Temperature is just molecules moving, and that is reductionism in one line
The warmth of a gas turns out to be nothing over and above the average energy of its jostling molecules. Explaining a whole by its parts has powered physics, chemistry and molecular biology. The fight is over whether everything, minds included, can be explained that way, or whether wholes have features no part possesses.
The Oxford Companion to Philosophy calls reductionism one of the most used and abused terms in philosophy and splits it three ways. Ontological reductionism says reality is built from a minimal set of basic parts. Methodological reductionism is the scientific habit of explaining things through ever smaller components. Theory reductionism says a newer theory does not simply replace an older one but shows it in more basic terms. Kepler's planetary laws and Galileo's laws of falling bodies both reduce to Newton's mechanics, which captures everything they explain and more.
The crude slogan that a whole equals its parts added up, and no more, is contested. A subtler view says a system is made entirely of parts yet can have features none of them has, which is the core of emergentism. Reductionists can accept emergent behaviour as long as it is fully explicable by the underlying processes; strong emergentists say something genuinely new appears. Distinctions multiply: philosophers generally accept that each individual biological thing is a sum of chemical things, but often reject the claim that every biological kind reduces to chemical kinds.
Mathematics has its own version. Ernst Zermelo championed building all of mathematics on axiomatic set theory. Kurt Gödel's incompleteness theorems of 1931 dented that hope by proving that any consistent system strong enough for ordinary arithmetic contains true statements it cannot prove; Paul Cohen later showed the continuum hypothesis is undecidable in standard set theory. In computer science, reduction is precise and everyday: solving one problem by translating it into another already solved, the basis of complexity theory and of programmers reusing existing routines.
Resistance has a long history. Descartes split the mechanical material world from the free mind, and Kant placed free will in a noumenal realm beyond the deterministic laws of appearances. Theologians such as Friedrich Schleiermacher grounded religion in human feeling to protect it from reduction. Alfred North Whitehead condemned what he called the fallacy of misplaced concreteness, and even in physics some argue that reduction never goes all the way in practice.
Source: Reductionism
