Kripke: Identity and necessity

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Kripke Identity and necessity

• Nyelv és elme, 2007 tavasz
• Jakab Zoltán

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Are there contingent identity statements?

• Are there contingent identity statements?
• Senses of identity
• 1. Quantitative one and the same (my wedding
  ring)
• 2. Qualitative exactly similar (two brand-new,
  grey two-stroke Trabant 601s)
• 3. Personal identity, in the psychological sense
  (largely irrelevant in this context who am I,
  what kind of person, etc.)
• 4. What needs to be distinguished from 1. role
  filling. (John is a teacher. Contrast Mary
  Katharine Horony is Big Nose Kate) These cases
  are treated differently.

Big Nose Kate (1850-1940)
Tombstone, Arizona
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An argument

• (1) Substitutivity of identity
• ?x?y(xy) ? (F(x)? F(y))
• (2) Necessity of self-identity
• ?x ? (xx) ? means necessarily
• (This is not an uncontroversial notion, but we
  accept it now.)
• Substitute (2) in (1)
• (3) ?x?y(xy) ? (? (xx) ? ? (xy))
• that is (just to see the parallel)
• ?x?y(xy) ? (necessarily_identical_to_x(x) ?
• necessarily_identical_to_x(y))

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• But we can simplify (3), because the antecedent
  of the second conditional ? (xx) is
  satisfied for each and every entity x. So we get
• (4) ?x?y(xy) ? ? (xy)
• So, (4) says if two entities x and y are
  quantitatively identical, then they are
  necessarily quantitatively identical. (Worries
  could be raised about this conclusion due to (2),
  but if (2) is accepted, then the conclusion
  follows by logic.)
• Of course Nothing remotely similar is true of
  qualitative identity (the Trabants) nor of role
  filling (If John is a teacher, it does not follow
  that he is a teacher necessarily. He may quit his
  job tomorrow in fact, he might have been a car
  mechanic from the start.)

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The truth of ?x ? (xx)

• A worry can be raised about non-existent objects
  are they necessarily self-identical?
• Set this aside, says Kripke, and restrict the
  application of necessarily to cases where the
  objects mentioned exist.
• There are other worries that well address later.
• Next issue de re de dicto modality. ? This
  needs a digression

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De re and de dicto modality

• Remember de re means concerning the thing.
• De re modality modal terms apply to the
  possession of an attribute by an object
• De dicto modality modal terms apply to a
  statement or proposition. (concerning the
  proposition)
• Two examples follow.

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• The number of gospels necessarily exceeds three.
• De dicto reading
• The statement that the number of the gospels
  exceeds three is necessary
• necessarilythe x x numbers the gospels(xgt3)
• FALSE there are in fact four gospels, but that
  is not necessarily so.
• De re reading the number of the gospels (i.e.,
  the number four, the thing itself) necessarily
  exceeds three.
• the x x numbers the gospels necessarily(xgt3)
• TRUE (4gt3 is necessary)

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• If I am sitting, then I am necessarily not
  standing.
• De dicto reading the statement that if someone
  is sitting then she is not standing is a
  necessary one, so on de dicto reading, the above
  sentence is TRUE.
• This is because sitting and standing are
  disjunctively related sitting applies to a
  state of the body to which standing does not
  apply. That is, if thats how we use our words,
  then the above statement cannot be but true. (De
  dicto) necessity depends on how we describe the
  world.
• De re reading if I am sitting, then it is
  necessary that I am not standing. This is FALSE.
  It is a property of me that I am sitting at a
  given time, but not a necessary property. I could
  have been standing at that time.

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De re modality is the more controversial idea.

• Can a things possession of its properties be
  regarded necessary? This issue divides
  philosophers.
• E.g., Quine rejected de re modality, and accepted
  only the de dicto reading. On the de dicto
  interpretation only statements or propositions
  are said to be necessary.
• Kripke, on the other hand, accepted de re
  modality. This leads to essentialism (the theory
  of natural kinds).

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Natural kinds

• Natural kinds (water, gold, electron,
  electromagnetic field, etc.) have essential and
  contingent attributes.
• For instance, water is essentially H2O. If that
  stuff (e.g., the one which comes from faucets)
  did not have the chemical structure H2O, then it
  would not/could not be what it is.
• On the contrary, temperature is a contingent
  property of water.
• Underlying this notion is the idea of
  metaphysical realism the world is the way it is
  (nature has its joints) independently of how we
  conceive of it.

