The Question of Being part 2: Against ICR

I have done a previous post on the impossibility of ICR (Infinite Causal Regression). There are aspects of the subject that I didn't deal with in that so I am hoping to deal with them here. Stanford Encyclopedia of Philosophy has an excellent article on the Cosmological Argument. I am going to deal with issues raised in that article, issues pertaining to contingency and ICR. In counter to the argument of a necessary first cause Russell argues that the universe just is and requires no explanation. In the last post I argued that this is unsatisfying, Russell argued that we derive our concept of cause from observation, thus since we don't observe the final cause, or the cause of the universe (see objection 1 in link above). The obvious answer is that we don't have to observe ever aspect to extrapolate from what we do observe, that's the whole principle of inductive reasoning in scinece. I would argue that we do observe the contingency of the universe because it's all around at every moment, while we can't know the finality of it's contingency, we can see plainly that the only we have of the mode of being of the universe is contingency, which is in everything we see.

Rusell argued that the move from the parts to the whole, from contingent parts to wholly contingent universe, is the "fallacy of composition."

Russell correctly notes that arguments of the part-whole type can commit the Fallacy of Composition. For example, the argument that since all the bricks in the wall are small, the wall is small, is fallacious. Yet it is an informal fallacy of content, not a formal fallacy. Sometimes the totality has the same quality as the parts because of the nature of the parts invoked—the wall is brick because it is built of bricks. The universe's contingency, theists argue, resembles the second case. If all the contingent things in the universe, including matter and energy, ceased to exist simultaneously, the universe itself, as the totality of these things, would cease to exist. But if the universe can cease to exist, it is contingent and requires an explanation for its existence (Reichenbach, chap. 5).(from Stanford article above).

The assertion that the exact duplication of the building material in the overall wall is a red herring. The argument that the size of the bricks is the size of the all is not really analogous to the issue of contingency. The analogy would between the actual state of the material, not it's size divided into increments, but the material itself. A wall made out of all bricks is what we call "a brick wall" that is a wall made wholly of the materiel "brick." If a wall is made up of contingencies then it's a contingent wall.

Some reply that this argument for the contingency of the universe still is fallacious, for even if every contingent being were to fail to exist in some possible world, it may be the case that there is no possible world that lacks a contingent being. That is, though no being would exist in every possible world, every world would possess at least one contingent being. Rowe gives the example of a horse race. “We know that although no horse in a given horse race necessarily will be the winner, it is, nevertheless, necessary that some horse in the race will be the winner” (1975, 164).

Atheist answer:

Rowe's example, however, fails, for it is possible that all the horses break a leg and none finishes the race. That is, the necessity that some horse will win follows only if there is some reason to think that some horse must finish the race.

That is not a real answer because it doesn't prove that the universe is necessary it proves merely that there might be no universe at all. Since that means the universe itself could have failed to exist that makes it contingent (standard definition: that which could cease or fail to exist). The author of the article argues as a back up that we must have a reason to believe that something is necessary: "Similarly, his objection to the universe's contingency will hold only if there is some reason to think that the existence of something is necessary. " That's just the problem, we have no reason to assume the universe is necessary, we have an obvious reason to assume that being is necessary, since something can't come from nothing, there's ample reason to assume an eternal first cause. Being eternal it could not could not cease or fail, the logic of an eternal first cause makes it necessary a prori (ie Necessary: that which cannot cease of fail to exist). If something is truly eternal it could not cease or fail to exist. Consider the lunacy in saying that some thing has existed for ever with no cause but on June fourth, 1955 it cased to be. Why June 4, 1955, why not eons ago? It had infinite chances to cease, why would it do so on that one day and not another much sooner? Moreover, the concept of eternal being is limitless, unnumbered and infinite. To then have it cease would be to put a number to the infinite which is impossible. All of which is reason enough to assume eternal necessary being.

The article at that point goes off into what I think is a tangent arguing for the possible existence of a world with no contingent beings.

One argument given in defense of this thesis is that the existence of one contingent being may be necessary for the nonexistence of some other contingent being. But though the fact that something's existence is necessary for the existence of something else holds for certain properties (for example, the existence of children is necessary for someone to be a parent), it is doubtful that something's existence is necessary for something else's nonexistence per se, which is what is needed to support the argument that denies the contingency of the universe. Hence, given the contingency of everything in the universe, it remains that there is a possible world without any contingent beings.

I think he missed the point. The point is not that there must be a contingent being of some kind in every possible world, but that the state of contingency is mandated for all possible worlds (they are all dependent upon God) since they could all fail to exist. The author of the article, Bruce Reichenbach, argues in terms of individual beings. The point is that the whole is demonstrated as contingent because it is made up of contingent parts. This is not the fallacy of composition becuase if the parts are all the same the over all structure is the same as the parts. We can get off track by being literalistic and saying "the small bricks make a small wall" but they make a wall made of brick.

The fallacy of composition is when one reasons from the parts to the whole. In this case my argument (P2a) reasons from the fact that the universe is a collection of contingent things to the conclusion that the universe is contingent. But this is not my only argument for the contingency of the universe, be that as it may, it is not the fallacy of composition. The fallacy doesn't happen just any time one reasons in this way. It is not fallacious to argue form the parts to the whole if the parts are all alike.

Robert Koons on Leadership University

(12/12/03)

Phl 327
Contemporary Christian Philosophy
Fall 2000, University of Texas

The argument commits the fallacy of composition: from the fact that each part of the cosmos is caused, it fallaciously draws the conclusion that the whole cosmos is caused. Response: this is a misstatement of the argument. The argument assumes that all wholly contingent situations are caused. We can prove that the cosmos is wholly contingent, so it must have a cause.

The Nizkor Project

vistied 12/13/03

The second type of fallacy of Composition is committed when it is concluded that what is true of the parts of a whole must be true of the whole without there being adequate justification for the claim. More formally, the line of "reasoning" would be as follows:
The parts of the whole X have characteristics A, B, C, etc. Therefore the whole X must have characteristics A, B, C. That this sort of reasoning is fallacious because it cannot be inferred that simply because the parts of a complex whole have (or lack) certain properties that the whole that they are parts of has those properties. This is especially clear in math: The numbers 1 and 3 are both odd. 1 and 3 are parts of 4. Therefore, the number 4 is odd. It must be noted that reasoning from the properties of the parts to the properties of the whole is not always fallacious. If there is justification for the inference from parts to whole, then the reasoning is not fallacious. For example, if every part of the human body is made of matter, then it would not be an error in reasoning to conclude that the whole human body is made of matter. Similiarly, if every part of a structure is made of brick, there is no fallacy comitted when one concludes that the whole structure is made of brick.

Thomas Rauchenstein.Copyright 1997, (link is no good)

The argument (Cosmological) does not commit the fallacy of composition. Just as every part of a puzzle is red, so must the whole be red; if every part of a structure consists of stone, so must the whole consist of stone. Likewise, if every possible being is in potentiality, so the whole of all possible beings is in potentiality, and thus, needs to be actualized (caused). The very nature of the parts demand that the whole be caused as well.

If all the horses break a leg and no one finishes that is analogs to failure to exist not a defeat for the example. There is no reason to limit the example to just individual beings. ICR is made up of a string of contingent universes. For example where ICR is conveyed by the oscillating universe, big bang => big crunch, black whole, pops back out into another big bang, and another big crunch, another black and another popping out, on and on forever with no beginning and no end; the whole is made up of contingent parts. Take out the contingent universes, and you have no eternal string or series of infinite regression. The term "regression" refers to tracing the sting of c/e back infinitely. If the c/e is gone there's no string. Thus there is a possibility the string could have ceased at any point. That means the whole is contingent becuase it's made up of all contingent parts. Koons reflects this answer in his mermological argument:

To avoid any hint of the Fallacy of Composition and to avoid these complications, Koons (198–99) formulates the argument for the contingency of the universe as a mereological argument. If something is contingent, it contains a contingent part. The whole and part overlap, and by virtue of overlapping, have a common part. Since the part in virtue of which they overlap is wholly contingent, the whole likewise must be contingent.


Mememological Aggregation Axiom shows us that wholly congingent sitautions are wholly contingent


Dr. Robert Koons UT (Logician)

1) Every wholly contingent fact has a cause. (facts that are partly or wholly necessary need not)

2) Applying aggregation axiom, anything of a kin dk = such a thing as arrgigate of all kinds.

3) Aggreagates can't exist unless all parts exist (which means necessary aggregate must have Necessary parts, contingent aggregate must have contingent parts. The result is necessary and contingnet facts which means contingent aggregate as a whole). 4) Absolutely necessary facts cannot be caused, therefore, wholly contingent facts (those whith only contingent parts) can be caused.

5) Causal principle can be thought of as empirically supported (effects not limited to a particular region of space/time in the case of physical laws for example, :. we have reason to suspect that all contingent facts have causes).

For an explaination of the fact token/type situation I turn to Dr.Koons himself: www.leaderu.com/offices/k.../lec7.html

Phl 356
Western Theism
Spring '98, University of Texas

LECTURE #7: Contemporary Versions: My Argument

Facts are the kinds of things that make declarative sentences, like "Caesar has died", true. Facts enter into cause and effect relations with other facts. We can distinguish between "types" and "tokens", to use terms introduced into philosophy by C. S. Peirce. Each individual penny is a token, and the property or kind of penny-hood is a type. Each penny is a token of one and the same type, which is multiply realized in different places at different times. My argument concerns fact-tokens, not fact-types. For example, we can use the phrases "that Caesar died", "Caesar's dying" or "Caesar's death" to refer either to a fact-token, the particular, actual occurrence that constituted the ending of Caesar's life, or to a fact-type, the kind of occurence in which the individual Caesar dies. Thus, the token of Caesar's death includes the actual thrust of Brutus's blade, and that very token would not have existed had Caesar died in some other way, of old age, for example. In contrast, the type, Caesar's dying, could have been realized in many different ways, including the actual assassination and the non-actual dying in old age. My argument focusses on the actual token I call the cosmos. This token includes all of the wholly contingent fact-tokens in the world as parts -- had the slightest detail been different anywhere at any time, the particular token I am calling 'the cosmos'would not have existed. It would instead be replaced by a different token. The fact-type, the existing of a universe, could have been realized by many different possible tokens.

