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. :-)

False Senses of God's Goodness

Introduction:
What does God's omnibenevolence consist in? I think that we need to do a little more work on fully explaining what we mean by this. In fact I'm somewhat distraught, because it seems that if we affirm God's all-goodness we should already know what we're talking about. I think that some of the notions which are typically bound up with omnibenevolence really don't make sense.

In a post a while back I presented the Prussian Free Will Defense. I think the argument is sound. The conclusion that we end up drawing from it is the following. It will be important in determining what omnibenevolence can be and what it cannot be:

(C1) It is not the case that there is some moral principle in the nature of an omnibenevolent and omnipotent being which prevents him from creating a creature who does something immoral.

"Actualizing all possible goods":
I think it's relatively easy to understand omnipotence and omniscience. Omnipotence is just the ability to do all that is possible. Omniscience is just the knowing of all things. So does omnibenevolence consist in the actualizing of all good things?

I'm convinced that this notion is incoherent. (C1) shows that God's omnibenevolence is compatible with God's not actualizing worlds which he could have actualized in which all moral agents always freely choose to do the right thing. And that is certainly incompatible with God's omnibenevolence meaning that he actualizes all possible goods.

The idea that omnibenevolence means "actualizing every possible good" is probably in contradiction with the idea of omnipotence anyhow. One could think of two goods which are mutually exclusive but are both within the range of God's power. For example, my marrying Lucy and my marrying Edith are both goods which are mutually exclusive and possible for God to actualize. However, God can only bring about one of these. Hence, if God is omnipotent, he can't be omnibenevolent if that means that he actualizes every possible good; there are some goods which God could actualize but doesn't.

"Preventing all unnecessary evil":
It seems that the existence of an all-good being must preclude the existence of unnecessary evil. Responses to the problem of evil like Plantinga's Free Will Defense say that some evils which take place are justified by greater goods. But the atheist objects that there are some evils which are probably not justified by greater goods, and in general, the theist agrees that if this were true then an omnibenevolent God would not exist. The typical attempt to solve the problem is to claim that no evils are unnecessary.

But what if the theist were to take a different route and say that even if there were evils which could have been prevented that this doesn't rule out the existence of an all-good God? In fact, I think (C1) shows that this is true. For take again the possible world W1 in which all agents always freely choose to do what is good. (C1) shows that there is no moral principle in the nature of an omnibenevolent being which prevents him from actualizing a world W2 where an evil is committed even though he could have actualized W1 instead. But in that case, some of the evils which take place are unnecessary; they could have been prevented by God's actualizing W1.

A Problem:
So we see that, based on (C1), omnibenevolence cannot imply the actualizing of all possible goods. Neither does it imply the preventing of all unnecessary evils. Yet this seems to sap omnibenevolence of any real content. How could we call something "all-good" which allows needless suffering and withholds a great many good things from us?

To me this is a big problem. I want to find some possible ways in which we can understand omnibenevolence in light of these objections. Any thoughts?

What Does It Take to Be An Atheist?

Consider some valid theistic arguments and what an atheist must do to deny their soundness.

Argument A - A Necessary Concrete Entity:
(1) Possibly a necessary concrete being exists implies a necessary concrete being exists.
(2) Possibly, a necessary concrete being exists.
(3) Therefore, a necessary concrete being exists.

Assume further that it can be shown that the necessary being is God.

What must the atheist do to deny this argument? (1) is just axiom S5. Therefore they must deny (2). This implies that (a) possibly nothing exists or (b) necessarily, there exists at least one contingent entity. This also implies that all concrete entities are contingent.

Atheist Theorem 1 (AT1): It is not possible that a necessary concrete being exists.
Atheist Theorem 2 (AT2): Either (a) possibly nothing exists or (b) necessarily there exists at least one contingent entity.
Atheist Theorem 3 (AT3): For any concrete entity x, x is contingent.

Disproving AT1, AT2 or AT3 is sufficient for refuting atheism.

