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Substance is a core concept of ontology and metaphysics. Indeed, philosophies may be divided into monist philosophies, and dualist or pluralist philosophies. Monistic views, often associated with immanence, hold that there is only one substance, sometimes called God or Being. Dualist and pluralist views hold that two or more types of substances do exist, and that these can be placed in an ontological hierarchy. Platonism or Aristotelianism considers that there are various substances, while stoicism and Spinoza hold that there is only one substance.
The concept of substance in Western philosophy
This concept helps to explain, for instance, state transitions. Let us take a quantity of water and freeze it into ice. Substance theory maintains that there is a "substance" which is unchanged through this transition, which is both the liquid water and also the frozen ice. It maintains that the water is not replaced by the ice - it is the same stuff. If this is true, then it must be the case that the wetness of water, the hardness of ice, are not essential to the underlying stuff.
The Aristotelian view of God considered God as both ontologically and causally prior to all other substance; others, including Spinoza, argued that God is the only substance. Substance, according to Spinoza, is one and indivisible, but has multiple modes; what we ordinarily call the natural world, together with all the individuals in it, is immanent in God: hence the famous phrase Deus sive Natura ("God, or Nature").
Criticisms of the concept of substance
Friedrich Nietzsche and, after him, Martin Heidegger, Michel Foucault and Gilles Deleuze rejected the notion of "substance", and in the same movement the concept of subject. For this reason, Althusser's "anti-humanism" and Foucault's statements were criticized, by Jürgen Habermas and others, for misunderstanding that this led to a fatalist conception of social determinism. For Habermas, only a subjective form of liberty could be conceived, to the contrary of Deleuze who talks about "a life", as an impersonal and immanent form of liberty.
For Heidegger, Descartes means by "substance" that by which "we can understand nothing else than an entity which is in such a way that it need no other entity in order to be." Therefore, only God is a substance as ens perfectissimus. Heidegger showed the inextricable relationship between the concept of substance and of subject, which explains why, instead of talking about "man" or "humankind", he speaks about the Dasein, which is not a simple subject, nor a substance. 
Primitive concepts of substance theory
Two primitive concepts (i.e., genuine notions that cannot be explained in terms of something else) in substance theory are the bare particular and the inherence relation.
In substance theory, a bare particular of an object is the element without which the object would not exist, that is, its substance, which exists independent from its properties, even if it is physically impossible for it to lack properties entirely. It is "bare" because it is considered without its properties and "particular" because it is not abstract. The properties that the substance has are said to inhere in the substance. In substance theory of the mind, the objects are minds.
Another primitive concept in substance theory is the inherence relation between a substance and its properties. For example, in the sentence, "That the apple is red," substance theory says that redness inheres in the apple. Substance theory considers to be clear the meaning of the apple having the property of redness or the property of being juicy, and that a property's inherence in a substance is similar to, but not identical with, being part of the substance. The theory thus grants inherence the status of a primitive concept and requires no further definition of the word "inhere".
Arguments supporting the theory
Argument from grammar
The argument from grammar uses traditional grammar to support substance theory. For example, the sentence, "Snow is white," contains a subject, snow, and the assertion that the subject is white. The argument holds that it makes no grammatical sense to speak of "whiteness" disembodied, without snow or some other subject that is white. That is, the only way to make a meaningful claim is to speak of a subject and to predicate various properties of it. Substance theory calls this subject of predication a substance. Thus, in order to make claims about physical objects, one must refer to substances, which must exist in order for those claims to be meaningful.
Many ontologies, including bundle theory, reject the argument from grammar on the basis that a grammatical subject does not necessarily refer to a metaphysical subject. Bundle theory, for example, maintains that the grammatical subject of statement refers to its properties. For example, a bundle theorist understands the grammatical subject of the sentence, "Snow is white", as a referent to a bundle of properties, including perhaps the containing of ice crystals, being cold, and being a few feet deep. To the bundle theorist, the sentence then modifies that bundle of properties to include the property of being white. The bundle theorist, then, maintains that one can make meaningful statements about bodies without referring to substances that lack properties.
Argument from conception
Another argument for the substance theory is the argument from conception. The argument claims that in order to conceive of an object's properties, like the redness of an apple, one must conceive of the object that has those properties. According to the argument, one cannot conceive of redness, or any other property, distinct from the thing that has that property. The thing that has the property, the argument maintains, is a substance. The argument from conception holds that properties (e.g. redness or being four inches wide) are inconceivable by themselves and therefore it is always a substance that has the properties. Thus, it asserts, substances exist.
A criticism of the argument from conception is that properties' being of substances does not follow from inability to think of isolated properties. The bundle theorist, for example, says that properties need only be associated with a bundle of other properties, which bundle is called an object. The critic maintains that the inability for an individual property to exist in isolation does not imply that substances exist. Instead, he argues, bodies may be bundles of properties, and an individual property may simply be unable to exist separately from such a bundle.
In direct opposition to substance theory is bundle theory, whose most basic premise is that all concrete particulars are merely constructions or 'bundles' of attributes, or qualitive properties:
- Necessarily, for any concrete entity, , if for any entity, , is a constituent of , then is an attribute.
The bundle theorist's principal objections to substance theory concern the bare particulars of a substance, which substance theory considers independently of the substance's properties. The bundle theorist objects to the notion of a thing with no properties, claiming that one cannot conceive of such a thing and citing John Locke, who described a substance as "a something, I know not what." To the critic, as soon as one has any notion of a substance in mind, a property accompanies that notion. That is, to the critic it is not only physically impossible to encounter a bare particular without properties, but the very notion of a thing without properties is so strange that he cannot even form such a notion.
The indiscernibility argument from the substance theorist targets those bundle theorists who are also metaphysical realists. Metaphysical realism uses repeatable entities known as universals exemplified by concrete particulars to explain the phenomenon of attribute agreement. Substance theorists then say that bundle theory and metaphysical realism can only coexist by introducing an identity of indiscernibles creed, which substance theorists suggest is incoherent. The identity of indiscernibles says that any concrete particular that is numerically different from another must have its own qualitive properties, or attributes.
Since bundle theory states that all concrete particulars are merely constructions or 'bundles' of attributes, or qualitive properties, the substance theorist's indiscernibility argument claims that the ability to recognize numerically different concrete particulars, such as concrete objects, requires those particulars to have discernible qualitative differences in their attributes and that the metaphysical realist who is also a bundle theorist must therefore concede to the existence of discernible (numerically different) concrete particulars, the identity of indiscernibles, and a principle of constituent identity.
Discernible concrete particulars
- Necessarily, for any complex objects, and , if for any entity, , is a constituent of if and only if is a constituent of , then is numerically identical with .
The indiscernibility argument points out that if bundle theory and discernible concrete particulars theory explain the relationship between attributes, then the identity of indiscernibles theory must also be true:
Identity of indiscernibles
- Necessarily, for any concrete objects, and , if for any attribute, Φ, Φ is an attribute of a if and only if Φ is an attribute of b, then a is numerically identical with b.
The indiscernibles argument then asserts that the identity of indiscernibles is false. For example, two different pieces of printer paper can be side by side, numerically different from each other. However, the argument says, all of their qualitive properties can be the same (e.g. both can be white, rectangular-shaped, 9 x 11 inches...). Thus, the argument claims, bundle theory and metaphysical realism cannot both be correct.
However, bundle theory combined with trope theory (as opposed to metaphysical realism) is immune to the indiscernibles argument. The immunity stems from the fact that each trope (attribute) can only be held by one concrete particular, thus qualitive indiscernible objects can exist while being numerically identical and the identity of indiscernibles therefore does not hold.
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