What’s a negative property?

In discussing the Gödelian ontological argument recently articulated by Alexander Pruss[1] (here and here) there was a need to define what we mean by “positive property”. In the first post, we defined a positive property (in a very Anselmian way) as a property that is better or greater to have than not. In his second paper, Pruss suggests a different route: define “negative property” first, and then define “positive property” from that. That’s what we’re going to do here. If people don’t like the Anselmian intuitions behind our first definition, this should be a more acceptable route. Note what our goal is: we seek a coherent and non-gerrymandered definition of “negative” such that the axioms in the argument are true. I’m not here seeking to give an analysis of negative properties as if they’re an already established concept. Rather, I’m giving a definition.

Limitation as negativeness

We’ll try to flesh out the suggestion by Pruss[2]:

We might, however, proceed differently, by taking as our primitive the notion of a negative property, which is actually more natural than the Gödelian notion of a positive property. We can think of a negative property as one that limits a being in some way.

So, we’ll define a property of some being to be “negative” if and only if it is limiting to that being in some way. Perhaps this is too rough. After all, properties can be limiting in some circumstances but not others. We can be more specific, then, and say that a property of a being is negative if in every circumstance, it is limiting to that being in some way. What do we mean by “limiting to a being”? It seems natural to take this to mean something along the following lines: in exemplifying the property, the being has less control or is less capable in some sense than if it wasn’t exemplifying the property. That is, the property leads to more restrictions or hindrances to the being than its negation. Note that the property is limiting to the being. Self-existence, for example, is the ultimate form of ontological independence, and as such is limiting to a being’s dependence upon other beings. However, it is certainly not limiting to the being itself. As such, it isn’t a negative property.

We’ll say a property is “positive”, then, if and only if its negation is negative.

How about some examples? Sure: not knowing that 1+1=2 is a negative property, for no matter what circumstance a being (that exemplifies this property) finds itself in, it’s cognitive abilities will always be limited by not knowing that 1+1=2. Being trapped is a negative property since it limits the being’s freedom. Moving to more of the relevant properties, omnipotence is positive, since omnipotence is plausibly just perfect freedom of will and perfect efficacy of will[3], both of which are clearly positive properties. Since not being self-existent is limiting to one’s control, freedom and self-sufficiency, it follows that it’s negative. And so self-existence, which is the ultimate property of self-sufficiency and independence, would be positive. Omniscience would also be a positive property. Perfect goodness would also be a positive property, since being evil is limiting to a being’s goodness. We might be able to push this a bit further: surely not being the paradigm of moral goodness is limiting in the sense that there is a standard above one to which one must submit? In this case, being the paradigm of moral goodness (which is stronger than being merely perfect good) would be a positive property.

Back to the ontological argument

Ok, that seems like enough examples. Let’s turn back to the ontological argument from earlier. The following two axioms follow quite naturally from how we’ve defined negative properties:

F1*. If a property P is negative, then ~P is not negative.

F2*. If a property P is negative, and a property Q entails P, then Q is negative.

Awesomely, (F1*) and (F2*) entail (F1) and (F2) from our earlier post. Furthermore, since self-existence is positive and it entails necessary existence, it follows from (F2) that necessary existence is positive, giving us (N1).[4]

We could go through the whole argument again, this time maybe even talking in terms of negative properties rather than positive ones. But that’s too much effort, so once again, I leave it as an exercise for the reader 😛


  1. He’s formulated and defended this argument in two papers: “A Gödelian Ontological Argument Improved” in Religious Studies (2009) and “A Gödelian Ontological Improved Even More” in M. Szatkowski (ed.), Ontological Proofs Today (2012).
  2. This appears in the second of the two papers mentioned in the previous note.
  3. See “Understanding omnipotence” by Kenneth Pearce and Alexander Pruss, Religious Studies 48 (2012): 403-414. Even if we don’t accept their analysis of it, any good analysis of omnipotence should be that of having unlimited power, which is sufficient for it to be a positive property.
  4. We can also get their via the property of being the paradigm of moral goodness like before.

The gap problem

In the previous two posts (here and here) we looked at a Gödelian ontological argument from Alexander Pruss, which we’ll use a bit in this post.

