William of Woking comments:
(1) Tom runs
(2) that Tom runs
(3) It is true that Tom runs
We have agreed that (1) and (3) are semantically identical. Yes, they express the very same propositional content or thought. They have the very same meaning (Sinn). We also agree that (2) is verbally more complex than (1), likewise (3) is verbally more complex than (2). Yes, that's obvious.
Do you agree that it logically follows that in some cases, increasing the verbal complexity can reduce the semantic complexity? I argue as follows. Either (2) is semantically more complex than (1) or less complex. If more complex, then it follows that (2) is semantically more complex than (3), because of the semantic identity we agreed. In which case it logically follows that increasing the verbal complexity (in the move from (2) to (3)) reduces the semantic complexity. Therefore &c. Or (2) is semantically less complex than (1). In which case it logically follows that increasing the verbal complexity (from (1) to (2)) reduces the semantic complexity.
Your argument seems correct: in some cases increasing verbal complexity reduces semantic complexity. But what exactly do you mean by 'semantic complexity'? Verbal complexity seems clear: if one expression contains more words than another, then the first expression is verbally more complex. But you need to explain to us exactly what you mean when you say that one expression is semantically more complex than another. For example, (1) and (2) are semantically distinct. The first has a truth-value, the second doesn't. But which is semantically more complex? What criterion do you use to decide that? I don't see that (2) is semantically more complex than (1). If you think of 'that' as a sentential operator, then you can say that (2) results from (1) when 'that' operates upon (1). But that is not to say that (2) is semantically more complex than (1). For 'that' by itself carries no meaning. It is syncategorematical as opposed to autocaregorematical to use some Medieval lingo.
If you agree to this, then I have a large part of what I propose, for nearly all your negative arguments rest on the observation that a token of the same verbal expression (i.e. with the same verbal complexity) may appear to lack the assertoric component that the other has. My reply here is that this is consistent with 'semantic subtraction' operators. The token of the expression (1) above ('Tom runs') is identical to the token included in the that-clause in (2). No, they are distinct tokens; they are only type-identical. Yet (2) as a whole appears not to be an assertion. To be precise: (2), by itself, cannot be used to make an assertion. You would argue, in general, that this is because there is no such thing as a semantic component of assertion. I reply, in general, that this is because of the 'negative effect' of the 'that operator'.
I'm afraid this is still very unclear. Consider the sentence 'Tom sucks.' Now consider two tokens of this sentence type. (T1) 'Tom sucks' uttered by Tanya to express contempt for Tom. (T2) 'Tom sucks' uttered by Tony to describe how Tom is ingesting his cola. From the point of view of grammar, both tokens are in the indicative mood. But only one is being used to make an assertion. Therefore, there cannot be an assertoric component in indicative sentence types. And whether there is anything assertoric about a token depends on how it is used in a concrete situation.
In any case, what is the wider relevance of all this? What's at stake here? Where are you going with this?