Kripke's Meter-Stick
I've been having some difficulty understanding how Kripke in Naming and Necessity dissolves or removes the concept of essentialism from identification of entities across possible worlds.
Let's take the example of the meter-stick that Kripke brings up. Nowadays a meter stick is defined as:
Quoting John MacFarlane
So, a meter stick is defined circularly through the substitution of the caesium-133 atom's properties along with the speed of light.
So, here's the confusion of mine. Namely, if we assume that properties of names are what define them, as in the case of the standard meter stick, then how can we know that the same properties apply in any other possible world?
One solution to this issue is to assume that accessibility relations between possible world are the same as in the actual world. Or in other words, the laws of physics are the same in another possible world as in this one. Kripke never specifies any accessibility relations between possible worlds; but, I suppose it needs mentioning that for water to necessarily be H2O, or for the meter stick to maintain rigidity, one has to assume that the accessibility relations of our world are compatible with other possible worlds. But, get this... If we assume that accessibility relations are the same across possible worlds, then that assumes a form of scientific essentialism. This is because rigidity and necessary conditions are guaranteed through adhering to properties that are immutable, such as the laws of physics and nature.
Any thoughts about this?
Let's take the example of the meter-stick that Kripke brings up. Nowadays a meter stick is defined as:
Quoting John MacFarlane
Today, a meter is defined as the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second. A second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. So in effect, we have substituted the caesium-133 atom for the standard meter bar. The same points could still be made, but we’ll stick with the meter bar for simplicity.
So, a meter stick is defined circularly through the substitution of the caesium-133 atom's properties along with the speed of light.
So, here's the confusion of mine. Namely, if we assume that properties of names are what define them, as in the case of the standard meter stick, then how can we know that the same properties apply in any other possible world?
One solution to this issue is to assume that accessibility relations between possible world are the same as in the actual world. Or in other words, the laws of physics are the same in another possible world as in this one. Kripke never specifies any accessibility relations between possible worlds; but, I suppose it needs mentioning that for water to necessarily be H2O, or for the meter stick to maintain rigidity, one has to assume that the accessibility relations of our world are compatible with other possible worlds. But, get this... If we assume that accessibility relations are the same across possible worlds, then that assumes a form of scientific essentialism. This is because rigidity and necessary conditions are guaranteed through adhering to properties that are immutable, such as the laws of physics and nature.
Any thoughts about this?
Comments (39)
Yes, possible worlds are stipulated; yet, I'm highlighting the fact that their accessibility relations must be the same as those of the actual world to be able to rigidly refer to their status as rigid designators.
But accessibility relations are determined by the properties of the modal logic in use (basically which worlds can quantify over other worlds given certain properties like transitivity or Euclideanness), they aren't properties of the possible worlds themselves, right? I'm not sure if this is essentialism.
Well, yeah. It's somewhat a trite truism to state that an accessibility relation holds if we can change the axioms of the possible world's properties at will or at leisure? What do you think?
I mean if we are going to assume certain properties as equivalent to our own world, then we might as well restrict the domain of stipulating possible worlds to a certain set of circumstances. But, that just renders the whole issue as tantamount to nothing determinate.
I typically think of "accessibility" as features of the world that endow or enable us to speak about counterfactuals.
My point here is that if we have no sense of counterfactual definitiveness (or an accessibility relation that is true for all possible worlds, such as the laws of physics) defined in the axioms of a stipulated possible world, then all this seems to amount to is hand-waving.
Setting up a possible world to conform (altering the accessibility relations) to a certain set of circumstances instead of having it (rightly so) , the other way around of the world dictating or determining states of affairs.
What are you having difficulty understanding?
All this. It’s difficult for me to parse.
So, let me provide the rationale behind what I'm trying to say.
Now, with the above in mind, isn't Kripke setting up the properties of what constitutes "Nixon" as a rigid designator, as a certain feature of accessibility relations that adhere to some form of essentialism?
I feel as though Kripke is setting the cart in front of the horse when he talks about rigid designators, that are bona fide dependent on the actual world to be true. Again, hand waiving comes to my mind.
Or even another way. How is trans-world identification possible?
“Nixon” is a rigid designator so we know who we are talking about in other stipulated possible worlds. It’s a contingent truth that he was president because we can logically conceive of him not being president. It’s a necessary truth that he is not a cow, for example. We wouldn’t be talking about Nixon then.
We can logically conceive of him being called “Smith” in a possible world that he was adopted. However, “Nixon” is still a rigid designator because that is how we know we are talking about the same person. It’s a rigid designator, but that name given to him is a contingent truth.
