No Error from Error

INTRODUCTION

In this paper I am going to discuss Saul Kripke’s famous posits, namely the necessary a posteriori and the contingent a priori; and in so doing, strengthen the Objection from Error. To do this I will, first, discuss the naming-relation theories relevant to Kripke’s claims. Next, I will explain both of Kripke’s claims and, further, elaborate the logical functions and scope of the modal operators within each posit. Then, I will illustrate how the Objection from Error falls out consequently from the connection between the necessary a posteriori and the contingent a priori claims after which I will, finally, both hypothesize and refute objections.

BACKGROUND

A significant amount of inquiries in the Philosophy of Language come by way of paired questions, one general question usually cut and dry while the other being more profound and philosophical. The inquiry of the reference-relation for names is no exception, for this naming-relation asks respectively both what does a name refer to and what is it in virtue of that a name refers to what it does. In the hunt for the reference-relation for names we will pursue the buck, the latter question.

The Ideal Description Theory of the Naming-Relation is an attempt to uncover in virtue of what does a name refer to its referent. It has four components: the name/word (W), the referent/object (O), a population of language users such that W is a word in their language (N), and an individual concept (F). The F does not refer to word types or tokens, but as its clearly stated, to a particular concept, a mental representation. The F is stipulated as a mental representation because of the Primacy of Properties Thesis– the thought that any individual can only think (conceptualize) of an object by way of that object’s properties. Hence, the F is a concept consisting of a property or properties of an object and, further, each F may (not must!) be particular to the individual thinking about that F. This theory is greater complicated when discussing N and the competency of individuals within N of any given W. Though for our purpose it will suffice to grant individuals of N competency of any W so we may recognize the desired end product of this naming-relation. Therefore, the theory will produce that a language user of N is competent in W iff she associates W with her F and the F refers to O. An example to illustrate this more colloquially could be that I’m competent in the name Tommy Caldwell just in case I associate that name with “the first person to free climb pitch 15 of the Dawn Wall” and that concept refers to the person who is Tommy Caldwell.

Another way to think of the F in the above theory is that the concepts are mental representations of definite descriptions. Definite descriptions are phrases of the form ‘the so and so’ such that the “so and so” states specific properties and the “the” restricts reference of the phrase to exactly one object (if there is any such object that suffices the given properties). In the case of Tommy Caldwell is the first person to free climb pitch 15 of the Dawn Wall, ‘first person to free climb pitch 15…’ is the property and Tommy Caldwell is the referent of the “the.” Neil Armstrong may suffice the definite description of “the first man on the moon” just as “the person who is lead role in Seinfeld” is sufficed by Jerry Seinfeld, etc. Therefore, in giving the naming-relation this function we create an identity statement of the form ‘the word W is the concept F.’ Further, we can substitute any name in such a statement by replacing it with the definite description being conceptualized to read the F is the F. These appropriate substitutions seem to create necessary statements as is the case for logical statements of the form ‘x=x.’ The first man on the moon is the first man on the moon is just one example. This may have held steadfast as a solution to the naming-relation had rigid designators not been introduced.

A rigid designator is “an expression that refers to the same object in any possible world (in which it refers to any object at all)” (Kierland, PHIL308, 3–10–15). That is in any possible world that my “being” exists whatever is the expression that acts as a rigid designator in this actual world with me as the referent, that expression will refer to me in all possible worlds. Although we discuss possible worlds in English, it is not the case that the rigid designator expression must be qualitatively similar to that which it is in English in this actual world to successfully refer in any particular in a counterfactual world. There is a possible world in which “tree” picks out paper, but this is nothing more than an acknowledgement of language’s intrinsic arbitrariness. What is captured by the rigid designator is that object’s essence (whatever that essence is), not mere qualities or properties that objects obtain in this actual world. A final note, names work as rigid designators.

