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Metalanguages are formal metaphors

 In a logic class, the professor tells his students: "Yesterday, while talking with my Sufi gardener about happiness, we ended up talking about metalanguages, because he said that orchids are 'chambers where light plays between amorous encounters.' I told him: 'You have to be a poet to talk about poetry.' He replied: 'You just have to be human.'" In what way can we say that my gardener is proposing that every metalanguage is a formalized metaphor for its object language and what would be the metaphor for arithmetical addition? Furthermore” -he asks-how does this little narrative show that Kurt Gödel was a Platonist?

One student answers:
“The gardener uses orchids as a metaphor for biological reproduction, and from this he makes a second-order metaphor at the human level, calling reproduction a loving encounter. The gardener is a Sufi; in Sufi ontology, the word 'encounter' is used as equivalent to 'existence,' a double meaning (Wujud). On the other hand, the word 'light' is one of the Names of God (Nur). With this reference, what the gardener is saying is: 'God manifests himself in the play of beauty as an expression of love.'

“In our story, the professor replies: 'You have to be a poet to speak about poetry.' That is, understanding the gardener's metaphor requires a deep knowledge of poetic technique and the most important schools of aesthetics. However, the gardener replies no, that being human is a sufficient condition. By this, he is implying that poetry is a metalanguage of the language common to all humans, and anyone can speak about it.

“If we unravel the metaphor of the Sufi gardener with 'Russellian' overtones about orchids, we could translate it as something like this: 'God manifests himself in the play of beauty as an expression of love.' A complex metaphorical construction that leads the professor to respond that to understand a complex system, one must understand it from within. However, the gardener contradicts him and asserts that it is not from within, but from a more general system: poetry is a metalanguage of common language.

In a sophisticated manner, our professor suggests a hypothesis to his students based on their short narrative: what happens if we consider that every metalanguage is a formalized metaphor for its object language? In the case of Gödel's theorems, which is what the professor intends to clarify to the students, accepting this hypothesis implies that the concept of 'provability' is a metaphor for the concept of addition, and that the projected metaphorical core is that of a recursive mechanical iteration. But this is not the case with the notion of 'truth,' which is metalinguistic with respect to the arithmetic system and the metasystem constructed by Gödel. This implies a Platonic ontology.

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