Issues in Contemporary Metaphysics

1
Issues in Contemporary Metaphysics

• Lecture 2 Properties

2
Recap

• Last lecture I introduced what ontology consists
  in finding out what things exist, namely
  numbers, works of music, properties etc.
• I tried to give you some idea of why people think
  these kinds of questions are open questions.
• Importantly I introduced the notion of Quinean
  ontological commitment and paraphrase.
• Quine says that to find out the commitments of
  sentences, we figure out the logical form (in
  first order predicate logic) of the proposition
  that sentence expresses.

3
Recap

• So the sentence The average man has 2.4
  children might be thought, due to its surface
  grammar, to express the proposition
• The average man exists, and stands in the is a
  parent of relation to 2.4 children.
• That sentence has the logical form
• ? x ? y1 ? y2 ? y3 ( x average man y1 is a
  child y2 is a child y3 is 40 of a child
  xRy1 xRy2 xRy3 )
• Where R is the relation of being a parent of

4
Recap

• So the sentence The average man has 2.4
  children might be thought, due to its surface
  grammar, to express the proposition
• The average man exists, and stands in the is a
  parent of relation to 2.4 children.
• That sentence has the logical form
• ? x ? y1 ? y2 ? y3 ( x average man y1 is a
  child y2 is a child y3 is 40 of a child
  xRy1 xRy2 xRy3 )
• Where R is the relation of being a parent of

5
Recap

• So the sentence The average man has 2.4
  children might be thought, due to its surface
  grammar, to express the proposition
• The average man exists, and stands in the is a
  parent of relation to 2.4 children.
• That sentence has the logical form
• ? x ? y1 ? y2 ? y3 ( x average man y1 is a
  child y2 is a child y3 is 40 of a child
  xRy1 xRy2 xRy3 )
• Where R is the relation of being a parent of

6
Recap

• So the sentence The average man has 2.4
  children might be thought, due to its surface
  grammar, to express the proposition
• The average man exists, and stands in the is a
  parent of relation to 2.4 children.
• That sentence has the logical form
• ? x ? y1 ? y2 ? y3 ( x average man y1 is a
  child y2 is a child y3 is 40 of a child
  xRy1 xRy2 xRy3 )
• Where R is the relation of being a parent of

7
Recap

• So the sentence The average man has 2.4
  children might be thought, due to its surface
  grammar, to express the proposition
• The average man exists, and stands in the is a
  parent of relation to 2.4 children.
• That sentence has the logical form
• ? x ? y1 ? y2 ? y3 ( x average man y1 is a
  child y2 is a child y3 is 40 of a child
  xRy1 xRy2 xRy3 )
• Where R is the relation of being a parent of

8
Recap

• So the sentence The average man has 2.4
  children might be thought, due to its surface
  grammar, to express the proposition
• The average man exists, and stands in the is a
  parent of relation to 2.4 children.
• That sentence has the logical form
• ? x ? y1 ? y2 ? y3 ( x average man y1 is a
  child y2 is a child y3 is 40 of a child
  xRy1 xRy2 xRy3 )
• Where R is the relation of being a parent of

9
Recap

• So the sentence The average man has 2.4
  children might be thought, due to its surface
  grammar, to express the proposition
• The average man exists, and stands in the is a
  parent of relation to 2.4 children.
• That sentence has the logical form
• ? x ? y1 ? y2 ? y3 ( x average man y1 is a
  child y2 is a child y3 is 40 of a child
  xRy1 xRy2 xRy3 )
• Where R is the relation of being a parent of

10
Recap

• So the sentence The average man has 2.4
  children might be thought, due to its surface
  grammar, to express the proposition
• The average man exists, and stands in the is a
  parent of relation to 2.4 children.
• That sentence has the logical form
• ? x ? y1 ? y2 ? y3 ( x average man y1 is a
  child y2 is a child y3 is 40 of a child
  xRy1 xRy2 xRy3 )
• Where R is the relation of being a parent of

11
Recap

• But thats nuts, so you might offer a paraphrase.
  
