New Thoughts on My New Gödelian Ontological Argument

Going Deeper

The Argument

One morning I woke up with an unusual thought. The thought was this: positive properties do not entail negative properties. I don’t know why I had this thought, but I pondered its potential significance. The thought was a seed for a new ontological argument.

I did not realize it at the time, but my thought about positive properties is a key premise in a certain type of ontological argument inspired by the mathematician, Kurt Gödel. Here is a summary of this type of argument:

1. Absolute perfection (AP) is (purely) positive—i.e., contains only positive (value-entailing) properties (e.g., goodness, beauty, knowledge, love, etc.).

2. No (purely) positive property entails a negative (disvalue-entailing) property.

   1. For example, being wise doesn’t entail being bad.

3. Therefore, AP does not entail a negative property.

4. Impossible properties entail every property, including negative ones (by explosion).

5. Therefore, AP is not impossible.

6. AP is either impossible or necessary [support].

7. Therefore, AP is necessary.

8. Therefore, something is absolutely perfect.

To see an elaboration and defense of this type of argument, I recommend Bernstein’s “Giving the Ontological Argument its Due.” For a critique, I recommend Oppy’s Gödelian Ontological Arguments.”

To my mind, the most vulnerable premise is (2): no (purely) positive property entails a negative property. I consider this vulnerable because, by the light of (4), I see that (2) is only true if all (purely) positive properties are possibly instantiated. Why think that’s true?

That’s where my new ontological argument comes in (which I presented here). My new argument is about the positivity of perfection itself: I suggested that AP is too positive to entail negative properties. The general form of this argument supplies a new support for the key step, (2):

2.1. Whatever is (purely) positive has no negative property.

2.2. The property of entailing negative properties is itself negative.

2.3. Therefore, no (purely) positive property entails a negative property.

Notice that this argument focuses on whether positive properties have negative properties, not whether they entail negative properties. My thought was that it may be easier to discern which sort of properties AP has than to discern which sort of properties it entails. In particular, perhaps one can see that AP has no negative property by directly inspecting AP in one’s mind. By direct inspection, one can see that AP lacks negativity—it’s too positive for that.

This idea then unlocks a new support for a Gödelian argument. Suppose AP indeed lacks negativity. Suppose, furthermore, one can see that the property of entailing negative properties is itself negative. If so, then one may infer that AP does not entail a negative property. Hence, we have an independent way to arrive at the key step, (2), in the Gödelian argument.

Reflection

In retrospection, I’m not so sure that my premise (2.1) is actually any more (or less) plausible a priori than the original thought I woke up with—which was (2). My interest in (2.1) was in response to a worry I had about (2). My worry about (2) was this: some entailments might, for all I can see, lead to a negative property; these entailments don’t necessarily come into view just by inspecting AP. But a similar worry applies to (2.1): some properties of AP might, for all I can see, include negative properties; these properties don’t necessarily come into view just by inspecting AP, maybe. It’s not perfectly clear to me, one way or the other. In the end, I’m not sure if I can rule out negative properties just by inspecting AP closely. (I’m not sure I can’t, either.)

On the other hand, examples do seem to me to support at least treating (2) as a good rule of thumb. That is, examples suggest to me that there is a presumption to think that for any given positive (purely) property P, that property probably does not entail a negative property. After all, one need not be 100% sure of this principle to consider it generally reliable, based on the track record of examples. Thus, perhaps one could consider the examples as supplying at least some (defeasible) reason in support of (2).

Questions and Answers

I have received various questions that have invited me to think more about my Gödelian argument. I offer some thoughts on a series of questions here. (I may expand this section as I consider more questions.)

I begin with a disclaimer. The questions and the topic take me to the edge of my thinking. So, I take my steps tentatively and point to them for others to explore and illuminate with greater lights. 

Question 1. How do you define absolute perfection, positivity, and possibility?

My answer. One definition I've given is this: absolute perfection is the highest degree of value/greatness. That might work for this argument.

More recently, I've been thinking about a definition in terms of a purely positive nature. Example: absolute perfection is a nature that includes positive properties (e.g., knowledge, goodness, beauty) and no negative properties. A property is positive, let's say, if it contributes value or greatness. For example, being wise is positive. I leave open whether "value" may have a further analysis, such as in terms of intrinsic likability or likability for its own sake. 

