rigid application michael johnson hong kong university
DESCRIPTION
Outline 0. Outline 1.Rigid Designation 2.Rigid Application 3.Biological Kind Terms 4.Natural Phenomenon Terms 5.Substance Kind TermsTRANSCRIPT
![Page 1: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/1.jpg)
Rigid Application
Michael JohnsonHong Kong University
![Page 2: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/2.jpg)
0. OUTLINE
![Page 3: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/3.jpg)
Outline
0. Outline1. Rigid Designation2. Rigid Application3. Biological Kind Terms4. Natural Phenomenon Terms5. Substance Kind Terms
![Page 4: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/4.jpg)
1. RIGID DESIGNATION
![Page 5: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/5.jpg)
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.
![Page 6: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/6.jpg)
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.
![Page 7: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/7.jpg)
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.
![Page 8: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/8.jpg)
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.
![Page 9: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/9.jpg)
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
![Page 10: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/10.jpg)
Today’s Fundamental Question
What makes a general term, as opposed to a singular term, rigid?
![Page 11: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/11.jpg)
2. RIGID APPLICATION
![Page 12: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/12.jpg)
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.
![Page 13: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/13.jpg)
2.1 Rigid Application Thesis
Rigid Application Thesis RAT: A general term G is rigid iff G is a rigid applier.
![Page 14: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/14.jpg)
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.)
![Page 15: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/15.jpg)
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.)
![Page 16: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/16.jpg)
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)
![Page 17: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/17.jpg)
3. SECONDARY QUALITY PREDICATES
![Page 18: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/18.jpg)
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).
![Page 19: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/19.jpg)
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.).
![Page 20: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/20.jpg)
Painting and RAT
![Page 21: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/21.jpg)
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.
![Page 22: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/22.jpg)
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.
![Page 23: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/23.jpg)
3. BIOLOGICAL KIND TERMS
![Page 24: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/24.jpg)
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.
![Page 25: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/25.jpg)
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).
![Page 26: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/26.jpg)
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.).
![Page 27: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/27.jpg)
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).
![Page 28: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/28.jpg)
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).
![Page 29: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/29.jpg)
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.
![Page 30: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/30.jpg)
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.
![Page 31: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/31.jpg)
4. NATURAL PHENOMENON TERMS
![Page 32: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/32.jpg)
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).
![Page 33: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/33.jpg)
Redshift/ Blueshift
![Page 34: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/34.jpg)
Redshifts and RAT
Photons which were formerly ‘light’ can become non-‘light’, for example, if they are redshifted into the microwave spectrum.
![Page 35: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/35.jpg)
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.
![Page 36: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/36.jpg)
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.
![Page 37: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/37.jpg)
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.
![Page 38: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/38.jpg)
5. SUBSTANCE KIND TERMS
![Page 39: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/39.jpg)
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).
![Page 40: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/40.jpg)
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.
![Page 41: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/41.jpg)
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).
![Page 42: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/42.jpg)
Cesium 137 to Barium 137
![Page 43: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/43.jpg)
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.
![Page 44: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/44.jpg)
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.
![Page 45: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/45.jpg)
CONCLUSION
![Page 46: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/46.jpg)
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)
![Page 47: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/47.jpg)
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).
![Page 48: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/48.jpg)
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’
![Page 49: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/49.jpg)
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’
![Page 50: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/50.jpg)
We might want a better theory of rigidity for general terms…
![Page 51: Rigid Application Michael Johnson Hong Kong University](https://reader035.vdocument.in/reader035/viewer/2022062412/5a4d1aec7f8b9ab05997b10a/html5/thumbnails/51.jpg)
We might want a better theory of rigidity for general terms…See Johnson (forthcoming, hopefully).