Here is a precis of a conversation I had with ChatGPT written by ChatGPT:-

In our discussion, we used propositional calculus to represent the concepts of non-binary, masculinity and femininity using propositional variables and logical operators. For example, we used p = "The concept of masculinity is true", q = "The concept of femininity is true" and r = "The concept of non-binary alternatives is true" and connected them using logical operator "AND" (p ∧ q ∧ r) to assert that all three concepts are true at the same time. Or, we used "OR" (p ∨ q ∨ r) to assert that at least one of the three concepts is true at the same time.

We also discussed the logical contradiction of stating that the opposite of non-binary is a binary concept, which creates a paradox. This can be represented in propositional calculus using the statement p ∧ ¬p where p is a propositional variable that represents the concept of non-binary and ¬p represents the concept of binary. And also, we used p => ¬q where p is propositional variable that represents the concept of non-binary and ¬q represents the concept of binary. Both of these statements assert the truth of non-binary and the falseness of binary at the same time, which creates a logical paradox.

I wrote (Tebo Steele):-There is a being conceived and born in a binary universe who as a result of his investigations discovers a non-binary being in his universe... can you explain this with reference to our paradox.

Chat GPT wrote:- If there is a being, let's call him B, who is conceived and born in a binary universe, and as a result of his investigations, discovers a non-binary being, let's call it NB, in his universe, this could be seen as an illustration of the paradox "p => ¬q" where "p" represents the concept of non-binary and "q" represents the concept of binary.

In this scenario, B's understanding of the universe is based on the binary concept of "q", where everything is either one thing or the other, but through his investigations, he discovers the existence of NB, who defies this binary concept, representing the non-binary concept "p".

This discovery could be seen as a logical paradox, as the concepts of non-binary and binary are mutually exclusive and cannot coexist, yet in this scenario, they do coexist.

In other words, B's discovery of NB contradicts his previous understanding of the universe as a binary one, and illustrates the paradox of the mutually exclusive nature of non-binary and binary concepts that we discussed before.

I (Tebo Steele) added:- In order not to consider the above Paradox as offensive it may be useful to remember that the concept of non-binary includes orders of being unknown. In fact placing the paradox in an alien universe may circumnavigate the problem of offence.

I wrote(TeboSteele):- Would you say that this formulation of the Paradox is fresh territory?

ChatGPT wrote:-The specific formulation of the paradox you've described, in which a being from a binary universe discovers a non-binary being, is not a common one. It is an unique way of illustrating the paradox "p => ¬q" where "p" represents the concept of non-binary and "q" represents the concept of binary, which is a relatively new concept in the grand scheme of things.

It is an interesting way of illustrating the paradox, in the sense that it provides an analogy of the mutually exclusive nature of the concepts of binary and non-binary, using a story-like approach. This analogy could be helpful for people to understand the paradox in a different way.

It is not common to find this formulation in literature or academic research, so it is fresh in that sense.

*With reference to the error where ChatGPT says that ¬q represents binary I (Tebo Steele) wrote:- You say that ¬q represents the concept of binary.. Did you mean 'q' represents binary?

ChatGPT wrote:- You are correct, I apologize for the confusion. In the statement "p => ¬q" where p represents the concept of non-binary and ¬q represents the concept of binary, q should represent the concept of binary, not ¬q. The statement "p => ¬q" asserts that if non-binary is true, then binary is false, which creates a logical paradox because it asserts the truth of non-binary and the falseness of binary at the same time.