You didn’t know, possibly, that when he thought we was dying, he showed the notebook to one of his colleagues, who copied out the proof:
In an unsanitized, politically incorrect (but factual) history, Selmer Bringsjord talks about how the tormented genius Kurt Gödel took up a quest that dated back a thousand years to prove the existence of God by formal logic. His original version didn’t quite work but his editor’s version passed an important logic test:
“When we go to Gödel, we skip over the modern advocates of this argument. It’s harsh—I’m just going to say it—from the standpoint of someone who’s reasonably well-versed in formal logic, I think it’s a bit of a doldrums, despite some of the attention, until Gödel does his thing.
Gödel does it formally and then some folks in Germany, doing automated reasoning, verified it a few years back. They verified the version that Dana Scott copied out of the notebook. That is, what they verify is that there is no doubt; it’s machine-verified proof. So now we’re left with just the truth of the premises and how we judge them.”
News, “Gödel and God: A surprising history” at Mind Matters News
Further reading:
Faith is the most fundamental of the mathematical tools: An early twentieth century clash of giants showed that even mathematics depends on some unprovable assumptions. (Daniel Andrés Díaz-Pachón)
and
God’s existence is proven by science. Arguments for God’s existence can be demonstrated by the ordinary method of scientific inference. (Michael Egnor)
Genesis 22:9-12
Although I now regard myself as agnostic/atheist, I was raised a Christian and I genuinely believed. I was taught that the true Christian needs only faith, not science or mathematics, just faith.
Later, I became aware of the contradictions in the Biblical accounts, such as how could an omniscient God possibly not know what was in Abraham’s heart, the real strength of his faith? So what purpose could this immoral test possibly serve?
^^^^^^^^ Ironic,
Seversky accuses Christians of having blind faith and no reason, yet he himself has abandoned all reason in his blind faith towards atheism.
As I pointed out the other day, the fact that Atheism itself cannot ground reasoning is powerful evidence against Atheism being true.,,, In short, “anyone who believes in reason must also believe in God.”
https://uncommondescent.com/intelligent-design/when-beliefs-dont-depend-on-reason/#comment-700669
Conclusion of preceding link,,,
@ Seversky, Your perception of god is only contradictory because it is extremely limited in the first place.
Unlimited capacity to do anything with no ability to control or choose to do so
That appears to be the standard you hold God. This is not God
Seem to be hung up on a question that I asked my parents when I was 4
Can god create a rock that God cannot lift?
If the answer is yes then God can’t do everything
If the answer is no then God can’t do everything
Seems that you’re hung up on if God knows everything then etc…..
If Seversky would take time to understand what Abraham had been raised around, he would know that child sacrifice happened with all the deities worshiped. It was not a lack of understanding on God’s part, but Abraham’s. By stopping Abraham at the moment just before sacrifice, it was made clear to him just how different God was from the other deities in the region.
Most who claim to be atheists are not atheists. You do not give human characteristics to something that does not exist. You only do so out of anger over something and desire to blame God.
Without God, there can be no life. There is not one hypothesis that comes close to satisfying the question of origin when God is removed. It is only through the inclusion of intelligence far beyond human understanding that you can get life from no life.
For Pete’s sake get a new tune, Seversky. You’ve sung that one half a dozen times.
Sev,
fideism is a strawman caricature of well founded Christian or even wider theistic faith. That said, given the Agrippa trilemma, the roots of our worldviews cannot be turtles all the way down and cannot be turtles in a circle, so the last turtle has to stand somewhere, at finite remove.
Our challenge is to have reasonable, responsible faith-points when we reach that root level, averting question-begging through comparative difficulties analysis. This requires facing the fact that all worldviews bristle with difficulties and so our challenge is to compare, across factual adequacy, coherence and balanced explanatory power. The last points to grand inference to the best explanation, the opposite of a demonstration on generally accepted axiomatic presuppositions. Mind you, there are self-evident truths that serve as plumb-line tests, but these cannot be enough to compose the framework for a worldview.
