Monday, October 27, 2008

Updated: Brian's proof of the existence of God

Reader Brian has been kind enough to send along his proof of the existence of God. I am having a bit of a busy week, so I haven't had a chance to read it yet, but since I haven't posted much else and won't have time to go over it until the weekend, I probably shouldn't keep people waiting. I did glance through the first few pages, and it's clear I'm going to have to Google some terms, and/or take a philosophy course. Perhaps the second option... if only there were time.

Anyway, have a great week, everybody, and happy reading!

UPDATE, November 2nd: Brian e-mailed me a small addition he meant to include in this (Proposition 4a). I've added it in.

From here until the end of the post is Brian (Paladin)'s work.


Notice: the following is for entertainment purposes only. The author assumes no extraordinary liability toward the reader for mental injury or facial injuries due to boredom-induced collapse into computer keyboards, nor can the author be held accountable for any program of hair-replacement therapy necessitated by the frustrated removal of the original follicles by the reader. Besides, the author doesn't have any money to pay a lawsuit; so there.

The Necessary Existence of God?

Definition A: By "cause", this argument will mean "ontological cause", or "that which is responsible for bringing an object into existence," or "that which bestows existence to another object." (It's true that Aristotle, Aquinas, etc., suggested many types of causes; I'll be abstracting from and/or conflating them, in general. Time will tell if such a move is well-advised.)

Definition B: By "object", this argument will mean anything which in any way holds ontological existence.

Definition C: By "eternal", this argument will mean that which is completely independent of time.

Definition D: By "intrinsic [essential] existence", this argument will describe that which exists by necessity, and by its very nature; that which is causeless.

Definition E: By "extrinsic [essential] existence", this argument will describe that which is dependent upon an ontological cause for its existence; that which does not exist by necessity.


Assumptions (assumed to be self-evident):

Lemma #1: An object must exist in order to act.
Lemma #2: An object cannot use or extend that which it does not possess
(corollary to Lemma #1).


Proposition #1: No object can be its own cause.

Proof: There are only two possibilities for any object, re: causation: an object is either caused, or uncaused.

a) If an object is uncaused, then Prop. #1 is trivially true.

b) If an object is caused, then its cause must (by Lemma #1) have existed in order to enact that causation. It is therefore manifestly true that a non-existent object cannot act to bring itself (or anything else) into existence.


Proposition #2: Causation is necessarily bound to the definition of "change."

Proof: Any change is an event by which an object either loses or gains characteristics--by which an object (in one or more ways) moves from potentiality to actuality, or from actuality to potentiality. (It will be necessary, before finishing the proof, to discuss the mode of continued existence of any given object.) Since "cause" (as per definition #1) denotes an event by which an object gains ontological existence, the definition of "change" is thus satisfied. (Discussions of change regarding "loss" will be described below.)

An object's existence can be conceived as being either (a) intrinsic, by its very nature (i.e. uncaused); or (b) extrinsic (i.e. caused and maintained). It might be argued that an object could, hypothetically, be "caused, but independent (i.e. not maintained)" in the sense that it required an "initial cause", but needs no "maintenance" of that acquired existence; such a suggestion stems from a misunderstanding of--among other things--the nature of time, in that an object's existence at any given moment subsequent to its causation is dependent on its existence in prior moments (up to that moment of causation--which is then dependent on the extrinsic cause), just as surely as the existence of a 100m object is dependent upon the existence of, say, the first 99m. Such a suggestion, therefore, cannot be maintained.


Objection #1: Cannot an object have discontinuous existence? Cannot an object exist for a burst of moments, blink out of existence, and then re-appear, for an indefinite number of repetitions?

Reply #1: Even if that were possible, it would merely push the case back to smaller intervals; the very same propositions would hold for each small "segment" of existence, and each "annihilation" would require its own cause, as would any subsequent "recreation". If an object has intrinsic existence, then (by definition) it will never cease; if an
object has extrinsic existence, then it is dependent on an extrinsic cause for that existence. No object can "cycle" between existence and nonexistence by its intrinsic nature--if for no other reason than the fact that any object which ceases to exist (a) is shown to have non-intrinsic existence, and (b) would be helpless to enact its own "recreation" (cf. Lemma #1).

There are only two ways by which characteristics can be lost: by active negation (i.e. an event, force, etc., which actively cancels an existing characteristic), or by privation (i.e. by having the "maintaining source" discontinue its maintenance). Both cases require an extrinsic cause.

Similarly, there is only one way by which attributes can be gained: by extrinsic cause (since an object cannot bestow upon itself that which it does not itself possess, as per Lemma #2).

