Acknowledgement Paradox {VII Lacanian take}

The Acknowledgment Paradox and Hegelian Recognition (continued)

## VIII. Lacanian Analysis: The Other and the Structure of Desire

### The Symbolic Order and the Big Other

Lacan's distinction between the **other** (petit autre) and the **Other** (grand Autre) illuminates the deeper structure of your paradox. N's demand that X acknowledge 837 operates on both levels:

**X as petit autre (imaginary other):**

- X functions as N's mirror image, the place where N seeks recognition

- The demand for acknowledgment reflects **imaginary identification** - N's ego depends on X's validation

- This creates what Lacan calls the **aggressive rivalry** of the imaginary register

**The Symbolic Other behind the demand:**

- N's real demand is addressed to the **Symbolic Other** - the law, language, social order that determines what counts as a legitimate problem

- X becomes the **supposed subject of knowledge** about what constitutes a real problem

- The paradox emerges because N tries to make X speak for the Symbolic Other

### The Subject Supposed to Know

Your formalization captures what Lacan calls the **subject supposed to know** (sujet supposé savoir). N treats X as if X knows the ultimate truth about problem attribution:

```

P ↔ ¬A(N, R(X, A(X, Prob(X, P))))

```

This formula shows N's **fundamental fantasy** - that X holds the key to resolving N's relationship to their own lack (837). The circular dependency reveals that **there is no Other of the Other** - no ultimate guarantor of meaning or problem attribution.

N doesn’t merely want X to *acknowledge* 837; N wants **X to recognize N as the subject for whom 837 is a problem**. 

This requires X to *renounce their own position* as the "subject supposed to know," which is impossible without collapsing the Symbolic framework.  

Recognition fails because X cannot grant N legitimacy *without undermining the Symbolic Order* that defines X’s authority.

### Desire and the Impossibility of Full Recognition

The paradox reflects Lacan's insight that **desire is always desire of the Other**. N doesn't simply want to solve 837; N wants X to want N to not have 837 as a problem. This creates an **impossible demand** because:

- **N's desire** = for X to acknowledge that 837 is X's problem

- **But this means** N wants X to desire what X cannot authentically desire

- **The impossibility** is built into the structure of desire itself

### The Real and Symptomal Knowledge

The "837" represents what Lacan calls **the Real** - that which resists symbolization. The paradox emerges precisely because N tries to **symbolize the Real** through X's acknowledgment. But the Real cannot be symbolized without remainder - hence the logical impossibility.