Posts on: Metaphysics
Here's an attractive picture. All there really is, at a fundamental
level, are fields in spacetime (or something like that). The world as we
know it, with its rocks and chairs and cats and people, somehow emerges
from this basis: all truths about rocks and chairs etc. are made true by
truths about fields in spacetime. But how? To explain this, it would
help if we could locate the familiar objects – rocks and chairs etc. –
in the physical description of reality. With the help of classical
mereology, which is plausibly analytic, this
seems possible: ordinary objects can be identified with aggregates of
spacetime points. They are regions in spacetime. With this, we can
explain how simple facts involving ordinary objects can emerge. For
example, what makes it true that my chair has steel legs is that its
region has a certain kind of subregion with high-amplitude excitations
of quark and electron fields in a certain arrangement.
The Best-Systems Account of chance promises to explain why beliefs about chance should affect our beliefs about ordinary events, as formalized by the Principal Principle. In this post, I want to discuss a challenge to any such explanation.
First, some background.
For any candidate chance function f, let [f] be the set of worlds of which f is (part of) the best system. According to the Best-Systems Account (BSA), the hypothesis "Ch=f" that f is the true chance function expresses the proposition [f]. In what follows, I'll assume that a world is simply a history of "outcomes", and that the candidate systems can be compressed into a single (possibly parameterized) chance function.
Humean accounts of physical laws seem to have an advantage when it comes to explaining our epistemic access to the laws: if the laws are nothing over and above the Humean mosaic, it's no big mystery how observing the mosaic can provide information about the laws. If, by contrast, the laws are non-Humean whatnots, it's unclear how we could get from observations of the mosaic to knowledge of the laws. This line of thought is developed, for example, in Earman and Roberts (2005). Chen (2023) (as well as Chen (2024)) argues that it rests on a mistake. Eddy suggests that Primitivists about physical laws have no more trouble explaining our epistemic access than friends of the Best-System Analysis.
Gómez Sánchez (2023) asks an important and, in my view, unsolved question: what kinds of properties may figure in the laws of "special science" (chemistry, genetics, etc.)?
For the most part, the patterns captured in special science laws are not entailed by the fundamental laws of physics, nor by the intrinsic powers and dispositions of the relevant objects. Some kind of best-systems account looks appealing: the Weber-Fechner law, the laws of population dynamics, the laws of folk psychology etc. are useful summaries of pervasive and robust regularities in their respective domains. They are the "best systematisation" of the relevant facts, in terms of desiderata like simplicity and strength.
There's a striking tension in Lewis's philosophy. His epistemology and philosophy of mind, on the one hand, leave no room for (non-trivial) a priori knowledge or a priori inquiry. Yet for most of his career, Lewis was engaged in just this kind of inquiry, wondering about the nature of causation, the ontology of sets, the extent of logical space, the existence of universals, and other non-contingent matters. My paper "The problem of metaphysical omniscience" explores some options for resolving the tension. The paper has just come out in a volume, Perspectives on the Philosophy of David K. Lewis, edited by Helen Beebee and A.R.J. Fisher.
I've long been puzzled by the nature of quantities, but I've never really
followed the literature. Now I've read Jo Wolff's splendid monograph on the
topic. I'm still puzzled, but at least my puzzlement is a little better
informed.
The basic puzzle is simple and probably familiar. On the one hand, being 2m high
or having a mass of 2kg appear to be paradigm examples of simple, intrinsic
properties. On the other hand, these properties seem to stand in mysterious
relationships to other properties of the same kind. First, there's an exclusion
relationship: nothing can have a mass of both 2kg and 3kg. Second, there are
non-arbitrary orderings and numerical comparisons: one thing may be four times
as massive as another; the mass difference between x and y may be twice that
between z and w. If 2kg and 8kg are primitive properties, why couldn't an object
have both, and where does their quasi-numerical order and structure come from?
In chapter 3 of The Powers Metaphysic, Neil Williams presents a nice problem for dispositionalists: the "problem of fit".
Dispositionalists hold that there are fundamental dispositional properties. Now consider a particular rock and a particular glass. The rock might have a disposition to break the glass when thrown at it. And the glass might have a disposition to survive impact of the rock. These dispositions are incompatible: if the rock is disposed to break the glass, the glass can't be disposed to survive the impact. But if dispositions are fundamental, then what prevents the rock and the glass from having the incompatible dispositions? The dispositionalist seems to require a mysterious ban on recombination.
Friends of primitive powers and dispositions often contrast their
view with an alternative view, usually attributed to Lewis, on which
modal facts about powers, dispositions, laws, counterfactuals etc. are
grounded in facts about other possible worlds. But Lewis never held
that alternative view – nor did anyone else, as far as I
know. The allegedly mainstream alternative is entirely made of
straw. The real alternative that should be addressed is the
reductionist view that powers and dispositions are reducible to
ultimately non-modal elements of the actual world.
It is tempting to think that there is nothing more to physical
quantities than their nomic role: that to have a certain mass just is
to behave in such-and-such a way under such-and-such conditions.
But it is also tempting to think that the "Galilean equivalence" of
inertial mass and gravitational mass is a true identity; i.e.,
that
Inertial mass = gravitational mass.
However, the role associated with "inertial mass" is completely
different from the role associated with "gravitational mass". So if
having such-and-such inertial mass is having the relevant
dispositions associated with "inertial mass", and likewise for
gravitational mass, then the Galilean equivalence could not be an
identity. It would rather state an empirical law, according to which
two distinct quantities always have the same value.
The two-dimensionalist account of a posteriori (metaphysical)
necessity can be motivated by two observations.
First, all good examples of a posteriori necessities follow a priori
from non-modal truths. For example, as Kripke pointed out, that his
table could not have been made of ice follows a priori from the
contingent, non-modal truth that the table is made of wood. Simply
taking metaphysical modality as a primitive kind of modality would
make a mystery of this fact.
I used to agree with Lewis that classical mereology, including
mereological universalism, is "perfectly understood, unproblematic,
and certain". But then I fell into a dogmatic slumber in which it seemed
to me that the debate over mereology is
somehow non-substantive: that there is no fact of the
matter. I was recently awakened from this slumber by a footnote in
Ralf Busse's forthcoming article "The
Adequacy of Resemblance Nominalism" (you should read the whole
thing: it's terrific). So now I once again think that Lewis was right. Let
me describe the slumber and the awakening.
Necessitarian and dispositionalist accounts of laws of nature have
a well-known problem with "global" laws like the conservation of
energy, for these laws don't seem to arise from the dispositions of
individual objects, nor from necessary connections between fundamental
properties. It is less well-known that a similar, and arguably more
serious, problem arises for dynamical laws in general, including
Newton's second law, the Schrödinger equation, and any other law
that allows one to predict the future from the present.
A lot of what I do in philosophy is develop models: models of
rational choice, of belief update, of semantics, of communication,
etc. Such models are supposed to shed light on real-world phenomena,
but the connection between model and reality is not completely
straightforward.
For example, consider decision theory as a descriptive model of
real people's choices. It may seem straightforward what this model
predicts and therefore how it can be tested: it predicts that people
always maximize expected utility. But what are the probabilities and
utilities that define expected utility? It is no part of standard
decision theory that an agent's probabilities and utilities conform in
a certain way to their publicly stated goals and opinions. Assuming
such a link is one way of connecting the decision-theoretic model with
real agents and their choices, but it is not the only (and in my view
not the most fruitful) way. A similar question arises for the agent's
options. Decision theory simply assumes that a range of "acts" are
available to the agent. But what should count as an act in a
real-world situation: a type of overt behaviour, or a type of
intention? And what makes an act available? Decision theory doesn't
answer these questions.
The following principles have something in common.
Conditional Coordination Principle.
A rational person's credence in a conditional A->B should equal the
ratio of her credence in the corresponding propositions B and A&B;
that is, Cr(A->B) = Cr(B/A) = Cr(B)/Cr(A&B).
Normative Coordination Principle.
On the supposition that A is what should be done, a rational agent
should be motivated to do A; that is, very roughly, Des(A/Ought(A))
> 0.5.
Probability Coordination Principle.
On the supposition that the chance of A is x, a rational agent
should assign credence x to A; that is, roughly, Cr(A/Ch(A)=x) = x.
Nomic Coordination Principle.
On the supposition that it is a law of nature that A, a rational agent
should assign credence 1 to A; that is, Cr(A/L(A)) = 1.
All these principles claim that an agent's attitudes towards a certain
kind of proposition rationally constrain their attitudes towards other
propositions.
Humeans about laws of nature hold that the laws are nothing over
and above the history of occurrent events in the world. Many
anti-Humeans, by contrast, hold that the laws somehow "produce" or
"govern" the occurrent events and thus must be metaphysically prior to
those events. On this picture, the regularities we find in the world
are explained by underlying facts about laws. A common argument
against Humeanism is that Humeans can't account for the explanatory
role of laws: if laws are just regularities, then then laws can't
really explain the regularities — so the charge —
since nothing can explain itself.
In On the Plurality or Worlds, Lewis argues that any account
of what possible worlds are should explain why possible worlds
represent what they represent. I am never quite sure what to make of
this point. On the one hand, I have sympathy for the response that
possible worlds are ways things might be; they are not things
that somehow need to encode or represent how things might be. On the
other hand, I can (dimly) see Lewis's point: if we have in our
ontology an entity called 'the possibility that there are talking
donkeys', surely the entity must have certain features that make it
deserve that name. In other words, there should be an answer to the
question why this particular entity X, rather than that other entity
Y, is the possibility that there are talking donkeys.
In "Ramseyan
Humility", Lewis argues for a thesis he calls "Humility". He never
quite says what that thesis is, but its core seems to be the claim
that our evidence can never rule out worlds that differ from actuality
merely by swapping around fundamental properties. Lewis's argument, on
pp.205-207, is perhaps the most puzzling argument he ever gave.
Lewis begins with some terminology.
An amusing passage from a recent
paper by Erik and Martin Demaine on the hypar, a pleated hyperbolic
paraboloid origami structure:
Recently we discovered two surprising facts about the
hypar origami model. First, the first appearance of the model is much
older than we thought, appearing at the Bauhaus in the late
1920s. Second, together with Vi Hart, Greg Price, and Tomohiro Tachi,
we proved that the hypar does not actually exist: it is impossible to
fold a piece of paper using exactly the crease pattern of concentric
squares plus diagonals (without stretching the paper). This discovery
was particularly surprising given our extensive experience actually
folding hypars. We had noticed that the paper tends to wrinkle
slightly, but we assumed that was from imprecise folding, not a
fundamental limitation of mathematical paper. It had also been
unresolved mathematically whether a hypar really approximates a
hyperbolic paraboloid (as its name suggests). Our result shows one
reason why the shape was difficult to analyze for so long: it does not
even exist!
So the hypar joins the ranks of phlogiston,
the planet Vulcan,
the largest
prime, or the quintic
formula: objects of inquiry that turned out not to exist.
How much can you say about the world in purely logical terms? In
first-order logic with identity, one can construct formulas like
'(Ex)(Ey)~(x=y)'. But arguably, this doesn't yet mean anything. As we
learned in intro logic, formulas of first-order logic have no fixed
interpretation; they mean something only once we provide a domain of
quantification and an assignment of values to predicate and function
symbols. As it happens, '(Ex)(Ey)~(x=y)' doesn't contain any
non-logical predicate and function symbols, so to make it mean
anything we just need to specify a domain of quantification. For
example, if the domain is the class of Western black rhinos, then the
formula says that there are at least two Western black rhinos.
I'll begin with a strange consequence of the best system
account. Imagine that the basic laws of quantum physics are
stochastic: for each state of the universe, the laws assign
probabilities to possible future states. What do these probability
statements mean?
The best system account identifies chance with the probability
function that figures in whatever fundamental physical theory best
combines the virtues of simplicity, strength and fit, where fit is a
matter of assigning high probability to actual events. So when we say
that the chance of some radium atom decaying within the next 1600
years is 1/2, what we claim is true iff whatever fundamental theory
best combines the virtues of simplicity, strength and fit assigns
probability 1/2 to the mentioned outcome. As a piece of ordinary
language philosophy, this is not very plausible. For one thing, people
speak of chances even when it is assumed that the fundamental dynamics
is deterministic. Moreover, by ordinary usage, chances are logically
independent of actual frequencies, which is incompatible with the best
system account. Nevertheless, the account may be plausible as a
somewhat revisionary explication of one strand in the mess that is our
ordinary conception of chance.
In The Metaphysics within Physics, Tim Maudlin raises a
puzzling objection to Humean accounts of laws. (Possibly the same
objection is raised by John Halpin in several earlier papers such as
"Scientific law: A perspectival account".)
Scientists often consider very different models of putative
laws. Such models can be understood as miniature worlds or scenarios
in which the relevant laws obtain. On Humean accounts, the laws at a
world are determined by the occurrent events at that world. The
problem is that rival systems of laws often have models with the very
same occurrent events. Whether this is a problem depends on what we
mean by "the relevant laws obtain". Maudlin:
For every way things might have been there is a possible world where
they are that way. What does that tell us about the number of worlds?
