Russell on Existence in TPLA II: Russell's Second-Order View of Existence

In my last post I introduced the topic of Russell on existence. Now I'll deliver. Let’s see what Russell thinks.

First, it is helpful to understand some of Russell’s technical vocabulary. In particular, for our purposes, we should consider his notion of a name, of a definite description, of a proposition, and of a propositional function.

For Russell, a logically proper name (or, for short, just a name) is a word whose meaning is a particular, i.e., an individual object or entity. For instance, intuitively, the name “Socrates” directly denotes the particular object, Socrates. Or the name “Paco” directly denotes my Chihuahua, Paco. Now, this is simplifying a little bit, since Russell has a whole theory of what a particular is and which words actually are proper names, but this isn’t really essential to his account of existence. One could hold to views about existence that are basically the same as Russell’s even if one modified his account of particulars and the extent of the proper names.

What is important, however, is that proper names be contrasted with definite descriptions. A definite description is some phrase that is meant to describe a particular, unique individual. For instance “the Chihuahua that I have had since 6th grade” is a definite description. (As it turns out, it does successfully denote something: my dog Paco.) “The dragon flying above my head” is a definite description too, though to my knowledge it is one that does not refer to anything.

Note: Names are not definite descriptions and definite descriptions are not names. The meaning of a name is just the object it refers to; the meaning of a definite description includes all of the predicates mentioned in the description (for instance, in the last example, "dragon," "flying", and "above my head" are all part of the meaning of the description).

It is important to bring up this contrast between definite descriptions and proper names because Russell gives a separate account of existence statements for each. What we are interested in when talking about “individual existence” statements is existence statements whose subject term is a proper name. This is the type of existence statement Russell will say is meaningless.

A proposition for Russell is, in essence, something that can be asserted, or something that can be true or false. For instance, that it is raining is a proposition, or that Paco is black is a proposition. Once again, this is simplifying a bit, but the particular details of Russell’s views on propositions are not essential here.

Finally, there is the notion of a propositional function. Russell says that a propositional function is “any expression containing an undetermined constituent, or several undetermined constituents, and becoming a proposition as soon as the undetermined constituents are determined.” Examples include ‘x is a man’ or ‘n is a number’ or ‘(x+y)(x-y)=x2-y2’. So, if we were to “fill in the blanks” so to speak we would have a full proposition. For instance, replacing ‘x’ with ‘Paco’ gives the proposition that Paco is a man. Replacing 'n' with '2' gives the proposition that 2 is a number.

Russell's propositional functions can be necessary, possible, or impossible. Russell defines this as follows. A propositional function is:

• Necessary, when it is always true;
• Possible, when it is sometimes true;
• Impossible, when it is never true.

Russell technically says that we have to take at least one of these locutions – “always true,” “sometimes true,” etc. – as undefined. But intuitively, “always true” means that every instance of the propositional function is true. For example, ‘x is x’ is a propositional function that is “necessary’ in Russell’s sense, since it is “always true,” whereas ‘x is a man’ is a propositional function that is possible but not necessary. These locutions are clearly not meant in a temporal sense.

(Interesting side-note: Obviously Russell's definition of "possible" and the like is not at all the definition we would immediately think of when we hear these words. What's interesting is that it's not clear whether he even meant to capture what we do with possible worlds semantics. He makes it explicit that he thinks previous thinking about modality is confused and problematic in some way, but it's not clear whether his discussion of modality is trying to capture some sort of traditional modal phenomenon as opposed to just making stipulations, nor whether his attitude toward traditional notions of modality is one of revision or rejection. Another interesting question: Is there any way to modernize Russell here? Is he on to anything at all? Anyway, enough of this digression...)

That brings us finally to Russell’s theory of existence. Russell’s official view is that “existence is a predicate of a propositional function.” In particular, if F is a type or kind of entity, then to say that F’s exist is just a shorthand way of saying that the propositional function ‘x is F’ is possible:

• (EXIST): F’s exist iff ‘x is F’ is possible (in Russell’s sense above).

For instance, dogs exist iff ‘x is a dog’ is possible. Or men exist iff ‘x is a man’ is possible.

This makes Russell's view a "second-order" or "second-level" view of existence. If we think of individual objects or entities as the "first level" and we think of things that apply to individuals -- propositional functions -- as the second level, then existence is a property of things at the second level, since it is a property of propositional functions. Hence Russell's view has been variously described as a "second-order", "higher-order", or "higher-level" view of existence.

So, according to Russell, “It is of propositional functions that you can assert or deny existence.” On the other hand, to say of a particular thing in the world that it is exists or not is “strictly nonsense.” After all, it doesn’t make sense to say of a particular object a that it is “possible” or “sometimes true.” Hence, individual existence statements are meaningless.

This is of course rather shocking on the face of it. We seem to make true individual existence claims all the time. But on Russell’s view, “John exists” isn’t simply false. It isn’t even a loose way of speaking. It’s simply nonsense. Moreover, the seemingly indubitable inference from “I think” to “I exist” is not invalid on this view; it isn’t even an argument, since arguments have to have propositions as their conclusions, and “I exist” isn’t even a comprehensible thought. What one might have thought incorrigible turns out to be unintelligible.

