by Corry Shores
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[The following is summary of Priest’s text, which is already written with maximum efficiency. Bracketed commentary and boldface are my own, unless otherwise noted. I do not have specialized training in this field, so please trust the original text over my summarization. I apologize for my typos and other unfortunate mistakes, because I have not finished proofreading, and I also have not finished learning all the basics of these logics.]
Summary of
Graham Priest
An Introduction to Non-Classical Logic: From If to Is
Part II:
Quantification and Identity
16.
Necessary Identity in Modal Logic
16.5
Names and Descriptions
Brief summary:
(16.5.1) We now wonder about classifying noun-phrases as being either rigid or non-rigid designators. Definite descriptions, like “the number of symphonies composed by Beethoven” are usually non-rigid (although with some exceptions, like “the least natural number,” which is 0 in all worlds). (16.5.2) So descriptions are often non-rigid. We wonder now about proper names. They are often understood as non-rigid. But a description assigned to a proper name, like “teacher of Alexander the Great” as being the equivalent of Aristotle, can take a different value in a possible world where someone other than Aristotle teaches Alexander, thereby making the logical tautology “The teacher of Alexander the Great is the teacher of Alexander the Great” false (given the equivalence of “Aristotle” and “teacher of Alexander the Great”. (16.5.3) “It is therefore plausible to suppose that proper names in a natural language (at least when appropriately disambiguated to a particular object) are rigid designators. Thus, they latch on to the object they denote, not via some implicit descriptive content, but by a more direct mechanism” (358). (16.5.4) In Kripke’s account, the coiner of a name baptizes the denoted object with that name, which then refers to its denoted object rigidly in all worlds. “(They may single x out with a certain description, but if they do, in any other world the name still refers to x, not to whatever satisfies the description at that world.)” (So perhaps in the Aristotle example, when we define him as “the teacher of Alexander the Great,” in the world where Alexander has a different teacher, this noun-phrase still refers to Aristotle and not to the other teacher.) There is then a causal interaction between speakers that communicates that rigid denotation, and thus it is called the causal theory of reference. (16.5.5) However, the causal theory of reference does not explain cases where the transmission of designations breaks down, like how a miscommunication led to the island now called Madagascar getting this name by means of a misunderstanding between the European explorers who asked what the island’s name was and the Africans who were given the impression that they should give the name for some region on the African mainland. (In other words, the naming was not caused by transmissions linking back to a baptism, as the theory suggests it should happen.)
[Classifying Noun-Phrases as Rigid or Non-Rigid. Definite Descriptions as Non-Rigid.]
[Proper Names as Descriptions but not as Non-Rigid Designators]
[Proper Names as Rigid Designators Latching on to Their Denoted Object not by Description but by a Direct Mechanism]
[Kripke’s Baptismal Naming and Causal Theory of Reference]
[Problems with the Causal Theory of Reference: The Misnaming of Madagascar]
Summary
[Classifying Noun-Phrases as Rigid or Non-Rigid. Definite Descriptions as Non-Rigid.]
[We now wonder about classifying noun-phrases as being either rigid or non-rigid designators. Definite descriptions, like “the number of symphonies composed by Beethoven” are usually non-rigid (although with some exceptions, like “the least natural number,” which is 0 in all worlds).]
[In section 16.4 we discussed rigid and non-rigid designators. Recall from section 16.4.3 and section 16.4.4:
the noun phrase β, ‘the number of symphonies written by Beethoven’ is a noun phrase that may change its denotation from world to world. In some worlds, Beethoven wrote eight symphonies, in some two, in some 147
(Quotation of Priest, p.354, section 16.4.3)
When we consider a constant as having world-invariant denotation (like β, ‘the number of symphonies written by Beethoven’, being understood as being 9 in all worlds), it is a rigid designator, and we write it under the form: v(c). However, constants that do vary with the world are called non-rigid designators (like β, ‘the number of symphonies written by Beethoven’, being understood as potentially taking a different value in different worlds, like 2, 9, or 147), and we write them accordingly under the form vw(c). (“Compare predicates, where extensions may change from world to world, and we write vw(P), not v(P))” (354-355).