For an explaination of Meremology I again turn to Dr. Koons:

"My argument focusses on the particular token that actually realized this type.If we assume that every fact has a cause, then there could exist no uncaused fact. Instead, I assume that every wholly contingent fact has a cause. Facts that are partly or wholly necessary need not, and indeed cannot, be caused. Since facts are concrete, actual things, we can talk meaningfully about the parts of a fact. Consequently, I use the principles of the mathematical theory of mereology, the theory of the part-whole relation. The most important principle of mereology is the aggregation axiom. This axiom states that, if there are any things of kind K, then there is such a thing as the aggregate of all the K's. For example, there is such a thing as water, so we can talk meaningfully about the aggregate or "mereological sum" of all the world's water. I assume that an aggregate cannot exist unless all of its parts exist. This means that a necessary aggregate must have only necessary parts, since if an aggregate has a contingent part, then that part might not exist, which would mean that the aggregate would not exist either. Aggregates are not like bodies or institutions, which can go on existing without the same parts. However, a contingent aggregate can have necessary parts. If we glue together some contingent and necessary facts, the resulting aggregate is contingent as a whole. I assume that an absolutely necessary fact cannot be caused. If a fact is caused, then all of its parts are caused. So, any fact that contains a necessary fact cannot be caused.


Therefore, it is only wholly contingent facts that can be caused. A wholly contingent fact is a fact that has only contingent parts.I argue that the causal principle should be thought of as empirically supported. We find that a wide variety of facts are caused. This includes conditions both small and large (from atomic physics to astronomy and cosmology), both recent and ancient, both transient and long-lasting. We even discover that many everlasting conditions have causes. For example, the fact that the physical world is approximately Newtonian is caused by certain features of general relativity. Similarly, the ideal gas laws are caused by the underlying dynamics of the gas molecules, and Brownian motion is caused by atomic collisions. In these cases, the effects are not limited to a particular region of space or time. Thus, we have good empirical reason to believe that every fact that can be caused, that is, every wholly contingent fact, has a cause.

Cyclial Universe

The concept that the universe is eternallay ocillating between big bangs and big crunches. When the matter from the explosion of a Big Bang reaches a certain point the gravitational pull draws it back, it callapses into superdense black hole and pops back out again. This notion does not require an initial cause, the cyclical universe is just always there always going through its cycles.

a) Universe continuing to expand

Evidence from three recent studies reveals that the final fate of the universe will be to drift apart and cease all useful functions capable of supporting life due to missing mass, which can't produce gravitational pull to bring it all back together and start again, and heat death in which case energy is useless for work. Several major studies show this to be the case.

[New Scientist Magazine, archive 11, April 98, archive; originally Oct. 96] you should be able to click here, but here's the url just in case) [http://www.newscientist.com/ns/980411/features1.html

"ON THE night of 5 March last year, the huge telescope of the Cerro Tololo Inter-American Observatory in Chile intercepted a message from deepest space. Transmitted a billion years before the Earth was born, its contents have proved to be of truly cosmic significance. The message was barely readable after its journey halfway across the Universe, and an international team of experts laboured for months to decode it. In January, Saul Perlmutter of the Lawrence Berkeley Laboratory in California and his colleagues revealed to the world what they believe to be its gist: "The Universe will never end." A month later, a team led by Brian Schmidt of the Mount Stromlo and Siding Spring Observatories near Canberra in Australia published the decoded contents of more of these cosmic missives, which arrive as bursts of light from supernova explosions in far-flung galaxies. The message was the same. Now Chris Kochanek and his colleagues at the Harvard-Smithsonian Center for Astrophysics in Cambridge, Massachusetts, are about to publish more evidence, this time from light that has been bent and sculpted by the gravity of unseen galaxies."

*

Omega force = Continued expansion forever (no Big Cruch)

"These three sets of cosmic missives all suggest that instead of collapsing in on itself in a big crunch, our Universe will go on expanding forever. And that's not all. They also hint that the expanding Universe is in the grip of a mysterious force that is fighting against gravity--a force that pervades the entire cosmos and springs literally from nothing."(Ibid.)

[mysterious force = "omega" ie the equation of gravitational force vs. mass needed to close the universe; omega must = 1 to close]

*

Missing Mass.

[New Scientist article April 1999] "If it [the universe] contains enough matter, gravity will eventually slow its expansion, stop it, and reverse it--producing a cataclysmic big crunch billions of years hence. But if there is too little matter--or if there is an extra source of "oomph" at work in the cosmos--then the Universe will expand forever.... Cosmologists call the ratio of the actual density of matter in our Universe to this critical density 'Omega.' And whole armies of astronomers have spent decades trying to work out if Omega is less than, more than or equal to 1.,... "Studies of the gravitational effects of clusters of galaxies have revealed that there must be at least 10 times as much mass tied up in invisible "dark matter" in the Universe as there is in the familiar form of luminous stars and gas. Yet even when all this dark matter is thrown into the equation, it still doesn't make the theorists happy. Despite searching every cosmic nook and cranny, astronomers have never found anything like the amount needed to make Omega equal to 1."

"So the take-home message looks the same as that now emerging from the supernova and quasar surveys: the Universe is going to expand forever, and it may yet prove to be flat. Certainly the idea of the big crunch seems to have gone for good, but the exact values of Lambda and Omega, and the fate of the cosmologists' theories, are still up for grabs. These values may finally be nailed early in the next century, with the launch of NASA's Microwave Anisotropy Probe (MAP) and the European Space Agency's PLANCK missions. These will use the heat left over from the big bang to try yet another way of measuring Omega and Lambda, which may lay the question to rest for good ("Genesis to Exodus", New Scientist," 19 October 1996, p 30).

Flat Universe means no contraction

Andre Linde, Scientific American, Sept 1997

"A second trouble spot is the flatness of space. General relativity suggests that space may be very curved, with a typical radius on the order of the Planck length, or 10^-33 centimeter. We see however, that our universe is just about flat on a scale of 10^28 centimeters, the radius of the observable part of the universe. This result of our observation differs from theoretical expectations by more than 60 orders of magnitude." [Messuer is a leading physicist and one of the first to invent the inflationary universe theory]

ABC News.com: Scientists: Universe is Flat another link Physics. ucsb.edu

Wayne Hu of the Institute for Advanced Studies, School of Natural Sciences in New Jersey said "temperature maps of the CMB form a snapshot image of the Universe when it was extremely young." "The...result supports a flat universe, which means that the total mass and energy density of the universe is equal to the so-called critical density," Wu wrote. "A perfectly flat universe will remain at the critical density and keep on expanding forever, because there is not enough matter to make it recollapse in a 'big crunch.'"

c) End of Universe reveals beginning--universe would have already ceased.

Energy of the universe is being expended, as it burns up,it becomes useless for work. The fate of the universe will be eventual death in ciy darkness as all of its suns burn out and their energy dissipates][New Scientist, April 1999, oct. 96

"But even if the Universe lives forever, its inhabitants will not be so lucky. A mere thousand billion years from now, all the stars will have used up their fuel and fizzled out. There will still be occasional flashes in the perpetual night: the death throes of stars so large that they have collapsed in on themselves to form black holes. Even these will eventually evaporate in a blast of radiation. For the next 10122 years, this Hawking radiation will be the only show in town. By then even the most massive black holes will evaporate, leaving the Universe with nothing to do for an unimaginable 10 to the power of 1026 years. Quantum theory then predicts that atoms of iron--the most stable of all elements--will undergo "tunnelling" and disappear into tiny black holes, which will themselves end in a final fizz of Hawking radiation. In the beginning there may have been light, but in the end, it seems, there will be nothing but darkness. ".[New Scientist April 1999]

Given infinite time and possibility all potentialities would have already come to fruition, the chain would have already been broken before our universe came into being. This just illustrates the impossibility of an infinite series of events. (being a series of events it would be "in time" so it's really redundant to say "an infinite series of events in time.") In other words, if this universe drifts apart because it lacks mass to produce omega, than the last universe would have too because energy and matter would be the same amount, just formulated differently (energy cannot be created or destroyed). The absurdity of the notion of an infinite series of big bang/crunches is driven home; how could there be an "infinite" series if one of the links in the chain can't make it? It can't "already be infinite" and then stop because infinite means no beginning and no end.

Note: If the Skeptic does not agree to this principle, that given infinite time every possibility comes to fruition than he can neither argue infinite chances nor multiple universes against the fine tuning argument.

d) Universe contains finite stock of order, connote be eternal (because it would have burned out by now)

*Scientific consensus:

Paul Davies, in his article, "Space-time Singularities and Cosmology," says,"If we extrapolate this prediction to its extreme,we reach a point when all distances in the universe have shrunk to zero. An initial cosmological singularity therefore forms a past temporal extremity to the universe. We cannot continue physical reasoning, or even the concept of space-time, through such an extremity. For this reason, most cosmologists think of the initial singularity as the beginning of the universe. On this view, the Big Bang represents the creation event; the creation not only of all the MATTER and ENERGY in the universe, but also of space-time itself."[ P. C. W.Davies, "Space-time Singularities in Cosmology," in The Study of Time III, ed. J. T. Fraser (Berlin: Springer Verlag, 1978), pp. 78-79.]

* Laws of Physics break down at singularity

The laws of physics break down at the singularity. 1st Thermo. would apply after the Big Bang, then the fixed amount of energy that is "put in" to the universe (as Davies puts it) would be finite (in quantity) and subject to 1st and 2nd Thermo.


* 1 LTD applies to matter also. Thirdly, the 1st Law of Thermo. applies to matter ALSO. If you argue that energy is eternal, you've got to argue that matter is eternal, which goes against all the empirical evidence we have for the Big Bang.

