Thursday, 15 May 2025

Do Mysterians Believe That Science Will Leave the Mysteries Unexplained… Forever?

 It’s helpful to distinguish two types of mysterian: (1) Those who both yearn for, and depend upon, mysteries. (2) Those who discover what they deem to be “mysteries” through philosophical analysis and looking at the available science. Mysterians of type (1) don’t want science to even consider that which they believe to be (essentially) mysterious. Chomsky, McGinn, Fodor, Pinker, etc. are mysterians of type (2).

The Mysteries and Cognitive Closure

“Free will, for instance, looks upon early inspection to be impossible, so we try to find some conception of it that permits its existence, but this conception always turns out to be dubiously reductive and distorting, leaving us with the unpalatable options of magic, elimination or quietism. [ ] so we hop unhappily from one unsatisfactory option to the next; or dig our heels (squintingly) into a position that seems the least intellectually unconscionable of the bunch [ ].”

If readers were to accept McGinn’s account above, then that would clearly show us why free will — and many other “mysteries”— have been the (to use a common phrase) “perennial problems of philosophy”.

Mysteries Forever?

Colin McGinn’s P

Colin McGinn

“it must be in virtue of some natural property of the brain that organisms are conscious”.

McGinn then concludes:

“There just has to be some explanation for how brains subserves minds.”

Why must P be natural?

Scientism

“new mysterianism is a postmodern position designed to drive a railroad spike through the heart of scientism”.

This passage brings forth a rather predictable binary oppositionmysterianism vs scientism.

“[Scientism is] an exaggerated trust in the efficacy of the methods of natural science applied to all areas of investigation (as in philosophy, the social sciences, and the humanities). [] [S]ome scholars, as well as political and religious leaders, have also adopted it as a pejorative term [].”

Scientism can be seen as a position (or stance) on the huge importance of science to philosophy, and — often more broadly — to just about everything else. Thus, this position needn’t be taken to be a philosophy which advances independent arguments (or positions) on philosophical subjects. Indeed, if it did do such things, then it would be like a position within philosophy (just like idealism or physicalism)…

Pseudo-Mysterians

Richard Wright, Rebecca Goldstein and David Chalmers

Religious/Spiritual Mysterians

“The ‘old mysterians’ were dualists who thought that consciousness cannot be understood scientifically because it operates according to nonnatural principles and possesses nonnatural properties.”

Here Flanagan ties the “old mysterians” to the dualists. The dualists, in turn, believed in “nonnatural principles” and “nonnatural properties”. [See note.]

Note:

(1) It may seem odd that mysterianism is sometimes seen as “a form of nonreductive physicalism”. That’s mainly because idealists and spiritual philosophers deem physicalism to always be “scientistic”, whichever form it takes.

Tuesday, 13 May 2025

Gödel’s Logical Proof of God’s Existence Depends on Religious Assumptions

Kurt Gödel’s proof of God’s existence may well work logically. Indeed, it may even be logically flawless. However, it doesn’t actually prove that God exists. Instead, it proves that *if* the axioms are taken to be true, *then* we must conclude that God exists.

(i) Introduction
(ii) The Philosophy and Metalogic of Gödel’s Proof
(iii) Things “Logically Follow” From False and Absurd Axioms
(iv) Is Gödel’s Proof a Language Game?
(v) Gödel’s Theo-logical Proof?
(vi) Conclusion: Gödel’s “Fourteen Points”

The first version of Kurt Gödel’s ontological proof of God’s existence dates back to 1941. However, Gödel didn’t tell anyone about it until 1970, when he believed he was dying.

It’s not entirely clear why Gödel kept his proof to himself. One commentator wrote the following words:

“The shy Gödel feared ridicule. He probably told Einstein about his God Proof, but he told nobody else until 1970, and he never went public.”

And, in 1970, the German mathematical economist Oskar Morgenstern wrote (in his diary) that Gödel wouldn’t publish his proof because he was afraid that other people may think that “he actually believes in God”.

