Recap: Alyssa Ney's Metaphysics: Chapter 1 - Ontology

1.1 - Ontology

• The first metaphysical question we encounter is one of Ontology. What is there? What exists? What is the world made of? In order to discover what there is we need a methodology for determining our ontological commitments. Without a proper methodology, we will run into problems.

1.2 - The Platonic Riddle

• The first ontological problem we run into is what WVO Quine calls the Platonic riddle of non-being.
• Consider the creature Pegasus, the white winged horse tamed by the Greek hero Bellerophon. Pegasus was instrumental in the killing of the Chimera.
• Pegasus is a mythical creature. He—yes, he’s a stallion—does not exist. But how can I say Pegasus is a stallion? Or that Pegasus was instrumental in the killing of the Chimera? If Pegasus is or was, then Pegasus exists, or existed.
• This brings us to the Platonic riddle of non-being. To say “Pegasus does not exist” is, hopefully, to say something meaningful. But then ‘Pegasus’ must mean something. But if ‘Pegasus’ means something, then there is something that ‘Pegasus’ refers to. So Pegasus exists.
• Now, it’s tempting to think 'Pegasus' refers to an idea. But Quine rejects this. When we say “Pegasus does not exist”, we do not mean that a certain idea does not exist. That idea does exist! We mean Pegasus itself does not exist. So ‘the idea of Pegasus’ corresponds to the idea of Pegasus while ‘Pegasus’ corresponds to Pegasus. So then what is Pegasus if not an idea?
• My intuition: Pegasus is the white stallion with wings that was captured, etc. This is an “is” of identity, not of predicate. I am saying 'Pegasus' means “the white stallion with wings…” Based on that meaning, we can say ‘Pegasus’ corresponds to something that does not exist (fails to refer) while ‘the idea of Pegasus’ corresponds to something that does exist (succeeds to refer), referring to our thoughts about Pegasus. Just because something has a meaning does not mean it’s real. Things can mean and yet not refer. 'Pegasus' means something but does not refer to anything. 'Mountain made out of gold' is meaningful but not real. Anything wrong with this idea?
• Quine then entertains the idea that ‘Pegasus’ refers to something that is real, but does not exist. These are unactualized possibles, real objects that lack existence.
• My intuition: I don’t like unactualized possibles. This sounds to me like, “Pegasus is real, he just isn’t real.”
• Quine rejects this on the basis that it conflicts with common sense, which says Pegasus is not real, not that Pegasus is real but lacks existence. Quine affirms there is only one kind of existence. You can’t have real things that aren’t actual.
• Peter van Inwagen gives the following 4 theses of existence:
• Thesis 1: Being is not an activity.
• Thesis 2: Being is the same as existence.
• Thesis 3: Existence is univocal; everything that exists exists in the same sense.
• Thesis 4: This singular kind of existence is captured by the existential quantifier ∃.
• Open Question: Are there different types of existence? Kris McDaniel argues in the affirmative in his book The Fragmentation of Being. But the standard picture, following Quine, is that there is only one type of existence. (Peter Geach, Terence Parsons, Edward Zalta are more examples of philosophers who argue, in one sense or another, that there are different types of existence. But the dominant view in metaphysics today is that existence is univocal.)

Note: When we speak of identity we mean numerical identity or strict identity. If you had a twin, you may be qualitatively identical to your twin to some degree, but you are numerically identical only to yourself. This strict identity is what’s meant in math and logic when we use ‘=’, like in the case of the The Law of Identity: ∀x(x=x).

Note: Quine came up with the use/mention distinction. We can mention a word without using it by placing that word in single quotes as done above.

