Issues in Contemporary Metaphysics

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Issues in Contemporary Metaphysics

• Lecture 3 Possible Worlds I

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Recap

• Two of the important things weve done so far
• Introduced the notion of ontological commitment
  and paraphrasing to show why some people think
  certain things appear in their ontology.
• Introduced the notion of theory choice and the
  cost/benefit analysis.

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Possible Worlds

• Youve probably heard the term used before.
• Over the next two lectures we will see
• The benefits of possible world talk.
• Why this talk makes some people think they exist.
• What possible worlds might be if they do exist.
• How some people think we can have the benefits of
  possible world talk without worlds

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Possible Worlds

• The last three are similar to things weve
  already done with properties.
• We saw why some people think properties exist
• Abstract Reference
• The Argument from Resemblance

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Possible Worlds

• Youve probably heard the term used before.
• Over the next two lectures we will see
• The benefits of possible world talk.
• Why this talk makes some people think they exist.
• What possible worlds might be if they do exist.
• How some people think we can have the benefits of
  possible world talk without worlds

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Possible Worlds

• The last three are similar to things weve
  already done with properties.
• We saw why some people think properties exist
• Abstract Reference
• The Argument from Resemblance
• Weve seen what properties might be if they do
  exist
• Universals
• Sets of objects

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Possible Worlds

• Youve probably heard the term used before.
• Over the next two lectures we will see
• The benefits of possible world talk.
• Why this talk makes some people think they exist.
• What possible worlds might be if they do exist.
• How some people think we can have the benefits of
  possible world talk without worlds

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Possible Worlds

• The last three are similar to things weve
  already done with properties.
• We saw why some people think properties exist
• Abstract Reference
• The Argument from Resemblance
• Weve seen what properties might be if they do
  exist
• Universals
• Sets of objects
• Weve seen how people try and live without
  properties if they dont exist
• Austere Nominalism

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Possible Worlds

• Youve probably heard the term used before.
• Over the next two lectures we will see
• The benefits of possible world talk.
• Why this talk makes some people think they exist.
• What possible worlds might be if they do exist.
• How some people think we can have the benefits of
  possible world talk without worlds

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Possible Worlds

• One big difference between properties and
  possible worlds is that you routinely talk about
  properties already.
• You accept that property talk is legitimate
• Blue is a colour
• There are as yet undiscovered properties
• But many people (particularly students!) wonder
  why philosophers started talking about possible
  worlds.
• What is the point in such talk?

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Modal Logic

• The answer is straightforward possible worlds
  help formalise modal sentences.
• Modal statements are about what could have been.
• Hitler could have won World War II
• I could have been a fisherman
• The speed of light could have been twice as fast
  as it actually is
• Swans could have been black
• Its impossible for there to be round squares
• Necessarily, 224

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Modal Logic

• Modal statements also include counterfactual
  statements
• Scientific If the speed of light were faster,
  atomic explosions would be more deadly.
• Ethical If you hadnt have made the deceased
  play on the motorway, he wouldve lived.
• Everyday If I hadnt have gone out last I
  wouldnt have a hangover.

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Modal Logic

• Modal statements can cover a variety of different
  types of modality.
• Logical Possibility Its logically possible for
  me to grow wings and fly to New York.
• Physical Possibility Its physically impossible
  to grow wings and fly to New York.
• Why stop there?
• Economic Possibility Its impossible for me to
  fly to New York.

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Modal Logic

• First order predicate logic cant deal with
  modality very well.
• Take the following argument
• Nikk is a philosopher
• Therefore Nikk could have been a philosopher
• or
• Nikk is essentially a material object
• Therefore Nikk is a material object
• Try formalising them in predicate logic.

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Modal Logic

• First order predicate logic cant deal with
  modality very well.
• Take the following argument
• Nikk is a philosopher
• Therefore Nikk could have been a philosopher
• or
• Nikk is essentially a material object
• Therefore Nikk is a material object
• Try formalising them in predicate logic.

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Modal Logic

• The predicates __ is a fisherman and __ could
  have been a fisherman are different.
• Call the former F and the latter G.
• The form of the first argument would then be
• Fa
• Ga
• So its an invalid inference in first order
  logic.
• But the argument is valid!
• I leave it to you to try the second the same
  problems emerge.

