Is there any reason why special sciences like chemistry , biology , neuroscience and psychology would need their own immutable laws that aren't reflective of physical laws ?
In the case of the "hard" natural sciences (like chemistry, solid-state electronics, astrophysics, etc.), the first principles upon which they are based can be traced back to physics, and therefore the laws governing them have their roots in the laws of physics.
The field of psychology does not belong on the same list because it contains no universal laws in the same sense that for example electrical engineering does.
Chemistry biology and neuroscience are hard physical sciences, so the laws they have are physical laws. Perhaps you meant, is there any reason they might not be reducible to physics?
There is a kind of contradiction or tautology, from Hume's 'no miracles' argument: any regularities revealed, will become the new laws of physics - even the intervention of a mind or spirit from 'outside' the system and it's internal laws, as discussed by analogy with the simulation argument here Are gods also bound to the laws of physics?
It is important to think about what laws or axioms are Does reality have axioms? We can look at axiom choice as a way to make the best headway in creating effective models Are mathematical axioms arbitrary?
There is a specific problem with laws, where for instance the universe is described as deterministic in principle, eg across Many Worlds, and that is pictured as different to being indeterministic. But if alternate outcomes are truly innaccessible, are they real? What about events beyond cosmological horizons, which in an expanding universe can never interact with us?
In physics properties of some simple systems are deduced by understanding it's Hilbert space, the imaginary space of all of it's possible configurations. And, that seems to have a kind of reality, when we can calculate it. But as a system gets bigger it rapidly becomes impossible to do so. Taken to the extreme, are all the possible outcomes from the big bang, one type of multiverse 'real'?
We need to think carefully about what real means.
I suggest there is something like Turing completeness, the ability of one system to simulate or mutually translate with another, that is the source if unity of knowledge, expressed in the idea of being reducible to physics.
Soft sciences & humanities involve historical and biological contingencies, which limit how much they can be generalised from.
The whole concept of laws and what they are etc. is a big complex area and which approach you favour will affect that approach you take to this type of question. The general literature from which the type of response I give below is drawn often treats laws as 'true universal generalisations that support counterfactuals' or equivalent. One could alternatively quite respectably define laws in a way that would almost by definition restrict this concept to fundamental physics.
But the standard response to this type of reductionism is around multiple realisation. So say that it is a law of psychology that 'persons who are slighted become resentful'. (I can't be bothered to do the c-fibers/pain example!) There is presumably some social definition of what being slighted would mean, which competent language users could agree on, and equally a definition of being resentful, and if this claim is truly lawlike we could use it to make predictions about the behaviour of people in different situations. So can we reduce this to physics... well:
There could be multiple types of organism to which the psychological law applies, say humans, some type of intelligent alien with different cognitive apparatus, conscious intelligent AIs. For each of these the psychological law may apply perfectly well. But if you try to reduce to physical laws you will have a complete mess because the underlying physics will be different in each case so your reduced law will be a disjunction of incredibly complicated physical claims bearing no clear relation to each other articulable at the level of the physics. So the most powerful and sensible level to formulate the claim seems to be that of psychology not physics.
Just a perspective of mine, but I think that when philosophers talk about reducing claims to physics they are often glib about the absurd complexity involved. To be clear - we cannot analyse even very simple systems, like a block sliding down an inclined plane that you analyse in high school mechanics, using fundamental physics. Specifying such a system and using the Schrodinger equation to model its time evolution is utterly and completely beyond our capabilities, and always will be, and would be an absurd way to approach the problem in any case. The idea of using quantum field theory or whatever to analyse social behaviour or economics or other high level claims is ridiculous, even though these higher level systems ultimately supervene on underlying physics.
Your assumption is not entirely correct. Isn't the part of Physics in Chemistry acceptable? When you deal Chemistry filtering out Physics, it must show its 'individuality', right? If not, what is meant by Chemistry...? No matter whether it is science or non-science, you can find this 'individuality' in any subject. So I can't see anything wrong in it.
Physics deals only with mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms. Please note, 'mind' is not included in these branches.
Biology, neuroscience and psychology are related to living things, an important part of which is related to the mind.
Is there any reason why special sciences like chemistry, biology, neuroscience and psychology would need their own immutable laws that aren't reflective of physical laws ?
Mind affects the subjects you mentioned. There must be something higher than Physics that connects all things (living and non-living) in nature (especially, biology, neuroscience and psychology). When mind plays an important role, the dimension of these subjects changes. So they can't be reflective of physical laws.