A God not bound by logic?

A third view is that "logic is isomorphous with mind functioning, that humans by their constitutions are unable entertain contradictions once they become apparent. Our brains are simply constructed ("hardwired"😉 so as to reject logical inconsistencies. But logic is not a branch of psychology or physiology; and we have as yet only a rudimentary understanding of brain functioning. A theory so dependent on unknowns is not one securely based. "

nuff said.

The fourth view is simpler: the laws of logic are verbal conventions. We learn through social usage the meanings of and, and not, true and false. In one, trivial sense this is undeniably true. But if the terminology is arbitrary, we still cannot rationalize away our sense of truth and correctness is this manner. The sentence "p and not-p" remains a contradiction, whatever term we give it.

Originally posted by vistesd
O how easily I am one-upped! 🙂

Logics that aim to represent situations in simple, context-free sentences are called sentential (also propositional, or propositional calculus), after Gottlob Frege who founded modern mathematical logic. Sentential logic is built with propositions (simple assertions) {3} that employ logical constants like not and or, and and and if - then. Such logics cannot deal with expressions like he believed her (which appeal to the common understanding of the human heart) but are very powerful in their own field.

So we come to symbolic logic -- one of the most difficult series of courses I ever took.

according to Classical Logic. Stewart Shapiro. Oct. 2000. http://plato.stanford.edu/entries/logic-classical/

"Once connectives are used ( &, ~, &exist, &sup, ∀ and, not, some, supposing, all) very complex sentences can be built up where the truth value of the whole sentence is dependent only on the truth values of its components. We arrive not only at secure judgments, but see clearly how the individual propositions systematically play their part in the overall truth or falsity of the sentence.

"Symbols are commonly used. Take a sentence like: John exists. We recast that as : There is something that is John, and that something is identical to John. Expressed symbolically that becomes: (&exist x) (x = John). Everything is green becomes: (&forall x) (Green (x)). Using the negative ~ we can express: everything is green as: it is not the case that everything is not green: ~ (&exist x) ( ~ green (x)).

"Is this helpful? Immensely so. Numbers can be defined in this way. Perplexing sentences like: The King of France is bald can be re-expressed as a conjunction of three propositions: 1. there is a King of France, 2. there is not more than one King of France, and 3. everything that is a King of France is bald. Put another way, this becomes: there is an x, such that x is a King of France, x is bald, and for every y, y is a King of France only if y is identical with x. In symbols: (&exist x) (K(x) & b(x) &(y)(K(y) &sup (y =x))). "

Originally posted by Scriabin
"Gödel's proof states that within any rigidly logical mathematical system there are propositions (or questions) that cannot be proved or disproved on the basis of the axioms within that system

I knew that, but had not heard the following before:
and that, therefore, it is uncertain that the basic axioms of arithmetic will not give rise to contradictions.
Nor do I see how it follows. Do you understand it, or must I go and do the research myself? 🙂

Kurt Gödel "proved" that if you are totally contained within a subset system, then the math, logic, and our commonly accepted sense of what is true developed within that system have no relation whatsoever to any universal truth. I wonder what happens if we apply that prinicipal to Gödel's own proof ....
Again, I do not see it as following trivially from the initial theory. Surely universal truths are also truths in all subsets and must therefore have a relationship to them? Or am I simply not understanding you?

Originally posted by Scriabin
Are we confusing logic with truth? Logic pertains to validity -- that which follows logically from a premise. A valid argument can logically follow from a false premise. But the answer, however logical, cannot be true.

So, logic, alone may be quite beside the point.

Indeed, why all this emphasis on logic when the premises on which many of the "debat ...[text shortened]... ersal truth. I wonder what happens if we apply that prinicipal to Gödel's own proof ....

What about logical positivism?


I think I still have my old copy of Ayers' Language Truth and Logic. In it Ayers explains (using the Wiki's words) "that the principle of verifiability may be used as a criterion to determine whether a statement is meaningful. To be meaningful, a statement must be either analytic (i.e. a tautology) or capable of being verified.

"According to Ayer, analytic statements are tautologies. A tautology is a statement which is necessarily true, true by definition, and true under any conditions. A tautology is a repetition of the meaning of a statement, using different words or symbols. According to Ayer, the statements of logic and mathematics are tautologies. Tautologies are true by definition, and thus their validity does not depend on empirical testing.

"Synthetic statements, or empirical propositions, assert or deny something about the real world. The validity of synthetic statements is not established merely by the definition of the words or symbols which they contain. According to Ayer, if a statement expresses an empirical proposition, then the validity of the proposition is established by its empirical verifiability.

