In “On Denoting,” by Bertrand Russell (1905,) Russell presents fundamental statements in such a way that show the reader how they must make a series of deductions while considering built-in assumptions. He creates formulas to show how we analyze even basic statements as being true or false based on multiple criteria while providing the logical framework for denotation. In this, Russell presents what he calls “primary and secondary occurrences” which are the steps taken in the logical analysis of subjects and deductions in any given sentence.
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While this is presented in a complex manner that apparently reveals serious logical issues in previous assumptions, P.F. Strawson (1950) through “On Referring,” criticizes Russell’s presentation on all levels while managing to break through the core representations of logic in Russell’s work and simultaneously providing some alternative theory for the primary and secondary occurrences. Overall, Strawson successfully manages to reduce the strength of Russell’s arguments, though the combination of their viewpoints allows the reader to have the tools for maximum logical consideration and philosophy.
Russell proposes a problem regarding the King of France, citing the law of the excluded middle. According to this law, by definition and using the King of France as an example, the King must either undoubtedly be bald or undoubtedly not be bald. Russell points out that this person would not be included in either comprehensive lists, if formed, of either exclusively bald or exclusively not bald things. Russell questions the reasoning for this and explains through distinctions he refers to as primary and secondary occurrences.
These occurrences are applied to denoting phrases, hence the title, “On Denoting.” The issue considers the statement and the interpretation to mean that there is a King of France, and only one King of France, and this particular person is bald if one attempts to say “The King of France is bald.” As there is no King of France in reality, although proposed, this creates the problem in assumptions. The denotation involved by stating “the King of France” makes an assertion of his existence, and is a primary occurrence in this regard, since it forces the reader to assume this existence to be fact. Of course, once one realizes there is no King of France the baldness factor becoming irrelevant.
Russell creates a formula as a model for these elements, given by ∃x[(Kx & ∀y(Ky → y = x)) & Bx] (Russell p.1). This formula model the proposition of the King of France, while expressing the combination of the three statements as one of these is false. Here, the king’s baldness is the untrue component. The case of the king not being bald can also be shown when the denotation is instead interpreted as having a primary occurrence where only one King of France exists while this king is not bald, as can also be modeled, here with ∃x[(Kx & ∀y(Ky → y = x)) & ∼Bx] (Russell p.99).
Here too the reader is forced to perceive a denoting phrase that actually denotes nothing. Even with this modeling, there is still more logic to be constructed to avoid the loopholes which can be found in the components of the initial problem. To perform this task, it must be shown that the King of France is not bald while expressing this in such a way that it can be seen as factually true. The King of France not being bald should also be reworded to include what Russell calls a secondary occurrence in a denoting phrase (Russell p.99). To model the specific instances of the case to exclude the existence of one sole King of France that is bald Russell gives the model ∼∃x[(Kx & ∀y(Ky → y = x)) & Bx] (Russell p.99).
Here the proposition becomes wholly true and is an accurate model for solving the proposed problem. The summary of the analysis, as given by Russell, is “That is, “the King of France is not bald” is false if the occurrence of “the King of France” is primary, and true if it is secondary. Thus, all propositions in which “the King of France” has a primary occurrence are false; the denials of such propositions are true, but in them “the King of France” has a secondary occurrence. Thus we escape the [Hegelian] conclusion that the King of France has a wig” (Russell, p.103).
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Russell creates another problem by asking how a non-entity can be a subject for any proposition. For example, (label) 1 could be different from (label) 2, and here in this scenario, assumptions made are saying that the case is true and there is in fact a difference between 1 and 2 in saying “1 is different than 2.” However, Russell questions how it is even possible to claim that 1 is not different from 2 since the difference in question is by definition not an entity.
Russell clarifies this in another way in proposing the distinction between 1 and 2 does not subsist (Russell, p.98). Here the created proposition apparently reifies that which is not an entity. It also causes a generalized claim of nonexistence to transform into a solid affirmation of nonexistence, and as such is effectively a denoting phrase not including denotation. Here as well there is a distinction between primary and secondary occurrences while they must be employed to avoid unnecessary challenges.
