Does the God of Christianity exist? -- Brian Bosse vs. Pervy

[KnightWhoSaysNi]

This thread has been set up for a formal debate between Brian Bosse and Pervy who will debate the following resolution:

"Resolved: The God of Christianity exists."

Brian Bosse will affirm and Pervy will oppose. The debate will proceed in turns in the following special format, per the parameters (http://www.iidb.org/vbb/showthread.php?p=4046119#post4046119).

Part I: Introductory arguments

Round 1: Brian Bosse opens; Pervy rebuts
Round 2: Brian defends; Pervy rebuts

Part II: Cross-examination (3 statements per round)

Round 3:
- Brian Bosse submits 3 questions
- Pervy submits 3 answers
- Brian Bosse submits 3 replies

Round 4:
- Pervy submits 3 questions
- Brian Bosse submits 3 answers
- Pervy submits 3 replies

Part III: Conclusion

Round 5: Brian Bosse concludes; Pervy concludes

A Peanut Gallery (http://www.iidb.org/vbb/showthread.php?p=4048073#post4048073) is set up in the Existence of God(s) forum for the rest of us to comment on the debate.

Enjoy the debate!

- KWSN, FD Moderator

[KnightWhoSaysNi]

Part I: Introductory Arguments

[Brian Bosse]

Preliminary Remarks

I would like to thank the Internet Infidels Discussion Board and Nightshade for providing this opportunity for rational exchange. I would, also, like to thank my opponent, Pervy, for being willing to engage me in this manner. Lastly, I am a Christian by the grace of God, and pray that God may use this exchange as a means of grace to others.

Introduction

The ontological argument I am presenting is a formal modal argument based on possible world semantics. If the reader has a basic understanding of propositional logic, then he should have no problem following the argument. For those not familiar with propositional logic, I will provide an informal summation of the argument. To begin, I would like to explain what I mean by possible world semantics and modal logic.

In propositional logic, there are functions that assign truth-values to atomic sentences, and functions that assign truth-values to more complex sentences built up from these atomic sentences using the sentential connectives: ¬, →, ↔, Λ, V. In modal semantics, a set W of possible worlds is introduced where these truth-value functions assign a truth-value to each sentence for each of the possible worlds in W. It is possible for particular sentences to be assigned different truth-values in different possible worlds. For instance, in some possible world it is true that Germany won World War II; whereas, in another possible world, it false that Germany won World War II. This makes truth-value relative to a particular possible world. We can now introduce the modal operators of ‘necessity’ and ‘possibility’ that make up modal logic.

Modal Operators

□p = ‘p’ is necessarily true. For ‘p’ to be necessary (□p), then ‘p’ is true in all possible worlds.
◊p = ‘p’ is possibly true. For ‘p’ to possible (◊p), then ‘p’ is true in at least one possible world.
p = ‘p’ is actually true. For ‘p’ to be actual (p), then ‘p’ is true in the real world. It is my burden to prove the actuality of the existence of the Christian God.

It should be noted that we can define both □ and ◊ in terms of each other.

Rule N: □p ↔ ¬◊¬p. That is to say, ‘p’ is necessarily true if and only if it is not the case that ‘p’ is false in at least one world.
Rule P: ◊p ↔ ¬□¬p. That is to say, ‘p’ is possibly true if and only if it is not the case that ‘p’ is false in all possible worlds.

Modal logic is essentially propositional logic combined with the modal operators □ and ◊ as defined above. The logical rules I will be using in my proof are as follows:

Logical Rules

A. Disjunctive Syllogism: [(a V b) Λ ¬b] → a
B. Modus Ponens: [(a → b) Λ a] → b
C. Modal Modus Tollens: [□(a → b) Λ □¬b] → □¬a
D. Substitution: [(a V b) Λ (b → c)] → (a V c)
E. Becker’s Postulate: □a → □□a; ◊a → □◊a (Modal status is always necessary.)
F. Excluded Middle: a V ¬a
G. Modal Axiom: □a → a

A Formal Presentation of the Ontological Argument

Let ‘p’ stand for the proposition: “The God of Christianity exists.”