The gap problem

Right, so what is the gap problem? Simply put, solving the gap problem involves bridging the gap between (i) the first cause or necessary being that we arrive at in cosmological arguments and (ii) the God of classical theism. Different philosophers have approached this problem in different ways and here I hope to survey and briefly discuss some of those. I haven’t read nearly enough to give any sort of comprehensive list, but this is a start.

Now, there are two things we need to keep clear. First, there are many properties of the God classical theism, and for each of these properties we can come up with different arguments. For example, in section 5 of his Blackwell Companion article on Leibnizian Cosmological Arguments, Alexander Pruss briefly deals with agency, goodness, simplicity, and oneness. Or, in his paper “From a Necessary Being to God”, Joshua Rasmussen argues for properties such as volition, infinite power, infinite knowledge, and infinite goodness. In this blog pos, we will concern ourselves only with the personhood of the first cause/necessary being. Second, in each case the arguments we mention will depend on what being we’re talking about. For example, the first cause that we arrive at with the Kalam argument does not have to be necessary or the explanation of every contingent fact. This limits what we can deduce about it. In each of the cases, I will make clear exactly what being I’m working with. Ok, so let’s get started.

Using the ontological argument #1

Assume we’ve arrived at the existence of a necessary being. In our previous posts in this series, we pointed out that both necessity and omniscience are positive properties. Thus, using essentiality of contingency or S5, it follows that there exists a necessary being who could have been omniscient. Now, we could assume that there are two necessary beings, but there’s no reason to think that these aren’t the same being and explanatory tools like Occam’s Razor suggest we should conflate them until we have some reason to think them distinct. So, it’s plausible then, that our necessary being could have been omniscient. But only persons can know things. Thus, this necessary being is probably personal.[1]

Using the ontological argument #2

Consider another way to use the ontological argument, which ends up building a quasi-ontological argument from an explanatory principle of a cosmological argument. For this we need the EPSR or a stronger explanatory principle:

EPSR. Everything has an explanation for its existence, either in the necessity of its own nature or in an external cause.

Now, we can use this to avoid commitment to the idea that necessity is a positive property. Again, clearly omniscience is a positive property. So is being the creator of everything else (itself, strictly weaker than aseity). So, in some possible world there is a being N who is the creator of everything else and omniscient. But, by the EPSR this being must be necessary. Then, by S5 or essentiality of contingency, this being exists and is necessary and personal. If we used Brouwer, we’d get a being who exists, is personal and could have been the creator of everything. Of course, if we take “being the creator of everything” as a strongly positive property then Brouwer will also give us a personal necessary being.

Explaining the BCCF

Imagine now we’ve arrived at our necessary being via one of the following equivalent explanatory principles[2, 3]:

PSR. Every contingent fact has an explanation.

WPSR. Every contingent fact could have had an explanation.

POE. If only one putative explanation can be given of a phenomenon, then that putative explanation is correct.

Now, we call the conjunction of all contingent facts the Big Contingent Conjunctive Fact (BCCF) of a possible world. When these principles get applied to the BCCF of the actual world, we arrive at a necessary being and a necessary fact involving the causal activity of that being[ which explains the BCCF[4]. Is this being personal? Well, since we have a necessary fact explaining a contingent fact, the explanation must be non-entailing, and non-entailing explanations are either statistical or libertarian. But statistical explanations seem inherently contingent, for there doesn’t seem to be any reason why the relevant probability couldn’t have been something like 0.00000000000000000001 more or less than it actually is. Thus, the explanation in this case must be libertarian, which means that the necessary being is an agent with free will (in the libertarian sense), and therefore personal.

Principle of determination

In his various writings, William Lane Craig has defended three reasons for thinking the first cause that we arrive at from the Kalam Cosmological Argument (KCA) is personal[5]. I’ve recently come to appreciate two of them which we’ll look at now. First there’s the argument from determination which starts with a peculiarity: assuming we have a first cause which is beginningless and changeless sans the universe (which is the conclusion from the KCA) it is rather puzzling that we find ourselves in an ever-changing universe. If the conditions for the effect had been met from eternity, then why is the effect not co-eternal with the cause? That is, why is the effect not changeless too? The puzzle is really about how the first event came about; about how change was effected from a changeless state.

