Rigid Application

Michael JohnsonHong Kong University

0. OUTLINE

Outline

0. Outline1. Rigid Designation2. Rigid Application3. Biological Kind Terms4. Natural Phenomenon Terms5. Substance Kind Terms

1. RIGID DESIGNATION

Designation

For simplicity’s sake, let’s assume that ‘designation’ is a technical concept defined as follows:

A name designates the object it refers to.

Designation

For simplicity’s sake, let’s assume that ‘designation’ is a technical concept defined as follows:

A definite description ‘the so-and-so’ designates the unique object, if there is one, that is so-and-so.

Rigid Designation

A singular expression (e.g. ‘Aristotle’ or ‘the teacher of Alexander’) is a rigid designator

iff

The expression designates the same individual with respect to every possible world.

Rigid Designation

So the singular expression ‘Aristotle’ is rigid because one and the same person is Aristotle in every world where there is an Aristotle.

But the singular expression ‘the teacher of Alexander’ is non-rigid because different people are the teachers of Alexander in different worlds. For example, in other worlds, Speusippus was Alexander’s teacher.

Rigid Non-designation

Kripke says, however, that many general expressions are rigid, including:1. ‘hot’, ‘yellow’: Secondary quality predicates2. ‘ouranguatan’: Biological kind terms 3. ‘light’, ‘lightening’: Natural phenomenon

terms 4. ‘gold’: Substance kind terms

Today’s Fundamental Question

What makes a general term, as opposed to a singular term, rigid?

2. RIGID APPLICATION

2.1 Rigid Application Thesis

A general term G is a rigid applier

iff

If that term applies to an object O relative to the actual world,

then it applies to O relative to all worlds.

2.1 Rigid Application Thesis

Rigid Application Thesis RAT: A general term G is rigid iff G is a rigid applier.

Example: ‘Prime’

Clearly, ‘prime’ is a rigid applier (and hence rigid by RAT).

For if x is prime in world w, x is prime in all worlds.

(2, 3, 5, 7, 11, 13, etc. are actually prime but also necessarily so.)

Example: ‘Gold’

Intuitively, ‘gold’ is also a rigid applier (and hence rigid by RAT).

For if x is gold in world w, (intuitively,) x is gold in all worlds.

(It seems silly to suppose that chunk-of-gold X might instead have been drop-of-water Y.)

2.2 Adequacy of RAT

If Kripke was correct, and RAT is correct, then the following types of terms should be rigid:

1. Secondary quality predicates (e.g. yellow)2. Biological kind terms (e.g. ourangutan)3. Natural phenomenon terms (e.g. light)4. Substance kind terms (e.g. cesium)

3. SECONDARY QUALITY PREDICATES

RAT Prediction

If, for example, ‘yellow’ is a rigid applier, then if some object O is yellow in some world W, then O is yellow in any other world W*.

But W might equal W*, so if O is yellow in W, then O cannot be non-yellow in W. Otherwise, O would be yellow in some world (W) and not in some other world (W again).

RAT Prediction

If, for example, ‘yellow’ is a rigid applier, then if some object O is yellow in some world W, then O is yellow in any other world W*.

That is, any object O that is actually yellow (blue, red, etc.) could not persist through a change that made it a non-yellow (non-blue, non-red, non-etc.).

Painting and RAT

Painting and RAT

So we have an object O (= a wall) that is yellow in the actual world (in the past) which persists through a change that makes it non-yellow, that is, when it is painted red.

Painting and RAT

So we have an object O (= a wall) that is yellow in the actual world (in the past) which persists through a change that makes it non-yellow, that is, when it is painted red.

Therefore ‘yellow’ is not a rigid applier.

3. BIOLOGICAL KIND TERMS

3.1 Biological KindsFor our purposes here, a biological kind is a species, subspecies, or higher taxon (e.g. family, genus, phylum…).

As a criterion of adequacy, we suppose that any account of rigidity for general terms should count biological kind terms as rigid.

For example, ‘tiger’, ‘animal’, ‘mammal’, etc. should be counted as rigid.

3.2 RAT Prediction

If, for example, ‘tiger’ is a rigid applier, then if some object O is a tiger in some world W, then O is a tiger in any other world W*.

But W might equal W*, so if O is a tiger in W, then O cannot be a non-tiger in W. Otherwise, O would be a tiger in some world (W) and not in some other world (W again).

3.2 RAT Prediction

If, for example, ‘tiger’ is a rigid applier, then if some object O is a tiger in some world W, then O is a tiger in any other world W*.

That is, any object O that is actually a tiger (mammal, animal, etc.), could not persist through a change that made it a non-tiger (non-mammal, non-animal, non-etc.).

