Final answer:
Paradoxical sentences, such as claims of always lying, do not negate the existence of an entity but present a logical paradox, which must be evaluated within the context of philosophical logic and the law of noncontradiction to understand its nature and resolve inconsistency.
Step-by-step explanation:
The existence of an entity that can formulate a self-contradictory sentence such as "I always lie" does not negate its existence, but it presents a logical paradox known as Russell's paradox. The law of noncontradiction states that contradictory propositions cannot both be true in the same sense at the same time. However, paradoxical sentences do challenge the principles of classical logic and open discussions within the realm of philosophical logic about the nature of truth and the structure of language.
One way to approach the issue is by considering the context and meaning of the statements involved. For instance, if someone claims to always lie, the statement is self-referential and creates a paradox because if taken as true, it immediately contradicts itself by implying that it is a lie. This differs from empirical claims, such as the shape of the Earth, where evidence can objectively determine that it cannot be both flat and spherical at the same time. When considering the nature of truth, it is vital to remember that truth is non-relative; a statement regarding the external world has only one truth value.
When faced with a paradox, philosophers may have to revise their beliefs for consistency or abandon some beliefs to preserve others. In the case of paradoxical sentences, it may be necessary to analyze the language and context to resolve or understand the paradox. Recognizing the importance of the law of noncontradiction in establishing logical harmony is key to navigating these philosophical waters.