Advanced Topics in Metaphysics with Professor Barry Loewer

January 24th, 2014 Seminar

On Lewis

People say that he is the major metaphysician of the 20th century.
Pretty standard view of metaphysics, trying to figure out what exists in a general way.
What exists “is like.”
What Aristotle was doing.
For Lewis, would could be and what is are very related.
He is most famous for his realism about possible worlds.
What makes something part of the same world?
- Spatio-temporal relations
How are worlds specified? If you’re making worlds, what’re you doing?
- You make a spatio-temporal manifold/structure.
- You need to fill it up with perfectly natural properties in spots.
- Natural properties and natural relations.
- You can think of it as being “decorated.”
If you’re going to specify spatio-temporal structure, what’re you going to do?
- Points and metrics on the points.
- People have thought about physics without points.
- The more he says about possible worlds, the fewer possibilities there are.
Possible worlds have this structure of natural properties and particulars.
- He thought natural properties were the job of physics.
- What is it about the nature of physics that it’s related to natural properties?
If you made a gigantic list of things that exist, some of those things would be possible worlds.
- What is it for one thing to be reduced to another?
Physics has the job of what is actually instantiated.
- Mosaic of natural properties is what things actually reduced to.
- Lewis’ general metaphysics is a scientific metaphysics.
In the philosophy community, the realism about possible worlds was greeted with “incredulous stares.”
We’re interested in his views about “nomological varieties.”
- We’re interested in his account of laws, which is the Best Systems Account.
- Which hinges on his account of objective chance.

Objective probability is one of the must useful tools in the natural sciences, but we have no idea what it is.

He uses this account to give an account of counterfactuals, and these play a gigantically big role in his account of everything else.
- Nelson Goodman, “Fact, Fiction, or Forecast”
In showing that something is sufficient in trying to indentify the laws is by looking at instances, at their role.
- This is a reductive enterprise.

On Laws

What was background for Prof. Loewer and what’s background for us, those he’s teaching, is different.
- When he went to graduate school, the idea of thinking about the metaphysics of laws just wasn’t there.
- There were pragmatic or semantic accounts of laws, but about asking the general way of what it means to be law.
- Philosophers were using “law” to explain what an event is.
  - He made use of the idea of law with reference to Goodman on laws.
The way that Lewis got people to think about metaphysics just wasn’t on the table.
In recent times, “What is a law?” was put right on the table by Dretske and Armstrong in the 70s and 80s.
- No one has written a history of the scientific account of laws.
Hume thought that laws were sentences that applied in a certain way (pragmatic).
Ayer had a non-factual view.
Hempel and “positive instances of a general law confirm it.”
What are laws? They are of the form:
$$(x)(Fx \to Gx)$$
- If you open a textbook in classical or quantum mechanics, you will no longer see sentences of this form.
- How damaging is this to their project?
Loewer’s introduction to philosophy was when he was Amherst College and he wanted to date someone who thought a date was going to a talk by Max Black.
What is it to be “law-like” and what is the nature of law?
Hempel’s paradox or the Raven paradox.
- How do we understand “confirms”?
If you have a paradox, you can say that a premise is bad, the reasoning form the premises is bad, or you accept the conclusion.

If something is worth doing, it’s worth doing wrong the first time.

There’s less than meets the eye to Goodman’s paradox.

Laws are very special projections.
Later, many philosophers adopted Goodman’s language.
- A law is a generalation, but not any generalation.
- Only predicates that pick out natural properties.
There’s a relationship of support between laws and counterfactuals.
- This is at least epistemological because if we know the law, we know the counterfactual. But the truth of the counterfactual doesn’t mean the law is true.
How can a regularity explain anything?
- This is the really err intution.
- A regularity like all Fs are Gs.
- A law explains why something is true.
- Is the law doing the explaining?
- It’s certainly an idea that people like Dretske and Hempel.
An explanation is a law along with an initial condition.
Armstrong thought that laws were some other part of reality, and they took from Goodman that the predicates must refer to certain kinds of properties.
- Gru does not pick out a universal.
- Does Armstrong think that Green is a universal?
- A universal is supposed to, those features that are the things that have them are exactly similar to one another.
- From the point of view of the science of color …
For things to be an electron, it’s a natural kind, universal.
An obvious consequence of the powers side is that if laws are things that cannot help but be instantiated.
- All the people Loewer knows think that when there are these powers there are these metaphysical connections, if they don’t hold this they have to explain what these connections are.
- Metaphysically necessary connections.
Shoemaker thinks that there is only one possible world — this one.
- All truths are necessary truths.
Take a look a Salmon about Humean and nonHumean.

Next time

Step back to talk about Lewis
New Work on the Theory of Unverisals

January 30th, 2014 Reading

“New Work for a Theory of Universals” by David Lewis

Introduction

The “compulsory question” for systematic philosophy: the question of one over many.
- D.M. Armstrong thinks the answer is a theory of universals, but Lewis doesn’t.
- But universal can do other things.
Although universals may be dispensible.
Lewis’ ontology consists of posibilia.
- Along with the “iterative hierarchy of classes built upon them.”
- Properties are not much like universals, and they cannot do the work of universals.

Posibilia: Particular, individual things, some of which comprise our actual world and other of which are unactualised.

Are universals better emplyed as a replacement for posibilia in Lewis’ metaphysics?
- Not to be considered in this paper.
In the next section, Lewis will sketch Armstrong’s theory of universals, constrasting them with properties understood as classes of posibilia.
- Then, he will say why the “One over Many” argument is unconvincing.
- Then, how universals help him in connection with the topics of:
  - Duplication
  - Supervenience
  - Divergent worlds
  - Minimal form for materialism
  - Laws and causation
  - Content of language and thought
- And perhaps the list could be extended

Universals and Properties

Language offers several more or less interchangable words, that is “universal” and “property” and “quality” and “attribute” …
- Also “characteristic” and “kind” and “sort” and “type.”

Universal: Those entities, if such there be, that mostly conform to Armstrong’s account.
Property: Classes, any classes, but formemost classes of things.; To be a member of a class.

Why call them properties as well as classes?
- They do not need to be classes of actual things.
- The property of being a donkey is the class of all the donkeys.

Relation: Arbitrary classes of ordered pairs, triples, … A relation among things is a property of tuples of things. With no restriction to actual things.

Universals and properties are different in two ways.
1. Their instantiation
  - It is a contituent part of each particular that has it.
  - A property is “spread around.”
  The property of being a donkey is partyly present wherever there is a donkey, in this or any other world. Far from the property being part of the donkey, it is closer to the truth to say that the donkey is part of the property. But the precise truth, rather, is that the donkey is a member of the property.
  - Thus universals would unify reality in a way that properties do not.
  - Things that share a universal have not just joined a single class. They literally have something in common. They are not entirely distinct. They overlap.
  - Universals defy intuitive principles. *The intuitions were made for particulars*.
  - Is copresense transitive? No.
  Round, silver, golden. Silver and round are copresent, for here is a silver coin. Golden and round are copresent, for there is a round coin; but silver and golden are no copresent.
2. Their abundance. This is the difference that qualifies for different work.
  - Universal are sparse in Armstrong’s work. *There are the universals that that there must be to ground the resemblences and causal powers of things, and there is no reason to believe in any more.* These would be rejected:
    1. Not golden
    2. Golden or wooden
    3. Metallic
    4. Self-identical
    5. Owned by Fred
    6. Belonging to class C
    7. Grue
    8. First examined before 2000 A.D.
    9. Being identical
    10. Being alike in some respect
    11. Being exactly alike
    12. Being part of
    13. Owning
    14. Being paired with by some part in R
  - The world’s universals should comprise of a minimal basis for characterizing the world completely.
  - Universals that do not contribute to this or are redundant are unwelcome.
  - A non-linguistic counterpart of a primitavely vocabulary for a language capable of describing the world exhaustively.

Copresent: Two entities are copresent if both are wholly present at one position in space and time.

It is quite different for properties.
- Any class of things, regardless of characteristic of the class, is a property.
  - So they are of immense abundance.
- There are so many properties that those specifiable in English, or in the brain’s language of synaptic interconnections and neural spikes, could be only an infitesimal minority.
There so many properties that any two things share an infinite amount of properties and fail to share inifitely many as well.
- This is so whether the two things are duplicates or utterly dissimilar.
  - Properties do not capture resemblence.
- Properties are causally irrelevant.
- Properties “carve reality at the joints.”

Natural properties: Properties whose sharing makes for resemblance, and the ones relevant to causal powers.
Perfectly natural properties: If the members of the class are all and only those things that share some one universal.

An adequate theory of propeties is one that recognizes an objective difference between natural and unnatural properties.
A Nominalistic theory of properties could achieve adequacy by drawing primitive distinctions between particulars.
A Nominalist in pursuit of adequacy might prefer to rest with primitive objective resemblance among things.

Nominalism: the doctrine that universals or general ideas are mere names without any corresponding reality, and that only particular objects exist; properties, numbers, and sets are thought of as merely features of the way of considering the things that exist.

At this point, it could be a good idea to believe in universals *as well as* properties.
- “Properties have work of their own, and universals are ill-suited to do the work of properties.”
Consider these sentences:
1. Red resembles organge more than it resembles blue.
2. Red is a color.
3. Humility is a virtue.
4. Redness is a sign of ripeness.
Prima facie, these sentences contain names to denote individual things.
It is unlikely that there are universals for colors, especially particular colors.
- Unless you subject the phrases to paraphrasing.
Let x range over things, P over properties (classes) of things. Then:
$$\exists_1 P \Box \forall x (x \in P \equiv 0x)$$

One Over Many

Armstrong’s main argument is the “One over Many” argument.
- It is because that Lewis finds this unsatisfactory that he is seeking alternatives.
An effort at systemic philosophy must give an account of purpoted fact.
- There are three ways:
  1. I deny it.
  2. I analyse it thus … .
  3. I accept it as primitive.

Moorean fact: one of those things that we know better than we know the premises of any philosophical argument to the contrary

An adequate Nominalism is a theory that takes Moorean facts of apparent sameness of a type as primitive.
- Universals are one possible solution, but not the only, and not even the best (?).
Early in Universals it “undergoes an unfortunate double transformation.”
- The analysandum becomes the schema:
  
  a has the property F.
- The turning point takes only two sentences:
  
  How is [the Nominalist] to account for the apparent (if usually partial) identity of numerically different particulars? How can two different things both be white or both be on a table?
  - “There are no universals but the proposition a is F is perfectly alright as it is.” (Dodging the question.)
Class Nominalism fails because it employs predications of class membership, which predications it cannot without circularity analyze in terms of class membership.
Resemblance Nominalism fails to analyze predications of resemblance.
Predications of particpation evade analysis.

Duplication, Supervinience, and Divergent Worlds

From now on, they’ll only be natural, unnatural, or more-or-less natural properties.
Beginning the analysis with duplication.

Duplication

Duplication: Ex, uing a copying machine. A perfect copier would make the two items the same in terms of atomic structure, making the two items, the copy and the original, indiscernible.; Two things are duplicates if and only if they have precisely the same intrinsic properties, however much their extrinisic properties might differ.
Intrinsic property: Property P is instrinsic if and only if, for any two duplicate things, not necessarily from the same world, either both have P or neither does.
Extrinsic property: Property P is extrinsic if and only in there is some such pair of duplicates of which one has P and the other lacks P.