A property is negative if it detracts from value or greatness in some way. For example, being powerless is negative. (Note that detracting from value goes beyond merely entailing some disvalue. Consider that impossible properties trivially entail everything, including disvalue. But that doesn't mean impossible properties all thereby detract from value. For example, suppose goodness were impossible. It would not thereby follow that good things would, in virtue of their goodness, lack value. On the contrary, goodness would still be intrinsically positive, even if nothing could instantiate it.)

A perfect being, then, would have a purely positive nature. (Maybe this nature is its most fundamental nature -- i.e., not grounded or explained by other properties it may have or generate...) 

Finally, in this context, we can think of 'possible' as logical possibility, by which I mean it is consistent with all truths of reason -- i.e., does not entail a contradiction (by any sequence of deductions one could see a priori). I say more about this notion of 'possible' here: https://joshualrasmussen.com/s5/

Question 2. Second, I keep reading and hearing that impossible properties entail everything (for technical reasons), and I think I sort of get why. (P entails Q just in case there is no possible world in which P obtains and Q does not obtain. Right?) But could you please explain/provide a technical deduction? The formal proof of S5 you have on your website, as opposed to just a general intuition, has been extremely helpful to me, so I would love to see the proof of impossibilities entailing everything.

My answer. Suppose P is impossible. Then P entails a contradiction (on my account of 'impossible' above). 

So we have:
1. P and not P.

2. Therefore, P. (By And Elimination). In general, if two things are both true, then each is true. 

3. Therefore, P or Q, for any Q. (By Or Introduction). In general, if something is true, then it or (inclusive or) anything else is true.

4. Not P. (From 1 and applying And Elimination again). 

5. Therefore, Q (3, 4, and Disjunctive Syllogism). In general, if you have two options (at least one is true), and one is false, then the other is true.

Question 3. If we show that impossibilities entail everything, and if we show that perfection does not entail any one thing, we can show that perfection is possible, right?

I've been thinking about this argument: 1. Impossibilities entail everything. 2. Therefore, if perfection is impossible, then perfection entails everything. 3. Perfection does not entail Q (where Q is something such as supreme wickedness, imperfection, or no-maximality). 4. Therefore, perfection does not entail everything. 5. Therefore, perfection is not impossible.

What do you think of that? This would imply that we don't need to focus on whether or not perfection is purely positive, and if positive properties entail negative properties. Our task is easier: we can ask, "Is there literally anything perfection does not entail?" And by looking through the window of the concept of perfection, I think we can see the answer is "yes".

My answer. That is a nice idea to explore. In fact, that is basically the approach of this Gödelian-style argument: https://philpapers.org/rec/BERGTO. 

The reason I take a step further is that I'm worried about entailments that might be out of view, so that perfection might entail an imperfection via a path of deductions I don't see. So, to add light to the path, I focus on the positivity of perfection (i.e., the value/greatness it contributes or has). It does seem to me that entailing an imperfection would detract from the positivity of perfection. If that's right, then perfection doesn't have the negative property of entailing imperfection. In other words, perfection doesn't entail imperfection, not even by a path of deductions out of view. This idea shines additional light on your proposal.

Question 4. It seems to me that, prima facie, there are positive properties that do entail negative ones. For example, curiosity seems to entail ignorance. Courage entails fear. Forgiveness entails a moral evil to forgive. The property of being reconciled entails the property of having been separated. The property of being healed entails the property of having been ill. And so on. Am I missing something here?

My answer. You are seeing well. So, to be more precise, I want to restrict the non-entailment principle (that positive properties don't entail negative ones) to purely positive properties, which don't include any properties that are not positive. This restriction also points in the direction of your proposal, which is to give the argument directly in terms of absolute perfection. Absolute perfection is special because it includes no negative (value-detracting) properties within it (given my second definition). By cutting out the negative properties, we cut away opportunities to entail negative properties.

A principle at work here may be this:

Principle of perfection: a perfect nature, which includes only value-contributing properties, does not have (exemplify) a value detracting property. 

(Alternatively, a perfect nature doesn't have a property that would detract from the value / greatness of that nature.)