* 2 LTD Energy burn to heat death

Fourthly, if you opt for 1st Thermo. before the Big Bang, try being consistent and applying 2nd Thermo. as well. If the energy (AND matter) of the universe is eternal, it would have reached MAXIMUM heat death an INFINITE amount of time ago.

Theoretical physicist Paul Davies, in his book God and the New Physics, states:

"If the universe has a finite stock of order, and is changing irreversibly towards disorder - ultimately to thermodynamic equilibrium - two very deep inferences follow immediately. The first is that the universe will eventually die, wallowing, as it were, in its own entropy. This is known among physicists as the 'heat death' of the universe. The second is that the universe cannot have existed forever, otherwise it would have reached its equilibrium end state an infinite time ago. Conclusion: the universe did not always exist."

If you deny that the universe has a finite stock of order, you are essentially denying the 1st law of thermodynamics, as it requires a fixed finite amount of matter and energy. (check your Encyc. Britannica)

In your wider universe, does the 1st law of Thermodynamics apply WITHOUT the second? What reversed the entropy of this eternally existent universe? As we saw above, a universe containing eternal matter and energy would have reached maximum entropy an INFINITE amount of time ago. What organizing principle intervened 11-15 billion years ago and organized all that energy and matter that was no longer available for work? What or who (or Who) wound the universe up?

Fifthly, we observe that the universe is expanding uniformly in all directions. Had the universe existed for an infinite period of time, the density of matter would have become zero. (Koons) How do you explain the observable expansion of the universe? We measure the recession velocity of distant galaxies by using Cepheid variables, type Ia supernovas, and now Red Clumps as standard candles. And the microwave background radiation and redshift (Doppler effect that skews the red portion of the spectrum of starlight in proportion to the distance of the star) confirm this expansion also. Furthermore, within the very field equations of General Relativity, is embedded the fact of the expansion and deceleration of the universe. There are now 19 proofs of General Relativity in 12 isolated areas of Physics,making it the most exhaustively proven principle. Are you saying that General Relativity does not apply to our universe as a whole?!! It is accurate to better than a trillionth of a percent precision. Where is your scientific evidence for A) separate portions of the universe which General Relativity does not describe B) separate universes? If its not falsifiable, and there's no evidence for it, then its just not a threat to the standard BB model as it is not scientific.

Since the oscillating universe is the only workable mechanism for ICR it's really a theory in trouble. The other alternatives such quantum tunneling require that the particles cause themselves (soemthing form nothing) then travel in time into he past to continually cause themselves again and again. The other answer is string membranes which is still unproved as something that even exists.

The Modal Argument (part 1)

Charles Hartshorne 1897-2000
Modern Champion of the modal argument

I'm re-publishing this piece because I did a good job of explaining all about the argument, but I have more to say about. The background to the argument is complex and hard to summarize. This is a necessary first step to understanding the real issue which is "What does Tillcih do for the Modal Argument." That part 2 will come on Friday.

What follows is one of the most challenging subjects you will ever hear about. It is the best way to get a head ache, but I think it proves the existence of God. The problem is it requires a very specialized background to understand it. First you have to understand modal logic.

Modal Logic is so called because it turns upon the use of so called "modal operators." It's called "modal" because it is the logic of modes of being. "modes" as in what type of existence something exits in, weather it is dependent upon other things, weather it can cease or fail to exist and so forth. The modal operators are "necessity," "contingency" "impossibly," "possibility."

Necessity and contingency lie at the base of our modern understanding of cause and effect. They come from scholastic notions of logic, but the distinction between the notion our modern notions of c/e and the scholastic ones in the middle ages is not that great. The scholastic had more levels of cause, efficient cause, final cause and several others. But one could everything we have done in modern science using the scholastic ideas of c/e.

Necessity doesn't mean God has to exist. It doesn't mean God is necessary to the existence of the world (except in so far as if God exists then of course God is necessary to the world as creator--without God there would be no world). The modal argument does not begin with the assumption that God has to exist. It begins with the assumption that there is a valid distinction between necessity and contingency, which there must be.It proceeds along the lines of hypothetical consequence that obtain from different scenarios of God's existence. It concludes that is necessary. But by "necessary" it means not contingent, or not dependent upon something else for its' existence.

This is often misconstrued by atheists and taken to mean the argument proceeds from God's existence as an assumed first premise. This is not the case, the first premise is either/or. Either God's existence is necessary or it is impossible. This allows for the possibility that there is no God. So the argument does not begin by "defining God into existence."

Necessity means either non dependent or cannot cease or fail. By "fail" I mean there could not not be a God. That is the conclusion of the argument, not the premise.

Contingent means the opposite: that a thing is dependent upon a prior thing for existence, or that it could cease or fail to exist.

Impossible means logically impossible, something in the structure of the idea contradictions, such as square circles.

one of the sore spots that atheists get stuck on is the idea that God cannot be contingent. They will always leap to the conclusion that this is defining God into existence, because they don't understand the concept of God. God, by the nature of the concept, carriers certain parameters just as the existence of any human assumes humanity, or the existence of any tree assumes that the tree in question is a plant. To have to define that God is not contingent should not even come into it. The idea of God is that of eternal creator of all things. Thus God cannot cease to exits and cannot be dependent upon anything (or he wouldn't be the creator of all things). Atheists usually assume that all knowledge has to be empirical. they will argue this is defining God into existence. maybe God is contingent.

Maybe there is a begin like the one we talk about but he's not eternal or the creator of all things, but that means he's not the God we are talking about.



Hartshorne's version goes like this:

1) God can be analytically conceived without contradiction.
2) Therefore God is not impossible.
3) By definition God cannot be contingent.
4) Therefore God is either necessary or impossible.
5) God is not impossible (from 2) therefore, God is necessary.
6) Whatever is necessary by the force of Becker's modal theorem must necessarily exist.

Argument:my version

1) God can be analytically conceived, as eternal necessary being, without contradiction.

2) Therefore God is not impossible,(because no contradiction).

3) By definition God cannot be contingent (becasue God is eternal).

4) Therefore if God exists, God's existence is necessary, if God does not exist, it is because God is impossible.

5) God is not impossible (from 2) therefore, God is necessary.

6) Whatever is necessary by the force of Becker's modal theorum must necessarily exist.


A. The logic of the argument:

This argument is analytical, it proceeds from the basis in logic to argue that the concept of God is such that if we understood the meaning of the terms we would have to conclude that God must exist. Naturally that is a very controversial position. Many Christians and other theists reject the ontological argument on the grounds knowledge must be somewhat empirical. Nevertheless the argument has been used for a long time, and despite its many apparent deaths, it keeps returning in one form or another. Perhaps the best book on the subject is The Many Faced Argument by John Hick. Somehow the ontological argument just wont die. I feel that this is not so much because the argument itself is true as a proof, but because it gets at something deeper than proof, something to do with the way to think about God, and it strikes a deep cord in our consciousness, even though as a proof it may fail. For this reason alone it is important to know, if only to know the concept itself.

1) God can be analytically conceived without contradiction.
2) Therefore God is not impossible.
3) By definition God cannot be contingent.
4) Therefore God is either necessary or impossible.
5) God is not impossible (from 2) therefore, God is necessary.
6) Whatever is necessary by the force of Becker's modal theorem must necessarily exist.

(This is actually my re-statement of what Hartshorne is saying).

Hartshorne's actual modal logic looks like this:

The OA: an assessment:

by Ed Stoebenau

http://www.eskimo.net/~cwj2/atheism/onto.html Hartshorne's ontological argument is based on Anselm's second argument and claims that God's existence is logically necessary. Hartshorne's argument is given here, where "N(A)" means "it is logically necessary that A," "~A" means "it is not the case that A," "-->" is strict implication, "v" means "or," and "g" means "God exists":

g --> N(g)
N(g) v ~N(g)
~N(g) --> N(~N(g))
N(g) v N(~N(g))
N(~N(g)) --> N(~g)
N(g) v N(~g)
~N(~g)
N(g)
N(g) --> g
g



This argument is valid. Furthermore, given an Anselmian conception of God, premises one and five are sound. Premise two is just the law of the excluded middle, and premise three is a law of the modal logic S5. Premise nine is obviously sound, so this leaves premise seven as the only premise to question. Premise seven says that it is logically possible that God exists.



Yes, those funny lines, "g-->N(g)" are the argument, those are the formal symbols used in modal logic.

B. God's Possibility vs. Impossibility.

The argument turns on the distinction between necessity and contingency, and upon the distinction between mere possibility and the nature of necessary being as not mere possible. In other words, God is either necessary or impossible. If God exists than he is ontologically necessary, because he is logically necessary by definition. But if he does not exist than it is ontologically impossible that he exists, or could come to exist. This is because God cannot be contingent, by definition. A contingency is just not God. So if God is possible, he can't be "merely possible" and thus is not impossible, which means he must be necessary.

God is conceivable in analytic terms without contradiction:
The universe without God is not conceivable in analytical terms; it is dependent upon principles which are themselves contingent. Nothing can come from a possibility of total nothingness; the existence of singularities and density of matter depend upon empirical observations and extrapolation form it. By definition these things are not analytical and do depend upon causes higher up the chain than their being (note that the skeptic at this point probably denies the validity of analytic proofs but to reverse the argument must accept such proof).

Since the concept is coherent and not contradictory and is derived from analytic terms, to reverse the argument the atheist must show that God is impossible since the burden of proof is now on the one arguing that a contingent state of affairs could produce a universe in which being has to be.

D. Answering Objections:

1) The argument can be reversed

Atheists have tried to reverse the argument merely by saying:

1) either God exists or he doesn't
2) God is either necessary or impossible. Necessary if he exists, impossible if he does not
3) God is impossible
4) Therefore God does not exist.

