Notes on Kripke's "Naming and Necessity," Lecture 1, Part 1 of 2 (pp. 22-53)

1. On sense and reference

On page 30 of Naming and Necessity, Kripke says, 

If 'Aristotle' meant the man who taught Alexander the Great, then saying 'Aristotle was a teacher of Alexander the Great' would be a mere tautology. But surely it isn't; it expresses the fact that Aristotle taught Alexander the Great, something we could discover to be false. So, being the teacher of Alexander the Great cannot be part of [the sense of] the name.

Let us suppose that a student learns the name “Aristotle" by learning that 

(P) Aristotle was a teacher of Alexander the Great. 

The typical student will assume that Aristotle was a human who lived at a particular historical time, and could further deduce that Aristotle was a person of competence and reputation. Further deductions, based on knowledge of history, could include that Aristotle was a man, that he lived well into his adult years, and so on. Thus, P attributes a property to a person (from which other properties can be deduced), but our student has no way of picking out that person apart from this property. So what does “Aristotle" mean to the student? Just whatever properties can be deduced from the description.

Still, a reference has been made, and we want to say that the student has learned something about an actual person named Aristotle. Regardless of whether or not the student knows anything more about Aristotle, we want to say that the student can now refer to the actual person who history tells us was named Aristotle. Indeed, our student can respond to P by asking questions about Aristotle, and anyone listening would understand who they were referring to. 

On the one hand, we have what the name means to the student; on the other hand, we have the meaning of the name which is grounded in history. The student does not know the history, but must presume that it is reliable. This, more than anything else, is required for the student to accommodate the name.

If the lesson was interrupted by a news broadcast informing the world that Aristotle was not in fact a teacher of Alexander the Great, our student would not be confused about the meaning of the word “Aristotle." They would not think the whole lesson was a sham, or a hoax. They would just suppose that they had been talking about a person with roughly the same properties as they had assumed, though lacking the property of having taught Alexander the Great. They might ask questions to confirm this, such as, “But Aristotle was a teacher at that time, right?” “No? Well, he was a very well educated and highly respected man for those times, right?” “No? Well, he was at least a man at that time?” If all such questions were answered in the negative, our student would find the name “Aristotle" meaningless—which is to say, they would not know how to use the name at all. They would need another description. On top of that, they would question the reliability of the teacher and perhaps the school and other cultural institutions.

Which is to say, trust in the circumstance of instruction is crucial for the student to accept that “Aristotle" is the name of Aristotle, so that the student understands that their knowledge of Aristotle is not exhaustive. Still, if we ask what “Aristotle" means to them, we get a list of descriptions. What does “Aristotle" mean to the culture as a whole? Also a list of descriptions? If not, then what?

If the sense of “Aristotle" is a culture’s discursive knowledge of Aristotle, then P expresses one of its facts. The student learns P and understands that there is an interconnected body of knowledge of which P forms a small part. Each idea in this web of knowledge is a Fregean sense, a way of identifying or understanding Aristotle by description.

Yet, we want to say that there was a real person named Aristotle which determines whether the descriptions are true or false. We could have some false beliefs about Aristotle, after all. Thus, we want to say that the name refers and that the ideas are different competencies to correctly (or incorrectly) refer to Aristotle, and also to correctly (or incorrectly) reason about Aristotle. 

To say that the sense of a description is a set of truth conditions is to say that a description expresses a competence which can be judged to be either true or false according to an external standard of measurement. The sense of a description therefore depends on there being an external standard of measurement. So, our student must accept that there is a standard for identifying true statements about Aristotle before they will accept that "Aristotle" refers to anybody at all. They need not be able to employ the standard—the standard itself is not communicated, but its existence is presupposed. This is why the student trusts the institution and accommodates the information.

The common use of P is to state a contingent fact about Aristotle. This is how the attribution is made: the speaker meaning is that we are attributing a contingent property, and not a necessary property, to the name Aristotle. Thus, in a normal classroom setting, P attributes a property to a person while implicating that the truth of the attribution is contingent on a body of historical facts about the person so named. The sense of the name is derived from this contingency.