If this principle is true, then if one can see that the property, entailing a negative property, detracts from the value / greatness of a nature, then one can infer that a perfect nature does not have that property. In other words, one can then infer that a perfect nature does not entail a negative property. 

Question 5. My fifth question has to do with your final worry: can we see that a perfect nature is purely positive, or do we merely fail to see that a perfect nature has negativity? Why exactly does this worry you? Is it not as simple as this: if N entails something negative, then N is not absolutely perfect? Can't we see that a perfect nature does not have negativity (or just define perfection accordingly)? Joe Schmid, in responding to Godel's ontological argument, is "fine with granting" that perfections do not entail imperfections, as this is just "definitionally true". (He says that in this video.) I was surprised about your remaining worry, and I'm curious why you label it a "worry".

My answer. I think it may come down to whether one can apprehend a perfect nature through the concept of perfection. Such sight, if it is possible, will depend on one's concept of 'perfection' and how one unpacks it. Consider, for example, a certain "opaque" concept of perfection, which is merely stipulated, by definition, to not entail anything negative (any disvalue). This opaque concept might, for all we know, be empty (i.e., not correspond with any properties). After all, the definition on its own doesn't tell us whether there are any perfections (i.e., maximal great-making properties that don't, by explosion, entail negative properties). So, this mere stipulated definition is not by itself enough to give us insight into the positivity of perfection. 

Still, it does not seem to me that one must be in the dark behind an opaque concept. For it seems to me that one can inspect certain actual purely positive properties (such as knowledge, power, and goodness). Furthermore, it seems to me that one can inspect the positivity of these properties directly (without first having to discern whether they entail anything negative). In the case of a perfect nature (which includes purely positive properties), my thought is that one can see this nature (through the window of the concept of perfection) and directly discern its positivity.

My thought, then, is that these premises, if true, are not merely discernable by stipulation, but by a direct sense of the positivity of a certain nature.

Having said all that, my remaining worry, still, is about what might be out of view. Could a purely positive nature have properties out of my view that somehow entails something negative? I find it hard to see how it would, but I also want to be careful that my inferences are based on real insight (into a real nature), and not on deductions from an empty concept.

Here I'm at the edge of my thinking, and I don't feel my sight is perfectly precise (yet). I find my mind skating between two guiderails, with a definition of 'perfection' on the one side, and insight into the nature the definition picks out, on the other. I think there is more work to be done in illuminating these guiderails.

Question 6. Fundamental to most discussion and deliberation about ontological arguments is this (true) proposition: if perfection is impossible, perfection entails everything. There are two ways to go from here. The theist would argue that perfection is uniquely purely positive, and pure positivity does not entail anything negative. So, by modus tollens, perfection is not impossible. But the atheist would already, by their own lights, be convinced that perfection is impossible. So, by modus ponens, perfection entails everything. How do we determine which is the best path? This is perhaps my biggest question.

My answer. This question highlights the value of weighing one's total evidence. Everyone will see things by their total light, and I think reasonable disagreement here is possible. So, for example, if someone has reasons to doubt that a perfect being exists, then those reasons could translate into reasons to doubt a premise in this argument for a perfect being. 

Even still, I think one could find the premises in this argument independently plausible. For example, one might find it independently plausible that absolute perfection would, by its positivity, be free from negative properties and so free from the negative property of entailing a negative property. I think that could indeed strike one as plausible independently of any prior belief about what perfection may or may not entail. If so, then one will have an independent reason to accept the premise (even if not everyone is in the same position to accept that premise). I hope that makes sense.

Question 7. Also, are there parodies for no-maximality and supreme wickedness? It seems as though no-maximality does not entail maximal greatness (by definition), and supreme wickedness does not entail perfection (by definition). So, because impossibilities entail everything (including maximal greatness and perfection), no-maximality and supreme wickedness are possible. But we theists would not want to accept this conclusion. How would you respond?

My answer. I believe there is an important asymmetry between positive properties and negative ones. In particular, all negativity entails something positive. For example, being painful, wicked, or maximally bad entails the existence of a subject of consciousness, which has positive value. One might even define a negative property as a detraction of value from something positive. Positive properties, by contrast, aren't a detraction of disvalue from something negative. Instead they are simply a contribution of value. So while I think negative properties entail positive properties, I don't have a similar reason to think that positive properties entail negative ones. In light of this asymmetry, I don't think the parodies are in the same boat. 

