briggs on antirealist accounts of scientific law
TRANSCRIPT
Briggs on Antirealist Accounts of Scientific Law
Rachel Briggs’ (2009a) critique of “antirealist” accounts of scientific law – including
(Halpin 1994) – is part of a project meant to show that Humean conceptions of scientific law are
more problematic than has been commonly realized.1 Her introduction to the full project, (Briggs
2009b), nicely sets out the Humean view and her general objection:
One fundamental schism in the philosophy of science involves the status of nomological
properties: does the universe at bottom contain any laws, dispositions, or objective chances?
… The debate can be cast as an argument about Humean Supervenience: roughly, the thesis
that nomological facts supervene on non-nomological facts…. Closer attention to David
Lewis’s ‘Big Bad Bug’, (1986, xiv-xvi; 1994), may help advance the discussion. The Big
Bad Bug is an argument to the effect that objective chances fail to supervene on non-
nomological matters of fact. If sound, the Bug is disastrous for Humean Supervenience. I
argue that the Big Bad Bug is a stronger argument than many defenders of Humean
Supervenience have realized. (428)
Indeed, Briggs’ (2009a) argument provides a new challenge to the Humean, a thoroughly
epistemic version of David Lewis’ Bug. Still, I will argue, the antirealist (perspectivalist and
expressivist) accounts she criticizes have the resources to withstand the challenge and come out
stronger for it.
A Humean attempts to show that all facts supervene on a basis of non-nomological,
“occurrent” facts. As I would put it, a scientific account involving lawful connection, chance,
cause or other dispositional concepts provides an interpretative overlay for the totality of events.
For a typical proponent of “Humean Supervenience”2, nomic claims may count as true but only
insofar as nomic concepts are required for a best scientific systematization of all occurrences. At
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“bottom”, then, the world postulated by the Humean involves only non-nomic fact. But, Briggs
argues, Humean chance (seen as supervenient on non-nomic facts) proves problematic because
of chance’s close connection to epistemic probability or credence. She contends that though
antirealist accounts of law may provide Humean solutions to metaphysical issues regarding
chance, e.g., how to attribute chance to non-actual possible worlds, they leave untouched the
epistemological “Bug” for Humeanism: attribution of chance and credence for epistemic
possibilities.
After section one’s discussion of the Bug, section two of this article contends that a
perspectivalist (or, alternatively, an expressivist) account has a natural solution to Briggs’
epistemological argument. Still this antirealism has a cost, viz., relativity to point of view.
Section three argues that the price is right: there are significant advantages to a perspective
dependent account of laws.
1. Brigg’s Better Bug
Many contemporary Humean accounts of scientific law, including my own, are indebted to
Lewis’s definition in terms of ideal scientific theory. Put roughly, Lewis defines laws for a
possible world w to be the consequences of the best scientific systematization for that world’s
non-nomological facts. So to think about w’s laws, one is to imagine what ideal science would be
for w’s events and take w’s laws to be defined as the logical consequences of this “best-system”.
The details of just what constitutes “ideal” science or “best-system” (some sort of concise
description) are controversial but not at issue in Briggs’ critique. Rather, she is concerned with
the Humean’s treatment of the credence-chance relationship (i.e., the relationship between
objective single case probability and reasonable degree of belief). First consider the objective
side of the relationship. Lewis’s Humean Supervenience position defines truth about chance in
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terms of ideal science’s probability measure: a measure providing the best statistical fit to the
pattern of occurrences. Then insofar as the best system makes probability claims, these claims
are true. But as Lewis saw, this Humean reduction for chance may be problematic in its
relationship to credence; this is the “Bug” and requires a few paragraphs to develop.
Quantum mechanics is contemporary science’s attempt to give a best system for
fundamental physical reality. But a toy example of chance systematization, for normal coins and
their tosses, is sufficient here. For example, a Canadian loonie coming up tails (the loon
showing) has chance ½. No matter that loonies have not actually come up tails exactly half the
time: The conceptualization in terms of chance is far simpler than a flip-by-flip description yet
gives significant predictive value. According to Lewis’s Principal Principle (PP), in a broad
range of cases rational credence follows chance. Knowing only the chance 1/2 for a loonie toss
result, one should have a partial belief or credence of 1/2 in tails for that toss. PP spells out the
details and implies mixtures when chance is uncertain. However, we will need only a simple and
intuitive consequence. In normal contexts3 and for ‘X’ regarding future events, the principle
implies the following about a reasonable credence function.