If we were to explicate the full sense of the name “Aristotle,” it would be something along the lines of, “the person so named in accordance with our knowledge of historical facts.” To say P (in the given classroom situation) is to convey this sense. If all of the historical facts were proven false, there would be no sense at all to the name, and we would have no claim to its proper use. 

Imagine a portrait of Aristotle, and we point to it to show our student who he was. The student asks, “Ah, Aristotle was a man.” The teacher replies, “No!” The student is surprised, and says, “But he has a beard!” The teacher says, “No, no. That’s not what Aristotle looked like at all.” “Ah, um . . . Okay,” the student replies, confused as to what the picture was supposed to show.

Kripke wants to reject the notion of sense entirely (with respect to proper names), and claim that names just refer. His initial argument is that if a name meant one of its descriptions, then the attribution of the property so described would be a “mere tautology."

This is not clear. Imagine a speaker teaches P as a definition of “Aristotle.” In that case, it is a tautology. Would that be wrong? In what sense? Only in the sense that this is not how P is normally used. Okay, but similar cases of the same form of P are used as definitions, and it is not a mistake to use sentences this way. The point is, whether or not P is a tautology is a matter of how it is used.

2. On necessary and a priori truth

Consider the difference between P and

(Q) Three is a prime number.

In normal cases, the speaker meaning of Q implicates this as a necessary truth. We are not reporting a contingent fact. We can imagine otherwise—if, for example, a student is looking at a list of prime numbers in order to find an example of one, and sees “3" on the list. The student reports Q, not knowing whether or not this is a necessary truth. The speaker meaning is just to report what is on the list, and that is a contingent fact about the list, not about prime numbers. However, in this case, we can say the student does not understand what “prime number” means. 

We want to say that the sentence meaning really is an analytic truth, but this is only because we are so accustomed to regarding it that way. Of course “three" does not mean “a prime number,” but we still regard it as necessarily true. We can say Q is a tautology in so far as it follows deductively from our axioms. This is truth by virtue of the meanings of “three" and “prime number,” but that is speaker meaning. A person who understands prime numbers and the number three may fail to see that Q is a necessary truth. They may require a mathematical demonstration; and even upon receiving one, they may have doubts. We could say that they have not fully grasped the meaning of the terms, in so far as they are unable to produce the same results that we do with those concepts. Yet, they seem to understand the concepts. They just doubt that the mathematical conclusions are necessary. How can we be sure that three cannot have a factor in addition to 1 and itself? To prove this, we will have to get them to accept some basic axioms. If they are not willing to accept any as necessary truths, then they will never accept Q as such. Have they therefore misunderstood the meanings of the terms? What exactly have they missed, apart from the fact that Q is necessarily true?

How is P any different? The meaning of “Aristotle" is determined by our body of contingent knowledge. The truth of P is necessary to the extent that our body of historical knowledge is necessary. We do not know if the man named Aristotle could have not been the teacher of Aristotle. It may be that the universe is such that Aristotle had to have been the teacher of Aristotle. Thus, we might say that if P is true, it is necessarily true. However, we do not know that P is true by appealing to axioms; for us, it is contingent.

Let’s say our troubled student thinks that P is a necessary truth. If historians determine that Aristotle actually was not a teacher of Alexander the Great, our student will attempt to correct them. “No, no,” our student says, “Aristotle was the teacher of Alexander the Great, by definition! What you mean to say is that Aristotle did not do all of the other things that you normally associate with the man.” Our historians can point to the fact that the teacher went by a different name, but our student replies, “So what was Aristotle’s name back then?”

Our student is making a mistake, but of a curious kind. They agree with all of the facts. They just define “Aristotle" idiosyncratically, such that P is a priori true.