(From the brief summary to section 16.4.4, pp.354-355. Note that really β here is not properly understood as a rigid designator, but that possibility is considered here for the sake of simplified illustration.)
We now wonder about classifying noun-phrases as being either rigid or non-rigid designators. Here Priest refers to “the number of symphonies composed by Beethoven” as a definite description, but we have not yet encountered that term. In section 7.8.2 ‘the largest integer’ was called a description, as was ‘the old man with a white beard who comes down the chimney at Christmas bringing presents’ (for ‘Father Christmas’) in section 7.8.8. But in Priest’s Logic: A Very Brief Introduction, chapter 4, Priest says much more about definite descriptions. The following comes from our brief summary of that chapter:
A definite description specifies a thing satisfying certain conditions, for example, “the man who first landed on the Moon”. Descriptions can be formulated symbolically by the use of variables that are predicated. The overall formulation takes the form ιxcx. Here, the ιx means, “the object x, such that…”, and the cx gives the conditions specifying the object. In our example we could write ιx(xM & xF) to mean, “the object x such that x is a man and x first landed on the Moon”. […]
(From the brief summary of Priest’s Logic: A Very Brief Introduction, chapter 4.)
Priest says now that “Definite descriptions, of the form ‘the so and so’ are naturally taken to be non-rigid, as we have already observed, in effect, with the description ‘the number of symphonies composed by Beethoven’” (357). But there may be certain exceptions, like, “the least natural number,” which would be 0 in all worlds.]
Given the distinction between rigid and non-rigid designators, it may reasonably be asked of various noun-phrases in a natural language, such as English, which kind they are. Definite descriptions, of the form ‘the so and so’ are naturally taken to be non-rigid, as we have already observed, in effect, with the description ‘the number of symphonies composed by Beethoven’. (Though we might want to make exceptions for descriptions such as ‘the least natural number’ which, at least arguably, refers to the same object in all worlds, namely, 0.)
(357)
[Proper Names as Descriptions but not as Non-Rigid Designators]
[So descriptions are often non-rigid. We wonder now about proper names. They are often understood as non-rigid. But a description assigned to a proper name, like “teacher of Alexander the Great” as being the equivalent of Aristotle, can take a different value in a possible world where someone other than Aristotle teaches Alexander, thereby making the logical tautology “The teacher of Alexander the Great is the teacher of Alexander the Great” false (given the equivalence of “Aristotle” and “teacher of Alexander the Great”.]
[(I do not completely grasp the next issue, so it is best to consult the quotation below. My best guess at the moment is that Priest is noting the following issue. We next wonder whether proper names are rigid or non-rigid designators. Some might say that proper names are non-rigid designators, because they are covert descriptions. So “Aristotle” is the covert description, “the teacher of Alexander the Great”. Priest next gives reason to believe that in fact proper names are not non-rigid designators, but the reasoning here I do not follow. He says that
Aristotle is the teacher of Alexander the Great
| would mean the same as:
The teacher of Alexander the Great is the teacher of Alexander the Great
(357-358)
That part I do follow. But then he seems to say that “The teacher of Alexander the Great is the teacher of Alexander the Great” is false because there can be a possible world where Aristotle never teaches Alexander and rather someone else does. I do not see why that is false, because I would think that “The teacher of Alexander the Great is the teacher of Alexander the Great” holds regardless of who is teaching Alexander. So my best understanding at the moment is the following, but this is a huge guess. In this example, we do not think of the designator-designated relation as being “the teacher of Alexander the Great” and the person that happens to be in some world. Rather, the designator is the proper name “Aristotle” and the designated is “the teacher of Alexander the Great”. Thus when we say for this alternate world that “The teacher of Alexander the Great is the teacher of Alexander the Great”, we are implying that Aristotle is the teacher in that world, when in fact he is not. But then why do we need the sentence “The teacher of Alexander the Great is the teacher of Alexander the Great” rather than just “Aristotle is the teacher of Alexander the Great” to make this point? The real reason I do not know, because I am off-track on the reasoning here. But in accordance with my off-track reasoning, I would say that when we write “The teacher of Alexander the Great is the teacher of Alexander the Great” we find ourselves in the odd situation where we have a logical tautology that is false, rather than a mere contingent statement that is false. Let me quote so you can see for yourself):]
The situation is less clear with respect to proper names, such as ‘Aristotle’. Some have suggested that proper names are really covert descriptions, such as ‘the teacher of Alexander the Great’. But if so, the sentence:
Aristotle is the teacher of Alexander the Great
| would mean the same as:
The teacher of Alexander the Great is the teacher of Alexander the Great
and this is not false at any world (at least, at any world in which Alexander’s teacher exists). But this does not seem to be the case: in a possible world in which Aristotle whiled away his life in Stagira as a minor local official, and Alexander was taught by someone else, the claim would be false.
