@Tom_Storm
Iāll try a slightly different approach.
There is a common background presumption, usually unstated, that we can picture all language use as a kind of imitation of what is going on in the world; that what we say is always distinct from what is the case in a way analogous to a map being distinct from the territory.
It is a picture of a gap between what is said and how things are. Hence that picture brings with it a dualism between word and world. But it will not do for a general picture of how language as a whole functions.
Such a picture has its uses. There is often a difference between what we say and how things are. But not always. Sometimes - hopefully often - what we say is true.
Here we must differentiate between what is true and what is believed, and note that while some of the things we believe are not true, some of the things we believe are indeed true.
If the cat is on the mat, then the sentence āthe cat is on the matā is true; and in this case there is no distinction between the sentence and the truth. That the cat is on the mat is not mediated.
Thereās a but here that needs to be carefully considered. There is a difference between the sentence āThe cat is on the matā and the cat being on the mat, and there is some mediation between āthe cat is on the matā and the catās being on the mat - that the sentence āthe cat is on the matā is about the cat and the mat is indeed dependent on various features of our use of language. This is not being denied.
Rather, given that language use, if the sentence āthe cat is on the matā is true, then the cat is on the mat. There is no further separation to be accounted.
This is Davidsonās famous rejection of the āthird dogma of empiricismā, the dualism of scheme and content, the picture that we have on one side a conceptual scheme that sets out how things are, and on the other side a way things are to be matched against that scheme.
If we reject that dualism of scheme and content, as I think we must, then we have Davidsonās unmediated touch with the cat being on the mat.
Notice the careful use of quotes here. There can be explanations as to why āthe cat is on the matā - those words - are about cats and mats. But there need be no explanation as to the catās being on the mat being about cats and mats.
We are lead into a dualism between scheme and content by not noticing the difference between belief and truth. Sometimes what we believe is not true, yet sometimes we mistake the one for the other, and forget that we are talking about the world.
It might sound paradoxical at first reading, especially for someone who is enthralled by the dualism being exorcised; but our true beliefs are how the world is.
Your opening post, in asking about a supposed relationship between logic and reality, inadvertently presumes the distinction between scheme - logic - and content - reality.
As do Timās replies.