In that context, it is reasonable to ask about warrant [notice, much wider than “proof”] for belief in God.
For many, that is settled by living, life-transforming encounter. The Christian Faith points to this, in the context that the world without and our inner light of life within are adequate warrant to trust in God. That inner light in crucial part pivots on our moral government — the inescapable first duties of responsible reason I keep pointing out. Duties, that must truly be duties, on pain of utter incoherence and chaos in our inner lives: to truth, to right reason, to prudence [so, inter alia, warrant], to sound conscience, to neighbour, to fairness and justice etc. Your own arguments implicitly rest on our knowing these duties.
That such creatures [us] exist, constrains plausible candidates for the required, finitely remote world root. It must not only be causally adequate and temporally plausible but adequate to found moral government. Post-Hume, that requires bridging the IS-OUGHT gap, being inherently good.
Causal-temporal adequacy surfaces a form of the trilemma. We cannot traverse an actually transfinite temporal-causal succession of finite stages in steps, as can be seen through first focussing the relevant set for numbers, the hyperreals R*, not R, where we can see Z* as integer mileposts. (The definition of R is inadequate for what our teachers do with the algebraic number line in high school, much less other things.)
For a supposed transfinitely remote past there has to be a stage K’ [= -K in Z*] that would be actual past but is transfinitely remote; otherwise we are simply discussing finitely remote bpast points. K’, K’+1, K’+2 etc to K’+k goes on K’+k+1 etc, i.e. we can only successively advance to a finite span from K’; we never bridge to a finite span from 0 [take that as the singularity], much less a count forward to n, now. We are only warranted to speak of a finite past. Turtles all the way down fails. The same basic challenge extends to an infinite regress of warrant; our rationality is inherently finite and bounded.
We need to pause on logic of being, recognising that across the span of possible worlds, there are candidates impossible vs possible of being, the former due to the sort of contradictory core characteristics in say a square circle. Of possibles, contingent beings would or do exist in at least one possible world [but not in others]. Relevant factors tied to that are causes for such a being c. By contrast, necessary beings, n, exist in every possible world; i.e. they are framework elements for any possible world. (Try to imagine a world in which 2 does not exist or can cease from being.)
Many of these things are now unfamiliar (thanks to the spirit of our age and what we typically deem worthy of being studied), but that does not make them irrelevant. Ontology is foundational.
In this context, we need a finitely remote, necessary being root of reality causally adequate for a fine tuned cosmos hosting a world of cell based life that includes inescapably morally governed creatures with a built in natural law attested to by sound conscience. That requires inherent goodness thus also utter wisdom, simply to bridge the IS-OUGHT gap, where also necessary being is eternal. Were there ever utter non-being such would forever obtain, so if a world is, something — the necessary being reality root — always was.
That’s a pretty stiff bill to fill, and it drastically shifts our evaluation of the warrant for theism and the various forms of theistic argument.
Indeed, after centuries of debates, there is just one serious candidate to fill the bill: the inherently good, utterly wise creator God, a necessary and maximally great being. One, worthy of loyalty and of the reasonable, responsible service of doing the good that accords with our evident nature. A familiar figure (and definitely not the sort of scapegoat sketched out in Mr Dawkins’ strawman caricature that is definitive of the new atheism, so called).
This framework also spans the picture studied in philosophical and systematic theology.
It should change, too, how we look at the plausibility of the Godel-style, modal logic ontological argument. Even, the Anselm form, suitably adjusted if needs be.
BTW, as for your struggle with Gen 22, has it registered that even with the evening prayer by one’s bedside, God is not unaware of our needs before we articulate them and indeed beyond what we can put in words? So, prayer, faith, adventures of life cannot tell God something novel? Instead, our prayers, struggles and adventures are relational, tied to soul-making constrained by where we are. God can only give us safely what we have been opened up to handle. And in this case, an obvious element is to break the idolatrous pattern of trying to manipulate gods by child sacrifice.
