Interesting. Where do you get the idea that there are “greater beings of love” or god(s)? Are they necessary for your system, inspired by traditional philosophers, or based on your own observations? Seems similar to the Buddhist Mahayana notion of “Bhodisattvas”.
If you like this sort of mathematical play, you may well enjoy Hofsteader’s (sp?) book “Godel, Escher, Bach: an Eternal Golden Braid”. Fun stuff.
My own major influences are Chuang Tzu, Spinoza (to the extent that he is readable), personal observation and epiphanies.
I have never been convinced that any supernatural beings exist - be they gods or otherwise - outside of our mythologies and minds. But there is always a first time.
My own notion of “god” is that he, she or they are purely human creations - a natural focus for the religious impulse that is a part of being human. If a person has an epiphany, he or she is very likely to claim the interaction of the supernatural (absent a better explaination) - hence the origins of most religions in a single mystic or prophet, and usually in some sort of mystic episode (Jesus in the desert, Paul on the road to Damascus, Moses face to face with god, Mohammed in the desert, Buddha under the bhodi-tree [although that was not exactly a religion], etc.). In other words, it is based on experience and how that experience is understood.
Later, once the initial mystic/philosopher/prophet is gone, their followers base their notions on the written or spoken word, sometimes based on (confirmatory) experience (as in the Christian mystics of the middle ages). As people grow more and more concerned with reason, logic and consistancy, they turn away from the written word and come up with (more or less convoluted) logical and mathematical proofs for what had originally been based on experience and the written/spoken word.
In my opinion, one has to at some point re-visit the original experience, and try to see it for what it really was if possible. Obviously, no-one can go back in time and talk to Jesus, Mohammed etc., so there will always be controversy … but if epiphanies are a relatively normal thing, one can draw conclusions.
I
would be interested in seeing those cites from
Descartes and Luther.
OK, you’ve made an assertion, but it is one that plays
into another argument against monotheism. Namely,
that there is no test for omnipotence. That
is, no matter what act of power a being performs,
there is no way to be sure that another being could
not perform the same act. Hence, even if we should
agree that God, as you say, can violate the rules of
logic, there is no proof that other, similarly
powerful beings can do the same. At any rate, let’s
look at your assertion a little more closely.
One, it is not made by
man–it is perceived by man. Two, God cannot disobey
the rules of logic because we perceive that they are
inviolable.
When I say the
contrary, I am not making a gratuitous assertion, but
rather am asking to perceive, directly, that God could
not create a universe in which 2 + 2 = 5 but all else
was the same. It is an absurdity, yes, a
contradiction.
Now you assert that he can–but this is a gratuitous
assertion; that is, you have no basis whatsoever for
making it. It is a statement of faith, nothing more.
Now you may say that faith is what God is all about.
Very well. And I’ll say that you have your faith, and
St. Thomas had his, and Bid Laden has his. The world
of gratuitous assertion can be a very lovely or
hideous place, depending upon the asserter.
Faith?
No. Since any “proof” requires the law of
contradiciton to begin with.
Intuitively speaking, this is
absurd. It would seem that the essence of God could
be nothing in particular, if absolutely nothing were
demanded of that essence.
You have merely
demonstrated a sad fact of human nature: that there is
nothing so absurd that the human mind cannot accede to
it in an animal fashion.
Basically, this comes from information from the afterlife, mediums, testimony by others, etc.
Yes, a great book–I finally need to read it!
Hmm, I too admire Lao Zi and Chuang Zi–great thinkers, or, in any event, great writings.
Me either! I think all intelligences in That Which Is are evolved beings such as ourselves. In the afterlife, beings keep learning and growing without limit.
I don’t disagree with this entirely. We understand things by means of stories and myths. This is just as true of the Myth of Evolution as the Myth of Creation. This is not to say that the MoE is “untrue”–far from it. It’s just that we weave truths, facts into a coherent story. No matter HOW cold and factual a matter is, we still need to tell stories. So the story of God also has a good deal of truth in it–but as new facts appear, we need to build them into the story. We need to tell the truest and best story possible, I think.
Yes, the dark side of this being said person’s feeling/assertion that he has the only truth. It needs to be an axiom of human thought that no one person can ever be completely, exclusively right.
I agree that there has been an evolution here. We just shouldn’t get cocky and think we can ever transcend our tendency/necessity to mythologize, since we can’t.
Yes, I think they are normal. Each entity in That Which Is has a purpose in That Which Is (to further the vector in his/her unique way). To claim that one is the Way, the Truth, and the Life is fine; to claim that only oneself is such is wrong.
I say that the Law of Contradiction is a limitation on the human mind, but does not limit God.
Note the use of the phrase “I say.”
Now, in argument against this claim, I would have to abide by those same rules of pattern and number (which set includes logic and the law of contradiction) mentioned in the OP.
To which, I presume, you would say, “But I’ve already said that God transcends the law of contradiction; and if he can transcend that, then he would transcend whatever logic you have just used.”
But here’s the rub: God is not here to make such arguments: only you are. They are your words, your arguments. Hence, rather than reserving for God the right to ingore the law of contradicition (and any other logical principle), you are in fact reserving it for yourself!
In other words, you are reserving the right for yourself to trump any claim back up by facts and reason simply by saying, “I/God say otherwise.” Sir, I assure you, you possess no such right!
For I can further add, as you have said yourself in the bolded quote above, that the law of contradiction is indeed a limitation on the mind of man. Consequently, what it might mean for God to transcend this law is completely beyond your comprehension, and, being so, is inappropriate as a term in your argument.
