Paste your essay in here…In this essay, I will be discussing the improvement incomplete symbol analysis has made to analytic philosophy in comparison to analysis which proceeds via word-by-word definitions. Initially, Russell presented his realist approach to analysis by employing word-by-word definitions; however, this method of analysis contained inherent flaws and Russell consequently appealed to an analysis of incomplete symbols. The revision of Russell’s theory worked upon by Stebbing only improved the understanding of incomplete symbol analysis, running analysis via word-by-word definition redundant. In what follows I will present both Russell’s and Stebbing’s positions in order to showcase the improvements analytic philosophy has made since the proposal of word-by-word definitions.
I will begin by outlining a few key terminologies. Firstly, let us distinguish between complete symbols and incomplete symbols. A complete symbol is taken to be one which is directly referential and whose meaning does not consist of description (Janssen-Lauret 2018b, 3); for example, if we were to take ‘Theresa May’ to be a complete symbol then we know directly of its referent in our universe with every occurrence of ‘Theresa May’. In contrast, an incomplete symbol is taken to be one which does not possess its own referent. Instead, incomplete symbols are analysed by appealing to the context surrounding the symbol and subsequently providing an appropriate descriptive meaning with accordance to its context (Whitehead and Russell 1963, 66); for example, if you take ‘Theresa May’ to be an incomplete symbol then we can say that ‘Theresa May’ is ‘The current Prime Minister of the United Kingdom’. It is important to note that those in close relations with ‘Theresa May’ may attribute other descriptions to the symbol, such as “My wife” or “My friend”. Clearly, incomplete symbols can form various descriptive statements depending on the contexts of which they are moulded.
To begin, I will present Russell’s initial realist approach to analysis. Before Russell delved into the practice of incomplete symbol analysis, he proposed that analysis was to be conducted via word-by-word definitions. Word-by-word definition analysis stems from the role of complete symbols. This method of analysis takes each and every word of the statement to have a direct meaning, or a direct reference; in other words, all symbols are complete (Janssen-Lauret 2017, 11). This stance faced many criticisms. One crucial flaw this position encountered was that of a Meinongianist touch. The issue here is as such: Russell suggested we take each and every word in statements to hold a referent, but this suggestion does not uphold for statements made about the fictitious (Janssen-Lauret 2017, 11-12). For example, we may wish to say, ‘Aphrodite is a mythical woman’. This proposal is indeed true in our current reality; however, from a word-by-word definition analytic approach, we would have to take that there exists a referent for ‘Aphrodite’ even though no such referent exists, precisely since Aphrodite is a mythical woman. Due to the contradictory nature of this statement, we must concede that we cannot rely on an analysis which proceeds via word-by-word definitions. Furthermore, word-by-word definition analysis fails to distinguish truths from falsities and it is also not a sufficient method for constructing truths via referents (Janssen-Lauret 2018a, 3). I will showcase this as follows: The symbols ‘pigs’, ‘four legs’, and ‘six legs’ all have referents within our current universe. The statements “Pigs have four legs” and “Pigs have six legs” both consist wholly of referents; however, this means that it seems as though each statement holds just as much representation in our universe as the other (even though it is not true that pigs have six legs). Moreover, just because we are able to have referents for ‘pigs’ and ‘six legs’ separately, it does not entail that the statement “Pigs have six legs” is indeed a truth. Overall, word-by-word definition analysis proves to be futile. Before I move on, it is important to note that Stebbing also found word-by-word definition analysis distasteful; however, I will raise her concerns later in the essay once I introduce her position.
Once uncovering the fatal flaws protruding from word-by-word definition analysis, Russell progressed onto venturing into incomplete symbol analysis. As Russell states: “By an “incomplete” symbol we mean a symbol which is not supposed to have any meaning in isolation, but is only defined in certain contexts.” (Whitehead and Russell 1963, 66). This quote indicates that the upshot of incomplete symbol analysis is that the proposed incomplete symbol is analysed away once we acquire its descriptive meaning. From a previous example, once we analyse ‘Theresa May’ to be “The current Prime Minister of the United Kingdom” we notice that the name ‘Theresa May’ is no longer required within our analysis and understanding, hence, the incomplete symbol of ‘Theresa May’ disappears after analysis. Russell proceeds to conclude that the meaning of an incomplete symbol cannot be understood in isolation (Whitehead and Russell 1963, 67). With incomplete symbols disappearing from analysis, Russell concludes that can speak of fictitious objects without running into the contradictory consequences Meinongians face. Russell advocates that when we wish to analyse propositions containing objects of fiction, we analyse the proposition’s logical form, rather than centralising analysis around the grammatical subject of the proposition. If we were to solely consider the proposition’s grammatical subject, then we fall into the issue of desiring to find the grammatical subject’s referent, when no such referent may exist (Whitehead and Russell 1963, 66). To exemplify this, I will offer the proposition “Aphrodite is a human”. This proposition is of a grammatical subject-predicate form, with ‘Aphrodite’ being the grammatical subject of the proposition. If we were to take the Meinongian approach, we would assume that ‘Aphrodite’ is just a symbol name which holds a referent but, as I mentioned earlier, there is no referent for ‘Aphrodite’. Now, Russell notes that if we were to take the logical form of the proposition, things to look a little bit different. For the grammatical subject ‘Aphrodite’, we take the logical form to be as such: ∃x(Ax) & (∀y(Ay⟹x=y). Now that we are able to access the logical form, Russell contends that we are able to analyse such a proposition without running the risk of the falling into the pitfalls of word-by-word definition analysis. Here, the logical form of a grammatical subject results to a quantified expression consisting of free variables whereby which, if “[…] there is no value of x that makes it true […]” (Russell 1919, 208), the quantified expression can be taken as false, rather than contradictory (Russell 1919, 207-208). As Russell suggests, we cannot say that ‘Aphrodite’ is the name of anything as there is no referent for ‘Aphrodite’; instead, we can continue with incomplete symbol analysis to deduce descriptive statements from the symbol ‘Aphrodite’ (for example: “Daughter of Zeus and Dione”) and furthermore, any proposition we create consisting of ‘Aphrodite’ can be analysed in such a way so that for all x, the proposition is not true (Russell 1919, 208-209).
With his notion of incomplete symbols, Russell then introduced his supposition of logical constructions. As I have explained above, Russell took incomplete symbols to be symbols which consisted of various descriptive statements and disappeared once analysed. Russell continues to suggest that since we analyse away the given incomplete symbol, we are merely left with the constituent parts corresponding to the symbol; hence, once we analyse the incomplete symbol away, we are led to believe that the symbol was only ever a logical construction of the constituent parts used to form the symbol itself (Russell 1918, 511-512). If we were to analyse the incomplete symbol of ‘Theresa May’, we may infer its constituent parts to include, but not limited to: “The current Prime Minister of the United Kingdom”, “The leader of the Conservative Party”, “A female of 62 years of age”. As Russell would suggest, the incomplete symbol of ‘Theresa May’ is just a fiction logical construction of the constituent parts I just stated.