Case in point, here's commenter 'Jayman' sarcastically characterizing reductionism:
A water molecule can be reduced to hydrogen and oxygen. Hydrogen and oxygen are both flammable. Clearly water is also flammable as it is nothing but hydrogen and oxygen.I'll get to that in a moment, but first I'm going to summarize my objections to both the essentialist positions being put forth, and 'metaphysics' in general.
- On parsimony, there is no reason to assume that 'essences', 'natures', etc., exist. The physical description of an object (whether person, animal, tool, or natural object) fully accounts for what that thing is. It is an amalgam of physical components, and there's nothing demonstrably absent or insufficient about that material description. Obviously this is the meat and potatoes of reductionism, so more on this below.
- Supposedly 'metaphysical properties' like essences and natures are not only descriptively superfluous, but they raise more questions than they answer:
- What are they composed of?
- By what mechanism do they interact with physical reality?
- If they do not exist spatiotemporally, then in what sense do they exist, and how can and do they interact with the spatiotemporal universe?
- What laws govern their structure and behavior?
- What method of inquiry could provide falsifiable answers to these questions, demonstrating them true in lieu of alternative hypotheses?
- "Metaphysics" as an intellectual discipline is ambiguously and equivocally defined.
- What metaphysics are, exactly, is not universally or even generally agreed upon 
- What constitutes a metaphysical problem is not unambiguously established, and has changed significantly over the centuries
- Even if a small number of 'metaphysicians' can agree on what constitutes a metaphysical problem, there is no unambigously established methodology for weeding out erroneous hypotheses and establishing the veracity of a proposition.
- The language and assumptions of metaphysics have been largely abandoned by scientists, which should not be the case if metaphysics represent some deeper, more fundamental reality under which scientific inquiry is subsumed.
A water molecule can be reduced to hydrogen and oxygen. Hydrogen and oxygen are both flammable. Clearly water is also flammable as it is nothing but hydrogen and oxygen.Of course, water is neither hydrogen nor oxygen, but two hydrogen atoms bonded with one oxygen atom. This chemical bond causes new properties to emerge. Reductionism does not claim that composite objects are identical to their components or that they are the sum of their components, but that the state of an object is defined by the state of its components. Water has different properties than just hydrogen or just oxygen, because it is not just hydrogen or just oxygen. Physicist Brian Greene discusses this view in his book The Hidden Reality:
I believe that a physical system is completely determined by the arrangement of its particles. Tell me how the particles making up the earth, the sun, the galaxy, and everything else are arranged, and you’ve fully articulated reality. This reductionist view is common among physicists, but there are certainly people who think otherwise. Especially when it comes to life, some believe that an essential nonphysical aspect (spirit, soul, life force, chi, and so on) is required to animate the physical. Although I remain open to this possibility, I’ve never encountered any evidence to support it. The position that makes the most sense to me is that one’s physical and mental characteristics are nothing but a manifestation of how the particles in one’s body are arranged. Specify the particle arrangement and you’ve specified everything.The philosopher Alex Rosenberg, in a talk with John Dupree, asks us to think of an elephant. Let's imagine we can know the exact wave function for every subatomic particle composing the elephant. Now imagine there is, anywhere else in the universe, another identical arrangement of wave functions. Is there any coherent sense in which the second elephant is not identical to the first? For any macroscopic property of the second elephant to be different, so too the arrangement of its constituents would have to be different.
Greene hits the nail on the head in mentioning that much of the objection to the reductionist comes from what I think is wishful thinking — that humans have eternal souls that animate our bodies and rise off the brain in death. Sam Harris has artfully argued the incoherency of the latter proposition, while YouTuber 'QualiaSoup' has a great pair of videos concisely showing the incoherency of the former, and I believe the conceptual ambiguity of 'souls' is reason enough to dismiss it. But essentialists and other proponents of a 'metaphysical reality' are also concerned with abstractions; indeed Aristotle himself was greatly concerned with the implications of Platonic Realism . Are they 'non-physical objects'? Where and how do they exist? What about mathematics? Are numbers non-physical objects? And what the hell is a non-physical 'object', anyway?
Science, though, has given us a means to understand what abstractions actually are. And before I get to that, it bears emphasizing that science has a clear advantage over 'metaphysical' methods of inquiry in that it has a universally agreed-upon method of inquiry. While it's true that the limits of science is a question of longstanding philosophical dispute, there is little if any disagreement over the fact that science is centered on a well-defined methodology that allows competing explanatory hypotheses to be tested and erroneous ones to be identified and discarded. So at the very least, science has a structured way of examining abstractions, even if the answers are not immediately obvious or forthcoming.
Science has lifted the veil, and we now know what abstractions are: they are neural structures in the brain. Cognitive linguist George Lakoff elaborates in Philosophy of the Flesh:
Our most important abstract concepts, from love to causation to morality, are conceptualized via multiple complex metaphors. Such metaphors are an essential part of those concepts, and without them the concepts are skeletal and bereft of nearly all conceptual and inferential structure.
Each complex metaphor is in turn built up out of primary metaphors, and each primary metaphor is embodied in three ways: (1) It is embodied through bodily experience in the world, which pairs sensorimotor experience with subjective experience. (2) The source-domain logic arises from the inferential structure of the sensorimotor system. And (3) it is instantiated neurally in the synaptic weights associated with neural connections.
In addition, our system of primary and complex metaphors is part of the cognitive unconscious, and most of the time we have no direct access to it or control over its use.Lakoff, with Rafael Nunez, takes a similar approach in Where Mathematics Comes From:
1. Human beings can have no access to a transcendent Platonic mathematics, if it exists. A belief in Platonic mathematics is therefore a matter of faith, much like religious faith. There can be no scientific evidence for or against the existence of a Platonic mathematics.
2. The only mathematics that human beings know or can know is, therefore, a mind-based mathematics, limited and structured by human brains and minds. The only scientific account of the nature of mathematics is therefore an account, via cognitive science, of human mind- based mathematics. Mathematical idea analysis pr ovides such an account.
3. Mathematical idea analysis shows that human mind-based mathematics uses conceptual metaphors as part of the mathematics itself.
4. Therefore human mathematics cannot be a par t of a transcendent Platonic mathematics, if such exists.There's obviously much to unpack here that's beyond the scope of a short blog post, but the point is this: scientific inquiry has allowed us to understand what abstractions are, how they are structured in the physical brain, how they are formed, and how we think about them. At no point is any assumption of the existence of some Platonic reality, or some deeper 'metaphysical reality', required for us to have this understanding; reductionism gets the job done with parsimony fully intact: conceptual metaphors and abstractions are emergent properties of the physical brain. They do not 'rise off the brain' or 'emerge from the brain'; they are neural structures within the brain.
When I'm pressed to consider an anti-reductionist point of few, I have to ask myself a few questions:
- What is missing from the reductionist point of view?
- If something is missing does an anti-reductionist point of view fill in those blanks?
- Does the anti-reductionist position have to make dubious assumptions in order to fill in those blanks?