That is, if you were to say
God can transcend the law of contradiction.
it is equivalent to saying
**God can ----- **.
Until you can yourself understand “transcending the law of contradiction” (which you yourself admit you cannot), you cannot possibly know how to use that phrase correctly in a sentence.
Aeschines, I greatly value your insights and respect your position. You have shown that Thomistic monotheism is incorrect. As a Lutheran, I already agree.
It may seem that I am guilty of mere gratuitious assertion. But, in fact, nothing I have said proves (or attempts to prove) that monotheism is correct. You took upon yourself the assertion that monotheism is incorrect, and all I did was try to show that your argument is unsuccessful. The burden of proof appears to be yours.
I am not an ignorant, antirationalistic, fideistic fool. I merely start out with presuppositions and methods that differ from yours. While I don’t expect to convince you, I hope that you will take my views into account if it helps you to refine the argument for your position.
I’ll have to get back to you on this tomorrow.
I concede that there is no test by which we could recognize omnipotence. However, this does not prove that omnipotence is impossible. (It merely proves that omnipotence, if it exists, cannot be observed by humans.) Monotheism still stands.
I will grant that either (1) God created the laws of logic, which we subsequently perceive, or (2) God created us with minds that cannot conceive of things any other way. Either way, God is sovereign. (I just hope that God doesn’t change the laws of mathematics on the day of my qualifying exams. )
Anyway, formal logical systems are constructed by men. They are all “valid” because they define their own validity. They differ as to strength, weakness, and even results. A therorem proven true in one system can be undecided or false in another, depending on its initial axioms.
Your observation does not prove your claim that the Law of Contradiction is an absolute truth binding on God. However, it does prove the somewhat weaker claim that the Law of Contradiction is a limitation on human thought (in the Kantian sense of a rule by which we must constitute our world/interpret our experience). The Law is true in the sense that we cannot think of it any other way. I will grant that the laws of logic are inviolable from a human perspective.
Nothing you have said has proven that the perception of limited humans is a restriction on an unlimited God.
It is a circular, personal, subjective opinion to say that the Law of Contradiction is self-evident. But, it is true that you have to start somewhere. Luther would say that the Bible is self-evident, either you get it or you don’t, and needs no proof, so deal with it. Does this convince you? If not, give me the same consideration.
You imply that the truths of mathematics are self-evident. Is the continuum hypothesis intuitively true? Is the Goldbach conjecture self-evident? The axiom of choice seems intuitive, but has extremely counterintuitive implications, such as the Banach-Tarski paradox. Euclid’s parallel postulate: either you get it or you don’t?
Yes, I concede that “2 + 2 = 5” (assuming the standard definition of terms) is an absurdity, a contradiction, and a logical impossibility. However, it begs the question to assume that the Almighty cannot make it true.
Theorem: Not even God can accomplish an absurdity.
Proof: If God were to accomplish an absurdity, he would do something logically impossible. God cannot do the logically impossible because that is absurd, and not even God can accomplish an absurdity.
Slight digression: formally proven theorems like 2 + 2 = 4 experience a five-fold divorce from real, substantial fact.
I. The words of the theorem are defined in terms of atomic, undefined terms. This means that all theorems are ultimately meaningless.
II. Even if they did have meaning, all theorems are proven conditionally: they are true only upon the assumption (“gratuitous assertion”?) of unproven axioms/postulates. This means that the entire building is built on no proven foundation.
III. Even that is not enough. You still need a system of laws of inference such as that of Russell and Whitehead, etc. These laws of deduction (including the law of contradiction) are unproven.
IV. Notwithstanding all of the above, you cannot know that your system is consistent, for Gödel established that no consistent system can prove its own consistency. For all you know, the assumptions in II and III form an inconsistent set, and all theorems are simultaneously true and false.
V. Even if your system is consistent, it is necessarily incomplete (Gödel). There are true statements which are not provable in your system.
My basis for this assertion is the Word of God, of course.
First, intuition is sneaky. I find it intuitive that God exists. Intuitively, God must be sovereign, not subject to anything else. Otherwise that something else would be God. Therefore, God is the author of the universe and its laws.
Yes, I demand a lot from God’s essence. I demand that he be omnipotent. Furthermore, I insist that God is eternal, indivisible, onmipresent, omniscient, perfect in life, goodness, justice, and mercy, etc. Paradoxically, I also demand that God’s essence is consistent with itself.
If this was intended as an ad hominem insult, it needs no response. It seems that a pantheist, who believes all humans are divine, would have more respect for another person.
First, my friend, the “in an animal fashion” locution was one I had edited did we have the ability to do so. The tone did not come out right; I meant no insult. See my thread about dogma, which I call “the great sin of the mind.” It is the willingness to assert without any questioning an entire set of premises, such as, in your case “The Word of God.” This is what I was referring to: a flawed property of homo sapiens, the animal. I did not mean to refer to you in particular. Now, on to our argument.
Emphasis added. Now, there are two problems here:
If we grant that the burden of proof is mine, then I should be allowed, indeed, to prove my claims–which can only be done by applying the rules of logic. Yet you are denying me the very means by which to fulfill what you request by saying that your own assertion is true, logic be damned.
Atheists commonly say that the burden of proof of a God is on him who posits such a God. Contrariwise, he who does not believe is not required to disprove that there is a God. The atheists are correct.