If we relied on physical theory to be accurate and exhaustive, we might define duplication in physical terms.
- But this definition is no analysis because it presupposes the contigent physics of this actual world.
Duplication is better analyzed in terms of shared properties.
- To begin with natural properties and then move to intrinsic properties.
If Materialism were false and physics an utter failures, as it is in some deplorable worlds, there would still be duplication in terms of shared natural properties.
All perfectly natural properties are intrinsic properties.
- However, intrinsic properties can be disjunctive and miscellaneous and unnatural, so long as they never differ between duplicates.
Duplication is important for two topics in metaphysics: supervenience and divergent worlds.

Supervenience

A supervenience thesis is a denial of indepedant variation.
- It can be defined with posibilia.
- To say that so-and-so supervenes on such-and-such is to stay there can be no idefference in respect to so-and-so without difference in respect to such-and-such.
  
  Beauty of statues supervenes on their shape, size, and colour, for instance, if no two statures, in the same or different worlds, ever differ in beauty without also differing in shape or size or colour.
A supervenience thesis is cautiously reductionist.
The worst that can happen is that an ascription of a supervenient property is equivilent to an uncountably infinite disjunction of maximally specfic descriptions of the other property.

Local duplicates: Two worlds are local duplicates just in case they are divisible into corresponding small parts in such that that: 1. Corresponding parts of the two worlds are duplicates, and 2. The correspondence preserves spatiotemporal relations.

Divergent worlds

Diverge: Two possible worlds diverage just in case they are not duplicates but they do duplicate initial temporal segmant. For example, our world and another might match perfectly up through the year 1945, and go their separate ways thereafter.
Branching: Instead of duplicate segments, one and the same initial segment is allegedly share as a common part of two overlapping worlds.
Determinism: A system of laws of nature is Determinsitic just in case no two divergent worlds both conform perfectly to the laws of that system.; A world is Deterministic just in case its laws comprise a Determinsitic system.; Determinism is the thesis that our world is Deterministic.

Minimal Materialism

There is a difficulty in definining reductionist views as supervenience theses.
- The solution is to employ natural properties not only by way of duplication but in a more direct way also.

Materialism

The these that physics is a comprehensive theory of the world, complete as well as correct.

The world is as physics says it is, and there’s no more to say.

Materialism is not a thesis of finite translatability of all our language into the language of physics.

Materialism is not to be indentified with any one Materialist theory of mind. It is a thesis that motivates a varity of theories of mind:

Behaviorism
Functionalism
The mind-body identity theory
Mind is a mistake

Materialism is not just the theory that there are no things except those things indentified by physics. Materialism don’t believe in spirit, or other such nonphysical things.

Materialism is at least in part the thesis that there are no natural properties instantiated at our world except those recognized by physics. Couldn’t ther be a natural property X which is shared by the physical brains in worlds like ours and the immaterial spirits that inhabit other worlds? Or by thisworldy quarks and otherwordly particles that cannot exist under our physics?

(M1): Any two possible worlds that are exactly alike in all respects recognized by physics are qualitative duplicates.

This will not do. A world could differ in having Materialism false, as it is contigent and non-physical, and then you could have epiphenomenal spirits and not differ physically by not be a qualititative duplicate.

(M2): There is no differe, a fortiori no mental difference, without some nonmental difference. Any two worlds alike in all nonmental respect are duplicate, and in particular do not differ in respect of the mental lives of their inhabitants.

This fails, I think, because worlds can differ in the mental lives of the inhabitants but be physically identical (?).

(M3): No two Materialistic worlds differ without differing physically; any two Materialistic worlds that are exactly alike physically are duplicates.

Any world, however spirit=ridden, belongs to such a class.

(M4): Among worlds that conform to the actual laws of nature, no two differ without differing physically; any two worlds that are exactly alike physically are duplicates.

Less that Materialism because M4 could hold a world where Materialism is false but where spiritual phenomena are correlated with physical phenomena accords to strict laws.
More than Materialism because M\$ fails to hold at a Materialistic, spirit-free world if the laws of the world do not preculd the existence of epiphenomenal spirts. “Absent, but not outlawed.”

(M5): Among worlds where no natural properties are alien to our world are instantiated, no two differ without differing physically; any two such worlds that are exactly alike physically are duplicated.

Alien property

A property is alien to a world just in case:

It is not instantiated by any inhabitant of that world;
It is not analysable as a conjunction of, or as a structural property constractu out of, natural properties all of which are instantiated by inhabitants of that world.

Laws and Causation

Laws

What is it to be a law of nature?
- You need universals, or at least natural properties, to explain lawhood.
Armstrong’s theory holds that what makes regularities lawful are second-order state of affais N(F,G) in which the two ordinary, first-order universals F and G are related by a certain dyadic second-order universal N.
- The “lawmaker” N.
But I say that N deserves the name of ‘necessitation’ only if, somehow, it really can enter into the requisite necessary connections. It can’t enter into them just by bearing a name, any more than one can have mighty biceps just by being called ‘Armstrong’.
Necessary connection can be unintelligible even when they are supposed to obtain between existences that are not clearly and wholly distinct.
Some regularity is accidental, but laws are regularities.
- So we must be selective.
- Reject “lawlikeness” plus truth.
- A suitabl system has:
  - The virtues we aspire to in “our own theory-building.”
  - Has them to the greatest extent possible.
  - Must be entirely true.
  - It must be closed under strict implication.
  - It must be as simple in axiomatisation as it can be without sacrificing to much information content.
  - It must have as much information content as it can without sacrificing too much simplicity.
- The ideal system need not consist entirely of regularities, particular facts may gain entry if they contribute enough to collective simplicity and strength.

Causation

Causation involves laws
We need the kind of counterfactuals that avoid backtracking
Causation holds between events.
- If you put butter on the skillet, it melts, what causes this?
  - There is one event that we can call a moving of molecules.
Heat is that phemonemon.
- It occurs in virtue of two facts:
  1. That the skillet’s molecules are moving rapidly.
  2. That the region in question is part of a world where molecular motion is what occupies the heat-role.

The Content of Language and Thought

The principles of charity will impute a bias toward believing that things are green rather than grue, toward having a basic desire for long life rather than for long-life- unless-one-was born-on-Monday-and-in-that-case-life-for- an-even-number-of-weeks. In short, they will impute eligible content, where ineligibility consists in severe unnaturalness of the properties the subject supposedly believes or desires or intends himself to have. They will impute other things as well, but it is the imputed eligibility that matters to us at present.

January 31st, 2013 Seminar

Introduction

Next week, Armstrong

What is a law?

What are fundamental properties?

Both of these question involve “what is at issue” and “is there a fact of the matter?” and “what’s the methodology?”

Presentation on “New Work for a Theory of Universals”

Set Up

Armstrong: Accept an entity “wholly present whereever it is instantiated” that’s a “constituent part … of each particular that has it.” Accept universals! Universals make for objective similarity and unify reality – Similar things literally overlap.
Lewis: Has possibilia and classes of possibilia

Aim to show: Lewis needs to add something to his basic ontology to do some work.
- Strategy:
  1. Explain the difference between universals and properties
  2. Show how universals can do important work that properties cannot.
  3. Once this job is done, you can do a lot of other work.
The work:
1. Similarity
2. Duplication
3. Supervinience
4. Determinism
5. Materialism
6. Determinacy of content
7. Laws
8. Causation
Sidequest 1: Show that Amrstron’s argument for universals (one over many) isn’t good.
Sidequest 2: Show that we still need properties. Universal cannot do all the work.

Universals and Properties

Universals are located wholly where their instances are, are part of their instances.
- Properties are spread out, their instance are “part of” them.
Universals are sparse. There are only enough to account for the similarity facts.
- Properties are abundant, there are tons of them.

Basic Job – Similarity

Upshot of fact 2: Universal can account for similarity. Properties cannot.
Make some properties shin. They are the natural properties and account make for similarity.

Primitive naturalness: Some properties are natural, some aren’t.
Primitive resemblance: The members of this plurality resemble each other more than they do the members of any other plurality. Resemblance is primitive.

Duplication

Problem: Duplicate are analyzed in terms of sharing intrinsic properties. Intrinsic properties are analyzed as those shared by duplicates.
Solution: Duplicates are those things that share perfectly natural properties.; Duplications are those things whose parts bear isomorphisms and share natural properties and relations.

Supervenience

The As supervene on the Bs when similarity among Bs means similarity among As.
- Using our fancy new duplication stuff: If duplicating the Bs means match among As.

Determinism

Problem: “Every event has a cause” ignore probabilistic cause. “Ideal predictor” ignores “obstacle to calculation.”
Solution: Divergent worlds are not duplicates, but have duplicate initial segments. Deterministic laws don’t allow for digergent worlds. Determinstics worlds are worlds with determinstic laws.

Materialism

Problem

Want materialism to be:

Contigent
Involve physics
Allow for panpsychism
Account for the “something extraness” of spooks
Account for the “sufficiency of the physical”

Solution

Alien properties aren’t instantiated at our world, nor constructible from out natural properties. Materialism says that in worlds without alien properties, worlds alike physically are duplicates.

Content

Putnam

If content is fixed by what satisifes (idealidized) theory, it’s indeterminate.

Kripkenstein

No proper subsequence of use determines next element.

Solution

We need more constraints. If constraints are causal, natural properties “get in.”

Lewis

Some properties are inherently eligible to be referents to our words. Objects become eligible by instantiating eligible properties.

Eligibility is proportional to naturalness. Content is determined by maximizing fit with use and eligibility.

Laws

Problem

Why are some regularities laws and others not?

Armstrong

A regularity “All Fs are Gs” is a law iff necessitation holds between F and G

Lewis

This is unintelligible

We must treat regularities not one at a time, but rather as candidates to enter into integrated sysmtes. For a given regularity might hold either as a law or accidentally, depending on whether other regulairties obtain that can fit together with it in a suitable system.

A suitable system has virtues we can aspire to:
1. Truth
2. Closed under strict implication
3. Simple
4. Informative
Need a restriction on language we can use.
- Acount is trivialized otherwise.
- What is the primitive language of the laws? The perfectly natural properties, of course!
The best system yses perfectly natural predicates for its primitive vocabulary, has properties (1) and (2), and has the best tradeoff between (3) and (4).

BSA

BSA: A law is a regularity of the best system. A fundamental law is an axiom.

Causation

Lewis

C is a cause of E iff the closesnt non-bracktacking worlds in which C does not occur that evolve in accordance with the laws are were E does not occur.

Natural properties show up in laws, so they show up in causes too Non-backtracking is understood in terms of divergent worlds. Another place for natural properties.

Only genuine events can cause. Natural properties pick out genuine events.

Natural Properties and Physics

Physics “aspires to give an inventory of natural properties.” Why think this?
- There are three arguments:
  1. M5/Materialism
    
    “In putting forward comprehensive theories, physics proposes investorys of the natural properties instanstiated in our world.” Lewis claims that comprehensiveness of physics should be understood in terms of M5. The link between natural properties and duplication is supposed to support a link between natural properties and physics.
  2. Laws causes
    
    Physicists search for laws of nature and causes. If laws must be sated in the language of natural properties, then physicists search for natural properties and succeed when they find laws.
  3. Similarities and Differences
    
    Physicists seek to tell us about the real similarities and difference between things. “Cutting nature at its joints.” This is the first job of natural properties.

