“We cannot know completely. Kurt Gödel demonstrated that even the basic principles of a mathematical system while true cannot be proved to be true. This is his incompleteness theorem. Gödel exploded the myth of the possibility of perfect knowledge about anything. If even the axioms of a mathematical system must be taken on faith, is there anything we can know completely? No there is not. Faith is inevitable. Deny that fact and live a life of blinkered illusion, or embrace it and live in the light of truth, however incompletely we can apprehend it.”
Unfortunately, Arrington is not even wrong.
Firstly, the proof has nothing to do with the unprovability of the axioms of a system. The axioms are obviously unprovable — the theorems are what are proved based on the axioms. Arrington’s basic confusion between axioms and theorems suggests that we already off to a bad start.
Secondly, Godel’s incompleteness theorem demonstrates that in any formal system rich enough to express arithmetic, there will be true sentences of that system that cannot be proven within that system. That’s what it means to say that the system is “incomplete”. By contrast, first-order logic is complete, and the completeness proof of first-order logic is a standard exercise in undergraduate logic classes. (In fact, it was Godel who proved that first-order logic is complete.) The fact that arithmetic is incomplete, while logic is complete, shows us that one cannot reduce arithmetic to logic alone. That was a nail in the coffin of the Hilbert program.
Thirdly, the real source of the trouble lies in identifying “knowledge” with “certainty”. Rejecting the Quest for Certainty as even a regulative ideal for our inquiries does not entail that our knowledge is grounded in “faith”, and certainly not the kind of faith that matters for the religious way of life. The fact that our knowledge is vulnerable to experience — that our knowledge is both fallible (can be shown to be false in light of experience) and corrigible (correctable in light of experience) — does not mean that it rests on faith. It means that it does not rest on anything at all.
As Sellars eloquently put it:
“If I reject the framework of traditional empiricism, it is not because I want to say that empirical knowledge has no foundation. For to put it this way is to suggest that it is really “empirical knowledge so-called,” and to put it in a box with rumors and hoaxes. There is clearly some point to the picture of human knowledge as resting on a level of propositions — observation reports — which do not rest on other propositions in the same way as other propositions rest on them. On the other hand, I do wish to insist that the metaphor of “foundation” is misleading in that it keeps us from seeing that if there is a logical dimension in which other empirical propositions rest on observation reports, there is another logical dimension in which the latter rest on the former.
Above all, the picture is misleading because of its static character. One seems forced to choose between the picture of an elephant which rests on a tortoise (What supports the tortoise?) and the picture of a great Hegelian serpent of knowledge with its tail in its mouth (Where does it begin?). Neither will do. For empirical knowledge, like its sophisticated extension, science, is rational, not because it has a foundation but because it is a self-correcting enterprise which can put any claim in jeopardy, though not all at once.”
But doesn’t a baby begin with absolute certainty, and from there start to learn about toes, mommies, and bouncy balls?
No wait, we learn about “absolute certainty” after we’ve learned from our senses, using logic, and also from each other.
One could wonder why beginning with our perceptions is inevitable, a prerequisite to imagining absolute knowledge, and yet an inadequate basis for understanding the world in a manageable fashion. It’s the long shadow of Plato (taken up by religion), of course, but Kant really did show that all that really gives us is our way of knowing the world, and nothing certain beyond.
Glen Davidson
KN,
I was about to post an OP on this, but you beat me to it.
Arrington’s mangling of Gödel is reminiscent of the folks who interpret Einstein as saying “everything is relative.”
To be fair, Arrington is not the first to mangle Gödel, and he surely won’t be the last.
Oh here come the lawsuits!
I like this:
Further addenda . . .
(1) the self-correcting nature of empirical knowledge and science does not obviously extend to other kinds of knowledge — mathematical knowledge, for example, or ethical knowledge. Though I’m quite enough of a pragmatist to think that these too are self-correcting enterprises, they cannot be self-correcting in the same way that empirical knowledge and science are. So some further account would be required here.