Is the truth of P determined by the meanings of “Aristotle" and “the teacher of Alexander the Great”? We want to say “no,” because P expresses a contingent relationship, but this is the speaker’s meaning, not the sentence meaning. The sentence can be used differently, depending on how we choose to define “Aristotle.” Truth is not determined by sentence meaning, nor is the distinction between contingent and necessary truth a matter of sentence meaning. It is a matter of how the sentence is intended.

Kripke’s problem might be this: He believes names require necessary conditions for their meaning, and not simply contingent conditions. He thinks there must be a use of “Aristotle" that expresses a necessary relation and not a merely contingent one. While all of our knowledge of Aristotle might turn out to be false, he could say, we are still referring to Aristotle. The problem, perhaps, is that the only necessary relations of this sort are what I think he calls “baptisms.” He requires a perfect sequence of baptisms, through the centuries, where the name “Aristotle" is traced to us directly from the source. The necessary meaning of “Aristotle" is the baptismal meaning fixed through a causal chain of references.

If this is true, and names are only meaningful via baptism, then we could never give a proper name to an indeterminate person. Let’s say Jennifer the security guard has lost her job. I assume, without evidence, that she will be replaced, and I decide to refer to her eventual replacement as “Jennifer Two.” This works with my circle of acquaintances, and we all get used to this new name before a new guard is hired. Finally, a man is given the position, and a friend tells me, “Jennifer Two is a man! His name is Ralph.” We may still prefer to call the new guard Jennifer Two. I can say “Jennifer Two is Ralph” to somebody confused about who I am referring to with the name “Jennifer Two.” However, the meaning of Jennifer Two preceded the baptism of Jennifer Two as Ralph. The meaning referred to whoever would be the person to fit the right description. The fact that it is Ralph is a contingent truth.

Kripke might say that “Jennifer Two” is not a proper name, and Ralph would probably agree! But what is the basis for this? Why can’t proper names be decided before a baptism?

Imagine parents who decide on the names of their children before they are biologically conceived. They refer to “Casey,” knowing that will be the name of their first born regardless of sex or gender, and before there is any pregnancy at all. Then they have a baby and name it Casey. Were they not talking about Casey before the official naming of their child? It seems they were, and the name had meaning for them. It referred to whatever child would eventually fit the description.

Imagine that they have a child but at the last minute decide to name it Chris. When they announce the birth, their friends ask, “How is Casey?” Are the friends referring to Chris? Yes, of course, though now we can say it is with the wrong name. Was it the wrong name before the child was named Chris? No. The name was simply replaced.

It might be that Casey never exists, and they never have a child. That does not mean the name was meaningless. It means that the description was never true.

Okay, Kripke might say, a baptism need not involve a reference to an existing being. It can pick out a being that does not exist in the actual world, but still exists in possible worlds, such that the name picks out the same individual in all possible worlds in which that individual exists. But here we are determining the meaning of the name by appealing to the definite description!

Kripke seems tied to two different ideas: (1) the meaning of a name is fixed by a causal chain of baptisms; and (2) a name is not a definite description. Are these ideas related?

If a baptism can occur without a causal chain, and by virtue of a description alone, then (1) and (2) are false.

3. Side note on Searle's "Proper Names"

Kripke mentions Searle’s 1958 paper on proper names. In it, Searle makes a lot of points similar to my own, but then he goes in a strange direction. He says proper names are “pegs on which to hang descriptions”—their existence being attributed to the pragmatic role of allowing for public acts of reference without description. Yet, he claims this is so that we are not “forced to raise issues and come to agreement on what descriptive characteristics exactly constitute the identity of the object.” His argument is, first, that if it were otherwise, proper names would just be abbreviated descriptions, and would have no purpose. Their function is therefore to refer without explicitly attributing any particular properties. So the question of what properties describe what is named need not arise, as Searle says. But here we should remember that this only works when a shared set of descriptions is presupposed. And if that is the case, isn’t the name just a shorthand for what has already been established? What is really being avoided here? Nothing at all, or so it seems.