See, this is like trying to have it both ways. We stipulate according to some criteria the rigidity of Nixon being a rigid designator according to some properties that are assumed. What are those properties?
Everything is defined circularly, by the way. That's how definitions work. All the words in a dictionary are defined in the dictionary by other words being defined in the dictionary. If you don't have any intuitive semantic grasp of some of those words, it's just one big circular mess and you'd be stuck.
Quoting Wallows
We don't know that anything in particular applies in any possible world. Possible worlds are a combo of our individual imaginings, our individual abilities to conceive of various things however we're conceiving of them, and things we're stipulating.
Is that so? What do you think, @Banno?
A metre is hence the same length in all possible worlds.
In some possible worlds "metre" is used to refer to a length other than one metre.
That's not circular.
Why can't I conceive of him being a cow? If he had a Nixon face, a Nixon personality, a Nixon Watergate scandal, and Ford was his VP, yet he had a bovine everything else, he'd be Nixon. I get @Wallows essentialism concerns. Necessary and contingent truths are just another way of saying primary and secondary qualities aren't they?
So is the essence of the meter stick its length and not that it's a stick. If it were in the form of a cat, is it still a meter stick. Is a meter stick the same as a metre stick. We don't even have a rigid name for it is seems.
Maybe. I’m not sure. AJ Ayer only accounted for the necessary a priori (analytic truths) and the contingent a posteriori (synthetic truths). Kripke added two more categories.
I think you missed the entirety of the OP. It is the properties of the meter stick that maintain its rigidity in all possible worlds where the same accessibility relations (laws of nature) are the same.
Then it is instantiated or obtains through something that cannot be disputed, such as the laws of physics or nature.
The metre stick is not rigid. It might be different lengths in other possible situations. But the metre is rigidly designated by "one metre"
And accessibility is not about laws of nature. It's more about which individuals are in which world. But the explanation needs some decent formal logic. Someone else might like to explain it for us.
We can't dispute the las of nature? Shoot the physicist then, we don't need them anymore.
Let's at least try and not be obtuse here. The length of the meter stick is rigid in all possible worlds where the accessibility relation of one world also guarantees nomological necessity in another. Those accessibility relations, or if you prefer, "properties" of said object are outlined in the OP's quoted text.
See:
https://en.wikipedia.org/wiki/Accessibility_relation#Philosophical_applications
So, that is to say, that the stipulation that the meter stick is the same as a meter, is true in all possible worlds, and talking otherwise would invoke some nonsense or senseless declarative statement.
Very droll.
But it isn't. The length of the stick might have be other than it was.
Did you mean "The length of the meter is rigid in all possible worlds"? That works.
Well, yes. Here's is what I'm referencing again:
Quoting John MacFarlane
Had the speed of light been any different in another possible world, then the above would simply not be true or nonsensical wrt. to define the length of a meter in that world. I don't see how you can quibble over that.
My point seems to be that there is no difference between the two. If we are to assume a possible world where the nomological necessity of the length of the meter stick is defined by the conditions quoted text in the OP, which obtains due to being the same as our world, then stating otherwise is nonsense.
I'm not being stubborn here, so help me out. What is a rigid designator other than a certain type of precise definition, where a definition of the form X is Y is reducible to X is X because there's perfect synonymity?
Could you provide an example of a flexible designator? My point will be (spoiler alert) that all designators are flexible.
What am I missing?
So the man who was first on the moon was Armstrong.
But someone else, perhaps Aldrin, might have been first, had things gone differently. Had things been different in this way, then the phrase "The first man on the moon" would have referred to Aldrin, and not to Armstrong.
But notice that in this alternate story, the name "Armstrong" still refers to Armstrong, and the name "Aldrin" still refers to Aldrin.
Kripke calls a designator (in this case a proper namer) rigid if it refers to the same thing in all such stories - that is, in all other possible worlds.
SO, a rigid designator refers to the very same item or individual in every possible world in which that individual exists.
In contrast, "The first man on the moon" refers to Armstrong in this world, but in some other possible world it refers to Aldrin. SO it is not a rigid designator.
An important side note: This is not to say that Armstrong could not have had a different name. In some possible world, Armstrong might have been named "Fred". But notice - and this is a point that seems to escape many folk - that Armstrong might have been named "Fred" is about Armstrong. So he is still rigidly designated, even if his name has been changed in another possible world.
Notice also that a possible world is just a story about what might have happened, had things been different. Some folk think that somehow these worlds blink into existence as a part of the logic of possibility. They don't.