• The surface grammar might make it sound like it
  commits to 40 of a child, but we can instead say
  it actually expresses a different proposition.
• Say
• The number of men divided by the number of
  children equals the 2.4
• ? x ? y ? z ( x the number of men y the
  number of children z 2.4 Rxyz )
• Where R is the three-place relation __ divided
  by __ equals __

12
Recap

• So hopefully that goes someway to explaining what
  a paraphrase is meant to be.
• The sentence has a surface grammar, but expresses
  a different proposition that doesnt commit us to
  the existence of unwanted things.
• Is that the correct paraphrase?
• Maybe not, after all it still commits us to
  numbers

13
On with the show

• So, with that all in mind, lets move on to doing
  some ontology.
• Along the way, well see other facets of how
  ontology is studied and practised.
• Today well look at properties.
• Do they exist? (i.e. should we be realists or
  anti-realists with regards to properties)
• If they do exist, what are they like?

14
On with the show

• So, with that all in mind, lets move on to doing
  some ontology.
• Along the way, well see how other facets to how
  ontology is studied and practised.
• Today well look at properties.
• Do they exist? (i.e. should we be realists or
  anti-realists with regards to properties)
• If they do exist, what are they like?

15
Realism vs. Anti-realism of Properties

• Well look at two reasons to believe in
  properties Abstract reference and the problem
  of universals
• This isnt exhaustive. For instance, David Lewis
  has more to say in New Work for a Theory of
  Universals.

16
Abstract Reference

• Before turning to the motivation for properties,
  lets just look at some simple sentences.
• All footballs are round
• ? x ( Fx ? Gx )
• Where F is the predicate __ is a football and
  G is the predicate __ is round.
• The prime minister is Scottish
• ? x ( Fx Gx )
• Where F is the predicate __ is the prime
  minister and G is the predicate __ is Scottish
• Theres something over there, and its either
  blue or pink
• ? x ( Fx v Gx )
• Where F is the predicate __ is pink and G is
  the predicate __ is blue

17
Abstract Reference

• Before turning to the motivation for properties,
  lets just look at some simple sentences.
• All footballs are round
• ? x ( Fx ? Gx )
• Where F is the predicate __ is a football and
  G is the predicate __ is round.
• The prime minister is Scottish
• ? x ( Fx Gx )
• Where F is the predicate __ is the prime
  minister and G is the predicate __ is Scottish
• Theres something over there, and its either
  blue or pink
• ? x ( Fx v Gx )
• Where F is the predicate __ is pink and G is
  the predicate __ is blue

18
Abstract Reference

• So simple sentences like that dont (under the
  Quinean theory of ontological commitment) commit
  us to the existence of properties.
• Well see, when we turn to the problem of
  universals, that not everyone agrees this is
  true.
• But for now, lets just examine things from the
  Quinean point of view.
• Given those sentences there is no commitment to
  properties.
• All we commit to are material objects, and then
  say how they are. Theres no commitment to
  properties as well.

19
Abstract Reference

• This was the view of Goodman and (the early)
  Quine.
• No properties, just things being one way rather
  than another.

20
Abstract Reference

• But if only things were so simple.
• As you might remember from last lecture, not
  every sentence is so easy.
• Lets try some harder ones.

21
Abstract Reference

• (1) Your car and my car are both blue
• Slightly harder, but still pretty easy. Let F be
  __ is blue
• (1) ? x ? y ( x my car y your car Fx
  Fy)
• But now try
• (2) Our cars are the same colour
• Cant use (1), as (2) could be true even though
  our cars arent blue.
• They could both be yellow.

22
Abstract Reference

• Perhaps make it a disjunctive paraphrase?
• ( x is blue y is blue ) v ( x is red y is red
  ) v ( x is yellow y is yellow )
• Of course, even this wont work!
• Imagine I asked you to paint some cars.
• You paint one azure, and the other Alice Blue.
• Thats pretty different, but theyre both blue.
• Clearly two cars painted like that wont, in most
  contexts, be the same colour.

