Judeo-Christians understand God as a being that is perfect in knowledge (Ps. 147:5), power (Job 42:2), presence (Ps. 139), acts (Ps. 18:30) and has none greater (Heb. 6:13) nor equal (Ps. 40:6).
Following Anselm’s “credimus te esse aliquid quo nihil maius cogitari possit“¹, God is understood to be a Being that exhibits maximal perfection. God is, borrowing Alvin Plantinga’s words, a being “having an unsurpassable degree of greatness—that is, having a degree of greatness such that it’s not possible that there exist a being having more.” (Plantinga 2002: 102 emp. removed)
God is thus understood to be a being having maximal excellence with respect to power (omnipotence), knowledge (omniscience), presence (omnipresence), and is morally perfect (this is why, for example, God cannot lie or be unrighteous).
From S5 modal logic the existence of such a being(God) is either impossible or necessary. The concept of contingent existence of God is a contradictory idea since (i) necessarily, “a being is maximally great only if it has maximal excellence in every world” and (ii) necessarily, “a being has maximal excellence in every world only if it has omniscience, omnipotence, and moral perfection in every world.” (2002: 111)
Thus either the existence of God is impossible or necessary. The existence of God is not impossible. Therefore it is necessary. Therefore God, as understood by Judeo-Christians, exists.
Is this a persuasive case for existence of such a Being? I think it is not persuasive. Nevertheless it does show that Judeo-Christians’ understanding of God is rationally acceptable. Theists do have warrant in believing in a being with unsurpassed degree of greatness (God).
_____________________
¹ Anselmus Cantuariensis Prologion: Trans. [W]e believe that You[God] are a being than which nothing greater can be conceived.
Plantinga, Alvin (2002) God, Freedom & Evil. First published by Harper and Row., 1974. Reprinted 2002.
“Thus either the existence of God is impossible or necessary. The existence of God is not impossible. Therefore it is necessary. Therefore God, as understood by Judeo-Christians, exists.”
I find this statement stunningly naive. There may well be a Creator God, but it is quite a leap to assume that this Creator MUST be the Judeo-Christian god, who, by his own statements in the Old Testament, had a very faulty understanding of modern science and cosmology.
The Judeo-Christian god is the invention of ancient middle-eastern nomads as their best explanation for the mysterious, dangerous world in which they found themselves. Modern science and astronomy has increased our understanding of our universe to the point that this ancient explanation of our environment and universe is no longer needed.
Let’s honor the Judeo-Christian belief system for its contributions to human development, but it is time to move on, folks.
There’s a problem with applicability of the axiom in S5 that entails that if x is possibly necessary then x is necessary.
Let U be the set of all things, necessary, impossible and merely possible. (e.g U contains the Law of Non-contradiction, a square circle and an Everton victory at West Ham tomorrow). “Merely possible” can be taken to be possible and not necessary.
Pick one item at random from U, “X”. As X is chosen at random from a set of necessary, impossible and merely possible things it is possible that X is necessary. It is also possible that X is impossible and possible that X is merely possible.
From S5, as X is possibly necessary then X is necessary. It is, though, possible that X is merely possible: possible and not necessary. If this is the case then X is necessary, possible, and not necessary: a clear contradiction.
Your argument is false.
You have confused epistemic possibility with metaphysical possibility. It is only epistemically possible that “X” fits in one of those three categories, but it is only one of those metaphysically speaking. The S5 Axiom focuses exclusively on metaphysical possibility.
In other words, the first premise states that God is metaphysically possibly necessary. Your attempted reductio-proof is “X is epistemically possibly one of these things.”
That’s just a category error.
Show me the categories of modality in S5. They aren’t there within the system, as your reply below shows. Without making the distinction the move from possibly neccessary to necessary can be made (S5). With the distinction “epistemologically possibly metaphysically necessary entails (whichever type) of necessary” is obvious bunk.
