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Switch to Forum Live View Hatcher's Proof of the Existence of God
3 years ago  ::  Sep 28, 2011 - 5:01AM #1
Lilwabbit
Posts: 2,921

Late logician, mathematician and philosopher William S. Hatcher (1935-2005) formulated a novel proof of God's existence based on contemporary first-order logic. As a former student of formal logic I had once the privilege of listening to his formulation first-hand.

Hatcher's proof is unique on several counts. Unlike virtually all earlier arguments for the existence of God, it does not regard the notion of inifinite regression of causes (in time) as absurd. The notion is, in fact, irrelevant to Hatcher's proof. Secondly, the proof addresses, as Hatcher terms it, a "minimalist" concept of God. He is essentially making a case for the existence of a single self-caused cause of the universe that is not the universe itself. Some may reasonably question whether "a single self-caused cause of the universe that is not the universe itself" qualifies as "God". Many an atheist may not have any issue with such a "God" but would rather question the label. A theist, on the other hand, would recognize that a "single self-caused cause of the universe that is not the universe" can be logically translated into religious terminology as "the One and Self-Subsisting Creator of the universe". Rather than getting carried away with the usual squabble between atheists and theists, Hatcher's proof may in fact offer a unique common ground: a well-reasoned possibility of the existence of a single self-caused cause of the universe that is not the universe itself -- call it what we may. After establishing a common ground, the atheism-theism debate could move on to other areas of contention: does this single self-caused entity have other properties such as intelligence and love? How can anything other than a supernatural (metaphysical) entity be self-caused? What is the relationship of such a single self-caused universal cause with the universe? Et cetera.

Like with all logical proofs, Hatcher's formulation is based on axiomatic premises and, further, draws on a simple and unproblematic ontological assumption. He propounds three axiomatic premises and the objective empirical observation that "something exists." As Hatcher explains, these premises are "empirically grounded" as well as unproblematic to most atheists with a background in logic and rigorous scientific inquiry. He calls these three premises the principle of sufficient reason (which is not fully identical with the famous PSR as articulated by Leibniz centuries earlier), the potency principle and the principle of limitation. As with all logical proofs, a rationally well-founded rejection of any one of these premises or the empirical observation that "something exists" renders the proof invalid. Hatcher however frequently stated as having never read neither heard a rationally well-founded rejection of any of the three premises nor a well-founded argument against the unmistakable observation that "something exists".

In the following I have included a more complete and narrative-style formulation of Hatcher's proof. For those who are unfamiliar with formal logic, I am more than happy to clarify Hatcher's formulation. The logic of the proof itself is far more rigorous and logically sound than any of the earlier and fuzzier "logical" proofs advanced in earlier centuries. Should anyone prove his/her intellectual prowess in finding a palpable error in Hatcher's logical deduction, I would be more than curious, as well as ready to examine their critique on purely logical grounds.

With kind regards,

LilWabbit

***

The Existence of God

The following is a excerpt from pages 82 through 86 of "Love, Power, and Justice: The Dynamics of Authentic Morality" by William S. Hatcher.

Copyright 1998 by William S. Hatcher

Chapter 3, section 4

The Existence of God

Our purpose in undertaking this study is to establish the existence of God on a totally objective basis, as a necessary logical feature of the overall structure of reality itself.

By the term reality we mean the totality of existence, everything there is. A phenomenon is some portion of reality, and causality is a relationship between two phenomena A and B, which holds whenever A is a cause of B (symbolized A → B). This means that A contains a sufficient reason for the existence of B. More generally, everything B that exists must either be preceded by a cause A different from B (A → B and A ≠ B), or else contain within itself a sufficient reason for its existence (B → B). In the former case, we say that B is caused or other-caused and in the latter uncaused or self-caused. The principle that every existing phenomenon must either be caused or uncaused (and not both) is the principle of sufficient reason.

Another basic relation between phenomena is the relation of part to whole: we write A ∊ B whenever the entity A is a component of the system (composite phenomenon) B. Notice that A may also be composite, but must be an entity (not just an arbitrary system) in order to be a component of another system B (whether the latter is an entity or not). Two systems (whether entities or not) may also be related by one being a subsystem of the other. We write A ⊂ B whenever A is a subsystem of B. This means precisely that every component E ∊ A is also a component E ∊ B. For example, a single leaf would be a component of a tree, but all the leaves together would constitute a subsystem of the tree. If E is either a component or subsystem of B, then E is a part of B.