(2) I am by no means averse to the very idea of certainty. The trick is to recognize, as Wittgenstein nicely put it, that knowledge and certainty are different categories. It makes sense to know something only if it is intelligible to us that one could doubt it. For only if doubt is intelligible does to make sense to need a justification. What is certain, Wittgenstein argues, are those things that it does not make sense to doubt.
I can intelligibly doubt whether there is food in the fridge, or how far the sun is away from the earth, or whether there is intelligent life elsewhere in the universe. But I cannot intelligibly doubt that I am embodied, that I perceiving and interacting with objects the existence of which does not depend on my thinking or will, that there are other minded beings with whom I have meaningful interactions, and so on. (When I teach Descartes, I pretend to doubt these things.)
So I do not reject the very idea of certainty; what I reject is that knowledge depends on certainty, which is another way of saying that knowledge does not rest on a foundation. In my many exchanges with Murray and Kairosfocus on Uncommon Descent, the closest we ever got to mutual understanding was when I pointed out that I’m an anti-foundationalist. But I was not able to convince them that pragmatic anti-foundationalism does not entail nihilism or skepticism.
One point, interesting to me, is that I do not draw conclusions, based on someone being an Idist, about st or must not believe in science.
For example, I see Michael Denton saying he accepts the whole nine yards of the mainstream history of the universe, including evolution and common descent. He thinks it was designed, but he accepts scientific explanations as the best available explanations of how things work.
But the converse doesn’t seem to hold.
Idists — particularly theists — seem to think that because evilutionists are committed to the dogma of evilutionism, we must believe things that we don’t believe and do things that we do not do, reality be damned.
It’s interesting to me that much of the “ethical evolution” that’s occurred in recent history seems to have been closely related to the increase in empirical knowledge, particularly of human biology and culture, that has been brought about by scientific exploration. I’m not sure that the self-correcting nature of ethical knowledge is necessarily all that different than the self-correcting nature of scientific knowledge.
Self correcting nature of Science depends on whether influential scientists hold the correct view. For 100s of years Earth was center of Solar system. Only when the influential set of scientists died did Sun became the center of solar system. Blackhole and String theory exist because of influence of Physicist – not because it is not absurd.
Generations of humans will hold the wrong view because a group of scientists think the views are right, so science is not self correcting. In fact, we don’t know if the self corrected view is correct till it is self corrected further in future and self corrected again and again.
If you get near a point, please feel free to make it.
There was a time, 220 years ago, when certain features of living things were best explained by design.
What “scientists” thought the Earth was the center of the universe? And how were they using the scientific method at the time?
CC:Self correcting nature of Science depends on whether influential scientists hold the correct view. For 100s of years Earth was center of Solar system. Only when the influential set of scientists died did Sun became the center of solar system
It was the improvement of astronomical tools and data which shifted the model of the solar system, data is the self correcting mechanism of science not the mortality of scientists.
Unfortunately I don’t have enough nebulous words and convoluted sentences to make a philosopher understand. May be that’s why I agree with Lawrence Krauss with respect to some philosophers :
No only the King and his horses thought Earth was the center of Solar system.
How naive !
Physicist Max Plank :
coldcoffee,
Your rebuttal to velikovsky is an argument from authority? Really? Hasn’t it occurred to you that Planck might have just been mistaken on this specific point?
A flippant joke; a comment on how scientists (and indeed all people) as they age tend to be less open to new results that challenge what they learnt when younger. In actual fact, science, especially physics, is largely a young person’s game, and no-one waits for the old scientists to die. The history of Quantum Mechanics is a classic case study. Schrodinger was the old man, in his mid thirties. Einstein, being exceptional, still made contributions, but he became an ever more peripheral figure due to his unwillingness to change.
No, there wasn’t such a time. Design (as it was conceived then) does not really constitute an explanation – at least not a scientific explanation.
Then you can no doubt cite the name of the people who had to die before the adoption of Newtons laws, or Einsteins two versions of relativity, or the Bohr atom, or penicillin, or the various vaccines.
Prior to Darwin there was no scientific explanation, nor any expectation of finding one.
I simply said it was the best available.