If we identify ways things might have been ("propositions") with
sentences of a particular language, or with semantic values of such
sentences, the answer will depend on the language and will generally
be small (countable). But that's not what I have in mind. It might
have been that a dart is thrown at a spatially continuous dartboard,
and each point on the board is a location where the dart's centre
might have landed. These are continuum many possibilities, although
they cannot be expressed, one by one, in English.
Many of our best scientific theories make only probabilistic
predications. How can such theories be confirmed or disconfirmed by
empirical tests?
The answer depends on how we interpret the
probabilistic predictions. If a theory T says 'P(A)=x', and we
interpret this as meaning that Heidi Klum is disposed to bet on A at
odds x : 1-x, then the best way to test T is by offering bets to Heidi
Klum.
Nobody thinks this is the right interpretation of probabilistic
statements in physical theories. Some hold that these statements are
rather statements about a fundamental physical quantity called
chance. Unlike other quantities such as volume, mass or charge,
chance pertains not to physical systems, but to pairs of a time and a
proposition (or perhaps to pairs of two propositions, or to triples of
a physical system and two propositions). The chance quantity is
independent of other quantities. So if T says that in a certain type
of experiment there's a 90 percent probability of finding a particle
in such-and-such region, then T entails nothing at all about particle
positions. Instead it says that whenever the experiment is carried
out, then some entirely different quantity has value 0.9 for a certain
proposition. In general, on this interpretation our best theories say
nothing about the dynamics of physical systems. They only make
speculative claims about a hidden magnitude independent of the
observable physical world.
In a nice little paper, "The Non-Transitivity of the
Contingent and Occasional Identity Relations", Ralf Bader argues
that if identity is relative to times or worlds, then it becomes
non-transitive and thus no longer qualifies as real identity.
Following Gallois, Bader assumes that a proponent of occasional
identity must insist that identity statements are always relativised
to a time. Now he considers a case where between times t1 and t2, two
objects B and D simultaneously undergo fission in such a way that one
fission product of B fuses with one fission product of D. Of the three
resulting objects A, C and E, one (C) is a fission product of both B
and D. Bader argues that at the initial time t1, it is then true that
A=C and C=E, but not that A=E. So identity at t1 is not
transitive.
In the (Northern) summer, I wrote a short survey article on
contingent identity. The word limit did not allow me to go into many
details. In particular, I ended up with only a brief paragraph on
Andre Gallois's theory of occasional identity, although I would have
liked to say a lot more. So here are some further thoughts and comments
on Gallois's account.
In his 1998 monograph Occasions
of Identity, Gallois defends the view that things can be identical at some
times and worlds and non-identical at others. For simplicity, I'll
focus only on the temporal dimension here. Gallois begins
with a long list of scenarios where it is intuitive to say that things
are identical at one time but not at others. For example, when an
amoeba A fissions into two amoebae B and C, it is tempting to say that
B and C were identical prior to the fission and non-identical
afterwards.
It is natural to think of a possible world as something like an extremely specific story or theory. Unlike an ordinary story or theory, a possible world leaves no question open. If we identify a theory with a set of propositions, a possible world could be defined as a theory T which is
- maximally specific: T contains either P or ~P, for every proposition P;
- consistent: T does not contain P and ~P, for any proposition P;
- closed under conjunction and logical consequence: if T contains both P and Q, then it contains their conjunction P & Q, and if T contains P, and P entails Q, then T contains Q.
It is often useful to go in the other direction and identify propositions with sets of possible worlds. We can then analyse entailment as the subset relation, negation as complement and conjunction as intersection. Of course, we may not want to say that a world is a (non-empty) set of (consistent) propositions and also that a consistent proposition is a non-empty set of worlds, since these sets should eventually bottom out. But that doesn't seem very problematic, and it is easily fixed as long as there is a simple 1-1 correspondence between worlds and logically closed, consistent and maximally specific theories. In particular, one might suspect that on the present definitions, every logically closed, consistent and maximally specific theory uniquely corresponds to a possible world, namely the sole member of the intersection of the theory's members.
In metaphysics, "Humeans" are people who believe that truths
about laws of nature, counterfactuals, dispositions and the like
(truths about what must or would be the case) are in
some sense reducible to non-modal truths (about what is the
case).
One way to be a Humean is to deny that there are any laws
of natures, non-trivial counterfactuals, etc.: if there are no modal
truths, then trivially all modal truths are reducible to non-modal
truths. On this account, there are no "necessary connections between
distinct existences": eating arsenic might in fact be followed by
death, but it could just as well be followed by hiccups or anything
else.
A judge in the New South Wales Supreme Court has decided that Bart and Lisa Simpson are persons under the age of 16.
This is odd. According to The Simpsons, Bart and Lisa are certainly persons under the age of 16; but 'according to The Simpsons, P' does not entail P, I would have thought. Indeed, according to the Simpsons, Bart and Lisa exist, while in reality they don't. And since Bart doesn't exist, no-one is Bart Simpson; so in particular, every person under the age of 16 is not Bart Simpson; therefore Bart Simpson is not a person under the age of 16.
Sometimes, a property A entails a property B while B does not entail A, and yet there seems to be no interesting property C that is the remainder of A minus B. For instance, being red entails being coloured, but there is no interesting property C such that being red could be analysed as: being coloured & being C. In particular, there seems to be no such property C that doesn't itself entail being coloured.
This fact has occasionally been used to justify the claim that various other properties A entail a property B without being decomposable into B and something else. I will try to raise doubts about a certain class of such cases.
Daniel Nolan and I once suggested that talk about sets should be analyzed as talk about possibilia. For simplicity, assume we somehow simply replace quantification over sets by quantification over possible objects in our analysis. This appears to put a strong constraint on modal space: there must be as many possible objects as there are sets.
But does it really? "There are as many possible objects as there are sets." By our analysis, this reduces to, "there are as many possible objects as there are possible objects". Which is no constraint at all!
As a principle of plentitude, Recombination for Individuals is far too weak. If there happens to be nothing that is both red and dodecagonal, the recombination principle for individuals gives us no world where anything is. Likewise, if it happens that no red thing is on top of a blue thing, the principle gives us no world where this is different. But combinatorial reasoning seems to give us such worlds.
Many versions of the recombination principle are floating
around in the literature. Most of them are principles for individuals,
saying, roughly, that you get a possible world by patching together
(copies of) arbitrary parts of other possible worlds. (I will have
more on principles for properties later.)
It is surprisingly difficult to make this precise. All attempts I
know of fail in one way or another. To illustrate some of the
pitfalls, let's begin with this classic version from Daniel Nolan's
"Recombination Unbound".
Let F be a fundamental property, understood as a maximal class of possible things that are perfectly similar in one respect. (This is one of Lewis's four proposed definitions of fundamental properties, and I think the best one.) And suppose I have F. What would it take to know that I have F?
Given that F is some class { Wo, Fred, ... }, and given that having F means being a member of F, it might seem puzzling how I can be ignorant about whether or not I'm F: how could I fail to know that I am a member of { I, Fred, ... }? But here we are substituting corefering expressions in a (hyper)intensional context, which is illegitimate. If I knew that F = { I, Fred, ... }, then I probably ought to know that I am F. So if I don't know that I am F, that's because I don't know that F = { I, Fred, ... }.
Some properties are inherited from wholes to their parts: if x is (completely) made of steel, then its parts are also (completely) made of steel; if x is in the top drawer, then its parts are also in the top drawer. Other properties are upwards inherited from parts to wholes: if a part of x contains steel, then x contains steel; if a part of x touches the ground, then x touches the ground. Yet other properties are not inherited either way: if x is a hand, then x usually has non-hands as parts and is part of non-hands.
I believe that there is such a property as being two meters away. -- Not two meters away from me, or from somebody else, or two meters away from something or other. Just two meters away.
Admittedly, there is a sense in which something can be two meters away only relative to some point of reference. But compare properties like being empty and being bent. There is a sense in which, strictly speaking, persisting things can be empty or bent only relative to a time: this cup here is empty at the present time while it was full 5 minutes ago. Likewise, at least prima facie many things are empty or bent only relative to worlds: the cup is empty at the actual world, but full at other possible worlds. That's why properties are often modeled as something like functions from worlds and times to sets of objects.
Here is a short paper version of my GAP.6 talk "Modal metaphysics and conceptual metaphysics", to appear in the GAP.6 proceedings. It has a lot less formulas than the talk.
I distinguish two metaphysical projects: modal metaphysics and conceptual metaphysics. I show that the two projects really are distinct, and that Frank Jackson's argument for the opposite conclusion doesn't work. Then I have a closer look at how the projects come apart, and suggest that when they do, the modal project always becomes metaphysically uninteresting. Thus the term "metaphysical modality" is a misnomer: metaphysical entailment only matters for metaphysics insofar as it coincides with conceptual entailment.
I suppose I should say a little more on what I call "modal back-reference", and on the sense in which what a sentence expresses can be conceptually independent of how things are in the actual world: doesn't what a sentence express always depend on what the sentence means? Unfortunately, I don't have a simple and uncontroversial answer to that, so I just ignored this point. Hopefully no-one will notice.
Brian argues that our intuitions about whether an action C causes somebody's continued survival is linked to the applicability of causative notions like "opening", "closing", "protecting", "threatening": if C inadvertently causes the survivor to be threatened but at the same time protects him from the threat, we are more inclined to count C as causing the survival than if C threatens the surviver but at the same time inadvertently causes him to be protected.
Just when I thought all viruses are specific, I caught an 'unspecific virus' last weekend -- at least that's what the doctors at the hospital identified it as. So I've been knocked out for about a week, but now I'm back with an exciting new theory of modality.
The theory is simple. It says that everything is possible. Pace Kripke, there are possible worlds where Queen Elizabeth is a poached egg and where Hesperus isn't Phosphorus. And pace almost everybody else, there are possible worlds where squares are round, bachelors married and where Hesperus isn't even self-identical.
Some philosophers believe that the second world war is a triple of a thing, a property and a time. Others have argued that my age is a pair of an equivalence class of possible individuals and a total ordering on such classes. It is also often assumed the number 2 is the set {{{}},{}}; that the meaning of "red" is a function from contexts to functions from possible individuals to functions from possible worlds to truth values; that possible worlds are sets of ... sets of properties; and that truth values are the numbers 0 and 1 (aka the sets {} and {{}}).
To my surprise, there are quite a few people here at ANU who believe that probabilities of various kinds can be modeled in terms of relative size of propositions: something has probability 1 if it is true in all (or 100%) of the relevant worlds, probability 0 if it is true in none (or 0%), and probability 0.5 if it is true in half of the worlds (or 50%). I also find it surprisingly hard to explain why I think that's wrong. Here are two arguments I've come up with so far (apart from obvious worries about making sense of these fractions in infinite and proper-class cases).
Let's say that something X is nomologically possible if it is true at some world where the actual laws of nature are true. The actual laws may or may not be laws at this world. All we require is that they are true there.
Now consider a chancy law according to which a coin tossed in some standard way has a 50 percent chance of landing heads. For this to be a law at some world w means that it is part of the best theory of w, or that it represents the actual propensities in w, or something like that. What does it mean for it to be merely true at a world?
Is it metaphysically necessary that like charges repel? One might think so: one might think that "charge" is partly defined by its theoretical role, so that this claim comes out analytic. Or one might think that science reveals to us the essence of properties, and that it is part of this essence of charge that like charges repel.
If that law about charges is metaphysically necessary, one might suspect that quite generally, nomological necessity coincides with metaphysical necessity (though see below for an argument against this suspicion):
Sorry, the server has been down quite a lot recently. Hope it's back to normal now.
Here's the talk I gave at Kioloa. It's partly identical to the talk I gave at GAP.6 in Berlin, but with more speculative ideas towards the end and less missionary appeals in between.
Are all truths entailed by logical truths? Depends on what we mean by "all truths" and "entailed" and "logical".
Let's understand a truth to be a true sentence of English, possibly enriched by logical vocabulary. As for entailment, let's distinguish metaphysical entailment (necessarily, if P then Q) from analytical (or conceptual or a priori) entailment. The precise definition of these notions, and the differences between them, won't matter.
So I was given a replacement computer now until the other one arrives. If you're waiting for a sign of life from me, I'll probably contact you soon.
But first some philosophy. I want to argue that necessitarianism is compatible with Humean recombinatorialism because powers aren't intrinsic in the sense relevant to this. I also want to suggest that in an ontology of powers, what's fundamental aren't really the powers, but the causal or nomic relations.
Necessitarianism is the view that properties like mass and spin have their causal or nomic role essentially: if a property doesn't behave like mass, it isn't mass. It follows that the laws about mass are metaphysically necessary. (There are many different views in the vicinity here, maybe more about this later.)
Here's an odd passage from Armstrong's A Combinatorial Theory of Possibility, p.116:
[Hume's Distinct Existences Principle], as we shall uphold it, may be stated thus:
If A and B are wholly distinct existences, then it is possible for A to exist while no part of B does (and vice versa).
The principle applies straightforwardly to individuals, properties and relations. [...]
It is interesting to notice that the converse of Hume's principle also seems to be true:
In their contributions to Lewisian Themes, Rae Langton and Jonathan Schaffer both argue that quidditism -- the claim that possible worlds may differ only in which intrinsic properties play which causal/nomological roles -- does not entail skepticism about intrinsic natures because standard replies to skepticism about the external world carry over to skepticism about intrinsic natures.