From the strictly logical point of view, the defining or characteristic feature of an entity A is that A can be a component of some system B, A ∊ B. In other words, entities are components while systems have components (they are composite phenomena). Moreover, some systems also are components. Thus, with respect to composition, we have three distinct categories of phenomena. A phenomenon may be noncomposite (have no components), in which case it is necessarily an entity. A phenomenon may be a composite entity, in which case it both has components and is a component. Or, a phenomenon may be composite without being an entity, in which case it has components but can never be a component.

Causality and composition are related to each other by the obvious potency principle, which says that if A → B, then A must also be a cause of E, where E is any component or any subsystem of B. In other words, to be a cause of B is to be a cause of every part of B -- its components and its subsystems. This means that our notion of causality is that of complete cause (philosophy recognizes several different notions of "cause").

Finally, the existence of a whole system obviously cannot precede the existence of its components (rather, the constitution of a whole obviously supposes and depends upon the prior or simultaneous existence of its components). We thus have the principle of limitation, which asserts that, for every composite phenomenon A, A cannot be a cause of any of its components.

It follows immediately from these principles that no composite phenomenon can be self-caused, for suppose A → A where A is composite. Then, by the potency principle A → E, where E is any component of A. But this contradicts the limitation principle.

In fact, from these valid principles of causality and composition, we can logically deduce the existence of a unique, noncomposite, self-caused, universal cause G. This entity, whose existence we prove, is God (by logical definition). This God is not some abstract figment of our imagination but the actual, ultimate cause of all existing phenomena and entities, the origin of all being.

Since the proof is easy, we give it here in full. However, the reader who already accepts and understands the existence of a universal uncaused cause (i.e., God) can safely skip the details of the proof without diminishing his or her understanding of the subsequent sections of the course.

Let V be the collection (universe) of all existing entities. Since V is composite it cannot be self-caused (see above) and so must have a cause G (different from V itself). Thus, G → V, G ≠ V Moreover, every existing phenomenon A is either an entity, and thus a component of V, or else a system all of whose components are in V -- in which case A is a subsystem of V. Thus, G is either a component or a subsystem of V. But, in either case, G → G by the potency principle. Thus, G is self-caused and hence noncomposite (no composite can be self-caused as shown above). Finally, since G → V and every phenomenon A is a part of V then by the potency principle, G is a universal cause (the cause of every existing phenomenon, including itself).

Finally, we show that G is the only uncaused phenomenon, for suppose there is another such phenomenon G'. Then G → G' (since G is a universal cause). But since G' is self-caused it cannot be other-caused by the principle of sufficient reason. Thus, G = G' and the uniqueness of G is established.

This clear, logical proof of God's existence and uniqueness is due in its essentials to the great Muslim philosopher Avicenna (ibn Sina, 980 - 1037). By making use of a few notions of modern logic, our presentation here somewhat simplifies Avicenna's exposition.

The relationships of causality and composition, and the logical connections between them, give us the knowledge of God's existence. This naturally raises the further question of God's nature (what is God like?). To answer this, we need now to consider the value relation ≥, mentioned in chapter 1, and which only holds between (i.e., is meaningful for) entities. To say that the entity A is as valuable as the entity B, A ≥ B, means that A is either more refined (higher) -- or at least no less refined -- than B.

For example, in the physical world, humans are higher (more complex) than animals, animals higher than plants, and plants higher than minerals (inorganic substances)....
 
The fundamental logical connection between causality and value is given by the refinement principle: where A and B are entities, if A → B then A ≥ B. This means that any causal entity must be at least as refined as its effect. Since God is the unique universal cause, God is also the most refined entity in existence.

In particular, humans have the positive qualities of consciousness, intelligence, feelings, and will. Moreover, although each human soul has these qualities to a specific, finite, and limited degree, there is no limit to the degree that these qualities can exist generally in human beings. (For example, no matter how intelligent a given human being may be, it is possible for another human to be more intelligent.) Since God is the unique cause of every human being, God must have these positive qualities (and undoubtedly others) to a degree greater than every limited (finite) degree, thus to an unlimited (infinite) degree. Hence, God is infinitely conscious, infinitely knowing, infinitely loving, and infinitely willing (all-powerful). In fact, since God is the only Being whose existence is absolute (i.e., uncaused), God has these qualities to an absolute degree.