Where there is a denoting phrase that does not include denotation that contains a primary occurrence, says Russell, then “the proposition containing the occurrence is false; if the occurrence is secondary, the proposition may be true” (Russell, p.103). As such, when 1 and 2 are without a difference, the proposition that there is a single entity that is a clear difference between 1 and 2 but does not subsist is thus not true. This primary occurrence is thus accompanied by the proposal that the case does not contain the elements that there is only a single entity that is a distinction between A and B that does subsist is true, and thus serves as the secondary occurrence.
If it can be regarded as fact that the credibility of and theory in logic can be examined by the ability of the theory to find solutions to any issue, in this case as Russell wrote, then it is seemingly true that the theory of denotation is in effect proven through analyzing the challenges in logic as presented in the cases and scenarios. However, Strawson (1957) adds to Russell’s approach in many ways. First, in “On Referring,” Strawson claims denoting expressions including specific references are especially of concern with regards to Russell’s reasoning.
The specific references used by Russell include definite descriptions, while Russell’s overall Theory of Descriptions, says Strawson, contains logical flaws. Strawson outlines the mistakes he claims Russell makes in the foundations of the processes he describes. Strawson considers Russell’s analysis of statements with references that do not actually refer to anything while questioning how such sentences can have a purpose in any way. As Russell himself defines purpose to be a trait of his propositions which can thus be proven to be either true or not true, statements with references that do not actually refer to anything are to be reduced into either true or untrue propositions.
Russell’s analysis of denotation contains statements such as those discussed in the King of France example have what are seemingly sentences that are of the subject-predicate variety, while there is a clear distinction between sentences of grammatical and the logical subject-predicate type (Cronk). As Strawson writes, these are not logical by definition or in logical deduction (Strawson p. 108). Russell claims his statements are propositions that are existential while additionally contain complex sophistication in the nature of his writing, however according to Strawson, they need to be reworded so that they can be more properly expressed both in terms of grammar and logic. This would remove their similarities with statements that contain subject-predicate propositions.
Russell’s methodology suggests the statements he makes, including references that do not actually refer to anything, are not subject-predicate sentences. Strawson writes that “[if] there are any sentences which are genuine of the subject-predicate form [then] there is something referred to by the logical (and grammatical) subject” (Strawson p.108). Overall, Strawson is not in agreement with either of the three implications of Russell’s logic in his theories.
Strawson also claims that Russell’s sense of names which are regarded as logically proper is not agreeable by his terms and logic (Strawson p.108). The names Russell uses are only the real subjects of a wholly genuine subject to predicate statements, while they point to a sole entity, and the definition of something to be considered logically proper by name is simply that object chosen by the definition, or as Strawson writes, the definition is “just is the individual object which the expression designates” (Strawson p.108). Strawson claims the general idea of a “proper” name with regards to logic can be associated with or even regarded as a myth.
Essentially, there are no “proper names,” in Strawson’s view, since in this assumption one would have to further consider that all referral expressions could be employed by distinctly different individuals under different circumstances with regards to different entities. As such, if people are to fully embrace Russell’s description of a true subject-predicate statement, they must effectively exclude the notion of the existence of such statements because Russell’s description of this is (as mentioned) based on the false mythological pretenses of a proper name in the logical sense (Strawson p.109).
Continued argument by Strawson over Russell’s thinking claims Russell offers (or either is himself) “confused” and as a result “thought that if any expressions were having a uniquely referring use, which wwaswhat they seemed (i.e., logical subjects) and not something else in disguise, their meaning must be the particular object which they were used to refer to” (Strawson p.113).
Strawson claims Russell could not perceive that actual reality of the definition of “uniquely referring” methods in expressions, as this meaning of expression should be “not the set of things or the single thing it may correctly be used to refer to; the meaning is the set of rules, habits, conventions for its use in referring” (Strawson p.113). The issue of the importance and purpose of a statement or general expression does not relate to the specific uses, that may or may not be either true or referring, while the purpose and importance of a statement can be discovered in the reasoning for even using the kind being considered.
Russell has essentially created a couple of true and a couple of false statements with regards to expression including references that do not actually refer to anything. Here, the true statements are the sentence has significance and the speaking of a sentence serves as a real claim only were facts are observable to back up the claims. The false statements thus are that the current speaking of the statement must be either false or true, while the speaking would be a claim of the current presence of a sole subject.