Natural Properties and Induction

Lewis doesn’t say a whole lot to link natural properties and induction. It seems he is poised to answer Goodman’s riddle. He got a way of separating green and guem and that’s the important thing. But we still need a way to explain why natural properties are projectable.
The closest thing we find to a treatment is in the “Content” bit.
- Paraphrase: “We need principles of charity. Such principles call for interpretations accord to which the subject has attitudes we deem reasonable. They impose presumptions about what inductive biases someone may be righly interpreted to have. We need natural propertoes. Principles of charity impute a bias towards believing green rather than grue.”
- Two ways to take this:
  1. Induction first: Natural properties detemine which properties it is reasonable to project directly. Content is fixed by that somehow. (Weatherson)
  2. Content first: Natural properties determine which contents are eligibile. Rationality of induction is fixed by that somehow.
- Perhaps most reasonable: natural properties play a certain role in lawlikeness and counterfactuals. This allows them to figure into two roles Goodman identified for projectable predicates.

Physical Magnitudes and Determinates

We should expect some physical mangitudes (mass, charge) to be perfectly natural. We should be surprised is some determinaites are perfectly natural.
But magnitudes and determinates exclude each other.
- Nothing is 5 and 7kg. Nothing is red and blue. How is this possible? Necessary connections among distinct existents?
Two proposals:
1. Add some necessary connections!
2. Exclusion is nomically necessary, based on nomic necessity of magnitudes and dense linear orders.
  - Exclusion of dense linear orders is logically and metaphysically necessary.

Febuary 1st, 2013 Reading

What is Humean Supervenience?

Human Supervenience
1. Truth supervenes on being
  - All the facts about the world supervene on facts about which individuals instantiate which fundamental properties and relations.
  - This is the core part of Lew’s metaphysics.
  - Lewis thinks the fundamental properties and relations of the world characterize the world without redunancy
  - If earlier than and later than are fundamental, then there is some redunadancy in the characterization of the world in terms of fundamental properties.
    - But it’s hard to see how one is fundamental and the other isn’t.
  - We’ll stick to fundamental properties characterizing the world completely.
2. Anti-haeccaetism
  - All the facts about a world supervene on the distribution of qualitative properties and relation.
  - Rearranging which properties hang on which ‘hooks’ doesn’t change any facts.
  - Consider what it would be like for anti-haeccaetism to fail. There would have to be two worlds, with the same distribution of qualitative properties, but with different facts obtaining in each.
3. Spatio-temporalism
  - The only fundamental relations that are actually instantiated are spatio-temporal, and all fundamental properties are properties of points or point-sized occupants of points.

Supervenience

Strong Modal HS: For any two worlds where the spatio-temporal distribution of fundamental qualities is the same, the contigent facts are the same.

It is consistent with HS that there could be fundamental non-spatio temporal relations.
- HS claims that there are no such relations instantiated.

Local Modal HS: For any two worlds at which no alien properties or relations are instantiated, if the spatio-temporal distribution of fundamental qualities is the same at each world, the contigent facts are also the same.

“Enduring objects” would generate counterexamples.

Familiar Modal HS: For any two “worlds like ours” if the spatio-temporal distribution of fundamental qualities is the same at each world, the contigent facts are also the same.

What is Perfect Naturalness?

We do need to understand what it is to be fundamental and perfectly natural.

…two things are duplicates if and only if

they have exactly the same perfectly natural properties, and

their parts can be put into correspondence in such a way that corresponding parts have exactly the same perfectly natural properties, and stand in the same perfectly natural relations.

(Lewis, 1986a, 61)

Perfectly natural properties

There is a small class of properties and relations such that the facts at any world supervene on the distribution of these properties and relations.
Each of these properties is an intrinsic property.
At the actual world, the only relations among these which are instantiated are spatio-temporal, and all the contigent facts supervene not merely on the distribution of fundamental qualities and relations, but also on the distribution of fundamental qualties and relations over points and point-sized occupants of points.

Humean Supervenience and the other Humean Thesis

There are three views that Lewis endorses that can broadly be described as “human”:

HS

See above.

Nomological Reductionism

Nomological properties and relations (including lawhood, chance, and causation) are not among the fundamental properties and relations.

Modal Combinatorialism

Roughly, anything can co-exist with anything else.

February 3rd, 2013 Armstrong, What is a Law of Nature?

Introduction

The importantance of our topic

The question, “What is a law of nature” is central to philosophy of science.
- But also to epistemology and metaphysics.
- In this section, Amstrong will establish why it’s important both narrowly and broadly.
Natural science has three tasks.
1. Geography and history of the universe.
  - Taking “geography” to cover space and “history” to cover time.
2. Discover what sorts of thing and what sorts of property there are in the universe and how they are constituted.
3. State the laws which the things in space and time obey.
It may not be obvious that there is a second task to be distinguished from the third.
- Heat is molecular motion is not a historical or geographical truth.
  - This is not a law of nature or a “bridge law”
  - It is something different, a constituate of a property or range of properties in terms of more ultimate properties.
These three inquiries are inextricably linked.
- They can only be pursued in conjunction.
If discovery of law is of the traditional tasks of natural science, then the nature of a law of nature must be a central ontological concern for philosophy of science.
The question of “What is a law of nature?” has a wider and philosophical importance.
- The only relation that allows us to move from observed matters of fact to unobserved matters of fact is cause and effect.
  - Without this, we cannot move beyond observation.
If you appeal to Hume, you can say that inferences to particular unobserved phenomena would be unreliable without laws of nature.
But you don’t have to.
- The proposition is obvious enough in itself.
- The scientist trying to establish the geography and history of the ubobserved universe must depends on laws.
- When we make day-to-day inferences, it’s not as important.
  - It’s still irrational to make inferences without laws.
Hume: “Inference from the observed to the unobserved is central to our whole life as humans.”
- Without such laws, inferences would not be reliable.
- Hence, important question for epistemology.
- If so, we want to know about its ontology.
  - We will want to know what a law is.
The view that would evade this arguments would the view that, “althought there are regularities in the world, there are no laws of nature.”
- It “denies that the world contains anything except these regularities.”
Problem with this view: What reason we can to think the world is regular.
- Problem of induction, too.

A possible difficulty in investigating our topic

Paradox of Analysis: If we ask what sore of thing an X is then either we know what an X is or we do not. If we know, then there is no need to ask the question. If we do not, we have no way to begin the investigation.

The solution? We have a fuzzy notion and we’re reflecting on it.
If we can securely get instances of X, you can “tie the inquiry down.”
- If we can be sure that an a is an X, then we can use other things which we know or believe about a to check the proposed account of X.
The Problem: There are no secure paradigms of laws of nature.
- Consider contemporary natural science. It is perfectly epistemically possible that we dont know a single law of nature.
  - This may be the handicap to answering the question, of what is a law of nature.
Even though we can point to no secure paradigm of laws, the scientific theories we now work with contain what at least some real laws of nature.
- If our theories do no nearly grasp the truth, we would be unable to explain why so many predictions are succesful.
- We do theoritical calculations allow us to get safely to and from the moon?
  - Can hardly be mere fantasy.
- We can make an inference to the best explanation from the predicition success of contemporary science to the such theories have tolerable accuracy.
Even some pre-science laws are pretty good.
- Consider these examples:
  - Fire burns
  - Bread nourishes
  - Water suffocates
- If these were not true, then we would all be dead.
This indicates the importance of fighting skepticism about this topic.
- He considers this a reply.
The secone response to the objection is that we know the forms that the laws take.
- Consider these forms that use dummies:
  1. It is a law that Fs are Gs.
  2. It is a law that an F has a certain probability of being a G.
  3. It is a law that the quantities of P and Q co-vary in such a way that Q is certain functino of P (Q = f(P)).
- We can largely proceed with these schemata.
  - Philosophers cannot make any serious contribution to the scientific project of actually determining the laws.
  - To every subject, its appropriate level of abstraction.
If concrete examples are required, there are examples in current and earlier science.
- Newton’s Law is not strictly a law, but an approximation of a wide range of phenomena.
- It makes for a good stand-in for a law of nature.

Assumptions

Assumption: The truth of a Realisitic account of laws of nature.
- That they exist indepedantly of the minds which attempt to grasp them.

Law-statements: May be true or fase. If they are true, what makes them true is a law.

Behind all anti-Realist views of laws stands the RT.
- Regularities are the Realistic component of anti-Realist theories of laws.
  - As a result, a destructive critique of Regularity theory will undermine anti-Realist theories of laws.
Assumption: On Realism about universals.
- Not even the Regularity theory can be developed without universals.
- The Realist about laws who wishes to go beyond Regularity must use universals.
Assumption: Actualism

Actualism

We should not postualte any particulars except actual particulars, not any properties and relations save actual, or categorical, properties and relations.

This debars us not from the past and future, but from using the merely possible, both logical and physical.

The Regularity Theory

There are many who would like regularity theory to be true.
- This influence makes it powerful.
In the course of the criticism, we’ll see what a good theory of laws ought to do.
After disposing of Regularity theory, it will be shown that any satisfactory account of laws must involve universals, and irreducible relations between them.

Critique of the Regularity theory (1) The problem of accidental uniformities

Laws of nature characteristically manifest themselves or issue regularity
Philosophers usually think of a Regularituy theory of causation, but what is considered here is a Regularity theory of laws.

RT of Causation

That causal connection is a species of law-like connection.
That laws are nothing but regularities in the behavior of things.

The naive regularity theory of law

George Molnar’s criticism of Regularity theory of laws
- Outline of a theory called RT of laws of nature, called Naive Regularity theory.
- He then considers an argument against such a theory, an argument from unrealized physical possibilities.
- He then argues that none of the judicious modifications in spirit of the theory are satisfactory.
But the tactic can be generalized to RT in general, not just laws.

p is a statement of a law of nature just in case:

p is universally quantified

p is [omnitemporally and omnispatially] true

p is contigent

p contains only non-local empirical predicates, apart from logical connectives and quantifiers.

Classification of ciriticisms of the RT

If we take “Humean uniformities” and try to identify them with “the laws of nature”, difficulties of identification arise.
- There are Humean uniformities that are not laws.
  - Being a Humean uniformity is not sufficient to be a law of nature.
  - There are laws that do not apply at all times, there are laws which are probabilistic.
  - So it’s also not necessary that a law of nature be a Humean uniformity.
Even if these difficulties can be overcome, there are others.
- It is a law that all Fs are Gs just in case all Fs are Gs where the latter is a Humean regularity
The “intensional” difficulties are in Chapter 4.
Chapter 5 will Chisolm until it is clear it’s not worth it.

Single-case uniformities

The laws of nature are, at best, a sub-class of the class of HUs.
- A recognized research programme is finding a wa to cut out the unwanted HUs will remaining faithful to RT.
- This first case is against Naive RT, which identifies laws and HU.
Probably, every object in the univers differs in its properties from every other object.
- By this, general, non-local properties.
  - “Living in Australia” is not a property.
  - “Being a light-second distant from proton A” is not a general relation property.
  - “Being a light-second distant from a proton” would be satisfactory.
For each particular, therefore, it is likely that there exists at least one individual conjunction of properties, that is, a conjunction of properties.

How to pass from single-case uniformitie ot multi-case uniformities

Given a plurality of single-case HU, we can immediately construct plural-case HU which have no reason to believe are manifestations of laws of nature.
- Consider individuating conjuctions of properties A, B, and C associated with particulars a, b, and c.
  - We can say that whenever an object is of the sort then it further has the property.
The problem of to exclude a disjunctive set of affairs is a close cousing to the problem introduced by Nelson Goodman with the predicates “grue” and “bleen.”
- Suppose all things green turn blue after 2000, and all blue things green.
- Rlative to the predicates “green” and “blue” all things change.
- The problem is to say why one set of predicates should have preference over the other.
A Regularity account of laws to be developed in a Realistic way must be stipulated that only certain non-local predicates can be used to state “uniformities.”
- Admissible predicates must carve reality along some join, natural, unified, objectively resembling class of phenomena.
  - Otherwise these “uniformities” are not uniformities.

