Russells On Denoting - Essay Example

Russell’s On Denoting INTRODUCTION The concept of denotation has been considered as significant not only in the study of the fields of logic and mathematics, but that it holds and plays an integral role in the understanding of knowledge and truth itself. (Russell 1905) In lieu with this, Russell’s critiques regarding some theories on denotation and his elucidation of his own theory on denotation have paved the way for a newer perspective and approach regarding the understanding of denotation. As such, this paper will intend to take a re-look on Russell’s On Denoting and from there learn what are Russell’s criticisms on existing theories on denotation, what is Russell’s theory on denotation and on how his theory accounts for the errors or gaps in the existing theories, hence, it can be impugned that Russell’s theory provide a better narrative on denotation. Thus, in the end, this paper aspires to gain an unambiguous comprehension of the concepts the underlie Russell’s theory on denotation. RUSSELL ON MEINONG AND FREGE Articulations and explanations regarding the idea of denotation have long been undertaken by philosophers, and the beginning of twentieth century is no different. Two philosophers of the age of analysis, namely, Meinong and Frege have provided their own explication regarding the concept itself. In fact, Russell’s exposition of his own theory has started by pointing out the weaknesses, difficulties and gaps which are encountered in Meinong’s and Frege’s theories respectively. Russell (1905) claimed that Meinong’s theory had difficulties as it “regard denoting phrases as standing for constituents of the propositions in whose verbal expression they occur… This theory regards any grammatically correct denoting phrase as standing for an object” (p 482). And the main difficulty of this theory was that it was “apt to infringe the law of contradiction” (p 483). Russell’s critiqued on Meinong’s theory raised three important points: first, on the concept of subsistence. Russell maintained that if we presupposed that ‘It is false that A differs from B’, then ‘the difference between A and B does not subsist’. However, in Meinong’s theory since a denoting phrase was standing for an object, then, the denoting phrase ‘the difference between A and B’ must stand for an object. Therefore, the ‘difference between A and B’ must subsist. In this case, the self-contradiction was made apparent. As it was affirmed that ‘the difference between A and B’ must subsist (Meinong’s theory), so too the preposition ‘the difference between A and B does not subsist’ is affirmed on the statement “It is false that A differs from B”. (Sutler 1967). The second counter-argument rests on the concept of existence. Take the example ‘The King of France is bald.’ Again, using Meinong’s theory, as grammatically correct denoting phrase stand for an object then the statement must be true. But it is a known fact, within the frame of a particular time the preposition ‘the King of France is bald.’ does not stand or signify for any object. Thus, it can be impugned that Meinong’s theory holds that the statement ‘the King of France is bald.’ is both true and false at the same time, thereby, entering into infringement of the law of self-contradiction. And the third argument is regarding ‘entities’ such as round square, “…the round square is round and also not round” (Russell 1905, p 485). Again, propositions that utilize denoting phrase whose subject is non-existent and non-subsisting present a violation of the law of contradiction. With these criticisms, Russell provided very strong counter-arguments against Meinong’s theory. The other theory which Russell criticised was Frege’s theory on denotation, specifically his distinction between meaning and denotation. According to Russell, the weakness of Frege’s theory lies on the notion that the distinction between meaning and denotation as Frege raised was really difficult to ascertain. To drive his point, Russell used the example ‘the first line of Gray’s elegy’. He contended that the proposition ‘the first line of Gray’s elegy and ‘The curfew tolls the knell of parting day’ can be interchanged since the two propositions have the same value since the phrase ‘the first line of Gray’s elegy’ denotes ‘The curfew tolls the knell of parting day’. This is the denotation. Thus, when a “denoting phrase occurs it is the denotation that we are speaking about” (1905, p 486). But when we look into the meaning, we encounter a difficulty; the meaning of a denoting phrase is the denoting phrase itself. What does it mean? Take for example the phrase ‘the present king of France’. Following Frege’s distinction between meaning and denotation, the phrase ‘the present King of France’ has a meaning even if there is no existing object that may refer to it or it does not have a denotation. And this has become possible on Frege’s theory as he has “some adopted some purely conventional denotation for the cases in which otherwise there would be none...though it may not lead to actual logical error, is plainly artificial and does not give an exact analysis of the matter” (Russell 1905, p 484) RUSSELL’S THEORY ITSELF At the beginning of On Denoting, Russell has stated that “ the principle of the theory of denoting I wish to advocate : that denoting phrases never have any meaning in themselves, but that every proposition in whose verbal expression they occur has a meaning.” (p480) But to be able to understand this, what is a denoting phrase? According to Russell (1905), a denoting phrase is any of the following: a man, some men, any man, all men, and the present king of France etc. What is noticeable is that a denoting phrase is introduced by quantifiers “all, some, few, any, every, and the likes, thus, “a phrase is denoting solely in virtue of its form” (p 479). Furthermore, he has stipulated that there are three cases wherein a phrase may denote. The first case is that phrase may denote something but not really denote anything. For example, imaginary objects like round square, unicorns, dwarfs and the likes. The second case wherein phrase may denote is when it denotes a particular or definite object. For example, the present Queen of England, the Pres. of United States and many more. The third case is a phrase may denote ambiguously. This happens when the phrase refers generally. This means the phrase does not refer or stand for any definitive or particular object. And it is recognised that this kind of denoting phrase is open to differing interpretation leading to a difficulty. (Russell 1905) Going back to the principle of his theory, we can now infer the following. First, a denoting phrase does not have any meaning on its own. For example, a man, all men, any man does not have any meaning when they occur by themselves. Second, a denoting phrase has meaning only within