I am making a stronger claim: that, by means of reason alone, we CAN disprove that God as conceived by Jews/Christians/Moslems exists. One proof I have to offer is in the OP.
Even if we grant that that my proof has failed, then the burden of proof that God exists is still on your shoulders.
I have only reason to offer as a proof, for that is what proof means. Reason and logic. As I have said, you have no right (logically speaking) to assert, as a kind of lawyer for God, that God transcends reason. You can make the verbal statement, but you can’t possibly comprehend what you are saying, just as I can say “square circle” (and even conjure some interesting pictures in my mind of circles folding into squares) without the locution “square circle” having any value whatsoever.
It is indeed an interesting argument.
I must fervently disagree. I would say that “God is omnipotent” and “God can do anything” are empty locutions much like “square circle” above. Why? Not only is there no standard of proof for the quality, on the contrary, it is easily proved that no such standard is possible. Hence, “omnicience” is an empty category. You might as well say that God has indeterminate “quality X.”
Now, this might be considered a straw man if were were actually to encounter a being with extremely great power. For example, we encounter a being in shining robes who says he can do anything. We say, Heal the sick. He does so. We say, Make the planet Mars disappear. He does so. I would be impressed and ready to grant, for practical perposes, that this being was omnipotent. For practical purposes.
But we DO NOT encounter such a being, and the argument is NOT a strong man vis-a-vis the abstract concept of God. We are asked (nay, demanded and threatened with hell!) to believe that an entity that we do not encounter possesses “omnipotence,” a quality which cannot, as you admit, be proven. This demand not only defies reason, it tries sorely a reasoning person’s patience and calm.
Where does this need to believe in this imaginary, mythical God come from? I am not referring to basic spiritual longing and aspiration. I am talking about the need/compulsion to believe in THIS God, THIS holy book, THIS set of dogma–reason be damned! No, I cannot comprehend it. I cannot abide it. It is clear that you are arguing from premises that you do not feel free to question. This, my friend, is the dogmatic approach!
Yes, but the truths they reveal or express are not created by men or any other entity.
[quote]
They are all “valid” because they define their own validity.
I would differ as to terminology–“validity” has particular meaning in logic. An argument can be “valid” within a system; a system itself is not “valid.” It is not true, however, that any system of logic can be a vehicle or medium of truth. A logical system must meet certain criteria in order to be accepted by Reason.
Perhaps, but I if you’re implying that no inviolable rock-bottom principles of pattern and number pertain to That Which Is, then I would disagree.
Your logic here implies that we can think about God without thinking. If we agree that we cannot think (correctly) without being bound by the law of contradiction, then it follows that we cannot think (correctly) about God without being bound by that same law. In contrast, you are saying that you can somehow conceive of (think about) God yet somehow avoid this limitation. I agree that it is possible (what I meant about “in an animal fasion,” physically) to write the words “God transcends logic” on a piece of paper and nod in their direction, but this is not the same thing as thinking and understanding. “Square circle” and all that.
Here we return to the burden of proof issues, as you are positing an “unlimited God.” Again, why the compulsion to assert that such an entity exists when reason dictates otherwise?
Mathematics must be this way. Geometry has its undefined terms (undefined!) of point, line, and plane. The human mind has the amazing ability to perceive pure, atomic truth.
Unlike Luther, I am not stating arbitrary dogma. I am simply using reason and asking people to perceive that particular states are true and must be true. You can verify them for yourself. Do you really think Luther’s dogma and logical arguments belong in the same category.
Further, I can see that you are far too intelligent to assert that the contents of the Bible–a lovely, deep, meaningful, and well-written work, yet rife also with ugliness, violence, degradation, and absurdities–is “self-evident.” You are intelligent enough and observant enough to know that there is a wide variety of dogmas in existence on this planet, some quite palatable, others violent and ugly. I trust that you would not care to call Bin Laden’s interpretation of the Koran “self-evident”? Do not take this as a personal insult–I find it genuinely scary that people can do such evil based upon an unquestioning approval of a set of propositions.
It is clear that you are far more erudite in the area of mathematics, and you earn my respect. But you are twisting here. Difficult mathematical proofs are definitely NOT things that the average person can intuit, and most people probably couldn’t even understand them if they tried. But the basic elements of mathematics, upon which such proofs are built, are indeed intuited, and, as atomic or near-atomic truths, they MUST be intuited. (I.e., no proof is possible that 2 + 2 = 4. Rather, proof itself is conjectured upon the elements at work in this equation.)
But you have already conceded that such an Almighty cannot be proved able to make 2 + 2 = 5. Hence, begging the question (which implies an unproved assertion at work) is disingenous.
Your knowledge may trump mine here. Is 2 + 2 = 4 a “theorem”? At any rate…
Really, so all Euclidean geometry is “meaningless”? Ultimately, language itself is based entirely upon intuited or experienced things.
That’s correct: not proven, but rather intuited or perceived. This is the way it MUST be.
Modus ponens, etc. These too are perceived as invioably true.
Very true. But this does not mean that you cannot prove that a system is inconsistent. One flaw found is all it takes. Trust me: one or more flaws has been found in the Bible and Christian teachings.
Yes, and I think that this has vast implications for understanding That Which Is. Namely, being itself could never be bound within finity. Here we can find a truer understanding of what “God” might be: being unrestricted from becoming more than it is. But all being must be bound by the rock-bottom rules of pattern and number.
I find it intuitive that there must be something rather than nothing. I find the notion that one being could create all else from nothing without actually BEING what it creates philosophically untenable
And it sounds as though your religion demands a lot from you in regard to you demands regarding God. Just say “no” to dogma! It’s scary at first, but oh so free afterward!