1.3 - Quine’s method for determining our ontological commitments

• Quine wants to affirm the common sense notion that Pegasus does not exist and yet ‘Pegasus’ is a meaningful word. So we need to keep meaning without being committed to the existence of something just because it is meaningful.
• Enter regimentation. We regiment sentences into logic so we can see what is quantified over; that’s what we are committed to. Slogan: To be is to be the value of a bound variable. So if you have ∃xFx, then x is the bound variable. If something is x, then it exists.
• That is, if something can substitute for x to make a sentence you are committed to the truth of, then you are committed to the existence of that thing. For example, here is a sentence: ∃x (Ex = p)
• In the case of Pegasus, we can write: ¬∃x (x = p)
• That Pegasus is the value of a bound variable is denied. Therefore, Pegasus does not exist (we are not committed to Pegasus).
• However, I would say: ∃xIx where I is an idea or a thought about Pegasus. This statement sounds true to me, so I'm committed to the existence of thoughts about Pegasus.

Note: Quine is doing something called semantic ascent. This is when you start with an ontological question (do non-existent objects exist?) and ascend to the semantic plane and ask a semantic question (What does ‘Pegasus does not exist’ mean?). The idea is that by first getting clear on what we mean, we can get clear on what exists. (We might call this a method of disambiguation.)

• Names as definite descriptions. Quine says that while ‘Pegasus’ means something, it need not name something (which sounds like what I said). Following Russell, Quine says that names are disguised descriptions. So if we take ‘Pegasus’ to mean “winged, a horse, and captured by Bellerophon”, we can show this as: (Wx∧Hx)∧Cx [winged horse that was captured].

• We would then show that this does not exist by: ¬∃x((Wx∧Hx)∧Cx) [There is nothing such that it is a winged horse and captured].
• However, this shows there is no indefinite object that meets these criteria. But Pegasus is a definite object; he is the winged horse captured by Bellerophon. To add the definite clause, we add:
• ∀y(((Wy∧Hy)∧Cy)⟶y = x)
• Why can’t we write this without the implies symbol like: ∀y((Wy∧Hy)∧Cy), y = x) ?
• After all we write: ∀y(y = x), not ∀y (⟶y = x)
• Answer: Because you aren’t saying that all ys are xs, only the ys that meet the criteria. Consider: All philosophers are happy. We don’t want to say all things are happy, only those things which are philosophers. So: ∀x(Px⟶Hx).
• Altogether the description is: ((Wx∧Hx)∧Cx)∧∀y(((Wy∧Hy)∧Cy) ⟶ y = x)
• Adding the negation and existential quantifier: ¬∃x(((Wx∧Hx)∧Cx)∧∀y(((Wy∧Hy)∧Cy) ⟶ y = x))
• Quine’s method (verbatim from book):
• Step 1: Decide which sentences you take to be true.
• Step 2: Regiment the sentences by symbolizing them in the language of first-order predicate logic.
• Step 3: Commit yourself to all and only those entities needed to stand in as the values of the bound variables in order to make the sentences true.

EXERCISE 1.2

Some donuts have sprinkles.

• ∃x(Dx∧Sx) (There is something such that it is a donut and has sprinkles.)
• We would only be committed to donuts.
• Or: ∃x∃y((Dx∧Py)∧Hxy) (There is something x and something y such that x is a donut and y is pink sprinkles and x has y)
• Then we would be committed to both donuts and pink sprinkles, but not pinkness.
• Or: ∃x∃y∃z(((Dx∧Sy∧Pz)∧Hyz)∧Hxy) (There is something x and something y such that x is a donut and y is sprinkles and z is pinkness and y has z and x has y)
• Then we would be committed to donuts, sprinkles, and pinkness.

Some donuts contain holes.

• ∃x∃y((Dx∧Hy)∧Cxy) (There is something x and something y such that x is a donut and y is a hole and x contains y.)
• We would be committed to donuts and holes.
• Question: Does Quine's method lead to ambiguity because there are multiple valid ways to chop things up?
• Question: I thought we were only committed to those things that stand in for x. But if we are committed to the capital letters then on pg 46 we are committed to dancing, provocativeness, bathrooms, and midnight. Are we committed to descriptions? On pg 41, are we committed to cross fertilization?
• Question: Quine’s method doesn’t tell us what things are made out of. If I say pink sprinkles exist, what is that? If I am committed to pink sprinkles, then aren’t I committed to all that makes up pink sprinkles? I would be committed to pinkness, sugar, etc?