Once we alllow categories of modality the, of course, the issue disappears. But then we’re not using S5. Which was rather my point: there’s a problem with S5
This problem arises if you use it for both epistemic and metaphysical modality at the same time. That’s why I said there’s a problem with the applicabilty.. If you use S5 for epistemic and metaphysical modalities at the same time you get silly results (as I showed).So you shouldn’t use it for arguments involving both epistemic and metaphysical modalities. Argumrnts like, say, the Modal Ontological Argument.
Show you which categories? Epistemic possibility versus metaphysical possibility? Modal logic only handles metaphysical modality, and has nothing to do with epistemology.
That is why your argument is faulty. You say Epistemically possibly [Insert modal status here], when in reality, the modal status of the thing never changes, and what ought to be said is Metaphysically possibly [insert modal status here]. You already conceded that.
As can be seen, you are acting dishonestly, as the argument, as anyone can see, does not use “epistemic modalities” at all.
Your criticism is entirely wrong.
“The existence of God is not impossible”.
In the sense we seem to be taking of “epistemic possibility”, I take that to be an epistemic possibility.
“As can be seen, you are acting dishonestly”
That’s rather offensive. I would say “uncharitable” but it’s a little beyond that. It’s unpleasent, nasty, not conducive to any sort of discussion. Mean spirited trolling that, even though it’s the internet, is rather saddening.
But you are being dishonest, and I have explained why:
This argument, as I have shown above, and as you have acknowledged, has nothing to do with epistemic possibility. Bringing up such a concern as though it is worthy of notice is not an honest tactic, at least if you know that it is irrelevant.
“(A)s I have shown”, no you haven’t.
“(A)s you have acknowledged”, no I haven’t.
“This argument … has nothing to do with epistemic possibility”, yes it does.
I have shown that this has nothing to do with epistemic modality: the S5 axiom is about metaphysical modality, period. Thus, I have proven this.
If you have not acknowledged this, it’s a shame that I have misunderstood you this whole time, and I apologize profusely.
Regardless, you are wrong, because epistemic modality has nothing to do with S5, and this is what refutes your argument: that you apply what is irrelevant to knock it down.
How does S5 entails that if x is possibly necessary then x is necessary? 🙂
Interesting question.
Putting it crudely, in modal logic, the S5 Axiom says that the last modal operator in a series of modal operators describing some proposition is the one we will use. In other words, “Possibly necessarily p” and “Necessarily possibly necessarily p” are the same as “Necessarily p,” because the final modal operator is “necessarily”; the previous operators describe the modality of the following symbol. (See here for a better description: http://plato.stanford.edu/entries/logic-modal/#ModLog)
But that’s using only metaphysical definitions of possibility and necessity, not epistemic definitions.
We have ◊□A→A given (B) A→□◊A. But what you claim is ◊□A→□A which I do not see justification for it. Let me know your thoughts 🙂
Yeah, I find it puzzling.(Although I don’t claim “◊□A→□A”, I claim “S5 claims ◊□A→□A”) Unless □◊A→◊A entails ◊□A→□A (and it’s beyond me to prove it) then there are a number of systems S5 (the “S5” in this: http://amzn.to/1HbnhS5 has it).
But then, if S5 doesn’t licence the inference then another system (call it “PLS5”) does and it seems to be the one we’re actually talking about. It’s implicit in Plantiga’s modal ontological argument, explicit in your fellow bloggers exposition of Plantiga’s argument here: http://www.christianapologeticsalliance.com/2015/04/19/plantingas-modal-ontological-argument-explained-by-sean-choi/
Sean also calls it “S5”:
“(S5) If []p, then []p (English: if it is possibly necessary that p, then it is necessary that p).”
Isn’t it also implicit in your argument above? (“The existence of God is not impossible. Therefore it is necessary”).
No it is not implicit in my argument because It not S5 but the law of excluded middle. It is in this form:
1. Either God existence is not possible or necessary.
2 It is not not possible
3. Therefore it is necessary(1&2)
S5 holds ◊□A→A given (B) A→□◊A.