Thus, the logical answer to the question "what is God's nature?" is to say that "God is like us except for possessing none of our limitations and all of our positive qualities to an infinite degree." Of course we cannot really imagine what it means to possess such qualities as consciousness or will to an infinite degree, but the refinement principle does nevertheless give us at least a minimal, purely logical notion of God's nature.

***

"All things have I willed for you, and you too, for your own sake."
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3 years ago  ::  Sep 28, 2011 - 10:22AM #2
F1fan
Posts: 11,825

Sep 28, 2011 -- 5:01AM, Lilwabbit wrote:


After establishing a common ground, the atheism-theism debate could move on to other areas of contention: does this single self-caused entity have other properties such as intelligence and love? How can anything other than a supernatural (metaphysical) entity be self-caused? What is the relationship of such a single self-caused universal cause with the universe? Et cetera.



Many of the debates are along the lines of the nature of the various gods claimed to exist.  I don't see many theists satisfied with the idea that a god exists without the attributes they ascribe to it.  They would surely take what they can get if it comes down to a god existing versus no god.  We have to be careful what is called a god since many theists are eager to abduct any implication of a god and expand it into their own version quickly.  If there is some natural force there has to be some meaning to the word "god" if it is going to be used as a label.  The self-caused cause may be little more than a spark that sets off a keg of TNT.  The effect is huge, but the spark is quite insignificant compared to the result.



In particular, humans have the positive qualities of consciousness, intelligence, feelings, and will. Moreover, although each human soul has these qualities to a specific, finite, and limited degree, there is no limit to the degree that these qualities can exist generally in human beings. (For example, no matter how intelligent a given human being may be, it is possible for another human to be more intelligent.) Since God is the unique cause of every human being, God must have these positive qualities (and undoubtedly others) to a degree greater than every limited (finite) degree, thus to an unlimited (infinite) degree. Hence, God is infinitely conscious, infinitely knowing, infinitely loving, and infinitely willing (all-powerful). In fact, since God is the only Being whose existence is absolute (i.e., uncaused), God has these qualities to an absolute degree.



The problem with this is what I warned about: people ascribing attributes to a force labeled "god" with specific traits.  Yes, an intelligent human has to concede that there might be a more intelligent human out there.  But humans actually exist.  Intelligence can be measured.  So to leap to a god (which may just be an insignificant spark) into a creator of all humans, is infinite, still exists, has positive qualities, is conscious, knows anything, is loving, and willing is completely unjustified.  I thought the point of this was to present a case that a general god MIGHT exist as a cause. 

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3 years ago  ::  Sep 28, 2011 - 10:53AM #3
Crowhed
Posts: 1,625

Sep 28, 2011 -- 5:01AM, Lilwabbit wrote:



For example, in the physical world, humans are higher (more complex) than animals, animals higher than plants, and plants higher than minerals (inorganic substances)....




Humans are animals. We are not more complex- we are more successful than any other animal at surviving in most ecological ranges from the tropics to the arctic. We have a complexity of intelligence, but to say that makes us more complex is anthrocentric.



 
The fundamental logical connection between causality and value is given by the refinement principle: where A and B are entities, if A → B then A ≥ B. This means that any causal entity must be at least as refined as its effect. Since God is the unique universal cause, God is also the most refined entity in existence.




Equivalence. "Entities" here means simply things that exist, and below it turns into 'sentient beings'.



In particular, humans have the positive qualities of consciousness, intelligence, feelings, and will. Moreover, although each human soul has these qualities to a specific, finite, and limited degree, there is no limit to the degree that these qualities can exist generally in human beings. (For example, no matter how intelligent a given human being may be, it is possible for another human to be more intelligent.) Since God is the unique cause of every human being...




A linguistic quick change. If it wasn't intentional (doubt that), then it is an instance of the stupidity of using the word 'god' in these kind of arguments in the first place. It always ends up with the same sort of conclusion;



Thus, the logical answer to the question "what is God's nature?" is to say that "God is like us except for possessing none of our limitations and all of our positive qualities to an infinite degree." Of course we cannot really imagine what it means to possess such qualities as consciousness or will to an infinite degree, but the refinement principle does nevertheless give us at least a minimal, purely logical notion of God's nature.



We are the indication that God exists, and that God is sentient, and sentient in kind to our sentience, just better.


That's not logic, it's word play. 

