The Methodology of Metaphysics

The Methodology of Metaphysics

As is obvious from the discussion in Section 3, the scope of metaphysics has expanded beyond the tidy boundaries Aristotle drew. So how should we answer our original question? Is contemporary metaphysics just a compendium of philosophical problems that cannot be assigned to epistemology or logic or ethics or aesthetics or to any of the parts of philosophy that have relatively clear definitions? Or is there a common theme that unites work on these disparate problems and distinguishes contemporary metaphysics from other areas of inquiry?

These issues concerning the nature of metaphysics are further connected with issues about the epistemic status of various metaphysical theories. Aristotle and most of the Medievals took it for granted that, at least in its most fundamental aspects, the ordinary person’s picture of the world is “correct as far as it goes”. But many post-Medieval metaphysicians have refused to take this for granted. Some of them, in fact, have been willing to defend the thesis that the world is very different from, perhaps radically different from, the way people thought it was before they began to reason philosophically. For example, in response to the puzzles of coincidence considered in Section 3.3, some metaphysicians have maintained that there are no objects with proper parts. This entails that composite objects—tables, chairs, cats, and so on—do not exist, a somewhat startling view. And as we saw in Section 3.1, other metaphysicians have been happy to postulate the reality of concrete merely possible worlds if this posit makes for a simpler and more explanatorily powerful theory of modality. Perhaps this contemporary openness to “revisionary” metaphysics is simply a recovery of or a reversion to a pre-Aristotelian conception of a “permissible metaphysical conclusion”, a conception that is illustrated by Zeno’s arguments against the reality of motion and Plato’s Allegory of the Cave. But no matter how we classify it, the surprising nature of many contemporary metaphysical claims puts additional pressure on practioners to explain just what they are up to. They raise questions of the methodology of metaphysics.

One attractive strategy for answering these questions emphasizes the continuity of metaphysics with science. On this conception, metaphysics is primarily or exclusively concerned with developing generalizations from our best-confirmed scientific theories. For example, in the mid-twentieth century, Quine (1948) proposed that that the “old/intermediate” metaphysical debate over the status of abstract objects should be settled in this way. He observed that if our best scientific theories are recast in the “canonical notation of (first-order) quantification” (in sufficient depth that all the inferences that users of these theories will want to make are valid in first-order logic), then many of these theories, if not all of them, will have as a logical consequence the existential generalization on a predicate FF such that FF is satisfied only by abstract objects. It would seem, therefore, that our best scientific theories “carry ontological commitment” to objects whose existence is denied by nominalism. (These objects may not be universals in the classical sense. They may, for example, be sets.) Take for example the simple theory, ‘There are homogeneous objects, and the mass of a homogeneous object in grams is the product of its density in grams per cubic centimeter and its volume in cubic centimeters’. A typical recasting of this theory in the canonical notation of quantification is:

∃Hx∃Hx & ∀x(Hx→Mx=Dx×Vx)∀x(Hx→Mx=Dx×Vx)

(‘HxHx’: ‘xx is homogeneous’; ‘MxMx’: ‘the mass of xx in grams’; ‘DxDx’: ‘the density of xx in grams per cubic centimeter’; ‘VxVx’: ‘the volume of xx in cubic centimeters’.) A first-order logical consequence of this “theory” is

∃x∃y∃z(x=y×z)∃x∃y∃z(x=y×z)

That is: there exists at least one thing that is a product (at least one thing that, for some xx and some yyis the product of xx and yy). And a product must be a number, for the operation “product of” applies only to numbers. Our little theory, at least if it is recast in the way shown above, is therefore, in a very obvious sense, “committed” to the existence of numbers. It would seem, therefore, that a nominalist cannot consistently affirm that theory. (In this example, the role played by ‘the predicate F’ in the abstract statement of Quine’s “observation” is played by the predicate ‘…=…×…’.)

Quine’s work on nominalism inspired a much broader program for approaching ontological questions. According to “neo-Quineans”, questions about the existence of abstract objects, mental events, objects with proper parts, temporal parts, and even other concrete possible worlds are united to the extent that they are questions about the ontological machinery required to account for the truth of our best-confirmed theories. Still, many questions of the new and old metaphysics are not questions of ontology. For example, many participants in the debate over causation are not particularly worried about whether causes and effects exist. Rather, they want to know “in virtue of what” something is a cause or effect. Few involved in the debate over the mental and physical are interested in the question whether there are mental properties (in some sense or other). Rather, they are interested in whether mental properties are “basic” or sui generis—or whether they are grounded, partially or fully, in physical properties.

Is there a unified methodology for metaphysics more broadly understood? Some think the task of the metaphysician is to identify and argue for explanatory relations of various kinds. According to Fine (2001), metaphysicians are in the business of providing theories of which facts or propositions ground other facts or propositions, and which facts or propositions hold “in reality”. For example, a philosopher might hold that tables and other composite objects exist, but think that facts about tables are completely grounded in facts about the arrangements of point particles or facts about the state of a wave function. This metaphysician would hold that there are no facts about tables “in reality”; rather, there are facts about arrangements of particles. Schaffer 2010 proposes a similar view, but holds that metaphysical grounding relations hold not between facts but between entities. According to Schaffer, the fundamental entity/entities should be understood as the entity/entities that grounds/ground all others. On Schaffer’s conception we can meaningfully ask whether a table is grounded in its parts or vice versa. We can even theorize (as Schaffer does) that the world as a whole is the ultimate ground for everything.

Another noteworthy approach (Sider 2012) holds that the task of the metaphysician is to “explain the world” in terms of its fundamental structure. For Sider, what unites (good) metaphysics as a discipline is that its theories are all framed in terms that pick out the fundamental structure of the world. For example, according to Sider we may understand ‘causal nihilism’ as the view that causal relations do not feature in the fundamental structure of the world, and so the best language for describing the world will eschew causal predicates.

It should be emphasized that these ways of delimiting metaphysics do not presuppose that all of the topics we’ve considered as examples of metaphysics are substantive or important to the subject. Consider the debate about modality. Quine (1953) and Sider (2012) both argue from their respective theories about the nature of metaphysics that aspects of the debate over the correct metaphysical theory of modality are misguided. Others are skeptical of the debates about composition or persistence through time. So theories about the nature of metaphysics might give us new resources for criticizing particular first-order debates that have historically been considered metaphysical, and it is common practice for metaphysicians to regard some debates as substantive while adopting a deflationist attitude about others.

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