Sorry about the delay. Not only do I have work for my classes, but I also needed time to research and reevaluate my position. Here’s Descartes but not Luther yet.
“The truths of mathematics, which you call ‘eternal’, were established by God, and entirely depend upon Him, much as do all the rest of His creatures. Actually, it would be to speak of God as a Jupter or Saturn and to subject Him to the Styx and to the Fates, to say that these truths are independent of Him . . . You will be told that if God established these truths He would be able to change them, as a king does his laws; to which it is necessary to reply that this is correct. . . . In general we can be quite certain that God can do whatever we are able to understand, but not that He cannot do what we are unable to understand. For it would be presumptuous to think that our imagination extends as far as his power.” Descartes, Letter to Mersenne, 15 April 1630, in: Elizabeth Anscombe & Peter T. Geach, Descartes’ Philosophical Writings
“God was as free to make it false that the radii of a circle are equal as to refrain from creating the world.” Letter to Mersenne, 27 May 1630
“As for the difficulty in conceiving how it was a matter of freedom and indifference to God to make it true that the three angles of a triangle should equal two right angles, or generally that contradictions should not be able to be together, one can easily remove it by considering that the power of God can have no limits. . . . God cannot have been determined to make it true that contradictions cannot be together, and consequently He could have done the contrary.” Letter to Mesland, 2 May 1644
[Note, it has been subsequently proven that non-Euclidean geometries (in which the sum of angles in a triangle is NOT 180 degrees) are just as consistent as Euclidean geometry. Furthermore, these non-Euclidean geometries are just as consistent with our everyday experience. ]
“I would not even dare to say that God cannot arrange that a mountain should exist without a valley or a sum of one and two which would not be three; but I only say that He has given me a mind of such a nature that I cannot conceive of a mountain without a valley or a um sof one and two which would not be three; and so on, and that such things imply contradictions in my conception.” Letter to Arnauld, 29 July 1648
Aeschines, I am not denying you the use of reason. I am not saying, “It doesn’t matter what you say, God trumps your reasoning.” I believe that reason is a gift from God and, the non-use of reason is a great sin. (This is the big flaw of the fundamentalists, that they read the Bible without thinking.)
However, you must still provide evidence for your view. Now, your OP argument is valid, but unsound. You just have a false premise. Your premise is
The law of non-contradiction applies to God in the same way that it applies to humans.
The burden of proof is on you to prove your premise, and you have not yet given any solid reason to believe it. Why should a human concept be a limitation on God?
You bring up a number of irrelevant ad hominem points: That I’m being dogmatic, I have no right to be a lawyer for God, I have no reason to believe in God’s existence, I have not explained how I arrived at these beliefs, I’m too intelligent to believe, I cannot comprehend my own claims, etc. While I have good responses for all of these, none of these points has any bearing on whether your own OP argument is faulty. It would be a weird universe if the soundness of your attack on monotheism depends on my personal epistemic situation.
Furthermore, the burden of proof is not mine, since nowhere does my argument presuppose that God actually exists! Let me explain: Suppose person A constructs a fallacious argument for the non-existence of leprechauns: “Bill Clinton said that leprechauns do not exist. Bill Clinton is infallible. Therefore, leprechauns do not exist.” Academic integrity demands that person B, without even presupposing the existence of leprechauns, has every right to point out that A’s argument is unsound: It relies on a false premise. Now, whether or not God actually exists, your argument fails if your premise is wrong. In fact the concept of a “limitation on God” is self-contradictory and incoherent. (In this thread, I am not going to prove that God exists. How should I prove God’s existence/omnipotence? Starting from your premises, proof is impossible. Starting from my premises, proof is trivial.)
Your premise is not merely an innocent law of inference (like modus ponens) but a real theological claim. The truth or falsity of your premise will change the entire universe: it clearly requires more evidence.
I won’t be a jerk and insist you prove an infinite regress of premises. You must prove your premise from other premises that most people will accept. If conclusive proof is not possible, at least give an argument why a rational person could believe it. To me, it is reasonable and intuitive that there must be no limits or restrictions on God, who by definition is unlimited and unrestricted. (I am not engaging in mere assertion here. If you try to disprove monotheism, you must interact with the proposiitional content of monotheism: that God is existentially primary, autonomous, not subject to any higher power or thing, and certainly not subject to human opinions.)
What about this premise: The laws of Indiana apply to God in the same way that they apply to humans.
A rational person has every reason to deny both this premise and yours. There is no reason to suspect that laws governing human behavior or thought apply univocally to God’s abilities. The law of contradiction could be a human construct by which we interpret the world.
You have cited “logic” and “intuition” as grounds for your premise.
I. Logic
You say that your premise is a necessary truth of logic. This does not appear to be true. I have never seen any textbook which contains a limitation on God as a fundmental law of logic. It is an arbitrary dogma, a real theological claim. The denial of your premise is “God can violate the law of contradiction.” Now, this proposition is not formally self-contradictory. (It is not of the form “P and not-P.”) You will need to add premises to yield a contradiction. Therefore, your premise is not a necessary truth.
You say that God cannot violate the law of contradiction, because the law of contradiction is “inviolable.” You are begging the question. Before you can say the that the law of contradiction is “inviolable” without exception, you must first demonstrate that not even God can violate the law of contradiction. But, this is the very issue you want to prove. Logic doesn’t help you here. Is that why you rely on intuition?