But I agree that ID has never been science and has never proposed a scientific explanation.
I wonder how would we distinguish between “scientific explanations” and “non-scientific explanations” (“pre-scientific explanations”). Presumably testability, and confirmation from repeated tests, has got something to do with it.
The ‘argument from design’ goes back to antiquity — several of the Presocratics regarded design as a brute fact, and it was only in response to the anti-design metaphysics of the Epicureans that later philosophers — the Neoplatonists and Stoics — really emphasized the ‘argument from design’. (I put ‘argument from design’ in scare-quotes because it’s better thought of as an argument from order to design. Once the implication from order to design has been made, the imputation of a designer follows analytically.)
All this was worked out by Plato, Platonists, and the Stoic philosophers Zeno and Chrysippus long before the argument from design was co-opted by Christian philosophers. In fact — though I’m not entirely sure of this! — I suspect that the appropriation of this argument by Christian philosophers is a very modern move — indeed, central to the Enlightenment — as a reaction to the renaissance of Epicureanism in the 16th century.
The big 3, QM, Godel’s theorems and fractal geometry are each weird enough to spawn their own industry of cranks. Yet I can’t help feeling that somehow they really are pointing at something weird. Something which breaks our entire set of assumptions including a few we consider axiomatic. But in so doing, they also present opportunity for enterprising charlatans.
I’m not sure the “there’s no smoke without fire” argument is a useful axiom beyond avoiding unwanted fires.
ETA spelling
I’m not thinking any of those are weird. I see Gödel’s incompleteness results as a side effect of us going infinite in mathematics. And I see it as having no relevance to reality. QM perhaps points to a limitation in the attempt to give a completely mechanistic account of reality.
I take form QM the idea that explanations form layers like an onion and alternate between analog and digital. I don’t know what this has to do with reality, but I fancy it’s layers all the way down.
Any, there’s plenty to do while waiting for the sun to go red.
The meme is becoming popular though. Compared to the memes of “it’s just a theory” or “it’s just a model” it is fantastically truthy and sciency sounding. Excellent for playing to the rubes. The Wall Street Journal printed a LttE just a few weeks ago using exactly this.
http://bit.ly/1hzwrwz
I beg your pardon for the condescension inherent in the LMGTFY link but it’s the only way I know around the WSJ paywall.
coldcoffee,
So coldcoffee is a (misapplied) Kuhnist?
What velikovskys said. People who insist that science is exclusively dependent on funerals are ignoring the accumulation of data that ever improving technology has enabled. It is new data conflicting with old theory that gives young scientists the chance to make new science. The dependency is between science and technology. Copernicus could never have advanced beyond being a forgotten footnote without Galileo’s telescope and Tycho’s superior instrumentality and skill.
llanitedave,
I think it is reasonable to say that science as it was best understood at that time claimed the Earth was the center of the Universe, backed by no less then the authority of Aristotle. The other misunderstanding, the Earth is flat, is not reasonable. At no time was there ever a scientifically, as ever understood in any time period, valid claim for a flat Earth. That would have been a strictly lay view.
And an interesting side note on just that subject. A few days ago Senator Cruz was interviewed on CNN where he was given to chance to spew ignorance about climate disruption in reply to Secretary Kerry calling climate denialists Flat Earthers. Cruz made exactly that claim; that once upon a time it was the scientific consensus that the earth was flat and only the efforts of skeptics caused the consensus to be changed. The Ignorati strike again!
This could just as well fit in the ‘Concepts’ post but since the quote is coming from Arrington…
Barry Arrington,
Has anyone ever pointed out that the desperate, endless sophistry pretty clearly gives the game away that ID has no science? They are reduced to arguing about MOAR META(!!!!!) because they haven’t got the goods to do otherwise.
I refute it thus.
And since Arrington is a lawyer there is even a relevant lawyer joke.
There are lots of versions but this is the one in my memory.
If you have the facts of the case on your side, argue the facts.
If you have the law on your side, argue the law.
If you have neither the facts nor the law, attack the opposing attorney.
The IDists have no science so they claim the game is rigged against them.