Posts on: Lewis
I finally got around to adding the papers from Janssen-Lauret and Macbride
2023 to the search corpus at https://www.david-lewis.org. It's
a wonderful collection with lots of treasures. I want to comment on an
intriguing passage on pp.71f., from an abandoned 1969 textbook project
on confirmation theory.
First, some context. At this point in the manuscript, Lewis has
introduced \(\mathcal{M}\) as a
probability measure on the propositions expressible in a language \(\mathcal{L}\) with classical boolean
connectives; \(\mathcal{C}\) is the
associated conditional probability measure, defined by the ratio
formula. Lewis notes that conditional probabilities are often read as
"the probability of C if A", which suggests that \(\mathcal{C}(C/A)\) might equal \(\mathcal{M}(C\textit{ if }A)\), where
'\(C\textit{ if }A\)' is the material
conditional. But that's obviously false. Lewis continues:
In "Quasi-Realism is Fictionalism" (Lewis 2005), Lewis seems to
suggest that Blackburn's quasi-realism about moral discourse is a kind
of fictionalism. The suggestion is bizarre. Has Lewis made silly
mistake? (Spoiler: No.)
Let's compare what quasi-realism and fictionalism say about moral
discourse.
Blackburn's quasi-realism (as presented, e.g., in Blackburn 1984,
ch.6 and Blackburn 1993) is a brand of
expressivism. According to Blackburn, moral statements like (1) don't
serve to describe special facts, but to express moral attitudes.
I've decided to write somewhat regular short pieces on interesting papers I've recently read. This one is about Smithies, Lennon, and Samuels (2022).
Smithies, Lennon, and Samuels (henceforth, SLS) criticise the view that there are a priori connections between having a belief with a certain content and other states that would be rational given this belief. A simple example of the target view says that believing P is being disposed to act in a way that would bring one closer to satisfying one's desires if P were true. A more complicated example of the target view, on which SLS focus, is Lewis's. According to Lewis, for a mental state to be a belief state with such-and-such content, the state must, under normal conditions, be connected in a certain way to behaviour, perceptual experiences, and other propositional attitudes. SLS deny this.
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.
The latest issue of The Monist contains an outline of an unpublished paper by Lewis: "Nihil Obstat: An Analysis of Ability", along with a useful commentary by Helen Beebee, Maria Svedberg, and Ann Whittle.
Lewis's analysis of ability goes as follows:
You're able to φ iff, for some basic action
(1) doing it would be φing, and
(2) there is no obstacle to doing it.
It is clear from this analysis, and from the context in which it is presented, that Lewis is only interested in a rather specific sense of 'ability'. He wants to spell out the sense in which we are able to perform particular intentional actions that we don't actually perform, even if the world is deterministic. He is not interested in our ability to regrow injured skin, or in the ability of tardigrades and steel to withstand high temperatures. He also isn't interested in what are sometimes called "general abilities", like my ability to play the piano that I have even when I don't have access to a piano. (At any rate, this kind of ability is not covered by his analysis, and it isn't relevant to compatibilism.)
In my 2014 paper "Against Magnetism", I
argued that the meta-semantics Lewis defended in "Putnam's Paradox" and pp.45-49
of "New Work" is (a) unattractive, (b) does not fit what Lewis wrote about
meta-semantics elsewhere, and (c) was never Lewis's considered view.
In a
paper forthcoming in the AJP, Frederique Janssen-Lauret and Fraser Macbride
(henceforth, JL&M) disagree with my point (b), and present what they call
"decisive evidence" against (c). Here's my response. In short, I'm not
convinced.
Last week, I gave a talk in Manchester at a
(very nice) workshop on "David Lewis and His Place in the History of Analytic
Philosophy". My talk was on "Lewis's empiricism". I've now written it up as a
paper, since it got too long for a blog post.
The paper is really about hyperintensional epistemology. The question is how we
can make sense of the kind of metaphysical enquiry Lewis was engaged in if we
accept his models of knowledge and belief, which leave no room for substantive
investigations into non-contingent matters.
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.
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.