Then Searle leaps to this conclusion: “Thus the looseness of the criteria for proper names is a necessary condition for isolating the referring function from the describing function of language.”  Huh?  First he said there was necessarily no criteria, and now it is “loose" criteria? And why would this be necessary for isolating these two functions of language?

Rene Descartes - his surname denotes his place of origin, thus describing him as one of that place. What of proper names of Native Americans? Their names are descriptive.

Searle also makes the mistake of supposing that “the teacher of Alexander the Great” is a contingent fact about Aristotle. Contingent only with respect to our knowledge! But okay, look. At birth, Aristotle could have been called by a name which codes the exact time and place of his birth, so that the use of his name described him as the child born at that time and place. (If another child was born at the same time and place, they could be differentiated by numbers.) The fact is that his given name does not afford us any means of identifying him beyond any number of descriptions for which he became famous. This is not the result of any special proper of proper names. It is a result of the fact that his given name happens to be extraordinarily vague. It was presumably not too vague for the people who needed it during his life, which explains why he never felt the need to change his name. For us, however, the name is meaningful only with respect to the many descriptions for which he is famous.

Still, we can trace a lineage of usage to the origin, and this might be important.

4. More notes on Kripke

4.1. He distinguishes between “a priori evidence” and “a posteriori evidence” (p. 35). He uses a number a bit like my prime number example, but with a computer that can calculate prime numbers. Our “a posteriori evidence” about the computer allows us to conclude that an output is a prime number. That this is a prime number “can be known a priori,” he says, but that doesn’t mean it “must be known a priori.” 

Hmmm . . . What is “a posteriori evidence”?  Presumably evidence that relies on experiences which can be doubted. We might question the integrity of the computer hardware or software when deciding if we can trust the output. Okay, but this is true of any person calculating prime numbers, too. There is always room for doubt! So on Kripke’s account, all mathematical knowledge is based on a posteriori evidence, because it all requires computation! What could qualify as a priori knowledge? Apparently only knowledge which can be known without thinking. Perhaps phenomenal knowledge, then, and nothing more!

4.2. Kripke uses the example of Goldbach’s conjecture to motivate a distinction between a priori and necessary truth. First, he assumes that every mathematical assertion is either true or false. Therefore, the Goldbach conjecture is either true or false, and which ever one it is, it is that necessarily. To motivate the addition of “necessarily,” he appeals to verifiability: If the conjecture is true, then “it can be shown . . . by direct computation” with respect to the entire (infinite) set of even integers. However, it cannot be shown (yet). Does that mean it is not true (yet)? Not according to Kripke, so this is a bit baffling. Then he turns to a priori knowledge of the conjecture, which he says is totally lacking. And he says it would be non-trivial to claim that the conjecture can be known a priori. But if it can be known at all, it would have to be knowable a priori. And he appealed to the possibility of knowing the truth of the conjecture by direct computation in order to motivate the claim that its truth would be of necessity. So what kind of distinction is he trying to draw here? None is apparent.

4.3. He attempts to reconstruct motivations for thinking that necessity and a priori truth are the same. He raises the idea that "there can't be a way of knowing about the actual world without looking that wouldn't be a way of knowing the same thing about every possible world.” So, to have a way of knowing the actual world without looking is to have a way of knowing the same thing about every possible world? Meaning, I guess, that (since we are not looking) our knowledge could be of any world at all, and therefore must be true of every one which is possible. But this is just to say that a priori knowledge is true in every possible world, because it is not dependent on the actual world. He says this “involves problems of epistemology and the nature of knowledge; and of course it is very vague as stated”(p. 38). Is it, though?

4.4. Kripke accepts analyticity, and acknowledges that analytic statements are both necessary and a priori. Shouldn’t we think that Goldbach’s conjecture is analytic? If it is true, it is because its truth follows from the meaning of its terms, right? What else could determine its truth?

4.5. Of certainty, Kripke says that a priori truths can be uncertain—if, for example, we are not certain that we have made a mistake in our mathematical calculations. But then necessary truths can be uncertain for the same reason. So what’s the difference?