1.4 - The method of paraphrase

• As we saw above with the donuts and sprinkles, there are different ways to cash out existence claims.
• Paraphrasing is an add-on to Quine's method where if regimentation commits you to entities you don't think you're really committed to, you can paraphrase the claim so that it makes sense to you.
• For example, take the sentence: ∃x(Sx∧Cx) [There are some species that are cross-fertile.]
• Quine is skeptical that species exist, because a species is arguably an abstract object, like a set of all individual animals that fall under that species.
• So Quine can paraphrase this into: ∃x∃y((A1x∧A2y)∧Mxy) ∨ ∃x∃y((A1x∧A3y)∧Mxy)... [There is an x and y such that x is Animal 1 and y is Animal 2 and x can mate with y and produce offspring, OR there is an x and a y such that x is Animal 1 and y is Animal 3 and x can mate with y and produce offspring...]
• This repeats for every combination of animal. Each number of animal represents a new species. So by this regimentation Quine is committed to all the individual animals that make up their species, but is not committed to species per se.

1.5 - Occam’s Razor

• Step 1 of Quine's method has us first take the sentences we find true. But how do we decide what things are true?
• "We prefer theories that can state what the world is like using the smallest set of assumptions, positing the fewest number of kinds of entities." (pg 47)
• In metaphysics, just as in physics and the other sciences, we aim to find those theories that 1) are articulated, understandable, and logically consistent; 2) explain the data as broadly and deeply as possible; and 3) do not posit more assumptions or objects as needed to explain the data.
• That last criterion is known as Occam's Razor, which is a principle that says we should shave off all the superfluous assumptions and objects contained in our theories. You only posit what's necessary to explain the data.
• Criteria 1-3 of a good theory are known as theoretical virtues. The three virtues are consistency, explanatory power, and simplicity (aka parsimony).
• There are different ways to cash out why simplicity matters. One way is to say that complexity adds mystery, and mystery reduces explanatory power, and so complex theories actually lack explanatory power compared to simple theories when all else is equal.
• For example, let's say I come home and find that one of my windows has been smashed inward so that glass is on my floor. There's one set of muddy footprints leading up to my TV, and my TV is missing.
• Naturally, I conclude that a robber broke into my home and stole my TV. But what if I concluded that two robbers broke into my home? Then that would introduce mystery, because why isn't there a second set of muddy footprints?
• Another way to cash out the virtue of simplicity is by probability of truth. More complex theories have more assumptions that can turn out false, or more entities that can turn out to not exist. And so, all else equal, more complex theories are more likely to be false. Let's think again about that second robber. Given that the data only supports one robber breaking in, positing two makes the theory more likely false, because it's likely that there was no second robber.

Note: Token vs type. Tokens are individual entities while types are types of entities. When applying Occam's Razor, we aim for the fewest types of entities. Tokens don't matter as much.

1.6 -  Where should metaphysical inquiry begin?

• When building our metaphysical theories, do we start with common sense beliefs about the world, or with what science tells us?
• Some philosophers emphasize science over common sense, citing ways in which common sense leads us astray. James Ladyman and Don Ross, as well as Peter van Inwagen, fall into this group.
• Other philosophers emphasize the importance of common sense. Kit Fine is an example here.
• Alyssa Ney makes the point that we cannot ignore common sense altogether, because metaphysics should be about those issues that matter to us. But the question remains as to how far we should let common sense guide us before we let counterintuitive scientific results overturn common sense.
• Common sense is something of a measurement of the ease of getting people on board with your theories. The more common sensical your views, the easier it will be to get others to agree with you. That's a really nice thing. But it's only nice if your theories are also actually true.