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Natural kinds continued

• Realist intuition It is a mind-independent fact,
  for instance, that two elephants are more similar
  to one another than an elephant to a butterfly.
• Two intuitively plausible ideas (1) categories
  in the world are independent of our conceptions
  of them, (2) some properties play more important
  role than others in distinguishing objective
  categories from each other. Categories or types
  have essential properties (and contingent ones).
  Being essential, of course, is category-relative.

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• For example, take two samples of liquid, if both
  have the chemical composition H2O, then they are
  of the same (chemical) kind, regardless of the
  fact that one has the temperature 2 ?C, and the
  other 90 ?C. So, chemical composition is an
  essential property it outlines categories, or
  natural kinds, in nature. However, temperature is
  also a natural kind (MKE of molecules), or so it
  is assumed by Kripke. So a bottle of water and a
  bottle of alcohol can have the same temperature
  at a time, and be in the same objective category
  in that respect. Finally, there are properties
  that are not really essential for any category
  i.e., ones that do not outline natural kinds. An
  example is, being alive from t1 to t2. Another
  example of such properties is mind-dependent
  attributes, like being red. All and only red
  objects do not have anything in common
  mind-independently all they have in common is
  that they look red to us.
• Some think very few properties are essential in
  the sense of corresponding to natural kinds,
  namely only fundamental physical properties.
  Others are inclined to say, being a natural kind
  is a matter of degree.

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De re and de dicto identity statements.

• Next example
• The first person in space might have been Alan
  Shepard.
• De dicto reading
• Possiblythe x 1st_person_in_space(x)(xAlan
  Shepard)
• It says that there is some counterfactual state
  of affairs in which A.S. was the first person
  into space. TRUE
• De re
• the x 1st_person_in_space(x)possibly(xAlan
  Shepard)
• This says that the person who happened to be the
  first into space (i.e., Gagarin) is such that
  there is some conterfactual state of affairs in
  which he is (identical with) A.S. FALSE.

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Another interesting case

• It is necessary that Mark Twain is Samuel
  Clemens.
• First, note that since there is no description in
  this sentence, just names, scope ambiguity of the
  sort shown above is missing too.
• In de re reading, this is true. The person
  referred to by Mark Twain is such that he is
  necessarily identical with the person referred to
  by Samuel Clemens.
• In de dicto reading, however, it is also true.
  Given how we use these proper names (considering
  also that, for Kripke, names are rigid
  designators), the statement Mark Twain is Samuel
  Clemens cannot be false.
• This however, raises an interesting problem

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There is a counterfactual possible world

• in which, hm, a numerically distinct person has
  the name Mark Twain, whereas Samuel Clemens
  referred to the very same person as it does in
  the actual world. That is

Actual world
Counterfactual world (W2)
- Arrows indicate reference - Transparency
assumed (Kripke)
Samuel Clemens
Samuel Clemens
Mark Twain
Mark Twain
Problem If Necessarily, Mark Twain is Samuel
Clemens is true both de re and de dicto, then
what reading expresses the above possibility,
namely that in W2, Mark Twain is Samuel Clemens
is apparently false, so this sentence cannot be
necessary after all.
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Solution

• One of the names should be swapped for a
  description, say
• The person called Mark Twain in W2
• Now of course, the sentence
• The person called Mark Twain in W2 Samuel
  Clemens
• is false, and this will be our way to interpret
  the utterances in W2 of the sentence Mark Twain
  is Samuel Clemens which denizens of W2 take to
  be false.
• Another way to put the point Mark Twain in our
  world and in W2 is not the same name (they need
  to be indexed apart, e.g., Mark TwainA, Mark
  TwainW2), because their reference differs. Now
  Mark TwainA is Samuel Clemens remains true (and
  necessary) whereas Mark TwainW2 is Samuel
  Clemens will be necessarily false.

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If there are two descriptions in a sentence, then
there are three readings of the modal form

• Kripkes example Necessarily, the inventor of
  the bifocals is Americas first Postmaster
  General.
• 1. De dicto reading it says that the proposition
  The inventor of the bifocals is the first
  Postmaster General of the US is necessary.
  (I.e., whoever filled one role filled the other
  by necessity.) FALSE
• 2. Intermediate reading the guy who is the
  inventor of the bifocals is such that he
  necessarily filled the role of Americas First
  PG. FALSE.
• 3. De re The guy who happened to invent the
  bifocals, and the guy who happened to be the
  first postmaster, are one and the same, therefore
  necessarily so. TRUE.

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Quiz

• Given the Russellian formalism of a sentence
  containing two definite descriptions, insert the
  necessary operator in three different places
  corresponding to the three readings on the
  previous slide.