Now, I’m going to phrase the actual argument differently to how Craig does, but it captures the same ideas he discusses:

  1. There was a first event, caused by a changeless and beginningless being. (KCA)
  2. The first event was either the effect of state-state causation, event-event causation, or agent-event causation. (Premise)
  3. It was not the effect of state-state causation or event-event causation. (Premise)
  4. Therefore, it was the effect of agent-event causation.

From (4) the first cause is an agent, and therefore personal. (1) comes from the KCA, so we won’t concern ourselves with that here. (2) is a list of possible ways causation can happen, and it seems to me to be comprehensive. Someone might suggest something like “state-event” causation, but I don’t think any coherent interpretation of this can be given that doesn’t eventually collapse into state-state or event-event causation. We can see (3) is true by seeing why each of its conjuncts are true. First, we’re considering the first event, and so it clearly can’t be the effect of state-state causation. Second, we considering the first event, and so there just are no prior events, be it logically, causally, or temporally.

Best candidate for explanation

The second reason Craig gives goes as follows: the first cause must be immaterial and timeless sans the universe. The only things we know that are both of these are unembodied minds and abstract objects. But abstract objects are by their very nature causally effete. Therefore, the first cause is probably a mind. This is a clear-cut case of inference to the best explanation, and for a long time I thought one could easily get around this by saying that an impersonal, [non-deterministic,] immaterial, and timeless being was the cause. But this is not an equally good explanation, because this doesn’t actually give us a candidate that does the explaining. All it does it list a bunch of properties. Now, if all we knew was that the cause was personal or impersonal and had no potential candidates for either of these, then I think such a move would be alright. But once one of the sides gives a concrete candidate that fits a set of properties, then if the other side can’t give a putative candidate, its position becomes explanatorily weaker since it gratuitously postulates unknown entities and if it can’t give any reason for not accepting the candidate from the first side, then its position also becomes ad hoc. Consider an analogous scenario: Alice and Bob find prehistoric tools, and Alice suggests that there was some sort tribe that made them. Bob, however says they weren’t made. Alice asks if Bob knows of anything that could explain the tools? Bob can’t give a candidate, but says it must’ve been some impersonal tool-forming process that occurred. Clearly Bob’s suggestion is explanatorily deficient, for he neither knows of any such process nor does he have any good reason for rejecting Alice’s explanation. Alice on the other hand, didn’t just say it was some personal tool-forming process: she gave a candidate. Now, inference to the best explanation isn’t conclusive and is usually tentative, but it lies at the foundation of scientific enquiry[6] and does contribute to a cumulative case for the personhood of the first cause. We shouldn’t let an unwelcome conclusion stand in the way our own consistency.

Moral arguments

If we don’t consider the cosmological argument in isolation, we can use the other theistic arguments to give us reason for thinking the first cause/necessary being is personal. We could, for example, launch the moral argument. This argument arrives at a personal being and it seems that the creator (ie. first cause) is a non-arbitrary candidate for this being who imparts duties to us. Not much more needs to be said about this.

Design arguments

We could also look to fine-tuning and complexity arguments. For example, in their paper “A New Cosmological Argument”, Pruss and Gale point out that “The actual world’s universe displays a wondrous complexity due to its law-like unity and simplicity, fine tuning of natural constants, and natural purpose and beauty” which suggests that the cause is intelligent and therefore personal. Now this is interesting to me, because I personally think the combination of the many-worlds hypothesis and the weak anthropic principle, while disgustingly gratuitous and usually driven by unchecked biases, is a sufficient to block the theistic conclusion of the existence a cosmic designer. But here we are not using the fine-tuning as an argument for the existence of the first cause/designer. We have already come to the conclusion that the universe has a cause, and are noting that the fine-tuning of the universe is best explained by this cause being intelligent. If the detractor is going to suggest an an infinity of universes to escape merely the move to personhood, they’re going need a good reason. Otherwise this suggestion’s ad hocness and lack of simplicity will count significantly against it, making the personal alternative a better explanation. I like how Robert Koons addressed this issue in his paper “A New Look at the Cosmological Argument” (note that he uses “cosmos” to refer to the many-worlds ensemble):

A standard non-theistic response to the data underlying the anthropic principle is to suggest that there may be an infinity of parallel universes, representing every possible permutation of possible physical laws and initial Big Bang conditions. Only an infinitesimally fraction of these permit the development of life and consciousness, but it is not surprising that we inhabit one of these vanishingly rare universes, since otherwise we would not be here to observe it….