Argument B - The Scotistic Cosmological Argument:
(1') Whatever is possible is contingent or necessary.
(2') A first cause is possible.
(3') Therefore, a first cause is contingent or necessary.
(4') Any contingent substance is possibly actualized by another substance.
(5') A first cause is not possibly actualized by another substance.
(6') Therefore a first cause is not contingent.
(7') Therefore, a first a cause is necessary.

What must the atheist do to deny this argument? The atheist can only really deny either (2) or (4).

Atheist Theorem 4 (AT4): Either (a) a first cause is impossible or (b) some contingent substance is not possibly actualized by another.

Hence, disproving this disjunction AT4 is sufficient for refuting atheism. Saying that (b) is false also leads to some interesting consequences about infinite regresses.

Argument C – A Modal Cosmological Argument:
(1*) Every contingent entity possibly has an external cause.
(2*) If the sum total of contingent concrete entities C has an external cause, that cause is necessary.
(3*) C is a contingent concrete entity.
(4*) Possibly, C has an external cause.
(5*) Therefore, possibly there is a necessary cause of C.
(6*) Therefore, there is a necessary cause of C.

What must the atheist deny? All premises seem quite strong. He must then deny (1*).

Atheist Theorem 5 (AT5): For some concrete contingent entity x it is impossible that x is caused.

Disproving AT5 is sufficient for disproving atheism.

Thus far we have Atheist Theorems 1-5:

AT1: It is not possible that a necessary concrete being exists.
AT2: Either (a) possibly nothing exists or (b) necessarily at least one contingent entity exists.
AT3: For any concrete entity x, x is contingent.
AT4: Either (a) a first cause is impossible or (b) some contingent substance is not possibly actualized by another.
AT5: For some concrete contingent entity x it is impossible that x is caused.

Disproving one of these theorems is sufficient for disproving atheism. Showing a contradiction between these beliefs and other atheist beliefs is sufficient for showing atheism as such to be incoherent. To me all of these propositions seem quite implausible in their own right.

Essences and Truthmakers

After reading David Oderberg's book Real Essentialism I've been concerned with getting a clear understanding of what "essences" are. Essences are not substances in themselves, over and above the entities which have them. On the other hand, they are supposed to provide explanatory power for the objects that have them, and they are supposed to have a specific sort of causal importance, in Aristotle's terms what is called "formal causation". In trying to make sense of these notions I have found truthmaking to be somewhat helpful (provided of course we have a good account of truthmaking). Here's an analysis:

Essence: For any entity X the essence of X is the truthmaker of the proposition that the real definition of X is [such and such].

To begin with, let's be clear about what exactly a truthmaker is. A truthmaker is some fact or aspect of reality in virtue of which a truthbearer, such as a proposition, statement, belief, etc., is true. How exactly is truthmaking helpful here? Well, it describes a real aspect of a thing.

Kit Fine provides a popular neo-Aristotelian definitional account of essences, saying that we can give real definitions of not only words, but entities, in order to explain what they are. These real definitions of objects are their essences. More work needs to be done on getting to the heart of what real definitions are and how we come to know them. (A possible account of what they are, which I am now somewhat doubtful of, is here.) But provided we have a clear understanding of this, Fine's account certainly seems to be on the right track, especially in the face of the failure of some modalist accounts. But according to the classical account, essences not only make things to be what they are; they provide explanations for causal powers. Definitions, which are linguistic entities, obviously do not.

As Kathrin Koslicki puts it in her paper "Essence, Necessity, and Explanation", "A definition, according to Aristotle, is a formula or statement of the essence, i.e. of what it is to be a certain kind of thing." She continues, "On Aristotle’s way of thinking, then, the explanatory power inherent in definitions, in their role as the linguistic correlates of essences, is a direct reflection of the causal power of essences." Since real definitions are the linguistic correlates of essences, truthmaking provides a way to get back to the essence itself.

