Issues in Contemporary Metaphysics

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Issues in Contemporary Metaphysics

• Lecture 6 Laws of Nature

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Two Issues in Causation

• Causal relations.
• Example the bomb exploding caused the bridge to
  collapse the car breaking caused a screeching
  noise.
• Causal laws.
• Example Newtonian laws of motion laws of
  chemistry

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Two Issues in Causation

• Causal relations.
• Example the bomb exploding caused the bridge to
  collapse the car breaking caused a screeching
  noise.
• Causal laws.
• Example Newtonian laws of motion laws of
  chemistry

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Laws as Propositions

• Here are some example propositions.
• (1) Gordon Brown is Prime Minister.
• (2) The capital of Djibouti is Djibouti.
• (3) All uranium-230 isotopes have a half life of
  20.8 days.
• (4) All small objects near a large mass are
  gravitationally attracted to it.
• Only (3) and (4) are laws of nature!

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This Lecture

• We look at a variety of ways to trying to see
  which propositions are laws of nature.
• The Naïve Regularity view
• The Mill-Ramsey-Lewis view (MRL)
• The Dretske-Tooley-Armstrong view (DTA)

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This Lecture

• We look at a variety of ways to trying to see
  which propositions are laws of nature.
• The Naïve Regularity view
• The Mill-Ramsey-Lewis view (MRL)
• The Dretske-Tooley-Armstrong view (DTA)

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Preamble

• What then makes a proposition a law of nature as
  opposed to not?
• First, it has to be true.
• Second, it has to be contingent.
• Example The laws of mathematics.
• Third, it must be some form of generalised
  statement All Fs are Gs (or some variant
  thereof ?x ?y (Fx ? Gy))

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Preamble

• Even then there are problems.
• (4) All soldiers who fought for Ghenghis Khan
  died by the age of 65.
• But surely (4) isnt a law of nature.
• We might demand that it cannot have reference to
  specific places or people we may only use
  general terms.

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Regularity Theory of Laws

• Just as there is a naïve regularity analysis of
  causal relations, there is a naïve regularity
  view of laws.
• P is a law iff it is
• i) contingently true and
• ii) is a universal generalisation containing only
  general terms.
• So, once again we are poised in battle with the
  Humeans

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Problems

• Lets look at X problems
• There can be accidental regularities
• There can be vacuous generalisations
• There can be laws of nature containing
  non-general terms

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Problems

• Lets look at X problems
• There can be accidental regularities
• There can be vacuous generalisations
• There can be laws of nature containing
  non-general terms

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Accidental Regularities

• The naïve regularity view has its problems.
• There can be accidental regularities just like
  we had when analysing causal relations last
  lecture!
• Examples from Reichenbach
• (5) All gold spheres are less than one mile in
  diameter.
• (6) All spheres of uranium are less than one
  mile in diameter.
• The above analysis would say that the accidental
  regularity counted as a law. Thats not right.

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Problems

• Lets look at X problems
• There can be accidental regularities
• There can be vacuous generalisations
• There can be laws of nature containing
  non-general terms

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Vacuous Generalisations

• (7) All dragons travel faster than the speed of
  light.
• There are no dragons.
• Reach back to logic and recall that if the
  antecedent of a conditional is false and the
  consequent true, the whole conditional is true.
• So the material conditional (Fx ? Gx) turns out
  true. The proposition therefore turns out to be
  true. But surely its false!
• Another example
• (8) All humans with eight kidneys can process
  arsenic.

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Vacuous Generalisations

• OK just stipulate that vacuous generalisations
  are always false.
• Isnt that reasonable?
• No consider Newtons First Law of Motion (that
  all objects unacted upon by forces will move in a
  straight line)
• There arent any such things.
• So Newtons Law would be false.

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Problems

• Lets look at X problems
• There can be accidental regularities
• There can be vacuous generalisations
• There can be laws of nature containing
  non-general terms

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Smiths Garden

• It also appears that the regularity analysis
  rules out possible laws that do make reference to
  specific, and no general, items.

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Smiths Garden

• If the world were that way, would we not have
  reason to believe that
• (9) All fruit in Smiths Garden are apples.
• Was a law of nature?