Next, undermining. Suppose we are testing a model H according to
which the probability that a certain type of coin toss results in
heads is 1/2. On some accounts of physical probability, including
frequency accounts and "best system" accounts, the truth of H is
incompatible with the hypothesis that all tosses of the relevant type
in fact result in heads. So we get a counterexample to simple
formulations of the Principal Principle: on the assumption that H is
true, we know that the outcomes can't be all-heads, even though H
assigns positive probability to all-heads. In such a case, we say that
all-heads is undermining for H.
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.
Lewis, in "Causal Decision Theory" (1981, p.308):
Suppose we have a partition of propositions that distinguish worlds
where the agent acts differently ... Further, he can act at
will so as to make any one of these propositions hold, but he cannot
act at will so as to make any proposition hold that implies but is
not implied by (is properly included in) a proposition in the
partition. ... Then this is the partition of the agent's
alternative options.
That can't be right. Assume I "can act at will so as to make hold"
the proposition P that I raise my hand. Let Q be an arbitrary fact
over which I have no control, say, that Julius Caesar crossed the
Rubicon. Then I can also act at will so as to make P & Q true. (By
raising my hand, I make it true, by not raising it I make it false.)
So, by Lewis's definition, P is not an option, since I can act at will
so as to make a more specific proposition P & Q true (a
proposition that implies but is not implied by P). By the same
reasoning, all my options must entail Q. So they don't form a
partition: they don't cover regions of logical space where Q is
false.
To what extent are the beliefs and desires of rational agents
determined by their actual and counterfactual choices? More precisely,
suppose we are given a preference order that obtains between a
possible act A and a possible act B iff the relevant agent is disposed
to choose A over B. Say that a pair (C,V) of a credence function C and
a utility (desirability) function V fits the preference order
iff, whenever A is preferred over B, then A has higher expected
utility than B by the lights of (C,V). Now, to what extent does a
rational preference order constrain fitting credence-utility
pairs?
A lot has been written in the last 10 years or so on updating
self-locating beliefs, mostly in the context of the Sleeping Beauty
problem. One thing almost all of these papers have in common is that
they quote Lewis's remark in "Attitudes de dicto and de se" (1979,
p.534), where he says:
it is interesting to ask what happens to decision theory
if we take all attitudes as de se. Answer: very little. We replace the
space of worlds by the space of centered worlds, or by the space of
all inhabitants of worlds. All else is just as before.
This is supposed to imply that Lewis took standard
conditionalisation to be the correct update rule for self-locating
belief.
There is a mistake on page 49 of Lewis's "Counterfactual dependence
and time's arrow" (1979). Since the mistake seems to be repeated all the
time, it might be worth pointing it out.
Page 49 is where Lewis lists similarity standards for his analysis
of counterfactuals. The analysis, recall, says that "if A were the
case, then C" is true iff the closest A-worlds are C-worlds (or, more
precisely, iff either there are no A-worlds or some A&C-worlds are
closer to the actual world than any A&~C world). Closeness is a matter
of similarity, and Lewis indicates what the relevant respects of
similarity might be for certain ordinary counterfactuals in section
3.3 of his 1973 book, and again in the 1979 article on counterfactual
dependence. Roughly, the closest A-worlds are those that perfectly
match the actual world across as much of spacetime as possible without
diverse and widespread violations of the actual laws. This won't do
for indeterministic worlds, where generally no laws need to be
violated at all in order to ensure perfect match of futures even after
earlier divergence. So Lewis restricts his standards to deterministic
worlds, returning to the indeterministic case in the 1986 postscript
to the 1979 paper.
Rational credence should match the expectation of objective
chance. Here I will have a brief look at what happens
to this connection between credence and chance on the assumption that
credence is centered and chance is not.
1. Fixing the time. Both credences and chances evolve over time. When a
coin is tossed twice, the chance of two heads may initially be 1/4;
after the first toss has come up heads, it is 1/2. So when your
beliefs should match the assumed chance, it can only match the chance
you assume to obtain at some particular time. At what time?