Aristotelianism and the Christian Worldview

Originally posted here.

Introduction:
Throughout the centuries the Christian tradition has had a love-hate relationship with Aristotle. His logic and metaphysical categories provided strong tools for developing and formalizing such classic doctrines as the Incarnation and the Holy Trinity. On the other hand, he famously held that the universe was eternal and that there was no first man such as Adam, putting him at odds with Christian belief. Yet in the midst of this conflict, there is much to be gathered and adopted by the Christian. Here I’d like to examine a few of Aristotle’s ideas about the essences of things and see how they relate to the Christian view of man.

Essences:
The first thing to note is that humans, along with every other kind of thing, have “essences” or “natures”. An essence is simply that in virtue of which a thing is what it is. It’s what makes the definition of a thing true. It’s also the grounding of a thing’s essential properties, i.e. those properties which are intrinsic to that type of thing. Without essences we could not form inductive laws, we could not differentiate between kinds of things, and we couldn’t even properly define our concepts.

Essences entail that things have natural ends or functions (what Aristotle calls the “telos”). It would be incorrect to understand “function” in terms of the functions of human artifacts such as wheels or fishing rods. Rather, things have functions in the sense that they function in a certain natural way. So we can see clearly that by their very essences things like dogs or snakes have natural functions, including sensory perception, reproduction, self-change, and sustenance. This is what makes it good for them to pursue certain goals, like eating food or reproducing. To generalize, it is good for them to fulfill their functions.

This may seem irrelevant, but it has truly significant consequences for us as well. It gives medicine a normative structure, making sense of the strong and reasonable intuition that things such as broken bones or tumors are defects, while other things such as firmness of muscle or thorough digestion are indicators of health. It means that we all have certain functions which it is objectively good for us to fulfill. This can provide a foundation for objective morality and a guide to living our lives. Thus understood, essences are both indispensable and significant.

The Christian Picture:
So what is essential to humanity? Well, recall that essences are what differentiate things from entities of other kinds. In attempting to discover our essence then, it would be useful to see how we differ from other things. We share some characteristics with non-living things because we too are made of matter and have mass. But we are different from them precisely in virtue of the fact that we are alive. We are different from some living things like plants due to our sensory capabilities which we have in common with other animals. Yet we humans can be distinguished even from these creatures by our rationality. Unlike other animals, we can abstract from concrete particulars to general universal truths. Thus, humans are by their very essence rational animals.

How well does this fit into the Christian view of things? Consider the idea that God is a being with infinite knowledge, and thus an intellect. In Romans 11:33 for instance, Paul the Apostle praises God’s omniscience: ” O the depth of the riches of the wisdom and of the knowledge of God!” Aristotle’s view confirms precisely what the believer says, that is, that humans are by their very essence endowed with an intellect and will like God’s. As Genesis 1:27 says: “God created man to his own image: to the image of God he created him: male and female he created them.” Every human, male and female, is essentially made in God’s image.

We can also conclude from Aristotle’s view that, because humans have an essence with natural ends, there are some things that are objectively good for all of us, and that these objective moral truths are available to anyone who uses his or her reason and conscience. This confirms what we find in Romans 2:14-15: “For when the Gentiles, who have not the law, do by nature those things that are of the law; these, having not the law, are a law to themselves. Who show the work of the law written in their hearts, their conscience bearing witness to them.”

Much more could be said about all of these ideas. Yet it becomes clear how strongly these Aristotelian theses can be used to support what the Christian affirms. Hence, there is much fruit to be found by the Christian in the Aristotelian tradition, making the ancients very worthy of our attention.

Real Definition

In attempting to define things we can end up with a large amount of vagueness. For example, take the case of a kitty. When someone asks "what is a 'kitty'?" it is clearly insufficient to simply list properties which hold truly of it. For instance, in reply one might say that it is something small, furry, and cute. This would all be true. But that doesn't really help us to get at what a kitty is, does it? What we need here is not a mere nominal definition. We need a real definition.