(*) If theory T logically implies that Chance(X)=p, then Credence(X|T)=p.
Lewis (1986) stresses a concern with so-called “undermining” worlds, worlds he feared
might be the ruin of Humean Supervenience. The idea is easily spelled out using the loonie
example. The probabilities assumed, 50% each for heads or tails with each toss result
independent of the others, leave open a wide range of future sequences. For example, if loonies
are tossed a settled n times in the future, then there is a chance, 1 in 2n, that every future toss
lands with the loon up. Given a long run of all tails, future observers might well conclude that
the loonie coin was unfair – even were there no discernable structural asymmetry – so assign
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chance in a non-standard way. However, by our hypothesis, a conclusion assigning non-standard
chance would be wrong: the coins just happen to all come up tails. The Humean, though, has
difficulty with this judgment. The future coin tosses – even if all loon-up – are part of a history
determining truth about chance. If the loonie results form part of a pattern best fit by an
alternative probability theory, then chances are not 50% after all. This is undermining for the
Humean: A theory of chance may allow a possible future which together with past and present
facts implies a contrary theory of chance.
Worse, argues Lewis, such undermining leads to contradiction given the Principal Principle.
To state Lewis’s argument, I will use ‘F’ as a parameter assigned an undermining world and let it
do double duty naming the world and the proposition that this world occurs. For this section, take
F to indicate the loonie world just discussed in which all future loonie tosses come up tails. On
the best-system account, F undermines T and so implies that T is false. Thus, the credence of F
given T should be zero. On the other hand, our theory of chance T gives F a probability 1/2n for
the assumed n future tosses. So, by PP (and specifically * with ‘F’ in place of ‘X’), our credence
for F given this theory should also be 1/2n, contradicting the first result of zero. In Lewis’s terms,
this reductio is the “big, bad bug” for Humean Supervenience.
Lewis’ argument explicitly concerns metaphysically possible but non-actual worlds
(those extending the actual past and present but with a non-actual future that currently has some
chance). Thus, the undermining relationship, that F implies ~T, is a matter of logical entailment.
I will restate the first half of the reductio, this way:
i) F logically entails the denial of theory of chance T, thus Credence(F|T) is zero.
The second half of the reductio can be compactly formulated as
ii) PP is true, so Credence(F|T)=Chance(F) which is non-zero.
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By his (1994), Lewis is prepared to reject PP (replacing it with a new principle relating chance to
credence, “NP”) while continuing to premise F as a non-actual world.
My (1994) perspectivalist best-system account of laws is meant to preserve PP by rejecting
the premise of i), that F logically entails the denial of T. A practical understanding, I argue, takes
actual laws and projects them onto a counterfactual world like F. This is the normal and
appropriate scientific perspective to take on a nomically possible world. We understand it as
having our laws because that interpretation illustrates these laws and their chances and so
provides a scientifically useful model. (Again, the Humean assumes only a world of occurrent
facts while law attribution is an interpretive overlay on these facts. Thus, there need not be a
single right way to attribute laws to a world. After all, a world may be a model of many different
and conflicting scientific theories.) From this normal scientific point of view, we assign F actual
laws including T, so F does not contradict T, the first half of the reductio is false, and Lewis’s
version of the Bug fails given the perspectival best-system account.
Briggs, however, argues that these modal considerations – regarding non-actual but
nomologically possible worlds like F – are not relevant to the underlying epistemic problem: the
contradictory credence claims.
Anti-realist accounts of chance make significant headway against four metaphysical
problems related to the Bug. They do not, however, address the Bug itself. Their failure is
no accident: the Bug is driven chiefly by epistemic modality rather than nomological
modality, and by Humeanism rather than HS. Humeanism entails that if there are chances
at all, they can be constructed from categorical facts (perhaps together with facts about
the observer’s interests). Thus, anyone with epistemic access to the array of categorical
facts (perhaps together with the facts about her own interests) can rule out some theories
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of chance which grant nonzero probability to the array of categorical facts. But according
to PP, knowledge of the categorical facts is sufficient reason to dismiss a theory of
chance only if theory assigns probability 0 to the categorical facts. At bottom, the Bug
involves a conflict between two principles of rational credence. Tinkering with
nomological modality misses the point and leaves the Bug intact. (Briggs 2009a, p. 91-
92)
The reductio, then, need not suppose F to be a nonactual possible world. Instead, because the
Bug depends on credence, taking F to be epistemically possible is sufficient for the reductio. To
see this, follow Briggs and replace logical entailment with a priori entailment in i):
i′) F a priori entails ~T, so Credence (F|T) is zero.
