If Darwinism fails then supernatural causes are back on the table and should be included in science.
I do not think there can be a science of the supernatural.
I do not think that if Darwinism fails that supernatural causes will become acceptable.
If the hope of ID is that supernatural causes will be allowed back into science if they can only just get rid of Darwinism, ID is doomed.
The tools and methods of ID cannot differentiate a supernatural cause from a natural cause anyways.
Thoughts?
So I think you are on the right track in this. As I understand Godel’s completeness results, the key is to separate what is provable from what is true.
A statement S is provable from axioms if S can be derived just by starting with the axioms and then proceeding to syntactically manipulate symbols according to the rules. If one can derive S that way, then S is provable.
On the other hand, the notion of truth requires a model. That is, truth needs some possible world where all the symbols in the statement have a reference. So to model “Socrates is a Man” we need a reference for the name ‘Socrates’ and also a reference for the predicate ‘is a Man”. Then we can check truth of S for a possible world by checking if indeed the named entity satisfies the predicate as modeled in that world.
Godel’s first completeness theorem says for first order (ie predicate) logic, both of the following hold
– if a sentence is provable then it is true in all interpretations, and
– conversely that only true sentences can be proved.
That result does not hold for systems complicated enough to capture arithmetic. I think the intuitive reason is such systems are rich enough to talk about themselves. They can encode statements about theories of what the system can prove to also capture a claim about the properties of integers. So the Godel sentence “I am not provable” plays the neat trick of having “I” refer both to itself as a claim about the system and at the same time to a theorem in arithmetic.
BruceS,
In the real world, seems to me, statements that attempt to describe or model reality are neither true nor false and simply vary on a scale of accuracy, somewhat how map detail varies with scale. Broad brush vs pedantic nitpick.
That is my understanding as well. There are things that are true but are not provable in a given system.
Neil seemed to be saying that incompleteness means that there are things which are neither true or false. Or things for which we can not know whether it was true or false.
When instead it simply means that not all true things are provable within any sufficiently complex system.
God can of course know whether things are true or false and he can reveal that information to you.
peace
Is it true that statements that attempt to describe or model reality are neither true nor false?
peace
fifthmonarchyman,
It’s neither true nor false. Nor is it useful.
So it’s just your useless opinion. Then why bring it up?
I like ice cream, do with that what you will it’s worth about as much.
peace
fifthmonarchyman,
Nope. We can check our opinions against reality. That’s the scientific method.
What does it mean to say “I like ice cream”?
Probably there is a gene for that.
About the same thing it means to say “In the real world, seems to me, statements that attempt to describe or model reality are neither true nor false and simply vary on a scale of accuracy”
peace
Unless they are neither true nor false.
peace
I suspect preference, list, craving for sweet things has a genetic element. It’s not limited to humans. Horses like sweet stuff.
Nope. We can check for accuracy in our description.
1) Does accurate equal true?
2) Is it true that accurate equals true?
3) If not why should anyone give a dam?
peace
fifthmonarchyman,
I think it’s simpler to try and see the world as it is rather than as we imagine it to be.
Not quite.
LOL so it’s almost true then?
You do know that almost true is still false don’t you?
1) Is it true that it’s simpler to try and see the world as it is rather than as we imagine it to be?
2) Is it true that you can ever see the world as it is rather than as you imagine it to be?
peace
The system can neither prove nor disporve the Godel sentence. I did not see Neil’s post, perhaps that is what he meant. I do think that truth is not relevant for Godel’s proof.
I also agree that we from the outside can see the Godel sentence is true under the standard understanding of arithmetic. Note also that it can be false under non-standard interpretations.
Now some argue that we can only see it is true because we are fallible/inconsistent and so not subject to same limitations as the formal system capturing arithmetic (which we assume is consistent).. Others say there is no reason to think that we can see the truth of any Godel sentence for a given formal system where the proof applies.
God is infallible and all-knowing so neither of those apply to God. But God is not subject to the limitations of the proof rules of formal systems just as God is not limited by the effective computing rules of Turing machines. So I think God knows the truth of the interpretation of any statement in a consistent system.
All this assumes the system under consideration is not self-contradictory (ie it is consistent), for if it is self-contradictory then anyone can prove anything within it.
Just to be clear, all this is about the concept of an omniscient God. I am agnostic about whether such a Being exists.
Did you mean to use the uncapitalized male pronoun to refer to God?
Glad you finally grasped my point.
fifthmonarchyman,
Back to square one. Do you like goldfish?
They are find to swallow for a drunken prank. Not so for catfish.
https://www.livescience.com/64588-catfish-swallowed-stuck.html
BruceS,
Not a great outcome for the catfish other than posthumous fame. 😯
That Aeon article is way too long.
Yesterday EJ Winner posted a comment to Dan Kaufman’s blog. His final paragraph: “Philosophy is the literary genre with the most profound rhetorical strategies for helping us become who we are – if it would only abandon ‘the truth,’ (i.e., the quest for certainty), and address us as we are.”