23
Abstract Reference

• So the paraphrase must be extended even more! A
  disjunct for every shade of blue (and red! And
  yellow! And green!)
• And of course, even then there will be different
  hues of Azure that differ.
• There are infinitely many different hues of
  colour!
• (2) ? x ? y ( x my car y your car ( x
  is colour 1 y is colour1 ) v ( x is colour 2
  y is colour2 ) v ( x is colour 3 y is
  colour3 ) v ( x is colour 4 y is colour4 ) v
  ( x is colour 5 y is colour5 ) v ( x is
  colour 6 y is colour6 ) v ( x is colour 7
  y is colour7 ) v ( x is colour 8 y is
  colour8 ) v ( x is colour 9 y is colour9 ) v
  ( x is colour 10 y is colour10 ) v

24
Austere Nominalism

• This attempt to live without properties, and
  instead offer paraphrases, is called austere
  nominalism
• (sometimes ostrich or mirage nominalism)
• So austere nominalists can give a paraphrase for
  that sentence.
• But its infinitely long, and contains an
  infinite number of colour predicates.
• This is one of the facts that makes people wonder
  whether austere nominalism is true and whether we
  can live without properties.

25
Austere Nominalism

• So far weve looked at figuring out the
  commitments of theories.
• But we havent discussed how to weigh up those
  theories in light of those commitments.
• Lets talk about that to see why austere
  nominalism appears to have negatives.

26
Comparing Theories

• What criteria do we use?
• Well, thats not settled.
• We look at the costs and the benefits and then do
  the cost/benefit analysis.
• Heres some examples
• Avoid paradoxes and cohere with our beliefs.
• Offer an explanation.
• Parsimony.
• Simplicity.

27
Criterion One Avoid Paradoxes and Problems

• If P and Q entail a contradiction, you need a
  theory that either misses out P or Q, or explains
  how they dont entail a contradiction.
• Such paradoxes (the NSE paradox) plague those who
  believe in properties, and there are alleged
  paradoxes about material objects (statue/clay).

28
Criterion One Avoid Paradoxes and Problems

• A good theory will also cohere with things we
  know to be true (by necessity).
• And its generally better for it to cohere with
  things we intuitively think to be true.
• 224 should be true!
• Pockets should have holes!
• Some things are cars, or are blue!
• Blue is a colour!
• Of course, we can make sacrifices this is
  philosophy after all.
• And some things are always up for grabs
• (Spoils to the victor as Lewis puts it)

29
Criterion One Avoid Paradoxes and Problems

• Compare with ethics.
• A theory is awful if it says torturing five year
  olds for pleasure is fun.
• A theory has issues (but still believable) if it
  says you have to give up on some minor ethical
  belief say that speeding drivers are morally on
  a par with those who run over people.
• Sometimes we take these issues to be big enough
  to think the theory unbelievable.
• Alternatively we might take those issues as
  generating results.
• So we might take that issue as being a result of
  the theory.

30
Criterion One Avoid Paradoxes and Problems

• Similarly in metaphysics.
• Theories that cohere with intuition are better
  than those that dont.
• And some intuitions are more deeply held than
  others.
• So contradicting certain intuitions is more
  costly than contradicting certain other
  intuitions.

31
Criterion Two Explanatory Power

• Not only should your theory cohere with things we
  generally think to be true, it should explain
  other truths.
• For instance, there is a law concerning how fast
  objects that fall accelerate towards the planet
  Earth.
• Similarly, the are other laws concerning how fast
  objects accelerate on other planets.
• But all of those laws are explained by a single,
  more general, law concerning gravitation in
  general.
• So one truth (the general law concerning
  gravitation) explains other truths (the specific
  laws concerning gravitation on other planets).