I do not know whether ◊□A→□A could be derived from S5. Let me know your thoughts 🙂
I take it you hold
1. □G→G
and you have
2. □¬G or □G (“Either God existence is not possible or
necessary”)
These two would entail
3. ◊□G→□G
if there was no interpretation that would make 1, 2 and the negation of 3 true.
The negation of 3 is:
3’. ◊□G & ¬□G
So we need to know if there is an interpretation that will
make the following true:
4. (□G→G) & (□¬G or □G) & ◊□G & ¬□G; alternatively:
4’. ((□G→G) & □¬G & ◊□G & ¬□G) or
((□G→G) & □G & ◊□G & ¬□G)
The second element in the disjunction, ((□G→G) & □G &
◊□G & ¬□G), is clearly contradictory.
It has both “□G” and “¬□G”.
From the first consider the element “◊□G”. This means:
5. there must be at least one possible world (say “w1”) with □G.
6. As □¬G, w1 also has ¬G.
7. From 5 and 1 w1 has G
8. From 6 and 7 w1 has ¬G and G;
there is no interpretation that makes 1,2 and the negation of ◊□G→□G true and, so, 1 and 2 entail ◊□G→□G.
(Your question gives me an idea of how we might show that S5 entails ◊□G→□G. If we can show how S5 entails □¬G or □G we can take that with □G→G and prove ◊□G→□G. I have difficulty with it because of being not-very-good at natural deductions from axioms (the above took me ages). I can (if I get the book to remind me how!) prove things with logic trees but that exposition of S5 defines it by means of possible world semantics and I can’t relate that back to axioms!
It does seem though to be accepted that S5 entails ◊□G→□G. Take the Stanford Encyclopedia of Philosophy on S5:
“(I)n S5, strings containing both boxes and diamonds
are equivalent to the last operator in the string. So, for example, saying that it is possible that A is necessary is the same as saying that A is necessary.”
Pretty well everyone will agree that “(t)he existence of God is not impossible” but they’re usually talking a different category of modality. The atheist would agree on the basis of “well I firmly believe that God does not exist but I could be wrong”. The agnostic doesn’t even think he knows: so he’s open to the possibility either way. The faithful obviously believes that God is and is necessary but may accept that there is some possibility
that she is wrong.
So, malgré Paradox, God is possibly necessary, possibly impossible and possibly merely possible (it’s possible you and Anselm have got the modality of God wrong) in much the same way as my random entity X is.
I do hold 1. □G→G but not
2. □¬G or □G (which is not “Either God existence is not possible or necessary(¬◊G V □G)” but “necessary God doesn’t exist or necessary God does exist”)
I hold 2′. ¬◊G V □G
Thus:
1. □G→G
2′. ¬◊G V □G
3”. ¬¬◊G
4. ∴□G
5. ∴ G
Even if we grant 2., which I do not hold, I do not see how it would have entail 3. Could you be kind to help me see the entailment?
¬◊G is the same as □¬G
The first says “G is in no possible world”. In each possible world there must be G or¬G, so in those possible worlds were G isn’t (i.e. all of them) there must be ¬G. The second says “there is ¬G in all possible worlds”.
I am not sure they are the same. See we could grant:
1. It is not the case that there is a possible world w where it is the case that G.
2. Necessary it is not the case there is a possible world w where it is the case that G(from 1 & ¬◊P→□¬◊P )
But 2 is □¬◊G and not □¬G. Let me know your thoughts.
Syntactically, that is to say with regards
to the rules of the system, ¬◊G is the same as □¬G. From the Stanford article on modal logic:
“The operator ◊ (for ‘possibly’) can be defined from □ by letting ◊A = ~□~A”
There are four ways of having the box (□X, ¬□X, □¬X ,¬□¬X) and four ways of having the diamond (◊X, ¬◊X, ◊¬X ,¬ ◊¬X). Each “box” way can be expressed in an equivalent “diamond” way:
□X = ¬◊¬X
¬□X = ◊¬X
□¬X = ¬◊X
¬□¬X = ◊X
Semantically, which may persuade you that the rules are sensible, consider that there are three mutually exclusive and exhaustive arrangements of possible worlds with respect to X:
1. X is in each possible world. (e.g. {(W0,X)
and (W1,X)})
2. X is in no possible world (e.g. {(W0,¬X)
and (W1,¬X)})
3. X is in at least one possible world and absent from at least one possible world (e.g. {(W0,X) and (W1,¬X)})
We can list out for each of these arrangements the expressions that hold true in the arrangement. For box:
1. □X, ¬□¬X;
2. ¬□X, □¬X;
3. ¬□X, ¬□¬X.