4.6. Regarding the belief that events could have turned out differently, Kripke says it is intuitive, and that such intuitions are the only basis for believing anything, ever (p. 41). He also says that a person who believes this is not doing philosophy. (His implication is that the job of philosophy is to challenge, not support, our intuitions.) Yet, he overlooks the fact that a person who believes that events could have turned out differently is assuming a non-deterministic universe. For some people, that runs counter to their basic beliefs, and so would seem very “philosophical."

5. On possible worlds and metaphysical necessity

Kripke warns against thinking of popular worlds as places we could visit or peruse (p. 44). He says a more “intuitive" view is this:  “A possible world is given by the descriptive conditions we associate with it.” (Italics are his.) He explains this by saying that possible worlds are things we imagine could be (or could have been). He then calls them “stipulations,” as opposed to “discoveries." 

In a footnote, he misrepresents Lewis’ counterpart theory. He says, "Thus if we say 'Humphrey might have won the election (if only he had done such-and-such), we are not talking about something that might have happened to Humphrey but to someone else, a “counterpart.”" That is incorrect. According to Lewis (1968), if you talk about something that “might have happened to Humphrey” in a non-actual world, then you are talking about a counterpart. 

What Kripke fails to accept is that, once we start talking about possible worlds, we are introducing different causal relations. Kripke wants to be able to say that the only difference between a person in the real world and in the actual world can be extra-personal: it need not be a difference between the person and what Lewis would call their counterpart. Yet, Lewis might reply, in order for that difference to be relevant to the person, it would have to change them somehow. 

So, if we say “Nixon might have lost the election,” then we are saying that Nixon might have led a different life—even if everything up until losing the election was the same for him and his counterpart. When Kripke insists, “We can point to the man, and ask what might have happened to him, had events been different,” Kripke is missing the point entirely. 

Kripke introduces the concept of rigid designators immediately after rejecting Lewis’ counterpart theory. He insists that names can denote the same object in different worlds, and even in all possible worlds. He calls designators “strongly rigid” if they refer to an object that necessarily exists in every possible world. He then identifies proper names as rigid designators.

On the surface, what Kripke is proposing is that we use proper names to ground stipulations about individuals (for we stipulate possible worlds via the imagination). So, he says, we can talk about “criteria of transworld identity” because we can stipulate that a name refers to the same individual in all possible worlds (p. 49). (Lewis could presumably say that this is just naming the set of all counterparts, right?) 

But this seems backwards. In order to imagine an individual in a possible world, we must imagine that individual with some properties in a possible world. We might not consider those all as necessary transworld properties, but they will at least be sufficient for our stipulation. Some will be necessary, however, assuming every individual has necessary properties to begin with; however, we do not need to identify which are necessary in order to carry on with the stipulation. We must, however, be able to stipulate sufficient properties, or else we would not be able to imagine that individual in a possible world at all. Thus, to say that a name refers to the same individual in all possible worlds is to say that it refers to an individual vis a vis those sufficient properties. So, if rigid designators can be used at all, they entail descriptions of sufficient properties. If an individual lacks sufficient properties—on Kripke’s account—it cannot be given a proper name.

Kripke denies this. He seems to be assuming an essentialism about particulars. A name refers to what is essential in an individual without knowing what that is. He is clear about this: he is talking about what is “metaphysically" necessary, not what is epistemologically knowable (a priori or a posteriori). But how can we use a name in this way if we do not know what is metaphysically necessary? 

Jason Stanley says that semantics is metaphysics, apparently meaning that what is “metaphysically necessary” is what is analytically true—what must be stipulated according to the meaning of the terms we are using. Perhaps that is Kripke’s point: that the name “Nixon" refers to whatever must be stipulated according to the meaning of the term. What is this, if not minimal sufficiency? 

Searle would say it is a pragmatic benefit of proper names that nothing in particular must be stipulated according to the meaning of the terms, but he adds that the sense of proper names requires that they connect a heterogenous set of descriptions, however loosely. So perhaps Searle would agree with Kripke that the name “Nixon" refers to the same individual in all possible worlds, but only in the sense that there is no limit to how loosely we can hang our stipulated descriptions on that name. 

