Clear Language, Clear Mind

December 11, 2009

An argument against traditional monotheism

Filed under: Religion — Tags: , , — Emil O. W. Kirkegaard @ 18:55

Merely a translation of the danish version here.

Translation keys


D:x = things

D:y = things

D:t = moments

One variable predicates

Ex = x exists

At = the world was created at time t

Two variable predicates

Cxy = x created y

Three variable predicates

Kxyt = x created y at time t


g = God

a = The world

n English Symbols Explanation
1 God exists. Eg Assumption for reductio
2 That God exists, logically implies that God created the world. Eg→Cga Premise
3 God created the world Cga 1, 2, MP
4 For all things and for all things, that a thing created another thing logically implies that there exists a moment such that that moment is before another moment at the first thing created the second thing at that other moment (∀x)(∀y)(Cxy⇒[(∃t)(t<t1∧Kxyt1)]) Premise
5 There exists a moment such that that moment is before another moment and God created the world at that other moment. (∃t)(t<t1∧Kgat1) 3, 4, MP
6 For all things there exists a moment such that that moment is before another moment and that thing created the world at that other moment, logically implies that there exists a moment such that that moment is before another moment and the world was created at the other moment. [(∀x)(∃t)(t<t1∧Kxat1)]→[(∃t)(t<t1At1)] Premise
7 It is not the case that there exists a moment such that that moment is before another moment and the world was created at that other moment. ¬[(∃t)(t<t1At1)] Premise
8 There exists a moment such that that moment is before another moment and the world was created at the other moment, and it is not the case that there exists a moment such that that moment is before another moment and the world was created at that other moment. [(∃t)(t<t1At1)]∧¬[(∃t)(t<t1At1)] 4, 5, conj.
9 It is not the case that God exists. ¬Eg 1-8, RAA

Some explanations to the premises

(2) is true when we are dealing with traditional monotheism. Traditional monotheism in the sense that there exists a God and God created the world.

(4) is reasonable when one considers it. If something is created at a moment by something else, then the first thing did not exist immediately before it was created by the other thing. There is at least one moment before a thing was created by another thing where it did not exist. That is what “created by” means.

(6) merely removes the creator so that the moment may be isolated.

(7) since time is a part of space-time and that space-time did not exist before the world was created, then there wasn’t a moment before the world was created. The world is here understood as the physical world in some sense that makes it possible that there is a non-physical world wherein God exists.

February 27, 2009

Tough modal logic formalization

Filed under: Logic,Religion — Tags: , , , , , — Emil O. W. Kirkegaard @ 00:13


Gamgee wrote:

In the Ontological Argument, Anselm refutes Guanilo’s Perfect Island criticism by stating that God has Aseity. Anselm does not, as far as i know, make any attempt to prove that God has Aseity, or even if Aseity is logically possible.

I argue that it is not, for the following reason:

1) We accept that God does not exist in the physical world.

2) Therefore, there must exist some realm outside of normal time and space (realm x, for conveniency)

3) God exists in realm x

4) Therefore, God requires realm x to exist so that he can exist in it.

5) Without realm x, God would not exist

6) Therefore, God is contingent upon realm x for his existence. Aseity is false.

Any obvious holes in my logic?

It’s not that bad but it’s badly structured. I’ll help you:


D:x ≡ things

D:y ≡ things

Ex ≡ x exists

Fxy ≡ x exists in y

Cxy ≡ x in contingent upon y.

a ≡ God

b ≡ non-physical world

c ≡ physical world

Desired conclusion: God is contingent upon the non-physical world.

Desired route: Something to do with worlds.

Version one

1a. Ea

God exists. (Premise)

2a. ¬Fac

God does not exist in the physical world. (Premise)

3a. (∀x)(Ex→(Fxc∨Fxb))

For all x, if x exists, then x exists in the physical world or x exists in the non-physical world. (Premise)

4a. ⊢ Fab (1, 2, 3)

Therefore, God exists in the non-physical world.

5a. (∀x)(∀y)((Ex→Fxy)∧¬Ey)→¬Ex

For all x, if x exists in y and y does not exist, then x does not exist.

6a. ((∀x)(∀y)((Ex→Fxy)∧¬Ey)→¬Ex)→Cxy

If, for all x, for all y, if, if x exists, then x exists in y and y does not exist, then x does not exist, then x is contingent upon y.

7a. ⊢ Cab (5, 6)

Therefore, God is contingent upon the non-physical world.