February 7th, 2014 Seminar

Review of Lewis’ Fundamental Ontology

What makes a possible world concrete?
What makes a possible world?
- Unclear: Sometimes he writes as though there spacetime points, sometimes he writes as though there are others.
- If he wrote a list:
  - Spacetime structure
  - Spacetime points
  - Fields, particles
- His ontology becomes very sparse.
  - I guess he’s commit to a substanvilism (…)
Natural properties, one way of understanding them is special sets.
- Special in a couple ways:
  1. Exemplifictions in all possible worlds (…)
  2. Supervinience
Everything is made true by something in his ontology.
He didn’t want to rule out alien, that is unconcievable, properties, structures, and individuals.
It’s easy to think that the natural properties have intrinsic natures.
- He’s open to the idea.
Strawson has this idea that we’re acquinted with intrinsic natures.
- What’s the intrisic nature of being a quark?
  - For him, that is Strawson, it’s an experiential argument.

Property: Set of possibilia
Possibilia: Possible worlds.

Natural relations supervene on natural properties
- What does Lewis say about this and extrinsic/intrinsic?
  - There’s a footnote in New Work that covers this, very complicated.
- Two people are trans-world duplicates if they share all relations, including extrinsic. However, any individual is a trans-world duplicate doesn’t require extrinsic properties.
If the world were gruesome, scientists would come up with predicates and terms, reference magnetism would make their laws false.
- As a matter of fact, the world is gruesome, but the predicates used aren’t. If this was the kind of thing that happened, then scientists would formulate laws which would satisfy them, but from the POV of Lewis’ God, it’d be unsatisfactory.
- The question is, about grue, is this epistemically accessible?
  - If physicists could be fooled by this sort of gruesomeness, this would be bad for Lewis.
The thought that the theory of content will make it the case because of the use-features in an ideal theory look like it may not mitigate against … because the theory is ideal.
- Predicates in such a theory have to pick out natural predicates.

No Work for a Theory of Universals by M. Eddon and C. J. G. Meacham

Summary

What role does naturalnes play in Lewis’ BSA?

BSA of Lawhood: Laws of nature are (only the regularities or anything) entailed by the best system, which is the set of true sentences that best balances simplicity and informativeness.
The Problem of the F: Among the candidate systems, there are systems that are maximally simple, manixmally informative, yet obviously not the best, such as the system axiomatized by only one universal generalization whose predicate applies to all and only the things in the actual world.

Two potential ways to solve The Problem of the F:
1. Constaint the language that is used to formualte the candidate system.
2. Constrain the metric that is used to evaluate the candidate system.

How should we modify BSA if we give up naturalness?

If a reductionist gives up perfectly natural properties, what should she replace them wih in order to constrain the language?
- What should the reductionist say about the constraint on metrics.

Language-Objectivity: There is an objective, mind-indepedant language to formulate the candidate system in. Such a language contains predicates that only refer to perfectly natural properties.

Mike: It depends why you’re buying in to Lewis’ metaphysics. It depends if you’re a Humean or not.

Barry: We want it to be the case that the physicists pick out the laws that are true. … The distinction between natural and non-natural to be non-mysterious. There’s one sense in which natural and non-natural if these notions get their content from the theories proposed, then there’s a problem. Lewis places priority on natural properties and then includes it in his BSA, whereas others will use BSA to define the properties that are natural properties depending on the aims of science.

Barry: On one view, we’re chasing “something out there.” On another, what’s natural is not out there. (…)

Barry: Philosophers spend a lot of time convincing people that there’s a problem, and the rest of their time convincing people there’s no problem.

Niko: It’s just a part of the sociology of philosophers that if someone draws a primitive distinction, someone will complain and try to do the same work without it.

Barry: If the story of content guarenteed that the physicists got the laws, that’d be okay. It seems implausible that looking for simple and informative theories of the world would need natural properties …

Instead of starting with the language of natural properties and the various systems formulated in this language, start with both languages and systems together and evaluate them together, the laws will be the best combination of language and systems. What counts as the language? A supervinience base for a lot else – and some other things.

Language-Indexicality: The candidate system is to be formulated in the language of the speaker. The speaker’s assertion that p is a law is true just in case when the candidate systems are formulated in the speaker’s lanaguage, the best system entails p.
Language-Rigidity: The candidate system is to be formulated in our actual language.
Language-Relativity: The candidate system can be formulated in any language. “Best- system-hood” is relative to a given language. Thus, lawhoood is also relative to the language.
Language-Salience: The candidate system is formulated in the langauge of the system (out of systems formualted in any language) best balances simplicity, informativeness, and saleince. Roughly speaking, salience includes criteria of unity, usefulness, and explanatory power.

And some options for the Metrics Question

Metrics-Objectivity: This is an objective, mind-indepedant way to measure the extent to which a system satisfies the criteria of simplicity, informativeness, balance, salience, etc.
Metrics-Indexicality: The candidate system is to be evaluated in the language of the speaker. The speaker’s assertion that p is a law is true just in case when the candidate system are evaluated in the speaker’s metrics, the best system entails p.
Metrics-Rigidity: The candidate system is to be evaluated in our actual metrics.
Metrics-Relativity: The candidate system can be evaluated in any metrics. “Best-system-hood” is relative to a given metrics. Thus, lawhood is also relative to the metrics.

What’s the reference-fixing clause for the meaning of the word “law”?

“Law” is the causal structure of the world, and

Indexicals, are rigid,

The whole point Kaplan’s work is that you need to distinguish the proposition from the sentence, and their thinking that this is an example of

There’s no difference, a few students think, between language-rigidity and the language-indexicality. On the rigidity view, we take our standards and evaluate based on them.

Eddon and Meacham’s Choice Language-Salience and Metrics-Rigidity

E+M argue that the best options are LS and MR. They think that these two are not problem-free, but they stand on firmer grounds than the other options.
- Against the other options, they advance several objections.

Indexicality is too problematic

Imagine Aristotle, whose metrics are different from Newton’s, saying the following:

(2) If I had Newton’s metrics, then the laws would be Newtonian mechanics.

(4) If I had Newton’s metrics and I were to say, “The laws are Newtonian mechanics”, then my assertion would be true.

That is, (2) and (4) are intuitively false, but Metrics-Indexicality predicts that they are true. Note: The intended intuitive readings become obvious when you hold fixed the laws.

Relativity is too problematic

Our concept of lawhood is “deeply related” to modal, causal, and other philosophical concepts. If lawhood becomes relativized to languages or metrics, then the relativity may spread into other philosophical concepts, too.
- Moreover, there will be normative conflicts:
  - How to align our credences
  - Which act to perform
  - Whether someone has a certain duty …
- If we have to solve the above problems by relativising norms, then we might think it’s too high a price to pay for holding a particular concept of lawhood.

Language-Rigidity is too problematic, but Metrics-Rigidity is more plausible

If we rigidify our actual language, then both path and future scientists are likely to get the laws wrong.
- That seems false, because we usualy think that future scientists are in a better position to get the laws right.
If we rigidify an ideal version of our language, then this account will have counterfactual component whose truth value needs to be evaluated using lawhood.
- But our job right now is to analyze lawhood in terms of the language. This make it circular.
Metrics-Ridigity, accounrd to Eddon and Meacham, seems to be on firmer ground.

While it’s plausible that the language of the future scientific community will bear little resemblance to our current language, it’s less plausible that the metrics of the future scientific community will bea little resemblance to our metrics of simplicity, informativeness, balance, etc. (bottom of pg. 17)
But why think that? Why think that the future metrics will be similar to our current metrics? Here are some potential reasons:
- Current metrics in science resemble all past metrics in science (Aristotle and Newton).
- Current metrics in science resemble all past metrics in science since the Enlightenment (Verificationism).
- We cannot conceive of a futre scientific community whose metrics bear little resemblance to current metrics in science. (If we are not supposing Metrics-Objectivity or some particular psychological facts about the members of the scientific community, how do we get this intuition?)
- Current emtrics in science seem to be not for from the objectively right metrics. (But we are not supposing Metrics-Objectivity.)
Another worry: There may not be a consensus on the current metrics in the scientific community. If we rigidify an ideal version of our current metrics, we will run into the circularity problem again.

What about Language-Salience

Language-Salience allows the candidate system to be formulated in any language, but it adds an extra component to the metrics, namely, salience.
- When evaluating the candidate systems, we use the metrics of informativness, balance, and salience to pick out the best system.
  - The best system will come in its own language.
According to Eddon and Meacham, saliance means usefulness, unity, and explantory power.
- Presumably, they depend on certain psychological features of the assessors. This makes laws of nature depend on us.
  - They nothice this worry and reply that it depends on which answer to the Metrics question we pair it with.
Worry 1: Suppose we pair together the Language-Salience and Metrics-Rigidity. We rigidify our current metrics of salience.
- To be consistent, we should not appeal to any objective correctness of our current metrics.
- So it seems that the metrics of salience depends on us.
  - Hence, best systemhood and lawhood also depend on us.
Worry 2: A deeper worry (also acknowledged) is about the notion of salience itself. It seems less clear than the notions of simplicity and informativeness, although we disagree about conceptions of those.
- So how to flesh out salience is an open question on this reduction.
- At any rate, to keep the reductionist project consistent, fleshing out of these notions must avoid invoking naturalness, objectivity, or anything like that.

Extending the Account

Eddon and Meacham proposed an analysis of lawhood without using naturalness. They would like to extend the proposal to other Lewisian analyses to alos avoid invoking perfectly natural properties. Here is their strategy:
1. Take the laws given by the system of true sentences that, given our present metrics, best balances simplicity, informativeness, and salience.
2. Take all and only the properties deonoted by the predicates appearing in these laws. Call them surrogate properties.
3. Wherever a Lewisian analysis invokes perfectly natural properties, subsitute these surrogates.
- Example: Lewisian analysis of duplication.
  - Original: Two things are duplicates iff there is a bijection between their parts that preserves the perfectly natural properties and relations.
  - Modified: Two things are duplicates iff there is a bijection between their parts that preserves the surrogate properties and relations.
Eddon and Meacham try to handle three main worries.

A chaotic world

The argument:
1. If the world is utterly chaotic, then there are no laws.
2. If there are no laws, then there are no surrogate properties.
3. If there are no surrogate properties, then the modification strategy does not work.
4. Therefore, if the world is utterly chaotic, then their strategy does not work.
The response: Their strategy takes the surrogates from the actual world; since the actual world is not so utterly chaotic, it works.
The worry: How do we know the actual world is not chaotic?
Perhaps a better reply: Why thing (1) is true?
- Even if the world is utterly chaotic, there will be many truths about the world, such as the “chaotic dynamics of the Universe.”
- These truths can figure into the system that best balances the relevant criteria of assesment.
  - So there being no laws doesn’t follow from there being much chaos.
- Moreover, many chaotic systems display a great extent of order, which may be law-governed.

Surrogates are not all instrinsic

Here is a locational property: being two meters from an electron.
- Suppose it is in the best system, then some surrogates will be extrinisic. But in Lewis’s system, natural properties are intrinsic. They reply:
  1. It is unlikely to appear in the actual best system. Being two meters from an electron is less salient than being two meters from. (But isn’t it still extrinisic?)
  2. We might be wrong about intrinsicality.