But of course this is merely stipulation. They assume that what the argument is doing is just stipulating everything that has been said about God, but on the "Modes of Being" page I show that each of these modalities of existence are logical deductions.Either a thing exists or it does not. One can equivocate about the meaning the term "existence," but here I clearly mean concrete actual existence in the "real" world. If a thing does not exist it is either that it could, but just doesn't happen to exist, or that it cannot exist because it is a conceptual contradiction, such as square circles, or round triangles and so on. Therefore, if it does exist, it is either that it exists contingently or that it is not contingent but exists necessarily (that is it could not fail to exist without contradiction). These are the four most basic modes of being and cannot be denied. They could be subdivided, for example fictional contingency, such as Sueprman or Dick Tracy, that which would be contingent if it had real concrete actuality, but is merely a fictional concept. But the four modes are the basic logical deductions about the nature of existence.

The idea that the argument can be reversed just by switching the lines and declaring God impossible merely begs the question. Is God really impossible just because we can utter those words? Is God logically necessary just because we can utter those words?. No, but that's not what is being said. God is logically necessary as a concept. That is the nature of the God-concept, that's the idea of God. To deny that would be like saying "how do you know that tables are things to put things on?" Or "how do you know that triagles have three sides?"The question is one of actuality, so if it is possible that God exists than God is ontologically necessary and thus has real concede existence because since God is not contingent it cannot be that God is "merely possible." If it is at all possible that God exists, than it's not impossible. To show that the argument can truly be reversed the atheist must show why God is impossible, and to do that he/she must show that God cannot be understood analytically without contradiction.


Another attempt at reversing the argument, which is always used on message boards when I make this argument: just to put not in front of each line. "It is possible that god does not exist." The premise is they don't have to prove God is impossible, but just that the possibility of God's not existing reverses the argument.

The problem is, the premise is false. If god is not analytically impossible (contradictory) then God must exist. Thus it is not ture that it is possible that God does not exist. The logic works like this:


(1) If God is indeed possible, the God cannot be impossible.

(2) to say God is not possible is the same as saying god is impossible.

(3) if something is possible, it can't be impossible.

(4) you must show why God is impossible.

(5) I have shown why God is possible, becasue God is conceivable without contradiction.

(6) anticipating answer on entity and consciousness, consciousness is not a primary quality of God. Other things are consciousness, that is not something uniquely establishes God as God, logical necessity is such a thing.

(7) If God is possible, and can't be impossible, and can't be contingent, then to be possible for God is to be logically necessary. Thus it does not work to say God is not possible because it isn't true, thus it's a false premise.



To make good on any reversal they must show a contradiction in the concept of God. To this they always retort "well you can't prove that God is not contradictory." But I don't have to prove that. One can assume that if there is no contraction it is not contradictory. They are the one's seeking to make the reversal, so it's their burden of proof. But to prove that God is possible all one need do is conceive god analytically without contradiction. what else could one do to prove a possibility?


2) The assumption that we are merely loading the concept with terms that make it necessary, or that the definition of God as necessary is arbitrary.

This is really the same argument one must make to reverse the argument of necessary being. This is what atheists always argue. The first thing they say bout it is that we are just arbitrarily sticking on the term "necessary" and playing word games. Some go so far as to try and demonstrate this by sticking the term necessary on other things, such as "purple cow" or anything they think of, and that's supposed to show what we are doing. I regard this move as nothing more than a demonstration that they do not understand the concepts The necessity of necessity and why it must be applied to God is demonstrated on the "modes of being" page. Moreover, this move is nothing more than the perfect Island argument. It can't work because it merely enthrones contingencies. Our reason for saying that God is necessary is much more logical and organic and is much more than a mere word game.

While it is true that God as being itself is a pre-given postulate and is independent of proof because it is part of the definition of God, the realization that being has t be means that this must be the case.

3) The assumption that we are lending existence to a fictional being.

This is merely an assumption. The necessary existence of God is implied in the possibility of God's existence and the realization that the the only alternative is impossibility. God is possible and thus necessary. Some have tried to argue that they are breaking up the four categories with a 5th not seen, that of "fictional" but that applies to the category 4 that of non-existing contingency.

4) Equivocating between types of necessity.

The argument says that to say God is necessary as a postulate of definition is speaking of ontological necessity, than to assert the actuality of it is moving from logical to ontological necessity.

To say that a thing is logically possible is to say that it might have existed in the past or may exist in the future. But for God to exist he must always have existed; in the past, in the future, or all time. Given logical necessity the logical possibility of God 's non existence is impossible. Therefore, ontological necessity implies logical necessity. One implies the other and it is a rational move from one to the other.



This argument may seem like merely a trick of words, and modal logic may be controversial, but it turns on very basic logic, such as modus tolens or modus ponens which is accepted by all logicians. On Argument 1 I document Antony Flew saying that the logical categories of "Necessary" and "contingent" truth are accepted by all logicians.

TrentDougherty
Concise intero to the Modal Ontological Arugument for The Existence of God.

http://www.abarnett.demon.co.uk/atheism/ontol.html

TERMS

‘Modal’ – Pertaining to the modes of existence (de re) or of propositions (de dicto) as necessary or possible. ‘Necessity’ is a mode of being for a thing or proposition as is ‘Possibility’.
‘Ontological’ – from Greek ontoV for being.
‘Argument’ – designed to logically support a proposition (not to be confused with persuasion which is a psycho-social phenomenon, not a philosophical one).
Throughout this description I shall use standard notation and notation used when the font is restricted to a single typeset as in a text only document for HTTP purposes on the Internet.

The modalities are symbolized as follows:
A square or in typeset [] preceding an expression means “It is necessary that…” or “It is necessarily the case that…” or simply “Necessarily…” e.g. as applied to a propositional function.

Ps/[]Ps – “It is necessarily the case that s is P” where s is a constant referring to some individual and P is a predicate.
A Diamond à or in typeset <> preceding an expression means “It is possibly the case that…” or “It is possible that…” or simply “Possibly…”

SEMANTICS

Possibility is defined as consistency. àPs/<>Ps reads as “Possibly, s is P” and means that there is no contradiction in attributing P to s. Necessity is defined as “not possibly not the case”. If something cannot not be, then it must be.

Psº~à~Ps or []Ps=~<>~Ps
THE CALCULUS

There are many different ways to axiomatize a logic, just as there are different ways to axiomatize geometry. Axioms in some systems will be theorems in others, but since axioms and theorems have the same validity it is only a matter of formal difference. One of the most used systems of modal logic is called S5. There is an interesting theorem in S5 called Brouer’s Theorem.
(PàP)à(àPàP) or (P-->[]P)-->(<>P-->P)
This theorem is derivable in weaker systems as well.
The modal ontological argument for the existence of God is just a substitution instance for this theorem. There are only two propositions needed.
THE PROPOSITIONS

First comes the definition of God as a being who, IF he exists, does so necessarily, i.e. a Necessary Being. This is only the definition of what God would be like IF he existed. The proposition is formalized as
GàG or G-->[]G
“If God exists, then he necessarily exists.”
The other proposition is the assertion that it is possible that God exists.
àG or <>G
“Possibly, God exists.”
RULES OF INFERENCE

The only rule of inference needed is Modus Ponens.
PàQ “If P, then Q”
P
Therefore Q
Now we are ready to put the argument together.

THE ARGUMENT
1. (GàG)à(àGàG)
2. GàG
3. àG
4. àGàG
5. G
(Theorem, sub G for P)
(Def of God)
(premise)
(1, 2 MP)
(4, 3 MP)

or
1. (G-->[]G)-->(<>G-->G) (Theorem, sub G for P)
2. G-->[]G (Def of God)
3. <>G (premise)
4. <>G-->G (1, 2 MP)
5. G (4, 3 MP)

COMMENTARY

It is quite a simple argument which makes it hard to understand its fullness. The simple is packed with meaning. As you can see, there is one and only one premise, that it is possible that God exists. If this be granted, then his necessary existence follows. Since all efforts to show that the concept of God is contradictory have failed heretofore I conclude, somewhat reluctantly, that God exists. Kai Neilson tried to argue this in his debate with J.P. Moreland, but didn’t make much progress.

Now I realize that to the average person, this seems like a trick, but the average person is not particularly accustomed to following logical arguments at all, much less highly specialized forms of logical calculi developed by professional philosophers. Most professors at the University level don’t even know modal logic and many have never studied it and some have never heard of it. What do those who know it, but don’t believe in God say? They say that the concept of God is incoherent. I have not yet seen an even slightly plausible argument to that effect. Until I do, the OA will be cogent to me. I might add that I am a convert on this argument. I argued for years that the ontological argument was flawed until someone showed me the modal version. I have always followed Reason wherever it lead and, as usual, it lead to God.

SELECTED BIBLIOGRAPHY

Adams, Robert M., _The Virtue of Faith_, esp. “The Logical Structure of Anselm’s Arguments,” Oxford University Press: 1987.
Moris, Thomas V, _Anselmian Explorations_, esp. “Necessary Beings,” University of Notre Dame Press: 1987.
Plantinga, Alvin, _The Nature of Necessity_, esp. “God and Necessity,” Oxford University Press: 1974, 1992.
Plantinga, Alvin, _The Ontological Argument_, Anchor Books, 1965.
Swinburne, Richard, _The Coherence of Theism_, Oxford University Press: 1977, 1993.



Oddly enough that quotation is linked to a site by an atheist named Adrian Barnett who is attacking my older version of this argument, but he was gracious enough to put this quotation, which I think works against his argument, by a philosopher in the UK.


About Hartshorne


Hartshorne Lived to be 103, at the time of his death in the Fall of 2000, he was known as "the greatest living Metaphysician." Hartshorne was one of the major forces in the "back to God" movement in Philosophy (a term coined by Christianity Today in a 1979 article. His first and greatest calim to fame is as the second most influential voice in process philosophy, along with Alfred North Whtiehead, but he is also credited as the man who brought the Ontological argument back from ignominious defeat by Kant almost two centuries earlier. Hartshorne was also a recognized authority on birdsong, and an authority on bycicles, having never driven a car a single time in his centogenerian lifespan. Hartshorne devoted the last years of life to waging a letter's to the editor campaign to advocate social issues such as medical care.