the context of the sentence. However, the real meaning of the phrase is not what it appears to be. For example, “I met a man.” The denoting phrase ‘a man’ is ambiguous as it does not refer to any particular man. As such, there is a need to translate the sentence into the language of logic. And finally, only in the ‘translation’ that the real meaning of the denoting phrase appears. However, the translation is not arbitrary. In fact, the translation of the denoting phrase in the sentence in the language of logic is guided by three conditions. The first is the existence of the subject. It is F. There exist F. Fx. The second is the predication of the property to the subject. It is G. That has such and such a property. Gx. And finally the uniqueness of the subject. Nothing else is F. One and only one entity. These conditions are necessary since there is the general conception that the ‘the F is G’ is to be perceived as an existential generalization. With the role of the three conditions acknowledge, let us go back the sentence ‘I met a man.’ The sentence ‘I met a man’, the denoting phrase ‘a man’ means ‘I met x and x is human is not always false’ or ‘There is an ‘x’ such that ‘x’ is human and I met x.’ Or maybe we can also translate the sentence ‘I met a man.’ to ‘There is a being such that that being is human and I met that being.’ What is noticeable in both translations is that the denoting phrase ‘a man’ has disappeared already. Also let us look into the sentence ‘the father of Charles II was executed.’ The presence of quantifier the ascertains uniqueness. As such, the sentence ‘the father of Charles II was executed can be translated as ‘It is not always false of x that x begat Charles II and that x was executed and that if y begat Charles II., y is identical with x is always true of y.’ Or it can also be translated as ‘there is such an x such that x fathered Charles II, and for all y, if y begat Charles II, then, y=x, and x was executed. And as such, in the translation we are able to arrived at the real meaning of the sentence ‘the father of Charles II was executed. The real meaning of the sentence are: first, ‘there is one who is the father of Charles II.’ (existential claim). Second, ‘one and only one entity who has fathered Charles II (uniqueness) and finally ‘that entity was executed.’ (predication).Within the real meaning the denoting phrase ‘the father of Charles II’ has disappeared. Another example is the ‘the present King of France’ in the sentence ‘The present King of France is bald.” Using the three conditions for the translation of the sentence, ‘there is one entity who is the present King of France’ (existential claim). ‘One and only one entity is the present king of France’ (uniqueness) and finally ‘and that one entity is bald’ (predication). As such, we can now state that the Russell’s theory of denotation asserts the following: First, denotating phrases never have meaning in themselves and that it only becomes meaningful in context. Second, the meaning of the denoting phrase is not what it seems. And finally, the real meaning of the denoting phrases appears only after the translation the sentence into the language of logic with the necessary inclusion of the three conditions namely the existence of the subject, the predication of the property to the subject and the uniqueness of the subject. THE THREE PUZZLES AND RUSSELL’S THEORY Russell’s theory on denotation intends to solve three puzzles. These are the principle of substitutivity, the principle of excluded middle and the negative existential. The principle of substitutivity becomes a puzzle the moment it is combined propositional attitude. Take the example, ‘George IV wished to know whether Scott was the author of Waverly.’ Supposing that ‘Scott is the author of Waverly’ then we can translate this into Scott= the author of Waverly. Then can we say that ‘George IV wished to know whether Scott was Scott.’ Of course, the last sentence is false because what George IV wished to know whether Scott was the author of Waverly’ and ‘not whether Scott was Scott’. The principle of excluded becomes a puzzle since it may allow for logically true propositions like ‘Either the present King of France is bald or the present King of France is not bald.” However, neither option is acceptable since both disjuncts are not true. And the third puzzle is the negative existential. This becomes a puzzle since the moment that we claim or maintain that something or other does not exists, we can only do so by using phrase that denotes it. And if we have succeeded in coming up with a denoting phrase to denote its non-existence, then it will no longer be true to deny its existence. Russell’s theory on denoting was able to account and address these three puzzles. How? On the principle of substitutivity. Utilising translation, grammatical form to logical form, Russell was able to show that the sentence ‘Scott was the author of Waverly’ is not an identity statement, not Scott= the author of Waverly. Therefore, the phrase ‘the author of Waverly’ cannot be substituted for Scott. Hence, you cannot formulate ‘George IV wished to know whether Scott was Scott.’ For the principle of excluded middle and the negative existentials, Russell used his distinction between the primary occurrence of description which is a wide scope of description and the secondary occurrence which is narrow in scope. Though his distinction between primary and secondary occurrences were clearly elucidated in his other work Descriptions, what was important to note was the fact that via this disctinction the law of excluded middle has been preserved and the problem regarding negative existential have been uncovered as inauthentic – “we know the properties of a thing without having acquaintances with the thing itself, and without, consequently, knowing any single proposition of which the thing itself is a constituent.” (Russell 1905, p493) CONCLUSION Russell’s theory on denotation is strong one that even Meinong acknowledged the error in his theory. It was able to tackle and address the three puzzles that it has intended to address. It has provided as a means with which an ordinary language can be further analyzed and understood with resorting to the creation of anything that goes beyond the bounds of what we may possibly know and describe. However, Russsell’s theory although logically cogent misses one of the most important facets of natural language – it does not conform and work in the same manner as the language of logic. Natural language asserts existence and predication at the same time, it does not separate nor distinguishes. REFERENCES: Russell, Bertrand. (1905) “On Denoting”, Mind, New Series, Vol. 14, No. 56, p 479 – 493. Sutler, Ronald. (1967). “Russell’s “refutation of Meinong in “On Denoting”, Philosophy and Phenomenological Research, Vol. 27, No 4, p 512 – 516. Read More