First, a quick reminder of history. David Lewis once proposed a principle (the 'Principal Principle') linking rational credence and objective chance. It says (or rather, entails) that your rational credence in
any proposition A, on the assumption that the objective chance of A is x, should also be x, no matter what (further) evidence E you have:
OP: P(A | ch(A)=x & E) = x.
This principle, the 'Old Principle', is widely taken to suffer from two defects. First,
suppose your evidence E includes ~A. Then probability theory
ensures that P(A | ch(A)=x & E) = 0, irrespective of x. Lewis
responded by restricting OP to cases where E is 'admissible'. He suggested that a
(true) proposition is admissible iff it is entailed by the history of the world up to now
together with the laws of nature.
Mostly, when we don't believe something, we don't know it either. But arguably not always. The timid student thinks she's merely guessing, while in fact she knows. She knows, but she lacks the confidence required for belief. It would be nice to have an analysis of knowledge that allowed for such cases, but also explained why they are rare.
Lewis's analysis tries to do that. On Lewis's account, you know p iff your evidence rules out any relevant situation where ~p. Among the rules for what counts as 'relevant', the 'rule of belief' tells us that any possibility with non-negligible subjective probability counts as relevant. Now suppose you don't believe p. Then you give non-negligible probability to ~p situations. So you know p only if your evidence rules out all those ~p situations. Moreover, your present evidence 'rules out' a situation iff you have different evidence in that situation than you actually have. So if you have knowledge without belief, you must assign positive probability to situations where you have different evidence than you actually have. On a suitable understanding of evidence, those cases will be rare, because we are normally confident that we have the evidence that we have.
Here is Lewis's 1996 analysis of knowledge:
S knows proposition P iff P holds in every possibility left uneliminated by S's evidence. ("Elusive Knowledge", p.422 in Papers)
By evidence, Lewis explains, he means perceptual experiences and memories; a possibility W counts as eliminated iff the subject does not have the same evidence in W: "When perceptual experience E (or memory) eliminates a possibility W [...], W is a possibility in which the subject is not having experience E" (424). It follows that everyone trivially knows what perceptual experiences they have: In every possibility W in which I have experience E, I obviously have experience E.
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, ... }.
I gave a talk about the Canberra Plan on Tuesday (slides) in which I mentioned that I disagree with Lewis and Kim about the semantics of "pain": they say "pain" denotes whatever occupies the pain role in the species under consideration (or whatever is the relevant kind); I think "pain" rather denotes the property of being in a state that realises the pain role. One of the reasons I gave for my preference is that "pain" would be rather exceptional if it worked as Lewis and Kim believe.
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.
Long ago, I worried about how the Ramsey-Carnap-Lewis account of theoretical terms could be applied to predicates. I noticed two reasons why Lewis's proposal to just turn the predicates into singular terms ("Instead of [...] 'F ---', for instance, we can use '--- has F-hood'", HTDTT p.80) is no good: first, it entails that completely false theories, say about witches or gods, leave their theoretical predicates undefined, whereas in fact those predicates are clearly empty (and thus defined); second, the proposal can turn consistent theories into inconsistent theories. This second problem can be generalized: For many predicates, there is no corresponding property that could be denoted by a singular term. Exactly which predicates these are depends on one's theory of properties, but "having parts", "being self-identical", "being a set" and "being a property" are generally good candidates, besides of course "not instantiating oneself".
Peter Menzies and Huw Price, in their forthcoming "Is Semantics in the Plan?" have spotted a mistake in Lewis's "Psychophysical and theoretical identifications". But they don't spot that it's a mistake, and rather think it shows that the Ramsey-Carnap-Lewis-account of theoretical terms is severly limited.
The mistake is that Lewis identifies "theoretical role" with "causal role":
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.
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.
I had another look at Lewis's trust condition on linguistic conventions. It says that the members of a linguistic community generally take utterances of a sentence as evidence that the sentence is true. My opinion up to now has been that insofar as this condition is correct, it is redundant, and insofar as it is not redundant, it is incorrect.