Despite Morgenstern’s words, it’s clear that Gödel believed in both God and the afterlife long before he constructed his ontological proof. Indeed, he actually argued in detail that people should believe in an afterlife. [See here.]

Moreover, the Chinese-American logician and mathematician Hao Wang stated (in his book A Logical Journey: From Gödel to Philosophy) that Gödel’s wife (Adel) said that Gödel

“although he did not go to church, was religious and read the Bible in bed every Sunday morning”.

What did Gödel himself say?

In an answer to a questionnaire, Gödel described his religion as “baptized Lutheran”. He also went on to say that he wasn’t a “member of any religious congregation”. Gödel continued:

“My belief is theistic, not pantheistic, following Leibniz rather than Spinoza.”

The Philosophy and Metalogic of Gödel’s Proof

It’s quite incredible that Gödel provided no arguments as to why the axioms in his ontological argument are true. It seems that he must have taken them to be true primarily because they belong to a long and venerable philosophical tradition of “ontological arguments”. (This tradition involved the philosophers Anselm, Descartes, Spinoza, Leibniz, and many others. [See here.])

Since Gödel’s axioms aren’t argued for, then their embedded terms can be seen to be arbitrary. Indeed, they can even be seen as logical placeholders.

(Here’s some of those embedded terms and axioms: “Godlike”, “positive property”, “A Godlike object exists in every possible world”, “The property of being God-like is positive”, and “God, by definition, is that for which no greater can be conceived”.)

The Australian philosopher Graham Oppy picked up on all this. He argued that

“many other almost-gods would also be ‘proven’ through Gödel’s axioms”.

In other words, if the axioms referred to almost-gods rather than to God, then their existence would also be proven using Gödel’s very own logico-theological (or theo-logical) system.

Similarly, the theoretical physicist Manon Bischoff writes:

“[A]s logicians have shown, it is possible to construct cases where, by Gödel’s definition, there are more than 700 divine entities that differ in essence.”

In terms of the logic of logical systems.

Things “Logically Follow” From False and Absurd Axioms

From the axiom that (to take just one example)

“God, by definition, is that for which no greater can be conceived”

all sorts of things follow.

In simple terms. In logic, if the axioms (or premises) are taken to be true (or simply accepted as they stand), then all sorts of things will follow from them. Indeed, this is why there’s a metalogical distinction made between sound and valid arguments. [See here.]

As one writer put it:

“A proof does not necessitate that the conclusion be correct, but rather that by accepting the axioms, the conclusion follows logically.”

That sentence summarises the point being made here… However, I would dispute the use of the word “correct”. That’s because we should really have the following statement:

A proof does not necessitate that the conclusion be true.

… Unless, of course, this writer is simply using the word “correct” as a synonym for the word “true”.

In detail.

It’s usually the case that the moves in a logical argument (or in a proof) are said to be “correct”, whereas its premises (if not axioms) can be taken to be (or actually are) true or false. Thus, conclusions still “follow logically” from false premises or axioms.

In Gödel’s case, perhaps, conclusions still follow from false (e.g., “Napoleon is alive”) or even absurd (e.g., “The number 4 is happy”) axioms.

Let’s now discuss Gödel’s proof (or system) from a broader metalogical and philosophical point of view.

Is Gödel’s Proof a Language Game?

Perhaps Gödel’s proof constitutes a Wittgensteinian language game.

The term “language game” is used here because all the terms and arguments within Gödel’s ontological proof mutually reinforce each other. Relevantly, that’s without them necessarily having any meaning (or relevance) to anything on the outside of the actual system (or game).

Take Wittgenstein’s discussion of the Liar paradox.

Paradoxes like the Liar were seen — by Wittgenstein — to arise within various language games. At first glance, then, Wittgenstein was perfectly correct to use the philosophical term (his own) “language-game” to refer to the Liar Paradox.

To add to Wittgenstein himself.

The Liar Paradox (as treated by Gödel and others) is internal to a language game which allows a very specific — and very odd — kind of self-reference

But, again, why use the term “language game” here?

