Tag Gödel

Free – why science hasn’t disproved free will

Geir Isene 101 Comments

It’s a short book by Alfred Mele, a Professor of Philosophy at Florida State University. Mele was the director of the Big Questions in Free Will Project (2010-2013) and has authored several books and a large amount of articles on the subject.

Mele tackles the main scientific studies proclaiming that free will is an illusion. He takes them down, one by one, showing that they all suffer from several logical fallacies. But they have one fallacy in common, the Black Swan fallacy. That you have only seen white swans does not rule out the existence of black swans. That scientific experiments have not proven the existence of an agent of free will does not preclude the existence of free will. Some experiments doesn’t even look in the right places.

It’s an important book on the subject.

I take another route in my exploration of free will – a more principled approach if you will. And lately, I have revisited my “proof against determinism” and focused more on Alan Turing’s work. Looking at the Universe itself as one great computational device, Turing’s proof of the “halting problem” shows that there cannot be a Theory of Everything – there cannot be any all encompassing theory that will show everything as true or false. This is of course in line with Gödel’s Incompleteness Theorems, but it seems to be a more direct route in proving that the universe cannot be deterministic. Which in turn leaves existence open for free will.

Time and the incomplete universe

Geir Isene 35 Comments

It seems the Italian philosopher Giordano Bruno was ahead of Kurt Gödel by a few centuries with his hunch:

There is no law governing all things.

Statue of Giordano Bruno, Campo de’ Fiori, Rome

He also made an interesting statement regarding time:

Time is the father of truth, its mother is our mind.

Which brings me to a notion that I share with the Russian-American novelist Vladimir Nabokov:

I confess, I do not believe in time.

More on Gödel’s

Geir Isene 162 Comments

As the discussion on my previous blog post got rolling, Vinaire posted an excellent comment that I thought warranted a blog post on its own.

Reference links:

Vinaire’s comment:

Godel’s incompleteness theorem applies only to axiomatic systems capable of doing arithmetic. I do not know if Godel’s argument can be extended to as complex a system as the universe.

Definitions:

de•ter•min•ism (noun)
1. the doctrine that all facts and events exemplify natural laws.
2. the doctrine that all events, including human choices and decisions, have sufficient causes.

axiomatic system
In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems.

complete
A set of axioms is complete if, for any statement in the axioms’ language, either that statement or its negation is provable from the axioms.

consistent
A set of axioms is (simply) consistent if there is no statement such that both the statement and its negation are provable from the axioms.

e·nu·mer·ate verb (used with object)
1. to mention separately as if in counting; name one by one; specify, as in a list: Let me enumerate the many flaws in your hypothesis.
2. to ascertain the number of; count.

effectively generated
A formal theory is said to be effectively generated if there is a computer program that, in principle, could enumerate all the axioms of the theory without listing any statements that are not axioms. This is equivalent to the existence of a program that enumerates all the theorems of the theory without enumerating any statements that are not theorems.

Gödel’s first incompleteness theorem states that:

Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory…

Gödel’s theorem shows that, in theories that include a small portion of number theory, a complete and consistent finite list of axioms can never be created, nor even an infinite list that can be enumerated by a computer program. Each time a new statement is added as an axiom, there are other true statements that still cannot be proved, even with the new axiom. If an axiom is ever added that makes the system complete, it does so at the cost of making the system inconsistent.

There are complete and consistent lists of axioms for arithmetic that cannot be enumerated by a computer program. For example, one might take all true statements about the natural numbers to be axioms (and no false statements), which gives the theory known as “true arithmetic”. The difficulty is that there is no mechanical way to decide, given a statement about the natural numbers, whether it is an axiom of this theory, and thus there is no effective way to verify a formal proof in this theory.

This may mean that if this universe (with both its physical and spiritual aspects) can be expressed through a consistent set of principles, then there is a truth about this universe that cannot be demonstrated using those set of principles. That truth may look at this universe (as a whole) exactly for what it is. Such a truth may not be derivable from the set of principles that supposedly describe the universe.

Gödel’s second incompleteness theorem states that:

For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent.

The second incompleteness theorem does not rule out consistency proofs altogether, only consistency proofs that could be formalized in the theory that is proved consistent. The second incompleteness theorem is similar to the Liar’s paradox, “This sentence is false,” which contains an inherent contradiction about its truth value.

This may mean that this universe cannot contain the ultimate truth about itself. The ultimate truth is unknowable from the reference point of this universe.

If we go by the definition of determinism that all facts and events exemplify natural laws, we cannot say for certain if that is true or not. In other words, not everything may be predictable ahead of its occurrence.

Manifestations may be related to each other in strict logical sequence meaning that any manifestation may be shown to follow from another manifestation. However, it may be impossible to determine how a manifestation may come to be on its own. This is another version of saying, “Absolutes are unattainable.”

So a system may be deterministic only in a relative sense. It can neither be absolutely deterministic, nor can it be absolutely non-deterministic.

Link to article on Vinaire’s blog: Gödel and Determinism

Gödel and the complete and consistent Scientology bubble

Geir Isene 133 Comments

Was playing around with Xtranormal:

Peter: “Hello, I am a Scientologist. Have you heard about Scientology?”

Jane: “Oh! Isn’t that the weird science fiction cult created by that Blubbard guy?”

Peter: “No-no. Scientology is an applied religious philosophy which contains tools that anyone can use to improve their life. These are workable tools that have been proven to be uniformly successful if they are applied correctly. It provides a bridge to total freedom. It is complete and consistent. Complete and consistent.”

Jane: “Have you heard about the incompleteness theorems by… Gödel?”

Peter: “I missed that part of Scientology. Is it part of the class twelve course?”

Jane: “It’s part of the world outside the Scientology bubble.”

You can create a free account and submit a video if you like 🙂