Formal logic doesn’t create truths. It only links previously accepted statements together to deduce new statements. It only “pushes symbols around on paper.” It does not interact with the underlying meaning/content of the atomic symbols.
You say that I cannot understand what it means to violate the law of contradiction. Yes I can. There is a distinction between recognizing a contradiction (I can do that), and comprehending how a contradiction could possibly be true (I can’t do that).
A formal contradiction is something of the form “P and not-P.” (Let Q = “P and not-P”) The law of contradiction merely says that “Q is false.” Not meaningless, but false. If Q were meaningless, we could neither say that Q is true nor false. Similarly, the statement “Clinton is the current president” is not meaningless, it is false. It does have meaning, and that is how we know that it is false: its meaning does not conform to reality. Though, I can conceive of what it would be like for “Clinton is the current president” to be true.
Given that Q has a meaning, you must give your reasons why God does not have the power to change the meaning from “false” to “true.”
When constructing a logical language, we give rules by which wffs (well-formed formulas) can be distinguished from other strings. Then we give further rules that set apart some subset of the wffs that are called “theorems.” The first set of rules tells us which strings should count as having a meaning. In first-order classical propositional logic (and all others built on it) “P and not-P” counts as a wff. It has a respectable role in reductiones ad absurdum. It does have a meaning. In paraconsistent logics some contradictions can be included among the theorems.
Given a logical system, there are three possibilities: 1. All contadictions are false. 2. Some contradictions are true, and some are false. 3. All contradictions are true. All systems are equally “consistent,” and the choice is arbitrary. All of our “real-world” experience so far fits with either 1 or a subset of 2.
The first category includes the conventional logics, in which a contradiction implies that all statements are true. The second are the paraconsistent logics, in which a contradiction does not imply that all other statements are true. The third category is uninteresting.
You must show that one of the conventional logics is the only valid way of looking at the world.
II. Intuition
Kant claimed that we can never know or perceive things-in-themselves, but only things-as-they-appear-to-us. This seems reasonable, since we can never step outside of our own thoughts and perceptions to “verify” the things-in-themselves. The “necessary truths” of reason only give us insight into our own capacities. They are the way we are “wired” to interpret the world and the principles by which we establish the world of our experience. Kant claims that pure reason enables us to discover only the limits imposed by human understanding. Not insight into the world as it really is, but insights into the means by which we apprehend the world. For Kant, it seems, one must remain “agnostic” about the things-in-themselves, since reason only clarifies the way that we represent the world in our thought. A broadly Kantian framework allows for the complete autonomy of God, or nature, or things in themselves, whatever controls or constitutes the outside world. Reflection upon our own capacities cannot lead us to conclusions about what can and cannot be in itself.
Now the only way we could know about the true nature of God is if he intervenes in this world and tells us the truth. Christians believe that he has done this. (This is not a gratutous assertion, but a central part of Christian monotheism. You are claiming to disprove the entire system, and you must take this into account.)
Piaget showed that many cognitive functions (which I would have thought to be innate intuitive ideas) are a learned development in childhood. Examples are object permanence (the awareness of the existence of objects even when they are hidden from view) and the conservation of volume and area.
Mathematics. You say that the postulates of mathematics are “perceived to be inviolable.” The problem here is that there are arbitrary choices to be made when selecting starting postulates. My examples were intended to show that, between pairs of contradictory postulates, either one yields a consistent and satisfying system. These are not “inviolable.” Each set of consistent axioms forms its own “rock-bottom” foundation. 2 + 2 = 4 is not a rock-bottom truth, it is a theorem derived from the Peano postulates (or related systems).
My examples also show that certain theorems are equally true, yet differ in how intuitive they are. Thus, intuition is not a reliable guide to truth. Same for many results in modern physics, especially relativity and quantum mechanics, which are starkly counterintuitive.
From a technical standpoint, yes, the theorems of math are ultimately meaningless and unproven.
Spinoza, Descartes, Leibniz all built their systems on “intuition.” Yet they are all extremely different. Take any set of equally qualified, well-informed, intelligent philosophers, and they will all disagree. These philosophers lived in the same century in the same world and read all the same books. They knew and understood each other’s arguments. Why did they disagree about what was intuitive? In fact, your appeal to intuition is your downfall. Descartes, a mathematician and the King of Intuition, sincerely believes that God can do what is logically impossible. I am a rational being, and I, too, honestly perceive it to be an inviolable intuitive truth.
Empiricism. J. S. Mill taught that the truths of logic and mathematics are merely well-confirmed empirical truths. They are not necessary truths, but generalizations from innumerable observational experiences. If this is true, then there is no reason to believe these truths apply to God, since we have not been in a postion to test these claims in that setting.
Consider this from a materialist (naturalist/physicalist) standpoint. Our brains evolved to promote survival, rather than discover truth. There is no way natural selection can select for the trait “ability to discern eternal truth.” We were “designed” for certain practical benefits, and pattern recognition is a useful thing. Yet, there is no reason that we can be confident in our truth-discovering abilities. Psychologically, our pattern-recognition faculties tend to overgeneralize, and find patterns where they don’t exist. This is why atheistic materalism is self-defeating. If true, we would not have sufficient confidence to believe that it is true.
Intuition is the bane of empiricists, for there is no evidence. Without evidence, you have no reason to be certain that your intuition makes any true claims about the real world. Your personal, subjective opinion (which you call “intuition”) will not convince others. In fact, it seems that you are possibly bluffing, since you know that you cannot prove the law of contradiction, or prove that an all-powerful God is subject thereto.