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Kripke on tagging (97-8)

• Names simply refer, they do not describe their
  objects in any way (p97).
• Here is Kripkes view on assigning names to
  objects
• (i) Tagging can be made in all kinds of different
  ways.
• (ii) It is a contingent fact that we tag heavenly
  bodies and other objects in this, rather than
  that, way.
• (iii) However, once we in fact perform a given
  tagging (say, in the actual world) then the tags
  assigned will be description-independent rigid
  designators.
• (iv) Plus, remember, numerical identity is
  necessary.
• (v) What follows Identity statements using any
  pair of names that we please are necessary, if
  true.

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Rigid designators

• They presuppose transworld indentity, which is a
  problem notion (102-3).
• Kripkes reply transparency (104). Venus in one
  and the same object in every possible world where
  it exists.
• Transworld identity of properties is accepted as
  well this is even more crucial in comparing
  worlds.

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Modes of truth

• A priori (knowable without further experience,
  via reasoning1) vs. a posieriori (need further
  experience to decide2)
• and
• necessary vs. contingent
• come apart.
• NOTE a priori and a postariori are epistemic
  notions they have to do with our knowledge
• Necessary vs. contingent are metaphysical notions
  they concern how the world is (independently of
  our knowledge) or how it might have been
  independently of thought
• Recall modal facts!

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Contingent a priori

• The standard meter rod in Paris is one meter
  long.
• We know a priori that whatever the length of the
  bar that is regarded as the meter standard, that
  length will be called one meter since the bar
  is used to set the standard. All this comes from
  convention.
• BUT that length can vary in different worlds. It
  is not necessary that the bar used as the meter
  standard is of the same length in every possible
  world.

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Quiz

• Take this statement
• Necessarily, the standard meter rod in Paris is
  one meter long.
• What is its de re and de dicto reading? Which is
  true, and which is false?

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A posteriori necessity

• Knowledge of the essential properties of natural
  kinds belongs here. Pure reflection without
  empirical science would have never taught us that
  water is H2O.
• Kripkes example the lectern (formal argument,
  p108) the self-identity of particulars is
  necessary

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The wooden lectern

• Morals drawn
• (1) in order for something to be the very object
  it is, it has to be made of the same lump of
  material. (This wooden lectern could not have
  been made of ice) So quantitative identity of
  the material constituting a particular object is
  essential for the quantitative identity of the
  object itself.
• (2) The necessity in question is a posteriori.

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The self-identity of particulars

• The Necessary identity of an object with itself
  is not an uncontroversial notion.
• Part of this idea is, despite changes in its
  properties, the object remains the same. Mars was
  the same object millions of years ago, when it
  had lots of liquid water on its surface, for
  instance.
• However

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• Theseuss ship type of objections does my bike
  become a different object gradually as its parts
  get replaced over the years?
• If I have a hammer out of which I create a
  screwdriver i.e., out of the same chunk of
  material do I suddenly have a different object,
  or do I have the same object with slightly
  different properties?
• The self-identity of human beings a human being
  at the age of 2, and at the age of 30, say, is
  constituted by a completely different chunk of
  matter, yet we want to say that she is one and
  the same person...
• Kripkes theory requires a more complete account
  of indentity.

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Back to Kripke

• Claim Contingent identity statements involving
  names arise from misdescribing situations in
  various ways. Take
• (5) Hesperus might not have been Phosphorus.
• We might take this to involve descriptions, not
  proper names
• (6) The heavenly body seen in the evening sky
  might not have been the heavenly body seen in the
  morning sky.
• (6) is true, but it is misdescribes what was
  said in (5). (5) is a statement of identity
  between objects.

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Rigidifying descriptions

• The definite description the author of Hamlet
  picks out different people in different possible
  worlds.
• But, the definite description the actual author
  of Hamlet picks out, in all worlds, the person
  who is the author of Hamlet in our world W.
  Shakespeare.
• This is a rigidified description, which has its
  reference fixed it picks out the same person in
  every world, even in worlds where W.S. failed to
  author Hamlet.

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Names and descriptions (111-2)

• Even if we suppose that the reference of a name
  is fixed by a description, the name will not be
  synonymous with the description.
• Instead, the name will refer rigidly to its
  object, even in worlds where the object does not
  satisfy the description by which it is picked out
  in the actual world.
• Example water is the waterish stuff in this
  world not so in many other worlds. However, the
  word water refers to the kind of stuff which is
  our waterish stuff (namely H2O) in every possible
  world, even though we fixed its reference here by
  means of a contingent attribute.

