Analysis and Review of the Philosophy of Language - Essay Example

? Wittgenstein and the Philosophy of language: Plus or Quus? of Wittgenstein and the Philosophy of Language: Plus or Quus? It is easy to dismiss something which one makes no effort to understand. The purpose of what follows is to advocate the significance of a simple yet misunderstood concept in the philosophy of language, namely, “meaning.” One of the major topics that undermine the concept of “meaning” can be seen manifested in the rule following problem. Thus, this paper will address Ludwig Wittgenstein and Saul Kripke’s interpretation of the rule-following problem. Furthermore, this paper will focus on the possibility of establishing meaning with reference to a private language, as seen in one’s use of ‘+’ in our everyday language. When a mathematician is presented with the equation, 38 + 16, instinctively, the mathematician would respond by adding the two terms while computing for its sum. Thus, the mathematician would reply, claiming that the sum of 38 and 16 is equal to 54. Given this example, what does ‘+’ mean? Does the mathematician really know what was meant by ‘+’ in the equation? Does it pertain to the computational procedure for adding two values, or does it pertain to something else? How can one tell what the mathematician meant? This paper will attempt to formulate a sufficient theory of meaning with regards to the use of ‘+.’ In doing so, I will argue that an intensional framework must be taken into account as opposed to a purely extensional framework. From a general perspective, the issue revolves around the relation between two fundamental concepts, truth and meaning. Truth, from a logical point of view, has traditionally been thought of as extensional. So the truth of a given expression is associated with it’s meaning in terms of logical structure, reference, and truth-value. This move of neglecting meaning in relation to that of the sense of a given expression is what this paper shall argue against by using ‘+’ as its test case throughout the paper. For herein, to say that 36 + 16 = 54 could mean two things: ‘36 plus 16,’ and ‘36 quus 16,’ with both referring to 54. It is in this regard that a theory of intensions must be taken into account. For, if a person is presented with an equation involving ‘+’, how can one know as to whether that person meant ‘+’ as plus or ‘+’ as quus? What makes the interlocutor assume what is being referred to by the use of ‘+’? Herein is where the problem of rule following comes into light, for if what we are after is semantics, then it seems paradoxical that we refer to general rules from which a class participates in. Rule following applies in the level of syntax, for verifying what the individual knows privately is not required in such cases. Indeed, the problem with ‘+’, as explicated by Kripke is that ‘+’ is understood to represent a semantic rule rather than a syntactical rule, and a semantic rule following leads to several problems with regards to the meaning and truth of ‘+’ statements. Thus, Kripke argues that “it is possible to construct an unlimited range of related but non-equivalent semantic rules, incorporating the potential truth conditions C1, C2, … Cn respectively, such that there are simply no facts at all about the speaker’s use of ‘+’ that determines which, if any, of these possible rules the speaker has actually adopted” (Wilson, 2006, p.155). Therefore, this points towards the problem of indeterminacy, since according to Kripke, discovering the truth conditions of the speaker’s use of + is not possible, since there is no specific semantic rule that underlies one’s use of ‘+’, regardless of its truth function. However, this creates a problem with regards to the use of ‘+’ in language, for if ‘+’ could mean several things at the same time and in the same respect, then that would lead to the ambiguity of ‘+’ which cannot be, for it is used in disciplines such as mathematics and logic. It is a common thing to say that an argument is valid based on its logical structure or syntax, which in turn determines its truth. But then again, is that all there is to an argument’s truth? Or is there something else aside from extension, i.e. structure and reference, which gives us certainty that we know that a + b = c is true? If it is not the case that extensions are sufficient for the truth of our claims, then what constitutes the truth of a non-trivial arithmetic statement that involves ‘+’? In other words, what is it that makes 38 + 16 = 54 meaningful, and similarly, true in the first place? Frege’s Contribution to The Philosophy of Language The aim of a theory of intensions is to investigate meaning. But then again, what exactly is that? A