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The Problem of Negative Existentials

The General Problem

The problem of non-existence remains a fundamental logical and philosophical problem. When people think, they always think about something that exists or does not. It is peculiar that there still can be falsehoods and truths about something non-existent. Although the latter is dependent on what really exists, individuals can have non-existent objects of thought and even formulate accurate assumptions on their accounts. It conflicts with cone logical notion, truism, that the real world is limited by what exists. The conflict between these two ideas is one of the main problems that stem from the non-existence issue. People tend to hypothesize that some things, events, or properties exist and continue to talk about them due to the fragility of their epistemic efforts. Even if they are wrong, the language continues to play its role. There are two ways in which human beings think about something that does not exist. The first one is when people suppose something may naturally be and make the error. The second way is fiction: thinking about things that we know are non-existent.

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According to static semantic theories, the names of literary characters (Sherlock Holmes or Watson) do not have singular semantic values. Under those theories, if the simple declarative sentence uses or is based on empty singular NP, it cannot be viewed as a complete thought or proposition. To put it differently, the propositional composition is not possible when expressions are empty and lack semantic values. What is more, the sentence “Sherlock Holmes is a policeman” could not be evaluated with respect to truth or falsity. Under standard theories and frameworks, only complete thought or propositional structures can be judged as true or false. This utterance used in the example should be declared neither false nor true. It can be explained by the fact that there are no real-world correlates for tokens like “Sherlock Holmes”; thus, it does not have a semantic relation and truth value.

The same logic is hardly seen to explain the negative Existentials. The predicative adjective phrases in simple sentences with empty NP cannot relate to the actual properties of the character in question. On the contrary, the utterance of negative Existentials “Holmes does not exist” is literally true and expresses a complete proposition. It brings a significant contradiction to already mentioned standard frameworks since it still includes valueless NP not suitable for propositional composition but that successfully contributes to the true utterance. For that reason, true negative Existentials represent how things really occur in reality, add new information to understand the real world’s representation and express literally true thoughts.

Here NPs, still semantically empty, fulfill propositional and compositional functions when put in an adequate sentential environment. It can be explained by the fact that sides of conversation usually turn to additional cognition and information, creating a truth-evaluable proposition. When people read or hear sentences like that, they do not usually face any challenges to understand its deep meaning, despite misleading personal nouns (under standard theories). However, both Meinong’s and Russell’s approaches fail to succeed in understanding the negative Existentials’s nature. In order to solve this problem, one should embrace the idea that negative Existentials reject the referential presupposition their NP may hold.

Frege and the Problem

In his work on compound thoughts, Gottlob Frege phrased a thesis following the establishment and explanation of six different structures. He ultimately stated, “If one component of a mathematical compound thought is replaced by another thought having the same truth-value, then the resultant compound thought has the same truth-value as the original” (Frege, 1963, p. 17). Component meaningful expressions define the designatum (reference) of a compound expression. In this context, his theory resembles the already mentioned standard semantic theoretical frameworks, especially Russell’s. The philosopher also believed that NPs, which can be accompanied by other words and signs in expression, should have a definite object as their designatum. In other words, every term has its own referent, and every utterance has a truth value. Moreover, the same reference can be determined by a myriad of senses. For instance, one could say that “Trump was a president when the pandemic started” and “Trump was a president in 2020”. Both sentences have the same referent but different senses that specify them and bring different meanings.

What is more, under Frege, when language is ideally logical, every sign and the proper name relates to an object that does exist somewhere in the world. On the contrary, when the language is logically flawed, some signs or proper names fail to refer to the object. He believes that empty signs that do not designate definite objects lead to logical errors and hence should be avoided. The concept of extensionality states that “the designatum of a compound expression is a function of the things designated by the component meaningful expressions.” It means that phrase put in isolation does not convey the proper meaning.

Moreover, his principle of extensionality for non-designation asserts that if one of the meaningful component expressions of a compound expression fails to designate anything, then the entire compound expression itself also fails to designate anything. From this perspective, the sentence “Sherlock Holmes does not exist,” and NP does not have the designatum. “Sherlock Holmes” here plays the role of the personal noun that does not refer to the real person. Still, the form of true negative Existentials provides meaning that can be judged for truth. Even if there is no reference to which the name corresponds, the sense still can be possessed by a personal noun. Next, this essay will provide solutions based on Frege’s main doctrines.

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The Solution to the Problem

The German mathematician became an innovator in the philosophy of language by adding the concept of sense to the already existing idea of designation. The proper name indicates the reference (Bedeutung) to what is the object means. The sense (Sinn), also known as a mode of presentation, is a thought this name expresses. It reveals a unique aspect of the referent that may preserve no matter if the actual object exists. For instance, in the sentence “Sherlock Holmes the best detective ever does not exist,” the new descriptive meaning was added without changing the referent what the valueless personal noun is. Different proper names should have non-identical senses or meanings in order to be separated. If two different words have the same referent, the claim that they are the same may be valid.

Extensionality investigates if objects are equal in terms of their external properties. Frege found that the truth value of an entire sentence or utterance depends on the references its parts obtain. In the case of singular true negative Existentials, its specific linguistic context creates a situation when expressions do not possess their standard reference; instead, they refer to their usual senses. Another doctrine developed by Frege is the doctrine of Mode-Shift. Every object or relation can be understood in multiple ways. These conceptions should be recognized as conceptions of the same object. In general, the mode of presentation is a part of the term’s sense.

The same referent may be described in a different manner and using other signs, demonstrating its various aspects. According to Gottlob Frege, there are customary, self-designative (direct), and indirect modes (ungerede) of presentation. Some operators may shift from customary to the indirect mode of expressions or another non-default mode. For instance, the default (customary) mode is “Holmes has a younger sister,” while “Watson believes that Holmes has a younger sister” would represent ungerede mode.

Thus, the problem of singular negative Existentials could be solved by taking into consideration that the expression’s default sense is in its indirect designatum. Although such sentences or utterances consist of personal nouns that do not relate to natural objects, they still possess indirect sense. In the already mentioned example, “Sherlock Holmes” is not a genuine designation expression, while the predicate really means what it means – existence. Negative Existentials are explained by the fact that negation is usually applied not only to the predication but also to the whole sub-sentence, a part of a compound thought. Nevertheless, theories developed by Frege and Russell received criticism regarding the inability to address similar problems fully. It is currently believed that a dynamic semantic approach to negative Existentials has more potential to explain its contradictory features.

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