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Modal Logic

• So we supplement first order logic (in the same
  way that we supplemented propositional logic to
  get predicate logic).
• We introduce a possibility operator ?
• So Possibly, there could be dragons is ?P
• We then add in axioms.
• If something is actually the case it is possible
• ? ? ? ?

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Modal Logic

• Now formalise the argument.
• Nikk is a philosopher Fa.
• Nikk couldve been a philosopher ?Fa
• So we get
• Fa Premise
• Fa ? ?Fa axiom
• Therefore ?Fa conclusion
• And now its valid!

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Modal Logic

• We can also introduce a necessity operator ?
• It also has an intuitive axiom
• ? ? ? ?
• It can be interdefined with the possibility
  operator
• ? ? df ? ?
• ? ? df ? ?
• If you understand one, you understand the other.

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Modal Logic

• With that in place, we formalise the other
  argument.
• Nikk is essentially a material object
• Therefore Nikk is a material object
• Something a bit like this
• ?Fa Premise
• ?Fa ? Fa Axiom
• Fa Conclusion
• Go modal operators!

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Modal Logic

• So where do possible worlds come in?
• Some people think that we can formalise modal
  sentences using just the box and diamond (or
  variants thereof).
• Theyre called modalists.
• But modalism has big problems.

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Further Reading

• Melia, J. 2003. Modality Chesham Acumen.
• Prior, A. and Fine, K. 1977. Worlds, Times and
  Selves London Duckworth.
• Forbes, G. 1985. The Metaphysics of Modality
  Oxford Clarendon.

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Modal Logic

• Using just the box and diamond you just wont be
  able to satisfactorily formalise sentences like
  this
• (1) There are three ways to win this chess match.
• (2) There could have been one more thing than
  actually exists.
• (3) If Hitler had been a pacifistic clergyman, he
  would have been more similar to Desmond Tutu than
  he otherwise was.
• Ill let you either see the problems in those
  sentences by trying to formalise them yourself,
  or you can go and read about how they fail.

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Modal Logic

• Thats where the possible worlds come in.
• Logicians introduced possible worlds so they
  could formalise those kinds of sentences.
• So at this stage theyre just a heuristic,
  something introduced to make doing logic easier.
• How does it work?

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Possible World Talk

• There are all these possible worlds.
• One is special our world. The actual world.
• Things are true at those worlds.
• So a proposition can be true at one world and
  false at another.
• So Hitler won WWII is false at our world, but
  true at another one.
• Something is possible if its true at some world.
• ? P becomes ? ? (? is a PW and P is true at
  ? )
• Something is necessary if its true at all
  worlds.
• ? P becomes ? ? ( ? is a possible world ? P
  is true at ? )
• Something is impossible if its true at no world.

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Possible World Talk

• So Hitler could have won World War II because
  there is some world at which he does win WWII.
• 224 because at every PW, it is true at that
  world that 224.
• Something is actually true iff it is true at the
  actual world.
• So Im actually giving a lecture because at this
  world, the one were in, it is true that Im
  giving a lecture.

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Possible World Talk

• How does this help?
• (4) There could have been one more thing than
  actually exists.
• ? ? ? is a PW

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Possible World Talk

• How does this help?
• (4) There could have been one more thing than
  actually exists.
• ? ? ? is a PW ? x ( x exists at the actual
  world ? x exists at ? )

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Possible World Talk

• How does this help?
• (4) There could have been one more thing than
  actually exists.
• ? ? ? is a PW ? x ( x exists at the actual
  world ? x exists at ? ) ? y ( y exists at the
  actual world

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Possible World Talk

• How does this help?
• (4) There could have been one more thing than
  actually exists.
• ? ? ? is a PW ? x ( x exists at the actual
  world ? x exists at ? ) ? y ( y exists at the
  actual world y exists at ? )

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Possible World Talk

• How does this help?
• (4) There could have been one more thing than
  actually exists.
• ? ? ? is a PW ? x ( x exists at the actual
  world ? x exists at ? ) ? y ( y exists at the
  actual world y exists at ? )
• Note that we dont just need worlds!

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Possible World Talk

• How does this help?
• (4) There could have been one more thing than
  actually exists.
• ? ? ? is a PW ? x ( x exists at the actual
  world ? x exists at ? ) ? y ( y exists at the
  actual world y exists at ? )
• Note that we dont just need worlds!