This objection brings out the importance of considering evidence for design in the context of the cosmological argument. Without the cosmological argument, we would be forced to the conclusion John Leslie reaches, namely, that there are two equally good possible explanations of the anthropic data: a cosmic designer, and observer selection in a world of infinitely many, uncaused universes. However, once we know that the cosmos (including our universe) has a cause, the second hypothesis is excluded. It is still possible that the First Cause caused a junky cosmos, and that the evidence for intelligent design is illusory, but in the absence of positive evidence for these other universes, the reasonable inference to draw from the only universe we can observe is that the First Cause encompasses the existence of an intelligent designer.

There is another serious drawback to the junky cosmos hypothesis: if employed globally, it has the consequence that any form of induction is demonstrably unreliable. If we embrace the junky cosmos hypothesis to explain away every appearance of orderedness in the universe, then we should assume that the simplicity and regularity of natural law is also an artifact of observer selection. Universes would be posited to exist with every possible set of natural laws, however complex or inductively ill-behaved.

Now take any well-established scientific generalization. Among the universes that agree with all of our observations up to this point in time, the number that go on to break this generalization is far greater than the number that continue to respect it. The objective probability that every generalization we have observed extends no farther than our observations is infinitely close to one. Thus, relying on induction in such a universe is demonstrably futile.

In short, the junky cosmos hypothesis is both the most flagrant possible violation of Occam’s razor and a death sentence to all other uses of that principle. This hypothesis postulates an infinity of entities for which there is absolutely no positive evidence, simply in order to avoid the necessity of explaining the anthropic coincidences we have observed. This is the height of metaphysical irresponsibility, far worse than the most extravagant speculations of medieval angelology. Moreover, it undermines all subsequent appeals to simplicity or economy of explanation. If the junky cosmos hypothesis is true, it is demonstrable that the simplest hypothesis of astronomy or biology is no more likely to be true of our universe than the most complicated, Rube-Goldberg constructions. We would have absolutely no reason, for instance, to believe that the Copernican hypothesis is more likely to be true than a fantastically complex version of Ptolemy’s system, elaborated as far as necessary to save the astronomical phenomena.


I’ve summarised a bunch of different reasons for thinking the first cause/necessary being we get at the end of cosmological arguments is personal. Taken them by themselves, perhaps only a few are conclusive, but taken together I think they form a good cumulative case for the conclusion we want, and I see no reason for thinking the being should be impersonal. There are certainly more out there (I haven’t considered Joshua Rasmussen’s paper that I mentioned earlier, or arguments from the regularity of natural laws, and I didn’t mention epistemological arguments for a designer) but hopefully I’ve given you an idea of some ways personhood might be argued for. I’ll be sure to list new arguments as I come across them.


  1. If we get more specific and take omniscience to be a strongly positive property, then we have a necessary being who is probably omniscient too.
  2. Clearly PSR entails POE and WPSR. The other directions are argued for in Pruss’ book titled, The Principle of Sufficient Reason: A Reassessment.
  3. We could call the POE the “Sherlock Holmes principle”, for as the famous adage goes, “when you have eliminated the impossible, whatever remains, however improbable, must be the truth”.
  4. It involves the casual activity of this being because the BCCF includes positive existential facts, and these are plausibly only possibly explained causally. The being must be necessary for it cannot explain its own existence (unless, of course, its self-explanatory. But self-explanatory beings are necessary anyway, so that caveat is without relevance).
  5. See his book Reasonable Faith 3rd Edition, pp. 152-154, his essay in The Blackwell Companion to Natural Theology with James Sinclair, or even these Q&As from his website: http://www.reasonablefaith.org/is-the-cause-of-the-universe-an-uncaused-personal-creator-of-the-universe and  http://www.reasonablefaith.org/must-the-cause-of-the-universe-be-personal-redux.
  6. Modern physics and and evolutionary biology, arguably two pillars of modern science, both make extensive use of inference to the best explanation.

Fitch, Humberstone, and an omniscient being

I just read the paper “Omnificence” by John Bigelow[1]. In the preamble he recounts the following argument for an omniscient being

  1. Any fact (true proposition) is knowable by someone. (Premise)
  2. Therefore, every fact is known.
  3. Therefore, someone knows every fact.

