the origin thesis.

While it should be clear that the argument from independence does not
rely on any sufficiency of origin principle, one might think that
sufficiency reasoning is still at work in the justification of
independence itself.\footnote{Teresa Roberston emphasized the need for
this point.}  This impression may be dispelled. We suggested that
independence principles have their source in the principle of locality
of prevention: a production process can be prevented only by factors
which affect the raw materials, workers, tools, and facilities
involved. Where there are two such processes which need not affect one
another, they are compossible because nothing prevents both from
occurring together in some world. One way of understanding this
reasoning would invoke a sufficiency principle for processes. If one
thought that the process which actually leads from \Hone{} to \Tone{}
would inevitably lead to \Tone{}'s emergence, then any world
containing this unaltered process alongside some other such process is
a world containing \Tone{} and some other table.

We have emphasized that, while one may reason in this fashion, one
need not. Securing the truth of independence for a pair of
non-interfering processes, say those which take \Hone{} into \Tone{}
and \Htwo{} into \Ttwo{}, requires only that there be some world in
which we can run them both with these results. It is a matter of
indifference whether there are some other worlds in which running
these processes leads to tables other than \Tone{} and \Ttwo{}. It is
for this reason that we say that running the process which actually
leads from \Hone{} to \Tone{} in the presence of another process which
doesn't locally infringe \emph{can} lead to \Tone{}, not that it
\emph{must}.  Once again, sufficiency reasoning turns out to be
stronger than is required for the argument. We might also note that
questions about the necessary features of processes are bypassed on
our approach, for it is again a matter of indifference whether, say,
the process which actually led from \Hone{} to \Tone{} could have run
differently with the same result or, if so, how differently it could
have run. Given a pair of hunk-to-table processes, all that matters is
the possibility of running them unaltered and getting those same
tables in at least one world.

\section{Overlapping Origins}
(T-IND), as stated, is not problem-free. It turns out to be 
counter-intuitive when \Hone{} and \Htwo{} have much of their material 
in common. If \Hone{} is made into a table in such a case, then there 
may not be enough of \Htwo{} left to craft some table we might have 
otherwise obtained; the two tables compete for raw materials.  Such 
cases are also ones in which a necessity of origin thesis is 
implausible.  Couldn't \Tone{} have been made from slightly different 
matter?  Couldn't it therefore have been made from a hunk distinct 
from \Hone{}, but sharing much material in common?  If our claim that 
independence principles ground origin theses is correct, then it is no 
coincidence that origin theses seem implausible in cases where 
independence fails. Such cases also suggest that we may restore 
(T-IND)'s plausibility by restricting it, from distinct hunks, to 
non-overlapping hunks.
  \begin{description}    
    \item[(RT-IND)]Necessarily, given any two {\em non-overlapping} 
      hunks, \Hone{} and \Htwo{}, and a table, \Tone{}, made from 
      \Hone{}, for any table, \Ttwo{}, that might be made from 
      \Htwo{}, it is also possible that both \Tone{} is a table made 
      from \Hone{} and \Ttwo{} is a table made from \Htwo{}. 
  \end{description}
Such a restricted (T-IND) would support a similarly restricted and 
more plausible origin thesis, like that defended by Kripke, Salmon,
and others, that no table could have been constructed from a hunk
entirely disjoint from that table's actual originating hunk.
 
A second sort of case appears to be a counter-example to even this
restricted form of independence and complicates our defense of origin
theses. Suppose that \Hone{} is a block of petrified wood which comes
from \Htwo{} by petrification, a process in which all the organic
matter of \Htwo{} is replaced by minerals.\footnote{This case is due
to James Forrester.}  Once again, making a table from \Htwo{} will
preclude our making any tables from \Hone{}, despite the fact that the
two hunks share no matter. Making some \Ttwo{} from \Htwo{} and
allowing \Htwo{} to petrify into \Hone{} compete for raw
materials. \Htwo{} cannot both be made into the table \Ttwo{} and
remain available for petrification into the hunk \Hone{}. So (RT-IND)
is evidently false in this situation.

There are two issues here.  The first is the general truth of
independence-style principles. Even though \Hone{} and \Htwo{} do not
overlap in the sense of sharing matter, it is clear from the
perspective of the locality of prevention principle what is going
on. The processes which lead from \Htwo{} to \Ttwo{} and from \Htwo{}
through \Hone{} to \Tone{} overlap in their causal histories and
necessarily interfere with one another. This suggests that (RT-IND)
does not exhaust the content of the locality of prevention principle
and that one could develop a notion of `non-overlap' other than 
`disjointness of matter' which would validate independence principles.
Since it is not our primary aim to arrive at the truth about
independence principles, we will not pursue this suggestion here.  The
second issue, more important in this context, is the impact of such
examples on the plausibility of origin theses. Even if there is such a
sense of `non-overlap' which validates independence, it looks as if there
is no origin result in the offing with respect to some items in a
object's causal past, those whose role in the causal chain wholly
consumes them as a matter of necessity (so not, for instance, one's
grandmother). Even if such a version of independence remains true, it
will support only a weaker origin thesis, one which does not foreclose
the possibility that \Tone{} originate from a hunk whose causal
history is suitably entangled with \Hone{}'s.  In these cases, a
skeptic might claim that the independence approach must allow that
\Tone{} could have come from \Htwo{} instead of \Hone{}.