The premise of i′) may seem definitive of best-system theory: If undermining world F happens to
be actual, then the actual best system will be contrary to T. And, I want to admit, the conclusion
of i′) is a straightforward consequence of its premise. On the other hand, given PP, ii)’s
1 I am a bit uneasy with the “antirealist” characterization of the perspectivalist account of
science’s laws. For my concerns, see (Halpin 2003) on the objectivity of perspectivalist laws.
Still, as the pages below will indicate, I am much indebted to Briggs for her critique and
subsequent correspondence.
2 (Ward 2005), also criticized in (Briggs 2009a), gives an expressivist account of laws, so rejects
truth-claims about laws and any supervenience for facts about laws: there are no such facts. So,
in this sense he rejects Humean Supervenience. Still, he is a Humean for postulating no facts that
fail to supervene on the non-nomic occurrences.
3 “Normal” here means there are no crystal balls or other means to see directly into the future.
The full principle applies at all times when credence depends only on “admissible” evidence and
consequently is much more powerful than the simple (*).
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conclusion that Credence (F|T) is non-zero would seem inescapable. So, the contradiction
remains with i) replaced by Briggs’ i′).
Briggs argues that my (1994) account is subject to argument i′), summarizing my account of
laws (for world w from the perspective from which w is actual) as follows:
(**) “The laws of a world from the perspective of its inhabitants are completely fixed by
the world’s array of categorical properties.” (2009b, p. 87)
That is, there is a single perspective and so a determinate assignment of laws for a theorist’s
actual world; given a best-system account, these laws are just the consequences of the best-
system for the given world. Thus, if the actual world happens to have a future undermining T,
then the actual best system fixes actual laws contradicting T. This conditional would appear a
priori by the argument just given, consequently the premise of i′) is true and its conclusion, Cr(F|
T)=0, may seem inescapable.
In fact, I think, my (1994) and (1999) are both confused on this point about laws for the
actual world and specifically on the proper perspective of scientists working within a world
rather than taking a God’s eye view of the full world throughout all time. Nonetheless, the
perspectivalist can and should reject (**), i′), and Cr(F|T)=0 for reasons independent of the
undermining argument. Roughly, the laws properly assigned to the actual world depend on the
context of the assigner. To show this, I will argue that law and chance assignments for actual
world epistemic possibilities are perspectival just as for metaphysical possibilities. (Also, I will
briefly argue that the rebuttal works for Ward’s expressivism just as for the perspectival best-
system account.) For these purposes, F will be updated to a more fully-fleshed out undermining
world.
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2. Contextual Chance Assignments
The following story, an American loony story, is probably (indeed hopefully) false. Yet it is
an epistemic possibility regarding the former U.S. Republican party nominee for Vice President.
Sara Palin’s move into television entertainment and “tea-party” fame, the story goes, revitalizes
her public standing and launches her successful quest to become President of the United States in
2017. Mid-century her still-deluded admirers impose a tribute: The Sara Palin $100 coin (needed
after a long inflationary bout caused by the inept economic policies of her administration). The
story is a bit far-fetched but epistemically possible circa 2010. So too are many possibilities for
the large number, n, of coin-tosses of these American loonies. Suppose for our story that Palin’s
face comes up each and every time the coin is tossed. And suppose that this happens even though
the coin is minted in a normal way and tossed just like any other coin. One last detail: Barack
Obama lives to see the coin minted but refuses to touch the thing.
That is the story. How should this American loonie world (hereafter F replacing the F-world
of section one) be assigned laws and chances? I do not insist that there is a unique answer.
