How to define a FHE scheme whose plaintext space is infinite using boolean circuits? There are many kinds of fully homomorphic encryption scheme by using boolean circuits. And the plaintext space $\mathcal{P} = \{ 0,1 \}$.

If there is a -bit FHE scheme, we can construct a FHE scheme which can encrypt all the messages.
For a string $x \in \{ 0,1 \}^{*}$ and $x = x_{1} \Vert x_{2} \Vert \cdots \Vert x_{n}$, we can define 
$$\mathrm{Enc}_{pk} (x) = y = \mathrm{Enc}_{pk} (x_{1}) \Vert \mathrm{Enc}_{pk} (x_{2}) \Vert \cdots \Vert \mathrm{Enc}_{pk} (x_{n})$$
where $x_{i} \in \{ 0,1 \}$

However, if I want to define a FHE with $\mathcal{P} = \{ 0,1 \}^*$, there is a problem.

Naturally, 
$$\mathrm{Enc}_{pk}: \mathcal{P} \rightarrow \mathcal{C}$$
$$\mathrm{Dec}_{sk}: \mathcal{C} \rightarrow \mathcal{P} \text{ or } \{\, \bot \,\}$$
$$\mathrm{Eval}: \mathcal{B} \times \mathcal{C}^* \rightarrow \mathcal{C}$$
where $\mathcal{B}$ is the set of all the boolean circuits.

Given $C \in \mathcal{B}$ such that $C \colon \{ 0,1 \}^{n} \rightarrow \{ 0,1 \}^m$, if $c \leftarrow \mathrm{Eval} (C, c_{1}, c_{2}, \ldots, c_{l})$, we have 
$$|\mathrm{Dec}_{sk}\left( c_{1} \right)| + |\mathrm{Dec}_{sk}\left( c_{2} \right)| + \cdots + |\mathrm{Dec}_{sk}\left( c_{l} \right)| = n$$
and
$$|\mathrm{Dec}_{sk}\left( c \right)| = m$$
But, how can we know the size of $|\mathrm{Dec}_{sk}\left( c_{i} \right)|$ when we ask the access to $\mathrm{Eval}(\cdot, \cdot)$?
I believe we have a more fundamental problem with we try to handle arbitrary length plaintexts.

Suppose that we have any encryption scheme $\mathbb{B}$ (not necessarily FHE, or even asymmetric) that tries to handle arbitrary length plaintexts.  Suppose also we also had a $\mathbb{B}$ encrypted ciphertext, which we can see is 1000 bits long.  We don't know the key, however, we can deduce that there are, at most $2^{1000}$ possible plaintexts that this might correspond to.

What does that deduction give us (given that we don't know the value of any of those $2^{1000}$ plaintexts?  Well, it'd be a pretty good guess that the plaintext isn't more than 1 Gigabyte long, even if the decryption process could potentially have a plaintext which is longer than the ciphertext.

Because of this, there is a limit to the amount of length hiding we can do, if we try to handle unbounded plaintexts.