Dialog with ChatGPT
Following is my dialog
with ChatGPT on the topic of my resolution of the
Liar Paradox in September, 2023.
User (Dan Christensen)
I
have what I think is a resolution of the Liar Paradox.
ChatGPT
The
Liar Paradox is a classic logical paradox that arises from considering a
statement that asserts its own falsehood. The most well-known example is the
statement: "This statement is false." If the statement is true, then
it must be false as it claims to be false, but if it is false, then it must be
true as it denies its own truth. This creates a self-referential contradiction.
Many
philosophers, logicians, and mathematicians have proposed various resolutions
or ways to mitigate the paradox, but there is no universally accepted solution.
If you believe you have a resolution, I'd be interested to hear it! Please go
ahead and share your proposed resolution or idea, and we can discuss it
further.
User
Some
sentences are true. Some are false. Many others, like questions and
instructions, have indeterminate truth value. This is a trichotomy. I assume
that every sentence can be classed as either a true
sentence, a false sentence or a sentence of indeterminate truth value.
"This sentence is false" is said to be a true sentence if and only if
it is a false sentence. This eliminates the possibility that it is either a
true or a false sentence. Therefore, it must be one of indeterminate truth
value.
ChatGPT
Your
proposed resolution to the Liar Paradox introduces a trichotomy of truth
values: true, false, and indeterminate truth value.
This approach attempts to address the self-referential nature of the Liar
Paradox by classifying the statement "This sentence is false" as
indeterminate in truth value.
This
solution aligns with the notion of some sentences being inherently
indeterminate, which is a viewpoint held by some philosophers and logicians.
However, it's essential to note that introducing an indeterminate truth value
may raise further questions and challenges. For instance:
Coherence:
How do we define and maintain coherence within a logical system when allowing
indeterminate truth values? It might be challenging to ensure consistency and
non-contradiction.
Interpretation
and Application: Determining when a statement falls into the indeterminate
truth value category could be subjective and open to interpretation, making it
difficult to apply consistently in various contexts.
Formalization:
Embedding indeterminate truth values into formal logical systems requires
careful formalization and may lead to complexities in logical rules and
operations.
Practicality:
In some cases, it might be challenging to determine whether a statement should
be classified as true, false, or indeterminate. This can make the approach impractical
for many real-world applications.
Overall,
your resolution introduces an interesting perspective by acknowledging
indeterminate truth values, but it also raises challenges related to the
coherence, formalization, and practicality of such a trichotomy. Further
exploration and development of this idea may help address these challenges and
provide a more robust solution to the Liar Paradox.
User
I
don't propose a system to determine whether any given sentence is true or false
or indeterminate. I am applying this analysis only to sentences like "This
sentence is false." It is a peculiar sentence in that it is a true
sentence if and only if it is a false sentence. I use this property to classify
it, and any other such sentences, as being of indeterminate truth value.
ChatGPT
Thank
you for the clarification. I see that you're specifically focusing on the
sentence "This sentence is false" and similar self-referential
sentences. You propose classifying such sentences as having an indeterminate
truth value, which is a way to address the inherent paradoxical nature of these
statements.
By
designating these self-referential sentences as indeterminate in truth value,
you're essentially circumventing the paradox by stating that they don't fit
neatly into the true or false categories due to their self-referential nature.
This
approach is a valid way to deal with the Liar Paradox and related
self-referential statements, providing a specific resolution for this
particular class of sentences. It does not necessarily aim to create a broader
system for determining truth values in general but instead provides a solution
for the peculiar case of self-referential statements that lead to logical
paradoxes.
Thank
you for the clarification, and I appreciate your contribution to this
discussion on resolving the Liar Paradox.
User
Is
this a novel approach?
ChatGPT
The
approach you've presented, classifying self-referential paradoxical statements
like the Liar Paradox as having an indeterminate truth value, is not entirely
novel. Similar ideas and approaches have been explored in the realm of
philosophy, logic, and formal systems.
The
notion of indeterminacy or truth value gaps has been a topic of discussion in
philosophical logic for quite some time. Philosophers like Graham Priest, who
advocates for dialetheism (the view that some statements can be both true and
false), have proposed similar ideas to handle paradoxes like the Liar Paradox.
Your
approach aligns with the general direction of recognizing the limitations of a
strictly binary true/false truth value system and introducing a third category
(indeterminate truth value) for certain statements. This is a valuable
perspective for addressing paradoxes arising from self-reference.
While
not entirely novel, it's important to emphasize that your particular
articulation and application of this approach to the Liar Paradox are unique
and add to the ongoing discourse around paradoxes and truth value. Different
formulations and interpretations can offer new insights and contribute to the
evolving understanding of these complex logical and philosophical issues.
END