But it seems to me that there is an important difference: if quidditism is true, we not only lack knowledge about intrinsic natures, but also any beliefs about them.
Suppose some thing x turns F, and a little later some other thing y turns G. x is the only F throughout history, so on a Humean account of laws of nature, it may well be just a coincidence that y's being G followed x's being F. Suppose it is.
But now consider another world just like this one except that in the far future, lots of G-turnings follow lots of F-turnings so that in this world, it is a law that whenever something turns F and another thing is suitably related, then that other thing turns G. In such a world, x's turning F caused y's turning G.
I've learned a lot at the Lewis workshop, which was also enjoyable in every other respect. One thing I've learned is that my views about theory strength in Lewis's account of laws were rather naive.
Lewis defines a law of nature as a consequence of the best theory, where what makes a theory good is simplicity, strength, and fit (of assigned probabilities to actual occurrences). I claimed that objective standards for strength aren't hard to find: one could, for instance, use something like number and diversity of excluded possibilities (with a meaningful measure for 'number', these two criteria might coincide). But in the discussions, it turned out that this doesn't work, for at least two reasons.
I just realized that I don't know what my telephone number is. I used
to think it is 44717384. But 44717384 is a number, and the same as
252452510 in octal, or 2aa5548 in hexadecimal. Yet it sounds wrong to
say that my telephone number is 252452510 in octal, or that my
telephone number begins with 4 only in decimal notation. What's more,
telephone numbers are never pronounced "forty-four million, seven
hundred and seventeen thousand three hundred eighty-four". (I know an
old woman in a rural part of Germany whose number used to be 543; she, too,
always said "five four three".)
When sometime between 1986 and 2001, Lewis accepted (a certain version of) standard quantum physics, did he thereby accept that Humean Supervenience is false? I'm not sure. My knowledge of quantum physics ("knowledge" in the sense of "probably false, unjustified guesses" rather than "true, justified beliefs") doesn't suffice to see through this with any confidence. Anyway, here's some thoughts.
Humean Supervenience is the hypothesis that in worlds like ours, all
truths supervene on the spatiotemporal distribution of fundamental
properties at spacetime points. This appears to contradict what quantum physics says about entangled states: if two electrons are suitably entangled, their combined state is a superposition of X-spin(electron 1)=up & X-spin(electron 2)=down and X-spin(electron 1)=down & X-spin(electron 2)=up (![$m[1]](/texer/images/?format=gif&fontsize=12pt&tex=%5Csqrt%7B1%2F2%7D%7C%5Cmbox%7BX-up%7D%5Crangle_1%7C%5Cmbox%7BX-down%7D%5Crangle_2+-+%5Csqrt%7B1%2F2%7D%7C%5Cmbox%7BX-down%7D%5Crangle_1%7C%5Cmbox%7BX-up%7D%5Crangle_2)
, or so), which is not determined by any local qualities of the individual electrons: there are no spin states A and B such that whenever some electron is in A and another one in B, then their mereological fusion is in this entangled state. So Humean Supervenience is false.
This argument looks a lot better than it is:
Suppose some physical event E is causally necessitated by a certain distribution of physical properties P. Then if P occurs, E is bound to occur as well, no matter what else is the case. In particular, whether or not some non-physical event M also occurs before E will make no difference to E's occurrence. (Perhaps M nevertheless causes E, if E is overdetermined, or perhaps M is causally relevant in some even weaker sense, but at any rate M does not make a difference for E.)
To see the problem with this argument, consider a deterministic world where the occurrence of any event E at time t0 is causally necessitated by the state of the world at t-2 (before t): it obviously does not follow that the state of that world at t-1 makes no difference to E's occurrence.
The fundamental properties provide a minimal basis for all intrinsic qualities of things. That is, whenever two things are not perfect qualitative duplicates, they differ in the distribution of fundamental properties over their parts; whenever two things do not differ by that distribution, they are perfect qualitative duplicates. It follows that all fundamental properties are intrinsic. But not all intrinsic properties are fundamental: the fundamental properties provide a minimal basis for all qualitaties. Hence there is no fundamental property of having a mass of either 1g or 2g, because instantiation of that property is already determined by the distribution of mass 1g and mass 2g. For the same reason, there is no fundamental property of being the fusion of a round thing and a distinct rectangular thing. By and large, fundamental properties are never logically complex (like A or B) and never structural (determined by the distribution of properties over the parts of their instances).
About half a minute ago, I've poured tea into this cup. In a few seconds, I will take a
sip. What if I had taken a sip a minute earlier? I wouldn't have taken
a sip of tea from an empty cup: that is impossible. So there would
have been tea in the cup a minute ago. How did it get there? Maybe
I would have poured it in earlier. Or maybe it would have tunnelled
directly from the pot into the cup. Or maybe the tea would have
just materialized out of thin air. Some of these counterfactuals
do not sound very plausible, but let's assume that for the kind of
counterfactuals relevant to causation, they are all equally good so
that there is no fact of the matter about how the tea got into the cup
at the closest world where I take the sip a minute earlier: it does
so differently at different worlds that are equally close. (See Lewis,
"Counterfactual Dependence and Time's Arrow" for the standards of
evaluating such counterfactuals, and "Are we free to break the
laws?" for the indeterminacy of divergence miracles.)
Roughly, the principle of recombination says that anything can coexist and
fail to coexist with anything else. But that's too strong: things do
have essential extrinsic properties; if Kripke's origin is essential
to Kripke, Kripke cannot fail to coexist with his ancestors. However, a
perfect intrinsic duplicate of Kripke could fail to coexist with Kripke's ancestors.
So less roughly, the principle of recombination goes somehow like this:
For any things in any possible world there is a world
which contains any number of perfect intrinsic duplicates of all those
things and nothing else (i.e. nothing distinct from all these
duplicates).
What is a perfect intrinsic duplicate? Something that has exactly
the same intrinsic properties as the original. What
is an intrinsic property? A property that belongs to objects
independently of what exists and goes on around them. The
instantiation of an intrinsic property in some region of a world is
independent of the instantiation of intrinsic properties in other
regions.
I believe that the so-called problems of intrinsic change and accidental intrinsic properties are real problems. But I believe that their names are misleading, and that they have nothing to do with whether or not we construe properties as sets of things or as functions from worlds and times to sets of things.
Suppose we do the latter, and we also endorse counterpart theory and temporal parts theory. The property of being bent is a function that maps world-time pairs to sets of things. These things are temporal parts of world-bound individuals, ordinary fusions of particle segments, just like us, except that they are smaller along the time axis and all bent. This is a perfectly reasonable and common-sensical view, I believe (but of course I'm biased), and I don't think Lewis has any reason to reject it as turning properties into relations. There is after all a simple equivalence between being bent construed as a function and being bent construed as a Lewisian set: the set is the union of the range of the function; the function indexes all members of the set by their world and time.
For many things, there is no set that contains just those things. There is no set of all sets, no set of all non-self-members, no set of all non-cats, no set of all things, no set of pairs (x,y) such that x is identical to y, no set of (x,y) with x part of y, no set of (x,y) with x member of y.
If Lewis is right and there are proper-class many possibilia, there is also no set of possible philosophers, no set of possible dragons and no set of possible red things. However, if Lewis is right and there are proper classes, there will be proper classes of all these things. But there will still not be a class of all classes, a class of all non-self-members, a class of all non-cats, etc.
This is a follow-up to yesterday's entry.
Andy Egan argues that functions from worlds and times to sets of things are ideally suited as semantic values of predicates, even better than mere sets of things.
I agree, and so would Lewis. In fact, Lewis would say that functions from worlds and times are still too simple to do the job of semantic values. There are more intensional operators in our language than temporal and modal operators. Among others, there are also spatial operators and precision operators ("strictly speaking"). So our semantic values for predicates should be functions from a
world, a time, a place, a precision standard and various other 'index coordinates' to sets of objects. This is more or less what Lewis assigns to common nouns in "General Semantics" (see in particular §III). Other predicates like "is green" that do not belong to any basic syntactic category get assigned more complicated semantic values: functions from functions from indices to things to functions from indices to truth values. In later papers, Lewis argues that we may need several of the world and time coordinates and, more
importantly, a further mapping that accounts for context-dependence
(and to deliver the kind of truth-conditions needed in his theory of
linguistic conventions). Thus for predicates, we get something like a
function from centered worlds to functions from functions from possibly several worlds, times, places, precision standards, etc. to functions from such worlds, times etc. to truth values. (Alternatively, if we go for the 'moderate external strategy' (Plurality) and reserve "semantic value" for 'simple, but variable semantic values' ("Index, Context and Content"), we can say that the semantic value of a predicate in a given context is the value of the function just mentioned for that context.)
Andy Egan, in "Second-Order Predication and the Metaphysics of
Properties", argues that there is a bug in Lewis' theory of
properties which can be fixed by identifying properties
not just with sets but with functions from worlds (and times) to
sets. I disagree: there is no bug. But there are some interesting
questions about Lewisian properties nearby.
Here's the alleged bug. Consider the second-order property being
somebody's favourite property. This property belongs to
Green. So on Lewis' account, Green is a member of the
set being somebody's favourite property. But at another
possible world, Green is nobody's favourite property. So it is not a member of that set. Contradiction. In the parallel case of accidental properties of individuals, Lewis resorts to counterpart theory: If Graham Greene is a writer in our world and not in another world, that's not because Greene both is and isn't a member of the set writer, but because Greene is a member while one of his counterparts isn't. However, this solution doesn't work for Green because properties don't have counterparts.
I would like to believe that all necessary truths fall into the following two kinds.
1. Analytic truths. By processing the semantic content of such a sentence we can find out that its truth conditions are universally satisfied, no matter how the world turns out and no matter what
other world we talk about.
2. Truths whose evaluation at other worlds depends on contingent features of the actual situation. What we can know by linguistic processing is that if these features are so as to make such a sentence true, then it remains true even when we talk about other worlds, that is, when the sentence is embedded in "at world such-and-such" or "necessarily". For example, if we know that there are sheep, we can figure out that "actually, there are sheep" is necessary, because
it is a rule of our language that (roughly) "actually p" is true at a
world w iff p is true at the actual world. Knowledge about ordinary,
contingent features of the current situation together with linguistic
competence always suffices to learn that these a posteriori necessary
sentences are true.
OK, back. The bike trip was cool.
Meanwhile, in the comments, David Sanford raised the question whether sets gain and lose members. One might say yes, for arguably
*) If y is the set of all Fs, then x is a member of y iff x is F.
Since the wall in front of me is white and there is a set of white things, by (*), the wall is a member of that set. But last year, that wall was green, and surely it was never the case that something green was a member of the set of white things; so the wall was not a member of that set last year. It follows that the set of white things gained a member when I painted the wall.
If meaning is largely determined by use and inferential connections, then if a word is used very differently in two groups of people and if the two groups accept very different inferential connections, then the word does not mean the same thing in those groups.
On this account, mereological nihilists don't mean the same by mereological vocabulary as I (a universalist) do: they reject all ordinary examples of parthood, overlap etc.; they reject some of the most central theoretical principles governing these notions; and they ask unintelligible quesions, like:
Lewis argues that any theory of chance must explain the Principal Principle, which says that if you know that the objective chance for a certain proposition is x, then you should give that proposition a credence close to x. Anyone who proposes to reduce chance to some feature X, say primitive propensities, must explain why knowledge of X constrains rational expectations in this particular way.
How does Lewis's own theory explain that?
On Lewis's theory, the chance of an event (or proposition) is the
probability-value assigned to the event by the best theory. Those
'probability-values' are just numerical values: they are not
hypothetical values for some fundamental property; they need not even
deserve the name "probability". However, one requirement for good
theories is that they assign high probability-values to true
propositions. Other requirements for good theories are simplicity and strength. The best theory is the one that strikes the best compromise between all three requirements. So the question becomes: why should information that the best theory assigns probability-value x to a proposition constrain rational expectations in the way the Principal Principle says?
Some accounts of laws of nature make it mysterious how we can empirically discover that something is a law.
The accounts I have in mind agree that if P is (or expresses) a
law of nature, then P is true, but not conversely: not all truths are laws of nature. Something X distinguishes the laws from
other truths; P is a law of nature iff P is both true and X. The
accounts disagree about what to put in for X.
Many laws are general, and thus face the problem of induction. Limited empirical evidence can never prove that an unlimited generalalization is true. But Bayesian confirmation theory tells us how and why observing evidence can at least raise the generalization's (ideal subjective) probability. The problem is that for any generalization there are infinitely many incompatible alternatives equally confirmed by any finite amount of evidence: whatever confirms "all emeralds are green" also confirms "all emeralds are grue"; for any finite number of points there are infinitely many curves fitting them all, etc. When we do science, we assign low prior probability to gerrymandered laws. We believe that our world obeys regularities that appear simple to us, that are simple to state in our language (including our mathematical language). Let's call those regularities "apparently simple", and the assumption that our world obeys apparently simple regularits "the induction assumption".
A time traveler convention will be held at MIT on May 7. Apparently the organizers have in mind a branching universe model of time travel, otherwise this makes no sense:
Can't the time travelers just hear about it from the attendees, and travel back in time to attend?
Yes, they can! In fact, we think this will happen, and the small number of adventurous time travelers who do attend will go back to their "home times" and tell all their friends to come, causing the convention to become a Woodstock-like event that defines humanity forever.