32
Criterion Two Explanatory Power

• But some truths will be inexplicable.
• They will not be explained by other truths in
  your theory they are brute truths.
• Its generally thought to be a virtue for your
  theory to have as few brute truths as possible.
• In having less brute truths it has more
  explanatory power, and offers explanations where
  weaker theories just state things as inexplicable
  fact.

33
Criterion Three Parsimony about entities

• Sometimes called Ockhams Razor.
• Its a benefit to have less things in your
  theory.
• If youve got two exactly equivalent theories,
  say they both explain exactly the same things,
  but one has more things in it than the other,
  its clear you should choose the more
  parsimonious theory.

34
Criterion Three Parsimony about entities

• Example The dead body, me and the bloody axe.
• Theory A says I did it.
• Theory B says an invisible alien spacecraft did
  it.
• Example Physics.
• If there are two theories whereby theory one
  says one type of entity is responsible for some
  phenomena, and the other theory says fifty eight
  types of entity working in combination are
  responsible, its a bonus to pick theory one.
• Of course there might be a reason to favour a
  less parsimonious theory, say if youd seen the
  58 entities. Or you were the alien in the
  spacecraft.
• But then those theories wouldnt have equal
  explanatory power.
• More importantly, whilst the lack of parsimony is
  a cost it might not be a cost that outweighs
  certain other benefits.

35
Criterion Four Theoretical Simplicity

• Not only do we favour theories which are
  economical and have explanatory power we favour
  theories which are simple.
• Usually, this simplicity is captured by having
  few primitives.
• A primitive of a theory is a undefinable
  predicate.
• Lets have some examples.

36
Criterion Four Theoretical Simplicity

• Example one
• Maths.
• You could take __ is a triangle, __ is a
  square etc. as primitive predicates.
• As there are an infinite number of shapes, there
  would be an infinite number of primitives
• But most dont. We can explain what it is to be a
  triangle and a square
• x is a triangle df x has three sides which are
  connected at all and only their endpoints.
• x is a square df x has four sides which are
  connected at all and only their endpoints
• That would then explain all shape predicates in
  terms of three primitives (__ having n sides
  __ is an endpoint _is connected to __)
• Indeed these definitions and primitives can be
  supplanted by better definitions with a superior
  stock of primitives.

37
Criterion Four Theoretical Simplicity

• Example two
• You could take __ knows that P as primitive.
• But many people try to analyse it.
• So you might analyse it in terms of being a
  justified true belief.
• Think back to Gettier.

38
Criterion Four Theoretical Simplicity

• The consensus is that having less primitives is a
  good thing.
• In the same way that taking brute truths is a
  cost, taking on primitives is a cost.
• It means your theory is more complex.

39
The Cost/Benefit Analysis

• The idea is that once you figure out how a theory
  scores on these sorts of criterion (those listed
  are not exhaustive!) you can evaluate it.
• Where it does well on a criterion you have a
  benefit.
• Where it doesnt do well you have a cost.

40
The Cost/Benefit Analysis

• So the realists about properties score well on
  certain criteria.
• Their theory has one primitive __ instantiates
  __
• So it provides the benefit of theoretical
  simplicity.
• But it populates your ontology with lots of
  entities namely the properties.
• So it has issues with ontological parsimony.

41
The Cost/Benefit Analysis

• The nominalist, however, has no properties.
• They have a theory that is very ontologically
  parsimonious.
• But now we can return back to where we were
  before we went off on this tangent.

42
Austere Nominalism

• This attempt to live without properties, and
  instead offer paraphrases, is called austere
  nominalism
• (sometimes ostrich or mirage nominalism)
• So austere nominalists can give a paraphrase for
  that sentence.
• But its infinitely long, and contains an
  infinite number of colour predicates.
• Its that fact that makes people wonder whether
  austere nominalism is true and whether we can
  live without properties.

