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Discourse on Metaphysics
by Bryan Register

Date: 1 May 97
Forum: University of Texas at Austin
Copyright: Bryan Register

Note: The author may or may not still agree with the views expressed in this paper.

Section 8 of Leibniz' Discourse on Metaphysics is a discussion of substance which implies that human knowledge is analytic a posteriori. Leibniz comes to this conclusion for reasons dealing with God's powers, but I will examine only the consequences of the view.

Leibniz begins to define substance by saying 'It is indeed true that when several predicates are attributes of a single subject and this subject is not an attribute of another, we speak of it as an individual substance...' For example, the property 'deep' might be an attribute of the subject 'red', but since the subject 'red' is itself a property of some object, red is not a substance. But the object which is deep red is not an attribute, so it is a substance.

Leibniz is unsatisfied with this preliminary account, and believes it necessary to 'inquire what it is to be an attribute in reality of a certain subject.' We think of a substance - the term for which is an ultimate grammatical subject, never a predicate - as being its properties. For instance, a book is the number of pages it contains, the color of the ink on the pages, the cover art. The removal of all properties removes the entity, so all the properties together just are the entity.

Now he comes to a crucial sentence, which I shall separate by clauses: 'Now it is evident that every true predication has some basis in the nature of things...' This is correct on a correspondence theory of truth. Such a theory states that truth is the correspondence to reality of a proposition, such that 'X is Y' is true if and only if X is Y. Assuming the correspondence theory, a predication is true if and only if the predicate is in fact true of the subject. So 'X is Y' is true, if 'Y' is true of X, or if X has Y as a property.

Leibniz continues:

...even when a proposition is not identical, that is, when a predicate is not expressly contained in the subject, it is still necessary that it be virtually contained in it, and this is what the philosophers call in-esse, saying thereby that the predicate is in the subject.

This is a radical move. For a predicate to be 'contained in' the subject usually means that it is part of the definition of the subject term. If the definition of 'man' is 'rational animal', then 'rational' is 'contained in' 'man'. Contrariwise, even though all men are bipeds, 'biped' is not 'contained in' the subject term 'man', because it is not a term of the definition. But Leibniz suggests that a term can be 'contained in' the subject term, not expressly, but 'virtually'. For a predicate term to be 'contained in' a subject term, its predication on the subject must be analytic; but since it is not contained 'expressly', it must not belong to the definition of the subject term. Hence, there can be analytic truths which are not simply deductions from the definition of the subject terms.

How are we to represent substance under these circumstances? As Leibniz explains,

When we carefully consider the connection of things we see also the possibility of saying that there [were] always in [a substance] marks of all that had happened to [it] and evidences of all that would happen to [it] and traces even of everything which occurs in the universe...

This is correct. As a consequence of the view that all true predications are analytic, we must represent substance as including every term which is true of it. The subject term of a proposition needs to be represented as including all properties, actions, and relations of the substance, and the predicate term is simply one of these properties, actions, or relations.


Elmo = [red, waxen, sitting still, on the shelf]

where Elmo is a (random) name given to a red waxen thing sitting still on the shelf. When relational terms are introduced, we use simply the name of the related object to avoid a self-reference problem. And, since, as a pre-ontological fact, we can accept with Einstein that the universe is finite but unbounded, there is no infinite list of relational terms. Every other substance is included in the list, but this is a finite number.

A sentence, then, is of this form:

Elmo is [one or more of the things which Elmo is]. Since the subject term, 'Elmo', refers to the substance Elmo, and this substance is all of its properties, actions, and relations, the term 'Elmo' refers to all of Elmo's properties, actions, and relations. Hence, if the predicate is true of Elmo it is one of Elmo's properties, actions, or relations and will be included in the reference of the subject term 'Elmo'. Thus any true statement will be analytic.

Leibniz comes to this conclusion as well. The heading for section 9 of the Discourse claims 'That every individual substance expresses the whole universe in its own manner and that in its full concept is included all its experiences together with all the attendant circumstances and the whole sequence of exterior events.' That is, a thing contains its history and its relations as part of itself, as well as what it does and suffers. So a substance, for Leibniz, is not only its properties, but its actions and relations - every category the terms of which can be predicate terms.

Leibniz further claims that

...we are able to say that this is the nature of an individual substance or complete being, namely, to afford a conception so complete that the concept shall be sufficient for the understanding of it and for the deduction of all the predicates of which the substance is or may become a substance.

If one has the concept of a substance, one can deduce any term ever correctly predicable of it. If from the concept of a thing, one can deduce all true predicates of it, that thing is a substance. How one gets such a concept is a matter for epistemology; the answer is probably observation and induction - this is why knowledge is a posteriori. (For God, who has immediate access to all truths, there is no way to form such a concept, it is prior to any investigation or experience. Thus, for God, all truths are analytic a priori.) How one can deduce predicates is also an epistemological matter; the answer probably has to do with nothing more complicated than focusing on particular properties, actions, and relations of a substance, which one needs to focus on for current use.

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