"Propositions are statements which have conditions under which they can be verified. By the verification principle, meaningful statements have conditions under which their validity can be affirmed or denied.

"Statements which are not meaningful cannot be expressed as propositions. Every proposition is meaningful, although it may be either true or false. Every proposition asserts or denies something, and thus is either true or false."

But philosophy didn't stop with this -- and my prof candidly told me that Ayers had missed the boat. Things aren't that simple, he said.

Originally posted by vistesd
From time to time on here, someone will claim that God transcends, and is not bound by, logic. I never know quite what that is supposed to mean (and I’m not sure they do either), but I thought of two possible cases:


The [b]first case would be one in which God simultaneously knows something—call that something Y—and is also totally ign ...[text shortened]... might have some additional examples of what it could mean to say that God is not bound by logic…[/b]

I don't understand how God couldn't be completely bound by the laws of logic.

If God exists, and God is Infinite Mind, it should follow that the laws of logic are a reflection of His nature. That is, it would be more accurate to say that the laws of logic are bound by God, rather than say that God is bound by the laws of logic.

In other words, if the laws of logic are absolute and eternal; that is, if they do not depend upon anything in the world for their existence, then they were not created. The laws of logic were not created, therefore it could not follow that God is not bound by them. Instead, the laws of logic must be understood to be a reflection of the nature of God's mind.

Originally posted by twhitehead
I knew that, but had not heard the following before:
[b]and that, therefore, it is uncertain that the basic axioms of arithmetic will not give rise to contradictions.
Nor do I see how it follows. Do you understand it, or must I go and do the research myself? 🙂

Kurt Gödel "proved" that if you are totally contained within a subset system, then subsets and must therefore have a relationship to them? Or am I simply not understanding you?

maybe we both do not understand Gödel -- he's just a footnote, not someone I'm going to carry a flag for.

there are as many alternative theories, proofs, etc. as stars in the sky, it seems.

what I take away from it all is that 1. Logic is not the be all and end all; and 2. any concept of a God that we can understand or assume can be bound in the same way we are must be simply as poor a concept as is our understanding of the physical universe that we even can observe.

isn't it nice still to have mysteries?

And you can observe a lot, just by watching, said the great Yogi

Originally posted by epiphinehas
I don't understand how God couldn't be completely bound by the laws of logic.

If God exists, and God is Infinite Mind, it should follow that the laws of logic are a reflection of His nature. That is, it would be more accurate to say that the laws of logic are bound by God, rather than say that God is bound by the laws of logic.

In other wor ...[text shortened]... Instead, the laws of logic must be understood to be a reflection of the nature of God's mind.

why do you assume premises not in evidence?

I don't see how the alleged creator of the universe could be bound by anything of which we can conceive.

In fact, I only say "alleged" because the true nature of the how and when and why anything, including us, is here, is still beyond our ability to conceive, let alone reason out, or even perceive. We just aren't there yet.

Originally posted by Scriabin
...2. any concept of a God that we can understand or assume can be bound in the same way we are must be simply as poor a concept as is our understanding of the physical universe that we even can observe...

When we say we bind God to logic, in what way are we binding it? We saying that it should not be contradictory is a poor concept?
If one defines God to have particular unambiguous property X it is naive to expect that for some other well defined property Y (that cannot by its definition be true if X is true)cannot be true???

If someone says God can do X in some context, is it fine to accept their statement that Y is also true in the same context where Y implies God cannot do X?
Or how about God exists, and simultaneously that God doesn't exist. Is one binding God to existing by merely positing it exists

I would agree that it is somewhat foolish of humans to define a God in terms of what it can do and in most cases what it can't do (ie it can do anything or it can't lie etc...), but is logic really a human construct? or is it the rules and tools we have developed to understand that which is fundamentally true that is human created, and we denote these fundamental truths as 'logic'?

Originally posted by epiphinehas
I don't understand how God couldn't be completely bound by the laws of logic.

If God exists, and God is Infinite Mind, it should follow that the laws of logic are a reflection of His nature. That is, it would be more accurate to say that the laws of logic are bound by God, rather than say that God is bound by the laws of logic.

In other wor ...[text shortened]... Instead, the laws of logic must be understood to be a reflection of the nature of God's mind.

Perhaps we should instead say that God is not bound to our logic. I keep thinking of Job and his friends sitting there for days trying to understand how God could allow such calamity to befall him. In fact, they never got an answer, rather, they just all came to wrong conclusions using their own finite logic and knowledge about God.

Originally posted by Agerg
When we say we bind God to logic, in what way are we binding it? We saying that it should not be contradictory is a poor concept?
If one defines God to have particular unambiguous property X it is naive to expect that for some other well defined property Y (that cannot by its definition be true if X is true)cannot be true???