But 5 is false. It says that if x exist, then x does not exist. I got stuck there. Trying to figure out how to formulate it in some other way to avoid this.

Version two

1b. Ea→Fab

If God exists, then God exists in the non-physical world. (premise)

2b. (∀x)(∀y)((Ex→Fxy)∧¬Ey)→¬Ex

For all x, for all y, if, if x exists, then x exists in y, and y does not exist, then x does not exist. (premise)

3b. ((∀x)(∀y)((Ex→Fxy)∧¬Ey)→¬Ex)→Cxy

If for all x, for all y, if, if x exists, then x exists in y, and y does not exist, then x does not exist, then x is contingent upon y. (premise)

And here I got stuck. I couldn’t find a way to get to Cxy without assuming ¬Eb.

Version three

1c. ¬Eb→¬Ea

If the non-physical world does not exist, then God does not exist. (Premise)

2c. (∀x)(∀y)(¬Ey→¬Ex)→Cxy

If for all x, for all y, if y does not exist, then x does not exist, then x in contingent upon y. (Premise)

3c. ⊢ Cab (1, 2)

Therefore, God is contingent upon the non-physical world.

This works. Premise two is analytic. Premise one is sometimes true per definition.


This argument was remarkably hard to formalize for me.

February 17, 2009

Response to Cartesian's case for broad theism

Filed under: Religion — Tags: , , , — Emil O. W. Kirkegaard @ 19:14


I respond to Cartesian’s case for broad theism as argued with an argument from souls.


January 22, 2009

The source of … and definitions

Filed under: Logic,Religion — Tags: , , , — Emil O. W. Kirkegaard @ 20:36

The problem is how freely we are ‘allowed’ to define things. In this essay I will address a definition
similar to “x is the source of …”. I conclude that we ought not to allow such definitions.


January 4, 2009

Formel debat på FRDB: The logical problem of evil

Filed under: Religion — Tags: , , , , , , , , , , — Emil O. W. Kirkegaard @ 18:53

Jeg deltager i en formel debat på FRDB. URL:

Her er min modstanders første indlæg og mit svar:

Wiploc’s first post

The Logical Problem of Evil: If god exists, why is there evil? Doesn’t the existence of evil prove that god does not exist? The answer is yes. If evil exists, the tri-omni god does not exist.

Tri-Omni: A tri-omni god is omnipotent (all powerful), omniscient (all knowing), and omnibenevolent (all good-wishing).

Omnipotence: A truly omnipotent god could do anything, including contralogical things like making square circles. But you can’t draw logical conclusions about what would happen if logic didn’t work. So this discussion is about a punk-omnipotent god: one who can do anything except violate logic. And, from here on, that’s what I shall mean by “omnipotent.”

The absence of evil is not a square circle. An omnipotent god could prevent evil if he wanted to.

Omnibenevolence: An omnibenevolent god would choose to eliminate evil if he could. If there were a god both omnipotent and omnibenevolent, he both could and would eliminate evil. There would be no evil.

Therefore, if evil exists, it follows that the omnipotent omnibenevolent god does not exist.

Omniscience: We throw in omniscience so nobody can say, “Well, what if god was that powerful, and was that benevolent, but was too stupid or ignorant to realize that evil exists? (What, for instance, if Jehovah assumed circumcision would cure all our problems?)

An omniscient god knows everything. He knows the future; knows counter-factuals (what if Hitler had died as a child?); knew at the time of creation (per Plantinga) every choice that would ever be made in every possible and impossible world. (Which means that, if he chose to create this world, he did so knowing that it would contain evil.)

Tri-omni gods, then, are omniscient, omnibenevolent, andomnipotent: they know all about evil, want to prevent evil, and are able to do so. If such a god existed, there would be no evil. If evil exists, there is no such god. Evil and the tri-omni god cannot logically coexist.

Benevolence is the desire for good, the desire that there not be evil. In the case of omnibenevolence, this desire is total, infinite, unalloyed, unconflicted, on the front burner.

Good and evil: I hardly care how these are defined. Given the definitions already established above, it is clear that the tri-omni god cannot exist if evil exists. But, nonetheless, here’s my understanding: good is anything that causes happiness; evil is anything that causes unhappiness. Stubbing your toe is both good and evil if it makes one person happy and another person unhappy.

Evil is distinguishable from sin. Sin is doubting or disobeying god. In the Adam and Eve story, evil is the punishment for sin. Sin that causes unhappiness is moral evil.

