An Argument against Correspondence Theory of Truth

Recently, I engaged in random reflection which inadvertently lead me to create an argument against the correspondence theory of truth. In philosophy, there is a debate on what constitutes truth between proponents who support the correspondence theory of truth and those who opt for the coherence theory of truth. The former asserts that truth is simply when statements corresponds to reality, whereas the latter believes that truth involves coherent relationship among beliefs that justify each other. There are problems with both positions, however I recently thought of an objection against correspondence theory that I find to be interesting. I am not sure if this objection has already been made, so I admit ignorance in this subject. Nonetheless, I will like to go over the argument.

Here is the argument, which I will try to clarify and defend:

1. For every existing thing there is a corresponding statement about it. 
2. For two things to corresponds both must exist 
3. A true statement that corresponds to an existing object about it. 
4. A true statement exists as well as the object it is about. 
5. However, if the true statement exists, then according to Premise 1 there should be another true statement about the existing true statement. 
6. However, the true statement about the existing true statement also exists, thus it would require another true statement about the true statement about the true statement.
7. Therefore, there is an infinite regress 

Basically, the argument suggests that if we accept the first premise and the second premise, then we have an infinite regress since for everything that exist, there needs to be a corresponding statement, but the corresponding statements also exists, thus we need to have statements for those too. But the statements also exist, so we need more statements for those, and so on to infinity. 

However, there are at least two objections I can think of against my argument. First, statements do not need to exist in order to correspond to an object. This is the denial of the second premise. If the second premise is false in so far as we do not need two corresponding things to exist in order for correspondence to obtain, then the statements do not need to exist to correspond to an existing object. There simply does not need to be a statement that literally exists in the sense that it floats above an object or is literally attached to an object. This is because there is something queer or unusual to believe in the existence of statements in that sense, it would commit us in believing in the existence of abstract object which seems implausible. Second, the infinite regress argument leads to superfluous infinite redundancy, because a true statement about another true statement essentially asserts the same thing, and so on. There is no need for infinite redundant statements, so we should "shave off" (so to speak) those redundant statements with only one statement corresponding to an existing object. 

However, I do not think these objections pose a problem to my argument for the following reasons. The first objection simply says that statements do not need to exist to correspond to objects, but if that's the case then what follows is that non-existing statements can correspond to existing objects. However, there is something very unusual about this. How can you talk about correspondence between a statement and an object when the statement doesn't exist? How can that which is non-existent correspond to the existent? The objection simply does not provide a positive account on how correspondence is possible. The second objection is simply false, since a statement about another statement does not need to be false. For example, suppose that there is a cat. If there is a cat, then there is a statement about the cat which asserts "There is a cat". However, if the statement exists, then there is another meta-statement (statement about the statement) which asserts "There is the statement which asserts 'There is a cat'". The second statement is not identical to the second statement, however it does assert about what was already asserted. However this apparent redundancy is not sufficient for it to be tautological in the sense that both the meta-statement and the statement are identical. 

So far it seems that the correspondence theory of truth is in trouble, if we accept it then we have an infinite regress. However, if we try to avoid an infinite regress by insisting that statements do not need to exist in order to correspond to objects, then we have to come up with a new account of correspondence.