theory of intensions aims to make a formal account of what it takes for some expression to have meaning. Such an account also captures the individual’s ordinary intuition about meaning. But a theory of meaning cannot easily be constructed, since we have differing conceptions of what it is. It is here where Gottlob Frege’s account of ‘meaning’ becomes instructive. Frege (1948) proposes that there are two distinct aspects of meaning, which are constitutively tied to our understanding of an expression – Sinn and Bedeutung, i.e. Sense and Reference. Similarly, a theory of intensions deals with meaning in relation to truth by distinguishing two different aspects of meaning – intension and extension. One could understand an intension as the Sinn of an expression, while an extension, the Bedeutung of an expression. The Bedeutung of an expression is what is commonly construed as an expression’s reference or truth-value. So from an extensional point of view, it has been widely accepted that ‘meaning is equated to truth’. However, it is not the case that meaning can always be equated with truth, for there are some contexts wherein ‘meaning determines truth’. Contexts wherein meaning determines truth are known as intensional, but not all forms of intensionalism hold that meaning determines truth. Nevertheless, it is this aspect of meaning that this paper will focus on. For even if extensionalism rejects the intensional account of meaning, it is not counter to intensionalism per se, for not all forms of intensionalism commit to the view that ‘meaning determines reference’. And for this reason, this paper argues that Kripke’s interpretation of Wittgenstein’s rule following problem, as well as his solution to the problem, will not suffice, for Kripke does not account for meaning in the manner by which an individual’s use of ‘+’ is justified as meaningful. It only accounts for meaning in an extensional sense, i.e. to members of a community rather than to individuals considered in isolation (Humphrey, 1998). For Kripke, “it is only in a community setting that there can be substantive assertion conditions for the attribution of correct or incorrect rule following. Such is Kripke’s case for the impossibility of private language” (Humphrey, 1998, para.4). However, it is not the case that there can be no substantive assertion conditions meant by ‘+’, and it is not the case that ‘meaning’ any given word does not exist as well, as seen in Wittgenstein’s theory of meaning as explicated in his Philosophical Investigations. For, in the light of an intensional account of ‘+’, ‘meaning’ is justified. It is in this regard that the importance of ‘+’ is secured as used within disciplines such as mathematics and logic; thus escaping the problem of the skeptic. In the next section, I turn to an explanation of Wittgenstein’s theory of meaning in relation to his analysis of rule following. This will serve as a background on Kripke’s interpretation on Wittgenstein. Wittgenstein on Rule Following and Meaning Wittgenstein’s attitude towards rules can be expressed as follows: "any interpretation still hangs in the air along with what it interprets, and cannot give it any support. Interpretations by themselves do not determine meaning" (1968, p. 198). For instance, supposing you send your brother to the store to buy some eggs and bread. For him not to forget what you want him to buy, you give him a slip of paper bearing the expression “five eggs and ten pieces of hot bread.” You then tell your brother to give this slip of paper to the seller together with the money that you gave him. Your brother does exactly what you told him to do, and after a while, he goes home with the appropriate items and change. The question is, how is it possible that the seller interprets the piece of paper, which only bears “five eggs and ten pieces of hot bread,” to mean that your brother is buying five eggs and ten pieces of hot bread, with your brother not saying anything at all? The meaning of the said expression cannot be explained simply in terms of the references of the words comprising the expression. Imagine your brother gives the slip of paper to a policeman instead, how would the policeman interpret its meaning? Wittgenstein says we can explain the meaning of such expression by calling attention to how the words are used in the given language game. Wittgenstein’s use of the word “language-game” is meant to call attention to the similarities between speaking a language and playing a game. The similarities are the following. One is that speaking a language and playing a game both require certain rules. One simply cannot play a game without knowing its rules; the same is true of speaking a language. The significant