Nonetheless, the story’s provenance suggests a preferred account. The possible Palin-coin-
tossing results of F are generated by thinking about the standard chances for a standard coin,
again 50% chance of heads, allowing a 1 in 2n chance for the all-heads sequence. Thus, we are
inclined to see hypothetical F as a bizarre statistical anomaly. Or so I claim. Here is another way
to make the same intuitive point about our perspective on hypothetical F. Again, F may or may
not represent the actual future. But on the hypothesis that F is actual, we may ask about what
would happen if in his old age Barak Obama were (counter to the facts of hypothetically actual
F) to lower himself to flip a few Palin-coins. Because the coin in question has normal symmetry,
and because there is no reason to see the hypothetical coin toss results of F as anything but an
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anomaly, one plausibly thinks Obama would likely get about half the coins Palin-up. That is,
from our early 21st century perspective, one naturally assigns the Palin coin normal chance.
I take it to be part of rationality to model the future in accordance with the known or
justifiably believed chances. We apply our best theory to model both clearly counterfactual
possibilities and epistemic ones like the American loony story at hand. Of course, given that the
loony story is undermining, if it happens to be actual, scientists of the future will disagree with
our chance theory when they see the data come in. We can imagine these scientists first
skeptical, then very puzzled as their own repeated tests find nothing awry with the coin’s
construction or the claim it always comes up heads. They will be exasperated, no doubt, when
their own tosses all result in Palin glibly smiling up at them. (I imagine these theorists concerned
that some sort of cheating or even magic is afoot and then, perhaps, minting and testing other
coins with similar representations – the Tina Fey coin?, the George W. Bush coin? Perhaps some
may even be drawn to Plantinga’s Augustinian science. Still, the circa 2010 point of view sees all
this as mistaken. If the future holds in store what we now see as a statistical glitch, then the
resulting science will be wrong because based on a huge accident.) In any case, I take there to be
a good puzzle of hypothetical disagreement:
Present theorists interpret F as a world governed by T (so as a statistical anomaly) while
those possible theorists of the year 2060 who are inhabiting F (and may be in our future)
disagree and do so on the basis of more information, albeit information we take as mere
accident.
This hypothetical disagreement will seem puzzling on any account of law: Why should we
rational thinkers disagree with potential future experts, better informed observers, about their
possible future, a future we may in fact share? It is odd to say that they are just wrong about their
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world but that we will come to agree with them if only (a) per improbable, it turns out that they
are in the actual future and (b) we wait fifty years and ourselves became better informed. For
present purposes, I want to explore only how the perspectival best-system account should handle
the American loony world and its puzzle of epistemic disagreement.
On the perspectival account, I think, this puzzle is straightforwardly resolved. We of the
early 21st century tentatively accept T. It is, then, practical to project T even onto undermining
possibilities. This projection is justified for the reasons noted above in the Canadian loony case:
attributing laws to a model of those laws is useful, indeed almost irresistible. Thus we see the
American loony possibility (F) as a statistical glitch governed (or, better) generated by T. That
said, if indeed the facts turn out in the shocking way described by the American loony story,
future theorists will rightly attribute contrary laws and chances to this same possibility F.
(Assuming that F is clearly undermining, future theorists will reasonably reject T for the good,
practical reason that a better overall system is available for the actual data.4) Accordingly, one
ends up with two reasonable perspectives on F rather than real disagreement.
Taking stock, Briggs’ reductio (as I have restated it) goes as follows:
i′) F a priori entails ~T, so Credence(F|T) is zero, while,
ii) PP is true, so Credence(F|T)=Chance(F) which is non-zero.
But I have just argued against i′). Even for the actual world, we bring perspective and, from the
point of view of the second decade of the 21st century (well before any Palin coins might be
made), see F as a statistical anomaly assigning it the 50% theory of chance, T. Thus from our
perspective, F does not a priori entail ~T and the reasonable credence of F given T is small but
non-zero as PP requires.
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I believe that Ward’s view is consistent with this perspectival analysis though his account of
laws replaces claims about chance facts with scientific “norms”, e.g., “model following the 50%
chance rule”, to be projected onto possible worlds.