Given the above, you must prove your confidence in intuition. I find it hard to believe that we, mere humans created by God, could discover laws to which even he must bow.
I will have to admit that, in a debate on theism from scratch, the burden of proof is on the theist. Thus, I would probably lose. The arguments on both sides are tricky.
I have not found a valid theistic argument that begins with premises an atheist would accept. Aquinas’ Five Ways are atrocious. Some ontological arguments are valid, but an atheist should not believe the premises.
I think the argument from design backfires. The valid inferences are from a perfect world to a perfect designer, or from an imperfect world to an imperfect designer. The deduction from an imperfect world to a perfect creator is a problem.
Rager. Thank you for the post, into which it is clear that you put a lot of work. I wish, however, you had responded more directly to the actual points I made, as I am not more or less required to say the same things over.
Re the Descartes quotes. They are interesting, and I appreciate the references. Still, ol’ D is merely asserting his belief—he offers not evidence or proof of his opinions. In no way convincing.
OK, on to the debate…
It may be that I have a false premise, but you are not stating it correctly. The actual premise is as follows:
We perceive that there are at least some principles of pattern and number that could not be other than they are.
The rest of the argument, stated in brief, is that no matter what God is, if he in fact even exists, he cannot be master over these principles (by virtue of the premise above). He is thus subordinate to them and is NOT existentially primary; which contradicts the version of monotheism held by Jews/Christians/Moslems.
Yes, the premise above is itself unproved. It must, in my view, be intuited directly. I don’t think this is difficult, however. The example which I keep providing is, Could God make a universe exactly similar to ours, but in which 2 + 2 = 5. The absurdity involved here is so great that it almost makes one laugh to think about it. And if we grant that it is absurd, that it is truly impossible, if everything in our mind says a big NO! to it, then it follows that there is at least some principle of pattern and number that is inviolable.
Again, unproven. And I say further, unprovable. You and Descartes clearly believe otherwise. In both cases, I see gratuitous assertions on your and his part. The reason why both of say otherwise is also clear: a faith in a version of God with which certain locutions must be predicated: “omnicient,” “omnipotent,” “unlimited.” As any negation of these locutions is unacceptable to you, in order to preserve them (regardless of their logical or philosophical content), you are willing to challenge your own perception of truth, to the extent that you are willing to concede that God could alter even that which you perceive as unalterable. This is the tail of Faith wagging the dog of Reason.
But you have a certain conception of God, which you have described in this thread. I will say with confidence that your belief that all things are subject to alteration by God violates your very conception of God and Reality. Implicitly. Here is a simple but poignant example.
You say,
Furthermore, I insist that God is eternal, indivisible, onmipresent, omniscient, perfect in life, goodness, justice, and mercy, etc.
Let’s take another old but effective argument against monotheism and apply it to the problem. The argument goes like this: If God himself determines that which is good, then whatever God wills to be considered good must be considered so. Thus, if God were to say that killing the innocent is good, then it would be so. But this is absurd, since if killing the innocent is “good,” then the word “good” as we employ it has no meaning.
This, in general, is a good argument, and the above is just a crude expostulation of it. But if grant your premise that God has utter dominion over everying, including logic and number itself, then it follows that what we call “good,” including all the qualia we associate with the concept (warm, fuzzy feelings; the conviction we are on the side of the right; etc.) are completely arbitrary creations of God. Hence, it makes no sense whatsoever to say that God is good in some fundamental way, but only that goodness is an arbitration creation by him, just as 2 + 2 = 4 is.
We can carry this to further absurdities. You say that God’s omnipotence is such that he could make a world in which 2 + 2 = 5. Descartes says in your quotes that God could make it such that two radii would not equal the diameter of the circle. Now, these are truths of math, and their contradiction is not ugly or unpleasant.
You said that God could make the universe absolutely anything he wanted it to be, correct? OK, God could make the universe such that….
Jesus Christ decides not to save the world; he damns all of mankind to hell.
Jesus decides not be the savior and instead becomes an evildoer. God then punishes Jesus for his rebellion.
God announces from the sky in the year 2004 that he made an error: Satan is actually good and from now on he will have dominion over the universe. Satan then destroys the universe.
Or, since God can do anything he makes himself cease to exist but the universe remains without him.
Or God trades place with Satan, and Satan is now God.
Jesus isn’t the savior; instead, Adolf Hitler or Idi Amin, etc. etc., is.
There are 11 Commandments, and one of them says, “Commit at least one hideously evil act a day.”
The world is exactly as it is, but God damns good Christians to hell anyway, just for kicks.
These are all idiotic examples, even blasphemous (and I intend no insult!). But their very absurdity should illumine the contradiction implicit in your statement that God is completely free to make the universe anything, including contradictory.
And so on. God, since he is unlimited, could have made it so. Is that correct, dear friend? Does this fit with your vision of God’s omnipotence? You say that God could make 2 + 2 = 5. Although we cannot comprehend how it could be so, God could do it! Well, I cannot comprehend how God could (or would) do Nos. 1-8 above, but, based on your reasoning, I must assume it could be true.
Returning for a moment to my pantheistic system, the origin of good and evil is no problem, since the principle of goodness arises from the same principles of pattern and number. It is NOT arbitrary, which conforms to our feeling that the nature of the good is not an arbitrary creation.