Foreign properties

Surrogates are supposed to play the role of naturalness.
- Possible there are foreign properties not instantiated at the actual world.
  - But surrogates are all from the actual world?
  - So there will be objective dissimilarity that cannot be analyzed by surrogates.

February 14th, 2014 Seminar

Lewis has “spatio-temporal” manifolds, everything is determined by points in this (sometimes) perfectly natural properties.
- “Intrinsic to the regions which they specify.”
For Lewis, the fundamental metaphysics of the world is determined by the decoration of the spatio-temporal manifold.
- The laws are determined by what best specifies the manifold.
  - The best systemization is a language, whose predicates refer to the perfectly natural properties.
- You want to build a universe? Get a space-time manifold, get perfectly natural properties and decorate your manifold.
Problem: It is a possibility that there is a best systemization whose language’s predicates do not refer to perfectly natural properties.
- In fact, if you compare it to the BSA with predicates that have perfectly natural properties, the system without it even looks better.
This seems opposed to Lewis’ project, so:
- Is it really a problem for Lewis?
- Is there something within Lewis’ overall view to deal with it?
- Working out the alternative, you have to say something about what counts as laws.
There two ways of specifying what it takes for a world:
- Fundamental properties and space-time
- Just a world
  - Where it’s the project of science to pick out what the fundamental structures of the world are.
Loewer on Similarity: Our notions about similarity are informed by properties which can be picked out by physics.

Semantics of “Law” and Laws

Daniel: This view is really useful when I’m doing this thing, and this other theory is useful when I’m doing this thing. Lets roll with the relativism.

Response: I do not want to go that way.

There has to be at least really one if we can “pick our favorite.”

Mike: This means laws will give you contradicting advice.

Niko: I thought Daniel’s worry was that the fundamentality is relativied to communities with interests. By picking a “select” community, you’re not helping.

Loewer: The word isn’t realtivised to the community, it’s that the very idea of scientific law is one in which the content is determined by the practice of our scientific community.

What to take away

Two pictures of fundamental properties:
1. Lewis picture: Epistemic worry, best theories which don’t pick out single sets of laws.

Armstrong’s Critique of RT

He beats a horse he thinks he’s killed.
- Props up Naive RT
Armstrong is interested in:
- “It is a law that Fs are Gs.”
- “Fs make it x probable that Gs …”
Assuming you have lawful generalizations, Armstrong thinks that the Humean account fails dreadfully.
His objections:
- HU that are not laws.
- Laws that are not HUs.
“Clearly this isn’t right.”
Armstrong thinks there are vacuous (uninstantiated) laws.
Armstrong also thinks that HU is not necessary for lawhood.
Interested for methodological reasons.
Tooley’s garden.
- Tooley’s intuition is that it is law but not a HU, because it is limited to Smith’s garden.

Presentation by Megan Feeney

Background on Armstrong’s theory of universals

Armstrong appeals to a theory of universals he developers in his 1978 work Universals and Scienctific Realism. Different theories of universals will place different constraints on accounts of natural laws as relations between universals.

Principle of instantiation

Only real particulars have properties and relations, so only real particulars instantiate universals.
- Armstrong accepts actualism but rejects presentism. The real paticulars are actual entities from the past, present, and future. So accord to the principle of instantiation, there are no universals uninstantiated by actual things.
- Principle of instantiation is supposed to be naturalistically motivated.

For Armstrong, what the laws are in a world will depend on what universals are instantiated in that world. We’ll return to this.

Principle of rejection of bare particulars: Particulars (like universals) do not exist independantly of actual states of affairs.

The bare particular and uninstantiated universal are “vicious abstractions” from states-of-affairs and are metaphysically impossible. Particularity and universality, however, are non-vicious
We determine the universals a posteriori “on the basis of total science” (pg. 83). If our final science involved laws with negative or disjunctive predicates, I suspect that Armstrong would say that it had failed to discover universals, (maybe that the science was the best we could do, but not ideal). He wants to be a full-fledged realist about universals.
Many general predicates do not express universal. For example, being a game probably doesn’t express a universal because there is not something identical in all games that makes them games.
On Armstrong’s view, there are no dijusctive or negative universals. But there are conjectuive universals. Conjuctionive universals, but not disjunctive or negative universals, can caputre the role that universals play in causal explanations and the sense in which all the particulars that instatiate a universal (roughly) must have something in common.
For Armstrong, a relation between universals holds always an everywhere within a world. It cannot happen that a universal F bears relation R to G at some time and places, but not others. That’s because a universal is the same (identical) wherever/whenever it is instantiated; it is wholly present in its instantiations (pg. 79). However, universal will be related in different possible worlds.

Natural laws as necessitation relations between universals

Armstrong offers the following account of natural laws:

(1) It is a law of nature that Fs are Gs iff N(F, G).
Fness and Gness are first-order universals.
- N is a second-order necessitation relation that holds between first-order universals.
- It is a relation of contingent rather than logical necessitation.
  - So N(F, G) symbolizes the state-of-affairs of the relation N holding between Fness and Gness.
N(F, G) entails the state of the corresponding Humean uniformity, baring for now any ceteris paribus worries:

(2) $N(F, G) \to (x)(Fx \supset Gx)$
But a stament of a Humean uniformity does not entail that the corresponding necessitation holds:

(3) $\lnot ((x)(Fx \supset Gx) \to N(F, G))$
“$\supset$” is the material conditional. It is an important question what “$\to$” symbolizes
Three worries about the entailment relation between N(F, G) and $(x)(Fx \supset Gx)$ in 2.
1. David Lewis proposes the following dilemma:
  - First horn: On one hand, the entailment might hold because because (2) would be better expressed by some other logical form. in that case, we could replace “$\to$” with the material condition.
    - For example, perhaps 2 should be expression as $(P \land Q) \to P$, where P is a statement of the Humean uniformity.
    - But then what is Q? Or perhaps the trugl logical form is $P \to (O \lor Q)$. But it is unclear how to translate 2 into this form.
  - Second horn: If 2 is not better expressed by some other logical form, it seems that we must say that the entailment obtains in virtue of an additional metaphysical necessity relation, holding between N(F, G) and the Humean uniformity. But this new necessity relation is mysterious! Is it primitive or does it hold in virtue of something else?
2. One might also worry whether Armstrong’s account is substantive. What is the necessitation relation besides that which is required to ensure uniformities, whatever “ensure” means?
3. There are different kinds of uniformities;
  - It might be that all Fs are Gs, that not Fs are Gs, that if one kind of thing is an F, then another kind of thing is a G. How can N(F, G) explain diferent kinds of uniformities if N is a single relation?
In a way, these three worries are closely related. Armstrong hopes to appeal to the laws to explain the uniformities.
- But if the laws are to do this explanatory work, Amrstrong must say something infromative about how the laws “produce” or “ensure” that the unformities hold.
  - Much of the chapter concerns this

Laws as first-irder universals

Armstrong ultimately takes the necessiation relation (N) to be primitive.
Howver, he hopes that its primitiveness will be less mysterious if we think of N(F, G) not only as the state of affairs of necessitation relation holding between two universals, but also a complex, first order universal itself.
- He also hopes that treating N(F, G) as a universal will provide at least a partial solution to the entailment worry.
What kind of think is N(F, G)?
- First, it is a second-order state of affairs. It involves first-order universals (Fness and Gness) falling under a second order
- Armstrong holds that N(F, G) is also a cmoplex, first-order universal.
  - In particular, it is a dyadic relation between first-order relation between first-order states of affairs. It is instantiated by positive instance of the law.
- An examples of a positive instance of the law,
  
  (N(F, G))(a‘s being F, a‘s being G)
How is treating laws as first-order universal supposed to clairfy the relation between laws and uniformities?
- Armstrong wants to assimilate the relation between laws and their positive instantiations. Thus, a Humean uniformity is the collection of all the positive instantiations of the corresponing law, understood as instantiations of a first-order universal.
- Any mystery surrounding the instantiation relatino wouldn’t be a problem facing Armstrong’s thoeyr of laws per se. It would be a more general mystery facing realists about univerals.
Three potential difficulties:
1. How illuminating is this solution? Do we now better understand the relationship between laws and uniformitites? The necessitation relation is still primitive.
  - “This reproach is just, I think, but the inexplicability of necessitation just has to be accepted” because it is explanatorily indispendible (pg. 92).
  - But maybe we can still get an independent grasp on necessitation (next section). At this point, Armstrong still thinks he can say more about the entailment.
2. Is the solution ad hoc? Does treating laws of nature as first-order universals make other substantiated predictions? Is its sole motivation to allay the entailment worry?
  - Armstrong suggests that treating laws as first-order universals explns in what sense laws are abstract.
    - Laws are abastractions because they are relations between universals, which themselves are abstract.
    - Universals are abstract, for Armstrong, because they obey the principle of instantiation, that is, they do not exit indendantly from actual states of affairs.
    - By holding that laws are first-order universals, Armstrong can explain what they are abstraction from: their positive instantiations.
  - The explanation depends on the controversial principle of instantiation, rejected by Platonists.
    - If we deny this principle, then we also deny that the abstractness of laws in Armstrong’s sense is something that needs to be explained.
3. It is logically kosher for N(F, G) to express both a state of affairs, which is well-formed by itself, and a universal, which requires arguments?

Singular causation, singular necessitation, and the “independant fix”

Armstrong holds that purely singular causal connections are logically impossible.
- Suppose it’s a‘s becoming F causes b to become G. Must this be an instance of some F to G law?
- For Armstrong, it is only an instance of an F to G law if a‘s becoming G in virtue of universals F and G.
  - But it is logically possible that a‘s becoming F causes b to become G not in veritue of the universals.
  - It ould just be a matter of this particular event causing that particular event.
Thus, purely singular necessitations are logically possible
- Causation cannot be indentified with necessitation because there are cases of necessitation that are not cases of causation.
  - But purely singular causation would be a case of purely singular necessitation.
- It is logically possible that:
  1. It is not a law that Fs are Gs, and
  2. a‘s becoming F necessitates a‘s becoming G and,
  3. b‘s becoming F necessitates b‘s becoming H, (where being a G is incompatible with being an H, and a is not b).
Armstrong suggests that we now have an indepedant grup on the necessitation relation and the mysterious entailment between laws and uniformities.
- The necessitation relation is N(F, G) is the same as the necessitation relation operative in cases of singular necessitation.
  - Is the notion of singular necessitation more perspicuous than the notion of necessitation between universals?
It is clear then that if such a relation holds between universals, then it is automatic that each particular F determines that it is a G. That is just the instantiation of the universal N(F, G) is particulars cases. (pg. 97)
- What role does singular necessitation play in this explanation? The key idea here seems to be that laws are first-order universals.

Some advantages and disadvantages of Armstrong’s view

Difficulties

We want to admit that there are some uninstantiated natural laws. But if laws are relations between universals, and there are no universals that are uninstanted in the actual world, we might wonder how Amrstrong’s view can accommodate uninstantiated laws.
- Response: Strictly speaking, there are no uninstantiated laws, but we can ask what laws would hold in counterfactual situations.
How will Armstrong’s theory account for Smith’s garden case?
- Response: We will introduce quasi-universals.
  - Being a fruit grown in Smith’s garden. These are repeatable features of the world whose predicates involve esnetial reference to particulars.
  - Armstrong’s view mau be too permissive if necessitation relations between quasi-universals and universals count as natural laws.
    - He may only want to acknowledge those quasi-universals “required for a law,” but which ones are those?