The Question of Being part 2: Against ICR

I have done a previous post on the impossibility of ICR (Infinite Causal Regression). There are aspects of the subject that I didn't deal with in that so I am hoping to deal with them here. Stanford Encyclopedia of Philosophy has an excellent article on the Cosmological Argument. I am going to deal with issues raised in that article, issues pertaining to contingency and ICR. In counter to the argument of a necessary first cause Russell argues that the universe just is and requires no explanation. In the last post I argued that this is unsatisfying, Russell argued that we derive our concept of cause from observation, thus since we don't observe the final cause, or the cause of the universe (see objection 1 in link above). The obvious answer is that we don't have to observe ever aspect to extrapolate from what we do observe, that's the whole principle of inductive reasoning in scinece. I would argue that we do observe the contingency of the universe because it's all around at every moment, while we can't know the finality of it's contingency, we can see plainly that the only we have of the mode of being of the universe is contingency, which is in everything we see.

Rusell argued that the move from the parts to the whole, from contingent parts to wholly contingent universe, is the "fallacy of composition."

Russell correctly notes that arguments of the part-whole type can commit the Fallacy of Composition. For example, the argument that since all the bricks in the wall are small, the wall is small, is fallacious. Yet it is an informal fallacy of content, not a formal fallacy. Sometimes the totality has the same quality as the parts because of the nature of the parts invoked—the wall is brick because it is built of bricks. The universe's contingency, theists argue, resembles the second case. If all the contingent things in the universe, including matter and energy, ceased to exist simultaneously, the universe itself, as the totality of these things, would cease to exist. But if the universe can cease to exist, it is contingent and requires an explanation for its existence (Reichenbach, chap. 5).(from Stanford article above).

The assertion that the exact duplication of the building material in the overall wall is a red herring. The argument that the size of the bricks is the size of the all is not really analogous to the issue of contingency. The analogy would between the actual state of the material, not it's size divided into increments, but the material itself. A wall made out of all bricks is what we call "a brick wall" that is a wall made wholly of the materiel "brick." If a wall is made up of contingencies then it's a contingent wall.

Some reply that this argument for the contingency of the universe still is fallacious, for even if every contingent being were to fail to exist in some possible world, it may be the case that there is no possible world that lacks a contingent being. That is, though no being would exist in every possible world, every world would possess at least one contingent being. Rowe gives the example of a horse race. “We know that although no horse in a given horse race necessarily will be the winner, it is, nevertheless, necessary that some horse in the race will be the winner” (1975, 164).

Atheist answer:

Rowe's example, however, fails, for it is possible that all the horses break a leg and none finishes the race. That is, the necessity that some horse will win follows only if there is some reason to think that some horse must finish the race.

That is not a real answer because it doesn't prove that the universe is necessary it proves merely that there might be no universe at all. Since that means the universe itself could have failed to exist that makes it contingent (standard definition: that which could cease or fail to exist). The author of the article argues as a back up that we must have a reason to believe that something is necessary: "Similarly, his objection to the universe's contingency will hold only if there is some reason to think that the existence of something is necessary. " That's just the problem, we have no reason to assume the universe is necessary, we have an obvious reason to assume that being is necessary, since something can't come from nothing, there's ample reason to assume an eternal first cause. Being eternal it could not could not cease or fail, the logic of an eternal first cause makes it necessary a prori (ie Necessary: that which cannot cease of fail to exist). If something is truly eternal it could not cease or fail to exist. Consider the lunacy in saying that some thing has existed for ever with no cause but on June fourth, 1955 it cased to be. Why June 4, 1955, why not eons ago? It had infinite chances to cease, why would it do so on that one day and not another much sooner? Moreover, the concept of eternal being is limitless, unnumbered and infinite. To then have it cease would be to put a number to the infinite which is impossible. All of which is reason enough to assume eternal necessary being.

The article at that point goes off into what I think is a tangent arguing for the possible existence of a world with no contingent beings.

One argument given in defense of this thesis is that the existence of one contingent being may be necessary for the nonexistence of some other contingent being. But though the fact that something's existence is necessary for the existence of something else holds for certain properties (for example, the existence of children is necessary for someone to be a parent), it is doubtful that something's existence is necessary for something else's nonexistence per se, which is what is needed to support the argument that denies the contingency of the universe. Hence, given the contingency of everything in the universe, it remains that there is a possible world without any contingent beings.

I think he missed the point. The point is not that there must be a contingent being of some kind in every possible world, but that the state of contingency is mandated for all possible worlds (they are all dependent upon God) since they could all fail to exist. The author of the article, Bruce Reichenbach, argues in terms of individual beings. The point is that the whole is demonstrated as contingent because it is made up of contingent parts. This is not the fallacy of composition becuase if the parts are all the same the over all structure is the same as the parts. We can get off track by being literalistic and saying "the small bricks make a small wall" but they make a wall made of brick.

The fallacy of composition is when one reasons from the parts to the whole. In this case my argument (P2a) reasons from the fact that the universe is a collection of contingent things to the conclusion that the universe is contingent. But this is not my only argument for the contingency of the universe, be that as it may, it is not the fallacy of composition. The fallacy doesn't happen just any time one reasons in this way. It is not fallacious to argue form the parts to the whole if the parts are all alike.

Robert Koons on Leadership University

(12/12/03)

Phl 327
Contemporary Christian Philosophy
Fall 2000, University of Texas

The argument commits the fallacy of composition: from the fact that each part of the cosmos is caused, it fallaciously draws the conclusion that the whole cosmos is caused. Response: this is a misstatement of the argument. The argument assumes that all wholly contingent situations are caused. We can prove that the cosmos is wholly contingent, so it must have a cause.

The Nizkor Project

vistied 12/13/03

The second type of fallacy of Composition is committed when it is concluded that what is true of the parts of a whole must be true of the whole without there being adequate justification for the claim. More formally, the line of "reasoning" would be as follows:
The parts of the whole X have characteristics A, B, C, etc. Therefore the whole X must have characteristics A, B, C. That this sort of reasoning is fallacious because it cannot be inferred that simply because the parts of a complex whole have (or lack) certain properties that the whole that they are parts of has those properties. This is especially clear in math: The numbers 1 and 3 are both odd. 1 and 3 are parts of 4. Therefore, the number 4 is odd. It must be noted that reasoning from the properties of the parts to the properties of the whole is not always fallacious. If there is justification for the inference from parts to whole, then the reasoning is not fallacious. For example, if every part of the human body is made of matter, then it would not be an error in reasoning to conclude that the whole human body is made of matter. Similiarly, if every part of a structure is made of brick, there is no fallacy comitted when one concludes that the whole structure is made of brick.

Thomas Rauchenstein.Copyright 1997, (link is no good)

The argument (Cosmological) does not commit the fallacy of composition. Just as every part of a puzzle is red, so must the whole be red; if every part of a structure consists of stone, so must the whole consist of stone. Likewise, if every possible being is in potentiality, so the whole of all possible beings is in potentiality, and thus, needs to be actualized (caused). The very nature of the parts demand that the whole be caused as well.

If all the horses break a leg and no one finishes that is analogs to failure to exist not a defeat for the example. There is no reason to limit the example to just individual beings. ICR is made up of a string of contingent universes. For example where ICR is conveyed by the oscillating universe, big bang => big crunch, black whole, pops back out into another big bang, and another big crunch, another black and another popping out, on and on forever with no beginning and no end; the whole is made up of contingent parts. Take out the contingent universes, and you have no eternal string or series of infinite regression. The term "regression" refers to tracing the sting of c/e back infinitely. If the c/e is gone there's no string. Thus there is a possibility the string could have ceased at any point. That means the whole is contingent becuase it's made up of all contingent parts. Koons reflects this answer in his mermological argument:

To avoid any hint of the Fallacy of Composition and to avoid these complications, Koons (198–99) formulates the argument for the contingency of the universe as a mereological argument. If something is contingent, it contains a contingent part. The whole and part overlap, and by virtue of overlapping, have a common part. Since the part in virtue of which they overlap is wholly contingent, the whole likewise must be contingent.


Mememological Aggregation Axiom shows us that wholly congingent sitautions are wholly contingent


Dr. Robert Koons UT (Logician)

1) Every wholly contingent fact has a cause. (facts that are partly or wholly necessary need not)

2) Applying aggregation axiom, anything of a kin dk = such a thing as arrgigate of all kinds.

3) Aggreagates can't exist unless all parts exist (which means necessary aggregate must have Necessary parts, contingent aggregate must have contingent parts. The result is necessary and contingnet facts which means contingent aggregate as a whole). 4) Absolutely necessary facts cannot be caused, therefore, wholly contingent facts (those whith only contingent parts) can be caused.

5) Causal principle can be thought of as empirically supported (effects not limited to a particular region of space/time in the case of physical laws for example, :. we have reason to suspect that all contingent facts have causes).

For an explaination of the fact token/type situation I turn to Dr.Koons himself: www.leaderu.com/offices/k.../lec7.html

Phl 356
Western Theism
Spring '98, University of Texas

LECTURE #7: Contemporary Versions: My Argument

Facts are the kinds of things that make declarative sentences, like "Caesar has died", true. Facts enter into cause and effect relations with other facts. We can distinguish between "types" and "tokens", to use terms introduced into philosophy by C. S. Peirce. Each individual penny is a token, and the property or kind of penny-hood is a type. Each penny is a token of one and the same type, which is multiply realized in different places at different times. My argument concerns fact-tokens, not fact-types. For example, we can use the phrases "that Caesar died", "Caesar's dying" or "Caesar's death" to refer either to a fact-token, the particular, actual occurrence that constituted the ending of Caesar's life, or to a fact-type, the kind of occurence in which the individual Caesar dies. Thus, the token of Caesar's death includes the actual thrust of Brutus's blade, and that very token would not have existed had Caesar died in some other way, of old age, for example. In contrast, the type, Caesar's dying, could have been realized in many different ways, including the actual assassination and the non-actual dying in old age. My argument focusses on the actual token I call the cosmos. This token includes all of the wholly contingent fact-tokens in the world as parts -- had the slightest detail been different anywhere at any time, the particular token I am calling 'the cosmos'would not have existed. It would instead be replaced by a different token. The fact-type, the existing of a universe, could have been realized by many different possible tokens.