Nor I, since I am merely asserting (as a premise, as you correctly say), that whatever God is, he cannot violate the rules of pattern and number. You say I am arguing fallaciously—no, I’m not. For you are assuming that God is some known quantity, about whom certain qualities can with certainty be predicated. I am assuming no such thing.
It is only self-contradictory if you assume a particular definition of God, which I do not.
Now, my itch-meter is telling me that you are going to come back and say that I am assuming the monotheistic definition of God in order to make my argument. Do not make this error. I am saying, rather, that whatever definition of God that a monotheist should provide, that definition may not include God’s dominion over pattern and number, since I assert (without proof, since proof is impossible), that these principles are inviolable.
I trust this difference will be clear.
Ah, but once we see that some restrictions must apply (the rules of pattern and number), then we see that this definition of God is untenable. That was my original argument!
Straw man + equivocation, since you yourself admit that certain rules of pattern and number are conceptually inviolable, whereas the laws of Indiana (my home state, thank you) are clearly arbitrary.
We perceive that this law is inviolable directly. We cannot conceive of them being otherwise. This is the starting point. I do not start out directly with a premise about God himself.
You said Q was “P and not P” at once, and indeed this has no meaning. “It is a circle and not a circle.” No meaning.
I’ve already dealt with this. You’ve already said that God’s dominion is in no way limited by what we understand to be true; hence, no matter what I prove or disprove, you would still say that God could make it otherwise.
But according to your premise that God could make Reality whatever he wants, similar to the points above he could simply be lying in what he says about the Bible. In fact, God could even be lying about his own existence (a contradiction, but God can make a contradiction real if he chooses, as you say).
Absolutely not, a gross misstatement. I say merely that we perceive at least some principles of pattern and number to be inviolable. It is not even necessary for me to specify which in order for the argument to be true.
The intuition belongs in quotes here, indeed. Because I am merely saying that rock-bottom truths must be intuited—they cannot be proved. It does not follow, however, that I am claiming that everything that is intuited must be proved.
This is easy: he was wrong.
No bluff—I admit it outright. Beyond a certain point, things cannot be proved—they must be perceived directly. For example, I cannot prove that I’m hungry—I perceive it and that’s that. Modus ponens can’t be proved—we perceive directly that it is an operation that advances truth.
I am greatly enjoying this discussion and hope that it continues. Thanks for your words and insights.
Very interesting post Aeschines! I like your logic and I’m actually in the process of reading a book that covers some of the areas you’ve hit on.
The only thing I’m wondering, and I might have missed it, was your justification for pantheism as opposed to atheism. I seem to recall a basic good and evil in your discussion, but I’m unclear as to whether you believe that this is tied up with your mathematical argument or if it’s just a belief of yours.
Let’s see. ‘2’, ‘+’, ‘=’, ‘5’ are arbitraritly defined symbols, which, inherent in their definition, assign the phrase “2 + 2 = 5” a false value. As these definitions are arbitrary, god could come along and alter the definitions such that 2 + 2 =5 is true. (‘2’ = ‘fish’, ‘+’ = eats, ‘=’ = ‘has the eventual result that’, and ‘5’ = ‘a fish has eaten another fish’ is one such redefition). Noone denies God the ability to do redefinitions of this nature; heck, we do it all the time. (‘10’ has about as many meanings as there are bases.)
But, the redefining of terms CANNOT elimitate the fact that IF the original definition of terms is used, the original defined meaning is the result. As has been often noted, all of math is based on the condition of accepting a set of axioms. Mathematical systems are basically humongus conditionals. And since it is impossible, by definition to change the defined results of a system without altering the meaning of its axioms, God cannot falsify the results of a totally artificial system, within that system. Any attempt to do so would generate a distinct system, separate from the first, leaving the first one unaltered.
I can further prove that it is impossible to alter the universe at it stands such that 2+2=5 is now true (and 2+2=4 false) without altering any other fact. It is defined that if A = B is true, and B = C is true, then A = C is true. “5 = 1+4” is defined as true (since it is part of the ‘other facts’ that were not altered. ‘2+2 = 1+4’ is still false for the same reason. But, according to the definition of equality, under the new system we can substitute ‘2+2’ for A, ‘5’ for B, and ‘1+4’ in and, since 2+2=5 is now true and 5 = 1+4 still is, ‘2+2 = 1+4’ can be proven to be true - in spite of the fact it was previously false and God supposedly didn’t change the meaning. By example I have demonstrated that God cannot equate 2+2 to 5 without altering the system to accomodate. And then the change wouldn’t be alterations, but rather the use of an entirely new system.
Face it, mathematics is a self-contained theoretical construct – with no inherent attachement to created reality. As it stands on its own, it is not subject to alterations by ANY exteral agent, gods included.
The symbols “2,” “+,” “=,” “4,” and “5” are irrelevant to this discussion. We’ve invented notation to make it easier, but let’s see if you can interpret a brand new system of symbols:
… W … I … (J)
… W … I … (L)
It doesn’t matter how we write it; 2 + 2 = 4 is a fundamental fact that could not be changed by any being, supreme or otherwise.
A minor nitpick here - “P and not P” is, indeed, a meaningful statement; the words are not sapped of meaning for being in this form. The statement also has a truth value; it is defined to be false for all P. This fact can be used to, if not prove, strongly indicate that God cannot “break the law of contradiction”, ie, god cannot make a contradiction true.