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Smiths Garden

• Other examples have been cited.
• For instance, Keplers Laws say that the planets
  in our solar system move in a elliptical orbit.
• Is that not a law of nature with a specific term
  (our solar system)?

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The X-factor

• But just as we modified naïve analyses of causal
  relations, we can modify the naïve analysis of
  causal laws.
• Its a law iff its a regularity plus some other
  factor, X.
• What could X be?

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Counterfactual Considerations

• With regards to the naïve regularity view of
  causal relations, we turned to counterfactuals.
• With respect to accidental regularities and
  vacuous generalisations, here we could make
  reference to counterfactuals.
• So ?x (Fx ? Gx) is a law iff it is regularity and
  if it were the case that if an object x was an F
  it would be a G.

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Counterfactual Considerations

• So now we avoid the problem as gold spheres could
  been more than a mile in diameter, whilst uranium
  spheres could not.
• The counterfactuals do the work!
• And if dragons did exist then they still wouldnt
  be able to travel superluminally.
• If I had eight kidneys I still wouldnt be able
  to process arsenic.

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Counterfactual Considerations

• Alas, it is not to be.
• Recall the Stalnaker-Lewis analysis of
  counterfactuals
• A ?? B iff
• (i) there are no A-worlds (it is vacuously true)
• (ii) some A-world where B holds is closer to the
  actual world than any A-world where B does not
  hold.

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Counterfactual Considerations

• In some worlds gold spheres will be just like
  uranium spheres and explode.
• And in some worlds there will be dragons that can
  travel superluminally.
• In some worlds humans with eight kidneys will
  process arsenic.
• These worlds are all physically impossible, so
  maybe theyre arent close to this one?
• Recall closeness was determined (i) by similarity
  with respect to histories and (ii)

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Counterfactual Considerations

• with respect to laws.
• Doh! Circularity!
• So on the SL analysis of cfactuals we have to
  know what the laws are before we figure out the
  truth of cfactuals. So the cfactuals cannot in
  turn be used to figure out the laws.

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Epistemic Considerations

• Maybe X is somehow rooted in epistemic
  considerations?
• This is the line of Goodman, the role of the
  proposition in prediction is what makes it a law.
• But we will concentrate on a more popular theory
  that takes X to be connected to epistemic
  considerations.

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Mill-Ramsey-Lewis View

• MRL, or the web of laws view, says that any
  proposition that features as an axiom or a
  theorem in our best deductive theory.
• We determine which is best in virtue of the
  simplicity and strength of the system.

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Mill-Ramsey-Lewis View

• For example, imagine a world consisting entirely
  of three iron balls in a box, and the box is
  suspended at the top of a sphere held between
  another sphere.

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Mills-Ramsey-Lewis View

• A constant stream of air blows around the inside
  of the two spheres, passing through the box, and
  pushing the balls around.

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Mills-Ramsey-Lewis View

• A constant stream of air blows around the inside
  of the two spheres, passing through the box, and
  pushing the balls around.
• The lighter, smaller, ball accelerates faster.
• The medium sized ball accelerates slightly
  slower.
• The large heavy ball doesnt budge.

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Mill-Ramsey-Lewis View

• Consider two competing systems.
• System one has laws like this
• All air particles move at a constant velocity in
  a clockwise fashion.
• Balls obey the laws of Newtonian motion.
• There are laws of friction (that prevent the big
  ball from moving)

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Mill-Ramsey-Lewis View

• System two is diverges more from the laws of our
  world
• There are no laws of friction and momentum.
• When air travels through the box it sets up some
  special field.
• Anything in that field may or may not move
  depending upon whether it fits in one of three
  categories of size.
• Air particles move at a constant velocity, unless
  they are looked at by people named John (!)

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Mill-Ramsey-Lewis View

• Both systems describe what is going on they are
  both as strong as one another.
• But clearly system two is not as simple as system
  one. Its kinda weird!
• So, according to MRL, in that world the
  propositions that are part of system one, plus
  all the propositions entailed by those axioms,
  are laws of nature.
• But there are problems with this idea of
  simplicity and strength.

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Mill-Ramsey-Lewis View

• In our world, the axioms and theorems are more
  complex, but ultimately discoverable via physics
  (say).
• Note that theres a balance between strength and
  simplicity.
• Even the eventual physics we will come up may not
  entail everything that goes on for instance
  there may be probabilistic laws.