43
The Cost/Benefit Analysis

• The nominalist, however, has no properties.
• They have a theory that is very ontologically
  parsimonious.
• But now we can return back to where we were
  before we went off on this tangent.
• Their theory is very complicated.
• So much so, many people favour realism.

44
The Cost/Benefit Analysis

• Moreover, even if you are happy with that amount
  of primitives, there are other problems ahead.
• They might be able to paraphrase
• (2) Our cars are the same colour
• at the expense of theoretical simplicity. But
  some sentences look even more resilient to
  paraphrase.

45
The Cost/Benefit Analysis

• Try
• (3) Blue is a colour.
• Thats a bugger to paraphrase.
• It appears to assert ? x (x blue x is a
  colour)
• But thats to quantify over a property!
• Could paraphrase it as Everything that is blue
  is coloured
• Problematic in that if, by chance, all the blue
  objects were, say, whales then that would mean
  that Everything that is blue is a whale
• (3) Blue is a water borne mammal (?)

46
The Cost/Benefit Analysis

• Or try
• (4) There are as yet undiscovered physical
  properties.
• (5) Red resembles orange more than it resembles
  blue
• If we cant paraphrase these sentences at all,
  wed have a problem.
• I leave you to look at the literature concerning
  such paraphrases
• Although it was concerns like this that drove
  Quine to accept the existence of properties.

47
The Problem of Universals

• In the literature there is often said to be The
  Problem of Universals
• It is often advanced as a reason to believe in
  properties.
• Armstrong is the most famous contemporary
  proponent.
• There are lots of different interpretations of
  the Problem of Universals
• Everyone agrees on one thing it is poorly named.
• Its not a problem about universals at all! Its
  meant to be an argument for them!
• NB Sometimes called the One Over Many.

48
The Argument from Resemblance

• The interpretation Ill examine (which isnt the
  only one!) is to think its a problem about
  resemblance
• Universals are introduced to explain (or
  ground, or analyse) how two things can have
  something in common.
• We might also take this to mean how things can
  resemble one another.
• Is there a difference between those two?
• Well, thats just part of the problem of getting
  to grips with what the Problem of Universals is
  meant to be.

49
The Argument from Resemblance

• We arrange things into similarity classes.
• Example All the blue things are similar all the
  purple things all the men all the women.
• Some classes arent similarity classes.
• Example A class with you, me, a Burmese farmer,
  the left hands of the entire cast of Eastenders,
  Brad Pitts toilet, and the black hole Cygnus
  X-1.

50
The Argument from Resemblance

• Its not enough that things fall under the same
  predicate to be similar.
• Example x is F y is G, define H as being the
  predicate of being F v G.
• x is H and y is H, but they dont have anything
  in common (surely!)
• Its not a real resemblance.
• So we could make up a predicate that those
  dissimilar classes of entities fell under.

51
The Argument from Resemblance

• Properties would come to our rescue.
• Say Not every predicate is a property.
• Got to say that anyway because of NSE paradoxes.
• Things exactly resemble one another if and only
  if they have all their properties in common.
• Varying degrees of resemblance are matched by
  having varying numbers of properties in common.
• So whilst two objects both fall under the
  predicate H they may not resemble as they may
  still fail to have properties in common.

52
Recap

• So weve looked at some reasons to believe in
  properties.
• Weve looked at the basics of cost/benefit
  analysis, and how we weigh up which theories are
  better than other theories.
• Weve seen that living without properties
  allegedly gives you a complex theory.
• Moreover, we might have difficulty finding a
  suitable paraphrase at all
• Ive mentioned the Problem of Universals, and
  given you Armstrongs interpretation of it that
  we need properties to explain how objects
  resemble on another.
• Were done today for the motivations for
  believing in properties.

53
On with the show

• So, with that all in mind, lets move on to doing
  some ontology.
• Along the way, well see how other facets to how
  ontology is studied and practised.
• Today well look at properties.
• Do they exist? (i.e. should we be realists or
  anti-realists with regards to properties)
• If they do exist, what are they like?