Fitch[2] was responsible for showing that (2) follows from (1). One way to see this is a follows: for reductio assume, contrary to (2), that there is some fact p that is not known by someone. Then, p and no-one knows p is a fact, and by (1) is therefore knowable. Therefore, it is possible that someone knows p, and at the same time knows that no-one knows p, which is absurd. Thus (2) follows from (1).

The move from (2) to (3) comes from Humberstone[3]. Again, for reductio assume, contrary to (3) that for every person x, there is some fact p(x), that x doesn’t know. Now let X be the conjunction formed by taking all facts of the form p(x) and x doesn’t know p(x). Clearly this conjunction is true. By (2) it follows that there is some y who knows X. But one of the conjuncts of X will be p(y) and y doesn’t know p(y), and since y knows X, y also knows this conjunct, which is absurd. Thus (3) follows from (2).

I’m not going to argue for (1) here, although I must admit I struggle to imagine that there could be a fact that is in principle unknowable. What I found particularly interesting in Bigelow’s paper was the comment that logical positivism entails (1): take the verification principle of that movement, which said that a statement is meaningful if and only if it is verifiable. Now, only meaningful statements can take on a truth value, so it follows that every fact is verifiable, and therefore knowable.


  1. J. Bigelow, “Omnificence,” Analysis 65/3 (2005), pp. 187-196.
  2. F. Fitch, “A logical analysis of some value concepts”, Journal of Symbolic Logic 28: 135-42.
  3. I. Humberstone, “The formalities of collective omniscience”, Philosophical Studies 48: 401-23.

Atheism is self-defeating

I was thinking about the short argument I gave here and was wondering if it could be turned into a positive argument for theism. I came up with this:

  1. If God doesn’t exist, then our cognitive faculties arose from non-purposive processes.
  2. No purposive system can arise from non-purposive processes.
  3. Therefore, if God doesn’t exist, then our cognitive faculties are non-purposive.
  4. Rationality is purposive.
  5. Therefore, if God doesn’t exist we aren’t rational.
  6. Therefore, atheism is self-defeating.

It seems promising. Although, I suspect I should read JP Moreland, Alvin Plantinga and Victor Reppert to get a better idea of the contemporary debate around this stuff. I think (4) is pretty solid (see the previous post for why), and I’m uncertain any atheist will disagree with (1), lest they open themselves up to Aquinas’ fifth way. So, presumably, (2) is the key premise. But this certainly does seem plausible.

Modality and the ontological argument

Previously, I outlined what I find to be a compelling ontological argument from Alexander Pruss. In the post, we dispelled the idea that there is a single ontological argument and distinguished between a number of families on such arguments. The one we focussed on is a so-called Gödelian ontological argument, named after the famous mathematician Kurt Gödel. Gödelian ontological arguments construct an axiomatic system and use this to prove, as a theorem in the system, that something like God exists; and this is exactly what we did. If you’ll recall, we proved the following theorem:

Theorem 2 There exists a necessary, essentially omniscient, omnipotent, omnibenevolent being.

In fact, we noted that using the same methods we used to prove theorem 2 we could prove that there exists a necessary being who possesses all strongly positive properties. Now, in the proof of this theorem, we made use of a system of modal logic called S5. The goal of this post is to discuss this system, and consider some alternative (and weaker) systems that could be used to arrive at the same result.

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A Gödelian ontological argument

I’ve never really had a nice relationship with the ontological argument from Anselm. When I first heard of it, it seemed strange that existence would be greater than non-existence, so I pushed it aside. About 2 years later, I realised that existence could maybe be bootstrapped from other properties, like power. But by then I had come to realise the distinction between epistemology and ontology, and struggled to believe that this argument wasn’t confusing the two at some point. That’s where I’m at at the moment: existence-in-mind just doesn’t seem comparable to existence-in-reality in the way that’s needed for the argument to work. Maybe I’m wrong, but that’s where I’m at[1].

