-3
$\begingroup$

In the celebrated Free Will Theorem of Conway and Kochen it is made use of "free will" without giving a "mathematical definition" of it. The definition of the experimenter is the "choice" in the parameter of the experiment. The free will of the particle is the "choice" in the response to these parameter. I do not mean do be offending in any way, but I have searched for and not found on formal mathematical concepts of free will.

In mathematics proofs often start by choosing objects like a basis for a vector space, sometimes the result is irrelevant of the choice made, sometimes not. And then there is the Axiom of choice. So there seems to be an intrinsic notion of choice in mathematics. But what about free will?

My naive question is, if someone has some day made an effort in formalizing the notion of free will let's say in a mathematical toy model and what are the consequences of this effort? If there is no such notion yet, what would be a good candidate?

Thanks for your help! I have thought about this problem a little bit and tried to formalize my thought experiment a little bit. My naive idea is about the analogy:

  • one-way-functions exist -> pseudorandomness exists
  • free-will seems from outside like randomness
  • combining these analogies together I tried to formalize "free will" with the above mentioned thought experiment

)

Edit:

It seems that my questions has raised some confusion. Let me rephrase it:

My question aims at consequences of "free will" (toy) mathematical concepts borrowed from philosophy. For example Gödel borrowed from philosophy en.wikipedia.org/wiki/Barber_paradox and it turned out to be interesting in mathematics.

Improve this question
$\endgroup$
10
  • 16
    $\begingroup$ I did not downvote or vote to close, but if you read some of the philosophical literature on free will, you will see that the concept is far too murky and controversial to admit mathematical formalization. The most one can do is to invent some mathematical concept and call it "free will" because it bears some superficial resemblance to the philosophical concept. Or one can use the term informally, as Conway and Kochen did. So I would say that your question is off-topic for MO unless you pick a specific mathematical concept and ask a specific mathematical question about it. $\endgroup$
    – Timothy Chow
    Commented Jun 29, 2021 at 15:36
  • 4
    $\begingroup$ Timothy is right. Math is good at many things, but resolving perennial philosophical debates is not one of them. But given that this futility rarely dissuades mathematicians from trying, I expect this question will attract a lot of half-baked “ideas”. I have therefore voted to close. $\endgroup$
    – Andy Putman
    Commented Jun 29, 2021 at 15:44
  • 3
    $\begingroup$ See also W. Hugh Woodin's article concerning free will and determinism cambridge.org/core/books/infinity/…. This is the article in which he proved his universal algorithm theorem. $\endgroup$
    – Joel David Hamkins
    Commented Jun 29, 2021 at 15:53
  • 4
    $\begingroup$ @stackExchangeUser Just because some philosophical concepts can be mathematically fruitful does not mean that all of them are. You could similarly ask for a mathematical formalization of God, love, morality, politics, beauty, music, purpose, boredom, Harry Potter, or stamp collecting. Unless the question is more precise, it will not be a good fit for MO. $\endgroup$
    – Timothy Chow
    Commented Jun 29, 2021 at 15:55
  • 1
    $\begingroup$ @Tim, Birkhoff wrote a book about his mathematical formalization of beauty. Here's a link to a review: ams.org/journals/bull/1934-40-01/S0002-9904-1934-05764-1/… $\endgroup$
    – Gerry Myerson
    Commented Jun 30, 2021 at 1:37

1 Answer 1

Reset to default
11
$\begingroup$

Seth Lloyd published A Turing test for free will.

The theory of computation implies that, even when our decisions arise from a completely deterministic decision-making process, the outcomes of that process can be intrinsically unpredictable, even to – especially to –ourselves. I argue that this intrinsic computational unpredictability of the decision-making process is what gives rise to our impression that we possess free will. Finally, I propose a ‘Turing test’ for free will: a decision-maker who passes this test will tend to believe that he, she, or it possesses free will, whether the world is deterministic or not.

Improve this answer
$\endgroup$
0

Not the answer you're looking for? Browse other questions tagged .