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Possible World Talk

• How does this help?
• (4) There could have been one more thing than
  actually exists.
• ? ? ? is a PW ? x ( x exists at the actual
  world ? x exists at ? ) ? y ( y exists at the
  actual world y exists at ? )
• Note that we dont just need worlds!
• We need objects that dont exist!

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Possible World Talk

• How does this help?
• (4) There could have been one more thing than
  actually exists.
• ? ? ? is a PW ? x ( x exists at the actual
  world ? x exists at ? ) ? y ( y exists at the
  actual world y exists at ? )
• Note that we dont just need worlds!
• We need objects that dont exist!

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Possible World Talk

• So we need not just worlds, but non-actual
  objects. Call them possibilia.
• So Gandalf and Santa Claus are possibilia.
• Equipped with possible worlds and possibilia we
  can translate (4).

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Possible World Talk

• (5) If Hitler had been a pacifistic clergyman, he
  would have been more similar to Desmond Tutu than
  he otherwise was.
• This is true because there exists a possible
  world at which Hitler exists and is, in fact, a
  nice clergyman.
• That possibilia resembles Desmond Tutu (to a
  greater degree than the actual Hitler did).

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Possible World Talk

• So, thats why people often talk about possible
  worlds (and possibilia)
• Because it makes formalising modal sentences, and
  arguments containing modal sentences, easier and
  straightforward.
• Assume that everyone likes possible world talk.
• Not everyone likes possible worlds.
• Just as people talk about properties, but you
  have the austere nominalist, people talk about
  possible worlds but dont necessarily believe in
  them.
• Well see those guys next lecture.

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Possible World Talk

• Our interest is in the other guys.
• If you accept the idea that the only way to
  formalise modal sentences in logic is by using
  possible worlds talk.
• And you think that the way that logic says the
  world is tells us how the world is (like the
  Quinean says!) then you believe in possible
  worlds.
• So thats the first motivation that logic
  reflects reality (i.e. Quinean ontological
  commitment) and there are no decent paraphrases
  available for modal sentences.

39
Recap

• Two of the important things weve done so far
• Introduced the notion of ontological commitment
  and paraphrasing to show why some people think
  certain things appear in their ontology.
• Introduced the notion of theory choice and the
  cost/benefit analysis.

40
Recap

• Two of the important things weve done so far
• Introduced the notion of ontological commitment
  and paraphrasing to show why some people think
  certain things appear in their ontology.
• Introduced the notion of theory choice and the
  cost/benefit analysis.

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Possible Worlds

• The other motivation is that a theory including
  possible worlds yields greater benefits than one
  which does not.
• There are four benefits I will look at.
• (i) Solving the problem of which modal logic is
  right.
• (ii) Ontological Parsimony Properties
• (iii) Ontological Parsimony Propositions
• (iv) Theoretical Simplicity

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Which Modal Logic?

• There are many different modal logics.
• Some axioms of modal logic are obvious, and weve
  already seen.
• ? ? ? ?
• ? ? ? ?
• But others are more contentious
• ? ? ? ? ? ?
• or
• ? ? ? ? ? ?

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Which Modal Logic?

• These stacked modal operators make life more
  difficult.
• How are we to determine what the theorems are?
• But if we know what PW there are, were away!
• You look at the PW that exist, then look at
  whats true in them, and this tells us what the
  theorems are.

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Ontological Parsimony

• Lets turn to something were more familiar with.
• How possible worlds allow us to include
  properties and propositions into our ontology.

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Ontological Parsimony Properties

• Recall class nominalism.
• It had a problem that the set of all cordate
  things was identical to the set of all renate
  things.
• So being renate and being cordate wrongly turned
  out to be the same property.
• Or the counterfactual scenario where terrorists
  won and, whilst all honest, had left the rest of
  us dead.

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Ontological Parsimony Properties

• Recall class nominalism.
• It had a problem that the set of all cordate
  things was identical to the set of all renate
  things.
• So being renate and being cordate wrongly turned
  out to be the same property.
• Or the counterfactual scenario where terrorists
  won and, whilst all honest, had left the rest of
  us dead.
• But now with an ontology of possible worlds and
  possibilia, we can avoid this.

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Ontological Parsimony Properties

• Now being honest is the set of all honest people.
• Not just the actual honest people but all the
  honest people from every possible world.
• Those possibilia are members of the set of honest
  people.