Strawson says, which others may have found intuitively obvious before Russell fabricates new logic and standards by which to process it, that the majority of Russell’s cases are neither true nor false and thus the complex models presented may not have such a significance. Strawson further states that the question of whether the statements are true or false may not be relevant at all because the question is never implied, to begin with (Strawson p. 115).
Strawson does say that this does not suggest that the sentences are without meaning or importance, as the laws for employing these expressions are not related to lower priority or “secondary” applications of the kind. Strawson advises that the expressions should not be regarded as not true but rather understand that the sentence is fundamentally incorrect, while this is Strawson’s crucial blow to Russell’s fundamental logic being fundamentally incorrect in his original postulations. Strawson recommends secondary applications, similar to the rankings described by Russell, be used to differentiate between the secondary and outright incorrect (Strawson p.116).
Strawson’s dismantling of Russell’s theory, while perhaps seemingly light and only partial in the introductory reading of his work, surpasses even the attacks of the core fundamentals and continues in other areas. He does this is claiming that Russell’s thinking that the basic King of France statements is general assertions is flawed in some ways as well. Strawson argues that while these statements may suggest the complete conditions being present as defined for Russell’s conditions for existentialism, however, Strawson calls for an immediate distinction between implication, entailment, and assertion (Strawson p. 116).
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Strawson further writes that this statement does not entail or assert that which Russell claims, though it may imply, essentially the statements are “a part of the significance of expressions of the kind I am discussing that they can be used, in an immense variety of contexts, to make unique references. It is not part of their significance to assert that they are being so used or that the conditions of their being so used are fulfilled” (Strawson p.118). The exact reasoning for the continued criticism beyond the fundamentals is seemingly less precise or motivated than Strawson’s other arguments. It would appear that the main differences between Strawson and Russell relate to a difference between the meanings of implication versus implicit assertion.
In conclusion, Strawson’s attack of the fundamentals of Russell’s work in regards to theory, logic, and grammar is apparently with less flaw than Russell’s original work. The work, though fairly objective, may have been motivated by a clear disregard for nearly all of Russell’s thinking, while the title “On Referring” seems as if it was possibly mocking Russell’s original title while simultaneously offering a much-needed solution.
The most relevant flaws found by Strawson are likely the argument that the King of France statements are real subject-predicate kinds of sentences where the framework of the sentence retains its purpose regardless if it is employed correctly. Russell’s claim that such expressions are bound to be able to be reduced into propositions that are either wholly false or wholly true and further as represented by complex models, is highly debatable logic while Strawson provides an opportunity to consider why.
This does not properly consider the “secondary uses” proposed by Strawson, and though the foundations of Russell’s argument include primary and secondary occurrences, enough consideration is not given to other areas while an extraordinarily high and complex amount of consideration and theory is applied to simple elements.
Though highly informative, Strawson’s criticisms do not give wholly more adequate perspectives on Russell’s primary postulation or clearer distinctions and conditions for the uses of primary and secondary occurrences. Though Strawson did define the seemingly better “secondary uses,” an implicit assertion remains in the examples provided to show the fundamental points of Russell’s definitions. It is possible to simply point out the flaws in rules for general usage as Russell is debatably breaking or manipulating, however as one must consider the sentence on multiple levels it perhaps is appropriate to make distinctions as described by Russell for primary and secondary occurrences.
Overall, Strawson’s argument provides for a critical analysis of both the necessity of Russell’s postulations, to begin with as well as how it can be useful or defined so that it might be useful. While Russell was attempting to provide insight in the area of logical expression and the fundamentals of a variety of philosophical aspects, Strawson was able to pick apart many of his underlying processes and effectively either add to them so that they might be better employed or criticize them for not being adequately considerate. In the end, Strawson’s analysis and critique provide for a new consideration that, when combined with Russell’s original work, invokes a deep thought process where which the elements within can be applied to a number of philosophical and logical circumstances.
Cronk, George, “Russell and Strawson on the Nature of Reference”, Bergen, 2009.
Kremer, Michael, “The Argument of ‘On Denoting’, Philosophical Review 103 (1994), pp. 249-297.”
Strawson, Peter, “On Referring,” Mind, 320-344, 1950.
Russell, Betrand, “On Denoting,” Mind, New Series, Vol. 14, No. 56., pp. 479-493, 1905.