Samir,

Thank you for restating the thesis. I hope my remarks will not imply that you have not stated it clearly or that my adhering to your principles of clarity, logic and coherence are not taken amiss.

> In doing philosophy, one needs the following: 1) define and address the problem at hand clearly. 2) break down the general 'big' problem into a sequence of smaller problems. 3) reconstruct the 'general' problem according
> to the new findings. If ... (expand) not, philosophical analysis would lead to several forms of unproductive extended discussions (such as circular, vicious, infinite regress, misunderstanding, etc).

Your later comments seem to put in doubt your principle (2) here. Let me illustrate. In cosmology, it is not uncommon to suggest that levels represent constraints on more universal levels. If this be true, then analysis
won't work, for you can't infer that more universal level from knowledge of its constraint. Perhaps another example: We generally no longer adhere to the Enlightenment notion of human nature, but see what we are as
shaped in some way by society. If a social whole is emergent, which is to say that its observables cannot be reduced to the observables of individuals, then knowledge of individuals does not explain social wholes.

1. "There are laws" can mean at least two things: a) the epistemic meaning: experience leads to generalizations so universal that we have confidence in making predictions based on them; b) the ontological meaning:
there are universal forces that are independent of matter because the are non-contingent. That we presume laws in explanation and action does decide among these two meanings. I tried to suggest before that the trend
in the philosophy of science is to move from the ontological definition to a singular causality that describes causal mechanisms. All I am saying here is that "there are laws" is ambivalent, and whatever position one
adopts needs to be stated as a presupposition, and if the old positivist epistemological meaning is adopted, it probably needs some justification. 

2. "Nature is continuous." I believe you are right, for 16th-century neoplatonic mysticism, which presumed the coherence of the world seems to have been a precondition of modern science. However, the issue is just what
is the nature of this coherence. As you know, universal laws (ontological definition) have been offered as the basis of this coherence. But there are arguably other approaches (not just mysticism). Hempel's argument that
explanation arises from laws has been generally rejected. If reality consists of emergent processes, laws don't seem relevant except trivially. The laws generated by the 19th century laboratory model seems today only
an artifact of its closure more than de re natura.  In other words, "nature is continuous" really begs questions.

2a. You introduce "level" and presume an inside-outside dichotomy in reference to levels. What justifies these assumptions? You started by saying that one should not introduce new concepts, but it seems you do so
here. Level is an ambivalent term that requires definition before use, and the inside-outside dichotomy seems a hang over from the European Enlightenment. For example, before the Enlightenment people assumed
that things have extrinsic properties that are essential to them, such as people's relation to their god.

3. No idea what you mean by laws being unified hierarchically. If laws are universal, I should think they would be applicable however we choose to chop up reality, horizontally or vertically.

4. Someone I just finished reading (perhaps Robert Klee, Introduction to the Philosophy of Science - not sure) defined your point in terms of three rather than two categories. Something like a) a reductionism says
that emergent levels can be understood in terms of its base level, b) holism, which is that wholes have emergent properties that cannot be so reduced, c) an intermediate position, which he didn't but could have
called "level", that is simultaneously an effect of the base but also of the whole. The idea is not unusual, such as Koestler's holons and Bohm's implicate order. However, as far as I know, no one has provided an
analysis of this intermediate level in physical terms that are persuasive. My point is that the whole matter remains much too vague and unsettled to base an argument on it. For example, there are the quite
different meanings of reductionism: a) all phenenomena can ultimately be explained in terms of physics, b) wholes can be explained in terms of the observable properties of its base, c) emergent wholes can
be explained if the characterization of the base includes unobservables (extrinsic functional properties no longer taken very seriously, but there are others). 

4a. You seem to be reifying the reductionist and emergentist methods, but I'm not sure. In other words, is reductionism how we can study a problem or an ontological statement? The former works well, but the
latter is contentious. I'm not sure how law comes into this unless you are suggesting that emergence is the result of unobservable laws, but it seems that lawfulness contradicts the definition of emergence,
which is that a reductionism in terms of observables is impossible. Why is determinism "upward directed"? If I throw a rock through a window, let's assume for the sake of argument that the process is a
manifestation of mechanistic laws. What does "upward" refer to here? Not sure what a holistic "form" is or why it is probabilistic rather than mechanical. The decay of a radioisotope is probabilistic, but
in what sense is it holistic?  In some sense your generalizations may be right, but they seem rather intuitive at this point.

5. Au contraire. Reductionist methods are highly sucessful in natural science and more so all the time. I might be wrong, but I believe the issue is whether the practical success of a reductionist methodology
should be used to infer ontological implications of a universal nature. I won't argue the point, but I believe that reductionism works because the situation under study is relatively closed, physically and conceptually.
That is, within a given frame, such as the question being asked concerning a limited chunk of the world, a reductionist explanation can approximately work, particularly if the base system is described to include
unobservables (the argument, as I understand it, of Jaegwon Kim).  In my example above of throwing a rock through the window, I framed in in mechanistic terms, and so a reductionist explanation works very well,
and if I broaden the frame to include my unobservable intention, reductionism still works, although it begs the question of what explains my intention.

Re. your conclusion, all problems bring in axioms, concepts, accepted theory, etc. There is no issue that can be stated with a tabula rasa. If these presuppositions are conventional, we usually don't bother
to mention them; if they are not, they must be made explicit and justified. Have you read Imre Lakatos, "Falsification and the Methodology of Scientific Research Programmes", in Lakatos and Alan Musgrave,
Criticism and the Growth of Knowledge (1970)? I don't agree with his basic position, but he does a nice job presenting the critical empiricist case.        

What is an anti-reductive form of laws? You loose me here. Laws are not systems or levels, and I don't know what it means to reduce what are probably presumed to be primitives.

Haines Brown