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Ontological Parsimony Properties

• Now being honest is the set of all honest people.
• Not just the actual honest people but all the
  honest people from every possible world.
• Those possibilia are members of the set of honest
  people.
• So being honest and being a terrorist dont have
  the same members and are different properties.

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Ontological Parsimony Properties

• Now being honest is the set of all honest people.
• Not just the actual honest people but all the
  honest people from every possible world.
• Those possibilia are members of the set of honest
  people.
• So being honest and being a terrorist dont have
  the same members and are different properties.
• So introducing possible worlds (allegedly) lets
  us do without universals and/or tropes, and
  revive class nominalism.

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Ontological Parsimony Propositions

• We havent looked at propositions thus far.
• But you get the idea that the same sorts of
  questions arise are there propositions? Are they
  sui generis entities? Are they identifiable with
  other entities?
• With PW, propositions are sets of worlds.
• For any proposition P, P is just the set of all
  P-worlds.
• So at some worlds Hitler wins WWII, at others he
  doesnt (at most he doesnt even exist!).

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Ontological Parsimony Propositions

• The proposition Hitler won WWII is the set of
  those worlds.
• The proposition is true at a world iff that world
  is a member of that set.
• So its actually true iff the actual world is a
  member of that set.
• (which it isnt)

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Ontological Parsimony

• So if you have possible worlds and possibilia you
  can have a more parsimonious ontology.
• And, remember, thats a benefit!

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Theoretical Simplicity

• There are other savings to be made.
• Recall, a theory with less primitives is meant to
  be better.
• Some think possible worlds will allow us to
  analyse away modal notions.
• Weve seen this in action already!

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Theoretical Simplicity

• So rather than having a primitive notion of
  possibility we analyse it in terms of PW.
• The analysis for Possibly P is just P is true
  at some world
• That allows us to analyse away modal statements
  in terms of the non-modal.
• We do away with any primitive notion of
  modality.

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Theoretical Simplicity

• It also helps us analyse other modal notions such
  as counterfactuals.
• If P were the case, Q would be the case
• Given an ontology of PW we can (allegedly)
  analyse that, rather than just trying to play
  around with our brute intuitions.
• Well see that in lecture 5.

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Recap

• So weve laid out the reasons for believing in
  possible worlds
• We quantify over possible worlds when trying to
  account for modal sentences
• There are other assorted benefits associated with
  accepting possible worlds (which, allegedly, will
  outweigh the cost of accepting them into your
  ontology)

69
Possible Worlds

• Youve probably heard the term used before.
• Over the next two lectures we will see
• The benefits of possible world talk.
• Why this talk makes some people think they exist.
• What possible worlds might be if they do exist.
• How some people think we can have the benefits of
  possible world talk

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Modal Realism

• If you believe in possible worlds you are a modal
  realist.
• As you may have cottoned on, terminology in
  metaphysics sucks.
• Modal realism is also often used to refer to
  what I call genuine modal realists
• But Ill be using it for anyone who believes
  possible worlds exist.

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Modal Realism

• So far Ive introduced the following entities
• Material objects
• Sets
• Universals
• Propositions
• You might identify worlds with a certain type of
  universal sets of propositions an enormous
  conjunctive proposition or make them sui generis
  entities in a category of their own.
• Well look at these options (what are called
  ersatz possible worlds) next lecture.

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Modal Realism

• So far Ive introduced the following entities
• Material objects
• Sets
• Universals
• Propositions
• You might identify worlds with a certain type of
  universal sets of propositions an enormous
  conjunctive proposition or make them sui generis
  entities in a category of their own.
• Well look at these options (what are called
  ersatz possible worlds) next lecture.

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Genuine Modal Realism

• Sometimes called Concrete world realism or, as
  I said before, simply modal realism.
• Famous proponent is David Kellogg Lewis.
• It identifies possible worlds with objects like
  you and I.

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Genuine Modal Realism

• But which objects?
• Not just any old material object. Im not a
  possible world.
• A possible world is any object such (i) that
  every part of it is spatiotemporally related to
  every other

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Genuine Modal Realism

• But which objects?
• Not just any old material object. Im not a
  possible world.
• A possible world is any object such (i) that
  every part of it is spatiotemporally related to
  every other (ii) nothing exists that isnt a
  part of it but is spatiotemporally related to it.