For an explaination of Meremology I again turn to Dr. Koons:

"My argument focusses on the particular token that actually realized this type.If we assume that every fact has a cause, then there could exist no uncaused fact. Instead, I assume that every wholly contingent fact has a cause. Facts that are partly or wholly necessary need not, and indeed cannot, be caused. Since facts are concrete, actual things, we can talk meaningfully about the parts of a fact. Consequently, I use the principles of the mathematical theory of mereology, the theory of the part-whole relation. The most important principle of mereology is the aggregation axiom. This axiom states that, if there are any things of kind K, then there is such a thing as the aggregate of all the K's. For example, there is such a thing as water, so we can talk meaningfully about the aggregate or "mereological sum" of all the world's water. I assume that an aggregate cannot exist unless all of its parts exist. This means that a necessary aggregate must have only necessary parts, since if an aggregate has a contingent part, then that part might not exist, which would mean that the aggregate would not exist either. Aggregates are not like bodies or institutions, which can go on existing without the same parts. However, a contingent aggregate can have necessary parts. If we glue together some contingent and necessary facts, the resulting aggregate is contingent as a whole. I assume that an absolutely necessary fact cannot be caused. If a fact is caused, then all of its parts are caused. So, any fact that contains a necessary fact cannot be caused.


Therefore, it is only wholly contingent facts that can be caused. A wholly contingent fact is a fact that has only contingent parts.I argue that the causal principle should be thought of as empirically supported. We find that a wide variety of facts are caused. This includes conditions both small and large (from atomic physics to astronomy and cosmology), both recent and ancient, both transient and long-lasting. We even discover that many everlasting conditions have causes. For example, the fact that the physical world is approximately Newtonian is caused by certain features of general relativity. Similarly, the ideal gas laws are caused by the underlying dynamics of the gas molecules, and Brownian motion is caused by atomic collisions. In these cases, the effects are not limited to a particular region of space or time. Thus, we have good empirical reason to believe that every fact that can be caused, that is, every wholly contingent fact, has a cause.

Cyclial Universe

The concept that the universe is eternallay ocillating between big bangs and big crunches. When the matter from the explosion of a Big Bang reaches a certain point the gravitational pull draws it back, it callapses into superdense black hole and pops back out again. This notion does not require an initial cause, the cyclical universe is just always there always going through its cycles.

a) Universe continuing to expand

Evidence from three recent studies reveals that the final fate of the universe will be to drift apart and cease all useful functions capable of supporting life due to missing mass, which can't produce gravitational pull to bring it all back together and start again, and heat death in which case energy is useless for work. Several major studies show this to be the case.

[New Scientist Magazine, archive 11, April 98, archive; originally Oct. 96] you should be able to click here, but here's the url just in case) [http://www.newscientist.com/ns/980411/features1.html

"ON THE night of 5 March last year, the huge telescope of the Cerro Tololo Inter-American Observatory in Chile intercepted a message from deepest space. Transmitted a billion years before the Earth was born, its contents have proved to be of truly cosmic significance. The message was barely readable after its journey halfway across the Universe, and an international team of experts laboured for months to decode it. In January, Saul Perlmutter of the Lawrence Berkeley Laboratory in California and his colleagues revealed to the world what they believe to be its gist: "The Universe will never end." A month later, a team led by Brian Schmidt of the Mount Stromlo and Siding Spring Observatories near Canberra in Australia published the decoded contents of more of these cosmic missives, which arrive as bursts of light from supernova explosions in far-flung galaxies. The message was the same. Now Chris Kochanek and his colleagues at the Harvard-Smithsonian Center for Astrophysics in Cambridge, Massachusetts, are about to publish more evidence, this time from light that has been bent and sculpted by the gravity of unseen galaxies."

*

Omega force = Continued expansion forever (no Big Cruch)

"These three sets of cosmic missives all suggest that instead of collapsing in on itself in a big crunch, our Universe will go on expanding forever. And that's not all. They also hint that the expanding Universe is in the grip of a mysterious force that is fighting against gravity--a force that pervades the entire cosmos and springs literally from nothing."(Ibid.)

[mysterious force = "omega" ie the equation of gravitational force vs. mass needed to close the universe; omega must = 1 to close]

*

Missing Mass.

[New Scientist article April 1999] "If it [the universe] contains enough matter, gravity will eventually slow its expansion, stop it, and reverse it--producing a cataclysmic big crunch billions of years hence. But if there is too little matter--or if there is an extra source of "oomph" at work in the cosmos--then the Universe will expand forever.... Cosmologists call the ratio of the actual density of matter in our Universe to this critical density 'Omega.' And whole armies of astronomers have spent decades trying to work out if Omega is less than, more than or equal to 1.,... "Studies of the gravitational effects of clusters of galaxies have revealed that there must be at least 10 times as much mass tied up in invisible "dark matter" in the Universe as there is in the familiar form of luminous stars and gas. Yet even when all this dark matter is thrown into the equation, it still doesn't make the theorists happy. Despite searching every cosmic nook and cranny, astronomers have never found anything like the amount needed to make Omega equal to 1."

"So the take-home message looks the same as that now emerging from the supernova and quasar surveys: the Universe is going to expand forever, and it may yet prove to be flat. Certainly the idea of the big crunch seems to have gone for good, but the exact values of Lambda and Omega, and the fate of the cosmologists' theories, are still up for grabs. These values may finally be nailed early in the next century, with the launch of NASA's Microwave Anisotropy Probe (MAP) and the European Space Agency's PLANCK missions. These will use the heat left over from the big bang to try yet another way of measuring Omega and Lambda, which may lay the question to rest for good ("Genesis to Exodus", New Scientist," 19 October 1996, p 30).

Flat Universe means no contraction

Andre Linde, Scientific American, Sept 1997

"A second trouble spot is the flatness of space. General relativity suggests that space may be very curved, with a typical radius on the order of the Planck length, or 10^-33 centimeter. We see however, that our universe is just about flat on a scale of 10^28 centimeters, the radius of the observable part of the universe. This result of our observation differs from theoretical expectations by more than 60 orders of magnitude." [Messuer is a leading physicist and one of the first to invent the inflationary universe theory]

ABC News.com: Scientists: Universe is Flat another link Physics. ucsb.edu

Wayne Hu of the Institute for Advanced Studies, School of Natural Sciences in New Jersey said "temperature maps of the CMB form a snapshot image of the Universe when it was extremely young." "The...result supports a flat universe, which means that the total mass and energy density of the universe is equal to the so-called critical density," Wu wrote. "A perfectly flat universe will remain at the critical density and keep on expanding forever, because there is not enough matter to make it recollapse in a 'big crunch.'"

c) End of Universe reveals beginning--universe would have already ceased.

Energy of the universe is being expended, as it burns up,it becomes useless for work. The fate of the universe will be eventual death in ciy darkness as all of its suns burn out and their energy dissipates][New Scientist, April 1999, oct. 96

"But even if the Universe lives forever, its inhabitants will not be so lucky. A mere thousand billion years from now, all the stars will have used up their fuel and fizzled out. There will still be occasional flashes in the perpetual night: the death throes of stars so large that they have collapsed in on themselves to form black holes. Even these will eventually evaporate in a blast of radiation. For the next 10122 years, this Hawking radiation will be the only show in town. By then even the most massive black holes will evaporate, leaving the Universe with nothing to do for an unimaginable 10 to the power of 1026 years. Quantum theory then predicts that atoms of iron--the most stable of all elements--will undergo "tunnelling" and disappear into tiny black holes, which will themselves end in a final fizz of Hawking radiation. In the beginning there may have been light, but in the end, it seems, there will be nothing but darkness. ".[New Scientist April 1999]

Given infinite time and possibility all potentialities would have already come to fruition, the chain would have already been broken before our universe came into being. This just illustrates the impossibility of an infinite series of events. (being a series of events it would be "in time" so it's really redundant to say "an infinite series of events in time.") In other words, if this universe drifts apart because it lacks mass to produce omega, than the last universe would have too because energy and matter would be the same amount, just formulated differently (energy cannot be created or destroyed). The absurdity of the notion of an infinite series of big bang/crunches is driven home; how could there be an "infinite" series if one of the links in the chain can't make it? It can't "already be infinite" and then stop because infinite means no beginning and no end.

Note: If the Skeptic does not agree to this principle, that given infinite time every possibility comes to fruition than he can neither argue infinite chances nor multiple universes against the fine tuning argument.

d) Universe contains finite stock of order, connote be eternal (because it would have burned out by now)

*Scientific consensus:

Paul Davies, in his article, "Space-time Singularities and Cosmology," says,"If we extrapolate this prediction to its extreme,we reach a point when all distances in the universe have shrunk to zero. An initial cosmological singularity therefore forms a past temporal extremity to the universe. We cannot continue physical reasoning, or even the concept of space-time, through such an extremity. For this reason, most cosmologists think of the initial singularity as the beginning of the universe. On this view, the Big Bang represents the creation event; the creation not only of all the MATTER and ENERGY in the universe, but also of space-time itself."[ P. C. W.Davies, "Space-time Singularities in Cosmology," in The Study of Time III, ed. J. T. Fraser (Berlin: Springer Verlag, 1978), pp. 78-79.]

* Laws of Physics break down at singularity

The laws of physics break down at the singularity. 1st Thermo. would apply after the Big Bang, then the fixed amount of energy that is "put in" to the universe (as Davies puts it) would be finite (in quantity) and subject to 1st and 2nd Thermo.