Note also that there is a difference between not seeing an entailment vs. seeing a non-entailment. In the case of negative properties, there is nothing about those properties that allows me to see (or infer) an entailment or non-entailment. For example, I don't see that the properties are too negative to entail perfection. On the contrary, I see that all negative properties entail something positive (e.g., the existence of awareness or some ability), and they may even entail something purely positive. (If we are theists, then of course we have independent reasons to think these properties are not possible. But here the postulation of an entailment is not based on insight into the properties themselves.)  

Perfection is importantly different. By insight into the positivity of perfection, one might find it plausible that perfection is too positive (value-contributing) to have the negative (value-detracting) property of entailing negative properties. (This is the principle of perfection of above.) In that case, one may have reason to think one is seeing something about perfection (i.e., its positivity) that allows one to infer the non-entailment.

So, I don't think these parodies (or any others I've seen) are relevantly like perfection.

Nahoa Life followed up by asking how supreme wickedness, which entails negativity, might also entail perfection. In response, we should be careful to make a distinction. While it is true that supreme wickedness entails negativity, that by itself still leaves open whether supreme wickedness may also also entail opposite properties (because it is an impossible property). For comparison, consider the property being a 16-sided platonic solid (whose faces are all identical, regular polygons). That property entails having sides. So you might think it wouldn't also entail having no sides. But it actually entails both having sides and having no sides. For it turns out such a property is impossible (cannot be instantiated), and so, by explosion, entails a contradiction. The lesson I draw here is this: the mere fact that a property p entails some property q (like having sides or being negative) leaves open whether p may also entail properties inconsistent with q (if it is impossible). For this reason, if p entails negativity, that by itself leaves open whether p may not also entail contradictory properties. 

Perfection is different in this respect. For my proposed reason to think perfection doesn't entail negative properties is not that perfection merely entails positive properties. Rather, my argument is from the intrinsic nature of perfection itself. So, perfection includes purely positive properties. Then by insight into its pure positivity, I propose that perfection would not have the negative property of entailing negative properties. This premise is based on first having a sense of the positivity of perfection and then inferring what it entails or doesn't entail.

Does supreme wickedness include purely negative properties in its nature? Here I don't find myself having insight into a purely negative nature (that is intrinsically purely only negative). On the contrary, a supremely wicked nature would seem to include positive abilities and knowledge, so that it could carry out its evil schemes. And, to the extent that I have insight into a supremely wicked nature, I seem to be able to tease out a contradiction. For it seems that the more abilities a wicked being has, the more evil it can do. So, it seems that a supremely wicked being would have supreme ability and supreme knowledge to be able to carry out supremely evil schemes. Next, I have reason to think that supreme knowledge and supreme power entails supreme goodness, since its full knowledge precludes motivations for evil (cf. https://philpapers.org/rec/WEAEMR). Or, at least there is a potential argument here from supreme knowledge and power to supreme goodness, which contradicts supreme wickedness. So, at minimum, insight into the property does not itself give me insight into reasons to think it wouldn't entail a contradiction, and the opposite seems so.

As for the property of being such that there is no maximally great being, here again, insight into the property does not itself give me insight into whether or not there could be a maximally great being. Sure this property entails that there is no maximally great being. But that leaves open whether it might also entail that there is a maximally great being. It all depends on whether a maximally great being is possible. Per my first note, merely seeing that p entails q leaves open whether p might also entail not q. (Of course, there are independent arguments one might have against the coherence of a maximally great being, and my assessment here brackets those.)

In summary, a key difference between imperfection and perfection is in the intrinsic nature of perfection. It seems to me that I may be able to first discern its purely positive nature and then infer what perfection doesn't entail (i.e., it doesn't entail negativity). The negative properties, by contrast, don't have purely negative natures (but instead include and entail positivity). So I don't see how to infer from insight into their natures what they don't entail—or that they are possible. At least, that’s how it is looking to me at present.

Final note. We are in deep waters at the edge of time. This territory is ripe for sprouting new ideas and greater wisdom, whether to clarify how the argument may work or to clarify how it may not. 

Thank you for your consideration.