- In mathematics, reduction is the process of manipulating a series of equations or matrix into a desired 'simpler' format.
- In cooking, reduction is the process of thickening a liquid mixture such as a sauce by evaporation.
- In chemistry, reduction is the reverse of oxidation, i.e. the formal oxidation state of an atom (independant or within a molecule) is reduced by the addition of electrons.
Reduction is a difficult piece of philosophical terminology. The basic notion is this: If we reduce X to Y, then whenever we talk about X, we can be understood to be talking about Y instead.
So, for example, if we reduce the mental to the physical, then whenever we talk of pains, thoughts, and decisions, we can be understood as talking about physical events in the brain. Does that mean that we must then think that pains, thoughts, and decisions do not exist? Not necessarily and usually not.
Here is an example of a reduction from metaphysics. The BundleTheory says that objects can be reduced to collections of properties; so whenever we talk about objects, we can be understood to be talking about bundles of properties. Does this mean that the bundle theory says that objects do not exist ? Perhaps not objects as we had thought of them, but the theory is trying to give an account of what objects are; namely, they are bundles of properties. So the bundle theory is not denying that objects exist--just that objects are the same as bundles of properties. The only reason one would have for maintaining, then that the bundle theory holds that objects do not exist is if you think that, according to our ordinary concepts, something simply cannot both be a bundle of properties and an object.
Philosophers mean about the same thing when they talk about what exists ultimately. For example, the bundle theory says that ultimately, properties and bundles thereof exist, rather than objects. The things that exist "ultimately" are precisely the things to which other things are reduced.