Many people talk about Anselm’s ontological argument as the ontological argument. But, like many theistic arguments (and arguments in general, I suppose), to call it the ontological argument is a bit misleading. There are a number of ontological arguments out there, and Anselm’s one is but one of them. Descartes had another ontological argument which Leibniz worked on a bit, and in the 20th century we’ve had modal ontological arguments coming from Norman Malcolm, Charles Hartshorne, and Alvin Plantinga. Another “class” of ontological arguments are the so-called “Gödelian” ontological arguments. Kurt Gödel, the famous mathematician of Gödel’s Incompleteness Theorems, developed his argument using the primitive idea of a “positive property”. The arguments that follow this approach, like Gödel’s before them, are developed as formal axiomatic system with a theorem at the end that says that there is a God-like being who exists. Jordan Sobel showed, in 1987, that Gödel’s axioms also imply that every true proposition is necessarily true. This argument from Sobel is called the “modal collapse argument”, and it shows that Gödel’s argument is unsound. However, since then, there have been a number of Gödelian ontological arguments which have been formulated so as not to fall prey to the modal collapse argument. These have come from Curtis Anderson, Allen Hazen, Robert Koons, and Petr Hajek, to name four. And, then there’s the recent “Modal Perfection Argument” from Robert Maydole.

Of prime importance to this blog post is yet another Gödelian ontological argument formulated by Alexander Pruss[2]. While I’m not convinced by Anselm’s, Descartes, and many of the other ontological arguments, this one does certainly seem plausible to me. I’ll sketch it briefly in this post.

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The possibility premise of the simple existential cosmological argument

In my previous post I showed that even without the plausible S5 or Brouwer axioms, we can move from the possible explanation of the maximal simple existential fact (we called it K there), to the existence of a necessary being. Now I see no reason for thinking such an explanation is impossible, and it seems to me that since we’re merely asking for possibility, that premise should get the benefit of the doubt. Regardless, consider this argument for it

  1. If each fact in a collection of simple existential facts possibly has an explanation, then possibly the conjunction of those facts has an explanation.
  2. Any simple existential fact possibly has an explanation.
  3. Therefore, possibly, K has an explanation.

I can’t think of any counter examples to (1) and (2) seems plausible, at least until someone can give us an example of something for which it is impossible to explain it’s existence or non-existence (that is, not merely something that doesn’t happen to have an explanation, something that couldn’t have an explanation). Good luck with that.

A cosmological argument from simple existential facts

There are loads of different cosmological arguments out there and hopefully someday I’ll be able to write blog posts about some of them. Right now, however, I want to share an interesting version I came up with, thanks to an argument from Alexander Pruss: define a “simple existential fact” to be a true proposition reporting simply the existence or non-existence of a specific being[1,2]. So U doesn’t exist, where U is any specific unicorn and Roland exists, where Roland is me, are simple existential facts of the actual world. Now, let K be the conjunction of all simple existential facts of the actual world that don’t involve necessary beings. So, K only reports the existence or non-existence of beings which possibly fail to exist.

Now assume that possibly, K has an explanation. From this it follows that a necessary being exists. We now show this: Let α denote the actual world[3]. Since possibly, K has an explanation, there is some possible world w, in which K is true and there is some fact q that explains K. Since K involves existential facts, q must involve the causal activity of some being that exists in w[4], call it N. Now either N exists in α or it doesn’t. Assume it doesn’t. Then N doesn’t exist is a conjunct of K. Since K is true at w, it follows that N doesn’t exist in w. But this is a contradiction. Therefore, N exists in α. Is N necessary? Well, assume N isn’t necessary. Then N exists is a conjunct of K, and in w, N explains its own existence. But surely, nothing contingent can explain its own existence. So N is a necessarily existent being.

What’s really nice about this argument is that it doesn’t assume S5 or even the Brouwer axiom. Furthermore, even though I think the Principle of Sufficient Reason is true, to say that K has an explanation doesn’t commit one to the full-blown PSR. In fact, to say that possibly, K has an explanation doesn’t even entail that K actually has an explanation: while N could explain K, N needn’t actually explain K.


  1. “Specific” has a specific meaning here: rigidly designated. A rigid designator always refers to the same entity and is different from a definite description which changes depending on the current state of affairs. For example, “the president of the United States” is a definite description, whereas “Richard Nixon” is a rigid designator (of course, if there were more than one Richard Nixon we could be talking about, then some more specificity would be needed).
  2. I wonder if I couldn’t simplify this even further by saying “a specific being or class of beings” where class could be something like “unicorns”?
  3. That is, α is the rigid designator for this possible world.
  4. This was discussed very briefly here. It doesn’t seem possible to explain the existence of contingent beings “conceptually”.