“We are all without god – some of us just happen to be aware of it.” Monica Salcedo (Does anyone know who this is?)
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3 years ago  ::  Sep 28, 2011 - 10:55AM #4
Blü
Posts: 25,182

Lilwabbit


Here's my paraphrase, which I made to help me understand what you were saying - let me know if I got anything relevant wrong.  To this I've added my comments in indent.


 


'Reality' means everything that is.

A phenomenon is something real. 


[I assume A and B are always phenomena.]


If A is a cause of B, that relationship is 'causality'.

In the causal relationship A is said to contain a sufficient reason for the existence of B.


[But that would only be true if A were the sole cause of B.]


Every caused real thing B must EITHER be preceded by a cause A


[But again this suggests A is the sole cause, whereas it needn't be.]


OR else contain within itself a sufficient reason for its existence.


['Uncaused' is here said to be the same thing as 'self-caused'.  That can't be right, since no causality (as defined) can occur with only a single entity - 'self-caused' is therefore not a valid notion.]

['Uncaused' can't be a reason for existence, merely a description - it makes no sense to say, B exists because it is uncaused.  Therefore 'uncaused' can't be part of 'sufficient reason'.]


A ∈ B means A is one of the more-than-one components of B.

In this relationship, A is said to be an 'entity' of B, and B is said to be a 'system'.
 
A ⊂ B means system A is a sub-system of system B (so every component entity in system A is a compenent entity of system B).

Thus phenomenon A may be 'non-composite' or it may be a system and have components or it may  a subsystem and so both be a component and have components.

The potency principle says that if  A → B ['A causes B'] then A → E where E is a component entity or subsystem of B.

A system cannot pre-exist [any of] its components.  Thus A can't be the cause of any component of A (the limitation principle).

Thus no composite A can be self-caused.


[But as I noted above, under the definition of 'cause', nothing can be self-caused at all, composite or not. 


We also meet the notion here that the cause must pre-exist the effect - a second reason why nothing can be 'self-caused', composite or not.]



V is the set of "all existing entities".


[An entity is a phenomenon which is also a component.  Thus this implies that there's another set of the phenomena which are not components.  I wonder if V is meant to be the set of "all existing phenomena" instead.]


It can't be self-caused.


[Yes, both because of the limitation principle and because nothing can be self-caused for the two reasons previously noted.]


So V must have a cause, phenomenon G ie G → V.


[But any such cause - any G - must be external to V.  However, as defined, there's a whole set of phenomena which are not components in which case we have an unlimited range of Gs.


Alternatively, if (as I suspected) V contains ALL phenomena then EITHER G ceased to exist on the causing of V OR G is now included in V.


Each phenomenon A is either an entity [component of a system] or else a subsystem of a system. In either case, the system is V.


"Thus, G is self-caused and hence noncomposite"


[Except that nothing can be self-caused for the two reasons previously noted AND 'uncaused' can't be a reason for existence.]


"G is a universal cause"


[We need the clarification about 'entities'.  If it means what it says then we have unlimited Gs in the set of phenomena that aren't components.  If it means all phenomena then G has either ceased to exist or has become a component.]


[And I've already shown that the 'sufficient reason' argument fails.]


 


What have I missed?

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3 years ago  ::  Sep 28, 2011 - 12:47PM #5
redshifted
Posts: 2,283

Can an entity be logically deduced into existence?

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3 years ago  ::  Sep 28, 2011 - 9:24PM #6
JCarlin
Posts: 6,952

Sep 28, 2011 -- 5:01AM, Lilwabbit wrote:

Late logician, mathematician and philosopher William S. Hatcher (1935-2005) formulated a novel proof of God's existence based on contemporary first-order logic.


If you follow this logic diligently and believe fervently in its premises, you may be able to create a satisfactory God.  Prayer also helps. 

J'Carlin
If the shoe doesn't fit, don't cram your foot in it and complain.
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3 years ago  ::  Sep 28, 2011 - 10:13PM #7
amcolph
Posts: 17,986

Sep 28, 2011 -- 12:47PM, redshifted wrote:


Can an entity be logically deduced into existence?




Now you see why Philosophical Realism is important to many theists.


If logic exists objectively as part of the structure of the universe, then yes.


If logic is but a refinement of the process of human reason, then no.

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3 years ago  ::  Sep 28, 2011 - 10:34PM #8
mountain_man
Posts: 40,219

Sep 28, 2011 -- 5:01AM, Lilwabbit wrote:

Late logician, mathematician and philosopher William S. Hatcher (1935-2005) formulated a novel proof of God's existence based on contemporary first-order logic. ....


