1.When talking about intra-subjective transcendence of intentional matter it is about the possibility that one person can intend the same intentional matter in numerically and qualitatively different intentional acts, and the inter-subjective transcendence is about the possibility that it is intended additionally by multiple subjects. This shouldn’t be understood as some kind of division of intentional matter to separate types, specifically intra-subjective transcendence shouldn’t be understood as saying that intentional matter is in the subject vs. inter-subjective transcendence which wouldn’t be. Actually it is the one and the same intentional matter for which possibilities of intra-subjective and inter-subjective transcendence appear, which allows us to think many times about the issue or thing, and then to talk with somebody else about the same thing.
2.The issue of transcendence isn’t same with the issue of meaning (although connected). As argued in last post and other posts (see here for example), meaning is always meaning of something, be it written or spoken word or sentence, or different signs like nod with the head and so on, and implicitly assumes communication. Because of that, “meaning” can’t be used to refer to intentional matter, although what appears as intentional matter might be meaning of some word.
So, I might observe certain person, where the person is intentional matter of my act of observing, but while the person is intentional matter of my intentional acts, the person is not any kind of meaning, though while that person might have a name, which name would mean that person.
So, when talking about meaning we are talking about meaning of sign, and it is always connected to communication between multiple people. Even when I invent new word for something for which there is no word in the language community, it is hard to say that the word has some meaning, until I announce what I will mean by the word (by pointing or by explaining using other words). Also, when we have two persons, and one of them uses the word to mean one thing, and the other some other thing, still both people will assume that they are using the word with the meaning accepted in the language community. Hence, I think it is confusing to use “meaning” to refer to the intentional-matter, or to the inter-subjective or intra-subjective transcendence of intentional matter.
The further example which show that “meaning” isn’t used to refer to intentional acts or to the intentional matter per se, is for example, that we don’t use people who are thinking of something – “What meaning you are thinking of?”; we ask “What do you think of?”, also if somebody claims that he has just remembered something, we don’t ask “What meaning you have remembered?” , instead we ask “What did you remember?”.
3.As for relation of intentional matter and meaning, it seems to me that the later is dependent on the possibility for the former to be inter-transcendental. That’s a point I wanted to make with the story Given in the Woods. When two persons see some strange animal, for which they don’t have words, the first one can ask “What is that?”, only because he assumes that the intentional matter of his observation (namely that animal), is also intentional matter of that other persons observation, so that the intentional matter is inter-subjectively transcendent. If not, he would not ask “What is that?”
And the other way around, I argue that it is not true that inter-subjective transcendence is dependent on concept of meaning or communication (that there can’t be inter-subjective transcendence if there is no language). For example a person can hand me an apple, without her saying anything to me. I can then take the apple she gives me. And it is the same apple, hence the apple appears as intentional matter in both of us, without there be a need for any language, in which inter-subjective transcendence would be grounded.