Epistemological issues in the moral argument

I am a proponent of a moral argument, taken from William Lane Craig, given in the following form:

  1. If God doesn’t exist, then objective moral values and duties don’t exist
  2. Objective moral values and duties do exist
  3. Therefore, God exists

I’ve had a number of previous posts here dealing with specific details of this argument’s defence. Here I wish to discuss a defence of the second premise that goes like this:

  1. In the absence of any defeaters, we are rationally compelled to trust the deliverances of our various faculties
  2. In our moral experience we perceive objective moral duties and values
  3. We have no defeater for these deliverances of our moral faculty
  4. Therefore, we are rationally compelled to believe in objective moral duties and values

Clearly, this argument falls in the realm of epistemology. Perhaps it will be helpful to clarify a few terms for those who aren’t familiar with them.


First, some examples of the various faculties we have are our five senses, inductive reasoning, deductive reasoning, abductive reasoning[1], memory, and our moral sense. I suppose I should probably explain those three reasoning faculties a little more. Deductive reasoning uses principles of logic that seem to be objectively binding, like the principle of excluded middle (for any proposition A, A is either true or false), the principle of non-contradiction (for any proposition A, it is not possible for both A and not-A to be true at the same time), the validity of certain reasoning schemes (like, if A entails B, and A is true, then B is true), and so on. Our deductive reasoning faculty is that part of us that perceives that certain principles are true and others false, how to apply these general principles to specific examples, and so on. For example, I hope that everyone reading this will see that the examples I gave of logical principles are self-evidently true[2].

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Outrage, praise and empathy

I often defend the following formulation of the moral argument (taken from William Lane Craig):

1. If God doesn’t exist, then objective moral duties don’t exist
2. Objective moral duties do exist
3. Therefore, God exists

In defence of premise (2) I usually offer the following three points:

2.1. If objective moral duties don’t exist, then everything is permissible. But some things are not permissible.
2.2. If objective moral duties don’t exist, then moral outrage and praise is irrational. But they aren’t irrational.
2.3. We are rationally compelled to trust our perceptions until we are given a defeater for them. Since we perceive an objective moral realm and no defeater has been given, we are rationally compelled to trust our perceptions and so believe the existence of objective moral duties.

Now I’m not going to spend this post trying to defend all of this. I’ve tried in a previous post to defend 1, 2.1 and 2.3, so I thought I’d spend some time on 2.2 here.

So, what do I mean by the term “moral outrage”? In all honesty I don’t have a reductive analysis of it, but I think we all have an intuition for what I mean. Consider the following examples of moral outrage and praise:

  1. The daughter of two parents is raped and killed, and so they are outraged at the rapist when they come face to face with him.
  2. A gay pride stand is maliciously burnt to the ground as an act of homophobia, and onlookers are outraged at the people who did it.
  3. A group of people risk their lives to stop the oppression of women in a country, and they are praised because of it.
  4. A man stops another man from being shot by jumping in the way of the bullet and is praised for saving him at the cost of his own life.

These kind of situations are commonplace in normal life. They might not always be as extreme (sometimes we’re outraged at people because they are insensitive, arrogant or insulting and sometimes we praise people when they are selfless even when it doesn’t burden them all that much) but I think we can distinguish this outrage/praise from other forms. For example, with moral outrage we aren’t outraged at the effectiveness of the action. If I’m working with someone who is incompetent, I am outraged at their inefficiency. This outrage, I think, is better understood as irritation anyway. I can’t think of other kinds of outrage, but I’m sure there are others. I think if we keep a clear idea of the outrage and praise seen in the examples above we should be fine 🙂

Of Pens and Pain

Now, I hope most people would agree that the people in examples 1-4 are rational in their outrage or praise. But why? For the person who affirms the existence of objective moral duties we can quite easily see why: we are outraged at people who do what they ought not do and we praise those people who go beyond their duties[1]. So, the rapist in example 1 ought not have raped that girl and in doing so he has primarily wronged her and secondarily wronged the people who loved her dearly (such as her parents). It is wrong that he raped her and we are rationally compelled to be outraged at his actions because of it.

But suppose we deny the existence of objective moral duties.Read More »