The condition seems mostly redundant because the convention of truthfulness already requires of everyone to impute truthfulness to others. To be truthful means to try to utter sentences only when they are true. So by partaking in the convention of truthfulness in English, I already expect you to utter "it's raining" only when you believe that it's raining. So unless I believe your opinions about the weather are unreliable, I will take your utterance as evidence for rain. No need for an additional convention of trust.
I thought after finishing my PhD thesis I would spend less time thinking and writing about Lewis for a change. But just then, Brian started his Lewis blog raising all kinds of interesting issues, like how to handle theoretical terms in multiply realised theories. I think Lewis's early suggestion to treat the terms as empty in those cases is much worse than he realised (than he realised even later, when he dropped the suggestion). I hope to say more about that later.
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.)
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.
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?
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.)
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.
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.
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.
I've been invited to this year's German-Italian Colloquium in Analytic Philosophy, for which I've put together some remarks on the philosophy of mathematics: "Emperors, dragons and other
mathematicalia" (PDF). I mainly argue that mathematical sentences should be interpreted as quantifications over possibilia. Technically, this isn't really new. Daniel Nolan in particular has made a very similar suggestion (PDF). What hasn't been emphasized enough, I believe, is that this interpretation not only works from a technical point of view, but is quite attractive for various philosophical reasons. (Unlike Nolan, I argue that it isn't a reform, but a faithful interpretation of mathematics.)
Suppose
1) the facts about use etc. underdetermine the semantic value of term
x (to a certain degree).
But
2) the semantic value of x is not underdetermined (to that degree).
Let V1,V2,... be the semantic values between which x is
underdetermined, and suppose V2 is in fact the value (or range of values) of x. What is it
about V2 that makes it the semantic value? Not 'use etc'. But
suppose all obvious candidates like causal facts are part of 'use etc.'. Then the
relationship between x and V2 -- let's call it "reference" -- is
inscrutable insofar as knowing all ordinary facts about use and
causation and so on is not enough to find out that
x refers to V2. There must be something over and above all this that
privileges V2. Let's say (with Lewis) that V2 is a reference
magnet (with respect to x).
Stalnaker's "Lewis on Intentionality" (AJP 82, 2004) is a very odd paper. The aim of the paper is to show that Lewis's account of intentional content as developed in "Putnam's Paradox" -- global discriptivism with naturalness constraints -- faces various problems and conficts with what Lewis says elsewhere.
The first thing that's odd about this is that in "Putnam's Paradox", Lewis doesn't develop an account of intentional content. Rather, he discusses Putnam's model-theoretic argument and suggests that if one holds something like global descriptivism about linguistic content, adding external naturalness constraints on the interpretation of predicates would be an attractive way to block Putnam's argument for underdetermination.
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".)
Apropos conceptual differences, Lewis didn't seem to care much about whether his
analyses exactly matched other people's semantic intuitions:
In "Veridical Halluzination and Prosthetic Vision", he claims that
prosthetic vision is properly called "seeing". He continues:
If you insist that "strictly speaking", prosthetic vision isn't really
seeing, then I'm prepared to concede you this much. Often we do leave
semantic questions unsettled when we have no practical need to settle
them. Perhaps this is such a case, and you are resolving a genuine
indeterminacy in the way you prefer. But if you are within your
rights, so, I insist, am I. I do not really think my favoured usage is
at all idiosyncratic. But it scarcely matters: I would like to
understand it whether it is idiosyncratic or not. (p.280 in Papers
II)
Another example: In Convention, he suggests that a regularity to dress in a particular way doesn't count as conventional if many people conforming to the regularity want others not to conform (so that they can poke fun at them). Realizing that this classification isn't obvious he notes:
If the reader disagrees, I can only remind him that I did not
undertake to analyze anyone's concept of convention but mine. (p.47)
He speaks of reminding the reader because he had already mentioned in the introduction that there might be no clear common concept of
convention. But, he adds, "what I call convention is an important
phenomenon under any name" (p.3).
So Lewis says that a language L is used by a population P iff there prevails in P a convention of truthfulness and trust in L.
This requirement for language use seems far too strong, given Lewis's account of conventions.
