Are there such things as meta-facts, that is, facts about facts? Like, "1=1" is a fact, and "It is a fact that 1=1" is a meta-fact. Has anyone mentioned anything like this in the literature?
According to a common way of using the terms, it looks like you're confusing propositions with facts. Propositions (the linguistic/conceptual/psychological entities we believe, consider, deny, ascribe truth or falsehood to) are about facts (the metaphysical states of affairs that would be there even if no one considered any propositions about them).
Of course, you can always say that "it is true that it is true that... it is true that p", whenever it is true that p. You could show that with a simple truth-table.
I'm not sure, here, but let me try to argue the "no" position.
- Generally, we talk and act as if there are four kinds of things in the world -- consciousnesses, objects, events, and ideas.
- An idea is a relationship between two other things in the world.
- We can construct a rough formula of an idea, THING1 RELATIONSHIP THING2.
- Remember, things can be consciousnesses, objects, events, or OTHER ideas. This is what makes nailing down a definition of idea difficult, but I thinks solves the current question.
- A fact is a kind of idea, so it is a relationship.
- To state something as a fact is logically equivalent to this [IDEA1][CORRESPONDS TO THE SITUATIONS OF THE][WORLD OF OBJECTS, OTHER CONSCIOUSNESSES, AND/OR EVENTS].
- Look, though, the definition of a fact requires a definition of "a idea that corresponds to the reality of other things in the universe." The definition of fact is already a metafact.
- Therefore, every idea claims as a fact is already about it's fact-ness. Labeling some as meta is probably impossible.
I do think that it is a worthwhile project to establish levels of complexity for ideas, which I currently do as follows:
Idea Complexity (0) -- The thing on both the left and right side of the relationship is not another idea. Idea Complexity (1) -- One of the two sides in an idea's formulation is itself an idea. Idea Complexity (2) -- Both of the sides in an idea's formulation are themselves ideas.
That my car is blue is a fact. is already an idea at Complexity Level 2. Trying to make it more complex, like "The sentence 'That my car is blue is a fact' is untrue," does not create a more fundamentally complex idea, but only makes the ideas on both sides more convoluted.
Of course, complicating all of this is that sentences in any language really cannot involves non-ideas. You have to be able to imagine that an idea about the pencil before me is actually about the pencil and not about the word string "the pencil before me."