1. □(p → □p) (It is necessarily the case that if the God of Christianity actually exists, then the God of Christianity necessarily exists.)
2. ¬□¬p (It is possible that the God of Christianity exists. - See Rule P for this translation.)
3. □p → p (Rule G)
4. □p V ¬□p (Rule F)
5. ¬□p → □¬□p (Rule E)
6. □p V □¬□p (Rule D – 4 and 5)
7. □¬□p → □¬p (Rule C – 1)
8. □p V □¬p (Rule D – 6 and 7)
9. □p (Rule A – 8 and 2)
10. p (Rule B – 3 and 9)

Informally, if it is possible that the God of Christianity exists (premise 2), then by definition the God of Christianity exists in at least one possible world, w(1). If it is necessarily the case that “if the Christian God exists, then He exists necessarily” (premise 1), then we know this is true in all possible worlds, including w(1). So, in w(1) the following two proposition are true: “If the God of Christianity exists, then it is necessarily the case the God of Christianity exists” and “the God of Christianity exists.” By Rule B, “It is necessarily the case that the God of Christianity exists” is true in w(1). By Rule G, this means that the God of Christianity exists in every possible world including ours. That is to say, the God of Christianity actually exists. Premises (1) and (2) are the key premises that need to be established.

Justification for Premises (1) and (2)

Premise 1 is true by definition; that is to say it is true within the Christian worldview. If the God of Christianity exists, then He is the ground for all being and intelligibility. Therefore, He is the ground for every possible world.

Premise 2 simply states that it is possible for this God to exist. This is not an ambitious claim. For instance, the existence of green Martians or unicorns are both possible; that is to say, there is a possible world where their existence is true. The only way for the existence of a particular being to not be possible is for this being to be logically incoherent. This means that in order to refute premise 2, it must be shown that the God of Christianity is logically incoherent. There is no proof demonstrating this (baring my opponent’s presentation), and as such the possibility of this God’s existence remains. (Note: The word ‘possibility’ was italicized in the previous sentence because it was used it in a slightly different way than its technical Modal Logic sense.)

Concluding Remarks

The above proof is valid, and the premises are true. This makes the proof sound, and as such the conclusion stands: The God of Christianity exists. Q.E.D.

[Dean Anderson]

First of all, I would like to thank my opponent and IIDB for this debate opportunity. This opening post is my critique of my opponent's proof. To be honest, this critique seems somewhat redundant as my opponent's proof has already been fairly thoroughly demolished in the accompanying "Peanut Gallery" for this debate; but I shall attempt to give a reasonably definitive critique here (given the wordcount limitation).

The logic of my opponent's argument is valid - meaning that if we grant his premises then his conclusion does indeed follow - but here, I present what happens with only a minor change to my opponent's second premise:

1) □(p → □p) (It is necessarily the case that if the God of Christianity exists, then the God of Christianity necessarily exists.)
2) ¬□¬(¬p) (It is possible that the God of Christianity does not exist - See my opponent's Rule P)
3) ¬□p (Resolving Double Negation - 2)
4) □(¬p) (Modus Tollens - 1 and 3)
5) ¬p (Modal Axiom - 4)

Informally: If it is possible that the God of Christianity does not exist, and it is the case that "if the Christian God exists, then He exists necessarily" (my opponent's first premise) then he cannot exist.

This is simple when you think about it - my opponent's definition of the God of Christianity is such that he either exists in all possible worlds or in none. Therefore, if he exists in one possible world then he must exist in all of them; and conversely if he fails to exist in one possible world then he cannot exist in any of them.

The Achilles heel of such a definition is that we can invent any number of mutually exclusive entities with that definition and all possible ones must exist.

I now present my own god (the "Goddess of Perviness"). My definition is that if the Goddess of Perviness exists then She is the ground for all being and intelligibility. Therefore, She is the ground for every possible world. Furthermore, She is defined as being a jealous God - indeed, the only true god - meaning that if She exists then no other god can exist.

As can be seen, my definition is word for word identical to my opponent's definition of the God of Christianity - with the exception that I have added a monotheism clause. I trust that this monotheism clause will not be controversial; since although not made explicit by my opponent, monotheism is implicit in the Christian worldview and therefore in the definition of its God.

By my opponent's own logical sequence, substituting 'q' ("The Goddess of Perviness exists") instead of 'p' throughout, we see that if it is possible that my Goddess of Perviness exists (since her definition is identical to that of the God of Christianity in all aspects that affect this argument, if it is possible for one to exist then it is equally possible for the other to exist) then she must exist.