Those are just the definitions that I know. I’m not wedded to them. If Deleet, says, “What if god wanted to give people free will more than he wanted people to be happy?” that will mean that, by definition, god is not omnibenevolent. But, if he wants, we can change the definition. We can say that free will and happiness are both good. Then, god can have both of those desires and still be omnibenevolent. Of course, if those desires conflict, then god isn’t omnipotent—an omnipotent god could have both free will and happiness.

It hardly matters how we define good and evil, so long as they are opposites. If good were blue, and evil is other colors, a benevolent god would want things to be blue. An omnibenevolent god would want everything to be blue. The existence of other colors would prove that one or more of the following statements is true:

1. God isn’t omnibenevolent (he doesn’t want everything to be blue).

2. God isn’t omnipotent (he isn’t able to make everything blue).

3. God isn’t omniscient (he isn’t smart/knowing/wise enough to exploit his omnipotence so as to achieve omni-blueness).

So the LPoE (logical problem of evil) is bulletproof almost regardless of how good and evil are defined.

Five relevant responses to the LPoE: There are many irrelevant responses to the LPoE (logical problem of evil), like, “Atheists suck!” or like, “If god doesn’t exist, then morality doesn’t exist either.” But there are only five relevant responses:

1. God isn’t really omnipotent.

2. God isn’t really omniscient.

3. God isn’t really omnibenevolent.

4. Evil doesn’t really exist.

5. Belief in tri-omni gods is contra-logical.

Each of these “defenses” amounts to a concession that the LPoE is correct. The art, then, of “defending” against the LPoE consists entirely of not realizing what you have conceded. Or at least of not letting your audience realize it.

Thus, Plantinga says god is omnibenevolent, but follows that with the deadpan question, “Why would you believe that a good god would be good to you?” (Yes, I’m paraphrasing.) Thus, he claims god is “omnibenevolent,” but then he un-defines “benevolence” so his claim becomes meaningless. Thus, he concedes #3 without recognizing the concession.

All “defenses” against the LPoE are based on this sort of equivocation.

Conclusion: If a god were omnipotent, he could eliminate evil. If a god were omnibenevolent, he would want to eliminate evil. If he were omniscient, he would be smart enough to eliminate evil. If he were all three, there would be no evil.

Therefore: if evil exists, there is no tri-omni god.

Deleet’s first post


I would like to thank the people who make this debate possible and most of all my opponent, Wiploc, for debating me. I have more objections than the ones in this post but the limited amount of space restricts me from posting them until later. My position is that the LPoE is unsound and the EPoE is sound.

Problems, evil problems!

I would like to distinguish between the two different kinds of evil problems. The first one, which is the one this debate is about, is called the logical one. This is because that the problem, which is actually an argument, states that evil and a tri-onni god are impossible together; they cannot both exist at the same time. The logical problem of evil (LPoE) is committed to claiming that the set of propositions hereunder are inconsistent:

Set 1

1. God is omnipotent

2. God is omnibenevolent

3. God is omniscient.

4. Evil exists.

5. God exists.

The argument then goes that (1) through (4) are true and therefore (5) is false. In other words the LPoE is committed to this implication:

A. If (God is omnipotent and god is omnibenevolent and god is omniscient and god exists) then evil is nonexistent. [(1∧2∧3∧4)→ ¬ 5]

The evidential problem of evil is not committed to (A) but only to making the claim that (roughly) (1) through (4) implies that (5) is very probably false.

The question of this debate is then: is (A) true? Before I shall attempt to answer that however I will discuss the three attributes attributed to God.


This is, I think, the least controversial attribute. By that I mean that it is the least controversial attribute in terms of what it means. Wiploc thinks that omniscience means that one “knows everything”. I prima facie agree with this. Wiploc though believes that this implies that one knows what choices people will make before they make them. This may be impossible so I’ll just reword omniscience to: one knows everything that is possible to know. I hope that Wiploc will accept this.


Wiploc distinguishes between true omnipotent and punk omnipotence. The first includes the ability to “defy logic” and the second does not. The second is characterized (roughly) like this: one can do everything that is logically possible.

I used to be in favor of a such characterization of punk omnipotence but I have changed my mind. There is nothing logically impossible about traveling north of the north pole yet God presumably cannot do this. This is because logical possibility is not the only condition an action have to meet in order to be realizable. There is also what I call environmental possibility; being in position to do so.[i][ii]

Otherwise I accept Wiploc’s use of punk omnipotence instead of true omnipotence.