I very much agree with EJ — his entire comment, not just that quoted part. He thinks philosophy should look to pragmatism rather than truth. And he thinks it should look to biology rather than physics.
Yes, I agree. However, I would not use the word “accuracy” there — maybe “precision” would be okay.
Quite right.
That’s what god-bots and mathematical Platonists say. I disagree with them.
And, yes, Gödel was a Platonist.
That’s a trap that you fall into when you have made truth into a god.
Neil Rickert,
God is Truth!
That’s how I understood Neil’s post too. If it’s impossible to provide a proof for every possible statement within a formal system, it’s impossible for God too.
I’m not sure what it means to say “from the outside” here, Bruce. Seems to me Neil is right when he says that (mathematical) statements can only be said to be true or false in the context of a formal system.
Exactly right!!
By definition God knows this.
Any time I speak of God with out qualification I mean the Yahweh the Triune God of Scripture. All other gods are idols
peace
Plato is my homeboy as well.
But I think you knew that
peace
And I’m agnostic.
You are right that “from the outside” means intuitively in some sense and not by following the proof rules of the system itself.
Also, I should have also been clearer that I was referring to what the statement said about itself and the system, not the math theorem it also stands for. That is the part that is intuitive for me. I’m not sure exactly what a logician who had a deep understanding of the proof would find intuitive — maybe the truth of the encoded theorem as well.
So with that, here is what I meant by intuitive from this summary.
“Now let’s consider ‘This statement is unprovable.’ If it is provable, then we are proving a falsehood, which is extremely unpleasant and is generally assumed to be impossible. The only alternative left is that this statement is unprovable. Therefore, it is in fact both true and unprovable. Our system of reasoning is incomplete, because some truths are unprovable.”
So I am agreeing with what the quote says. The statement is true because it is indeed unprovable.
I did not talk about what God could prove, only what God would see as true under some interpretation of the system. That was because I am not sure what “prove” would mean in this case. I think you are right in previous posts that ‘prove’ means by following the rules and axioms, and so it would be logically inconsistent to make such a claim about proof for God. That is, saying God could do that would be a logical contradiction, and I don’t think even God can prove such things (given a system of logic to define ‘contradiction’, of course!).
It is actually very easy to have truth outside of a system of axioms. All you need to do is smuggle in additional unstated axioms, but be in denial that you are doing this.
For fifthmonarchyman, those unstated axioms are often called “revelations”. Among philosophers, the unstated axioms appear to be part of metaphysics.
Brilliant! Thanks Bruce
Only if they are true
Peace
Like I said before God does not need to prove. He just knows
Peace
He doesn’t know some proofs though
This is why I have commented about “technical uses of true.” Saying that something is intuitively true is not a technical use of truth.
I’m inclined to say that “P is intuitively true” only means “I believe P”. It could not mean “P is true” at least in any technical sense.
I don’t think that is a correct way of looking at it for the reasons I give above:
To start, proof means following the rules and axioms to derive the formula. It is applied syntactic manipulation only.
But knowing is Justified True Belief so knowing needs truth, but truth is a semantic notion that require reference to some possible world. Syntax on its own is not enough talk about knowledge. So proving is not the same as knowing.
In a similar vein, using “he” or even “He” to refer to God is an error, because human concepts of gender cannot be applied to God’s nature.
I don’t have a problem with that, although in this case many popularizations make the same claim so it is some kind of common intuition that leads to the belief.
On your other post, I am not sure why you think axioms have anything to do with metaphysics. Maybe you mean that the metaphysics of some possible world can be captured by a set of axioms? Even that sounds dubious and not something I have seen in the limited metaphysics I have read.
Or maybe you were just taking a swipe at philosophy, as you do from time to time.
When people agree on a common intuition, that becomes a social convention. And we can treat social conventions as axioms.
It’s important to remember that at least one of the persons in the Godhead has revealed himself in human form as a male and referred to another of the persons as Father.
So while there is no reason to believe that this revelation reflects God’s nature a-se. There is no reason why we can’t refer to him using that pronoun.
While we are on the subject I’d like to point out that because of the incarnation God exists both inside the system that is the universe and outside of it. So he can both know the truth of an axiom of the system and understand how that it works out in time.
peace
I do agree. I hope I did not give the impression that I did not.
peace
God is not truth then, because truth doesn’t “just know” a single thing.
Truth, however, neither proves nor knows.
God can’t know anything “by definition” if God = truth.
It’s not a trap at all, though FMM has indeed fallen into SOMETHING silly.
Where I live it’s just a mistake you made and now won’t own.
FWIW, that is entirely non-responsive. I said I don’t know what revealing knowledge means, and you “respond” by saying God can do it.
I would, but it’s kind of a waste of time. I get either Bible thumping or non-sequiturs or pissy little refusals to admit obvious mistakes, or some combo.
Re your hills, I think I hold fairly similar views, but you’d have to take “scientific” out of there for me, and I wouldn’t include moral values among the values that I think are objective. As I mentioned some time ago (I got spanked by keiths for changing my mind on it), I’d now limit my analysis to prudential values.