Advantages

We can appeal to the law N(F, G) to explain the existence of corresponding Humean uniformity. The naive regularity theory, by contrast, indentifies the law with the Humean uniformity and so cannot explain twhy the uniformity obtains.
Armstrong may have a way around the paradoxes of confirmation.
- Armstrong suggests that an observation confirms a law that Fs are Gs iff the law explains the observation.
- Both F/Gs and non-F/non-Gs are explains by the law and so confirm the law, although the latter have less confirmatory strength than the former.
  - But non-F/Gs do not confirm the law, because their observation would not be explained by the law.
The laws as relations between universals account can explain why laws support counterfactuals.
- When it is a lw that Fs are Gs, the necessiation relation between Fness and Gness ensures that, were x to be added to the calss of Fs, it would be a G (of necessity)
  - Caveat: The counterfactual is true iff the closest worl where x is F is not some distant world where the actual laws (and in particular the law that Fs are Gs) do not hold.
Armstrong’s theory may be able to explain why inductive inference is rational.
- Inductive inference from confirming instances to the laws is a species of inference to the best explanation.
- Insofar as inference to the best explannation is rational, inductive inference is rational.

February 21st, 2014 Reading

“Humean Supervenience” by Loewer

“Humean Supervenience” by Weatherson

February 21st, 2014 Seminar

If what Armstrong was asking for was a non-circular way of justifying indunction, he doesn’t get one.
- He gets IBE is rational.
Lewis’ account of laws, if we assume that the universe is lawful, we get a vindication of induction.
- We can demonstrate that we will zero-in on the best system, if our world is friendly to science.
Assumption: Let’s suppose we know the language of natural properties, and the best system in that language are pretty good.
- Someone might think that there are finitely many properties that are bound by some value (why?).
- The rabbit going into the hat.
As we do more and more experimentation, our credence step will get closer and closer to the true best system.
- We assign credence to better systems moreson, higher, high degree of credence to a family to a disjuction of BSA which includes the best system of our world.
- If the world is physics friendly, then we can elimnate all but one family.
  - In the opposite case, it’s called indetermination.
- How big the dijsuction will be will be based on how physics friendly will be.

February 28th, 2014 Reading

“The Metaphysics within Physics” by Maudlin

Chapter 1

Laws, Possibilities, Counterfactuals, and Explanations

Beliefs about laws of nature influence others.
- Three which we’re interested in:
  1. Beliefs about possibilities
  2. Beliefs about counterfactuals
  3. Beliefs about explanations
If you accept Eistein’s theory of relativity, you also accept that a Universe could be “open” or “closed”
- To be open is to continue expanding forever.
- To be closed is to collapse in a Big Crunch.

Chapter 2

Chapter 3

“Quantum Entaglement, Bohmian Mechanics, and Humean Supervienience” by Miller

February 28th, 2014 Seminar

Discussion

Armstrong thinks that regularity accounts has terrible problems with induction.
- Loewer thinks otherwise.
Imagine a world call a “Humean-world” where there only l-laws, and these bring about l-causation and l-counterfactuals.
Simple form from John Airman
- Think about a world where there’s only one particle, and it’s moving uniformly.
- This is a world where the Newtonian mechanics obtain.
- But the BSA under simplicity will just describe the one particle.
Our concept of law is funny because it has the idea of governing and because of Lewis’s best system account.
- The governing part seperates the fact from the law.
- As long it’s logically compatible, but they might not be compatible … on Lewis’ account.
- This is the beginning of the main worry behind Lewis’s account of chance.
If you remove a particle from a universe, then the laws should stay the same.
- Maybe it’s vague.
- Maybe it’s not true.
- Maybe there must be at least one.
There are intuitions that we have that are anti-Humean, and some of this arises from theological explanations of laws.
We have some grip of whats going on in the theological
Here are two views of fundamental ontology
1. There is the Humean mosaic, space-time structure manifold, and it’s decorated with fundamental properties and maybe it satisfies HS. And that’s it. Things supervene on this (???).
2. Fundamental state of the world and fundamental laws, which are entities over and above the categorical facts, as they take the state of universe at any given time, and determine the next state.
Changing the facts doesn’t always change the laws, but changing the laws will always change the facts.
Could the best system of the whole history of the universe that the laws enfored in this spatio-temporal region and then there are these laws in another spatio- temporal region, it’s a bit awkward.
- I don’t see in pricniple problem to this, however.

Weatherson

March 7th, 2014 Reading

“A Subjectivist’s Guide” by Lewis

“Humean Supervenience Debugged” by Lewis

March 7th, 2014 Seminar

Introduction

It’d be nice for metaphysics to hand over its problems to physics.
- Usually if you’re a clever metaphysicist you can find any argument in physics which rebuts your metaphysics.
- Different views of temporal passage run afoul of relativity theory.
One of the fun things metaphyscicians can do is spell out the various metaphysical commitments of various physical theories.
- A great example is quantum theories, which “wear their ontology on their sleeve.”
Lewis has a fairly spare ontology.
- Subsintivalism about spacetime.
- Metric structure
- Decorated by:
  - Natural properties
  - Instantiated points
  - No natural relations
Maudlin has a different ontology
- He also has spacetime.
- He thinks there’s an “intrinsic direction to time.”
  - This makes it different from space.
  - He sometimes says that “time passes” or “time flows.”
  There are a bunch of features of our world which support talking about time like this. You can change now what lunch you’ll have today but you can’t change now what you had for lunch earlier. You know more about your lunch earlier than you do about your lunch later.
- Fundamental FLOTE
- Objective probabilities
This is a sparse ontology because we have things like “late trains.”
What seems to be missing are those things like “qualia.”
Both are physicalists, both take lessons from physics, but different ones.
Maudlin thinks that fundamental laws are bedrock ontology, Lewis doesn’t.
- I think these are possibilia for Lewis.
For Maudlin, laws ar ein the fundamental stuff of the universe and make for the regualirity.
- Tim thinks that the practice of physics supposrts his pucture.
- And of course, we do have this idea of “temporal direction.”
The puzzle for Maudline, right at the surface, is what are the laws and what work do they do?
- This makes Loewer stubborn about accepting his view.

Comments on “Quantum Entaglment, Bohmian Mechanics, and HS” by Eddy Chen

The Probem of Quantum Entaglement

In standard non-relativistic quantum mechanics, we represent a physical system as a normalized vector in the Hilbert Space
- A unit vector in a complex-valued vector space with an inner product which satisfies a set of axioms.
- States of individual particles A and B can be represented as $\ket{\phi}_A$ and $\ket{\psi}_B$.
  - The state of a pair of particles A and B can be representated as $\ket{\Psi}_{AB}$.

Spin is a property of an electron and how it moves in a magentic field, it’s an interesting feature if a particle that they’ll be a certain probability of how it’ll move.

Two particles are not entagled when their joint state is seperable as the tensore production of their individual states:
$$\ket{\Psi}_{AB} = \ket{\psi}_A \oplus \ket{\phi}_B$$

What’s strange and novel here is that the state gives all the information about the features we’re interested. There’s an indetermincy.

Two are entangled when their joint state is not seperable as the tensor product of their individual states:
$$\ket{\Psi}_{AB} \not = \ket{\psi}_A \oplus \ket{\phi}_B$$
Suppose that $\ket{\Psi}_{AB}$ is the intrinsic property of the pair A and B, and $\ket{\phi}_A$ and $\ket{\psi}_B$ are the intrinsic properties of particles A and B, then we seem to have a case of the failure of HS.
- It remains to explore precisely which component of HS fails in this case of quantum entaglement.
  - A worry, of course, is whether we should interpret the states represented in Hilbert Space as instrinsic properties to the systems.
  - More on this later, from the perspectives of Bohmian Mechanics and C-Algebra.

There’s a “new way in which things” exist, things can exist in superposition.

There’s a big way of teaching QM in terms of description. But in terms of the way things are, you have to understand the mathematics, which is the mathematics of vectors. These properties can be in a deterministic state or it can be in a superposition of the two vectors.

Which Component of Humean Supervenience is the Target?

Separability: The complete physical state of the world is determined by (supervenes on) the intrinsic physical state of each space-time point (or each pointlike object) and the spatio-temporal relation between those points.

The challenge to Separability comes from observations of entaglement phenomena such as the case above.
- Moreover, Maudlin and many other philosophers of physics think that realism about quantum mechanics commit us to the following thesis:

Metaphysical Holism: There exist some whole whose intrinsic properties fails to supervene on the intrinsic properties of its fundamental (point-sized) constiuent parts plus their spatiotemporal relations.

Notice, the first thesis mentions the copmlete physical state of the world, while second only mentions the existence of some quantum whole, possibly distinct from the entire world.
- The implicit reasoning to their incompatibility, perhaps, is that any system (such as the entire world) containing such a quantum whole would fail to supervene on the instrinsic properties of some of its fundamental parts.
Miller’s goal, I take it, is to show that a commited Humean can embrace Metaphysical Holism and retain Separability, by adoptiing the de Broglie-Bohm interpretation of quantum mechanics.
- Her task, if it succeeds, can show the logical consistency and empiral adequacy of embracing both theses.

A Brief Tour through Bohmian Mechanics

The de-Broglie-Bogm interpretation of quantum mechanics, sometimes called Bohmian mechanics, is an empirally adequate and mathematically elegant interpretation of the quantum formlism. Importantly
1. Its dynamics is entiraly deterministic.
  - As for the dynamics, it adds a (explicitly non-local) guiding equation to the Shrodinger equation.
  - The Shrodinger equation determines the evolution of the wave function, while the guiding equation “looks at the wave function and the configurations of all other particles” and “completes” the dynamic determinations by specifying the velocties of the particles.
2. Given the Quantum Equilibrium Hypothesis, it predicts that there is an appearance of randomness in the world.
3. It predicts a probabilitic distribution conforming to the Born Rule.
4. It predicts the impossibility (“absolute uncertainty”) about gaining informaiton more than the probilistic distributino of Born Rule, agreeing with the Kocken-Specker theorem.
5. It permits both a N-particle-in-3D-space ontology and a 1-particle-3N-space ontology.
In a typical Stern-Gerlach measurement of particle A having spin-up state, a Bohmian would say that it is for A and other particles within the system and within the universe as a whole ot be moving in such away as to be certain to produce “up” indication among the particles of the Stern-Gerlach device.
- That is $\ket{\uparrow}_{A,t}$ just means (for a Bohmian) that, given the initial condition of the universe, particle A is traveling through spacetime at time t and is accompandied by other particles on the measure device registering the “up” outcome.
- The attribution of the spin-up state to particle A is not about the intrinsic state of A but its present and future motions as well as other particle’s present and future motions. To summarize the Bohmian idea:

Bohmian Realism: The state of a system represents a relational property, not an intrinsic property of the system.

Based on this principle, one can make an immediate reply to the argument for non-separability: quantum entaglement is not about intrinsic properties, and it no indication of a failure of whole-to-part superveinience of intrinsic properties, thus it is in no violation of Separability.
- But that’s too quick. There is still the pilot wave that fails to supervene on particles.

How to be a Humean about the Pilot Wave?

Be a 3N-Space Bohmian

Consider our N-Particle system in 3D space.
- It can be represented by a 1-Particle system in 3N space, where N is the number of particles in 3D space.
- 3N space is the space of all possible configuartions of N-Particle in 3D space.

3N-Space Bohmianism: 3N space is the fundamental space; 3D space is not fundmental, if not “illusory.”
3N-Space Bohmianism + Humeanism: Fundamentally there are no pilot waves. The universal wave function is fundamental. It is a field in the 3N space (the fundamental physical space), and it supervenes on the amplitutde and phase at each point in the 3N space.