This one, I think, is the most controversial attribute. This is because it is not clear what a being who is omnibenevolent wills. The prefix ‘omni-‘ simply means ‘all-‘. So we have to look up ‘benevolence’:

1. Desire to do good to others; goodwill; charitableness: to be filled with benevolence toward one’s fellow creatures.

2. An act of kindness; a charitable gift.

3. An inclination to perform kind, charitable acts.

4. A kindly act.

5. A gift given out of generosity.

6. Disposition to do good.

7. An inclination to do kind or charitable acts.

8. An act intending or showing kindness and good will.

Etc. [iii]

As we can see per the above it is not clear that ‘benevolence’ is the desire to remove evil. Perhaps something else is meant by an omnibenevolent person. Note that ‘do good’ can maybe be interpreted as ‘remove evil’ but it’s prima facie not very clear and needs a further and maybe implausible analysis.

Wiploc thinks that benevolence implies the will to remove evil, but this is not what the dictionary says. I’ll go with the dictionary until Wiploc can argue otherwise. Without ‘benevolence’ implying the will to remove evil, then (A) is false and thus the LPoE unsound.

A possible morally sufficient reason to not eliminate evil

The strongest objection to the LPoE (but not the EPoE) is to claim that there is a possible morally sufficient reason as to why God has not removed evil. If there is such a reason, then even an omnibenevolent being such as God does not want to remove evil if he could:

B. There is a possible morally sufficient reason for god not to remove evil.

If (B) is true, then (A) is false. So the LPoE depends on the falseness of (B) to work viz. if (B) is true, then (A) is false and the LPoE is unsound.

So the question now is: is (B) true?


How do we determine whether something is possible? First off we must ask: what kind of possibility are we talking about? We’re talking about logical possibility viz. the non-contradictory nature of something. The most widespread answer to the question above is conceivability. It goes roughly like this: If I can conceive of p being true without discovering a contradiction, then p is logically possible.

However I don’t think this is a good method because it gives wrong answers; if we later discover that something is logically impossible, then it was not possible before even though we could conceive of it without contradiction. Second I don’t think there is any reason to adopt this method.

I propose that we simply assume logical possibility instead of “making up an excuse” to believe that p is possible.

Given either of the “methods” above then (B) is true. This is because that I can conceive of there being a morally sufficient reason and so can others.[iv]

And so if (B) is true, then (A) is false and the LPoE is unsound.

i Such a characterization is dicussed in Omnipotence, Stanford Encyclopedia of Philosophy. URL:

ii See my earlier paper on the subject of contradictory divine attributes The incompatibility of omnipotence and omniscience. URL:

iii I found these at in a search for ‘benevolence’. I have omitted some irrelevant entries. URL:

iv See for instance the ones in this article. Also see Platinga’s book mentioned in the article. URL:

August 17, 2008

Re: Argument from movement

Filed under: Religion — Tags: , , , — Emil O. W. Kirkegaard @ 15:54

I want to add my comments to the argument from movement, as a “rationally compelling argument for the existence of God” as worded by punkforchrist (henceforth pfc). It might as well be called a rebuttal.

Pfc presents the first part of his case here, as a part of formal debate on between him and fellow atheist wiploc.

Pfc starts his case by stating that:

Aristotle referred to God as the ‘unmoved mover’. In my opening, I wish to defend two major contentions: 1) that such a being exists; and 2) that this being possesses attributes that are most consonant with the God of classical theism.

The main argument is as follows, a direct copy of pfc’s words:

1. If there is no unmoved mover, then there is no regularity of motion.
2. There is regularity of motion.
3. Therefore, there exists an unmoved mover.
Already, this argument strikes me as being very unclear. It seems pfc notices it himself when he wrote:

It is important to note that when we use the word ‘motion’ we simply mean change.

I’m confused as to why pfc then chose to word it mover and motion instead of change? Perhaps he wanted to keep to the wording of the original argument. Why?

As for the argument form, I find it quite strange. It looks like this:

1′. If no As, then ¬B.
2′. B.
3′. There is some As.

By ‘some As’ I mean at least one A. However, he could just have worded it positive, which is generally better, for instance, this form:

1”. If there is regularity of motion, then there is an unmoved mover.
2”. There is regularity of motion.
3”. There is an unmoved mover.

Let’s move on. As for the support for his premises pfc writes:

(2) ought to be uncontroversial. If anything is evident to our senses, it is that things change. We live in a dynamic universe, and we constantly observe change in things. So, what about (1)?