This leads us to the following:

1) □(p → □p) (My opponent's first premise - if the God of Christianity exists then he is necessary by definition)
2) □(q → □q) (My opponent's first premise with 'q' substituted for 'p' - if the Goddess of Perviness exists then she is necessary by definition)
3) ¬□¬p (My opponent's second premise - it is possible that the God of Christianity exists)
4) ¬□¬q (My opponent's second premise with 'q' substituted for 'p' - it is possible that the Goddess of Perviness exists)
5) (¬□¬p) Λ (□(p → □p)) → (¬□¬q) Λ (□(q → □q)) (¬□¬p) Λ (□(p → □p)) ↔ (¬□¬q) Λ (□(q → □q)) (Premise: 'p' and 'q' have identical definitions, so if one is possible then so is the other)
6) □¬(p Λ q) (Premise: By definition, two monotheistic gods cannot exist in the same possible universe)
7) (¬□¬p) Λ (□(p → □p)) → p (My opponent's argument - 1 and 2)
8) (¬□¬q) Λ (□(q → □q)) → q (My opponent's argument - 3 and 4)
9) (¬□¬p) Λ (□(p → □p)) → q (Hypothetical Syllogism - 5 and 8)
10) (¬□¬p) Λ (□(p → □p)) → (p Λ q) (Composition - 7 and 9)
11) ¬(p Λ q) (Modal Axiom - 6)
12) ¬((¬□¬p) Λ (□(p → □p))) (Modus Tollens - 10 and 11)
13) ¬ (¬□¬p) V ¬ (□(p → □p)) (DeMorgan's Theorem - 12)

Informally: If it is possible that the God of Christianity exists and it is possible that the Goddess of Perviness exists, and both are defined as existing necessarily if they do exist, then they must both exist. However, they cannot both exist (by definition; since they are both defined as monotheistic). Therefore, either it is false that "it is possible that the God of Christianity exists" (thus proving that it is not possible for the God of Christianity to exist) or it is false that "if the God of Christianity exists then he exists necessarily" (thus invalidating my opponent's entire argument).

My opponent is now left with three possibilities:

1) Show that there is some difference between the God of Christianity and the Goddess of Perviness (despite their identical definitions) which means that it is possible for the God of Christianity to exist but not possible for the Goddess of Perviness to exist. Even if my opponent manages this, he must still contend with the fact that if there is any possible world where the God of Christianity does not exist (and we can postulate an endless list of other possible worlds with alternate necessary entities to the God of Christianity should the Goddess of Perviness not suffice; and even postulate possible worlds with no necessary entities) then he cannot exist in any world including ours.

2) Concede that his first premise is false (i.e. that the God of Christianity is not necessary) by which he forgoes his entire proof.

3) Concede that his second premise is false (i.e. that it is not possible for the God of Christianity to exist) and become an atheist.

[Brian Bosse]

Before I begin my rebuttal, I want to acknowledge the very good discussion in the peanut gallery. I have enjoyed reading the analysis, and look forward to a spirited “after debate” session. Secondly, I want to acknowledge Pervy’s very creative argument. I would never have thought the debate would go in this direction, and even though I feel his critique fails and will attempt to demonstrate this, he should be applauded.

A Rebuttal of My Opponent’s Argument

Essentially, my opponent’s argument boils down to the following: Within the same proof, both the God of Christianity and the Goddess of Perviness are proven to exist. However, this supposedly leads to a contradiction being that both positions require monotheism. My opponent concludes:

Therefore, either it is false that "it is possible that the God of Christianity exists" (thus proving that it is not possible for the God of Christianity to exist) or it is false that "if the God of Christianity exists then he exists necessarily" (thus invalidating my opponent's entire argument).

Pervy’s argument is implicitly a reductio ad absurdum (http://www.christianlogic.com/brianbosse/archives/2005/09/aristotles_redu.html). He did not explicitly state every step in this argument form, but informally this is what he did. He started with a group of premises (steps 1-4) and derived a contradiction. Based on this contradiction, he then concluded that either steps 1 or 3 were false (my steps 1 and 2). However, this is not a valid conclusion. He should have concluded that either steps 1, 2, 3 or 4 were false. It is possible that steps 1 and 3 are true and that steps 2 and 4 are false! The first point being, Pervy’s argument, although very creative, falls short of disproving either steps 1 or 3 (my steps 1 and 2).

Secondly, Pervy assumes he has arrived at a contradiction by proving the existence of two different gods. Why does he assume they are different? Pervy goes out of his way to define the Goddess of Perviness using almost the exact same verbiage as I used in my proof when speaking of the Christian God. What if they are the same God using two different referents? If this is the case, then there is no contradiction. Pervy simply has proven the same God referring to it in two different ways.