* 1 LTD applies to matter also. Thirdly, the 1st Law of Thermo. applies to matter ALSO. If you argue that energy is eternal, you've got to argue that matter is eternal, which goes against all the empirical evidence we have for the Big Bang.

* 2 LTD Energy burn to heat death

Fourthly, if you opt for 1st Thermo. before the Big Bang, try being consistent and applying 2nd Thermo. as well. If the energy (AND matter) of the universe is eternal, it would have reached MAXIMUM heat death an INFINITE amount of time ago.

Theoretical physicist Paul Davies, in his book God and the New Physics, states:

"If the universe has a finite stock of order, and is changing irreversibly towards disorder - ultimately to thermodynamic equilibrium - two very deep inferences follow immediately. The first is that the universe will eventually die, wallowing, as it were, in its own entropy. This is known among physicists as the 'heat death' of the universe. The second is that the universe cannot have existed forever, otherwise it would have reached its equilibrium end state an infinite time ago. Conclusion: the universe did not always exist."

If you deny that the universe has a finite stock of order, you are essentially denying the 1st law of thermodynamics, as it requires a fixed finite amount of matter and energy. (check your Encyc. Britannica)

In your wider universe, does the 1st law of Thermodynamics apply WITHOUT the second? What reversed the entropy of this eternally existent universe? As we saw above, a universe containing eternal matter and energy would have reached maximum entropy an INFINITE amount of time ago. What organizing principle intervened 11-15 billion years ago and organized all that energy and matter that was no longer available for work? What or who (or Who) wound the universe up?

Fifthly, we observe that the universe is expanding uniformly in all directions. Had the universe existed for an infinite period of time, the density of matter would have become zero. (Koons) How do you explain the observable expansion of the universe? We measure the recession velocity of distant galaxies by using Cepheid variables, type Ia supernovas, and now Red Clumps as standard candles. And the microwave background radiation and redshift (Doppler effect that skews the red portion of the spectrum of starlight in proportion to the distance of the star) confirm this expansion also. Furthermore, within the very field equations of General Relativity, is embedded the fact of the expansion and deceleration of the universe. There are now 19 proofs of General Relativity in 12 isolated areas of Physics,making it the most exhaustively proven principle. Are you saying that General Relativity does not apply to our universe as a whole?!! It is accurate to better than a trillionth of a percent precision. Where is your scientific evidence for A) separate portions of the universe which General Relativity does not describe B) separate universes? If its not falsifiable, and there's no evidence for it, then its just not a threat to the standard BB model as it is not scientific.

Since the oscillating universe is the only workable mechanism for ICR it's really a theory in trouble. The other alternatives such quantum tunneling require that the particles cause themselves (soemthing form nothing) then travel in time into he past to continually cause themselves again and again. The other answer is string membranes which is still unproved as something that even exists.

The Modal Argument

Charles Hartshorne 1897-2000
Modern Champion of the modal argument

What follows is one of the most challenging subjects you will ever hear about. It is the best way to get a head ache, but I think it proves the existence of God. The problem is it requires a very specialized background to understand it. First you have to understand modal logic.

Modal Logic is so called because it turns upon the use of so called "modal operators." It's called "modal" because it is the logic of modes of being. "modes" as in what type of existence something exits in, weather it is dependent upon other things, weather it can cease or fail to exist and so forth. The modal operators are "necessity," "contingency" "impossibly," "possibility."

Necessity and contingency lie at the base of our modern understanding of cause and effect. They come from scholastic notions of logic, but the distinction between the notion our modern notions of c/e and the scholastic ones in the middle ages is not that great. The  scholastic had more levels of cause, efficient cause, final cause and several others. But one could everything we have done in modern science using the scholastic ideas of c/e.

Necessity doesn't mean has to exist. It doesn't mean God is necessary to the existence of the world (except in so far as if God exists then of closure God is necessary to the world as creator--without God there would be no world).The modal argument does not begin with the assumption that God has to exist. It begins with the assumption that there is a valid distinction between necessity and contingency, which there must be.It proceeds along the lines of hypothetical consequence that obtain from different scenarios of God's existence. It concludes that is necessary. But by "necessary" it means not contingent, or not dependent upon something else for its' existence.

This is often misconstrued by atheists and taken to mean the argument proceeds from God's existence as an assumed first premise. This is not the case, the first premise is either/or. Either God's existence is necessary or it is impossible. This allows for the possibility that there is no God. So the argument does not begin by "defining God into existence."

Necessity means either non dependent or cannot cease or fail. By "fail" I mean there could not not be a God. That is the conclusion of the argument, not the premise.

Contingent means the opposite: that a thing is dependent upon a prior thing for existence, or that it could cease or fail to exist.

Impossible means logically impossible, something in the structure of the idea contradictions, such as square circles.

one of the sore spots that atheists get stuck on is the idea that God cannot be contingent. They will always leap to the conclusion that this is defining God into existence, because they don't understand the concept of God. God, by the nature of the concept, carriers certain parameters just as the existence of any human assumes humanity, or the existence of any tree assumes that the tree in question is a plant. To have to define that God is not contingent should not even come into it. The idea of God is that of eternal creator of all things. Thus God cannot cease to exits and cannot be dependent upon anything (or he wouldn't be the creator of all things). Atheists usually assume that all knowledge has to be empirical. they will argue this is defining God into existence. maybe God is contingent.

Maybe there is a begin like the one we talk about but he's not eternal or the creator of all things, but that means he's not the God we are talking about.



Hartshorne's version goes like this:

1) God can be analytically conceived without contradiction.
2) Therefore God is not impossible.
3) By definition God cannot be contingent.
4) Therefore God is either necessary or impossible.
5) God is not impossible (from 2) therefore, God is necessary.



Argument:my version

1) God can be analytically conceived, as eternal necessary being, without contradiction.

2) Therefore God is not impossible,(because no contradiction).

3) By definition God cannot be contingent (becasue God is eternal).

4) Therefore if God exists, God's existence is necessary, if God does not exist, it is because God is impossible.

5) God is not impossible (from 2) therefore, God is necessary.

6) Whatever is necessary by the force of Becker's modal theorum must necessarily exist.


A. The logic of the argument:

This argument is analytical, it proceeds from the basis in logic to argue that the concept of God is such that if we understood the meaning of the terms we would have to conclude that God must exist. Naturally that is a very controversial position. Many Christians and other theists reject the ontological argument on the grounds knowledge must be somewhat empirical. Nevertheless the argument has been used for a long time, and despite its many apparent deaths, it keeps returning in one form or another. Perhaps the best book on the subject is The Many Faced Argument by John Hick. Somehow the ontological argument just wont die. I feel that this is not so much because the argument itself is true as a proof, but because it gets at something deeper than proof, something to do with the way to think about God, and it strikes a deep cord in our consciousness, even though as a proof it may fail. For this reason alone it is important to know, if only to know the concept itself.

1) God can be analytically conceived without contradiction.
2) Therefore God is not impossible.
3) By definition God cannot be contingent.
4) Therefore God is either necessary or impossible.
5) God is not impossible (from 2) therefore, God is necessary.
6) Whatever is necessary by the force of Becker's modal theorem must necessarily exist.

(This is actually my re-statement of what Hartshorne is saying).

Hartshorne's actual modal logic looks like this:

The OA: an assessment:

by Ed Stoebenau

http://www.eskimo.net/~cwj2/atheism/onto.html Hartshorne's ontological argument is based on Anselm's second argument and claims that God's existence is logically necessary. Hartshorne's argument is given here, where "N(A)" means "it is logically necessary that A," "~A" means "it is not the case that A," "-->" is strict implication, "v" means "or," and "g" means "God exists":

g --> N(g)
N(g) v ~N(g)
~N(g) --> N(~N(g))
N(g) v N(~N(g))
N(~N(g)) --> N(~g)
N(g) v N(~g)
~N(~g)
N(g)
N(g) --> g
g



This argument is valid. Furthermore, given an Anselmian conception of God, premises one and five are sound. Premise two is just the law of the excluded middle, and premise three is a law of the modal logic S5. Premise nine is obviously sound, so this leaves premise seven as the only premise to question. Premise seven says that it is logically possible that God exists.



Yes, those funny lines, "g-->N(g)" are the argument, those are the formal symbols used in modal logic.

B. God's Possibility vs. Impossibility.

The argument turns on the distinction between necessity and contingency, and upon the distinction between mere possibility and the nature of necessary being as not mere possible. In other words, God is either necessary or impossible. If God exists than he is ontologically necessary, because he is logically necessary by definition. But if he does not exist than it is ontologically impossible that he exists, or could come to exist. This is because God cannot be contingent, by definition. A contingency is just not God. So if God is possible, he can't be "merely possible" and thus is not impossible, which means he must be necessary.

God is conceivable in analytic terms without contradiction:
The universe without God is not conceivable in analytical terms; it is dependent upon principles which are themselves contingent. Nothing can come from a possibility of total nothingness; the existence of singularities and density of matter depend upon empirical observations and extrapolation form it. By definition these things are not analytical and do depend upon causes higher up the chain than their being (note that the skeptic at this point probably denies the validity of analytic proofs but to reverse the argument must accept such proof).

Since the concept is coherent and not contradictory and is derived from analytic terms, to reverse the argument the atheist must show that God is impossible since the burden of proof is now on the one arguing that a contingent state of affairs could produce a universe in which being has to be.

D. Answering Objections:

1) The argument can be reversed

Atheists have tried to reverse the argument merely by saying:

1) either God exists or he doesn't
2) God is either necessary or impossible. Necessary if he exists, impossible if he does not
3) God is impossible
4) Therefore God does not exist.