Nonetheless, as repugnant to common sense as this might seem at first, common sense is not infallible. And to be fair, we have only laid out Russell’s views and have not presented his arguments for them. In the next post I'll consider some of the reasons why, exactly, Russell might have come to this conclusion.

[Part III is here!]

Modal Realism and the Serviceability Argument

Here's a quote from David Lewis: "Why believe in a plurality of worlds? -- Because the hypothesis is serviceable, and that is a reason to think that it is true."

Question for David Lewis and other modal realists: Lots of worlds are serviceable, not just the metaphysically possible ones. Many times when we do semantics, discuss language, give thought experiments, etc., worlds which are strictly logically possible but not metaphysically possible are helpful. For example, one of the ways that intensional semantics deals with oblique transitive verbs, control verbs, etc. is by invoking worlds where, for instance, water is not H2O, or where Hesperus is not Phosphorus. Presumably these are not metaphysically possible worlds, but rather 'logically' possible worlds. (Sometimes metaphysically possible worlds are called 'broadly' logically possible worlds; by 'logically' possible worlds I mean what are sometimes called 'strictly' logically possible worlds.)

Do these exist too, in exactly the same way as the metaphysically possible ones? If yes, then we run into problems. After all, isn't it only the metaphysically possible worlds which can exist? If not, then what is the distinction between metaphysical possibility and mere logical possibility supposed to mean? In fact, if merely logically possible worlds exist just like the metaphysically possible ones then there is no distinction. But there is, of course, a distinction.

At the very least, aren't the metaphysically possible worlds the only ones which could be actual? But if 'actual' is indexical as Lewis thinks, and the logically possible worlds exist on a par with the metaphysically possible ones, then any of these worlds could be actual.

Personally, I think there's just as good reason to admit the existence of logically impossible worlds as there is to admit the existence of possible worlds (though I don't think there's much reason to admit the existence of either).  If we really needed possible worlds, I think we'd need impossible ones too. But if logically impossible worlds are serviceable too then that makes things even worse for the modal realist. After all, what would it mean to say that a logical contradiction actually holds true in a concrete world just like ours? Clearly there are no such concrete worlds, since whatever concretely exists must at least be possible. But even if one resists the need for impossible worlds, the metaphysically possible worlds are a proper subset of the strictly logically possible ones, and it should be clear that these latter are "serviceable" too.

In sum, if Lewis's argument works for the existence of concrete metaphysically possible worlds, then it works for the existence of metaphysically impossible worlds too. But these can't exist concretely; that's the whole point of making some metaphysically possible and others not. Hence, Lewis's argument does not work. This can be taken as either reason to abandon the 'serviceability' criterion of existence, or as reason for rejecting concrete possible worlds. I'm inclined to reject both.

Essence and Ontological Dependence

This is my term paper from my independent study last quarter on ontological dependence. I will say beforehand that I did not have enough time to make it great, and there is a lot more I could have said. However, I believe it contains a relatively good summary of Kit Fine's position, and I think the stuff toward the end about causation is somewhat original (albeit sketchy). So hopefully someone will find it interesting and useful.

I.  Introduction – Examples and What We Want

In many areas of philosophy, as well as common discourse, it is normal to say that one thing depends on another. Moreoever, one of these uses of the word 'depends' is a distinctly ontological sense, as opposed to, say, a notion of epistemological dependence or logical dependence. I will use the term 'dependence' throughout this essay to stand for this particularly ontological notion, unless otherwise stated. So for instance, we might say that a composite depends on its constituents. Or we might say a smile depends on the mouth of which it is a smile. Or that a hole depends on the thing which it is a hole in. This is a philosophical datum and the only reason one would deny it or feign incomprehension seems to be hard-headedness.

Thomistic vs. Molinist Predestination Part II

In my last post I explained that God does not cause1 our free actions, but only cause2's them; hence, there can be no conflict between God's efficaciously willing that one do an action and our doing it libertarianly freely. I'd argue that one's free actions being caused is only inconsistent if we are using 'caused' in the sense of cause1. This is how I understand physical determinism:

(PD) The past state of the world, together with the laws of nature are sufficient to render necessary one unique future.

Clearly then God doesn't determine my next action A in this sense in cause2ing it, since God could have just as well created everything with the laws of nature and the past state up to my current time and yet cause2ed me to do ~A. It's only the case that I must do A under the supposition that God wills I do A, but it's not absolutely speaking necessary that I do A, since God could have willed otherwise.  In other words, libertarian freedom is possible, since even given the laws of nature + the past state of the world I could have done otherwise if God had so willed.

But maybe God's cause2ing me determines me in some morally relevant sense (where a form of determinism is morally relevant just in case if it were true it would preclude moral responsibility and freedom) since his causing is 'logically prior' to my acting. So we can generalize determinism from physical determinism to 'logical determinism' as follows:

(LD) An event E is logically determined by some state S just in case (a) necessarily the proposition expressing E (i.e. the proposition that E is the case) is true if the proposition p expressing S is true and (b) p is true.