If someone says God can do X in ...[text shortened]... undamentally true that is human created, and we denote these fundamental truths as 'logic'?

logic is a creature of language and is human made.

it is meaningless to posit any premise that depends on the existence or characteristics of that which may or may not have made the physical universe, which we as yet cannot comprehend,

so the original question using the word "bound" or "binding" is meaningless.

every proposition depends on language as a referrant. and every referrant depends also on the context in which we agree those linguistic tools are appropriate.

why is a chair a chair? why in the room we are in is the ceiling above us and not below us?

every proposition you have tried to use depends as well on assumptions, not empirical observations.

have you read Ayers and then Russell and then Wittgenstein? I do not offer them as the truth, merely as a way to consider some of these questions.

Better to ask what people mean when they use the word "God." Once we know what we are talking about, we can discuss our disparate perspectives from the same sheet of music and the discussion might then stay in tune.

It is rather atonal, right now.

Originally posted by Scriabin
logic is a creature of language and is human made.

it is meaningless to posit any premise that depends on the existence or characteristics of that which may or may not have made the physical universe, which we as yet cannot comprehend,

so the original question using the word "bound" or "binding" is meaningless.

every proposition depends on languag ...[text shortened]... et of music and the discussion might then stay in tune.

It is rather atonal, right now.

Yes, it is rather atonal. The theists that I referenced in my opening post generally use the word “God” to mean something like a supernatural being who created the cosmos and transcends it. Neither the phrase “transcends logic” nor the phrase “is not bound by logic” are original with me. But they have been used from time to time by some theists when confronted with a statement about their God that is logically contradictory.

My opening post was an attempt at a humorous questioning of what a God-being who can violate the rules of logic might be like—what that might mean, what kind of contradictory nature such a God might display. The first case was just a logical contradiction, the second case just illustrates that one can construct a “valid” (not the scare quotes)grammatical sentence that is meaningless ( a whimsical example of what Wittgenstein referred to as being bewitched by one’s own language into thinking that one is making some kind of sense).

You are, of course, correct that a valid logical argument need not be true; but an invalid logical argument cannot be true. (I perhaps should have specified that I was referring to deductive logic.)

Thus the question was not about truth, but about coherence: can it be in any way coherent ( can it make any sense) to reference, say, “the colorless red”? Can it make any sense to say: “God is a being who exists outside of space-time dimensionality”? Whatever else one thinks about the plausibility of an actual referent in this case? I certainly don’t object to your expanding on that to considerations of actual truth claims—so let’s go there…

When you say “it is meaningless to posit any premise that depends on the existence or characteristics of that which may or may not have made the physical universe, which we as yet cannot comprehend”—in what way are you using that word “meaningless”? Do you mean to say that positing such a referent (or, I would say, positing a supernatural category) has no use-value for explaining what we cannot now comprehend of the natural universe? Do you mean that such a referent can only exacerbate incomprehensibility? Do you mean that there is simply no epistemic warrant for positing such a referent (that has been my position generally)? Or would you say that the notion of a supernatural being is itself incoherent?

___________________________________________

Note, behind all the fun and games on here, I’m basically a Zennist. My “bedrock referent” is simply the just-so-suchness (tathata) of reality, of which I also inseparably am, prior to all our thinking/concept-making about it. Adding a supernatural category is, for me, what is called “painting legs on a snake”. So is metaphysical speculation generally. You can imagine the Zen response to questions such as “why is a chair a chair?”. You’ve got some background there yourself, if I recall correctly.

Originally posted by epiphinehas
If God exists, and God is Infinite Mind, it should follow that the laws of logic are a reflection of His nature. That is, it would be more accurate to say that the laws of logic are bound by God, rather than say that God is bound by the laws of logic.

I really don't see how that follows.

In other words, if the laws of logic are absolute and eternal; that is, if they do not depend upon anything in the world for their existence, then they were not created.
Again, that doesn't follow trivially, can you explain it further?

The laws of logic were not created, therefore it could not follow that God is not bound by them.
Again, why?

Instead, the laws of logic must be understood to be a reflection of the nature of God's mind.
???

Originally posted by vistesd
You are, of course, correct that a valid logical argument need not be true; but an invalid logical argument cannot be true. (I perhaps should have specified that I was referring to deductive logic.)

The above I think was incorrectly stated. The conclusion of an invalid argument may in some cases turn out to be true; but its truth cannot be inferred from the terms of the argument.

EDIT: I'm moving my logical inquiries over to the "Is logic faith" thread...