As such, any change must necessarily require a cause or causes (since change, by definition, requires the gain and/or loss of attributes--and both require extrinsic causes). Conversely, any cause (so-called) would necessitate the existence of change--at least insofar as the object being "caused" is concerned (which changes in state from potential to actual--from nonexistence to existence).


Objection #2: "There seem to be many types of change which do not require gain or loss; what is gained or lost, for example, by an object moving from position A to position B?"

Reply #2: Such an object would lose its characteristic of occupying position A (to say nothing of a possible loss of being at relative rest), and it would gain the characteristic of occupying position B (to say nothing of having gained--albeit briefly--the positions of all intermediate locations, and having lost the state of potentiality inherent in *not* moving). No change can possibly occur without gain or loss. (It should be noted that the subjective ideas of "degradation" and "improvement" have nothing especially to do with the strict definitions of "gain" (moving from potential to actual) or "loss" (moving from actual to potential); it is not the purpose of this specific proposition to explore advancement toward, or retreat from, any sort of perfection.)


Proposition #3: Given any example of change(s), one must consequently posit one or more causes.

Proof: see Proposition #2. I assert that the visible universe does, in fact, offer many such examples of change (which consequently require causes), and that such a fact is self-evident.


Proposition #4: That which has intrinsic existence in its essence must be changeless in its essence.

Proof: from Proposition #3, any change would necessitate a cause; and that which has intrinsic existence is, by definition, causeless (cf. Proposition #2); therefore, that which has intrinsic existence cannot admit of change. Or, to put the matter differently: if the statement "that which admits of change(s) must thereby require a cause" is true
(which it is, by Proposition #3), then the contrapositive of that statement is also necessarily true: "that which does not require a cause (i.e. has intrinsic existence) does not admit of change"--which is the thesis statement of Proposition #4.

Proposition #4a: Every “chain” of extrinsically caused objects must have an uncaused cause (i.e. a cause with intrinsic existence) as its ultimate source; a hypothetical “infinite regression of extrinsic causes” would be empty of content (i.e. would not exist at all).

Proof: By definition, an extrinsically caused (i.e. contingent) object does not possess existence by its nature (as would an object with intrinsic existence); it must "borrow" (i.e. "depend/subsist on") existence from its antecedent cause (see Proposition #2). If the ontological antecedent of a contingent object is itself contingent, then it must in turn "borrow" existence from its own antecedent, and so on, in turn; but if there were a hypothetical infinite string of consecutive "ontological causes", none of which possessed ontological existence in and of itself (but which was dependent on its ontological antecedent), then the total ontological content of that string would be "... + 0 + 0 + 0 + ...", without reaching a term of actual value (i.e. the total content would be "0").

Illustrations for this idea abound, but here's a popular one: picture a string of people going to see a movie, and passing the ticket booth; and picture each successive person, when asked to pay for a ticket, point to the person in back, saying: "He'll pay for me!" If the string of movie-goers were infinite, the ticket-taker would never get paid.


Objection #3: "Cannot an object exist intrinsically in its essence, but extrinsically in its accidents and/or attendant attributes? In other words, cannot an object with intrinsic existence somehow contain accidental attributes which are extrinsic, and therefore subject to change?"

Reply #3: That question is not germane to the issue at hand; the only objection which could have weight against proposition #4 would be an instance where an object with intrinsic ESSENTIAL existence was subject to change in that essence. It is enough to say that, if there were (hypothetically) attendant accidents to an object with intrinsic essential existence, they would themselves require causes to the extent that they existed extrinsically, and certainly to the extent that they exhibited change.


Proposition #5: That which has intrinsic essential existence must necessarily be eternal in its essence.

Proof: Change, by its very nature, necessitates time, and vice-versa. Time is a dimension of space which has meaning (and even existence) only when some manner of change exists; functionally, time is a measure of change, and it cannot operate on that in which there is no change against which progress could be measured. Since that which has intrinsic existence is changeless by definition, it must necessarily be immune to time, and therefore eternal (by definition).


Proposition #6: Any uncaused cause must be eternal and unchanging in its essence; its essential existence must be utterly beyond space/time.

Proof: see Propositions #4 and 5. Note that the pseudo-converse of this proposition (i.e. "that which is in eternity must have intrinsic essential existence") is not necessarily true (and is known, by Divine Revelation, to be false: e.g. angels).


Objection #4: "These arguments depend entirely on the idea that objects are strictly simple ones--that each object is the result of only one cause. This cannot be maintained, since any composite object will necessarily have component parts which need causes--possibly from many different venues (e.g. color, shape, etc.)."

Reply #4: The above propositions are most easily applied to simple objects; that is true. However, composite objects are--by definition--reducible to simple parts, which themselves would be described by these propositions. Consider, also, that even a composite object *can* have a single ontological cause (though it need not), which would be covered under these scenarios.