The most precise and clear way of getting to a real definition is by what is called "genus-species classification". One must not confuse this with something like "biological species" which are these days based off of evolutionary lineage. In terms of giving real definitions of things, it usually has very little to do with that. The easiest way to understand this is with set theory and venn diagrams. In terms of set theory, a genus is just a type of superset and a species is a type of subset. A superset counts as a genus when all of the members of its subsets share certain particular attributes in common. A subset counts as a species when its members all have some special attribute which demarcates them from the members of the other subsets. This difference is called the "specific difference". So with the case of the kitty, the genus is "cat", since kitties have all of the attributes necessary to be included in the genus (superset) of cats. However, a kitty is different from other cats insofar as it is young. So the specific difference is the attribute of its youth. This creates a separate species from other cats, such as adult ones who have the specific difference of mature age. Maybe the venn diagram above is illuminating.

So to get a real definition of kitty we take the species and genus, giving us "young cat". Hypothetically, one could do this with any given natural kind of thing.

Problem of Evil, Free Will, and God's Obligations

The following argument is taken from a paper by Alexander Pruss. What I'm concerned about is the questions that it raises about God's nature; but before that I should explain the main point of the argument. Essentially, it is a variation of what is commonly known as the free will defense. I will call it the Prussian Free Will Defense. (That sounds like a chess strategy, doesn't it?) What the paper aims to show is that God's omnibenevolence and ability to make creatures with significant freedom does not preclude his creating creatures who freely choose to do evil. It essentially runs like this.

First off, the whole reason we are trying to make a free will defense is because we assume there is some moral principle of an omnibenevolent God which is incompatible with the actual existence of evil in the world. This is hopefully an accurate statement of how the atheist understands the situation to be. Let's call it the No Evil People (NEP) principle:

(NEP) There is some moral principle in the nature of an omnibenevolent, and omnipotent God which prohibits him from creating a creature who does something immoral.

We assume that significant freedom is a great good. That's how free will defenses work. This is what I mean by the phrase "significant freedom." Someone performs an action significantly freely just in case he freely refrains from a duty or freely refrains from doing something immoral. So someone who performs a significantly free action has significant freedom. Let's call the following the Significant Freedom Principle (SFP).

(SFP) It is not the case that God’s omnibenevolent nature contains a moral principle that would make it impossible for him to create a significantly free person.

Now, this is the general form of argument. What we argue for is the conditional C: If (NEP), then not-(SFP). If we take that as our first premise, and our free will defense says that (SFP) since we assume the great value of significant freedom, it follows that not-(NEP). And if not-(NEP) then there is no logical contradiction between God's creating a world with creatures which commit evil.

Here's how we argue for that conditional. First we need this Highly Plausible Principle (HPP):

(HPP) If it is logically impossible for someone to do something immoral, then he lacks significant freedom.

Classical theists usually understand God to be a necessary being, i.e. one which exists in all possible worlds. God is understood to be the creator of all things other than Himself. That means that necessarily, any contingent being is a creature of God. So if (NEP) is correct, and if it is logically necessary that every contingent being is a creature of God, then it is logically impossible that a contingent being does anything immoral. Thus, it is logically impossible that any person does anything immoral. Hence, by (HPP), it is impossible that any person have significant freedom. This implies that (SFP) is false, and thus our C is true. Modus tollens then, (NEP) is false.

I won't argue for the idea that God is a necessary being. I'd stand in the traditional theistic tradition by saying that any contingent entity can't be what is understood by the classical God. Besides, Pruss offers many arguments to show that C still holds should we understand God to be contingent. The main point is the conclusion that we have to draw from the Prussian Free Will Defense:

(conclusion) It is not the case that there is some moral principle in the nature of an omnibenevolent and omnipotent being which prevents him from creating a creature who does something immoral.

This raises some questions about the nature of omnibenevolence (can you see them?) which I hope to look at later.