(357-358)
[Proper Names as Rigid Designators Latching on to Their Denoted Object not by Description but by a Direct Mechanism]
[“It is therefore plausible to suppose that proper names in a natural language (at least when appropriately disambiguated to a particular object) are rigid designators. Thus, they latch on to the object they denote, not via some implicit descriptive content, but by a more direct mechanism” (358)]
[(ditto)]
It is therefore plausible to suppose that proper names in a natural language (at least when appropriately disambiguated to a particular object) are rigid designators. Thus, they latch on to the object they denote, not via some implicit descriptive content, but by a more direct mechanism.
(358)
[Kripke’s Baptismal Naming and Causal Theory of Reference]
[In Kripke’s account, the coiner of a name baptizes the denoted object with that name, which then refers to its denoted object rigidly in all worlds. “(They may single x out with a certain description, but if they do, in any other world the name still refers to x, not to whatever satisfies the description at that world.)” (So perhaps in the Aristotle example, when we define him as “the teacher of Alexander the Great,” in the world where Alexander has a different teacher, this noun-phrase still refers to Aristotle and not to the other teacher.) There is then a causal interaction between speakers that communicates that rigid denotation, and thus it is called the causal theory of reference.]
[(ditto)]
One account of the mechanism has been suggested by Kripke. The person who coins a name, selects a particular object, x. They then baptise x with that name, which refers to it rigidly – at all worlds. (They may single x out with a certain description, but if they do, in any other world the name still refers to x, not to whatever satisfies the description at that world.) When other speakers learn to use the name – ultimately from the baptiser – the reference goes with it. This is sometimes called the causal theory of reference, because of the causal interaction between speakers which transmits the use of the name. (Note that the account is quite compatible with speakers, generally, having false beliefs about what it is the name refers to.)
(358)
[Problems with the Causal Theory of Reference: The Misnaming of Madagascar]
[However, the causal theory of reference does not explain cases where the transmission of designations breaks down, like how a miscommunication led to the island now called Madagascar getting this name by means of a misunderstanding between the European explorers who asked what the island’s name was and the Africans who were given the impression that they should give the name for some region on the African mainland. (In other words, the naming was not caused by transmissions linking back to a baptism, as the theory suggests it should happen.)]
[(ditto)]
The theory is not without its problems. For example, folklore has it that certain Africans used the name ‘Madagascar’ for part of the African mainland. Some European explorers wished to know the name of a certain island off the coast of Eastern Africa. Their African informants, misunderstanding their question, told them that it was Madagascar, the name by which the island is now known. Clearly, the reference did not transfer between speakers on this occasion.
(392)
From:
Priest, Graham. 2008 [2001]. An Introduction to Non-Classical Logic: From If to Is, 2nd edn. Cambridge: Cambridge University.
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