Anyway, suppose no time travelers from the future show up at the convention. Does that decrease your credence in the physical possibility of time travel? If so, would your credence decrease by the same amount if the convention was (now) set to take place in the past, say on May 7, 2004? After all, there's little point announcing a time traveler conference in due time before the event.
Warning: another pointless exercise in conceptual geography.
Can intrinsic properties have their causal/nomic role essentially? It seems not. Suppose something x is P. If P essentially occupies a
certain causal role, say being such that all its instances attract one
another, we can infer from x's being P that either there are no other
P-things in x's surrounding or x and the other things will (ceteris
paribus) move towards one another. But if we can infer from x's being
P what happens in x's surrounding, P cannot be intrinsic. Being
intrinsic means belonging to things independently of what goes on
in their neighbourhood.
Fundamental (or 'perfectly natural') properties are properties on whose distribution in a world all qualitative truths about that world supervene. That is, whenever two worlds are not perfect qualitative duplicates, they differ in the distribution of fundamental properties.
This is not the only job discription for fundamental properties. If it were, far too many classes of properties could play that role. For instance, all qualtiative truths trivially supervene on the distribution of all properties, or on the distribution of all intrinisic properties, or (for what it's worth) on the distribution of all extrinsic properties. (That's because no two things, whether duplicates or not, ever agree in all extrinsic properties.)
A structural property is a property that belongs to things in virtue of their constituents' properties and interrelations. For instance, the property being a methane molecule necessarily belongs to all and only things consisting of suitably connected carbon and hydrogen atoms.
There is two-way dependence: Necessarily, if something instantiates a structural property, then it has proper parts that instantiate certain other properties; conversely, if the proper parts of a thing instantiate those other properties then, necessarily, the thing itself instantiates the structural property.
Imagine a world with nothing but infinitely many duplicate dragons, aligned in one long row. Consider the second dragon in the row. Call it "Fred".
Fred could have failed to exist. There are many worlds where he does not exist. (The actual world is probably one of them). Some of these worlds where Fred does not exist contain no dragons at all, others contain some of the other dragons in Fred's row. In particular, there are worlds where all the other dragons exist, but not Fred. The dragons are after all distinct existences, and there are no necessary connections between those.
Robbie Williams pointed out that in my recent musings on worms and stages, I ignore the following straightforward characterizations:
Worm Theory: the semantic value of predicates like "rabbit" is a set of 4D worms.
Stage Theory: the semantic value of predicates like "rabbit" is a set of 3D stages.
He's right. I believe that these theories both cannot work, so I don't want to define stage and worm theory that way.
I'm somewhat stuck with the parts/counterparts paper. One of the problems is to find an acceptable semantics for time travel situations.
Part of the problem is that I'm often unsure what to say about these cases. I guess if time travel were more common, we would need some new linguistic conventions. Anyway, here are some sentences that seem true to me in the following scenario: Tina decides in 2025 to meet her younger self back in 2005. So at some time t in 2005, the younger Tina is in the living room and weighs 60 kg while the older Tina is in the kitchen and weighs 70 kg. Now, these all seem true to me:
I've written a little paper about the difference between theories on which ordinary things are fusions of parts located at various places, times, and worlds, and theories on which they instead have counterparts there. The dull conclusion is that there is no difference. I'm not sure I believe anything in there, and it's all quite rough, so comments are welcome: Parts and Counterparts (PDF).
Update 2005-03-08: Robbie Williams points out that my translation between Counterpart and Fusion Theory does not handle fission cases correctly. I should at least (following Lewis's translation scheme) say that names in the fusion language are indeterminate between all maximal eligible fusions of the corresponding counterparts from the counterpart language. But this is only a partial fix. I hope to come up with something better soon, though as I'm on the road for the next couple of days, that will probably have to wait until the weekend.
Ordinary objects - persons, planets, rivers and tables - are unextended atoms. They occupy only one point of space at only one time at only one world.
At first sight, this might sound absurd. Don't ordinary things
obviously exist at many different places, times and worlds? Isn't the
Yangtze clean in Geladandong and dirty in Shanghai? Wasn't it clean in Shanghai in 1500? And isn't it clean in Shanghai now at some other possible world?
Fortunately, Atomism need not deny any of this. For even though the
Yangtze is an unextended atom that strictly speaking only occupies a
single point, it has many counterparts at other points. And
these counterparts make all those statements true.
According to the Stage View, ordinary objects are temporally unextended timeslices. "Ted sleeps" is true iff the present Ted-stage sleeps.
What if there is no present stage, as with "Socrates is wise" and "Socrates exists"?
The question is not what to say about "Socrates was wise" and "Socrates did exist". These are true because at some time in the past, there is a wise Socrates stage (see pp.27f. of Ted Sider's Stage paper). The problem is the tenseless "Socrates is wise".
Until recently, I thought that there are no quantifiers in ordinary discourse for which a substitutional interpretation is adequate, or helpful. I still think this is true for almost all cases, including quantification over fictional and intentional objects. But here are two cases where a substitutional interpretation looks ok.
First. The world can be completely described in precise vocabulary. There are no vague objects with irreducibly vague bounderies or heights or colours. Rather, for many terms, like "Mount Everest", it is indeterminate exactly which perfectly precise object they denote. But it is very natural to say that Mount Everest has
vague boundaries. Instead of denying it, I'm inclined to offer some kind of reinterpretation, such as: there are different objects slightly differing in their boundaries between which "Mount Everest" is indeterminate; or: for no precise boundaries b is it true that Mount Everest has boundaries b; or: for some precise boundaries b is it indeterminate whether Mount Everest has boundaries b. All these are true, and all of them could be meant by "Mount Everest has vague boundaries".
I don't share Lewis's strong intuitions that shape properties must be purely intrinsic rather than time-indexed. For me, the argument from intrinsic change works much better with certain relations, in particular mereological relations and identity.
Suppose x is part of y at time t1, but not at t2. Perdurantists can say that the temporal part of x at t1 is a part simpliciter of the temporal part of y at t1. Time-indexers will say that the whole of x stands in the part-at-t1 relation to the whole of y, where this relation is not analysable in terms of non-indexed parthood: time-indexed parthood is all there is. But no! Subsets are parts simpliciter of sets, battles are parts simpliciter of wars, the story of the Trojan War is a part simpliciter of the Illiad, geometry is a part simpliciter of mathematics, XPath is a part simpliciter of XSLT, and so on. These things are not part-at-time-related, but part-related.
Suppose there are at least proper-class many possibilia. Does it follow that some fusions of possibilia are not members of any set? For the last two years or so I thought it does. My reasoning was that if some of the possibilia correspond one-one with all the sets, then some atoms of possibilia also correspond one-one with all the sets (for there cannot be proper-class many fusions of set-many atoms); but since there are always more fusions of atoms than atoms, it follows that there must be more fusions of atoms of possibilia than sets, and hence that some (in fact, most) of these fusions lack a singleton. This does not take into account atomless possibilia, but I always thought the reasoning would easily carry over, by something like the fact that even with gunk
Well, I know what Counterpart Theory is not: it is not a theory according to which ordinary things do not really exist at other possible worlds.
There are two readings of "ordinary things do not exist at other worlds". The first is a neutral reading on which things exist at another world in the way they sleep at another world or win elections at another world: whatever possible worlds are, they somehow represent things as existing and sleeping and winning. In this sense, something exists at a world iff the world represents it as existing. Anyone who accepts possible worlds talk at all accepts that ordinary things exist at other worlds in this sense.
The difference between linguistic ersatzism, where possible worlds are replaced by sets of sentences, and modal fictionalism, where the pluriverse of all worlds is replaced by a large set of sentences describing all worlds at once, appears to be small. Nevertheless, I (still) think the analytic power of fictionalism is greatly diminished compared to that of linguistic ersatzism.
One of the great advantages of possibilia is that they provide a unified framework to reduce lots of kinds of things: properties can be identified with sets of possibilia, propositions with sets of worlds, meanings with functions from worlds to extensions, events with functions from worlds to regions, and so on. But suppose possibilia don't really exist, but exist only according to some fiction. Then properties can't be sets of possibilia. By the usual rule of interpreting statements about fictional entities, it will at most be true that according to the fiction, properties are sets of possibilia. But that doesn't help us if we're looking for a unified ontology. We'd like to know what properties really are, not what they are according to some fiction. If as fictionalists we think that properties really are sets of possibilia, then we have to conclude that properties don't really exist, just as the (other-worldly) possibilia don't really exist.
According to the Principle of Recombination,
for any things at any worlds there is a world containing a duplicate
of each of these things and nothing else (that is, nothing that is not
a part of the fusion of the duplicates).
Applied to the mereological fusion of David Hume and David Lewis, this says that there is a world containing nothing but a duplicate of the fusion of Hume and Lewis. This duplicate presumably has a part that is a duplicate of Hume and another that is a duplicate of Lewis. How are these parts spatiotemporally related?
Brian points to Gabriel Uzquiano's Cardinality Puzzle about Mereology and Set Theory (PDF), which he (Gabriel) introduced a while ago in the now-deceased Philosophy from the 617 weblog. I still don't know enough set theory and mereology to competently discuss the matter, but anyway, it seems to me that perhaps the puzzle can be strengthened, as follows.
The whole four-dimensional universe, including past, present and future times, does not change; it will not be different tomorrow; it remains the same at all times.
If the whole four-dimensional universe remains the same at all times, then presumably no part of it will ever fail to exist or has ever failed to exist.
So for example, the apple I'm just about to eat will never fail to exist. It will exist forevermore. As will I, and you, and this weblog.
There is but one totality of worlds; it is not a world; it could not have been different. (Lewis, Plurality, p.80)
If the totality of worlds could not have been different, then presumably no possible world could have failed to exist.
Then in particular, the actual world, @, could not have failed to exist.
So there is an actually existing thing, namely @, that could not have failed to exist.
Even worse, arguably @ has some of its parts essentially. So there are some actually existing things besides @ that could not have failed to exist.
One might even say that all worlds have all their parts essentially, simply because worlds do not exist at other worlds. Then it follows that no actually existing thing could have failed to exist.
It consumes energy and emits electromagnetic radiation. It contains a small wire filament. It is widely used all over the world. It was invented by Heinrich Göbel in 1854, though Americans often attribute its invention to Thomas Edison. What is it?
The electrical light bulb, of course.
But hold on. Is there really something that satisfies these conditions? What kind of thing would this be? It can't be any particular light bulb, say, the one in my bathroom. For this light bulb is used only in my bathroom, not all over the world, and most Americans don't even know that it exists. Nor can it be any other particular material thing. Nor can it be a mental object, something like the idea of a light bulb: ideas don't contain small wire filaments. This alleged thing, the light bulb, is a very strange kind of object. It is not a light bulb (all light bulbs are concrete, particular light bulbs), but like all light bulbs it contains a wire filament, consumes energy and emits electromagnetic radiation. It is is located in time (as it didn't exist before 1854), but presumably not at any particular location in space.
Oh dear.
Returning to philosophy, here is a remark by John Burgess about the possibility of translating ordinary sentences into sentences with seemingly less ontological commitment, as described in Prior's "Egocentric Logic" and Quine's "Variables Explained Away":
Thus whether one speaks of abstract objects or concrete objects, of simple objects or compound objects, or indeed of any objects at all, is optional. Or at least, this is so as regards "surface grammar". My claim is that if children who grew up speaking and arguing in Monist or Nihilist or some Benthemite hybrid between one or the other of these and English, it would be gratuitous to assume that the "depth grammar" of their language would nonetheless be just like that of English, with a full range of nouns and verbs denoting a full range of sorts of objects and connoting a corresponding range of kinds of properties. And any assumption that the divine logos has a grammar more like ours and less like theirs would be equally unfounded, I submit. It is in this sense that I claim any assumption as to whether ultimate metaphysical reality "as it is in itself" contains abstract objects or concrete objects, of simple objects or compound objects, or again any objects at all, would be gratuitous and unfounded. (p.18 of "Being Explained Away" -- Microsoft Word format, use Neevia to convert)
I'm not sure to what extent I agree with that. I do agree that there is something strange about asking whether numbers really exist. Burgess takes this to be the core question dividing nominalism and platonism about numbers. Thus he argues e.g. in "Nominalism Reconsidered" (MS Word again, coauthored with Gideon Rosen) that if nominalists agree that "there are numbers" is true -- while offering a nominalistically acceptable interpretation --, they have actually given up nominalism.
I've written a little paper in German about the connections between metaphysical (modal) and analytical implication for the Olaf Müller-Kolloquium here at Humboldt University: "Fundamentale Wahrheiten" (PDF). It brings together some things I've already written about here. The main ideas are entirely due to Lewis, Jackson and Chalmers.
Since I haven't slept last night and feel unable to do anything productive, here is an abbreviated translation.
1. There is nowadays considerable evidence for the existence of pulsars. Still, it isn't incoherent to worry that the evidence might be misleading and pulsars don't exist after all. But it is incoherent to worry that pulsars might be the apple trees in my parents' garden. These apple trees aren't neutron stars, and they don't emit regular pulses of electromagnetic radiation, and things that don't do that don't deserve the name "pulsar".