We can imagine if Nixon were a mouse, or a house, or a nebula. A poet would have no problem with this, though we would not say any of these are real possibilities. There is a difference between the possible worlds that are realistic and the possible worlds that are fantastical, but in both cases, we are talking about corporeal objects. (Even objects in fantastical worlds have a sense of realism that we can relate to the real world—what makes them fantastical is the combination of realistic elements, not the invention of elements which cannot be imagined in the real world. The idea of a magic love potion, for example, combines the realistic element of chemistry with the realistic element of love.)

Can we imagine if Nixon were the idea of south? Or the relationship between the circumference and the radius of a circle? There seems to be an obstacle here, because ideas are abstract relations. We can imagine the concept of Nixon in relation to any variety of corporeal objects, but we cannot imagine the concept of Nixon as the concept of something else. We can imagine if Nixon were an apple, but not if he were the concept of apple. Nor can we imagine if the concept of Nixon were the concept of apple. We might ask, “What if every time a person was talking about Nixon, they were really talking about apples?” That would make no sense.

Let’s regroup. There are limits to how we can realistically imagine Nixon. While we can imagine fantastical situations (in which Nixon is not a human being, say), those are not possible worlds—which is to say, those Nixons are not sufficiently like the actual Nixon. But we may not be able to draw a line between these two cases. What if Nixon had been born with mutations that made it hard to classify him as a human being. Is this conceivable? If so, would we say the creature born at the same time and place as Nixon, and of the same parents, an in precisely the same manner, was not Nixon? I believe we could say that, but it would depend on how much the creature resembled Nixon. If there was no resemblance to speak of, apart from some very general features shared by all mammals, say, then we could say it was not Nixon at all. Imagining such a case is not imagining if Nixon were an inhuman creature, but rather imagining that he had not been born at all, and that an inhuman mammal had been born in his place. If, however, the creature looked and acted similarly to a human being, then we would say that Nixon had been born an inhuman mammal. The point is that our use of the name “Nixon" is determined by both necessary and sufficient conditions relating to biological and historical facts about Nixon.

Kripke tries to elucidate the “problem" of transworld identification with the statement that England fought Germany in 1943. He says this statement might not be reducible to a statement about facts about individuals, but that it nevertheless can be deduced from facts about individuals. A complete description of the world can therefore include facts about people without mentioning facts about nations. He must mean something like “without mentioning those facts under that description,” because he says that facts about nations are nothing “over and above” facts about individuals. He compares this to facts about material objects not being facts “over and above” facts about molecules. He raises the Ship of Thebes problem (though not by name) via the example of a table remaining the same even when its molecules change, noting that there can be an “open texture” in the relationship between parts and wholes: we cannot reduce the names of objects to a description of their constituent parts, because we have no criteria for determining which parts (or configurations) are necessary or sufficient (pp. 50-51).

In a footnote (p. 51), Kripke notes that intransitivity can be a problem, because our descriptions are always somewhat vague, and we may never “reach a level of ultimate, basic particulars for which identity relations are never vague.” Uhh . . . the vagueness of “Nixon" cannot be removed by appealing to particle physics. I suppose that is not his point, though. He says (in the body of the text) that no “privileged” type of description is required to adjudicate indeterminate cases. We do not need to appeal to particular descriptions of Nixon to determine if the person in our possible world really is Nixon. We simply stipulate that it is. He says this is normally how we do things. We say, “Nixon could have lost the election,” without explicitly stipulating any particular properties. Yes, that is normal, but in that case, all sorts of properties are implicated. They can, after all, be cancelled, as in this case:  “Nixon could have lost the election if he had been an iguana born of two camels.” The fantastical nature of the subordinate clause negates the plausibility of the main clause, thus reversing the meaning of the statement. This indicates that conditions on Nixon’s biological status are implicated in the main clause.