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On the identity of kinds.

• Kripke Terms that refer to essential properties
  are rigid designators they designate the same
  property in every possible world.
• Intuition behind
• Water is H2O that kind of liquid in the glass
  is the very one to which the scientific
  characterization H2O applies. One and the same
  kind is designated by two different terms.
• Temperature is MKE of molecules If you have
  molecular oscillation, thereby you have
  temperature and vice versa.

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• When we imagine that in another world W2 water is
  not H2O, what we imagine is that waterish stuff
  is not H2O. (Therefore the word water in that
  world is different in meaning from our word
  water there are two different words here,
  which need to be distinguished, say, by indexing
  (waterA, waterW2). This we can imagine
  (remember the Mark Twain case).
• But, on pain of contradiction, we cannot imagine
  that H2O is not H2O, that some stuff has a
  particular essence and does not have it.

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• A number of philosophers have noted later that
  there is another thing what we can imagine
• Suppose some scientists discover that chemical
  theory (or thermodynamics) has gone totally wrong
  because some chemists/physicists made a few
  severe errors in their exmeriments and
  theorizing. Thus, it turns out that, say, the
  periodic system of elements needs to be redrawn.
  As a consequence if this, we have no longer any
  reason to hold that water is H2O. Most plausibly,
  it turns out, water is some other kind, in the
  actual world, and in all other possible worlds as
  well.
• Thus we can coherently imagine that Water is
  H2O is necessarily false, but not that it is
  contingently false.

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Heat is not the mean kinetic energy of molecules

• Another example of misdescription heat is
  identified by one of its contingent attributes,
  namely how it feels to us.
• True, the same feeling might have been evoked by
  some other physical cause. Under this
  (mis)description, Heat might not have been MKE
  comes out true.
• p114 the motion of molecules is rigid, says
  Kripke. At least this description picks out an
  attribute motion, or kinetic energy, of some
  particulars (of some molecules). Its like the
  deed of Shakespeare which made him famous.
• the author of Hamlet picks out a particular
  that has some attribute (a contingent one). So
  there is a subtle disanalogy between these two
  uses of definite descriptions.

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On the mind-body problem

• The basic disanalogy
• (i) heat might not have been MKE
• (ii) Pain might not have been C-fiber firing
  (i.e., it might not have been identical with its
  actual neural correlate).
• (i) is understood thus The kind of sensation we
  have on contacting warm/hot things might not have
  been caused by MKE, but rather, but something
  else.
• (ii) cannot be understood this way

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• for (1) the way we feel it is essential for
  being in pain is cannot be pain if it does not
  hurt, nor can it hurt without it being pain,
  moreover (2) the corresponding brain state type
  is also picked out by an essential
  (physiological, biochemical) attribute.
• Thus we have two rigid designators, and if they
  pick out the same thing in the actual world, then
  they do so in every possible world.

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The whole argument, reconstructed

• (1) There are two rigid designators two ways of
  picking out something by an essential property.
• (2) We also have an identity statement between
  the two things picked out this is the
  materialist thesis. Pain is a brain state of some
  sort.
• (3) Therefore (given the heat-MKE disanalogy) we
  should not be able to imagine that pain
  sensations could have existed without the
  corresponding brain state.
• (4) But we can imagine that pain sensations could
  have existed without the corresponding brain
  state.
• (5) Materialism at least the identity thesis
  is false.

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Does this argument generalize to functionalism?
(notes on endnote 17)

• We also seem to be able to imagine that someone
  is in a brain state that does occupy the
  appropriate causal role vis á vis stimuli and
  behavior (causes yelling, avoidance, etc.) yet it
  does not feel like pain. The same is suggested by
  the absent qualia (and the zombie) argument.
• The conclusion of these arguments is the same as
  what is suggested by Kripke, namely that pain is
  not identical with either a physiological or a
  functional state.

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How can we reply to this argument?

• For instance, we can say the following.
• What we can and do imagine, in Kripkean terms, is
  not that pain might not have been the
  brain/functional state it in fact is (i.e., that
  the identity is true in the actual world but
  false in some counterfactual possible worlds).
• What we really imagine (and what we can
  coherently imagine according to Kripkes account)
  is that this theory of pain is actually false
  that the two rigid designators do not pick out
  the same thing in the actual world (and hence not
  in any possible world either).
• That is, Kripkes theory is compatible with
  physicalism. (It had better be although D.
  Chalmers picks up the same line arguing that from
  epistemic premises we can reach dualist
  ontological conclusions.)

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