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Genuine Modal Realism

• Basically, then, this universe this spacetime
  is a possible world.
• Were parts of that possible world.
• Everything in this universe is part of that
  possible world.
• So theres a possible world a universe
  wherein Hitler wins WWII.
• Theres a possible world a universe wherein
  the speed of light is faster.
• Theres a possible world a universe wherein
  Gandalf battles a Balrog.

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Genuine Modal Realism

• These universes are different spacetimes.
• But theyre as real as you and I!
• They arent abstract, theyre physical things.
• So for Lewis, talking donkeys, flying
  superheroes, the characters of Eastenders etc.
  all exist.
• Just in a different spacetime.

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Genuine Modal Realism

• Thats pretty crackers.
• If you dont think thats crackers, you havent
  quite understood whats going on.

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Genuine Modal Realism Actuality

• But whilst these things exist, most of them dont
  actually exist.
• Lewis prises apart the two notions.
• What actually exists is what is actual i.e. what
  is part of the actual world.
• The actual world, for Lewis, is the spacetime you
  happen to be in.
• So dragons exist, but they dont actually exist.
• Some people think this makes it weirder.
• Actualists think that only actual things can
  exist.
• Some people think it makes it less weird.
• After all, you might say that intuitively dragons
  dont actually exist (GMR agrees) and then say
  you have little or no intuition over whether they
  exist.

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Genuine Modal Realism Counterparts

• This theory clearly has possible worlds.
• It also has possibilia. They exist too.
• Im a possibilum (just not a mere possibilum as
  Im actual).
• But dragons, Robert Langdon etc. they all exist
  too (as parts of their own respective worlds).
• Which is good, because recall that we needed
  possibilia to exist in order to accept possible
  world talk as being reflective of reality.

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Possible World Talk

• How does this help?
• (4) There could have been one more thing than
  actually exists.
• ? ? ? is a PW ? x ( x exists at the actual
  world ? x exists at ? ) ? y ( y exists at the
  actual world y exists at ? )
• Note that we dont just need worlds!
• We need objects that dont exist!

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Genuine Modal Realism Counterparts

• But I can exist at lots of worlds.
• Its true I couldve been a fisherman iff theres
  a possible world at which I am a fisherman.
• But Im, surely, only part of one world?
• Lewis gets around this by saying that the Nikk
  Effinghams at other worlds are my counterparts.
• So what grounds de re modal claims are
  counterparts things a lot like me, but not me
  existing at those other worlds.
• And something is my counterpart if its similar
  to me.
• This is very important because, as we shall see
  next lecture, not all modal realist theories
  include possibilia.

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Genuine Modal Realism Motivation

• Why believe this madness?
• Why believe in a plurality of worlds? Because
  the hypothesis is serviceable, and that is a
  reason to think that it is true. Lewis, D. On
  the Plurality of Worlds p. 3
• Lewis reckons
• (i) GMR can capture all of the motivations given
  before for possible worlds.
• (ii) No other theory can do this (more on this
  next lecture)
• (iii) These benefits outweigh any costs (say,
  breaching intuitions) for including an infinite
  number of spacetimes in your ontology.

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Genuine Modal Realism Replies

• There are three ways to reply to Lewis.
• Refuse to believe it The Incredulous Stare
• Demonstrate some other theory can get the
  benefits without the costs.
• Find hidden costs in the GMR enterprise that,
  in fact, it is committed to costly problems.

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Genuine Modal Realism Replies

• There are three ways to reply to Lewis.
• Refuse to believe it The Incredulous Stare
• Demonstrate some other theory can get the
  benefits without the costs.
• Find hidden costs in the GMR enterprise that,
  in fact, it is committed to costly problems.

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Genuine Modal Realism Replies

• Not much to say about the incredulous stare.
• Must surely be able to do better.
• Example Refusing to believe in quantum physics
  because its so whacky.

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Genuine Modal Realism Replies

• There are three ways to reply to Lewis.
• Refuse to believe it The Incredulous Stare
• Demonstrate some other theory can get the
  benefits without the costs.
• Find hidden costs in the GMR enterprise that,
  in fact, it is committed to costly problems.
• Well have to wait until next lecture to see why
  Lewis thinks the other theories have costs.

