Online research in philosophy

According Leibniz's thesis of universal expression, each substance expresses the whole world, i.e. all other substances, or, as Leibniz frequently states, from any given complete individual notion (which includes, in internal terms, everything truly attributable to a substance) one can "deduce" or "infer" all truths about the whole world. On the other hand, in Leibniz's view each (created) substance is internally individuated, self-sufficient and independent of other (created) substances. What may be called Leibniz's expression problem is, how to reconcile these views with each other, that is, how a substance that expresses the whole world, even in the sense that the whole world can be "inferred" from its complete individual notion, can be self-sufficient and internally individuated. The purpose of this paper is to give an exact account of this tricky problem of universal expression, an account that retains substances' self-sufficiency under the constraint that all truths about the whole world are to be obtained from complete individual notions. It will also be shown how the explication of universal expression to be given accounts for Leibniz's thesis of universal change, i.e. the view that any change in any substance is reflected as a real, internal change in each and every other substance.

According to the mainstream of metaphysical thought, the world consists of independent individual things that are embedded in a spatio-temporal framework. These things are individuals, because (a) they have a spatio-temporal location, (b) they are a subject of the predication of properties each and (c) there are some qualitative properties by means of which each of these things is distinguished from all the other ones (at least the spatial-temporal location is such a property). Qualitative properties are all and only those properties whose instantiation does not depend on the existence of any particular individual; properties such as being that individual are hence excluded. These things are independent, because their basic properties are intrinsic ones. Intrinsic are all and only those qualitative properties that a thing has irrespective of whether or not there are other contingent things; all other qualitative properties are extrinsic or relational. That is to say: Having or lacking an intrinsic property is independent of accompaniment or loneliness (see Langton and Lewis (1998) and for a refinement Lewis (2001)). The basic intrinsic properties, as well as the basic relational ones, are not disjunctive; that is to say, properties such as “being round or square” are excluded. This metaphysics can be traced back to Aristotle at least. Aristotle assumes that there is a plurality of individual things (substances) that are characterized by intrinsic properties (forms) each.1 A prominent contemporary formulation is David Lewis’ thesis of Humean supervenience. Lewis writes.

The paper argues that the final value of an object-i.e., its value for its own sake-need not be intrinsic. Extrinsic final value, which accrues to things (or persons) in virtue of their relational rather than internal features, cannot be traced back to the intrinsic value of states that involve these things together with their relations. On the contrary, such states, insofar as they are valuable at all, derive their value from the things involved. The endeavour to reduce thing-values to state-values is largely motivated by a mistaken belief that appropriate responses to value must consist in preferring and/or promoting. A pluralist approach to value analysis obviates the need for reduction: the final value of a thing or person can be given an independent interpretation in terms of the appropriate thing- or person-oriented responses: admiration, love, respect, protection, care, cherishing, etc.

A classification of models of reduction into three categories — theory reductionism, explanatory reductionism, and constitutive reductionism — is presented. It is shown that this classification helps clarify the relations between various explications of reduction that have been offered in the past, especially if a distinction is maintained between the various epistemological and ontological issues that arise. A relatively new model of explanatory reduction, one that emphasizes that reduction is the explanation of a whole in terms of its parts is also presented in detail. Finally, the classification is used to clarify the debate over reductionism in molecular biology. It is argued there that while no model from the category of theory reduction might be applicable in that case, models of explanatory reduction might yet capture the structure of the relevant explanations.

The main purpose of the article is to get clear what Leibniz's concerns about relations were. His: I do not believe that you will admit an accident that is in two subjects at the same time. My judgement about relations is that paternity in David is one thing, sonship in Solomon another, but that the relation common to both is a merely mental thing whose basis is the modifications of the individuals is best seen as akin to: Father is true of David. Son is true of Solomon. But Being a father of is not true of any individual. Leibniz, like modern nominalist Nelson Goodman, could not allow the ordered pair . To establish this I must argue against Hidé Ishiguro's claim that Leibniz should have straightforwardly constructed a logic of relations, and Jaakko Hintikka's claim that Leibniz could have allowed the use of relational predicates in such forms as (Ex) Rax and (Ey) Ryb. I must also argue that what they say about the windowlessness doctrine (especially the as if formulation) is beside the point.

The paper discusses Leibniz's theory of denominations, expression, and individual notions, the central claim being that the key to many of Leibniz's fundamental theses is to consider his argument, starting from his predicate-in-subject account of truth (that in a true statement the notion of the predicate is contained in that of the subject), against purely extrinsic denominations: this argument shows why there is an internal foundation for all denominations, why everything in the world is interconnected, why each substance expresses all the others, and why every change in the world is reflected as a real, internal change in every substance.