I realize many may not be satisfied with these rebuttals. They may judge this as me being let off the hook on mere technicalities. I do not wish to be unfair to my opponent or the audience, and as such I will dive a little deeper into the issue. My opponent failed to disprove steps 1 and 3 (my steps 1 and 2). However, if we grant there was an actual contradiction, then he did prove that at least one of the steps (1, 2, 3 or 4) is false. If Pervy were pressed to further define the Goddess of Perviness so as to make a clear delineation between this god and the God of Christianity, then the game would be afoot. At this point, I don’t have any more information about this god. But I will explain the essence behind the type of argument I would present to dispute steps 2 and 4. As Bobinius has pointed out in the peanut gallery, the existence of these beings in possible world semantics is based on a logical coherency. A being exists in some possible world if and only if the existence of that being logically coheres with itself and coheres with the rest of the possible world. I would attempt to show that at some key point where this goddess diverges from the Christian God is the very point it does one of two things: (1) looses its necessity, and/or (2) is not logically possible. However, whatever arguments I would make beyond this point would just be straw-man attacks. Pervy did not give any further information. Unfortunately, I don’t have another rebuttal to respond to new any arguments that he may bring up. Hopefully, he will argue against this rebuttal of mine.

Conclusion

My opponent’s argument was very creative. However, ultimately it falls short of disproving steps (1) and (2). He fails to adequately define the Goddess of Perviness in a sufficient enough manner to establish the contradiction, and even if we grant the contradiction, he only shows that at least one of the first four steps of his proof must be false. As such, the argument I presented in my opening statement stands: The God of Christianity exists.

[Dean Anderson]

My opponent is claiming that my logic failed to demonstrate that my premises 1 and 3 (originally his premises; and I will refer to them as being 'his' from now on) cannot both be correct. He asserts that they may be correct but my premises 2 and 4 may be incorrect instead. He doesn't mention premises 5 and 6, so I assume that he agrees that these are tautologically correct by their very definitions.

Firstly, I don't merely do a Reductio Ad Absurdum and say that since we have a paradox then at least one of the four premises is incorrect, and then wave my hand and say that it must be one of his rather than one of mine. I explicitly go down a logical path that shows that at least one of his premises must be incorrect.

In fact, I can go further and say that a symmetrical path will show that premises 2 and 4 must also be incorrect. That was my point. I was not arguing specifically that the possible existence of the Goddess of Perviness makes the existence of the God of Christianity impossible. I was arguing that the possible existence of more than one necessary and monotheistic gods makes the existence of any of them impossible (admittedly the unusually tight wordcount limit prevented me from explaining my points in as much detail as I would have liked. Indeed, I also had other independent arguments - but wordcount prevented me from presenting them.)

To clarify the basic point of my previous post: By definition, if it is possible for a necessary being to exist (i.e. if it exists in any possible world) then it must exist in all possible worlds. Therefore, any putative necessary being that can possibly exist (not just the God of Christianity) must exist in all worlds. Therefore, either it is possible for necessary beings to exist and an infinite number of them do exist (we can keep defining new ones indefinitely with only minor changes that don't affect whether the being is logically possible or not - and all the ones we define must exist) or it isn't possible for a necessary being to exist and therefore none do. However, the definition of the God of Christianity implicitly includes the fact that he is the only god and the only necessary being. This leads to the paradox that if it is possible for a necessary being to exist as the only god then an infinite number of necessary only gods must exist. Since this is impossible (if there is only one then there obviously can't simultaneously be an infinite number of them) then the only alternative is that it isn't possible for any necessary being who is an only god to exist.

Secondly, I addressed that very point last round:

Premise 2 is exactly the same as premise 1, since the definition of the Goddess of Perviness (for the sake of this proof) is identical to the definition of the God of Christianity. As such, premise 2 is as correct as premise 1 - and if my opponent can come up with some reason why premise 2 does not accurately describe a god who is described as "if X exists, then X exists necessarily" then it means that premise 1 also fails to describe his God of Christianity. In other words, he can argue that premise 2 is wrong if he likes, but given the definitions then his argument will also invalidate premise 1.

Similarly, he can argue that premise 4 is wrong and it isn't possible for the Goddess of Perviness to exist. This leads to the same difficulty. Because of the identical nature of the definitions, any reason my opponent can come up with that prevents the Goddess of Perviness existing will also prevent the God of Christianity existing and therefore if my opponent argues that premise 4 is incorrect then his argument will also invalidate premise 3.