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Genuine Modal Realism Replies

• There are three ways to reply to Lewis.
• Refuse to believe it The Incredulous Stare
• Demonstrate some other theory can get the
  benefits without the costs.
• Find hidden costs in the GMR enterprise that,
  in fact, it is committed to costly problems.

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Genuine Modal Realism

• These are the problems usually raised
• GMR says certain intuitively possible things are
  impossible
• GMR generates problems in ethics
• GMR says there are more things than there
  actually are
• GMR says that there can be no alien properties
• GMR leads to scepticism
• GMR has problems with counterpart theory
• GMR still misidentifies properties, just like
  class nominalism originally does

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Genuine Modal Realism

• These are the problems usually raised
• GMR says certain intuitively possible things are
  impossible
• GMR generates problems in ethics
• GMR says there are more things than there
  actually are
• GMR says that there can be no alien properties
• GMR leads to scepticism
• GMR has problems with counterpart theory
• GMR still misidentifies properties, just like
  class nominalism originally does

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Genuine Modal Realism Missing Possibilities

• Cant account for island universes
• An island universe is one where the spacetime is
  cut into two.
• For instance, we could imagine a chain of
  universes, where a connection between two regions
  gets smaller and smaller until it snaps and
  theres no way between them.

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Genuine Modal Realism Missing Possibilities

• These all seem possible.
• Two regions, traversable only by passing through
  a very small region of space.
• Indeed, this might be how our universe actually
  is.

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Genuine Modal Realism Missing Possibilities

• Such a universe seems possible in theory.
• Note that we need a disconnected spacetime.
• So it seems that its possible that island
  universes exist.
• If its possible then there is a possible world
  at which there are island universes.

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Genuine Modal Realism Missing Possibilities

• Given GMR possible worlds are maximal spacetimes
  and their contents.
• Thats why me and Gandalf arent in the same
  possible world we arent spatiotemporally
  connected.
• But given this definition, there cant be any
  island universes.

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Genuine Modal Realism Missing Possibilities

• Island universes are two disconnected spacetimes.
• So thats two possible worlds! Not one!
• Youll never have a possible world where there
  are island universes! Itll always turn out to be
  two!
• Thus, given GMR its impossible that therere
  island universes.

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Genuine Modal Realism Ethical Dilemmas

• Maybe we can rack up the cost by claiming GMR
  runs roughshod over our ethical intuitions.
• Utilitarianism runs into problems straight away.
• If we are to maximise happiness (or utility), how
  can we when the amount of happiness is fixed by
  necessity?
• Theres an infinite number of people. Whatever
  you do, theres an infinite amount of pleasure
  and pain.

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Genuine Modal Realism Ethical Dilemmas

• Cannot just restrict ourselves to this world
  (increase utility in this region of spacetime)
• Then it would be similar to other prejudiced
  principles (increase utility in the Western
  World, and screw the Third World Heh, lets
  all drive to the shops and back even though the
  walk only takes two minutes, screw the dying
  children in the Third World, I cant see them)

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Genuine Modal Realism Ethical Dilemmas

• More complex problems arise though.
• Imagine you see a child drowning.
• Imagine that theres a machine set up to drown a
  different child if you do.
• Imagine that if you dont save her, the machine
  is programmed to rescue the other child.
• Should you save her?
• My intuitions say it doesnt matter either way.

104
Genuine Modal Realism Ethical Dilemmas

• Given GMR, all possibilities must play out.
• If you save her, then in another world her
  counterpart drowns.
• If you dont save her then given GMR in that
  world her counterpart must be saved.
• Its just like the machine.

105
Further Reading

• Lewis, D. 1986. On The Plurality of Worlds
• Heller, M. 2003. The Immorality of Modal Realism,
  Philosophical Studies 114 1-22.

106
Genuine Modal Realism

• So we can say something against GMR other than
  just going Nah and giving Lewis odd looks.
• I would expect saying something different were
  you to choose this as an essay topic.

107
Recap

• Weve explained
• Why people use possible worlds talk
• Motivation One for PW Some people think this
  talk is representative of ontology
• Motivation Two for PW Some people think possible
  worlds provide other ontological benefits
  regarding parsimony, theoretical simplicity etc.
• Seen Lewis Genuine Modal Realism
• Briefly looked at two problems with that theory

108
Next Lecture

• How to believe in possible worlds without being
  Lewis
• How to try and live without possible worlds