Quantifiers

          Nathan Salmon proposes a conundrum in what David Kaplan calls the “naïve theory of language.” He offers an analysis of Frege and Russell’s view of denotations, particularly Frege’s modes of presentations and Russell’s propositional functions. In discussing Russell’s view, Salmon makes the distinction between deictic terms and denoting phrases, using the following example. The statements Socrates is wise and Someone is wise are both syntactically analogous. If the information encoded by a sentence corresponds to its syntax, then the subject Socrates and someone are functionally equivalent in that they are a “genuine name” of a united entity (Martinich and Sosa, 91). However, if Bob were to meet Socrates, he would call him “Socrates,” and in the second case, if Bob were to meet the someone who is wise, Bob would call him by the name which is revealed to him upon greeting. In other words, Bob would not call the someone “someone” after he becomes introduced to who fulfills that condition. From this principle, Russell concludes that quantifying names have no “meaning in isolation” (Martinich and Sosa, 99)

         Why do we have quantifiers in our language and use them? Let us observe two cases: someone and everyone, which is really not someone. First, someone. How does such a term come to be used? Contextually, there are an indefinite number of ways to use it. Bob sees water on the counter. This is a phenomenon which is experienced. Then, Bob has an interpretative model in his mind which connects aspects of things through logical connectives. So, after brief computation, Bob thinks, someone spilled their water and left. He then may say this in conversation to his friend Alice: “Someone spilled their water and left.” Note that it is not necessary for Bob to think cogently, a puddle of water implies an actor which created the puddle, which in this case is human. This is a principle apprehended in a previous time period which serves as an underlying logical current, or it is remembered by his brain in a single moment so quickly that his observing mind cannot see it.

         Let us play with this example. Say Bob lives with one roommate, Bill, who holds little company. Then, Bob would most likely think, Bill spilled his water. He may even say this to Alice, “Bill spilled his water.” Now, Bob lives with two roommates, Bill and Joe, but Joe is understood to be the type of person who is neurotic about being clean. Then, Bob would see the puddle and most likely think, Bill spilled his water. He may even say this to Alice, “Bill spilled his water.” Now, Bob lives with three roommates, Bill, Joe, and Craig, all of whom are generally understood to be slobs.  Then, Bob would see the puddle and most likely think, someone spilled his water. He may even say this to Alice, “someone spilled his water.” This goes to show that the usage of the quantifier someone is contained within the universe of the speaker’s associations, in relation to the particular context. When Bob says, “Someone,” he does not mean, in this instance, that his second cousin who lives in Alaska may have left the puddle. There is a particular type of someone which occupies Bob’s mind, and in this case it pertains to only three people: his roommates. In short, he is saying for some object a in the set A.

         Let us note that in thinking or stating that someone spilt water, Bob’s statement could be true or false, propositionally. The truth could be that there was a leak in ceiling, it could be that an animal knocked something over, or it could be any other situation which one feels compelled to drum up.  At the moment when Bob perceives the water, he is presented with what he has come to understand as incomplete information. In an effort to complete the information, he initializes a position that someone must have done it. Quantifiers can act as expressions of incomplete knowledge, applying cause to an effect.

         Consider a teacher who says, “Someone will get a perfect score on this test,” using the word someone to mean, “someone — I  do not know who.” Now, consider a teacher who says the same phrase using someone to mean “someone — I do know who.” Such differences in tone are accomplished through the establishment of a vocabulary of gestures and inflections which tend to communicate higher-order knowledge. The knowledge of the identity of the someone exists on a different plane than the usage of the quantifier itself. For, if the teacher did know the identity of the student, then she would still be using the quantifier to refer to him, instead of his name, which is a decision.

         What I have said may not be surprising – that one’s position towards unfolding phenomena is guided by the flow of their existing logical scaffolding, and that one’s statement using quantifiers is selective within a set which is relevant to the situation. These ideas being established, there is more to observe in the case of quantifiers. Consider:

A)   “That pillow is on that couch.”

B)   “There were some number of pillows on that couch.”