import of this observation is that just like the rules of games, the rules governing the use of language are a matter of convention, i.e. human agreement, and are therefore necessarily social or public. This means that words do not have meanings other than the rule governed uses that we make of them. Wittgenstein (1968) compares the uses of words to the function of tools in a toolbox; these tools do not have functions other than those that we give them. Another is that just like the boundaries of games, i.e. where one game ends and where another game begins, the boundaries of language-games are not always precise. Wittgenstein likens this to the streets crossing one another; sometimes it is not clear what particular street you are in. This accounts for the fact that we easily fall into misunderstanding – which happens when we are not mindful of the shifts of language-games. In addition, Wittgenstein holds that the meanings of psychological terms are the private mental states they refer to. For instance, if I say “I have a toothache,” the meaning of the term “toothache” is here understood as the specific pain it refers to. Wittgenstein makes a reduction ad absurdum of this thesis by showing that this thesis leads to the claim that the language of psychological terms is a private language, which Wittgenstein shows to be a logical impossibility. A private language is a language where the meanings of the terms comprising this language are private to a certain person. This means that only that person can understand the meanings of his terms. That this is logically impossible is due, for Wittgenstein, to the lack of an objective criterion of correctness. Accordingly, the person would not know when he commits a mistake in following his own private rules for his language. If one answers, what about his memory? Wittgenstein answers this by saying that one cannot check one’s memory by another memory. Wittgenstein (1968) likens this to someone who would like to check the contents of a certain newspaper by buying several copies of the same newspaper and comparing their contents. Consistent with his theory of meaning, Wittgenstein argues that the meanings of psychological terms are their uses in certain language-games. In the next section, I shall discuss Kripke’s interpretation of Wittgenstein’s theory of meaning, using his test case, ‘+’. Kripke and The Problem of ‘+’ Kripke asks us to consider the following scenario, wherein “x quus y is a function that takes x + y as its value if x and y are both below 57. Otherwise, it takes the value 5” (Ahmed, 2008, p.1). Now if a person was presented with an equation such as 14 + 35, what fact of the matter is there in virtue of which the person understood the meaning of ‘+’ to mean plus rather than quus? Kripke presents a number of proposals to answer the question, but concludes that there is no fact that is present by what the interlocutor meant plus or quus. This skeptical conclusion is what Kripke advocates when claiming: “There can be no such thing as meaning anything by any word. Each new application we make is a leap in the dark; any present intention could be interpreted so as to accord with anything we may choose to do. So there can be neither accord, nor conflict” (Kripke, 1982, 55). What does this imply? This implies that there is no such thing as ‘meaning’ as ascribed to words. However, this is problematic, for commonsense tells us that there are such ‘meanings’ as used in language. Thus, Kripke offers a solution to the problem by claiming that meaning takes place in the level of a community or class, wherein people customarily accept certain rules, and follow them as a basis for meaning ascriptions. Otherwise, language becomes impossible. Kripke’s solution reflects the possibility of language and rule following from a perspective of an extensional interpretation, i.e. interpretation that does not account for ‘meaning facts.’ Thus, in this line of argumentation, it seems that: We don't need "meaning facts" to justify our answers or our attributions of meaning. All we need are "conditions that legitimate the assertion" of such sentences. According to Kripke, we can turn our backs on the alleged need for "meaning facts" by switching from a truth-conditional account of meaning to a view of meaning and language based on assertion-conditions or justification-conditions (Humphrey, 1998) This switch is what Kripke understood Wittgenstein to mean as seen in his shift from the Tractatus to The Philosophical Investigations. Moreover, Kripke qualifies this possibility of meaning to reside in the level of a community, for such is the setting where rule following can take place. Thus, Kripke argues that it is not possible to ascertain what