I’m not sure how clear is the background of my posts here. If they make sense or not. So,in risk of repeating myself, here is another attempt to communicate this background more clearly…
Simple picture:
The phenomenal world is a physical world.
They are in relation of subject and predicate. The relation between subject and predicate, is where the subject contains the predicate, but also something more.
Like in “Cow is an animal”. Notion ‘cow’ contains all determinations of ‘animal’, and plus something else. To be a cow is to be an animal, and still to be determined differently. If by “abstraction” we mean focusing on some part of the thing or notion, and leaving outside others, then ‘animal’ is abstraction from ‘cow’. By ignoring some specifics of what makes a cow, you are left with just a general ‘animal’.
That is what we do in phenomenal world. We put attention on some characteristics and ignore others. We look at the phenomena, and take some of the properties to be dependent on us as observers. Colors, sounds – “they have more to do with our sensory apparatus and our brain, then with the world – remove them from our analysis of the world. We will loose nothing.”. But, in doing that, we are not analyzing any other world then the phenomenal world. We are approaching things in the phenomenal world in order to measure them, put them in furnace, etc… So, the physical world is abstraction of phenomenal world.- The phenomenal world is a physical world.
Complicated picture:
Usually there is that one assumption which comes along with the analysis of the world in terms of physics, and which can be connected back to Locke and his division to primary/secondary properties. “What we have ignored or abstracted from in the physical world are secondary properties… they are not in the world at all, properly speaking. The world is what our analysis has left.”, says such view, “The physical world, stripped down to its simple multiplicity of particles which behave so and so when they are in some field, is what there is. That world affects our senses, and what we have abstracted from appears only in the mental life.”
In this view, what we call “phenomenal world” is mere construct of our minds. It might be not properly named “phenomenal world” any more, but more likely – “phenomenal experience”. The first approach to this picture is usually the simple one, where the information from sensory organs is mapped to some kind of sense-data, and everything else in the phenomenal experience we hope to get from mental processes like association. And then it is seen that it won’t do… What is called “Phenomenal experience” is too complex to reduce to that. Now we find in this “phenomenal experience” those things which we abstracted from. But we don’t want to retrace and recheck the assumptions from which we start. We are left in this psychological view of the “phenomenal experience”, in which we now want to put not just simple things that are named “qualia”, but also intentionality, language, other people and their minds – everything that we abstracted. And all that we need to construct on base of brain. And look… there is a gap!
Of course there is a gap! How can there not be a gap, where the phenomenal world is stripped down to its basics and called physical world, and now from its simple notions, which are really a few quantified notions, we need to get to how it was from the start. It is as if we abstracted from two dimensions in three dimensional space as “secondary properties”, and now try to reconstruct them, using just one dimension.
And dualists acknowledging this gap, don’t retrace and check the steps already done, but want to “add” the missing things to the picture. But I think there are two problems.
- Dualists are trying to “glue” those missing things in the wrong place. They still work in the “phenomenal experience” paradigm. “The real world” is left as it is, cleaned-up to the abstract simplicity of few simple notions.
- The “gluing” doesn’t quite work anyway. If you can abstract B and C from A, that doesn’t mean that you can just “glue” B and C and get A.
I hope that I succeeded here to communicate at least in part my feel about the weirdness of the picture in which the physical world is not taken for what really is – an abstraction, but as self-subsistent, and indeed is taken as a ground of the phenomenal world from which it was abstracted.
Return to the simple picture:
In my thinking then, we need to give up the paradigm of “phenomenal experience” as a psychological phenomenon. I think that picture is turning everything on its head. We need to give up the picture where this our living in the world falls in the realm of psychology. Instead, I think, we should accept our phenomenal being-in-the-world as a genuine being in the world. A real being, real existence in a real world. A move towards naive realism, if you like.
So, having done this move I guess it makes it clear how phenomenological analysis in this picture should not be seen as psychological analysis, and how we can look in this our being in the world for basis not just of our experiences, but also for base of intentionality, concepts and even physics.
A brood comb 
If the physical world is made to be “real,” then you have come with that as the basis of “reality.” Also, it seems with the cow analogy and statement, that this is still synthetic knowledge. Analytic knowledge seems to be required to say that the phenomenal world is the physical world. Yet, this statement itself is a huge deduction or synthesis of knowledge. Whatever we decide, as did Kant, certain presuppositions are inevitable, based on an interaction between the physical world (objects) and forms or givens as cognitively based, such as for Kant, time and space. Although apparently in minimal fashion, the form and pure ideas of Platonism are preserved then in phenomenology as an offshoot branch of Kantian philosophy. If this be true, herein in my mind lies the link between saying one world, the phenomenal, is ….something (ex. “equal”)… to the physical world. What is at stake then, is that the phenomenal world with both its experience and a priori knowledge and the physical world with its “things in themselves,” have a common origin or ground. And so one world is grounded in the other and if not, then one world cannot relate to the other. Unfortunately, post-Kantian philosophy centers the subject of the person as replacing many of the givens inherent in Aristotelian/Platonic philosophy. Yes, then the world was indeed “naive” in its realism, relatively speaking to our day. But instead, we have only the after effects of such subjectivism, namely, the psychologising of our phenomenal world. I agree with your principle however, in this manner: the physical world is part and parcel of the phenomenal world and as such the phenomenal world has physical grounding. In other words, I am arguing that the correlation existing between the phenomenal and “physical” world, means that the phenomenal is no mere construct of the mind and thus no mere psychologising. But what is greater, the deduction of ideas from the physical world or the “things in themselves”? Intentionality to me implies our reading off of the physical world in order to find meaning in it. The physical world as much as we can know it, seems to imply non-intentionality beyond survival, reproduction, etc. Therefore, ideas or words which comprise ideas, may be the only place for intentionality to exist, or a morality for example as a subset of intentionality. As such then, form or ideas, in harkening back to Plato, exist as a greater reality, from which temporal things exist. In a sense, the science of anything goes nowhere without such vocabulary. But words and mathematics in another form than the equations and sentences we derive from or about the physical world exist holistically in the physical world. This opposes the Locke quotation you have given, and hence my conclusion that physics for example, is not only an abstraction or secondary property of “things in themselves.” What they also are not, and in agreement with Locke, is a direct correlation from one to the other, as in saying the phenomenal world equals the physical world and is thus the real world. Reality is the heart of the issue. Is not actual reality reduced by deduction of any kind? Any reality that cannot hold all thoughts, matter and knowledge or other “worlds” whether empirically or analytically, into a cohesive whole as understood and contained all at once, is ultimately not completely “real.” Seems that leaves us at the foot of God for the only absolute reality. Of course this can be conceived as a cop-out, but I think it makes the most sense, and explains the common grounding between the phenomenal and physical worlds, which no one in their right mind can deny, no matter if they be called “Cant.”