2. Suppose we are convinced by van Inwagen's arguments that fictional characters are abstract entities created by authors and denoted by our fictional names. This suggests the following picture: Over and above our material universe there is a special realm of abstract fictional characters. Everytime an author writes a novel, new entities pop up in this fictional realm. There is no causal connection from the fictional realm to our world. But then how do we know about the fictional characters? How can we be sure for example that the creation of fictional characters is reliable? Couldn't it happen from time to time that a fictional character fails to be created? If so, perhaps Madame Bovary exists, but Sherlock Holmes doesn't. In which case it would be false (on the Kripke-van Inwagen account) that Sherlock Holmes was invented by Conan Doyle or that he is a widely known fictional character. Isn't our confidence in such assertions rather mysterious and irresponsible given that really we have no access at all to the fictional realm? At the very least, the exceptionless correspondence between what our authors do here on Earth and what happens in the fictional realm cries for explanation!
Metaphysical debates about causation, consciousness, chance, change, mathematics, or modality have a lot in common. In all cases, metaphysical theories try to tells us what, if anything, makes a certain class of statements true. Among the possible answers, we usually find suggestions to reject the alleged phenomena, to declare them as primitive, and to reduce them in various ways to something else. But on closer inspection, there appear to be big differences, in particular with respect to what is required for a reduction.
In "Tharp's Third Theorem", Lewis agrees with Jackson that "all of us are committed to the a priori deducibility of the manifest way things are from the fundamental way things are (whatever that may be)" (TTT, p.96). His somewhat cryptic argument isn't quite the same as Jackson's though, and it seems that he avoids the mistake I mentioned yesterday.
Note that Lewis doesn't say we're committed to the a priori deducibility of all truths from the fundamental truths. Instead, he speaks of the "fundamental way things are", or from "contingent truths, supervenient on the fundamental way things are" (TTT 96). (In case that's not clear: Like Lewis, I use "truth" for "true sentence", not e.g. for "true proposition".)
Let logicalism ("logicism" was already taken) be the claim that all truths supervene upon purely logical truths, where a purely logical truth is a truth that contains only logical terms, including terms from second order modal logic.
Logicalism immediately follows from this purely logical truth ('[]' is the box, 'ACT' the actually operator):
p <-> []((x)(F)(Fx <-> ACT(Fx)) -> p)
While all truths therefore supervene upon the purely logical truths, not all truths are a priori deducible from the purely logical truths. For instance, that water covers most of the earth isn't. So we have a counterexample to the claim that whenever all truths supervene on the F-truths, then all truths are a priori deducible from the F-truths.
Serious Metaphysics, in Jackson's sense, tries to identify a limited set of truths (i.e. true sentences) that entail (i.e. strictly imply) all truths. So what about
*) Everything is just as it actually is?
((p)(p <-> actually p), or (x)(F)(Fx <-> actually Fx))
(*) is true. It entails all other truths: whenever S is true, then so is "necessarily, if (*) then S". And it is fairly simple and economic: for instance, it doesn't contain macrophysical or phenomenal terms. Still, it's not serious metaphysics. What's wrong?
Merlin is bound to disappear at noon, taking with him all physical
traces of his existence. Shortly before his magic disappearance, he
casts a spell. As a result, at noon on the following day, the prince
turns into a frog.1
In virtue of what does the spell cause the metamorphosis? For
instance, it is not at all clear that by Lewis's standards of
similarity, some world containing neither spell nor metamorphosis is
more similar to actuality than any world not containing the spell but
containing the metamorphosis. The problem is that the only trace left
by the spell, after Merlin's magic disappearance, is the
metamorphosis itself:
I'm back. Here's a question that occurred to me while I was listening to Dave Chalmers's talk on scrutability.
First some background. One might think that for every world w there is a complete description D true at w such that all and only the sentences true at w follow a priori from D: simply let D contain all sentences true at w. Then all sentences true at w will be a priori entailed by D. However, if "true at" is read counterfactually, sometimes sentences false at w will also be so entailed. Consider Twin World where XYZ occupies the water role. "Water doesn't occupy the water role" is true at Twin World. But "water occupies the water role" is a priori, and hence a priori entailed by everything1. Thus every complete description of Twin World a priori entails a contradiction (and every sentence whatever).
I need to tidy up this part of my belief space. Once I complained that literal trans-world identity (as opposed to trans-world identity based on similarity) is implausible because it entails that there can be no vagueness about a thing's essential properties (for determinate properties): either the thing has the property at all worlds or not. On the other hand, I also believe that there is no big difference between individuating things as worldbound and individuating them as trans-world fusions of worldbound counterparts. Unfortunately, these two views can't both be correct.
Lewis defends a kind of best system theory both with respect to laws of nature and with respect to mental content: something is a law of nature iff (roughly) it is part of the best theory about our world; somebody believes that snow is white iff (roughly) this is what best makes sense of his behaviour according to our belief-desire psychology.
In both cases, it looks on first sight as if the theory introduces an implausible relativity into its subject matter: We don't want to say that the laws of nature depend on what we happen to find simple (but simplicity is part of what makes a theory good), and we don't want to say that what someone believes and fears depends on what we think about his behaviour.
I haven't really checked the literature, but is there a general agreement on why the problem of temporary intrinsics is a problem of intrinsics and not a general problem about temporary properties? Certainly it is just as impossible for a thing both to have and to lack an extrinsic property as it is impossible for intrinsic properties. A while ago, I said that perhaps for temporary extrinsics, the problem is not really a problem because the relational answer is the obviously correct one: having extrinsic property F at time t clearly means being F-related to t. But in fact that doesn't sound obvious at all. Does being an uncle relate people to times? It seems not. It seems only to relate them to other people. If one intuits that being round is not a relation to a time, I don't see why one wouldn't similarly intuit that being an uncle is not a relation to a time.
There are two ways of denying that the future is real. One is to accept statements about the future as true but to interpret them in a way that does not require the existence of their subject matter. This is a kind of fictionalism or ersatzism about the future. (It's interesting by the way that abstract ersatz futures clearly don't count as futures, whereas it is controversial whether abstract ersatz worlds should count as real possible worlds.) The other way of denying the reality of the future is to reject the assumption that statements about the future are true. Then no fictionalist or ersatzist story needs to be told to account for their truth.
The standard solution to worries about time travelers' freedom to 'change the past' rests on a distinction between legitimate and illegimitae facts in such considerations. (See e.g. this great paper by Ted Sider.) Assume for simplicity that x is free to do y iff he really would do y should he decide to do y. Now consider Tina the time traveler. Is she free to kill her earlier self? I.e. is it true that
I started this as a comment on Brian Weatherson's latest posting. But it grew so long that I decided to post it here instead and test my trackback implementation on it.
Imagine a world in which there are nothing but two atoms.
This is ambiguous. Does it mean I should imagine a world in which there are two atoms and nothing else, not even the fusion of these atoms? Or is "nothing but" restricted to things distinct from the two atoms? I can follow the instruction on the latter interpretation but not on the former: a world with two atoms and nothing that is not identical to one of them is inconceivable to me.
In "The Varieties of Necessity", Kit Fine defends Modal Pluralism. Does he thereby threaten Modal Realism? He says he does (in footnote 5). But does he really?
Well, what is Fine's thesis of Modal Pluralism? Here is his summary:
I conclude that there are three distinct sources of necessity -- the identity of things, the natural order, and the normative order -- and that each gives rise to its own peculiar form of necessity. Neither form of necessity can be subsumed, defined, or otherwise understood by reference to any other form of necessity. (p.279 of Conceivability and Possibility)
It seems that he is mixing several different theses here. In particular,
In The Conceivability of Naturalism, Crispin Wright notes:
When we disjoin or existentially generalise on names, the results -- for instance, "Tom or John was to blame", "Someone was to blame"-- had better not be conceived as forms of expression involving reference to disjunctive, or existentially general objects. There are no such objects.
What does he mean? Is his point merely the semantical hypothesis that "Tom or John" and "someone" should not be treated as refering expressions? It is probably easy to create a semantics where they are assigned a reference. I'm not even sure (though I believe it) that such a semantics would be perverse, given that lots of people have argued that expressions like "Tom and John" should be assigned some kind of reference to account for sentences like "Tom and John ate the cake". But at any rate, this presumably isn't Wright's point. For even if there was a disjunctive object consisting of Tom and John, it doesn't follow that "Tom or John" must be interpreted as refering to it. So the converse is also invalid: it doesn't follow from the fact that "Tom or John" doesn't refer that there are no disjunctive objects. The passage rather sounds like Wright has independent reason to believe in the non-existence of disjunctive and existentially general objects; a reason that merely gives further support to the semantic claim that "Tom or John" and "someone" don't refer.
The problem of intrinsic change is often put in misleading terms, like: "how is it possible for a thing to have incompatible intrinsic properties at different times?", or: "how can I be first bent and then straight?" Putting the problem this way invites wrong kinds of answers, like:
- There really is no problem here. Why should things not have incompatible properties, as long as they
have them at different times?
- Well, a thing can change its instrinsic properties by consisting of a substratum to which different properties attach at different times.
- How can I be first bent and then straight? Why, by standing up.
When I first read Lowe's proposed solution, I thought what he offers belongs to this class of answers that don't answer the real problem. In fact, his answer looks much like the third one above: How can I be first bent and then straight? By having parts, such as legs and a torso, which can change their spatial arrangement. Sure. But does that answer the problem?
When first introduced to the distinction between three- and fourdimensionalism and between perduranitsm and endurantism, many, myself included, have the feeling that both are valid ways of looking at the same reality and hence that at bottom they must be somehow equivalent or inter-translatable.
I still believe some of this. Consider for example the question of interpreting temporal predications. Endurantists say that "x is F at t" is true iff (the whole of) x stands in the F-relation to t, or iff x instantiates-at-t F, or something like that. As a perdurantist, I need not deny that. Rather, I have a further analysis of what it means to stand in the F-relation to t, or to instantiate-at-t F: it means to have a temporal part located at t which is F. Similarly, I needn't deny that I am wholly present right now. Applying the perdurantist analysis, what this claim says is that I -- the entire worm, with all his spatial and temporal parts -- have a temporal part which is present right now. Perhaps I could even try to make sense of claims like "people don't have temporal parts" by appealing to restricted quantification. But somewhere around this point the translatability comes to an end. Endurantists usually build the rejection of perdurantism into the very heart of their account, and it is certainly uncharitable to re-interpret this rejection so that it is after all compatible with what it rejects. (Here is something odd, by the way: how can it be uncharitable to interpret someone's utterances in such a way that they come out true rather than in a way in which they are false?)
Sometimes the best argument for a certain assumption is that it proves fruitful in various theoretical contexts: Why believe in a plurality of worlds? Because the hypothesis is serviceable in semantics, decision theory, theories of intentional content, the interpretation of modalities, the definition of supervenience, etc. -- and that is a reason to believe that it is true. Another example, again by Lewis, is the argument for universals, or at least for a fundamental distinction between natural and unnatural properties: the assumption is serviceable to account for objective similarity, the determinacy of meaning and translation, the interpretation of some quantified sentences, the analysis of natural laws, etc. Similar arguments can be put forward for the existence of temporal parts, states of affairs, events and numbers.
These arguments presuppose that it is really the very same assumption, rather than a diverse family of similar sounding assumptions, that does all the work it is supposed to do. The case for numbers would be much worse if lots of different arithmetics were 'indispensable' in different branches of science. The problem is quite obvious for events: the events employed in relativity theory can hardly do as the events used in Davidsonian interpretations of English adverbs.
I just realized that I have inconsistent attitudes towards ontologically dependent entities, that is, entities x such that for some contingently existing entity y, i) necessarily, if x exists so does y, and ii) x and y are not parts or subsets or elements of each other. On the one hand, I don't believe that there are many such entities, except perhaps holes and borders. On the other hand, I also don't believe in general restrictions on the counterpart relation, or, perhaps equivalently, in restrictions on cross-world fusions of individuals. It follows that for any old property any world-bound thing has at our world, there is a thing which has this property essentially. For instance, there is somebody who leads exactly your life but who, unlike you, is essentially such that the cup in front of me is now empty. This somebody is a dependent entity: it can only exist if my cup does.
The other hand seems so obvious to me that I fear I must give up the one hand: there are lots of dependent entities. I can still say that they are not ordinary things, and that it is very hard or even impossible to refer to most of them (individually, of course -- I just managed to refer to them collectively). But still they exist. Hm.
If haecceitism is true, materialism is false. For if haecceitism is true, there is a world w just like ours except that you and I have traded places. By that I don't mean that in w someone with my origin or my DNA or my soul leads a life quite like yours. No, haecceitism holds that it is possible for us to trade places completely, so that in w not only my life is just like your actual life, but also my origin, DNA and soul are just like your actual origin, DNA and soul. w and our world do not differ in any qualitative respect at all. They differ only in facts that essentially involve you or me, such as the fact that in w it's you who is writing this posting. Whatever 'physical' means, it is clear that the physical facts are not of this kind. That's why materialism is false if haecceitism is true: Materialism demands that there is no difference at all between our world and any minimal physical duplicate of it.
Geoff at Too Much Text points out that the implausible hyper-essentialism implied by Kripke's account of rigidity can be avoided by adopting radical anti-essentialism, the view that there are no non-trivial (qualitative) essential properties at all. On this view, even though there is a precise boundary between a thing's essential and non-essential properties, the boundary is not very mysterious because it classifies virtually all properties as non-essential.