Notice that the two expressions in bold hold true in more than one arrangement but hold true together in only one. ¬□X &¬□¬X uniquely identifies arrangement 3. □X only holds true in arrangement 1 whilst ¬□X only holds true in arrangement 2 and, so, they uniquely identify arrangements 1 and 2 respectively:
1. Uniquely identified by □X
2. Uniquely identified by □¬X
3. Uniquely identified by (¬□X & ¬□¬X)
We can do the same exercise with diamond. The following are true in the various arrangements:
1. ¬◊¬X and ◊X;
2. ◊¬X and ¬◊X
3. ◊¬X and ◊X
and the arrangements are uniquely identified by:
1. ¬◊¬X
2. ¬◊X
3. (◊¬X & ◊X)
Each expression with box has a corresponding expression with diamond that is true in the same circumstances and uniquely identifies (either on its own or in combination) an arrangement
and
Each expression with diamond has a corresponding expression with box that is true in the same circumstances and uniquely identifies (either on its own or in combination) an arrangement
So the syntactic equivalences sketched out above make sense semantically.
It is not true that Anselm’s ontological arguments has being debunked. Strawman versions of them, perhaps. It is falsely assumed that the ontological arguments were long debunked in popular circles. In academia it is very alive, most in philosophical,not apologetical, circles. See their status in recent collection of essays: Miroslaw Szatkowski(ed.) Ontological Proofs Today, Ontos, 2012, 513pp.
None defined perfection as having property of existence. But some forms of ontological argument hold that necessary existence, not simply existence, is a perfection, else being equal.
The concept of perfect or greatest conceivable being is not analogous to perfect or greatest conceivable unicorn. Why? Because the greatest conceivable unicorn deals only with subcategory of unicorns while the greatest conceivable being deals with the who category of being(example latter one is about cars while former is about Hondai)
Another problem is that the concept of greatest conceivable unicorn is not possible. What is a unicorn? It is a being with one horn. But a being of one horn is a being composed of quantitative attributes, unlike God composed of qualitative attributes. If unicorn is composed of quantitative attributes, then it is a contingent being thus it cannot follow that it necessarily exist.
There are more counter objections that could be leveled to unicorns but we could begin with these two. Let me know your thoughts. 🙂
“Our primary concern is to promote the gracious, rational defense of the central claims of Christianity and the critique of opposing systems of thought. The CAA community is a diverse one of many denominations.”
What does the Holy Spirit have to do with we mortal’s “primary concern?” What does He have to do with “rational defense?” What has He to do with denominations? John 14:6, John 3:16-17, John 3:3, John 5:24, Romans 10:8-13. Where does one “find” a denomination in that? What is mortal man doing when he, himself, “finds?” What is the purpose of “finding” in the first place? It is all of grace.
The Holy Spirit has no “primary concern,” no “rational defense,” did not introduce and does not support denominations, nor is He involved in “opposing systems of thought.” All of that is secular “discussion,” having no weight in the realm of God. None. The Holy Spirit is revelatory. He does not reveal to Bill that water baptism is obligatory for salvation, then to Joe that it is not. Sheer, mental, intellectual mind-boggling nonsense.
God is Creator. Perfection is God. “Debating” Him or “explaining” Him is the equivalent of babble. He manifested Himself as Jesus. He occupies each Believer as the Holy Spirit. The Holy Spirit is the only Spiritual mentor, revelator, and contact, gifted to those who believe. We ignore Him when we seek to “explain” the Spiritual. God is.