Disadvantage: The loss of primitive ontology and 3D space. The confusion of the represnetation and the things represented.

Be a 3D-Space Bohmian; Go Nomic about the Wave Function

The world is fundamentally 3-dimensional. The universal wave function and its guiding equation express a fundamental law of physics.

3D-Space Bohmianism: Fundamentally, the world is 3D and there are many particles.
Nomic 3D Bohmianism: The unviersal wave function is a law of nature rather than a physical object.

But in addition to Separability, HS also has the following component:

Physical Statism: All facts about the world, including modal and nomological facts, are determined by its total physical state.

This seems to be violated by Nomic 3D Bohmianism, if the wave function does not supervene on the mosaic. A Humean reply:

BSA applied to the Wave Function: The univesal wave function is contained in the best summary of the Humean mosaic that balances simplicity, strength, and other criteria. Statements about the wave function are fundmentally statements about the entire four-dimensional Humean i mosaic.

Worries and Questions

Is the vafe function simple? The effective wave function of the subsystem, being gerrymandered and complicated, is not simple. But there is hope that the universal wave function is simple.
Is the wave function law-like? The effective wave function of the subsystem, being time-dependant and controllable, is not law-lie. But there is hope that the universal wave functionis stationary and uncrotrollable. The hope comes from observations of the form of the Wheeler-Dewitt equation (3) togetget with the Schrodinger equation (4):
$$H \ket{\Psi} = 0$$ $$i h \frac{d}{dt} \ket{\Psi} = H \ket{Psi}$$

But isn’t that too much to hope sine (3) is only a guess about how to quantize gravity? Also, there can be multiple soltion to (3), but we believe there is a unique universal wave function.
A general worry about Bohmian Mechanics: the challenge from relativity and Lorentz-invariance.
Another general worry: the challenge from superficiality features in physics to BSA.
A more general worry: being a realist about QM doesn’t automatically comit one to be a realist about the wave function. In elementary QM, there is a state space representated by the Hilbert space; there are also properties of the states sometimes represented by the Operators on the Hilbert space. In algebraic QFT, however, there is no unique way to represented the state space, several alternative representations are available and each representation has to “mentaion” the other alternatives, What is being represented, in this case, seems to be common core – the properties of the states, represeted by the C-Algebra. This seems to question the motivated of state-space realism, heance wave-function realism, hence the entaglement problem for HS as well as the reply to solve the problem.

March 14th, 2013 “Humean Supervenience Debugged” Outline

Introduction

Humean supervience: The thesis that the whole truth about a world like ours supervenes on the spatiotemporal distribution of local qualities.

There is one big bad bug: chance. It is here, and here alone, that I fear defeat.

But Lewis thinks he can now beat the bug. Here’s the roadmap:
1. Reviewing old ground, reintroduce Humean supervenience.
2. What might a Humean analysis of chance look like?
3. Why is chance a problem for Humean analyses?
4. Why are unHumean answers are not acceptable refuge?
5. The beginning of a solution that plagues the Humean analyses. Why is it not good enough?
6. The good news: How to complete the solution.

The resulting rescue of Humean chance won’t give us all we might wish, but I think it gives us enough.

Humean Supervenience

We may be certain a priori that any contigent truth whatever is made true, somehow, by the pattern of instantiation of fundamental properties and relations by particular things.
- That is, that truth is supervienient on being.
- If two possible worlds are discernible in any way, it must be because they differ in what things are in them or how those things are.
  - “How things are” is fully given by the fundamental, perfectly natural properties and relations that those things instantiate.
As an anti-haecceitist, Lewis would drop the “what things there are” clause, instead, all contigent truth supervenes just on the pattern of coinstatiation.
- Some will wish to add other fundamental properties or relations, like:
  - Armstrong’s immanent universals.
  - William’s families of exactly representing tropes.
- We may reasonably hope that physics will give the inventory of the perfectly natural properties and relations of this world.
Humean supervinience is another speculative addition to the thesis that truth supervenes on being.
- It says that the fundamental relations are exactly the spatiotemporal ones.
- It says that in worlds like ours, the fundamental properties are local qualities
  - Perfectly natural intrinsic properties of points.
  - Or of point-sized occupants of points.
- All else supervenes on the spatiotemporal arrangement of local qualities throughout all of history, past, present, and future.
Humean supervenience is inspired by classical physics, but physics isn’t classical anymore.
- The point of defending Humean supervenience is not to support reactionary physics, but resist the philosophical arguments that there are more things in heaven and earth than physics has dreamt of.
- Lewis is defending the philosophical tenability of Humean Supervenience.
But even classical physics raises a question for Humean Supervenience.

Is a vector field an arrangement of local qualities?
- Lewis said that qualities were intrinsic, that means they can never differ between duplicates; and two things can be duplicates even if they point in different directions.
Humean supervenience is meant to be contigent.
- It says that among worlds like ours no two differ without difference in the arrangement in qualities.
- But when is a world like ours?
  - Lewis used to say: “When it’s a world of the ‘inner-sphere’, free of fundamental properties or relations that are alien to our world.”
  - But this probably wont do.
- On the Armstrong spinning sphere or the Kripke spinning disk:
  - One lesson: One way to get a difference between worlds with the exact same arrangment of local qualities is to have things bilocated in spacetime.
  - Take two worlds containing spheres of homogenous matter, the only difference being that one is spinning.
  - The arrangement of local qualities is just the same.
    
    The difference between the spinning and the stationary sphere is a difference in the pattern of bilocation.
  - No worries fo Humean Supervenience, because Lewis believes our worlds to be a “temporal-parts-world”, and therefore neither of the worlds in the story is like ours.

Symmetry and frequency

Chance and credence

Chance: Objective single-case probability. For example, 50% is the probability that a certain particular tritium atom will decay sometime in the next 12.26 years.
Credence: Degree of belief, and notably not the same as chance.

But chance is connected to credence: if a rational believe knew that a chance of an event was 50%, then almost no matter what else he might or might not know as well, he would believe to the degree 50% that the event would occur.
If Humean Supervenience is true, then contigent truths about chance are in the same boat as all other contigent truths.
- They must be made true by the spatiotemporal arrangement of local qualities.
- How might this be?
  - The Principal Principle requires that the chancemaking pattern in the arrangement of local qualities must be something that would, if known, correspondingly constrain rational credence.
  - That is, that whatever makes it true that the chance is 50% must also be whatever makes it rational to believe to degree 50% that the event will occur.

Chance-makers and the indifference principle

Two candidates for chance-makers: symmetries and frequencies.
- On symmetries:
  
  Suppose a drunkard is wandering through a maze of T-junctions, and at each junction we can find nothing that looks like a relevant difference between the case that he turns left an the case that he truns right. We could well understand if rational credence had to treat the cases alike, for the lack of relevant difference. If the symmetry is something that would, if known, constrain credence, then it is suitable to serve as a chancemaker.
  - The principle of indifference.
An unrestricted principle of indifference is inconsistent.
- With alternative cases of ingeniously hoked-up properties, you can get it to say anything you like.
- But assume that you can somehow distinguish between that nonsense and then limit the principle only to natural properties. You get only natural partitions.

Symmetries as chance-makers

Some reservations about symmetries as chance-makers.
1. There is no reason to think that we have symmetries to underlie the chance phenomena that we there there are.
  
  It would be nice to think that each tritium atom contains a tiny drunkard in a maze of symmetrical T-junctions.
2. Symmetries are only defeasible constrainers of rational credence. Therefore, they can only be defeasible chance-makers.
  
  The symmetry of the T-junctions would no longer require 50-50 division of credence if we also knew that, despite this symmetry, the drunkard turns right nine times out of ten.

Frequencies as chance-makers

Now it looks as though frequencies are the real chance-makers.

Frequency

A pattern in the spatiotemporal arrangement of qualities.
- We can well understand how known frequencies could constrain rational credence.
Again, this will be worse than useless if we can’t distinguish natural from gerrymandered kinds, and again, we could get any answer we liked.
- But we can do it! And nature has been kind to us.
  
  Large chance systems seem to be put together out of many copies of very small chance systems; and very small chance system often do come in enormous classes of exact copies. You see on tritium atom, you’ve seen them all.

Problems for frequentism

Lewis thinks this simple frequency analysis is near enough right, but has limits.
- It is only plausible when we do have the enormous classes of exact copies.
- It has difficulty analyzing unobtainium.
  - Consider $\mathrm{unobtainium}^{346}$.
  - It’s hard to make the stuff, in all of space and time there have been only two.
  - One had a lifetime of 4.8 microsecond, and the other a life of 6.1 microsecond.
Further, consider $\mathrm{ubobtainium}^{349}$. The isotope is even harder to make, and there isn’t a single instance of it through space and time.
- Its frequency of decay in a given time is undefind, 0/0.
- If there’s any truth about its chance of decay, this undefined frequency cannot be the truthmaker.
The problem of unobtainium may make us think that it’s not about frequencies in the actual world, but rather counterfactual situations where unobtainium is abundant.
Another problem for simple frequentism:

If spacetime is finite and chance system get only just so small, then all frequencies are rational numbers. Yet the great majority of real numbers are irrational, and we have no pre-philosophical reason to doubt that chances in a finite world can take irrational values.
The answer to the problem of unobtainium is remembering that single-case chances follow from general probabilistic laws of nature.
- There are general laws of radioactive decay that apply to all atoms.
- Unobtainium atoms have their chances of decay not in virtue of decay frequencies for unobtainium, but rather in virtue of these general laws.

Onwards to laws

The appeal to laws only postpones the problem of chance.
- What pattern in the arrangement of qualities makes the chances?
- So we must now turn to a Humean analysis of laws, and make them probabilistic.

The best-system analysis of law

Improving Ramsey’s Best Systems Account

[Laws are] consequences of those propositions which we should take as axioms if we knew everything and organized it as simply as possible in a deductive system. — Ramsey

Lewis expands the definition like so:
- Take all deductive systems whose theorems are true.
- Some are simpler, better systemiztized than others.
- Some are stronger, more informative than others.
- These virtues compete: An uninformative system can be very simple and an unsystemiztized compendium of miscellaneous infromation can be information.
  - The best sytem is the one that strikes as good a balance as truth will allow between simplicity and strength.
  - How good this is will depend how kind nature has been.

A regularity is a law if and only if it is a theorem of the best system.

Some complaints

Lewis thinks thats Armstrong and van Fraassen are question begging.
- If you think that theorems of the best system are laws, then you should also think:
  - Underlie causal explanations;
  - Support counterfactuals
  - Are not mere coincidences;
  - That they and their consequences are necessary;
  - That they are confirmed by their instances.
- Others are more worrying. For instance, like any regularity theory, the best-system analysis says that “laws hold in virtue of patterns spread over all space and time.”
  - If laws underlie causations, then we are wrong to think that causal roles of brain states are an entirely local matter.
  - Unpleasant surprise, but Lewis bites the bullet.

The worst problem: standards

Where do the standards of simplicity and strength come from?
- It seems to be from us. But that can’t be right!
- If we don’t like the laws of nature, we can chance the laws, and make them always have been different, just by changing the way we think!
  - “Positive thinking.”
- Lewis uses to think that rigidification solved the problem.
  - That you don’t use hypothetical new stands, but rather the actual and present standards.
  - This is cosmetic only, Lewis now thinks. It only makes the problem harder to state.
The answer: If nature is kind to us, the problem needn’t arise.
- Simplicity and strength are partly a matter of psychology.
- It’s not because of how we think that:
  - A linear function is simpler than a quartic or step function
  - A short alternation of prenex quantifiers is simpler than a longer one.
- If nature is kind, then the best system will be robustly best.
  - If nature were unkind and disagreeing rival system were running neck-and-neck, then lawhood might be psychological.
- This trouble is with unkind nature, not on Lewis’ analysis.
  - Cross the bridge when we get there.