My opponent also argues that the Goddess of Perviness may actually be the God of Christianity or may be logically impossible for a different reason. This is missing the point. This isn't about the specific Goddess of Perviness. She is just a tongue-in-cheek example. We can define as many gods as we like, each of which is almost identical to the God of Christianity but differs only in details that don't affect their logical coherence - for example instead of a Son, one might have two Daughters.

[KnightWhoSaysNi]

Part II: Cross-examination

(Brian Bosse will begin with three questions for the first round)

[Brian Bosse]

My three questions for my esteemed opponent are as follows:

Question 1: You stated in step 5 of your proof that ‘p’ and ‘q’ are defined identically. In light of this, would you say your step 6 is valid?

Question 2: If ‘p’ and ‘q’ are not equivalent, then is step 5 in your proof valid?

Question 3: In light of questions 1 and 2 above, is the thirteen step argument you presented against my position in your initial rebuttal valid?

[Dean Anderson]

Question 1: You stated in step 5 of your proof that 'p' and 'q' are defined identically. In light of this, would you say your step 6 is valid?

Yes.

The statements themselves are not identical - 'p' is "The God of Christianity exists" and 'q' is "The Goddess of Perviness exists" - but the definitions of the subjects of those statements ("The God of Christianity" and "The Goddess of Perviness") are defined identically. Whilst these are separate entities (and are defined as being such), they are separate entities of exactly the same type and as such, if it is logically possible for one of these entities to exist then it must also be logically possible for the other entity to exist.

However, part of their definition (explicit in the case of the Goddess of Perviness, and implicit in the case of the God of Christianity) is that each entity is unique. Therefore, premise 6 is valid: since they are of the same type, and each is defined as being the only one of its type that exists, they cannot both exist.

Mundane example: if we define 'p' to be "Tree X is the only tree in the forest over 10m tall" and we define 'q' to be "Tree Y is the only tree in the forest over 10m tall", X and Y can have identical definitions (they are both defined identically as "a tree within the forest" although they are also explicitly defined as being different trees). Either statement is equally logically possible (my step 5), but since they are mutually exclusive, they cannot both be true at the same time (my step 6).

-------------------------------

Question 2: If 'p' and 'q' are not equivalent, then is step 5 in your proof valid?

As demonstrated in my last example, 'p' and 'q' must be equivalent, given the identical definitions of "The God of Christianity" and "The Goddess of Perviness". Given that these two distinct entities both have the same definition, then the logical coherence of each is identical, and as such the logical possibility of one existing is the same as the logical possibility of the other existing. Therefore, step 5 (which explicitly states that if one of them can possibly exist then the other can also possibly exist) is valid.

If 'p' and 'q' were not equivalent, then step 5 would not be a valid premise. However, statements 'p' and 'q' are equivalent by their identical wording and the identical definitions of the subjects of those statements.

As stated in my previous rebuttal, we are not just looking at 'p' and 'q' here. In the bigger picture, we have 'p0' all the way to 'p∞' which are all equivalent due to the infinite number of putative necessary unique entities that we can define with identical definitions to the God of Christianity. If it is logically possible for any one of these to exist then it is equally logically possible for all of them to exist - and since possible necessary beings must exist, if it is possible for any one of them to exist then they all must exist - which is paradoxical, since they are defined as being unique.

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Question 3: In light of questions 1 and 2 above, is the thirteen step argument you presented against my position in your initial rebuttal valid?

Yes.

Assuming that there is no error in the logic of steps 7-13 - and I am sure that if there was then someone would have pointed it out - then 7-13 follow soundly from premises 1-6.

As seen in my first answer, 6 is valid and is independent of 5.

Premise 5 states validly that if one entity is logically coherent and can exist in a possible world, then a second entity with an identical definition must also be logically coherent and can also exist in a possible world.

Premise 6 states validly that two entities with the same definition cannot both exist if they are both defined as being unique (i.e. they are defined such that each is - if it exists - the only entity with that definition that does exist).

Premises 1 and 2 are self-evidently true by the definition of the entities that they talk about.

This just leaves premises 3 and 4 - the premises that the God of Christianity and the Goddess of Perviness can possibly exist. Given their identical definitions, if one can possibly exist then the other can also possibly exist - therefore either 3 and 4 are both valid or neither of them are. These premises may indeed be false (my proof demonstrates that they must be false, unless premises 1 and 2 are). However, whichever set of premises are false (3 and 4 or 1 and 2), my opponent's argument for the existence of the God of Christianity fails.