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Mill-Ramsey-Lewis View

• But there will always be some system that is the
  strongest.
• For instance if the objects that exist are x1,
  x2, x3 and they engage in activities A1, A2,
  A3 then there is some system that consists of an
  infinite list of propositions saying Object x1
  does A1, Object x2 does A2 etc.)
• But then that system is nowhere near as simple as
  physics will be. So, on balance, we should take
  that system instead.

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Mill-Ramsey-Lewis View

• Similarly for simplicity.
• The simplest system would be, say, the one that
  considered solely of the proposition 224
• But that system has no strength!
• It doesnt entail anything about how the world is.

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Mill-Ramsey-Lewis View

• There are problems
• Problem one Multiple systems may be as good
• Problem two General problems with simplicity
• Problem three Extraneous laws

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Mill-Ramsey-Lewis View

• There are problems
• Problem one Multiple systems may be as good
• Problem two General problems with simplicity
• Problem three Extraneous laws

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Problem One

• What if there are multiple systems that are just
  as good?
• Answer Only take laws that feature in all
  systems.
• What if they are incompatible? (So no proposition
  features in any two systems)
• Answer Cross you fingers and hope Mother Nature
  is kind

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Mill-Ramsey-Lewis View

• There are problems
• Problem one Multiple systems may be as good
• Problem two General problems with simplicity
• Problem three Extraneous laws

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Problem Two

• We might have difficulty saying what counts as
  simple.
• Imagine a world with very different laws of
  nature.
• A universe of large cubes and spheres, medium
  cubes and spheres and small cubes and spheres.
  The large cubes and spheres are all black, the
  medium and small ones are either blue, yellow or
  pink.
• We observe that the medium and small cubes and
  spheres are accompanied by a certain sound when
  they pass by us, but the large are accompanied by
  no sound.

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Problem Two

• Law One All objects smaller than a certain size
  cause a certain sound.
• Law Two All blue, yellow or pink cubes or blue,
  yellow or pink spheres cause a certain sound.
• The first law seems simpler!

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Problem Two

• Now imagine a different culture.
• They have no phrase for smaller than.
• They are also less interested in colour they
  have no distinction between blue, yellow or pink,
  calling such things Blellink.
• They have an enormous range of words for shapes
  of different sizes large spheres are Leres,
  large cubes are Lubes, medium spheres are
  Meres, medium cubes are Mubes, small spheres
  are Smeres and small cubes are Subes.

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Problem Two

• Law One All meres, mubes, smeres and subes
  cause a certain sound.
• Law Two All blellink things cause a certain
  sound.
• Now the second law appears simpler!
• But Law Two is just a translation of Law Two,
  which in English is more complex.

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Mill-Ramsey-Lewis View

• There are problems
• Problem one Multiple systems may be as good
• Problem two General problems with simplicity
• Problem three Extraneous laws

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Problem Three

• Imagine a really simple world one with a ball
  moving in a straight line.
• Is it not possible that, even though the ball
  moves in a straight line at constant velocity,
  there are laws dealing with other things?
• Like whether salt dissolves in water, or what
  happens when the ball approaches the speed of
  light?
• And indeed, worlds where there arent such laws?

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Problem Three

• But given MRL the laws at those worlds must be
  the same.
• The best system for predicting will always be the
  same.
• If it cant vary, neither can the laws!
• And itll always predict that there arent
  extraneous laws, as that would make the system
  more complicated.

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Recap

• Weve looked at laws of nature.
• Weve seen the naïve regularity view, and three
  problems for that.
• Weve seen the MRL view, and three problems for
  that.
• Turn now to using universals to account for the
  laws of nature.

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Universals

• We will discuss Armstrong and Tooley.
• Armstrong believes in sparse universals, that are
  immanent.
• Tooley believes in sparse universals, that are
  Platonic.

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Dretske-Tooley-Armstrong View

• In 1977 three guys simultaneously came up with
  the same theory.
• Laws of nature are necessary connections between
  universals.
• So All Fs are G is not just a regularity, but
  a law of nature because the universal Fness
  stands in some necessitation relation to the
  universal Gness.
• So all uranium-235 has a certain half life
  because the universal being uranium-235 bears a
  certain necessitation relation to the universal
  having a half life of 704 million years
• That is, anything that instantiates the former
  necessarily instantiates the latter.