         If present, if actually perceiving the pillows on the couch, there is always the option for me to count the pillows. The use of “some number” arises out of an obfuscation of what is or was in front of me. It is a sort of alienation placed between my senses and the world as it is presented to me. Further computation can always remedy an initial incomplete perception, or a perception which has been distorted through time through memory. If I have dinner with Matt every Saturday, then the image in my memory of those dinners are more well-defined than if I had dinner with Matt or John every Saturday, which one being decided the day before. Memory in the latter case of the events would blend together. What really happened would be farther away by mixing them up. This principle is either illustrated in Spinoza’s Ethics or Sartre’s Being and Nothingness, and my inability to recall which is an example of the very principle I am describing. For another example, say Matt and John have different patterns for placing their napkins. If Matt always puts his napkin to the left, I may remember this easily if my phenomenon with Matt contains that unique time stamp of being what I do on Saturday evenings. If John sometimes puts his napkin to the left and sometimes to the right, then I may be incautious or hasty in remembering this detail and mix up whose pattern is what, especially if this pattern is one which I did not thetically perceive. This is assuming the pattern is one that I remembered unconsciously through image reproduction and not through cogent recognition of a logical condition which dictates that Matt does so-and-so and John does so-and-so. However, further engagement with the phenomenon always reveals more of it. Application of will reveals.  In the present, this looks like ‘giving-over’ to the meshing of curiosity and world apparition. In the earlier example of the pillows, it means allowing oneself to count the pillows. In the past, this looks like giving over to the details of memory.

         Everyone (not someone):

         Multiple times has one of Bob’s friends called him “short.” Thus, he goes to Alice, and he says, “everyone calls me short.”  What he really means in this case may be either that a quantity of people which I neglect to compute calls me short, or, that if the ones who call him short happen to align with another description, say, people in his acting group, a defined group which goes by another name [my acting group] calls me short. In the latter case, Bob is simply using a logical construction for all objects a in the set A. In the former case, this is where incomplete perception comes into play, as it did in the case of “someone.” It may be that Bob cogently thinks of three whole instances of being called short, two by Bill and one by John. Bob, moved by the force of remembering these instances, pushes his speech into the realm of universals, everyone, perhaps to produce a desired effect for his interlocutor, Alice. Perhaps Alice understands that it is really only Bill who has called Bob “short,” and a humorous response from Alice would be, “it seems to me like you have something to say to this Everyone.”

         Exercise: Name something “everyone” thinks of you, if one comes to mind. Enumerate the people who have expressly said or written this thought of yourself that you have witnessed. Compare this number to the number of people you have ever seen in your life.

Quantifier usage involves profile-building. Consider a princess locked in a tower who says to herself, “someone will rescue me from my tower.” She goes further to say, “this someone will have blond hair and a gallant disposition.” As opposed to the earlier case where Bob used someone to draw from a well-defined set, here a princess uses the pronoun someone to construct an entity drawing upon aspects from different sets of personality traits, appearances, and functional purposes. Rather than drawing upon her three roommates, she draws upon what she has collected from her knowledge of archetypes, constructing a vision to then project onto savior if arrived. If unmatched, the savior-image Someone is sacrificed. If matched, the S-image is imposed on the savior. The S-image is a simpler being than the savior, for it comes from proposition of mind while the latter from real Dasein. The imposition of the savior’s highlighted aspects onto the savior himself causes him to be overtaken by his aspects. The next phase of such a relationship would be continued involvement which reveals how the actual saviors originates from a different place than the savior-image, thus revealing the Someone to have been a constructed image of mind. In this way, in the movie Shrek, for Fiona to “know” her knight, i.e. consummate their mutual being through marriage, she must sacrifice the idol of the savior which she previously constructed. Whereas before, it seemed to her that Shrek’s identity in-and-of-himself was going to be beholden to his fulfillment of the S-image, the next phase of continued involvement leads to sacrificing her S-image so it becomes a relative mode of being for Shrek.

         These reflections bring out how quantifiers may be “meaningless in isolation,” as Salmon puts Russell to put it. Quantifying statements, logically based around the proposition “there exists,” are extensions of interpretation on incomplete facts involving purposeful or instinctual ambiguation.