It is important to be clear on what sort of skepticism these cases
might be thought to encourage. Such cases cannot support a broad
skepticism about origin theses for two reasons. First, there remain
many source-product pairs for which instances of the independence
principle are obviously true, and so corresponding instances of origin
theses will be true of them.  This delivers the paradigmatic cases of
origin theses, where there is no entanglement between productive
efforts: this table could not have been made of some other hunk of
wood grown in Australia, no matter how similar; nor could Elizabeth
Windsor have come out of Harry and Bess Truman's gametes.
Second, the coherence of examples like the petrified wood case turns
out to presuppose the acceptance of some origin theses.  Consider how
it is plausible to claim that the petrification of \Htwo{} into
\Hone{} necessarily competes for raw materials with the production of
\Ttwo{} from \Htwo{}.  There will be \emph{necessary} competition only
if \Hone{} could not have come from any hunk other than \Htwo{}.  That
is, the skeptic uses an origin thesis about hunk-productions to arrive
at a counter-example to independence principles for table-productions.
If our skeptic's aim is to undermine the plausibility of origin theses
in general, then her position is not coherent.

There remains a rather different sort of `skeptic,' one who endorses
the origin thesis in a wide range of cases, including, here, the
impossibility of \Tone{}'s coming from \Htwo{}.  Such a skeptic does
not deny that independence arguments give rise to origin theses, but
challenges our claim that independence is the full story of the
conceptual grounds of origin theses. It is, however, unclear to us
that this is genuinely impossible or that the independence approach
gives the wrong answer in this case.  Suppose, for instance, that the
craftsmen who actually made \Ttwo{} from \Htwo{} were rather more
indolent and allowed the wood from \Htwo{} to petrify in the course of
their activity.  Might not the product of their admittedly languid
efforts have been \Tone?  This would seem to be a case in which the
stone table \Tone{} might be produced from the wooden hunk \Htwo{}.
There is thus some temptation to treat this case as analogous to the
earlier case of overlap: because the origins are entangled,
independence fails and so does the necessity of origin. It is true
that the `overlap' is more generally spatio-temporal-causal in nature
than the mere sharing of matter, but there was already need for this
generalization.

We believe that it is difficult to pronounce on purported cases of the
origin thesis in a vacuum. Indeed, the point of any of the approaches
to origin theses is to ground them in more than fleeting intuitions.
Our imagined opponent thinks \Tone{} could not have originated from
\Htwo{}.  Could she appeal to either of the other two approaches to
support her case? The sufficiency approach will not help. The
petrification case is one in which even weak-independence fails. Not
even one table can be made from \Hone{} in the presence of a \Ttwo{}
made from \Htwo{}, contra (T-WIN). So the sufficiency approach does
not show that \Tone{} could not have been made from \Htwo{}. The
simple branching account appears to support the case, as \Tone{} and
\Ttwo{} lie, as it were, on different temporal branches. The simple
version, however, has problems precisely with avoiding making the time
and circumstances of creation a necessary feature of
objects.\footnote{
  See Penelope \citet{PMackie:1998} for a clear and sustained argument
  for this point.}
Presumably one might avoid these difficulties by providing a more
sophisticated account which achieves plausibility by allowing branches
before the time of creation.  Once we are permitted to take liberties
with the circumstances that predate \Tone{}'s advent, however, it is
more difficult to resist our little story about the indolent
craftsmen.  It would seem at first blush that a more liberal version
of the branching times approach faces the same difficulties in
handling the case of petrification as do the independence and
sufficiency approaches.  This is only a first impression.  It is
difficult to know whether or how a sophisticated branching times
approach might support an origin result in the petrification case
without being in possession of the details. But there is, as yet, no
compelling reason to abandon the claim that independence results alone
ground origin theses.

\section{Conclusion}
One measure of the strength of a philosophical approach is the
questions it allows one to frame and the resources it provides for
answering them. The independence approach shows such strength as one
moves beyond the model case of tables. The plausibility of origin
theses turns on a host of further questions about the truth and scope
of independence principles: Are there ways, other than competition for
raw materials, that creation processes can compete, giving rise to
necessary interference? What about competition for time, place, or
agent of creation? For what kinds of objects do we get independence
principles?  Are they all material? Do they all involve initial
constitution? Not every kind will support such a principle, as the
prototypical-table example shows, but what is the widest class? Is it
philosophically interesting? The independence approach, in turn,
suggests that we may answer such questions by considering the source
of independence principles, the invulnerability of creation processes
to non-local prevention.

Despite such questions, we draw two firm conclusions. First, there is
a valid, non-circular argument from independence principles to origin
theses. Second, the independence approach is distinct from both
branching and sufficiency approaches and does not rely on their
primary assumptions. What is more interesting, and more tentative, is
the idea that independence principles derive from a more basic and
general truth about processes of creation, that they are essentially
local phenomena. From this perspective, origin theses are mere
consequences of what has the look of a genuinely basic metaphysical
truth. We believe that the independence approach offers a novel and
insightful framework for thinking about origin theses and, ultimately,
for assessing their truth.\footnote{ 
  The ideas for this paper first emerged during a seminar at UCLA on
  Lecture 3 of \emph{Naming and Necessity} in the Fall of 1999.  We
  thank all of the participants in this seminar for their help.
  Special thanks are due to Joseph Almog, David Kaplan, Collin O'Neil,
  and Dominik Sklenar, for helping to ease this paper's birth-pangs.
  We also would like to thank Kit Fine, James Forrester, Paul Hovda,
  D.A. Martin, Nathan Salmon, Teresa Robertson, Takashi Yagisawa,
  Byeong-Uk Yi, and two anonymous referees for their helpful comments
  on various drafts and presentations.}

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