If chances are projections of our confidences, and our standards for projection are not so
stringent as to associate a unique chance with each total history, there need be no paradox
[of undermining]. (Ward 2005, 242)
Now, Briggs responds that the standards are strict enough to generate the Bug for Ward even if
not strict enough to assign a unique norm. About a world with an unusual number of coins
landing heads, she writes that if a rational believer “knew what the ideal observer knows—that
such a future is the actual future—then she would reject the ½ rule outright.” (2009a, 91) But this
last is wrong, or so I conclude from the analysis of the hypothetical disagreement puzzle: A fully
rational believer at the present time, somehow informed that F is true (i.e., given a God’s eye
4 In personal correspondence, Briggs describes a concern with “induction” to discover a best-
system rather than apply an accepted theory that is tentatively assumed best. As she points out, I
stress that Credence(F|T) is non-zero when projecting the settled view of 50-50 coin chances
onto F. However, she notes, when T itself is in question, it is important, e.g., when using Bayes’
theorem, that Credence(F|T) be zero. Quite right: Only from a perspective from which T is
tentatively accepted should one project T onto F and take Credence(F|T) to be non-zero. When
T’s status as best-system is in question, one is in something like the context of the exasperated
future scientists of the American loonie story, struggling with how the interpret/systematize the
data of world F. From this perspective, one of determining best-system and truth of T,
Credence(F|T) will be zero on the assumption that F undermines T. Halpin (1994) attempts to
deal with some of the complications of other perspectives and the PP for these.
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view of total history), would still understand that the ½ rule is appropriate for normally informed
believers of her time and thus not to be rejected outright.
3. Advantages
To many it will seem odd (if not absurd) to take nomic claims as perspective dependent.
But the Humean need not find this perspectivalism problematic. Again, the Humean postulates
that “at bottom” there is only the occurrent. The rest, all non-occurrent fact, is what I call
“interpretative” and perspective relative (that is, theorists interpret the patchwork of occurrences
by assigning nomic connections legitimized by their place in theory: laws, chances, dispositions,
etcetera). Moreover, there are significant advantages to this “antirealism”. These can be seen in
new light given Briggs’ epistemological concern regarding law-attribution for the actual world’s
possibilities.
First, reiterating, the epistemological problem for undermining futures – the hypothetical
disagreement puzzle – extends to all views about chance. However, a proponent of the
perspectivalist view has a straightforward solution: What appears to be disagreement is, for the
perspectivalist, a difference of point of view. Thus, even if F is indeed actual, we early 21st
century thinkers properly take the Palin-coin to have only a 50% chance of heads while future
denizens of our undermining world are right to see chance of heads as very high.
Next, there are well known apparent failures of Humean Supervenience used to argue
against best-system accounts. It is argued that there are intuitively clear examples of world pairs
with the same occurrent facts but different nomic truths. In other worlds, there is a supposed
metaphysical disagreement between possible worlds with the same occurrent facts. But the
perspectivalist can treat this difference just like the first: two perspectives rather than real
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disagreement. For example, Tooley and Carroll ask us to consider worlds with hypothetical
forces and particles. (Tooley 1977, Carroll 1994). In one case considered by Carroll, worlds w1
and w2 include X particles and Y fields: In w1 all X particles that enter a Y field follow law of
nature L1 and acquire spin UP. On the other hand, w2 is just like w1 excepting X-Y interactions:
In w2 when X particles enter Y fields they acquire spin DOWN as required by the laws L2 of w2.
Next consider what happens if a mirror were to deflect all X particles of both worlds away from
Y fields. The two resulting possibilities, w1′ and w2′ have exactly the same occurrences (we may
suppose). But, because inserting a few mirrors should not change laws of nature, it is intuitive to
see the first mirror world as having L1 and the second as having L2. So, the argument goes, the
two mirror worlds w1′ and w2′ have the same occurrences but different laws – a violation of
Humean supervenience. In contrast, the perspectivalist takes the differences between w1′ and w2′
as interpretive differences regarding one world rather than differences between two possible
worlds. From the point of view from which w1 is salient (e.g., considered actual) L1 is to be
projected onto the one mirror world. Here too there is no metaphysical disagreement but only
two perspectives; Humean Supervenience is salvaged – relative to a perspective. And, again, a
world like the mirror world is an epistemic possibility but wide open with regard to its nomic
interpretation.5
Another Briggs criticism, I believe, points instead to an advantage for perspectivalism.
She writes that the Bug bites my view “slightly harder” than Lewis’s view because “Lewis, who
adopted the philosopher’s perspective [i.e., a perspective assigning each world laws according to
its own best system], could abandon PP for an approximation called the New Principle” (2009a,
89). According to this new principle, NP, the credence for a claim given theory T is identical to
5 To be fair, Carroll is well aware of the contextualist response, indeed he highlights it in a
review article (forthcoming, p. 6).