54
Varieties of Realism

• This is where the terminology becomes rather
  confusing.
• Lots of people believe properties exist but
  they dont call themselves realists.
• In fact, they often go on to call themselves
  nominalists.
• Realism, with regards to properties, is usually
  to endorse the existence of properties as
  universals
• Whereas nominalism is taken to refer both to not
  believing in properties and to believing in
  properties but not as these universals

55
Varieties of Realism

• The term universal is normally reserved for
  properties that exist as sui generis entities.
• A sui generis entity is an entity in a category
  of its own
• That is, that things from that category cant be
  identified with things from other categories you
  already accept.
• Well come back to that notion in a bit.

56
Varieties of Realism

• There are divisions amongst those who believe in
  universals.
• They are divided along two dimensions
• Where are the properties?
• Which predicates correspond to properties?
• Connected Are there uninstantiated properties?

57
Varieties of Realism

• There are divisions amongst those who believe in
  universals.
• They are divided along two dimensions
• Where are the properties?
• Which predicates correspond to properties?
• Connected Are there uninstantiated properties?

58
Varieties of Realism

• If properties exist, where are they?
• Platonists think that the properties arent
  located anywhere.
• Theyre abstract and outside space and time.
• We saw some problems with that last week.
• Others say theyre in space and time.
• Locate them where their instances are located.
• So being a human is located where I am.
• And where you are.
• And where every other human is.

59
Varieties of Realism

• Heres the twist. Usually, such realists say the
  universal is entirely located at each instance.
• So whereas I am only entirely located at one
  place (a man shaped region), universals get to be
  multiply located
• Which is a bit weird (how can all of something be
  in exactly one place?)
• Example Red being 5m away from itself.
• Ill leave you to look into why they say these
  things.

60
Further Reading

• Parsons, J. 2007. Theories of Location, Oxford
  Studies in Metaphysics 3.
• Hudson, H. 2005. The Metaphysics of Hyperspace
  ch. 4.
• Gilmore, C. 2006. Where in the relativistic world
  are we? Philosophical Perspectives
• Armstrong, D. Various.

61
Varieties of Realism

• There are divisions amongst those who believe in
  universals.
• They are divided along two dimensions
• Where are the properties?
• Which predicates correspond to properties?
• Connected Are there uninstantiated properties?

62
Varieties of Realism

• Do uninstantiated properties exist?
• Platonists say yes, theyre all there in Platonic
  heaven.
• Aristotelians disagree somehow the universals
  depend on their being instantiated.
• If they do exist, where are they?
• If they dont exist, does that mean truths about
  uninstantiated properties turn out to be false?
• Example How can this be true
• (5) Red resembles orange more than it resembles
  blue
• If nothing is red, orange or blue and
  uninstantiated universals dont exist?

63
Varieties of Realism

• But there are other problems. Not every predicate
  can correspond to a property.
• Example There can be no property of not self
  exemplifying
• So which predicates correspond to a property?
  What universals/properties are there?
• Being a human? Being a monkey?
• Happy, Sad
• Depressed about being dumped by a crap
  significant other who then went on to run away to
  Barbardos with some girl called Julie?
• Red, Blue, Green?
• Crimson, Scarlet, Puce, Amaranth?

64
Varieties of Realism

• Also concerns about conjunctive, disjunctive and
  negation properties.
• If being a sword exists and being rusty exists is
  there a separate universal of being a rusty
  sword?
• If being a human exists and being a dog exists is
  there a separate universal of being either a dog
  or a human?
• If being a human exists is there a universal of
  not being a human as well?
• What are the conditions for a universal/property
  existing?

65
Varieties of Realism

• One answer is Armstrongs.
• He believes in sparse universals.
• The only way to find out what universals there
  are is a posteriori.
• The universals that exist are those posited by
  our best scientific theory.
• So the only universals will be things like having
  spin up, or being charged or having mass of 0.511
  MeV.