But of course this is merely stipulation. They assume that what the argument is doing is just stipulating everything that has been said about God, but on the "Modes of Being" page I show that each of these modalities of existence are logical deductions.Either a thing exists or it does not. One can equivocate about the meaning the term "existence," but here I clearly mean concrete actual existence in the "real" world. If a thing does not exist it is either that it could, but just doesn't happen to exist, or that it cannot exist because it is a conceptual contradiction, such as square circles, or round triangles and so on. Therefore, if it does exist, it is either that it exists contingently or that it is not contingent but exists necessarily (that is it could not fail to exist without contradiction). These are the four most basic modes of being and cannot be denied. They could be subdivided, for example fictional contingency, such as Sueprman or Dick Tracy, that which would be contingent if it had real concrete actuality, but is merely a fictional concept. But the four modes are the basic logical deductions about the nature of existence.

The idea that the argument can be reversed just by switching the lines and declaring God impossible merely begs the question. Is God really impossible just because we can utter those words? Is God logically necessary just because we can utter those words?. No, but that's not what is being said. God is logically necessary as a concept. That is the nature of the God-concept, that's the idea of God. To deny that would be like saying "how do you know that tables are things to put things on?" Or "how do you know that triagles have three sides?"The question is one of actuality, so if it is possible that God exists than God is ontologically necessary and thus has real concede existence because since God is not contingent it cannot be that God is "merely possible." If it is at all possible that God exists, than it's not impossible. To show that the argument can truly be reversed the atheist must show why God is impossible, and to do that he/she must show that God cannot be understood analytically without contradiction.


Another attempt at reversing the argument, which is always used on message boards when I make this argument: just to put not in front of each line. "It is possible that god does not exist." The premise is they don't have to prove God is impossible, but just that the possibility of God's not existing reverses the argument.

The problem is, the premise is false. If god is not analytically impossible (contradictory) then God must exist. Thus it is not ture that it is possible that God does not exist. The logic works like this:


(1) If God is indeed possible, the God cannot be impossible.

(2) to say God is not possible is the same as saying god is impossible.

(3) if something is possible, it can't be impossible.

(4) you must show why God is impossible.

(5) I have shown why God is possible, becasue God is conceivable without contradiction.

(6) anticipating answer on entity and consciousness, consciousness is not a primary quality of God. Other things are consciousness, that is not something uniquely establishes God as God, logical necessity is such a thing.

(7) If God is possible, and can't be impossible, and can't be contingent, then to be possible for God is to be logically necessary. Thus it does not work to say God is not possible because it isn't true, thus it's a false premise.



To make good on any reversal they must show a contradiction in the concept of God. To this they always retort "well you can't prove that God is not contradictory." But I don't have to prove that. One can assume that if there is no contraction it is not contradictory. They are the one's seeking to make the reversal, so it's their burden of proof. But to prove that God is possible all one need do is conceive god analytically without contradiction. what else could one do to prove a possibility?


2) The assumption that we are merely loading the concept with terms that make it necessary, or that the definition of God as necessary is arbitrary.

This is really the same argument one must make to reverse the argument of necessary being. This is what atheists always argue. The first thing they say bout it is that we are just arbitrarily sticking on the term "necessary" and playing word games. Some go so far as to try and demonstrate this by sticking the term necessary on other things, such as "purple cow" or anything they think of, and that's supposed to show what we are doing. I regard this move as nothing more than a demonstration that they do not understand the concepts The necessity of necessity and why it must be applied to God is demonstrated on the "modes of being" page. Moreover, this move is nothing more than the perfect Island argument. It can't work because it merely enthrones contingencies. Our reason for saying that God is necessary is much more logical and organic and is much more than a mere word game.

While it is true that God as being itself is a pre-given postulate and is independent of proof because it is part of the definition of God, the realization that being has t be means that this must be the case.

3) The assumption that we are lending existence to a fictional being.

This is merely an assumption. The necessary existence of God is implied in the possibility of God's existence and the realization that the the only alternative is impossibility. God is possible and thus necessary. Some have tried to argue that they are breaking up the four categories with a 5th not seen, that of "fictional" but that applies to the category 4 that of non-existing contingency.

4) Equivocating between types of necessity.

The argument says that to say God is necessary as a postulate of definition is speaking of ontological necessity, than to assert the actuality of it is moving from logical to ontological necessity.

To say that a thing is logically possible is to say that it might have existed in the past or may exist in the future. But for God to exist he must always have existed; in the past, in the future, or all time. Given logical necessity the logical possibility of God 's non existence is impossible. Therefore, ontological necessity implies logical necessity. One implies the other and it is a rational move from one to the other.



This argument may seem like merely a trick of words, and modal logic may be controversial, but it turns on very basic logic, such as modus tolens or modus ponens which is accepted by all logicians. On Argument 1 I document Antony Flew saying that the logical categories of "Necessary" and "contingent" truth are accepted by all logicians.

TrentDougherty
Concise intero to the Modal Ontological Arugument for The Existence of God.

http://www.abarnett.demon.co.uk/atheism/ontol.html

TERMS

‘Modal’ – Pertaining to the modes of existence (de re) or of propositions (de dicto) as necessary or possible.  ‘Necessity’ is a mode of being for a thing or proposition as is ‘Possibility’.
‘Ontological’ – from Greek ontoV for being.
‘Argument’ – designed to logically support a proposition (not to be confused with persuasion which is a psycho-social phenomenon, not a philosophical one).
Throughout this description I shall use standard notation and notation used when the font is restricted to a single typeset as in a text only document for HTTP purposes on the Internet.

The modalities are symbolized as follows:
A square or in typeset [] preceding an expression means “It is necessary that…” or “It is necessarily the case that…” or simply “Necessarily…” e.g. as applied to a propositional function.

Ps/[]Ps – “It is necessarily the case that s is P” where s is a constant referring to some individual and P is a predicate.
A Diamond à or in typeset <> preceding an expression means “It is possibly the case that…” or “It is possible that…” or simply “Possibly…”

SEMANTICS

Possibility is defined as consistency.  àPs/<>Ps reads as “Possibly, s is P” and means that there is no contradiction in attributing P to s.  Necessity is defined as “not possibly not the case”.  If something cannot not be, then it must be.

Psº~à~Ps or []Ps=~<>~Ps
THE CALCULUS

There are many different ways to axiomatize a logic, just as there are different ways to axiomatize geometry.  Axioms in some systems will be theorems in others, but since axioms and theorems have the same validity it is only a matter of formal difference.  One of the most used systems of modal logic is called S5.  There is an interesting theorem in S5 called Brouer’s Theorem.
(PàP)à(àPàP) or (P-->[]P)-->(<>P-->P)
This theorem is derivable in weaker systems as well.
The modal ontological argument for the existence of God is just a substitution instance for this theorem.  There are only two propositions needed.
THE PROPOSITIONS

First comes the definition of God as a being who, IF he exists, does so necessarily, i.e. a Necessary Being.  This is only the definition of what God would be like IF he existed.  The proposition is formalized as
GàG or G-->[]G
“If God exists, then he necessarily exists.”
The other proposition is the assertion that it is possible that God exists.
àG or <>G
“Possibly, God exists.”
RULES OF INFERENCE

The only rule of inference needed is Modus Ponens.
PàQ  “If P, then Q”
P
Therefore Q
Now we are ready to put the argument together.

THE ARGUMENT
1.      (GàG)à(àGàG)
2.      GàG
3.      àG
4.      àGàG
5.      G
(Theorem, sub G for P)
(Def of God)
(premise)
(1, 2 MP)
(4, 3 MP)

or
1.      (G-->[]G)-->(<>G-->G)  (Theorem, sub G for P)
2.      G-->[]G  (Def of God)
3.      <>G (premise)
4.      <>G-->G  (1, 2 MP)
5.      G  (4, 3 MP)

COMMENTARY

It is quite a simple argument which makes it hard to understand its fullness.  The simple is packed with meaning.  As you can see, there is one and only one premise, that it is possible that God exists.  If this be granted, then his necessary existence follows. Since all efforts to show that the concept of God is contradictory have failed heretofore I conclude, somewhat reluctantly, that God exists.  Kai Neilson tried to argue this in his debate with J.P. Moreland, but didn’t make much progress.

Now I realize that to the average person, this seems like a trick, but the average person is not particularly accustomed to following logical arguments at all, much less highly specialized forms of logical calculi developed by professional philosophers.  Most professors at the University level don’t even know modal logic and many have never studied it and some have never heard of it.  What do those who know it, but don’t believe in God say?  They say that the concept of God is incoherent.  I have not yet seen an even slightly plausible argument to that effect.  Until I do, the OA will be cogent to me.  I might add that I am a convert on this argument.  I argued for years that the ontological argument was flawed until someone showed me the modal version.  I have always followed Reason wherever it lead and, as usual, it lead to God.

SELECTED BIBLIOGRAPHY

Adams, Robert M., _The Virtue of Faith_, esp. “The Logical Structure of Anselm’s Arguments,” Oxford University Press: 1987.
Moris, Thomas V, _Anselmian Explorations_, esp. “Necessary Beings,” University of Notre Dame Press: 1987.
Plantinga, Alvin, _The Nature of Necessity_, esp. “God and Necessity,” Oxford University Press: 1974, 1992.
Plantinga, Alvin, _The Ontological Argument_, Anchor Books, 1965.
Swinburne, Richard, _The Coherence of Theism_, Oxford University Press: 1977, 1993.



Oddly enough that quotation is linked to a site by an atheist named Adrian Barnett who is attacking my older version of this argument, but he was gracious enough to put this quotation, which I think works against his argument, by a philosopher in the UK.


About Hartshorne


Hartshorne Lived to be 103, at the time of his death in the Fall of 2000, he was known as "the greatest living Metaphysician." Hartshorne was one of the major forces in the "back to God" movement in Philosophy (a term coined by  Christianity Today in a 1979 article. His first and greatest calim to fame is as the second most influential voice in process philosophy, along with Alfred North Whtiehead, but he is also credited as the man who brought the Ontological argument back from ignominious defeat by Kant almost two centuries earlier. Hartshorne was also a recognized authority on birdsong, and an authority on bycicles, having never driven a car a single time in his centogenerian lifespan. Hartshorne devoted the last years of life to waging a letter's to the editor campaign to advocate social issues such as medical care.