an individual person meant when confronted with ‘+’ in a given equation a + b. It is in this regard that a private language is impossible, for to employ the use of ‘+’ is to follow a rule in a given community or class wherein ‘+’ means addition or quus respectively. This impossibility is reflected in the fact that there is no way by which we can know what a person meant in its use of ‘+’ since this could mean both plus and quus. What goes on in a person’s head is something that we have no access to, regardless if the fact of the matter is true or false. Hence, if ‘meaning’ is to be ascribed in language, it is only from an extensional point of view. However, does Kripke really succeed in explicating the possibility of meaning in this light? In the next section, I shall argue that Kripke only succeeds in explicating ‘meaning’ in the level of extensionality. However, this will not suffice so as to serve as a theory of meaning for ‘+’, especially if what we are after is the semantic value of ‘+’ and not solely its syntactical meaning or reference. Theory of Meaning: Intension vs. Extension Given the aforementioned analysis of Kripke on Wittgenstein’s argument, it is in my contention that Kripke does not successfully show how ‘meaning’ is possible, for he only qualifies ‘meaning’ from an extensional point of view, i.e. in a community setting. Also, I believe that Kripke mistakenly interprets Wittgenstein, for his explication of meaning, which reduces the meaning of a word to its reference. However, it is not the case the Wittgenstein succumbs to advocating meaning as reference. It is in this light that a theory of intension and extension comes into light. Given an introduction on Frege, we come to know of the distinction between the Sinn and the Bedeutung of a word. This distinction can be applied further to sentences or propositions as well. The Sinn of a sentence is the “thought” expressed by it. According to Frege, a “thought” is the objective content of thinking, which is capable of being public or common to all. For example, the Sinn of the statement 2 + 3 = 5 is the ‘thought’ expressed by the statement, i.e. it asserts that the value of two numbers, 2 and 3, when added, equates to the value of 5. While the Bedeutung of a statement is its “truth-value”, i.e. it’s being ‘true’ or ‘false.’ In this case, the Bedeutung of the statement “2 + 3 = 5” is its being ‘true’. What is important herein is Frege’s recognition of Sinn in his theory of meaning, for there are certain problems that arise if we only consider Bedeutung. Wittgenstein acknowledges this fact as well, for Wittgenstein was against a purely referential theory of meaning. For, given a purely referential theory of meaning, all true statements are equally the same, and likewise, so are all false statements, i.e. they refer to either the “true” or the “false”. In the case of ‘+’, 2 plus 3 is 5, is the same as 2 quus 3 is 5, which is not the case. Also, there are some words, which appear to lack Bedeutungen. Given a purely extensional account, such names will therefore lack “meaning,” such is the contention of Kripke in his analysis of ‘+.’ Lastly, it is frequent that there is more than just one term referring to one and the same object. Given such cases, different words are not the same in the extensional manner, but are intuitively distinct from one another by virtue of their Sinn. Hence, Bedeutung cannot be all there is to “meaning,” i.e. reference cannot be all there is to the meaning of ‘+’ in any given equation. Indeed, as Wittgenstein remarks, “but we understand the meaning of a word when we hear or say it; we grasp it in a flash, and what we grasp in this way is surely something different from the ‘use’ which is extended in time” (Wittgenstein, 2001, p.46). Moreover, he contends that what we grasp in our understand determines the manner by which the word is to be used (Wittgenstein, 2001). This reflects Wittgenstein’s understanding of meaning in the light of the Fregean Sinn. This is what Wittgenstein may have thought of, in assimilating what goes on in our minds when we utter a word, i.e. the picture of the word as it fits the utterance of the word. Thus, in our stating that ‘2 + 3 = 5’, the rule of addition, for instance, may come before a person’s mind, which explains why that person meant ‘addition’ rather than ‘quus.’ As Wittgenstein (2001, p.69) remarks: It can be seen that there is a misunderstanding here from the mere fact that in the course of our argument we give one interpretation after another; as if each one contented us as least for a moment, until we thought of yet another standing behind it. What this shews is that there is a way of grasping a rule which is not an interpretation but which is exhibited in what we call “obeying the rule” and “going against it” in actual cases. Herein, Wittgenstein maintains that ‘meaning’ is possible not as a private semantic rule but as an “expression of a rule… that is exhibited in the behavior that we count as obeying or going against that rule” (Wilson, 2008, p.158). Moreover, he goes beyond rule following by asking “But is that all? Isn’t there a deeper explanation; or mustn’t at least the understanding of the explanation be deeper” (Wittgenstein, 2008, p.71)? Herein is where Wittgenstein differs from Kripke. For Kripke only explores meaning as it is manifested in a community, wherein people follow a certain rule based on custom. Final Remarks and Conclusion Given the said analysis on the distinction between intension and extension, it is evident that Kripke only explicates meaning in the level of extensionality, and neglects the importance of intensions. If ‘meaning’ in terms of semantic rule following only manifests in the level of communities or classes, then indeed, it would seem impossible to assign meaning to a statement involving the use of ‘+.’ Moreover, if meaning is impossible, then words, as Kripke concludes, do not possess any meaning. However, words do possess meaning, and a theory of intensions proves the importance and possibility of accounting for the meaning of a given word. The logic of language, as suggested by Wittgenstein, is a perfect background for the discussion about the relation between philosophy and language. Philosophy clarifies the meaning of words in the context of our everyday language. Wittgenstein interprets the real meaning of words in a specific manner, in a manner that goes beyond the word’s reference. Indeed, philosophical considerations about what ‘meaning’ is has been a crucial issue for Wittgenstein, as he states: “I see now that these nonsensical expressions were not nonsensical because I had not yet found the significant explanation, but that their nonsensicality was their very essence; for all I wanted to do with them was just to go beyond the world and that is to say beyond language, but it is impossible” (Wittgenstein 1968, pp.11-12). This shows our inevitable commitment to language, and in effect, our ontological commitment to meaning. A theory of intension concerns itself with meaning in relation to one’s pursuit of truth. It is in this regard that the use of ‘+’ in statements or equations is by nature both extensional and intensional. What is explicit is its extensionality, but implicitly, it admits of its own intensionality, just as we are committed to our own ontology. For, in dismissing the status of intensions, we dismiss the meaning and value of all our linguistic assertions, may it be extensional or not. For if what we are after is the “correct” and not the “incorrect” method of reasoning, then we will have to accept the fact we are inevitably committed to the “intensional aspect” of all our linguistic claims. If logic is the ideal model, as Wittgenstein thought it to be, of linguistic concerns in philosophy, then this should account for both meaning and reference, that is, intension and extension. For, logic is not logic without a theory of intension just as language is not language without a theory of meaning. However, if there is a need from which language will not suffice to explain the meaning of a word, it would be better if we do not attempt to engage in describing it. It is in this regard that “what we cannot speak about, we must pass over in silence” (Wittgenstein, 2001, p.89). References Frege, G. (1948). On sense and reference. (M. Black, Trans.). In P. Geach and M. Black (Eds.), Translations from the philosophical writings of Gottlob Frege (pp. 56 – 78). Oxford, UK: Basil Blackwell. Humphrey, J. (1998, July 14). “Brief overview of key parts and?key notions in Kripke's book. Retrieved from http://krypton.mnsu.edu/~witt/overviewk.html Kripke, S. A. (1982). Wittgenstein on rules and private language. Cambridge, MA: Harvard University Press. Ahmed, A. M. (2008, July 7). Wittgenstein philosophical investigations lecture 8 [PDF document]. Retrieved from University of Cambridge Philosophy Department Website: http://www.phil.cam.ac.uk/teaching_staff/ahmed/WittgensteinPhilosophicalInvestigationsLecture8.pdf Wilson, G. (2008). Rule-following, meaning, and normativity. In E. Lepore and B. C. Smith (Eds.), The Oxford handbook of philosophy of language (pp.151-174). New York, NY: Oxford University Press. Wittgenstein, Ludwig. (2003). Philosophical investigations. (G. E. M. Anscombe, Trans.). Oxford, UK: Blackwell Publishing. Wittgenstein, Ludwig. (2001). Tractatus logico-philosophicus. (D.F. Pears and B.F. McGuinness, Trans.). New York: Routledge. Read More