In my last post,
I said that I do not believe that every extended thing must have parts. Sam disgrees, arguing that whenever something is extended over length h, we can restrict our attention to a part of it with length h/n for any n < h.
I do agree that all ordinary extended things have parts. And I do agree that extended things without parts are really very strange. I'm just not sure that they are impossible.
There are lots of distinctions between perdurantism and endurantism (or better, between different perdurantisms and endurantisms). Here I want to talk about the following perdurantist claim:
1) Some things (that are not events) have temporal parts.
This does not imply that ordinary things like buildings and persons have temporal parts. And even if one believes the latter, it is still perfectly coherent to reject any account of intrinsic change in terms of temporal parts, or reject an account of personal identity in terms of (properties of) temporal parts, or reject an account of persistence in terms of temporal parts, or reject whatever else temporal parts are used to account for. It is also okay to accept only some of these accounts and reject others. (I for example am a perdurantist who rejects the account of persistence in terms of temporal parts: not only can I say what it is to persist through time without mentioning temporal parts, I even believe that it is possible for a thing to exist through time without having temporal parts.) That's how we get so many perdurantisms and endurantisms. (I think it would be very helpful if people discussing this matter exactly said what they say on each of these issues rather than vaguely asserting that, e.g., things are 'wholly present at different times'.)
What do types, sets, universals, increases, theorems, species and governments have in common that distinguishes them from sticks, stones, mountains, molecules and cities? It's not that only the latter are causally efficacious: on many accounts (e.g. those of Lewis and Kim), events -- the paradigm examples of causal efficacy -- are sets; and why shouldn't one say that if a thing's being charged produces an effect, Charge (the universal) is just as much responsible for this as the thing itself? It's also not that only the latter are located in space or time: impure sets, species, Aristotelian universals and governments arguably are spatiotemporally located as well. And by the Helen Cartwright Theorem Theorem, theorems are sometimes written on blackboards. Indeed, I'm not sure whether anything at all clearly fails to be located in time, unless we require that something located in time must undergo intrinsic change or have a beginning or an end, which sounds ad hoc. Without such restrictions, I can't see a reason to deny that e.g. numbers exist at every time. (Oddly, I'm less inclined to say that numbers exist everywhere. But I might get used to it.)
Everything is identical to itself, and nothing is identical to
anything except itself. No two things are ever identical. If A and B
are identical then "they" are one, not two.
These are platitudes about identity, or rather about a
somewhat technical use of "identity" common in mathematics and
philosophy.
No doubt there are other uses. For instance, "identity" and its
cognates are often used to express sameness of kind, as in "this
record is the same Jones bought last week". Sometimes, "identity" is
used as a singular term for a thing's characteristc properties or
individual essence, as in "the festival has lost its identity". The conceptual platitudes
above do not apply to these other uses.
Humeans distinguish between how things are in themselves and how they are related to other things. The latter, they say, is always a contingent matter: Even though this cup of tea is about 20m away from a book and stands on a table, it could very well not be 20m away from the book and not stand on the table. In slogan form, there are no necessary connections between distinct entities.
Understood literally, this leads to a position one might call strong humeanism:
Meinongians say that some things do not exist. In other words, existence is a property that befalls only some of the things there are. It follows that by 'existence' these Meinongians do not mean the trivial property that every thing whatever has. What else do they mean? Maybe they mean by 'existence' being in space or time, as Meinong sometimes does. Or maybe they mean an alleged primitive property of certain things. At any rate, I have no objection to this except that I'd rather not use the word 'existence' for that. But I can't really say that ordinary usage is on my side, given that a) ordinary quantification is almost always restricted (though not always in the same way), and b) there is hardly an ordinary usage of 'existence' at all. So far, Meinongianism is utterly trivial. It merely holds that some objects lack a certain property.
So there are several ways to make sense of restricted identities. Which is the right one? Maybe there is no fact of the matter.
The difference depends on which contexts are regarded as referentially transparent and which as opaque. And that in turn depends on how the referents are individuated. For instance, (de re) ascriptions of modal properties will be transparent iff the referents of singular terms are such that they determine the truth value of all such ascriptions, perhaps because they (the referents) are fusions of world-bound individuals with their counterparts, or because they are Carnapian individual concepts, or because they simply contain some hidden tag that determinately settles all their modal properties. At any rate, for de re modal contexts to be referentially transparent, the referents have to provide us with a function from worlds to world-bound individuals, as that's what we need to determine the the truth value of those ascriptions. Alternatively, if we hold that those contexts are referentially opaque, we decide that the referents do not contain that information. Instead, we put the information into another aspect of meaning, which we call the terms' intension. Is the difference really more than just a relabeling of semantic vocabulary?
Now restricted identities threaten to violate
Leibniz's Law: If R1 is identical with R2, then how can they differ in
their courses? If AD1 is AD2, how can they differ in their history?
If A1 is A2, how can they differ in their modal properties?
They can't. So either R1 and R2 (and AD1 and AD2, and A1 and A2) are
not really identical, or the don't really differ. Let's look at the
first option first. It says that R1 and R2 are not really
identical. Hence "R1 = R2" is false, even though
If you follow the Rhine upstream, you'll reach Reichenau in Switzerland, where its two tributaries, the Vorderrhein and the Hinterrhein, meet. As far as I know, it is undefined which of them, if any, is the Rhine. Obviously that's not a mystery but just a matter of stipulation. So let's stipulate that 'R1' is to denote the continuation of the Rhine through the Vorderrhein, and 'R2' its continuation through the Hinterrhein.
Sometimes we wonder whether some thing A is identical with some thing B: Is the man in the brown hat (the same as) my neighbour? Is the table in the mirror over there (the same as) the one here in front of me? Is the square root of 841 (equal to) 29?
What determines whether A really is identical with B? According to a view I find very irritating it's the identity conditions of A and B. The idea is that all things fall under kinds, and every kind comes with an associated identity condition. Different kinds may be associated with the same identity condition, but there is never more than one identity condition for a kind. So to find out whether A = B, we first have to find the relevant identity conditions of A and B. A good way to find those is to find the relevant kinds and look for their associated identity conditions. If the identity conditions differ, A is not identical with B. If they are the same, they tell us under which conditions A and B is identical, and we only have to find out whether these conditions obtain.
Albert is a time traveler. In 2015 he travels back to 1995. There he meets his younger self and tells him in great detail what he, the younger Albert, will do in the next 20 years: that he will quit smoking, be injured in a traffic accident at a certain date and location, that he will work very hard in a physics lab to build a time machine, and so on. All these predications come true.
Isn't that puzzling? For example, on the day of the predicted traffic accident, why did Albert, who knew about the prediction, not avoid getting to that particular location? Why does he always behave exactly as he was predicted to do? This is certainly not what ordinary people would do. If you claimed to know that I will raise my left hand in a minute and told me so, I would try not to raise my left hand. Does Albert never try to make the predictions false? Or does he, but always fails? That seems unbelievable. How can you try not to work hard in a physics lab but fail? In fact, we may assume that Albert is told by his older self that he will never even try to make the predictions false. Then he never tries and fails because he just never tries. How strange. And how stupid: Albert knows since 1995 that he will eventually travel back in time with a time machine. For he has already met his older self. So why does he work hard at the lab? Why not lie in bed and watch TV instead? No matter what you do, you can't change the past. So no matter what Albert does in 2003, he can't change the fact that in 1995, he arrived as a time traveler from the future. So he's a fool when he's working hard to make it happen (or rather, to make it have happened).
So I don't see any means to escape the conclusion that given mereological universalism, some things trivially move faster than light. Lots of things, in fact. Perhaps that's less troublesome than I thought because these things don't actually violate any physical laws.
For instance, I guess the principle that physics looks the same for all things that move with constant speed relative to each other has to be restricted to things with speed < c anyway. (At least Lorentz transformation doesn't make much sense if v = c.) If so, the exclusion of faster-than-light fusions from the principle is already built in and we don't need to worry about e.g. what such a fusion's proper time might be.
The Brock/Rosen objection against modal fictionalism goes as follows. The modal fictionalist holds that
1) Necessarily p iff according to the modal fiction, at all worlds, P*,
where P* is the modal realist's paraphrase of P, and the modal fiction is the modal realists' theory. But the modal realist holds that it is true at every world that there are many worlds. That is,
2) According to the modal fiction, at all worlds, there are many worlds.
It follows from (1) and (2) that
Let A and C be two distinct objects such that C exists at a later time and a
different place than A.
Let F be the mereological fusion of A and C. Question: Does F move from
the location of A to the location of C? I don't think so. If a thing moves
from one location to another, there should be a continuous path from the one location
to the other along which the thing moves.
So let B1, B2, ... be (continuum many) further objects (perhaps spacetime points, if nothing else is around)
that lie on a continuous spacetime path
between A and C, and let F be the fusion of A, B1, B2, ..., C. Does F now move? I'm not sure.
Maybe when a thing moves the later stages should depend causally on the earlier
stages. Or maybe the concept of movement is not applicable to gerrymandered fusions like F.
Lewis does not want to take the worldmate relation (that holds between two things iff they belong to the same world) as primitive. He proposes two alternatives. The first is that things belong to the same world iff they stand in ("analogously") spatiotemporal relations to each other. According to the second, more general, proposal things belong to the same world iff they stand in fundamental external relations to each other, whether or not these relatios are (analogously) spatiotemporal. I'm not sure if I fully understand the difference between these three alternatives. Here is why.
Re dense worlds, Dave Chalmers asks in what sense worlds that differ only in which intrinsic properties play which roles are indistinguishable. That's a very good question, and I'm afraid I don't have a good answer. He notes that those worlds differ in lots of respects, including their laws and quite probably the perceptions of their inhabitants.
What I want to say is that the worlds are somehow 'structurally alike', or 'isomorphic'. But that's hard to cash out. Is every Ramsey sentence that is true of one of them also true of the others? Then I would first have to restrict the 'old' terms of the Ramsey sentence. But that's a minor problem. What's worse is that this doesn't take care of more complicated rearrangements, where different parts of roles are played by different properties. Here the quantifiers of the Ramsey sentence would have to range over very gerrymandered (though intrinsic) properties. And given that gerrymandered properties are generally supposed to be causally inefficacious this is dubious. And finally, even if the Ramsey sentence account would work, I would still have to say why worlds that cannot be distinguished by Ramsey-sentences (or are otherwise 'structurally alike') are in any reasonable sense indistinguishable.
Yesterday I said that Lewis might just shrug off arguments about other-wordly people who, despite being in the same evidential situation as we are and despite using the same kind of reasoning, get the laws of nature and the reference of their terms completely wrong: He could agree that such people are just as possible as similarly deluded people in counter-inductive worlds or even more deluded brains in vats.
But Lewis himself uses an argument of the same form against the non-indexical account of actuality (Pluarlity, p.93):
My attempts to get a copy of 'Ramseyan Humility' were unsuccessful, so I searched the web in the hope that somewhere somebody might have said something about what Lewis says in that paper. This is how I came across Paul Mainwood's BPhil Thesis Properties, Permutations and Physics (PDF). It's a very good thesis and contains (in section 4) an extended discussion of some of the problems I'm struggling with.
I'm confused. It seems to me that the Dense Worlds Argument refutes Lewis' Humean Supervenience thesis: Not all facts about worlds without alien properties are determined by the distribution of fundamental properties over space-time points. But that's not what really worries me.
What worries me is that I don't know what to blame. I don't see any move that doesn't lead into further difficulties. Consider blaming HS. If HS is false, then our world either contains extended things (as opposed to points) that instantiate fundamental properties, or it contains things that stand to each other in fundamental but not spatio-temporal relations. Let's focus on the second possibility. It is certainly conceivable that fundamental properties are instantiated by extended things. But does this help? Suppose all fundamental properties are instantiated by cubes with a volume of 1 nm^3 (or stages of such cubes with volume 1 ns*nm^3). Then the same kind of shuffling as in the dense worlds argument still shows that the interesting facts about our world are independent of the distribution of fundamental properties. But this time HS is not among the assumptoins, so we can't use the argument as a reductio against it.
Assume that all facts in our world are determined by the distribution of basic intrinsic properties at space-time points. Some of the space-time points in our world might be empty, that is, no basic intrinsic property might be instantiated there (either by some particle or by the point itself). If so, consider another world which is exactly like ours except that at all these empty points some basic intrinsic property is instantiated (say, the basic intrinsic property that plays the role of a certain mass in our world -- "some mass", for short) which however has no effect at all on what goes on in the world. (So if that property is some mass, the laws of nature at this world must be different from the laws at our world since our laws don't accept masses that have no effects.) By the definition of "intrinsic" and a rather weak principle of recombination, such a "dense" world is possible. And obviously, it is in principle indistinguishable from our world.
One of my problems with Lewis is that he published so little on issues where he thought he had nothing new to say. Sometimes it's tricky to figure out what his views on these issues might have been. Knowing people who knew him personally, or having access to some of his communications would probably help. Have there already been efforts to collect his letters, or even to make some of his unpublished writings available somehow? (If this is really Lewis' computer, the data on it definitely should be backed up soon before it completely turns to dust...)