[Brian Bosse]

Rebuttal Answer #1

My opponent argues in step 6 that it is impossible for two monotheistic gods to exist. This follows if we are speaking about two different gods. If they are the same god going by different labels, then the statement is false. My opponent’s step 5 gives us good reason to assume that they are the same god. He makes statements such as…

'p' and 'q' have identical definitions…my definition is word for word identical to my opponent's definition of the God of Christianity…

I would grant that his bi-conditional in his corrected step 5 is true if the two entities are the same. If they aren't the same, then it does not follow that the necessity of one implies the necessity of the other since they are mutually exclusive. So, if step 5 is true, then step 6 is false because both entities are the same.

Rebuttal Answer #2

My opponent agrees that ‘p’ and ‘q’ are equivalent, but then in his very next sentence states that the subjects of these propositions are distinct. The problem with this is that if the subjects of these propositions are distinct, and if their existence is mutually exclusive as my opponent says they are, then the bi-conditional in corrected step 5 is not true. From a strictly formal perspective (i.e., we do not consider the meaning of the terms) the following is valid…

(□(p → □p) Λ ¬□¬p) → p

From a strictly formal perspective the following is not valid…

(□(p → □p) Λ ¬□¬p) ↔ (□(q → □q) Λ ¬□¬q)

unless ‘p’ and ‘q’ are equivalent. However, when we consider the material part of the argument (i.e., what the terms mean), then step 6 says ¬(p Λ q) is true, which makes step 5 false.

Rebuttal Answer #3

Steps 5 and 6 cannot both be true as explained above, and as such, my opponent’s proof is unsound. This means that he has failed to refute my original argument.

At this point, I want to acknowledge what I feel is a good argument against my position that avoids Pervy’s problematic step 5. Since my argument is formally valid, then one can substitute any being into the sentence “entity ‘x’ exists” and let ‘p’ stand for this in the proof. At this point, the proof would constitute a proof for the existence of this entity if premises 1 and 2 were true. Regarding this, one could ask why they should accept the proof for the existence of the Christian God over the existence of, say, the goddess of Perviness or even the god of Islam. I think this is where the best objection to my argument lies.

[KnightWhoSaysNi]

For the next stage of Part II, Pervy will now submit three questions to Brian Bosse.

[Dean Anderson]

Question 1: I define "dog" as "An animal of species Canis Lupus Familiaris", "Fido" as "Fido is a dog" and "Butch" as "Butch is a dog". Is it now true that Fido and Butch may be different entities but with identical definitions?

Question 2: If "I own one dog" is true, doesn’t this make "I own Fido" and "I own Butch" equally possible – since Fido and Butch have the same definition, if one statement is possible then the other must be and vice versa?

Question 3: Given the answers to 1 and 2, doesn’t the possibility of me owning either dog lead to the possibility of me owning the other (premise 5) and that (because I only own one dog) I can’t own both (premise 6)?

[Brian Bosse]

Answer to Question #1

The problem with the question is that there is an ambiguity in what is meant by “identical definitions.” In one sense, Fido and Butch have identical definitions. Fido and Butch are both of the species Canis Lupus Familiaris. However, in another sense they are not identically defined. Butch turns out to be a male Labrador retriever, and Fido is a female poodle. Let’s take a look at what happens when we draw logical conclusions without recognizing this distinction. Consider this argument:

Premise 1: Fido is able to have puppies.
Premise 2: Butch and Fido are identically defined.
Conclusion: Butch is able to have puppies.

Clearly, this is not valid. Yet, this is the type of argumentation my opponent is using in step 5 of his proof. He seems to think that because he has defined the goddess of Perviness with certain properties in common with the Christian God, then whatever is true for the Christian God must be true for the goddess of Perviness. This is patently false. Here is step 5:

5) (¬□¬p) Λ (□(p → □p)) ↔ (¬□¬q) Λ (□(q → □q)) (Premise: 'p' and 'q' have identical definitions, so if one is possible then so is the other)

If ‘p’ and ‘q’ are identical in every way, then whatever is true for ‘p’ is true for ‘q’. However, my opponent has repeatedly said that they are not identical in every way. There is nothing in my opponent’s argument that establishes step 5.