When one makes an argument, any statements that are known to be true may be used as premises. So, if god made a contradiction true, then it would be reasonable to put it in the premise list of any argument. (It is legal to put irrelevant true statements in premise lists, though it usually is not done because they don’t generally lead to any conclusions.) There is a known problem with having a contradiction in the premise list, though: it can automatically be used to prove the entire argument false, by contradiction. Here is a sample argument.
p1) P and not P -premise accepted becuase god made it happen
p2) There is a god -premise under consideration
c) P and not P -from p1 – contradiction
By the rules of proof by contradiction, we have just proven that there is no god!
Note that this works with any other premise; including “not (There is a god)”. Logically, once you have accepted the truth of one contradiction, you have implicitly accepted the truth of ALL contradictions; any statement and its negation are both false, and both true (by negation). The entire system of logic goes down with a logical blue screen of death. This will happen in any system of logic strong enough to model a simple truth table, which is to say, all of them. For those of us who think that logic models reality fairly well, this has very bad implications for reality as we know it.
Of course, you could argue that it could be the case that no logic system, at all, can model reality. (We’re not just talking about modeling God here, but also any reality in which God could cause a contradiction to be true.) Even if one discards all logic (other than rhetoric), a reasonable argument from intuition can be targeted to even the staunchest theist, indicating that god might not have this ability.
If God is ALL-all powerful, then god can divest effects from their causes, even pertaining to himself. In other words, if god can make a rock that he both can lift and can’t, then god can achieve his goals without fulfilling any natural requirements that those goals may have. This would imply that god is not constrained by demands of judgement and fairness; god is capable of satisfying judgement without actually punishing anybody; in fact he’s capable of punishing someone forever without actually doing it to them. In fact, whatever purpose God has in putting us here on Earth could be equally satisfied were he not to do so. Thus, the fact that we are on this earth, as it currently is, is a result of nothing more than god’s unmotivated whim. (Since God can diregard any motivations.)
This answers the problem of evil handily: we suffer because God likes us to suffer. Innocents die horribly because God prefers that they die horribly, and for no other reason. God is in fact evil. He must be, since nothing could have compelled or justified these actions, if he is immune to compulsion and the limits that enable justified actions. If no rules apply to god, then he LIKES things exactly the way they are, which no non-evil God would.
Since far and above most theists prefer to believe that got is not only ‘not evil’, but also ‘rather good all-in-all’, I doubt that you’d find many theists willing to accept premises yeilding the opposite result. And in this case the only premise is that god is unlimited by contradiction.
I think my system of pantheism (not that it’s very original) helps explain the nature of good and evil, and why the latter does exist in our system and probably must exist in any system or subsystem of That Which Is.
The One (the origin of That Which Is, pretty similar to the One of Plotinus) as pure potentiality bounded only by the rules of pattern and number. The One is beyond good and evil, since it has not yet been instantiated in any way. This potentiality is then instantiated in a near-infinity of ways, one of which was the Big Bang of our physical universe. Since the One is NOT an intelligent being (being closer to pure, empty, consciousness), it does not pick and choose what is to come into being. This is the first and most important point. There is no “God” that wills suffering and pain in our universe. However, the rules of pattern and number generally, as would be expected, lead to coherent systems. Any system or subsystem can only tolerate a certain maximum of suffering and conflict, otherwise, the system would not be self-sustaining. For example, we have some pretty nasty conflicts on our own planet, no doubt about it, but the worst we could do is nuke the planet, destroy it, and then suffering would be at an end.
Some systems are certainly bound to be worse than others, however.
Hence, these mathematical systems, or instantiations of the principles of pattern and number, tend toward balance and coherence. This is what I call the main vector of That Which Is, or the Good. In fact, I can’t prove it, but I would venture to guess that any given system is bound to become more full of sat-chit-ananda in the long run, or more full of being-consciousness-bliss. More full of being: going from cosmic goo to stars, planets, life. More full of consciousness: the evolution of conscious beings. More full of bliss: greater coherence and happiness.
The bad, or the forces that thwart the Vector to some extent, comes from various sources: an original lack of balance in the parts of the system, the fact that no system can be complete AND consistent (per Godel–hence, as a system follows the vector, there will always be new imbalances that need to be corrected), and the fact that conscious beings can choose bad instead of good (self-maximizing behavior instead of system-maximizing behavior).
Further, any overall system has positive energy in it, and I would also venture, negative energy. For example, life is delicate; feelings are delicate. Our interactions with others give us great potential for good. But one little moral slip can bring about disaster. It is almost as if there is a positive charge on us that is palpably itching to find its ground. This spirit, which is not a unified intelligence but something which computes its being through the vast system of transistors called humanity, delights in seing being, consciousness, and bliss destroyed. It was not the will of God for Satan to exist, but a Satanic force was implied in the original principles, just as the Good itself was. Good can never defeat evil entirely, but evil is dependent on Good for its shadow-existence.
There’s much more to it, and I’m still figuring it out myself, but the above, I think, is an accurate and intuitively pleasing explanation of the origin of good and evil.
This is an excellent analysis. I suppose Rager would say, God would just deal with those contradictions too. But I don’t want to put words in his mouth–Rager, you out there?
Interesting, but can’t the syllogism be put in a cleaner form? It would seem that your conclusion (at this point) would be merely that “God” did not cause “P and not P.” Can you knead this a bit more? I’m most curious…
This point is totally clear and ties in with what I was saying above about the arbitrariness of a God that could make a contradiction true. For all we know, he could declare Love to be Hate tomorrow, and that would be that.
LOL! Brilliant!
Tying it into the Problem of Evil argument, which is another monotheism killer.