66
Varieties of Realism

• But if the universals are sparse, how does that
  deal with the motivations?
• Being annoyed is worse than being happy is
  true, but apparently being annoyed isnt a
  property.
• So youll need a paraphrase!
• Wasnt avoiding that what realism was meant to
  help with?

67
Varieties of Realism

• Or the argument from resemblance, which is
  Armstrongs favourite motivation.
• If being a human isnt a universal, we cant
  resemble one another by sharing that universal.
• We could resemble one another by being charged,
  or having the same mass in MeV, but other than
  that, we dont.
• You should go off and read how Armstrong tries to
  deal with this by using structured universals

68
Recap

• So weve
• Looked at motivations to believe in properties
• If we do believe in properties they are either
  sui generis (universals) or not. Again, more
  on this notion to come
• What properties are like i.e. what ones there
  are? Where are they?
• Whilst most people talk about these solely in
  connection with universals, it applies to all
  those who think properties exist.

69
Properties without universals

• I said universals were sui generis in a
  category of their own.
• Perhaps theyre not.
• Why should one care? What does it even mean?
• Well, recall one of the principles of choosing
  theories.

70
Comparing Theories

• What criteria do we use?
• Well, thats not settled.
• We look at the costs and the benefits and then do
  the cost/benefit analysis.
• Heres some examples
• Avoid paradoxes and cohere with our beliefs.
• Offer an explanation.
• Parsimony.
• Simplicity.

71
Comparing Theories

• What criteria do we use?
• Well, thats not settled.
• We look at the costs and the benefits and then do
  the cost/benefit analysis.
• Heres some examples
• Avoid paradoxes and cohere with our beliefs.
• Offer an explanation.
• Parsimony.
• Simplicity.

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Properties without universals

• Austere nominalists achieved parsimony by not
  believing in universals at all.
• The realist thus far discussed takes a hit on
  parsimony by introducing properties as a new
  category of entities.
• So, say, they have objects and properties.

73
Properties without universals

• But theres another way to be parsimonious
  without eliminating properties entirely.
• We can identify (alternatively, reduce which
  may or may not be the same thing) properties to
  things we already believe in.
• For instance, to preserve various conservation
  principles physicists believed in neutrinos
  tiny little, hard to detect particles.
• Its also the case that theres a lot of
  unaccounted for matter in the universe dark
  matter. Its very hard to detect, but must exist
  for various calculations to make any sense.
• A proposed theory might say that a whole new
  category of entity exists dark matter.
• A more parsimonious theory would say that the
  dark matter exists, but its just the neutrinos.
• Theory one has two distinct categories of
  entities (neutrinos/dark matter) whilst the other
  theory still has those categories, but theyre
  just not distinct.

74
Properties without universals

• In ontology, we might do the same.
• For instance, if you start by believing in
  objects you might be a realist about properties
  but exact parsimony by saying that properties
  really are just objects property is a
  sub-category of object
• And, as its a sub-category, property isnt sui
  generis its not in a category of its own
• However this would be a whacky reduction. Surely
  properties arent objects!
• Exception mereological nominalism / exploded
  object nominalism

75
Properties without universals

• But maybe if our ontology had more categories of
  things, we could do better.
• For instance, if you believed in concepts we
  might be on a winner.
• So you have objects and then, in addition, you
  believe in concepts.
• You might then identify the property red with the
  concept red.
• And say that an object instantiates red if and
  only if it falls under that concept.

76
Properties without universals

• These realists about properties would be often
  called nominalists (so they believe in properties
  but not universals, as universals have to be sui
  generis).
• There are serious problems with concept
  nominalism Im using it as an example to
  demonstrate parsimony not suggesting its
  perfect.
• Well see another example of nominalism next week
  when we introduce sets.

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Recap

• Weve
• Looked at the motivations for properties
• Looked at different versions of theories that
  believe in universals.
• Explained what sui generis means and given
  examples of theories with properties that arent
  sui generis

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Next Lecture

• Numbers.