Though, in a sobering aspect, this points to the dilemma many a father and mother have confronted ever since: sending their sons into battle with a significant chance or even effective certainty that they will not come back. For, we live in a world of aggressive, violent, oppressive evil that sometimes has to be fought. Even, in tearing battles of attrition such as the Heurtgen Forest (there were dams that if blown would flood valleys blocking the advance), or Omaha Beach (required to bridge Utah on the Contentin peninsula with the UK-Canadian beaches and to take out key heavy gun batteries), or with the parachute divisions landing behind those five immortal beaches, or Stalingrad (the huge casualty figures of the European fronts of WW2 were in the East, right up to the battle for Berlin . . . the Russians lost nearly as many on the battle field as were lost in battle on all sides in WW1), or Verdun, or the Somme (an unready army had to take up a bleeding offensive to relieve pressure at Verdun), or Gettysburg or any number of other places and times.
I recall, then General Petain, watching 18 year old boys marching to the front at Verdun, his heart lurching.
I think some re-thinking is in order.
KF
PS: Rom 1:
Note here, Locke:
After reading the biographical bits, I’m struck by a metaquestion. If God exists, would he want his existence to be proved by a man who was so totally removed from the REALITY of God’s works that he couldn’t trust food? Godel lived in a universe of total infinite abstraction and symbolism, and handled those symbols better than anyone. Natural Law says a lot about the importance and blessings of food, but disdains overabstraction.
polistra, Godel was an eccentric genius with serious struggles. One of many, Newton springs to mind. KF
As to the ontological argument for God, Dr. Craig has made a video that explains the basics of the ontological argument for God in an easy to understand manner,, (much easier to understand than Godel’s proof which basically “looks like hieroglyphics” for the average layman):
Here are the basic steps of the ontological argument as laid out by Dr. Craig:
And as Dr. Craig points out in the following article, “it might be a surprise to learn that steps 2–7 of this argument are relatively uncontroversial. Most philosophers would agree that if God’s existence is even possible, then he must exist. So the whole question is: Is God’s existence possible? The atheist has to maintain that it’s impossible that God exists.”
And as Dr. Craig states in the following video, “It (the ontological argument) puts the atheist in a very awkward position. The atheist must deny, not merely that God exists, he must maintain that it is impossible that God exists. And that is certainly a radical claim that would require great justification.”
Where this gets VERY interesting is that atheists, in their appeal to an infinity of other possible worlds to try to ‘explain away’ the fine tuning of this universe,,,
,,, in their appeal to a multiverse to try to ‘explain away’ the fine tuning of this universe, atheists have, basically, completely conceded the necessary premise, i.e. that it is possible that God exists, to the ontological argument in order for the ontological argument to work.
Simply put, you cannot argue that it is possible that an infinity of other universes exist in which an infinity of other possibilities are playing out, while at the same time holding that it is impossible for a maximally great being to exist in one of those infinity of other universes:
The absurdity of the atheist’s predicament with his appeal to the multiverse is humorously laid out in the following article,
Thus once again, in another twist of atheistic irony, the atheist ends up shooting himself in the foot in his appeal to a multiverse in order to try to ‘explain away’ the fine-tuning of the universe and therefore avoid the implication of God, since his appeal to a multiverse, in and of itself, concedes the necessary premise to the ontological argument, i.e. that it is possible for God to exist, in order for the ontological argument to work.
Of supplemental note, I touched upon Godel’s incompleteness theorems yesterday in the following post:
BA77, in short the issue pivots on whether there is a serious candidate necessary being with key attributes that would lead to identification with the God of theism. Where, a being that exists in all possible worlds is a necessary not a contingent being. KF
PS: It’s math-roglyphics! A language all to itself, here modal logic.
PPS: A reason to believe God is impossible of being is __________, or, that he is not a serious candidate necessary being is __________ That is going to be fun to watch.