Well, in which other language would you ever find the seemingly-empty statement, “This sentence is false”? Indeed, even it’s supposed everyday translation — “I am a liar” — seems somewhat contrived.

Now compare “This sentence is false” to Gödel’s own “The property of being God-like is positive” (or to “A Godlike object exists in every possible world”).

Thus, these kinds of sentence simply don’t belong to everyday languages at all. They all belong to specific (technical) language games.

More specifically, if these statements (e.g., “This sentence is false” and “The property of being God-like is positive”) are scientifically and empirically empty, then perhaps we really don’t need to worry about the possibility of Gödel’s faulty circularity.

Of course, logicians can — and do — use weirder statements such as “Bricks have a sense of humour” or “The number 2 is blue” logically. That is, they can assign a truth value to such statements, and then treat them as pure syntactic stringsfrom which they can derive further statements and conclusions. Similarly, we can programme the words “The number 2 is blue” into a computer, and then that computer can grind out further conclusions or statements (i.e., if it’s programmed in the right way).

To repeat. Wittgenstein didn’t argue that such language games were bogus, or even that they have no value. Instead, he simply saw them as being part of particular (technical) systems. And from that, many other things followed.

To sum up with specific reference to Gödel’s ontological proof.

The whole of Gödel’s proof seems circular in that every term and argument relies on every other term and argument within the system. [See ‘Circular reasoning’.] Thus, if you buy into one of Gödel’s terms (such as “positive property” or “Godlikeness”), then all the other terms and conclusions seem to come along with it.

This is Gödel’s theo-logical package deal.

This is Gödel’s ontological proof.

Gödel’s Theo-logical System?

According to the German philosopher André Fuhrmann, “theology” is actually embedded in Gödel’s logical proof. [See here.]

Well, Gödel’s axioms certainly include the words “positive property”, “God-like”, “Godlikeness”, “essence”, etc. Thus, these terms certainly don’t belong to either science or logic. Indeed, Gödel did take his axiomatic terms as primitives. (Perhaps equivalent to David Hilbert’s “point”, “line”, “plane”, etc.)

Gödel’s axiomatic terms — though not their logical treatment! — are actually theological and aesthetic. Indeed, Gödel himself wrote (as quoted by Dr Thomas Gawlick):

“‘Positive’ means positive in the moral aesthetic sense [ ].”

Of course, all these extra-logical terms and assumptions can still be treated logically.

And Gödel did treat them logically.

But, again, terms like “positive property”, “God-like”, “essence”, etc. don’t belong to logic, even if they can be treated logically.

To sum up. Gödel’s proof may well work logically. It may even be logically flawless. However, it doesn’t actually prove that God exists. Instead, it proves that if the axioms are taken to be true, then we must conclude that God exists.

Conclusion: Gödel’s “Fourteen Points”

The extra-logical basis of Gödel’s proof of God’s existence can be seen in his “fourteen points”. So perhaps the true axioms — even if that term is used loosely here— of Gödel’s overall theo-logical worldview can be found in this set of fourteen points:

(1) The world is rational.

(2) Human reason can, in principle, be developed more highly (through certain techniques).

(3) There are systematic methods for the solution of all problems (also art, etc.).

(4) There are other worlds and rational beings of a different and higher kind.

(5) The world in which we live is not the only one in which we shall live or have lived.

(6) There is incomparably more knowable a priori than is currently known.

(7) The development of human thought since the Renaissance is thoroughly intelligible (durchaus einsichtige).

(8) Reason in mankind will be developed in every direction.

(9) Formal rights comprise a real science.

(10) Materialism is false.

(11) The higher beings are connected to the others by analogy, not by composition.

(12) Concepts have an objective existence.

(13) There is a scientific (exact) philosophy and theology, which deals with concepts of the highest abstractness; and this is also most highly fruitful for science.

(14) Religions are, for the most part, bad — but religion is not.

As stated, these 14 points are sufficient to establish an entire theological worldview. However, any discussion of them will have to wait until another time.