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Dretske-Tooley-Armstrong View

• Benefit one the mere regularities that pose
  Humean views a problem are no problem here!
• All Fs may accidentally be G without that being
  a law of nature (e.g. all gold spheres are less
  than one mile in diameter)
• That doesnt mean that Fness stands in the
  necessitation relation to Gness.

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Dretske-Tooley-Armstrong View

• Second benefit doesnt rely upon epistemic
  features like simplicity and strength.
• They caused MRL trouble what counted as
  simplicity? What counted as strength?
• No epistemic factors play a role in the
  metaphysics according to DTA.

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Dretske-Tooley-Armstrong View

• But there are, as always, problems.
• Uninstantiated laws
• What is necessitation?

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Dretske-Tooley-Armstrong View

• But there are, as always, problems.
• Uninstantiated laws
• What is necessitation?

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Uninstantiated Laws

• The final problem for MRL was that there can be
  two universes where the particulars (and their
  arrangements etc.) are identical but the laws of
  nature are different.
• Example A single ball in a world with/without
  laws governing whether salt dissolves in water.

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Uninstantiated Laws

• Imagine youre Armstrong.
• What differs between the worlds to explain the
  laws?
• Well, thered have to be differences between
  what relations obtain between the universals.
• But the universals and their relations are, ex
  hypothesi, the same!

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Uninstantiated Laws

• We could go Platonic, like Tooley does.
• So the requisite universals exist, but are
  uninstantiated.
• And in the two worlds, the relations this
  necessitation relation between the universals
  differs.

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Uninstantiated Laws

• We could go Platonic, like Tooley does.
• So the requisite universals exist, but are
  uninstantiated.
• And in the two worlds, the relations this
  necessitation relation between the universals
  differs.
• This will demand the existence of uninstantiated
  universals.
• Which many think are a problem!

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Dretske-Tooley-Armstrong View

• But there are, as always, problems.
• Uninstantiated laws
• What is necessitation?

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What is Necessitation?

• What is necessitation anyhow?
• Consider what has to be explained why are these
  regularities laws? Why does one fact (Fness
  standing in the necessitation relation to
  Gness) bring it about that all Fs are Gs?
• We want the analysis to be explanatory.

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What is Necessitation?

• But nothing thus far says this. What relation is
  picked out by necessitation?
• Without some idea of what that relation is, we
  have no idea whether what DTA says actually
  explains anything.
• For instance, imagine I want to explain why
  taking this drug knocks everyone out.
• Ah, I say, It is because it stands in some
  relation to those people! It stands in the
  necessitates knocking them out relation

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What is Necessitation?

• So when Armstrong says there is a relation N
  between two universals, F and G, such that N(F,G)
  Lewis retorts
• But I say that N deserves the name of
  necessitation only if, somehow, it really can
  enter into the requisite necessary connections.
  It cant enter into them just by bearing a name
• any more than one can have mighty biceps just by
  being called Armstrong
• Lewis, New Work for A Theory of Universals

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What is Necessitation?

• So some more work is required as to what this
  relation is, if any explanation is to be done.
• Thats not to say no-one tried both Tooley and
  Armstrong have had a stab at trying to tell us
  more about the necessitation relation.

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Recap

• Over the last two lectures we have looked at
  metaphysical matters that arent strictly
  ontological.
• But they do involve some of the ontological
  entities weve talked about.
• Lewis counterfactual approach talked about
  possible worlds.
• DTA approach talked about universals.
• So weve got a neat little demonstration of how
  ontological matters can bear on other areas in
  metaphysics.

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More Options?

• Not that these are the only options.
• There are more ways of handling the laws than the
  options laid out in this lecture.
• Doing them in terms of dispositions say.
• But Ill leave you to look at those options if
  you want to.

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Next Lecture

• Were done with all things causal.
• We return to ontology but not to more
  ontological questions concerning abstract things
  like numbers, properties and possible worlds.
• For the next three lectures we will look at the
  ontology of material objects.
• What objects are there? Are there things like
  tables? Are there things like you and me?