Onwards to probabilistic laws

So far we don’t have probabilistic laws.
- If we had chances, then we could put them into the axioms of the best system and go about our day.
  - But we don’t.

We decided that the chance-making patterns in the arrangement of qualities had to include the lawmaking patterns for the probabilistic laws that determine the chances in all the different cases.

The best-system analysis of law and change together

The solution: fit

Modify the best-system analysis to make it deliver the chances and the laws in one “package deal.”
- Take all deductive systems that pertain not only history, but also to what the various outcomes are in various situations (like the decay probabilities).
- Require these system to be true about history.
- You cannot require anything about chances, because we don’t know what that is.
Some of these system will fit the actual course of history better than others.
- The chance of that course of history will be higher according to some systems than according to others.
The virtues of simplicity, strength, and fit trade off.
- The best system is the system that get the best balance of all three.
- But now some of the laws are probabilistic!
  - We can now analyze chance: “The chances are what the probabilistic laws of the best system say they are.”
Like before, Lewis hopes that the best system is far ahead of the rest in terms of how robust it is so that the laws aren’t dependent on us.
- The prospect is best if the the chance events aren’t too few or too trivial.

Homogeneity

In the simplest case, the best-system reduces to frequentism.
- Suppose all chance events fall into one large and homogeneous class:
  - to fall silent about the chances of these events would cost too much to strength.
  - to assign equal single-case chances that differed from the actual probability would cost too much to fit.
- We get the best fit by equating chances to the frequency
  - The larger the class is, the more so.
Suppose the class isn’t very large, and that the frequency is close to a simple value, say 50-50.
- Then the system assigns uniform chances of 50% exactly gain simplicity and doesn’t lose too much fit.
Suppose the class is not homogenous.
- Then, “a system that assigns unequal chances in different subclasses will gain greatly in fit at not too much cost in simplicity.”
This is how we get the decay chances for $\mathrm{Un}^{346}$ and even for $\mathrm{Un}^{349}$, in virtue of chancemaking patterns that don’t involve decay frequencies for unobtainium itself.
But this is not epistemology!
- This is how nature determines what’s true about the laws and chances.
And this version of BSA, we can fix the big bad bug!

Undermining

What is chance undermining?

Suppose we have a Humean analysis which says that present chances supervene upon the whole of history, future, past, and present (but not upon the past and present alone).
- Then different alternative future histories would determine different present chances.
- Further suppose that the differences between these alternative futures are differences in the outcomes of present of future chance events.
  - Then each of these futures will have some non-zero present chance of coming about.
Let $F$ be some particular alternative future, and one that determine different present chances than the actual future does.
- $F$ will not come about, since it differs from the actual future.
- But! There is some present chance of $F$.
  - That is, there is some present chance that event would go in such a way as to complete a chancemaking pattern that would make the present chances different from what they actually are.
- Present chances undermine themselves.

An example of undermining

For instance, there is a minute present chance that for more tritium atoms will exist in the future than have existed, and each one will decay in only a few minutes.
- If this unlikely future came to pass, it would complete a chancemaking pattern on which the half-life would be much less than the actual 12.26 years.
  - This is so under both frequentism and best-system account of laws.
- Could this come to pass?
  - Yes, in the sense there’s a non-zero present chance of it.
  - No, in the sense that its coming to pass contradicts the truth about present chances.
- If it came to pass, then the truth about present chances would be different.
- It’s not that the present changes, but rather it would never have been different.
This is “no worse than peculiar.”

A closer look at the Principal Principle

The Principal Principle does rule out undermining!
- It was this that led Lewis to despair about the Humean analysis of laws.
Here’s the contradiction the Principal Principle leads to. Take some particular time and:
- Let $C$ be the rational credence function for someone whose evidence is limited to the past and ppresent.
- Let $P$ be the function that gives the present chances of all propositions.
- Let $A$ be any proposition.
- Let $E$ be any proposition that satisfies two condition:
  1. It specifies the present chance of $A$, in accordance with $P$.
  2. It gives no “inadmissible” information about future history, that is, no information about how chance events in the present and future turn out.
- The Principal Principle is therefore:
  $$C(A|E) = P(A)$$
- Now take $A$ to be $F$, our alternative future history that would yield present chances different from the actual ones.
- And let $E$ be the whole truth about the present chances as they actually are.
- Recal that $F$ had some present chance of coming about.
- So, by the Principal Principle:
  $$C(F|E) \not = 0$$ $$C(F|E) = 0$$

No refuge

It is because some of the pattern lies in the future that there is a possibility that the future could undermine present chances.
- Of course, it’d go away if we assume the pattern lay entirely in the past.
But we can’t assume this, and here’s why:

The Problem of the Early Moment

There might be a beginning of time, or a beginning of a certain kinds of chancy phenomena go on.
- What could make the chances at a moment not long after the beginning?

The Problem of Fluctuation

We usually think that there are laws, and hence regularities, of uniform chances.
- “All tritium atoms have precisely the same chance of decaying in a given period.”
- It is not to be expected that the different chancemaking patterns in these different segments will all make the same chance of decay.

The Problem of Drift

Take the two problems together, and you have the problem of drift.
- For simple frequentism:
  - Suppose early on, $J$s divide 50-50 between $K$s and not-$K$s, but so far there haven’t been many $J$s together.
  - Then we should expect that there might be a chance to be a run of $K$s or not-$K$s, that would significantly raise or lower the chance of the next $J$ to be a $K$.
  - Then the chance of being a $K$ would drift to one or zero, and remain there for a long time after.

unHumean

With all these problems, Lewis thinks his opponents will think he’s done all the work for them.
- So he should just admit defeat.
But there is no refuge here for the non-Humean.
- Posit all the unHumean whatnots you like, so long as truths supervene on being.
- But don’t call any allege features of reality “chance” unless you’ve already shown that you have something, knowledge of which would constrain rational credence.
  - How could knowledge that two universal stand in a certain special relation $N*$ could constrain rational credence about the future co-instantiation of those universals?
Unless you first convince Lewis that it’s a special chancemaking relation, where $J$ has a 50% chance of being $K$.
- But you can’t just say that, you have to show that.

The beginning of a solution

Our problem is, where $F$ is an un-actualized future that would undermine the actual present chances given by $E$, is that $C(F | E) = 0$ because $F$ and $E$ are inconsistent, but $C(F|E) \not = 0$ by the Principal Principle because $E$ specifies that $F$ has non-zero chance of coming about.
- If that use of the Principal Principle is fallacious, the contradiction goes away.
That use of the Principal Principle is fallacious, if the present chances are made by a pattern that extends into the future
- Then $E$ bears inadmissible information about future history.
- It excludes the future $F$.
- Since $E$ is inadmissible, the Principal Principle does not apply.
- The fatal move that led from Humeanism to contradiction is no better than such obvious blunders:
  $$C(\mathrm{coin : falls : heads} | \mathrm{it : is : fair : and : will fall : heads : 99/100}) = \frac{1}{2}$$
  
  or even
  
  $$C(\mathrm{the : coin : will : fall : heads} | \mathrm{it : is : fair : and : will : fall : heads}) = \frac{1}{2}$$
Victory!
- What we have just seen is that if chancemaking patterns extend into the future, then any use of the Principal Principle is fallacious.
- For any proposition that bears information about present chances thereby bears information about future history.
According to the best-system analysis, information about present chances is inadmissible because it reveals future history.
- But this information is not inadmissible, as witness the way it figures figures in everyday reasoning about chance and reasoning.
  - Contradiction.

The solution completed

Admissibility admits of degree

A proposition $E$ may be imperfectly admissible because it reveals something or or other about future history; and yet it may be very nearly admissible, because it reveals so little as to make a negligible impact on rational credence.
Degrees of admissibility are a relative matter.

The imperfectly admissible $E$ may carry lots of inadmissible information that is relevant to whether $B$, but very little that is relevant to whether $A$.
Near-admissibility may be good enough.

If $E$ specifies that the present chance of $A$ is $P(A)$, and if $E$ is nearly admissible relative to $A$, then conclusion that $C(A | E) = P(A)$ will hold, if not exactly, at least to a very good approximation.

Correcting the Principal Principle

We face a question. If the old Principal Principle applies only as an approximation, what is it an approximation to? How, exactly, is chance related to credence? Can we find a new, corrected Princpal Principle that works exactly when the old one works only approximately?

Here’s a correction applicable only to a special case of the old Principal Principle.
- Let $H_{tw}$ be the proposition giving the complete history of world $w$ up to and including time $t$.
- Let $T_w$ be the complete theory of chance for world $w$.
  - A proposition giving all the probabilistic laws and therefore all the true history-to-chance conditional that hold at $w$.
- Let $P_{tw}$ be the chance distribution at time $t$ and world $w$.
- If $T_w$ were admissible, then the conjunction $H_{tw}T_w$ would also be admissible.
  - It would specify the chance at $t$ at $w$ of any proposition $A$.
- So we could put it for $E$ in the old Principal Principle.
- Dropping the subscripts, we have:
  
  (OP) $C(A|HT) = P(A)$
  - “The credence you should assign to $A$ given the complete history of the world and the complete theory of chance is equal to the probability of $A$”
- The correction Lewis favor is:
  
  (NP) $C(A | HT) = P(A | T)$
  - “The credence you should assign to $A$ given the complete history and complete theory of chance at a world is equal to the probability of $A$ given the complete theory of chance of the world.”
- If $T$ were perfectly admissible, then (OP) would be correct derived as an instance of the old Principal Principle.
If there are undermining futures with non-zero present chance that make $T$ false, then $T$ rules out these undermining futures.
- If so, then:
  1. $T$ and $HT$ are not perfectly admissible.
  2. (OP) is not correctly derived.
  3. (OP) cannot be applied to determine $C(A|HT)$
  4. $P(T) \not = 1$
  5. Exception cases aside, $P(A) \not = P(A|T)$.
- If so, then accept (NP).
Conditionalize on $T$ to avoid undermining futures.

Against perfectionism

The new version of the Principal Principle is better by Humean lights, but the old one is more intuitive.
- So the old Principle is “key to our concept of chance.”

Chance can be defined as that feature of Reality that obeys the old Principle, yet chance doesn’t quite obey it! Isn’t this incoherent?

No.
- A feature of Reality deserves the name “chance” to the extent it occupies the role of chance.
- Occupying the role means obeying the old Principle.
- But undermining means that nothing occupies the role perfectly, so nothing perfectly deserves the name.
- But near enough is good enough.
- And if nature is kind, the chances ascribed by the probabilistic laws of the best system will obey the old Principle to a very good approximation.
  - Therefore, they will occupy the chance role enough to deserve the name.
  - To deny this would by silly.
Some equivalent silliness:
- Nothing deserves the name “sensation” unless it were infallibly introspection.
- Nothing deserves the name “simultaneity” unless it were a frame-independent equivalence relation.=
- Nothing deserves the name “value” unless it couldn’t possible fail to attract anyone who is well acquainted with it.

An event will have many future records, or recordings of it, but few prior or predictors or the event. JFK is assassinated — there are loots of recordings of it, but there very very few predictors, an awful lot had to go right!

mentaculus