Objection #5: "Some attributes of composite objects simply can't be 'parsed' like that; how, for example, could we speak of a cause for an apple's shape, another cause for its redness, another for its rigidity, etc.? It's equivocal to say that 'the apple exists', when in fact its shape, color, rigidity, etc., all exist as well."

Reply #5: This may well be a shortcoming of my argument due to a neglect of the various types of causes; a formal cause, for example, could well differ from an accidental cause or a material cause, and so on. However, the same principle holds: every "caused" object (be that object a "physical object" as considered by common idiom, or a single
attribute of any such object--which is an "object" in the sense of that which holds ontological existence, and has a cause which answers the question "WHY is that so?") must trace itself to an ultimately uncaused cause.


Proposition #7: Any uncaused cause will necessarily be identical with its very existence (i.e. its essence and existence must be equivalent).

Proof: First, consider three aspects of any object: (a) the object itself, (b) the object’s existence, and (c) the object’s reason for existence. When considering an uncaused cause, the reason for its existence is, by definition, contained within itself—i.e. it exists by its very nature. Thus, (b) = (c). It remains to be demonstrated that (a) = (c), which would consequently show that (a) = (b).

All objects have a "reason for existence" [hereafter: "reason"]; that reason would be either external (if the object is contingent) or internal (if the object is uncaused). Given that the reason for an uncaused cause is necessarily internal to it[self], this leaves three situational comparisons:

(#1) The object's reason exceeds the object.
(#2) The object exceeds its reason.
(#3) The object is identical to its reason.

Situation #1 would entail a contradiction of the definitions of "uncaused" and "internal", since a reason cannot be contained in (i.e. "internal to") its object if the reason exceeds that object.

Situation #2 would entail "parts" of the object which were distinct from the reason itself (i.e. which were not in the "province" of the reason); as such, those "remainder aspects" would be contingent on the (internal but distinct) reason, and would thereby "disqualify" themselves from "membership" in the utterly non-contingent, uncaused cause.

Therefore, #3 is the only situation which does not prove itself to be absurd. As such, (a) = (c), which necessitates that (a) = (b).


Objection #6: "Could it not be possible to speak of multiple "reasons" for an object's existence? For example, would it not be valid to suggest that a biological mother AND father would be reasons for a child's existence?

Reply #6: It is certainly possible to speak of multiple reasons for existence… provided that we are speaking of contingent objects (e.g. the child in question would have far more reasons for existence: proper temperature for survival, adequate food supply, etc.), but it's quite beside the point in this case. Even if a plurality of reasons within an uncaused cause were possible (and that will be shown to be untenable), the main issue of this idea is whether or not the reason(s) is(are)
INTERNAL or EXTERNAL to the object itself; the very same scenarios (a,b, and c, from proposition #7) would apply; the only difference would be that any multiple reasons, as a collective whole, would be identical to the object itself.


Proposition #8: Any uncaused cause will necessarily be identical with existence itself.

Proof: By proposition #7, any uncaused cause is identical to its own existence. In addition, all contingent objects have existence which is not theirs by nature; despite temporal illusions to the contrary, no contingent object is "given" existence in any essential way, as if it were somehow given existence apart from its cause (ref: Proposition #2).
A contingent object is no less contingent (i.e. dependent on its cause for existence) during any subsequent point in time than it is at its temporal beginning.

Since the sum-total of contingent existence (as reflected in the sum-total of existing contingent objects—we can call it “C”) is within (and "borrowed from") the uncaused cause (since no contingent object has existence in and of itself, but relies on the existence of its cause), and since the totality of existence (we can call this “T”) entails the union of contingent existence (“C”) and intrinsic existence (we can call this “I”); then that totality (“T”) of existence is identical to the uncaused cause itself (see Proposition #7).

Objection #7: Why can there not be several uncaused causes, which would entail SEVERAL sources of existence (rather than just one)? Wouldn't that undermine the equivalence of "uncaused cause" and "existence"?

Reply #7: This question anticipates Proposition #10; but again, it is beside this particular point. If, hypothetically, there were several uncaused causes, then it would still be necessarily true for the uncaused causes, as a collective, to be equivalent to existence as such, given the equivalence between an uncaused cause's reason and its existence, and given the utter lack of existence contained per se in the non-intrinsically-existing objects.


Proposition #9: Any uncaused cause (i.e. whose essential existence is intrinsic) must be unlimited in all respects.

Proof: Limitation, per se, is the extent to which something does not exist. For example: that which exists as a 4'-radius sphere does not exist beyond that radius; or, that which occupies 1 cubic foot of space at point X does not exist thusly at any point Y beyond the boundaries of that enclosed space; etc. That which exists in every way would necessarily be unlimited in every way; and that which was utterly unlimited would enjoy the fullness of existence.