Laporte on Biological Kinds

“[A]ccording to cladism, a species goes extinct whenever it sends forth a new side species. This is so even if the lineage undergoes no change after sending out the side branch, so that earlier members are indistinguishable from later ones” (Laporte, 1997, p. 103).

RAT and Cladism

So, for example, in the chart to the right, A ceases to exist (A ≠ B) when it sends forth branch C.

But if C never comes to be, then A persists (A = B).

RAT and Cladism

So we have an object O (= a member of species B) that is a member of species A in the actual world and is not a member of species A in some world (the world where A sends off branch C), even though O has the same ancestry, DNA, ecology, history, etc. in both worlds.

RAT and Cladism

So we have an object O (= a member of species B) that is a member of species A in the actual world and is not a member of species A in some world (the world where A sends off branch C), even though O has the same ancestry, DNA, ecology, history, etc. in both worlds.

Therefore ‘species A’ is not a rigid applier.

4. NATURAL PHENOMENON TERMS

RAT on Natural Phenomena

According to RAT, if ‘light’ is a rigid applier, then if some object O is light in some world W, then O is light in any other world W*.

But W might equal W*, so if O is light in W, then O cannot be non-light in W. Otherwise, O would be light in some world (W) and not in some other world (W again).

Redshift/ Blueshift

Redshifts and RAT

Photons which were formerly ‘light’ can become non-‘light’, for example, if they are redshifted into the microwave spectrum.

Redshifts and RAT

Photons which were formerly ‘light’ can become non-‘light’, for example, if they are redshifted into the microwave spectrum.

This is actually the nature of the cosmic microwave background radiation: light emitted from stars traveling away from us redshifted into microwave radiation.

Redshifts and RAT

So we have an object O (= a stream of photons) that is light in the actual world (in the past) and is not light in some world (the actual world in the present), because it has been redshifted into the microwave spectrum.

Redshifts and RAT

So we have an object O (= a stream of photons) that is light in the actual world (in the past) and is not light in some world (the actual world in the present), because it has been redshifted into the microwave spectrum.

Therefore ‘light’ is not a rigid applier.

5. SUBSTANCE KIND TERMS

RAT on Substance Kinds

According to RAT, if ‘cesium’ is a rigid applier, then if some object O is cesium in some world W, then O is a cesium in any other world W*.

But W might equal W*, so if O is cesium in W, then O cannot be non-cesium in W. Otherwise, O would be cesium in some world (W) and not in some other world (W again).

Beta Decay and RAT

In beta decay, one of the neutrons of an atom (1 up quark and 2 down quarks) becomes a proton (2 up quarks and 1 down quark) via the flavor change of one of its quarks (from down to up). It retains the same number of quarks and nucleons.

Beta Decay and RAT

For example, a cesium 137 atom (55 protons + 82 neutrons = 137 nucleons) can decay to a barium 137 atom (56 protons + 81 neutrons = 137 nucleons).

Cesium 137 to Barium 137

Beta Decay and RAT

So we have an object O (= an atom) that is cesium in the actual world (in the past) and is not cesium in some world (the actual world in the present), because it has undergone beta decay and become a barium atom.

Beta Decay and RAT

So we have an object O (= an atom) that is cesium in the actual world (in the past) and is not cesium in some world (the actual world in the present), because it has undergone beta decay and become a barium atom.

Therefore ‘cesium’ is not a rigid applier.

CONCLUSION

RAT (the Rigid Application Thesis) gets the wrong results for all the intuitively rigid general terms:

1. Secondary quality predicates (e.g. yellow)2. Biological kind terms (e.g. ourangutan)3. Natural phenomenon terms (e.g. light)4. Substance kind terms (e.g. cesium)

Objection

But, says Michael Devitt,

“it is a mistake to think that the primary task of the rigidity distinction is to distinguish natural kind terms from nominal kind terms. The primary task is to distinguish kind terms that are not covered by a description theory from ones that are” (2005, p. 154).

Reply Part 1

If that’s the primary task of the rigid/ non-rigid distinction, then it performs poorly for singular terms.

Rigid, covered by description theory: ‘the actual teacher of Alexander’

Non-rigid, covered by description theory: ‘the teacher of Alexander’

Reply Part 2

And it performs poorly for general terms:

Rigid, covered by description theory: ‘continuous,’ ‘prime’

Non-rigid, covered by description theory: ‘gold,’ ‘ourangutan’

We might want a better theory of rigidity for general terms…

We might want a better theory of rigidity for general terms…See Johnson (forthcoming, hopefully).