The Method of Metaphysics

Let’s develop a toolkit for doing metaphysics.

Make vague theories precise

People have philosophical beliefs, but those beliefs are vague, unclear, ambiguous. Philosophers try to take unclear philosophical beliefs and make them more precise.

• Example: I am a person and believe I have free will.
• Example: Dinosaurs roamed the Earth. \(P\bigl((\exists x)(\exists y)(Dx \land Ey \land Rxy)\bigr)\).

NoteRecipe for Clarification

1. Take your vague beliefs about the fundamental features of reality or the furniture of the world (what types of fundamental things exist).
2. Try to clarify these vague thoughts in the form of some precise statement by reflection and analysis.

This sounds like a good approach: start from vague common-sense beliefs about the world and work toward a precise metaphysical view of the world. However, there are many complexities. To name just one, it is unclear how we make a vague belief about the world precise through reflection and analysis.

Extract the truthmakers of a theory

Theories are expressed using sentences. A true sentence needs something that make it true: a truthmaker. “The cat is on the mat” is true iff there exists a cat on the mat. In this example, the cat and the mat and the cat sitting on the mat is what makes the sentence true.

NoteRecipe for Truthmakers

1. Take a precise statement about the fundamental nature of reality (or a theory about the world) and list out all of its sentences.
2. If the theory is true, then something in the world makes it true (its truthmakers).
3. Check whether these truthmakers exist.

Tally up all of the sentences that we take to be true and then use those sentences to determine what the world is like. For example,

graph LR
    accTitle: Truthmakers
    accDescr: A flowchart or circular diagram showing four nodes. Metaphysical theory points to Truthmakers. Truthmakers points to "Don't exist", "Don't exist" points to "Refutes", and "Refutes" points to "Metaphysical Theory."
    T[Metaphysical theory] --> TB[Truthmakers]
    TB --> NE[Don't exist]
    NE -->|refutes| T

If we accept the sentence “the cat is on the mat and the mat is on the floor” as true, then it seems we are committed to the existence of a cat, a mat, and a floor.

Use a cost-benefit analysis

A theory is taken to be better than its rivals when the arguments and evidence favor that theory more than its rivals. Take two theories: T1 and T2. T1 has three arguments in favor of it and one argument against it. T2 has three arguments against it and one argument in favor of it.

T1	T2
+	−
+	−
+	−
−	+

In short, there are more reasons to accept T1 and fewer reasons to reject it (as opposed to T1).

Quite obviously, not all arguments are created equally, so our cost-benefit approach also needs to consider the quality / strength of each argument.

NoteRecipe for Cost-Benefit Analysis

1. Consider all of the arguments for and against a particular ontological theory \(T\)
2. Assign some positive value \(x\) to each argument that supports \(T\) and some negative value \(y\) to each argument that undermines \(T\)
3. The overall quality of the metaphysical theory \(T\) is \(v(x_1+\ldots x_n -y_1-y_n)\).
4. Choose the theory with the highest value.

TipExercise

Try out the cost-benefit analysis by considering the evidence/arguments for and against the existence of God. In one column write a list of the pros (reasons for God’s existence) and, in another column, write a list of the cons (reasons against God’s existence). Now, given this pros/cons list, do you think God exists?

Check whether theories are consistent

Obviously theories should be consistent.

NoteRecipe for Consistency

1. Take the theory you are considering and list out all of the beliefs that it entails.
2. Check whether the theory is consistent with these beliefs.
3. If the theory is inconsistent with these beliefs, then decide whether to revise the theory, reject the theory, revise the conflicting beliefs, or reject the conflicting beliefs.

Test theories with science

There is controversy about how science and metaphysics should interact. There are a few different views:

1. Non-intersection: metaphysical theorizing and science are completely autonomous (separate)
2. Scientistic: there is no real need for doing philosophy at all since we can answer every metaphysical question by simply “reading off” scientific theories.
3. Canberra: If metaphysical theory clashes with the best science, then metaphysical theory is wrong. If it doesn’t, then your theory is not falsified.

NoteRecipe for Consistency with Science

1. Start by theorizing about what exists. We determine what exists (at least initially) by considering the ordinary sentences we accept as true, determining what truthmakers we are committed to or what things we appear to be ontologically committed to in virtue of these sentences.
2. Consider various arguments for and against these sentences and modify the sentences we accept according to whether or not they mesh with our intuitions.
3. Try to put our theory on scientific footing by connecting it with the results of science.
4. If the theory conflicts with the best science, we have evidence that something is potentially wrong with our theory and it should be adjusted.
5. If the theory is consistent with science, then we have a reason to accept the theory.

TipExercise

Let’s consider the scientistic approach with respect to the afterlife. Suppose you are worried you might die, but whether you worry stems from the fact that you are not sure whether there is or isn’t an afterlife. If there is, you’ll feel calmer about death (but not totally free from worry). If there isn’t, you’ll feel terrified. What kind of guidance does science give you?

Test theories with intuitions

Many people have beliefs about the world. Let’s call a person’s belief about the world “prereflective” if they believe it in the absence of thinking about it in depth or considering its pros and cons.

NoteDefinition – Folk Intuition

A folk intuition is a prereflective judgment about a topic that is held by most people.

In simpler terms, a folk intuition is a common-sense belief that most people hold without arriving at it through careful reasoning. Examples of folk intuitions include:

1. I exist.
2. I exist in the present moment.
3. Mass murder is morally wrong.
4. Fire burns.
5. If I run into this brick wall, I will hurt myself.

NoteDefinition – Rational Intuition

At time \(t\), \(S\) rationally intuits that \(p\) if and only if at \(t\), it intellectually seems to \(S\) that it is necessary that \(p\). (Pust 2000, p. 35; Bealer 1993, p. 165)

The key difference between a folk intuition and a rational intuition is that rational intuitions are “intellectually” regarded as necessarily the case.