Allan Hazlett, in his Against Fictionalism, says that if
numbers exist then "there is a fact of the matter about which sets numbers
are", even if we can't find it out. I don't think realism and
reductionsism about numbers implies this kind of determinatism. (Sorry,
"determinism" was already taken.)
The point is general. I believe in psychological states, and I believe
that psychological states are really just neurophysiological states. But I
don't believe that it is possible to isolate a single brain state that
realises the pain role, or the believes-that-the-meeting-starts-at-noon
role. The problem is that folk psychology is probably far too unspecific
to have a unique realisation. (This is not the problem of multiple
realisability, or not quite. Multiple realisability is usually taken to be
the problem that pain is or might be differently realised in different
individuals. It would be interesting to know more about the relation
between the two problems.)
Similarly, I believe in mountains, and I believe that mountains are really
just mereological sums of rocks, stones, sand, etc. But I don't believe
that it is possible to isolate a single sum of rocks etc. that is
(determinately) Mt. Everest.
Assume some sentence "Fa" is neither determinately true nor
determinately false. This might be due to the fact that
1) It is somewhat indeterminate exactly which object "a" denotes.
or
2) It is somewhat indeterminate exactly which property or condition "F"
expresses.
If neither (1) nor (2), then "a" determinately denotes a certain object A
and "F" determinately expresses a certain condition F. So whence the
indeterminacy? Maybe
Not much blogging these days because for some reason my wrist
hurts, and I think it's better to let it rest for a while. So here are
just a couple of brief remarks, typed with my left hand, about some
parallels between fictional and and historical characters.
We might distinguish two modes of speaking about historical
characters:
1. Past: Immanuel Kant is a philosopher; he lives at Königsberg;
etc.
2. Present: Immanuel Kant does not exist; he does not live at Königsberg;
etc.
This is part 2 of my comments on Fiction and
Metaphysics.
Amie Thomasson argues that fictional objects are not as strange and special as
one might have thought because they belong to the same basic ontological
category as works of art, governments, chairs and other objects of everyday
life. Doing without fictional entities, she says, would merely be "false
parsimony" unless one can also do without other entities of this category.
I have three complaints.
Brian has made so many puzzling remarks about fictional characters being
real but abstract that I've decided to read Amie Thomasson's Fiction and
Metaphysics. Here is my little review.
Thomasson's theory, in a nutshell, is that the Sherlock Holmes stories
are not really about the adventures of a detective who lives at 221B Baker
Street, but rather about the adventures of a ghostly, invisible character
who lives at no place in particular and never does anything at all. We
don't find this written in the Sherlock Holmes stories because, according
to Thomasson's theory, Arthur Conan Doyle simply doesn't tell the truth
about Holmes. In fact the only thing he gets right is his name: That
ghostly character he is telling wildly false stories about is really called
"Sherlock Holmes".
Here at Humboldt University, there's a reading group about analytic
philosophy (Sam already mentioned it). The flyer
advertising this group describes analytic philosophy as a sort of new and
fascinating kind of philosophy characterised by its perspicuity and
ignorance of philosophical tradition. The funny thing is that the
organisers of the reading group decided that we'll be discussing David
Wiggins' Sameness and Substance Renewed. I don't want to know
how much Hegel one has to read to find Wiggins perspicuous (and
ignorant of philosophical tradition).
This is a problem that cropped up several times in my thesis on Lewis,
but which I never seriously discussed.
Lewis argues, or rather, stipulates, that all fundamental ("perfectly
natural") properties are intrinsic. I agree that fundamental extrinsic
properties would be strange. For if a thing x's being F depends on the
existence and the properties of other things, it seems that F-hood should
be reducible to intrinsic properties (and relations) of all the things
involved. Moreover, fundamental properties are supposed to be the basis for
intrinsic similarity between things, and they could hardly be if they were themselves extrinsic.
A problem from Kit Fine, "The Non-Identity of a Material Thing and Its Matter", Mind 112 (2003):
Suppose a certain piece of well made alloy coincides with a certain
badly made statue. Al makes an inventory of well made things. The only entry on his list is "that piece of alloy". Question: Does the entry on Al's list refer to
a badly made thing?
Kit Fine intuits that the answer is definitely "no", irrespective of the
context in which that question is asked. From which it seems to follow
that the piece of alloy and the statue are not identical. At least I think this is what he thinks would follow. Anyway,
here is an extension of the above story where "the entry in Al's list
refers to a badly made thing" appears to be true.
This appears to be a problem for Lewis' theories of causation:
Let A,B,C,D be any events such that B depends counterfactually on A, and D
on C. Now consider the conjunction (fusion) B+C of B and C. If A had not
occurred, B+C would not have occurred. For then B would not have occurred,
and presumably B+C can't happen without B. And if B+C had not occurred, C
would not have occured either, so (unless the absence of B has some
surprising effects on D), D would not have occurred. Hence there is a
chain of counterfactual dependence between A and D. But since A,B,C,D were
arbitrary, this means that every cause causes every effect.
Hereby I stipulate that "fb13" is to denote the first human born in the
13th century. Hence it might seems that "fb13 was born in the 13th
century" is analytically true, true by definition. But if analytic truths
are closed under logical implication, "somebody was born in the 13th
century" would also be analytically true. Which it is not.
I don't think tinkering with closure under logical implication will help.
Hereby I stipulate that "fb23" is to denote the first human born in the
23rd century. However, if recent progress in civilization continues, there
might well be no humans in the 23rd century. And if no humans are born in
the 23rd century, "fb23 is a human born in the 23rd century" is false. So
it cannot be true by definition.
What, in general, does it mean that something A satisfies a predicate 'F'?
Traditionally, there are three candidates:
1) 'A is F' means that A is F. That' all. Simple predications can't be analysed.
2) 'A is F' means that A instantiates the property F. Except in some special cases,
in particular the case where 'F' is 'instantiates'.
3) 'A is F' always means that A instantiates the property F.
It is not entirely obvious how to locate Lewis here. In some places, when
discussing Armstrong's request for analyses (or truthmakers) for
predication, he sounds like he favours (1): "the statement that A has F
is true because A has F. It's so because it's so. It just is." ("A world
of truthmakers", p.219 in Papers)
Brian Weatherson tells me that Lewis does mention Goodman's 'New Riddle' as
a task for natural properties in "Meaning without use: Reply to Hawthorne".
Lewis says here that we should not be scared off by "Kripkenstein's
challenge (formerly Goodman's challenge)" to find a distinction between
natural and unnatural extrapolation (p.150 in Papers in Ethics and
Social Philosophy, similar remarks can be found in the introduction to
Papers in Metaphysics and Epistemology). So the first suggestion
is very probably right.
(Reading Brian's comments it now seems to me when I argued that natural
properties can't solve the New Riddle I've been confusing it with the Old
Riddle. All the New Riddle requires is an objective distinction between
good and bad extrapolations. That induction based on good extrapolations
might nevertheless yield systematically false predictions ("not work") is the
Old Riddle.)
I think these conditions match the dot-matrix test better than the ones I
proposed earlier. They are more complicated, but closer to the matrices
and not too unnatural:
A property F is natural to the extent that the following conditions are
satisfied, where (1), (3) and (5) weigh heavier than (2), (4) and (6).
1) The Fs resemble each other intrinsically.
2) The Fs resemble each other extrinsically.
3) Anything that exactly resembles an F intrinsically is itself F.
4) Anything that exactly resembles an F extrinsically is itself F.
5) There are few intrinsic F-gaps.
6) There are few extrinsic F-gaps.
Something y is an intrinsic (extrinsic) F-gap if it isn't F and there are
Fs x and z such that y intrinsically (extrinsically) resembles both of them
more closely than x intrinsically (extrinsically) resembles z.
RL satisfies all conditions except (3), whereas R only properly satisfies
(1).
In section 6 of "Redefining 'Intrinsic'" (Philosophy and Phenomenological
Research 62, 2001), Lewis introduces an interesting test for comparative
naturalness of properties. The test is based on two-dimensional dot-matrix
pictures, where distance along the horizontal dimension measures intrinsic
dissimilarity, and distance along the vertical dimension extrinsic
dissimilarity. Roughly (p.385), a natural property demarcates a regular
region in the dot-matrix. Less roughly (p.391), two aspects of the region
are important for naturalness: spread and scatter.
My logfiles indicate that people are more interested in silly
logic puzzles than in pointless remarks on footnotes in the
metaphysical writings of David Lewis. Let's see if I can get my readership
down to zero with this one.
Besides perfectly natural properties, Lewis also needs somewhat less
natural properties in his philosophy of language and elsewhere. What
determines how natural a property is? Lewis gives three different
answers, in four different places, none of them longer than two sentences.
David Lewis offers a lot of work for natural properties in his semantics,
his theory of mental content, materialism, supervenience, causation, laws
of nature, etc. Strikingly missing in this list (as opposed to the list of
Anthony Quinton, "Properties and Classes") is the solution of Goodman's New
Riddle of Induction. I don't know why Lewis never mentions this. Two
suggestions:
1) He thought it was just too obvious, and he disliked repeating arguments
of other philosophers (none of the items on Quinton's list occurs on
Lewis').
Things are counterparts iff they are sufficiently similar to each other.
They needn't be similar intrinsically: For example, in "Individuation by
Acquaintance and by Stipulation" (§2), Lewis allows for counterparts that
are similar in standing in a particular relation of acquaintance to some
person. In fact, they needn't be similar at all: In On the Plurality of
Worlds (§4.4), Lewis accepts that, speaking unrestrictedly, everything
is an individual possibility for anything. However, in "Things qua
Truthmakers" (§5), he denies that things could be counterparts by living in
a world in which there are no unicorns. I wonder why. Lewis says that
such a respect of similarity would be too extrinsic and strike us as too
unimportant. But other eligible respects are extrinsic too, and what
strikes us as important certainly depends on the relevant context. I can
imagine theists who believe that there is a big difference between
living in a world where there is a God and living a duplicate life in a
Godless world. So in some special contexts, those of our counterparts who
live in Godless worlds might be excluded as being too different. Conversely, an atheist might exclude counterparts that live in worlds with Gods a being too different.
Well, what do I mean by "extended"? If "extended" means
"having parts", nobody thinks that extended things lack parts. I guess
what I mean is "existing at several different (space-, time- or spacetime-)
coordinates". For instance, I find it hard to understand how something
could cover all of Berlin without having any part that covers Kreuzberg. I
see that this is precisely how immanent universals are supposed to exist,
but that doesn't help me much, because I find it equally puzzling here.
Perhaps I was wrong when I said that those who
claim that perdurantism is contingent think that things could undergo
intrinsic change without having temporal parts. I've just reread
Haslanger's and Lewis' remarks, and these appear to be compatible
with the view that only things that don't change might endure. For
example, Lewis only mentions the possibility that the spatial parts of a
spinning sphere might persist by enduring. And maybe those parts don't
ever change their intrinsic properties. Probably even the entire sphere
doesn't, because if you copy a particular sphere stage and rotate the copy
by 180 degrees, you still have an exact intrinsic duplicate of the original
stage. This would explain why Lewis doesn't announce a big change of view,
because he always accepted that some special entities, namely universals,
might endure.
My only complaint then is that this doesn't turn perdurantism into a contingent theory of intrinsic change (rather than persistance). And I still find it difficult to understand how extended things could lack parts.
I am not an expert on modal fictionalism, so probably something is obviously wrong with the following objection. But anyway, here it is.
Modal fictionalism claims that any statement S about possible worlds (and other possibilia) is to be analysed as "According to the possible-world-story, S". Now possible worlds are used in reductive analyses of all kinds of concepts: modality, counterfactuals, causation, laws, properties, propositions, meanings, probabilities, supervenience, fictions, etc. For instance, an analysis of indexicals usually talks about extensions in possible contexts of utterance. If fictionalism is right, then this analysis must in turn be analysed in terms of extension in possible contexts according to the possible-worlds-story. And this seems rather odd. Suppose I propose some theory T of indexicals (or laws or whatever). If fictionalism is right then T is correct iff it is implied by some story about possible worlds. Firstly, intuitively this is not at all what I would have thought my theory was about. Secondly, which possible-world-story is relevant here? If we take the five or six claims about recombination and other worlds being of the same kind as ours usually presented by fictionalists (e.g. Rosen 1990), all the analytic projects mentioned above appear to be doomed: That simple story will not imply anything at all about indexicals, or laws, or causation. Unless of course we extend it by some analysis of these notions. Which analysis? The obvious candidate is the analysis we believe to be true, that is, T. But then all the analytic projects mentioned above come out as trivially true: Even the craziest theory will be good enough to imply itself.
The principle of recombination states what other possible worlds there must
be, given the existence of some possible worlds. In sec. 1.8 of On the
Plurality of Worlds, David Lewis suggests something like this:
L) For any parts of any worlds there is some world containing
any number of duplicates of all those parts, and nothing else , provided that they all fit
into a possible space-time.
Daniel Nolan argues in "Recombination Unbound" that the clause 'and
nothing else' should be dropped, because if some thing B consists of two
duplicates of A, there couldn't be a world containing one B, one A, and
nothing else. Unfortunately, without the clause the principle doesn't
exclude the necessary coexistence of distinct possibilia. In fact, it is
even compatible with all possibilia having duplicates in all worlds. I
think it would be better to leave the clause and instead restrict the
principle to distinct parts of worlds.