The most obvious problem is the condition that for a
regularity to be a convention, it must be common knowledge in the
population that it is a convention. Lewis offers some weak readings of this condition, but even his weakest versions rule out that
sufficiently many members of the population may doubt or deny that the
regularity is a convention. So if there were sufficiently many French
speakers who believe that their language is completely innate, they would not partake in the convention of truthfulness and trust in French, and thus not use French, on Lewis's account. It even suffices if sufficiently many French speakers merely believe that there are enough who believe that, or believe that there are enough who believe that there are enough who believe it.
The main difference between Lewis's account of language use in
Convention and his account in "Languages and Language" (and later works) is that in the latter the convention required for a language L to be used is a convention of truthfulness and trust in L, whereas in the former it was only a convention of truthfulness. I wonder if there are any good reasons for this change.
Suppose in a certain community there exists a convention of truthfulness in L. On Lewis's analysis of conventions this means that within the community,
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:
Jonathan Schaffer argues (in Analysis 2001) that Relevant Alternatives Theories of knowledge (RATs) such as Lewis's fail because of Missed Clues cases:
Professor A is testing a student, S, on ornithology. Professor A shows S a goldfinch and asks, 'Goldfinch or canary?' Professor A thought this would be an easy first question: goldfinches have black wings while canaries have yellow wings. S sees that the wings are black (this is the clue) but S does not appreciate that black wings indicate a goldfinch (S misses the clue). So S answers, 'I don't know'.
We want to say that S doesn't know that the bird is a goldfinch. Yet it seems that S's evidence rules out all relevant alternatives. For situations with goldfinch-perceptions but no goldfinches are skeptical scenarios and usually regarded as irrelevant.
It is widely assumed that Lewis takes the objective naturalness of
semantic values to be an important constraint on semantics, needed to
prevent radical indeterminacy of meaning. On rereading some of his
remarks today, I found them a little confusing, and now I think the
situation is far more complicated.
Lewis discusses Putnam's model theoretic argument for radical
indeterminacy extensively in "New work for a theory of universals"
(NW) and "Putnam's paradox" (PP). In both papers, he says there is
something wrong with posing the problem as a problem about language,
because in fact the interpretation of language is settled by the
assignment of content to propositional attitudes (NW 49, PP
58f.). But, he says, focussing on attitudes only relocates the problem
without solving it, so that he might as well talk about language in
the rest of PP, which he does. He points at NW for a discussion of the
properly relocated problem.
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.
(This is a follow-up to the previous post.) I think I've found a better way to provide for things like population-dependence in a Lewisian semantic framework. The trick is to regard it as a kind of index-dependence without explicitly introducing population-coordinates into the indices.
Recall, we want "pain*" to denote whatever state occupies the pain-role in the relevant population. Unfortunately, the relevant population isn't just the most salient population in the context of utterance, for we want to say things like
This is going to get a bit weird and technical. I wonder how a Lewisian semantics (along the lines of "Index, Context and Content" and "General Semantics") for terms like "pain" can make true everything Lewis says about such terms.
Assume that
1) Necessarily, for all x, x is in pain* iff x is in a state that plays the pain-role in normal members of the kind to which x belongs.
By "the pain-role" I mean the causal role attributed to pain by folk psychology. By "pain*" I mean whatever satisfies the condition expressed by (1). So (1) is more like a definition than an assumption. Lewis believes that our ordinary concept of pain roughly satisfies (1), but for what follows this doesn't matter. I think it's clear that we could have concepts for which something like (1) holds. Lewis's example of having a certain number stored in memory, as denoting a state of pocket calculators, sounds plausible to me (with the pain-role replaced by the role attributed to the state of having a certain number stored in memory by folk pocket calculator theory).
According to the Lewis-Nemirow ability hypothesis, knowing what it's like to see red is having a certain cluster of abilities. According to almost everybody who writes about the ability hypothesis, the hypothesis also claims that knowing what it's like neither is nor involves any kind of knowledge-that. This is indeed suggested by some of Lewis' remarks, in particular by this one on p.288 of "What Experience Teaches" (in Papers):
The Ability Hypothesis says that knowing what an experience is like just is the possession of [...] abilities to remember, imagine, and recognize. It isn't the possession of any kind of information, ordinary or peculiar.