It is with this new term, rigid designator, and its implications that we can now highlight a flaw in the Ideal Description Theory of the Naming-Relation as follows. Definite descriptions pick out certain properties which then refer to the single object (if there is to be one) that obtains the given properties. But as noted, the certain properties obtained by the object in the actual world will not necessarily be the case in any possible world. For that reason, statements of the form ‘the F is the F’ (although obtaining a necessaryrelation) will contain contingent components. Neil Armstrong is the first man on the moon in this world, but his fulfilling the F is only contingently so and is determined by empirical evidence. This is the thought behind Kripke’s necessary a posteriori.

To respond to this Modal Objection made against the Ideal Description Theory it is proposed that the definite descriptions that obtain in the actual world be rigidified. This is accomplished by adding the term “actual” to the substituted definite description within statements of the form ‘the F is the F’ so one such case may read “the actual first man on the moon is the first man on the moon.” The use of the term “actual” causes the referent to apply to the person that obtained the properties in the actual world when observing any other possible world, even those in which the referent doesn’t obtain the properties of the definite description or exist at all. This is what motivated Kripke’s second claim, namely the contingent a posteriori.

MAIN THESIS

The Objection from Error arose to refute the rigidified descriptions response and does so by working in the following way. Remember, the rigidified descriptions response results in statements of which the substituted definite description in the identity relation refers to the actual person that suffices that description. So again we have the actual first man on the moon is the first man on the moon referring to Neil Armstrong because he was in actuality the first man on the moon. But for all we know Buzz Aldrin was actually the first man on the moon and not Neil Armstrong. Perhaps Armstrong paid Aldrin a bribe to keep the reality a secret, or maybe Aldrin made a costly financial mistake during the lunar adventure and NASA rebuked his actions by publicizing a lie rather than announce the truth, or maybe some early Egyptian with more advanced technology than we accredit was really the first man on the moon (whatever the case might be, let your conspiracies rip!). If you associate “the first man on the moon” with the word Neil Armstrong, then this name will (unintentionally) pick out whoever in actuality fits the description due to the logical functions of the actuality operator and the identity relation and, further, there is no suggestion to how you know the actual referent. This idea stands as an objection to the rigidified description theory, but, moreover, I claim that it is also implied by Kripke’s claims.

Another example that lead Kripke to the claim of the necessary a priori was the relationship between the names Hesperus and Phosphorus. Hesperus is the name of a heavenly body that appears at night. Phosphorus is the name for a heavenly body that appears in the morning. Although there are two names there is but only one object. That is Hesperus is Phosphorus, the two names refer to one and the same object. At the time of the baptism (the origin of the name, when an object is first attributed with a name) of the heavenly bodies, the one that appeared at night and one in the morning were regarded as distinct objects or at least a distinction was taken for granted. It was only later through empirical evidence that the discovery was made of the truth that Hesperus is Phosphorus. As it is now the case that Hesperus is Phosphorus, a string of peculiar necessities follows.

First, we can imagine a world in which Hesperus is not Phosphorus, namely one in which the baptizer referred to one object as Hesperus and to a different object as Phosphorus. And yet this cannot be as it is the case that Hesperus is Phosphorus. Names act as rigid designators so now in every possible world that there is an object that is Hesperus, there too is that same object that is also Phosphorus. Of course there may be a counterfactual world in which Hesperus doesn’t appear at night, but this is no worry as this property of Hesperus in the actual world is a mere contingency. Second, we grant that at the time of the baptism for these heavenly bodies the baptizer was ignorant of their being the same object (and not ignorant due to lack of study but rather epistemic impossibility at that time). Further, we could imagine a possibility in which the baptizer’s evidence was qualitatively identical and occurred in an identical epistemic situation and so there was at most two possible outcomes, namely either it would be that Hesperus is Phosphorus or it would not be that Hesperus is Phosphorus. These two disjuncts appear at the time of baptism to be of equal probability and so it seems a contingent matter which of the two would stand. However, by noting the four color theorem Kripke illustrates that although contingent disjunctions implies not necessary, upon a resolve the answer might well be necessary (further noting that ‘might’ is purely epistemic) (Kripke, 131). From all this I’ll quote the two most important truths: “first, that we do not know a priori that Hesperus is Phosphorus, and are in no position to find out the answer except empirically. Second, this is because we could have evidence qualitatively indistinguishable from the evidence we have and determine the reference of the two names by the positions of the two planets in the sky, without the planets being the same” (Kripke, 131).

