Logical Formulation of the Ending of "Ode on a Grecian Urn" by John Keats Thanks very much in advance to anyone who can help me on this problem.
Here is the well-known conclusion of "Ode on a Grecian Urn" by John Keats:
"Beauty is truth, truth beauty,"—that is all / Ye know on earth, and all ye need to know. 
How would this be expressed in a formula with symbolic logic? There seems to be three statements here: [1] Beauty is truth, truth beauty; [2] that is all ye know on earth; [3] and all ye need to know. Is this correct?
Would the first statement be something like: If B = Beauty, T = Truth, then B = T ˄ T = B, or a similar formulation?
A complication is that the urn is "speaking" to the poet, which accounts for the quotation marks. In different editions, the quotation marks may include only the first statement, the statements in both lines, or express the first statement as a quotation within a quotation. Do these variations affect the logical outcome? 
I have searched extensively to see if anyone has approached Keats's assertion formally and I will continue to do so while I work on some sort of solution. There is a Wikipedia article devoted to the poem:
https://en.wikipedia.org/wiki/Ode_on_a_Grecian_Urn
Again, thanks to everyone for any suggestions. 
 A: "Beauty is truth" and "truth [is] beauty" might be formalised in first order logic as an equivalence, $\forall x B(x) \Leftrightarrow T(x)$ ,between two atomic predicates, or (as you suggest) as an equation between two classes, $B = T$. For the rest, you need various kinds of modal logic: some kind of  epistemic logic to model "all you know", together with some kind of deontic logic to model "all you need to know", and, to model the urn's beliefs, some kind of doxastic logic.
A: "How would this be expressed in a formula with symbolic logic?"
The question betrays a misunderstanding. There is no "right" answer to this sort of question, because the adequacy of a symbolic representation depends entirely on how much logical structure it is appropriate, in the context, to symbolize.
Take a very simple example. Suppose you are given the single claim "Everyone who Mary loves loves Jo". How to symbolise this?
Sometimes, just the unstructured "$P$" is appropriate. [Consider the argument, "If everyone who Mary loves loves Jo, then Jack loves Jo. But everyone who Mary loves does love  Jo. So Jack loves Jo". The logically relevant structure in this case is just "$P \to Q, P \therefore Q$".]
Sometimes, the appropriate representation would be $\forall x(Fx \to Gx)$. [Consider the argument  "Everyone who Mary loves loves Jo. Mary loves Bill. So Bill loves Jo". The logically relevant structure in this case is symbolised "$\forall x(Fx \to Gx), Fb \therefore Gb$".]
Sometimes, the appropriate representation would be something like $\forall x(Lmx \to Lxj)$. And it doesn't stop there. Sometimes we might need to make explicit a domain of discourse as in $(\forall x \in D)(Lmx \to Lxj)$ in order to capture logically relevant features of what is said in the context. And so it goes.
Moral: there is no such thing as the right way of expressing something as a formula from logic. And that applies for Keats quote just as it does for more mundane claims! (That's why exercises in good logic books set things up to make it clear what level of logical detail is expected.)