One has to read the rest of the paper to find out that by "information", Lewis here most probably means exclusion of possible worlds. At any rate, it is clear from the rest of the paper that Lewis doesn't claim that all Mary learns are abilities.
In §7 of "Naming the Colours", David Lewis considers the view that colour terms can be analysed in terms of colour experiences which in turn are identified by "a simple, ineffable, unique essence that is instantly revealed to anyone who has that experience".
Then if it were also common knowledge that everyone in the community becomes acquainted with magenta early in life (and if the community were properly dismissive of sceptical doubts about inverted spectra, etc.), it would be common knowledge throughout the community that magenta is the colour that typically causes experiences with essence E.
Lewis goes on to reject this porposal because it contradicts (type-A) materialism. But he doesn't reject the general idea itself: "[The doctrine of revelation] is false for colour experiences. [Footnote:] Maybe revelation is true in some other cases -- as it might be for the part-whole relation."
Suppose theory 1 says that entity x has certain properties, and theory 2 says that entity y has those properties. If we believe both theories, should we conclude that x=y?
It depends. Sometimes we not only should but must conclude that x=y, for example when theory 1 says that x is the planet Venus and theory 2 says that y is the planet Venus. In other cases, there is little reason to draw the conclusion, as when the theories merely say of x and y respectively that it is some planet or other. In yet other cases, the conclusion can be motivated by methodological considerations. For instance, whoever first realized that Hesperus is Phosphorus probably realized that the identity makes for a simpler overall theory.
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.
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
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...)
It is controversial whether indicative conditionals with false antecedents
are generally true. As far as I know, which really is not very far at all,
it is equally controversial whether counterfactual conditionals with
necessarily false antecedents are generelly true. What's interesting is
the different kinds of counterexamples that are brought forward against
these views. For indicatives, the counterexamples are indicative
conditionals with false antecedents that nevertheless appear to be false,
e.g. "if I put diesel in my coffee, the coffee tastes fine." For
counterfactuals however, the alleged counterexamples (brought forward e.g.
by Field in §7.2 of Realism, Mathematics & Modality, Katz in §5
of "What mathematical knowledge could be", and Rosen in §1 of "Modal
fictionalism fixed") are counterfactual conditionals with necessarily false
antecedents that appear to be true, e.g. "if the axiom of choice
were false, the cardinals wouldn't be linearly ordered". Isn't this quite
puzzling? How can the fact that some instances are true be a problem for
a theory that claims that all instances are true?
Suppose some theory T(F) implicitly defines the predicate F. If we want to
apply the Ramsey-Carnap-Lewis account of theoretical expressions, we first
of all have to replace F by an individual constant f, and accordingly
change every occurrance of "Fx" in T by "x has f" etc. The empirical
content of the resulting theory T'(f) can then be captured by something
like its Ramsey sentence 
f T'(f), and the definition of f
by the stipulation that 'f' denote the only x such that T'(x), or nothing
if there is no such (unique) x.
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.
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.
I've been thinking about yesterday's problem from Brian Weatherson's
interactive philosophy blog. Instead of a solution I've found a name:
"Forrest's Paradox" (see §2.5 in Lewis, On the Plurality of
Worlds).
Knowing the name, it is now easy to create even stranger problems of the
same kind. First a reformulation of the original problem.
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.)
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').
Happy new year everybody. I'm still alive, and I still have questions and
comments on the metaphysics of David Lewis. This one is about Lewis'
philosophy of mathematics.
In "Mathematics is Megethology", Lewis argues
for structuralism in set theory: There is no particular relation of
membership, connecting particular things with particular classes. Instead,
there are just two sides of Reality, ordinary individuals on the one side,
proper-class many mereological atoms (called 'singletons') on the other.
Set theory is about all relations on this Reality that satisfy certain
constraints, like 'every individual stands in that relation to a singleton'.
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.
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.
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.
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.
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?
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.
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.