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the conditional chance of X given T: Credence(X|T)=Chance(X|T). For an undermining world F,
then, Credence(F|T)=Chance(F|T)=0 because F and T are seen as contradictory. This is “as
desired” writes Hall so that the Bug’s contradiction cannot be derived: ii) is not sound. (See Hall,
1994 p. 512.) Instead, the new principle allows only something like this pair of arguments:
i) F logically entails the denial of theory of chance T thus Credence(F|T) is zero,
iii) NP is true so Credence(F|T)=Chance(F|T) which is also zero.
Thus, PP’s problem of contradiction does not arise for NP.
Although the NP is Bug-resistant, it is not desirable when the concern is scientific use of
chance. Worlds like F are just extreme cases of statistical anomalies with respect to a theory like
T. Typical scientific analysis expects such glitches to occur from time to time in the universe.
Perhaps the first replicating molecule’s formation is such a glitch. Or again, multiverse theorists
usually see our pocket universe as anomalous because life-allowing physical parameters are so
unlikely. A straightforward analogy: we should have a minute credence that a coin will come up
loon-up in million straight trials given that the coin is fair. Accordingly, Credence(F|T) should be
minute but non-zero as PP advises but both NP (without perspectivalism) and iii) deny.
Yet another advantage for a perspectival account is its conceptual openness. Just as
chance claims are true (as Lewis supposes) in virtue of their place in ideal system, other
sciences’ concepts (I propose) can be similarly legitimized. The best-system is supposed to be
ideal and so a concise and useful description for the occurrent facts. How conciseness and
usefulness is best realized depends on perspective: compression of the data for a given purpose.
Biology may make use of functional and even teleological concepts (Millikan, 1990). Arguably,
psychology too systematizes the occurrent facts but with hugely different concepts and very
different standards from biology or physics. Still, there is no disagreement in this difference but
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only change in perspective.6 The actual world, then, is properly interpreted in very different
ways, e.g., as merely mechanical or as involving purpose or mind, depending on perspective-
dependent theoretical need.
One nice application of this conceptual pragmatism has to do with concerns about the
“elegant” or “rational” or “intelligible” universe. We human animals, the story goes, use a
mathematical science that “deciphers the Mind of God contained in His work of creation.”
(Heller and Coyne, 2008). Robin Collins (2008) argues that “[t]he beauty and elegance of the
laws of nature also point to Divine design” and that
the laws of Nature themselves seem to be carefully arranged so that they are
intelligible, and in addition discoverable, by beings with our level of intelligence--like
solving a clever puzzle. This has been stressed by many prominent physicists. Albert
Einstein, for example, famously remarked that "the eternal mystery of the world is that
it is comprehensible.... The fact that it is comprehensible is a miracle".
Now, if laws govern creation in a metaphysically significant way, i.e., are prior to and
responsible for the universe’s events, then laws might, I suppose, be both inelegant and either
completely hidden from human endeavor or incomprehensible to those with human conceptual
abilities. But given the perspectival best-system account, laws are not governing but descriptive.
Scientific concepts are not mystically deciphered, on this view, but are legitimized in scientific
6 The eliminative materialist about beliefs and desires refuses to systematize from an intentional
stance. Dennett, on the other hand, takes beliefs and desires to be real in virtue of the success of
intentional systematizing. For the proponent of the perspectival best system account, a zombie
world is just the actual world from a perspective refusing to systematize using mentalistic
concepts. Again there are not two worlds with metaphysical differences but one world viewed in
different ways. See Halpin (manuscript).
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theorizing given the concepts and standards of particular human perspectives. The resulting
concise descriptions, attempts at best-system, cover a broad range of phenomena, elegantly
unifying a subject matter. The consequence is discoverability, intelligibility, and elegance for the
perspectivalist’s laws.
Summarizing, Brigg’s epistemological argument provides a new and important challenge
to Humeanism. And she is correct to critique my conflation of epistemic and metaphysical
possibilities. Still, I have tried to show that the Humean “antirealist” has good reasons to resist.
Indeed, bringing perspectivalism to bear on epistemic possibilities (as well as metaphysical ones)
proves advantageous to the Humean in a number of ways: each of the advantages described in
this last section involve or may involve interpretation of epistemic possibilities. The upshot, I
have argued, is that the perspectivalist not only has the resources to meet her objection and
maintain the PP, but also solves certain problems of disagreement and failure of supervenience
while respecting conceptual openness in science.
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