Here is an alternate way to demonstrate the same idea: it is true that all "limited" objects must be caused, since any object which is limited cannot be identified with existence as such, and cannot contain its own reason for existence (as would be necessary with any uncaused object--see Props. #7,8). This establishes the conditional statement: "that which is limited, is caused." Given that this is a true statement, then its contrapositive must necessarily be true, which
reads: "that which is uncaused, is unlimited."


Objection #8: What of the aspects of reality which do not seem to imply lack? You wouldn't say that a male was limited in his existence to the extent that he wasn't female, would you? If so, then which one out of a man and woman would be limited by not being the other gender? In short: what about the cases where two seemingly "existing" things are mutually exclusive?

Reply #8: Again, as per reply #2, it is not the purpose of this proposition to make affective or subjective judgments about any given object. It is certainly true that a male simply does not have the faculties of a female, and vice versa... but any criticism of that state of affairs remains a subjective one; the fact that a male lacks female attributes, etc., is still a fact. It does not mean to imply that a male is not functioning properly by failing, for example, to be female. It merely shows one of many evidences that prove the limitation and non-universality of any contingent object.

In the case of a square and a circle, for example, one might say that a square could be a perfect square--and a circle could be a perfect circle--without containing the attributes of one another. While this is true, it is quite beside the point; save to give further proof of the limitations and non-universality of both.

It might help to consider the following: any order of being which holds mutually exclusive possibilities must be limited, by definition. There is no question of any circle, no matter how large, being unlimited in all respects, for example; its "circleness" requires a center and constant radius, or else it ceases to be a circle altogether. Its very
definition requires limitations.


Proposition #10: An uncaused cause cannot admit of plurality of nature (i.e. there cannot be more than one uncaused cause).

Proof: It is a truism in logic that any two objects which fail to differ in any way whatsoever are, in fact, the same object. If we can show that any two hypothetical "uncaused causes" do not differ in any way whatever (or if we can show directly that the two are identical), then that will suffice to show the uniqueness and singularity of the uncaused cause. (Note that this method can be extended to cover an arbitrary number of uncaused causes.)

Suppose (A) and (B) are uncaused causes. This implies that (A) is identical with existence (E) as such, and (B) is identical with existence (E) as such. It cannot be true that two objects which identity with existence, per se, admit of any differences whatever. Thus, since A = E and B = E, we conclude that A = B.


Conclusion: Here is the argument, thus far:

1) No object can be its own cause.
2) Causation implies change, and vice versa.
3) Any uncaused object is necessarily eternal.
4) Any uncaused cause is equivalent to existence per se.
5) Any uncaused cause must be unlimited and unique.
6) Our universe contains examples of changeable, non-eternal objects.
7) Ergo, an uncaused cause is required, as per #3-5.

Since it is self-evident that there exist both instances of change and
limited (i.e. contingent) objects, there must necessarily exist a cause
for these (i.e. to cause the change, and to be a source of existence for
the contingent objects) which is itself uncaused, eternal, unlimited,
unique, and identical to existence itself... and this we call God.


paladin said...

Wow... my name, up in lights! :)

One quick qualifier to readers: feel free to tear apart the "proof" as you will; my Faith isn't based on it, or anything! If so, I'll just tweak it (or scrap it and start over). I put it together for amusement value and intellectual exercise... though if it helps someone, praise God! Heaven knows, the think has been "tweaked" a few dozen times, already...

In Christ,

paladin said...

:) Myron, thanks for saving my absent-minded, space-cadet bacon again, with your timely editing!

"The guy can do a mean math problem... but boy, try to get him to remember to take out the garbage, remember where he left his keys, or keep track of where he saved the 10-20 scattered notepad (or sticky note) notes that his scattered brain uses when writing these proof things..."

In Christ,

Sarah said...

I did eventually make it through this post...

I'm NOT a math lover, hence all the propositions, proofs, and all those (a)=(b) scenarios DID result in some serious headaches (NUMEROUS cups of chai were consumed in the process in an attempt to maintain sanity); this was a little hard for me to wrap my mind around.

That said, I did agree with the final summation of facts and conclusion.

I arrived at the same conclusion about the existence of God, albeit through a slightly less scholarly route (I need more "real-life" analogies as opposed to mathematical proofs!).

But Brian, my hat goes off to you for attempting and completing this task :)

Myron said...

Hey, sorry Sarah, this sat in my inbox for a while - I thought I had clicked "publish", but I just logged in today and it was still sitting there unpublished.

My comments on this post will be available next weekend.