It can't be logic when it's based on a logical fallacy; an a priori assumption. He's assuming a god exists and is twisting "logic" to fit his assumption.

Dave - Just a Man in the Mountains.

I am a Humanist. I believe in a rational philosophy of life, informed by science, inspired by art, and motivated by a desire to do good for its own sake and not by an expectation of a reward or fear of punishment in an afterlife.
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3 years ago  ::  Sep 30, 2011 - 5:36AM #9
Lilwabbit
Posts: 2,921

Greetings F1fan,


Sep 28, 2011 -- 10:22AM, F1fan wrote:


Sep 28, 2011 -- 5:01AM, Lilwabbit wrote:


After establishing a common ground, the atheism-theism debate could move on to other areas of contention: does this single self-caused entity have other properties such as intelligence and love? How can anything other than a supernatural (metaphysical) entity be self-caused? What is the relationship of such a single self-caused universal cause with the universe? Et cetera.



Many of the debates are along the lines of the nature of the various gods claimed to exist.  I don't see many theists satisfied with the idea that a god exists without the attributes they ascribe to it.



Perhaps the issue is not so much whether or not the theists are satisfied with a minimalist concept of God as advanced by Hatcher, but that Hatcher offers the barest minimum of attributes for something to be reasonably called God. We, the theists and the atheists, may be able to find some common ground in accepting that these attributes could reasonably exist in one entity. Namely the attributes of a "single" entity (i.e. attribute of "oneness") that is "uncaused" (i.e. attribute of "self-subsistence") and a "cause" of all the other entities (i.e. attribute of "creator"). Hatcher seems to show that by accepting rather neutral premises it logically follows that such an entity exists. I find his reasoning interesting in the least.

Sep 28, 2011 -- 10:22AM, F1fan wrote:

In particular, humans have the positive qualities of consciousness, intelligence, feelings, and will. Moreover, although each human soul has these qualities to a specific, finite, and limited degree, there is no limit to the degree that these qualities can exist generally in human beings. (For example, no matter how intelligent a given human being may be, it is possible for another human to be more intelligent.) Since God is the unique cause of every human being, God must have these positive qualities (and undoubtedly others) to a degree greater than every limited (finite) degree, thus to an unlimited (infinite) degree. Hence, God is infinitely conscious, infinitely knowing, infinitely loving, and infinitely willing (all-powerful). In fact, since God is the only Being whose existence is absolute (i.e., uncaused), God has these qualities to an absolute degree.



I thought the point of this was to present a case that a general god MIGHT exist as a cause. 




You would be right in stating that the last 5 paragraphs of the cited proof in fact move on to a further discussion on other attributes of God and outside of the scope of the proposed "minimalist" God. Call it an "editorial glitch" on my part. Indeed, they should not be read as part of the actual proof in this discussion, but rather represent further considerations.

"All things have I willed for you, and you too, for your own sake."
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3 years ago  ::  Sep 30, 2011 - 5:53AM #10
Lilwabbit
Posts: 2,921

Hi there Mountain Man,


Sep 28, 2011 -- 10:34PM, mountain_man wrote:


Sep 28, 2011 -- 5:01AM, Lilwabbit wrote:

Late logician, mathematician and philosopher William S. Hatcher (1935-2005) formulated a novel proof of God's existence based on contemporary first-order logic. ....


It can't be logic when it's based on a logical fallacy; an a priori assumption. He's assuming a god exists and is twisting "logic" to fit his assumption.




Could you point out which one of Hatcher's assumptions is a priori (preceding experience) or otherwise unacceptable on account of reason? Could you also point out where Hatcher first assumes God exists and then twists logic to fit his assumptions? Finally, could you give a credible example of a proof based on first-order logic that is not based on any a priori premise? Then let us review again whether or not your criticism hits the target.


As I said in the beginning, the main issue with Hatcher's proof is whether its premises are reasonable or not. Not whether the logic is sound or not.


I think his proof is pretty straight-forward and there is nothing underhanded or crafty in his formulation. I've met him twice and he came across a humble and honest man. One who is acutely aware of the flaws in most "proofs" for the existence of God as well as the logical limitations in his own proof.


With kind regards,


LilWabbit

"All things have I willed for you, and you too, for your own sake."
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