Answer to Question #2

My opponent asks if it is “equally possible” that the propositions “I own Fido” and “I own Butch” are true. There are problems with this question, which once again results because of ambiguity. I will take this opportunity to clear up some confusion in the peanut gallery concerning this. By definition, ‘x’ is possibly true if and only if it is not the case that ‘x’ is false in all possible worlds. So, if ‘x’ is true in some world, then ‘x’ is possible. It is possible for ‘x’ be true in some possible world and false in another world. The following are valid inferences:

□x → x and x → ◊x

The following is not valid:

◊x → ◊¬x

The confusion in the peanut gallery (a confusion that is understandable) is that some fail to keep distinct ‘possible’ as used in modal logic versus common parlance. This is the problem with my opponent’s question. Consider this: “I own Fido” is true in 999,999 worlds and “I own Butch” is true in one world. In this sense, it would not be correct to say that both propositions are equally possible, although in a modal logic sense they are both possible. Let me ask my opponent this question (he may choose to answer if he so desires): Fido and Butch are both dogs. Does this make the propositions “Fido is able to have puppies” and “Butch is able to have puppies” equally possible? Step 5 is invalid.

Answer to Question #3

Premise 1: I own a dog.
Premise 2: Fido and Butch are dogs.
Conclusion: It is possible I own either Fido or Butch.

This is a valid argument.

Premise 1: It is possible for Fido to have puppies.
Premise 2: Fido and Butch are both Canis Lupus Familiaris.
Conclusion: It is possible for Butch to have puppies.

This is not a valid argument.

Premise 1: It is possible for the God of Christianity to exist.
Premise 2: The God of Christianity and the goddess of Perviness have some properties in common.
Conclusion: It is possible for the goddess of Perviness to exist.

This is not a valid argument.

There are certain properties a being must have in order for it to be necessary - just like there are certain properties a being must have in order to be able to have puppies. For my opponent to establish his step 5 he must show that the very properties making the Christian God both possible and necessary are the very properties the goddess of Perviness has. My opponent failed to do this. However, even if my opponent did do this, it would leave unclear the distinction between the two entities. There is a lot behind the claim of being both possible and necessary. I was hoping the debate would go in this direction, but, alas, it did not. Rather, it went the way of my opponent’s step 5, which has been shown to be invalid.

[Dean Anderson]

Rebuttal Answer #1

This completely fails to answer my first question.

I asked if Fido and Butch may be distinct entities with identical definitions. My opponent responded by changing the definitions of them - by defining one as a male Labrador and the other as a female Poodle - and then pointing out that in this case the conclusion doesn't follow despite their "identical definitions". Except they no longer have identical definitions due to his change, so his demonstration that the conclusion doesn't follow despite the "identical definitions" is utterly fallacious.

If he hadn't changed the definitions, then he would have been forced to answer that yes, they may be two distinct entities with identical definitions.

Not only that, but he mischaracterises my argument as defining the Goddess of Perviness "with certain properties in common with the Christian God", whereas I have in fact given her an identical definition to the Christian God.

Rebuttal Answer #2

Again, this completely fails to answer my question.

The answer, of course, is again yes – the two statements in my question are indeed equally possible given the identical definitions.

My opponent tries to turn the question back at me, but the answer to his question is still yes.

1) Fido and Butch are both defined as dogs (assuming we ignore my opponent's changed definitions).

2) It is possible for a dog to have puppies (because it is possible for a dog to be female and fertile and to have mated).

3) Therefore it is equally possible for Fido and Butch to have puppies given their identical definitions as dogs.

If my opponent wants to redefine Butch and Fido as he did in his previous question then it is no longer equally possible – but as a reader you must see that he needs to redefine my entities to make this happen.

Rebuttal Answer #3

Once again, my opponent completely fails to answer my question.

The answer is that yes, it's true that steps 5 and 6 are not mutually exclusive, and this example shows that.

I shall ignore his three premise/conclusion sets – since they are all based on the redefinitions and mischaracterisation that I have previously mentioned.

He says:


For my opponent to establish his step 5 he must show that the very properties making the Christian God both possible and necessary are the very properties the goddess of Perviness has.


Simple.

The Goddess of Perviness is defined as having those properties, using an identical definition to the Christian God.

This example with dogs has shown clearly: If any other putative divine entities we choose to invent have identical definitions to the Christian God, then my argument is valid and we are forced to conclude that either all exist or none exist.

[KnightWhoSaysNi]

Part III: Conclusion

[KnightWhoSaysNi]

Brian Bosse has requested a week's extension for his final statement (this shifts the deadline to Jan. 29). I have agreed to grant his request.

- KWSN, FD Moderator

[Brian Bosse]

I would like thank IIDB, our moderator, and my gracious opponent, Pervy. I have found the debate stimulating, and hope it has been beneficial to all involved.