Some examples of rational intuitions include:

1. In any world where I think, that is a world where I exist.
2. It would be wrong to punish an innocent person for a crime they didn’t commit.
3. Human beings can survive change.

There are several reasons we might reject intuitions as good evidence in support of a theory.

1. The intuition is shown false through science or further reflection
2. The intuition is shown to be unreliable because of the discovery of a cognitive bias
3. The intuition is shown to be problematic because it conflicts with other intuitions.

NoteRecipe for Consistency with Intuitions

1. Check whether the metaphysical theory is consistent with intuitions.
2. If it is consistent, then this counts in favor of the theory.
3. If it is not consistent, then check whether there are reasons our intuitions are false or biased.

TipExercise

What is an intuition that a lot of people have but is false? Here is an exmaple to get you thinking: Educators and business professionals often think you’ll get better results by assigning work to a group. Reality: studies tend to show that you’ll get better results if you simply assign the task to your highest performing individual (or divide up the labor to individual team members without having them “collaborate”).

Check whether the theory can resolve paradoxes

A paradox is a contradictory proposition that follows from a set of propositions that are seemingly true. Let’s consider two examples.

1. Liar Paradox: “This sentence is false.” The sentence is either true or false. (1) Assume it is TRUE. If TRUE, then it is true that “this sentence is false.” Therefore, the sentence is false. Therefore, if the sentence is TRUE, then it is FALSE. Contradiction! (2) Assume it is FALSE. If FALSE, then it is false that “this sentence is false.” Therefore, the sentence is true. Therefore, if the sentence is FALSE, then it is TRUE. Contradiction!
2. Ship of Theseus. Ship A is made of wood. Planks are replaced with new planks until none of the original remain. Call this ship Planks. Ship B is made from the old planks of ship A. Call it C. A=B because objects can survive change over time. A=C because objects can be disassembled and reassembled. If identity is transitive: \(B=C\) but \(B\neq C\). Contradiction!

NoteRecipe for Solving Paradox

1. Check whether the metaphysical theory can resolve a paradox.
2. If the theory can resolve a paradox, then this counts in favor of the theory. It is a reason to accept one theory over another.

Application: Holes

Let’s apply the above considerations to the existence of a hole. Consider two different theories about whether holes exist.

• T1: Holes exist.
• T2: Holes do not exist.

Since most people believe holes exist, T1 is the intuitive theory. We can use the intuitiveness of T1 to assign the burden of proof to T2.

┌─────────────┐
│      ○      │  hole
└─────────────┘

How can supporters of T2 argue for T2?

1. Show T1 is inconsistent with some more fundamental belief
2. Show T1 is inconsistent with our best science,
3. Show that the intuitions supporting T1 are biased
4. Show that T2 can resolve a paradox that T1 cannot, and so on.

In short, T2-ers need to provide a cost-benefit analysis that shows \(T_2>T_1\).

Let’s try to provide such an argument. First, a supporter of T2 might try to clarify what a hole is. Here is one attempt:

NoteDefinition – Hole

A hole is a kind of absence. A hole is the absence of existence surrounded by something that exists.

Take a hole in a shirt. The hole is nonexistence (or empty space) surrounded by something that does exist, namely the fabric of a shirt. Or take the empty space in a copper pipe. The hole is the absence of copper pipe surrounded by the copper of the pipe. There may be “stuff” in the hole (water, air, etc.) but this does not matter. The hole is the absence of another thing (the thing surrounding the hole).

With the concept of a hole clarified, now let’s consider an argument that holes do not exist.

• P1: Theory T1 says that holes exist.
• P2: A hole is the absence of some existing thing surrounded by an existing thing.
• P3: The absence of an existing thing is not an existing thing.
• C: Therefore, holes do not exist (contrary to T1).

Here is another argument (for causal inactivity):

• P1: If holes exist, then they can cause things to happen.
• P2: Holes are causally inactive (e.g., the dough of a donut can interact with things but not the hole).
• C: Therefore, holes do not exist.

One objection to the above arguments are that holes are not absences – they are not the non-existence of something. Instead, holes are real entities: (1) the empty space surrounded by some existent thing or (2) atmospheric particles surrounded by a solid. Note: if holes were the particles surrounded by a solid, then they could causally interact with other things.

A supporter of T2 might respond in several ways.

First, there is a problem of the hole’s lifespan. Consider the hole of the donut. If the hole of a donut were a separate existing thing (e.g., the particles of air or the space), then the hole would continue to exist even if the dough is destroyed. But, intuitively, the hole is destroyed when the dough is destroyed. Therefore, the hole can neither be (1) the space between the dough nor (2) the particles between the dough. In short, our intuitions that the hole is the space / particles entails that holes are never destroyed.

Second, there is a problem relating to the location and movement of holes. Imagine a donut in a display shelf. Suppose that a hole is the precise spatial region (or the microscopic particles occupying the spatial region) surrounded by the donut material. Now suppose the donut is moved from the display case to a customer’s plate. Intuitively, the donut on the shelf is the same donut given to the customer. It is not a new donut because it was moved. The donut’s material and shape remain roughly identical. But after the donut is moved, the spatial region (or particles) are not identical. There is either a new hole in the donut or holes do not exist. Intuitively, there is not a new hole in the donut. Therefore, holes do not exist. In short, our intuitions that the hole is the space / particles entails that there are ever-new holes in a single donut when the donut is moved.

TipExercise

The belief that “holes exist” is intuitive. If you were to tell someone “holes do not exist”, you would get “the incredulous stare” (people would look at you unwilling or unable to believe what you are saying). Try to rephrase one of the arguments above that “holes do not exist”. Use pictures / diagrams.