Working under the constraints of Variable Domain Quantified Modal Logics (VK), which I believe most appropriate for the evaluating of names and modality, I further diagnosed the components and the operators at play on them of the logical statements that result from the necessary a posteriori claim above. One claim being made is Hesperus is Phosphorus. This identity relation at work between the two names is strictly a posteriori because of the need for empirical evidence to determine its truth hood. And so it is possible that it could have been that Hesperus is not Phosphorus as there is a possible world in which the epistemic situation is fixed to actuality’s and the baptizer had qualitatively indistinguishable evidence from what occurred in actuality and the distinction held. However, as names act as rigid designators it must now necessarily be the case Hesperus is Phosphorus and in all possible worlds pick out the same object.

Logical statements that result from the contingent a priori claim have both different components and interactions. Rather than incorporate names it is definite descriptions that become the variables. An instance of the identity relation between identical definite descriptions such as “the first man on the moon is the first man on the moon” is both trivial and a priori, hence half of the name of the claim. It is when the term “actual” enters the scene that this still a priori relation now becomes a contingent matter, but the scope of the contingency is only a matter of what is referred to when the substituted definite description replaces the name, the W in statements of the form ‘the W is the F.’ As it is a matter of contingency the only evidence that could support one’s claim that the object O is the referent of the actual F is empirical evidence.

Now, I claim that empirical evidence is the bridge that connects the necessary a posteriori and the contingent a priori claims and the Objection from Error falls consequently from the possibility of qualitatively indistinguishable empirical evidence in an identical epistemic situation. Remember examples of the first man on the moon, and the possibilities go on ad infinitum. The actual F will always pick out the object that obtains the given properties in the actual world, but as empirical evidence is required to secure both the name and the F and their connection there will always be the possibility of error in baptism or predication of each respectively.

PREEMPTIVE DEFENSE

Objection

In VK, like all logic systems, names or variables will behave differently than predicates. From this fact it does not follow that a standard of epistemic and qualitative indistinguishability governing over identity relations of names (variables) will so too govern over predicates. In fact, there is no such operator that acts solely over predicates. Therefore, your standard of empirical evidence for successful predication of the definite descriptions to the object that obtains the given properties is not entailed and the Objection from Error does not result as a consequence.

Reply

It is correct that definite descriptions act as predicates, but they also act as names. Definite descriptions may reside under both categories due to the function of their formation ‘the so and so’ which both refers to a single object via “the” and predicates it with the given properties via “so and so.” Admittedly there is no such symbol, variable, predicate, operator, etc., within VK that acts just as definite descriptions do. Instead, to properly translate a definite description a combination of the aforementioned logical notations in a proper formation are required. Nonetheless, this inability to capture the entirety of a definite description within a single symbol does not weaken their reaches in actual language. Furthermore, in the case of substituting names with definite descriptions we are thereby using that definite description as if it were a name, especially in cases when the term “actual” is applied. It therefore follows that a similar standard of empirical evidence will govern and as the possibility of error is entailed in all evidence the Objection from Error follows consequently.

Objection

How is it, if your work is correct, that implication strengthens the Objection from Error? And does not the objection rely on an existential instantiation that there is some other object that obtains the properties of the definite description unbeknownst to the word user?

Reply

Implication strengthens the argument by discovering the problem as the claims unveil. It is an argument that eats its premises, in a sense. Further, I think this discovery hints at Kripke’s divergence from description theories and also may explain his hesitancy to claim his proposed picture as a theory as the problem of initially attributing a name to an object prevails. Yes, the objection does imply that there really is some other object but if the theories imply that there is always room for error, then that outcome is always one of the uneliminated possibilities.