Several people have claimed that perdurantism is only contingently true, or at
least a posteriori: Mark Johnston expresses something like this at the end
of "Is There a Problem about Persistence?"; Sally Haslanger in "Humean
Supervenience and Enduring Things"; Frank Jackson in section 2 of
"Metaphysics by Possible Cases"; and David Lewis in section 1 of "Humean
Supervenience Debugged".
One of the arguments for this claim seems to be that both perdurantism and
endurantism are to some degree intelligible, which is why philosophers
still disagree about the issue. I find that strange. Philosophers also
disagree about the existence of universals, arbitrary mereological fusions,
possible worlds, and numbers. Are these also contingent matters?
There are some arguments against the reducibility of tensed propositions to
tenseless propositions about times and things at times. But I've never
seen the following argument:
The reductionist claims that there are other times and that
things have all kinds of properties at those times. Clearly, it would be
circular to say that there are exactly those times that once existed or
will exist, and that x has F at some past time iff x once was
F. The reductionist must not use tensed statements in specifying exactly
what times there are and what things instantiate which properties at those
times. But it seems hopeless to find a completely tenseless, general, and
yet accurate rule.
This is silly, because a reduction is not the same things as a decision
procedure. Of course, if you reduce A-facts to B-facts, complete knowledge
of B-facts must in principle suffice to deduce all A-facts. But specifying
all the B-facts is in no way part of the reduction.
Isn't it puzzling that this silly kind of argument keeps being brought
forward against Lewis' reduction of modal facts to facts about possibilia
(e.g. in Lycan, "Two -- no, three -- concepts of possible worlds",
Proceedings of the Aristotelian Society (91): 1991; Divers and Melia, "The
analytic limit of genuine modal realism", Mind (111): 2002)?
It seems to be: I've never heard of anyone being converted to modal realism, or giving it up. In particular, Lewis himself endorses it in his earliest papers, e.g. in the conclusion of 'Convention'. According to this article from the Daily Princetonian, he "worked on" the topic already at the age of 16. Strange.
In "Two Concepts of Modality", Alvin Plantinga argues that propositions
aren't sets of worlds, because "you can't believe a set, and a set can't be
either true or false" [208]. I think this argument is better than it might
appear in the rather Ungerian context of Plantinga's paper, where he uses
several arguments of the same kind to support completely crazy views, like
that Lewis is an antirealist about possible worlds.
The traditional job description for propositions says that they are a) the
ultimate bearers of truth-values, b) the content/object of propositional
attitudes, and c) the meanings of declarative sentences. Plantinga is
right that sets aren't the most intuitive candidates for this job: Is the
empty set an 'ultimate bearer' of the truth-value false? Is it the content
of Frege's belief in Axiom 5? Is it what you have to know in order to
understand Axiom 5? Well, intuitively not, but I don't think intuition is
to judge questions like these. More importantly, there are reasons
against the identification of sets with propositions.
I'm currently writing a chapter on modal realism.
I don't like this topic because it always confuses me. Here is one such
confusion.
In some world w, pretty much resembling our world, there are two
individuals A and B. Let 'A-in-w' be an extremely rich descriptions of A
that implies every qualitative truth about w, similarly for 'B-in-w'
and B. Now the following two sentences might both be true:
1) If I were A-in-w, I would do X.
2) If I were B-in-w, I wouldn't do X.
It is easy to overlook that David Lewis has revised his worm view of ordinary things in 'Tensing the Copula', Mind 111 (2002). Here is the passage (p.5):
In talking about what is true at a certain time, we
can, and we very often do, restrict our domain of discourse so as to
ignore everything located elsewhere in time. Restricted the domain in
this way, your temporal part at t_1 is deemed to be the whole of
you. So there is a good sense in which you do, after all, have *bent simpliciter*.
In other words: Terms for ordinary things are indeterminate. They don't always pick out worms. Sometimes they pick out segments, and sometimes just stages, depending on the contextually determined domain of discourse.
I think this is an improvement over the worm theory. Is it general enough? Lewis says that our terms pick out the sum of all those temporal parts of the relevant worm that are inside the domain of discourse. But don't we also attribute bent-simpliciter to the whole of me in "I'm bent now, but I wasn't bent yesterday"? Yet here the domain contains yesterday's parts as well.
Brian Weatherson now says that 'the world exists' is exactly as natural as
'there is a G', where G applies to worlds that are exactly like this one.
I agree. But this only makes things worse, because the class G denotes
seems very natural: It contains our world and all its exact intrinsic
duplicates. Is this a gruesome gerrymander? We still need a
further restriction on best theories apart from naturalness.
Intuitively, some objects are more natural than others. For example, cats
are more natural than mereological fusions of cats and elephants. I think
that ultimately, naturalness of things should be definable in terms of
naturalness of the properties the things instantiate. I'm not quite sure
how exactly this is to be done, so for now I'll stick with the intuitive
notion of naturalness. Intuitively natural things are spatiotemporally
connected, constitute a causal unity, contrast with their surroundings,
etc. The world, that is, the mereological fusion of everything that exists
at any spacetime distance from us, does fairly well here: As far as I know,
it is perfectly connected, causally united (indeed, causally closed) and
contrasts clearly with everything outside of it (such as numbers or other
worlds, if such there be). Why then does Brian Weatherson think that the
world is gruesome?
I see two ways to exclude 'the world exists' as the best theory of
everything. The first is the one I already mentioned: to state that a good
theory must imply interesting truths a priori. The second is to
stipulate that a theory must not contain individual constants. I have some
sympathy with such a stipulation, though it may stipulate away haecceitism.
It is sometimes (e.g. in David Sanford, 'Fusion Confusion', Analysis 63,
2003) said that some things are not fusions of all their parts: cats
and fusions of cat-parts for instance seem to differ in tensed and modal
properties. It may be noteworthy that on the standard definition of
'fusion', this position is outright inconsistent: X is the fusion of
Y1,Y2,... iff all of Y1,Y2,... are parts of X and no part of X is
distinct from all of Y1,Y2,.... Hence if X is not the fusion of
Y1,Y2,... then either one of Y1,Y2,... is not a part of X or some part of
X does not overlap Y1,Y2,.... So nothing can possibly fail to be the
fusion of all its parts.
In her paper 'Logical
Parts', forthcoming in the december issue of Nous, L.A. Paul presents a nice
theory of objects according to which things are mereologically composed of
their properties. Here are a couple of potential problems.
First, the theory seems to conflict with Unrestricted Composition and
incompatible properties. For suppose that P and Q are incompatible
properties, like being square and being round. By Unrestricted
Composition, there is a fusion of P and Q (or, if you prefer, of P and Q
and Paul's red cup). This fusion has both P and Q as parts, hence, on
Paul's theory, it is both P and Q. But if P and Q are incompatible, nothing
can be both P and Q.
I have the vague impression that Lewis' paper 'Things qua truthmakers', and
in particular the appendix by Lewis and Rosen, proves something important.
But I'm not sure what it is. Maybe it's that the request for truthmakers
was thoroughly misguided in the first place.
The problem is that the truthmaker principle is saisfied so eaily: Let 'w'
be a name for our world that does not apply to any qualitatively different
world, nor to anything inside any world. (That is, 'w' denotes our world
under a rather strict counterpart relation.) Let T be any qualitative
truth. Necessarily, if w exists, then T, since otherwise 'w' would be
applicable to a world in which not-T, even though T holds at our world,
contrary to the rule just stated. Hence w is a truthmaker for T, that is,
for any truth whatsoever.
Let T be any theory. If you worry about T's overabundant ontology, there is
a simple way to translate it into a theory T_i with a very sparse ontology:
For every sentence S in T introduce a new primitive predicate P that
applies to a world w iff S is true at w. Then replace S by 'the world is
P'. A more elegant method would not introduce a new primitive predicate
for every sentence, but rather use structured predicates, that are
systematically built up in the way the sentence is built up. (See Quine,
'Variables explained away', and Prior, 'Egocentric Logic'). T_i is a
theory that says the same as T with an ontology of just one individual -
the world. The price to pay for this reduction in ontology is an
overabundant ideology: Who wants all these weird predicates? Nobody.
Supervaluationsism and structuralism ('eliminative structuralism', not
the kind of structuralism that postulates structures) almost coincide.
Structuralism about something t says that any sentence 'F(t)' is to be
interpreted as 'for all x (if x is a candidate for t then F(x))'. For
example, arithmetical structuralism says that '2+2=4' is to be interpreted
as 'for all [N,0,',+,.] (if [N,0,',+,.] satisfies the peano
axioms then 0''+0''=0''''). If we translate 'x is a candidate for t' as 'x
is the referent of a precisification of 't'', we get: F(t) is (super-)true
iff it is true on all precisifications of 't'.
One of the many drawbacks of studying philosophy in Germany is that nobody kicks you when you spend years on your M.A. thesis. So hereby I publicly kick myself. As a consequence, this blog might become even more occupied with David Lewis than it already is.
To start this trend, here is a question about Lewis' functionalism. When a property P is multiply realizable, we cannot identify it with its realizers because then we would identify the realizers with each other, too. All we can do is locally identify P-in-k with its realizer in k, where k is a world or species or individual. Now what is P itself? In Lewis' papers on mind, he usually says that 'P' is systematically ambiguous or indeterminate, denoting the contextually salient realizer. (At least this is what I take him to say. He is not particularly explicit here.) The alternative would be to identify P with the diagonal property of being a P-realizer. The main reason why Lewis rejects this option (e.g. in 'Reduction of Mind') is that it is difficult to see how this diagonal property can occupy the causal role associated with 'P'. Difficult, but not impossible: In 'Finkish Dispositions' he proposes a solution, and consequently prefers identifying fragility not with the contextually salient realizer but rather with the diagonal property. Since then he apparently hasn't written anything more on the issue, so I would like to know if he has changed his mind on mental states (and heat, etc.) as well. (There may still be problems if the theoretical role is not entirely causal, so that even if the diagonal property can do the causal work, it might not be able to do the rest.) Or has he completely endorsed the third alternative – to simply leave the question unanswered: 'The folk well might have left this subtle ambiguity unresolved' ('Void and Object'). Can anyone help?
When I tried to spell out the 'modus tollens' I mentioned on monday, I
came across something that may be interesting.
Frank Jackson argues that facts about water are a priori deducible from facts about H2O:
1. H2O covers most of the earth.
2. H2O is the watery stuff.
3. The watery stuff (if it exists) is water.
C. Therefore, water covers most of the earth.
1 and 2 are a posteriori physical truths, 3 is an a priori conceptual
truth.
Are all truths a priori entailed by the fundamental truths upon which
everything else supervenes? If 'entailed' means 'strictly implied', this
is trivially true. The more interesting question is: Are all truths
deducible from the fundamental truths (deducible, say, in
first-order logic) with the help of a priori principles?
If yes, then it seems that Lewis' 'primitive modality' argument against
linguistic ersatzism (On the Plurality of Worlds, pp.150-157) fails.
Recall: Lewis argues that if you take a very impoverished worldmaking
language then even though it will be feasible to specify (syntactically) what
it is for a set of sentences to be maximally consistent, it will be
infeasible to specify exactly when such a set represents that, e.g., there
are talking donkeys. Now if all truths are a priori deducible from
fundamental truths, and -- as seems plausible -- fundamental truths are
specifiable in a very impoverished language, then we can simply say that a
maximal set of such sentences represents that p iff p is a priori deducible
from it.
Unfortunately, I find the 'primitive modality' argument quite
compelling. So, by modus tollens, I have to conclude that not all truths
can be a priori deducible from fundamental truths. Does anyone know
whether Lewis himself believes the deducibility claim he attributes to
Jackson in 'Tharp's Third Theorem' (Analysis 62/2, 2002)?
If you're asked to explain how your preferred theory of everything -- that is, your brand of physicalism -- can accomodate some entity X, the first thing to try is the Canberra Plan. It goes as follows: First, collect features that could be said to characterise X. If you're lazy, simply collect everything the folk says about X. Next, say that since these features comprise the essence of X, whatever physical entity has (more or less exactly) those features is X. Finally, explain that of course there is such a physical entity, since otherwise statements about X wouldn't be true.
First: Are fundamental particles mereological atoms?
Fundamental particles are 'the ultimate constituents of the world',
those upon whose properties and relations everything else supervenes. Many
of us believe that the instrinsic properties of complex things supervene
upon the properties and relations of their consituents. Then maybe the
fundamental particles can be identified with the ultimate constituents of
the world, if there are any. In fact, when we find that some things are
composed out of smaller things, we will usually not call the complex things
'fundamental particles'. I think it is in this sense that fundamental particles are supposed to be
indivisible -- not because we lack the means to break them into parts, nor
because it is impossible 'in principle' to break them, but simply because
they lack (proper) parts.
An old puzzle: The average mother has 3.4 children. Yet the average
mother does not exist. So how can she have children? An old solution: She
doesn't. "The average mother has 3.4 children" is to be understood as
"the number of children divided by the number of mothers is 3.4". So
"average mother" is not a genuine predicate, but rather a meaningless part of
numerical predicates like "the average mother has ... children".
If this solution is correct, it is meaningless to say that average
mothers exist, that some of them influence others, and that all of them
are distinct. Which indeed it is.