Notice that what he writes does not support his (2). He writes that things change and that we live in a dynamic universe, but neither of those imply (2). Also notice how quick he is to move on. He didn’t even explain what ‘regularity of motion’ is supposed to mean. To his defense, it should be noted that the word limit for the opening statement is 1000, so he does not have much space, however, he only used about 900 words, leaving 100 open for elaboration.

Now, pfc wants to establish the justification of (1). Oddly enough, no makes special note of the ‘regularity of motion’ contrasted with motion. What regularity? Is he talking about like a specific time regularity? For instance, that motions happens every microsecond? All the time?

He goes on to say that regularity [of motion] must correspond to something unchanging, and states that otherwise it “wouldn’t be regular in the first place!”. Why is this? It reminds me of the moral argument, that if something is good, it must be good because we contrast it with something perfectly good. By this premise, there must exist a perfect car, which is false.

He then writes that it logically follows–how else can things follow?–that there exists something unchanging, which he identifies with immutable a common attribute to the Christian god.

Now, pfc wants to establish the godless, so to speak, of the unmoved mover that he thinks he has established.

He then defines the typical attributes of the classical theism god, but smuggles a nice little word on ‘being’, which implies personality. That certainly did not follow from his unmoved mover. Entity would have been a better choice of word.

Talking about immutability:

[…] something can be immutable if and only if there is no potentiality in it to change. Therefore, what is immutable must be purely actual.

Strange use of words. It can be P iff there is no potentiality “in it” to change. Does he mean that potentialities are intrinsic? Does potentiality mean possibility? Why the use of can in the beginning? Is he implying that there are multiple necessary conditions for immutability? I think he meant to type ‘is’.

Pfc then wants to establish ‘oneness’ of this entity:

However, something can only be purely actual if it is one. The reason why is because if there were more than one pure actuality, then there would be distinctions between them. But, distinctions entail limitations, and limitations entail potentiality; and because there is no potentiality in what is purely actual, the unmoved mover must be one.

Note the beginning. ‘can only’ implies a second necessary condition to pure actuality. He’s equivocating ‘one’ for ‘oneness’ here. Oneness is like a feeling, but here he talks about the amount of unmoved movers is one.

It’s not clear how these conditionals are true. Why does distinctions entail limitations? And why does limitations entail potentiality?

Pfc goes on to discuss his terminology of potentiality and actuality:

At one point in time, I was a fetus. This means that at that time I was a fetus in actuality, and an adult in potentiality.

Again he seems to be implying that potentialities are intrinsic. How was ‘he’ a fetus? How does pfc do personal identification? The energy I consist of could (physically) be something else, like a rock, does that mean that I am a potential rock? What about a female, they are slightly less in size, and thus we could rearrange the energy and I could be a female–in potentiality. Where do this get us?

Pfc goes on to make a non-sequitur:

Partly actual beings, like ourselves, possess some power, some knowledge, and some goodness. From this, we can infer that a purely actual being would have power to do all thing, would know everything there is to know, and would possess every good thing there is to possess.

Pfc then discusses a common objection:

Regarding the above, it is commonly objected that if God is purely actual, and as a result must be all-knowing, he must also be all-ignorant, which is a contradiction. However, this misconstrues the nature of what ignorance is. Ignorance is simply a privation; it is a lack of knowledge, and not something actual in and of itself. An ignorant person does not possess something a knowledgeable person lacks, but the other way around. Now, since God is pure actuality, He can only be described in terms of what is actual, and not of what is privative. The same can be said of weakness and evil.

I’m not sure how he is supposed to define evil as a privation; a lack of good I take it. That’s certainly not what I have in mind when I use the word ‘evil’. But, even if true, it would not save his god from his own argumentation. Just find some arbitrary attribute theists don’t accept that god has, show that humans have a little of them and that they are not a privation, then god ‘must’ have an absolute version of them. A candidate could be greed, a handicap and so on. Unless pfc wants to define a lot of things negatively (that seems indefensible on it’s own), then this is highly problematic.

In his conclusion pfc states another argument that:

I believe the above argument is sound. If this is the case, then we find confirmation for more traditional versions of the argument from motion […]

I won’t take that argument on at this moment.

My conclusion of this analysis was the same as my immediate impression:

Au contraire the above post. I find this argument very weak, however, I will await Wiploc’s rebuttal before I comment on it.

This article has also been posted here.

Powered by WordPress