Since necessarily if God wills that I do A then I do A, and God wills I do A, by this definition I'm logically determined to do A. So if this is a genuine morally relevant form of determinism, then God's cause2ing determines our actions and removes freedom. The problem with LD however is that it's not clear that it is a morally relevant form of determinism. After all, necessarily, if I do A then God wills I do A, and I in fact do A, but I don't determine God in any relevant sense to will that I do A. But if LD was a morally relevant form of determinism then I would.

I would simply hold to this: necessarily, God wills I do A if and only f I do A. This is true, but this is only meant to secure the efficacy and dependence of everything else for its existence on God's will.  This is similar to supervenience relations, and just like supervenience relations it only implies a necessary covariance; it does not necessarily imply any causal priority either of God's willing or my acting. To come back to the original point, we are working on different "causal plains" so to speak; I cause only in the sense of cause1, and God causes only in the sense of cause2. There is no causal priority of either of God's willing or my acting to the other.

Hence, I'm not sure this form of determinism, viz. logical "determinism", is a genuine form of determinism. I mean we can call it determinism (nomina significat ad placitum) but the question is whether it is a morally relevant kind, i.e. one which removes free will and moral responsibility. In the next and final post I'll come to the point about whether Aquinas's picture of predestination works.

All Perfections are Possibly Instantiated

My logic teacher and I were reflecting on the ontological argument and we came up with this. Forgive the cheap operators. A perfection is a property which it is better to have than to lack. Let A be any perfection (say, being perfect) and let B be any non-perfection (like being imperfect) and let 'PA' mean 'A is a perfection' and 'PB' mean 'B is a perfection'. Then let PP be the principle that perfections only imply perfections:

(PP) For any property J and any property K, [PJ & [](x)(Jx --> Kx)] --> PK

Since A is a perfection and B is a non perfection:

[Prem] PA & ~PB

Now, assume for reductio that ~<>(Ex)(Ax). This is equivalent to []~(Ex)(Ax) which is equivalent to [](x)~(Ax). Since necessarily A is not exemplified by anything, then trivially [](x)(Ax --> Bx). So by our premise, [PA & [](x)(Ax --> Bx)] But by (PP) [PA & [](x)(Ax --> Bx)] --> PB. It follows that PB. But by our premise, ~PB. This is a contradiction. So we must reject our assumption. So ~~<>(Ex)(Ax). So <>(Ex)(Ax).

Does Conceivability Entail Possibility?

The following should probably be pretty clear to some people. Just another way of showing that conceivability does not imply possibility. The proof will go somewhat informally with a few hidden premises, and I'm not even sure if it's any good.

Suppose
(1) If I can conceive of a possible world, then such a world exists. (This doesn't mean it's actual of course.)
Further,
(2) I can conceive of a possible world which is empty.
(3) Therefore, there is an empty possible world.
(4) I can conceive of a necessary being.
One can easily deduce from (4) that
(5) Therefore, there is no empty possible world.
(6) Therefore, there is an empty possible world and there is no empty possible world.
(7) Therefore, ~(1). (because 1 implies a contradiction, viz. 6)

By "empty possible world" I mean a world in which no entities exist. Some may object that this is harder to understand than at first sight, and may in fact be inconceivable. For those who agree that it is conceivable we've shown that (1) is false. For the skeptic's sake let's take a less controversial example. Let's say that in every possible world there exists at least one entity. This isn't to say that in each world it is the same entity, i.e. we're not saying there exists something x such that x exists in all possible worlds. To illustrate the point let's use a little bit of basic sets. Take two sets A = {1,2} and  B = {3,4). These two sets are disjoint. If you tried to find a set which has as its elements/members all x such that x is in A and x is in B you'd come up with an empty set. In other words, they have no members in common. In an analogous way we can conceive of two possible worlds being "disjoint", that is, not having any entities in common. So we can say

(8) I can conceive of two "disjoint" possible worlds.
(9) Therefore, there are two disjoint possible worlds.

Remember, this is consistent with our rejection of (2).

(10) If there are two disjoint possible worlds, then there are no entities common to all possible worlds.
(11) Therefore, there are no entities common to all possible worlds
(12) If a necessary being is possible, then there are some entities which are common to all possible worlds.
(13) Therefore, there are some entities common to all possible worlds. (One could easily show that this follows.)

We've of course come to our flat contradiction with (11) and (13) and shown (1) to be false.

Without (1) how can we learn about metaphysical possibility? It seems to me that we'll have to go back to those good ol' essences, thus raising the further question of how we can know both essences and their implications. I wonder though how we can figure out why anything exists at all. We can't turn to essences to learn about the modal properties of being. Being has no "essence", since it's a transcendental. The falsity of (1) also has implications for those who want to create modal arguments for God. We can't just go based on God's conceivability. It's interesting to note that Robert Maydole's proof of the Maximally Great Being's (MBG) metaphysical possibility seems to rely on the very essence of the MGB.

P.S. Now we've got Ss. Augustine, Anselm, and Bonaventure praying for us on the side. :-)