Conclusion

My opponent has agreed my proof is valid. He attacked the soundness of my argument with a proof of his own. The idea behind his argument is that different entities whose existences are not compatible with each other can be established as existing at the same time. My rebuttal to this argument has focused on two points: either (1) the two entities are not different (i.e., step 6 is false), or (2) if they are different, then the inference in step 5 does not necessarily follow. Either situation makes his proof unsound. This unsoundness was made explicit during the cross-examination phase – especially when one considers Pervy’s final response.

My opponent defined Butch and Fido as both being of the species Canis Lupus Familiaris. He then asked if it was true that they were different entities with the same definition. He claimed that I “completely failed” to answer his question. This is not true. I may not have been explicit, but I implicitly answered his question when I said, “In one sense, Fido and Butch have identical definitions.” What my opponent did not like was that I went on to illustrate an ambiguity with his conception of “identical definitions.” In one sense, Butch and Fido have identical definitions, but only in a limited sense. This limited sense is that they are both of the species Canis Lupus Familiaris. Yet, both dogs may have significantly different properties. I defined Fido as a female poodle and Butch as a male lab. Pervy claims this changes the definition. Yet, female poodles and male labs are both Canis Lupus Familiaris! So, in what sense did I change the definition? At best my opponent is equivocating on what he means by “identical definitions.” Within the species of Canis Lupus Familiaris there are key distinctions. In the cross-examination, I demonstrated how false conclusions could be drawn when these distinctions are not considered – like the conclusion that Butch could have puppies even though he was male. This is why step 5 in my opponent’s argument is wrong. Step 5 necessarily follows if and only if the two entities are identical in every way. Yet, if both entities are identical in every way then step 6 is false because they are the same entity. If they are not the same entity, then they are not identically defined in every way, and step 5 loses its necessity causing the proof to fail.

All one needs to do is study the cross-examination in this debate to see the failure of my opponent’s argument. Either the two entities are the same (i.e., step 6 is false), or step 5 is not valid. Pervy agreed my proof was valid, and the argument he presented against the soundness of my proof has failed - leaving us with the conclusion: The God of Christianity exists. Q.E.D.

[Dean Anderson]

My opponent's argument is as follows:

1) If it is possible for something to exist, then there exists a possible world in which it exists.

2) The Christian God is defined as an NE (Necessary Entity) - i.e. he must exist in all possible worlds because it isn't possible for a world to exist without him.

3) Therefore; if the Christian God can possibly exist then he exists in a possible world, and (by definition) if he exists in any possible world then he exists in all possible worlds - including our actual world.

4) Therefore; unless it is logically impossible for him to exist, he exists.

There are many reasons why this argument isn't sound proof of the existence of the Christian God, despite the logic being formally valid. Unfortunately, the constrained format and strict rules of this debate meant that I was only able to show one of them.

The reason I showed was as follows:

1) By my opponent's logic, any NE must exist in all possible worlds including our actual world unless its existence is logically impossible.

2) We can postulate an infinite number of distinct NEs.

3) Therefore, if it is possible for such a thing as an NE to exist, then an infinite number of them must exist.

4) This leads to paradox, since we can define multiple NEs each as the only NE in existence - which is implicit in the definition of the monotheistic Christian God. All these NEs must exist, so they can't all be the only one in existence.

5) Therefore, it must be impossible for an NE to exist - since the alternative leads to paradox.

My opponent never addressed this general argument, and it remains as a stake through the heart of his proof.

Instead, he spent the entire debate nitpicking about the specific example of another NE that I gave.

He asserted that if my entity has the same definition as his, then it must literally be the same entity, although he gives absolutely no support for his bizarre assertion that it isn't possible for there to be more than one instance of any defined type of entity.

However, this quibbling over the definition of my example entity has no bearing on the more general case that we can define as many other NEs as we like, and thereby cause a paradox.

The only defence my opponent had against the paradox was to somehow prove that every NE except his own (even ones that are identical except for a minor detail, for example it takes it 8 days to create a world, not 7) are logically incoherent and cannot possibly exist, yet conversely his is logically coherent and can exist.

He has singularly failed to do this; so we are left with the only alternative:

If NEs can exist, we have a paradox. Therefore NEs can't exist. Therefore the Christian God (who is defined as an NE) can't exist.

Thank you to all involved in this debate.

[KnightWhoSaysNi]

The formal debate is now complete. We would like to thank Brian Bosse and Pervy for their participation. Discussion can be continued in the peanut gallery.

- KWSN, FD Moderator