# Is free will compatible with determinism? (Ramsey theorem)

Do we have free will? Or everything is already determined? Are they mutually exclusive? I think they can coexist and have something similar to a proof here and would like to know your thought There is a theorem in math which is called Ramsey Theory. A simple version of it goes like this:

Consider a complete graph on six vertices (where every vertex has an edge connecting it with every other vertex, for a total of 15 edges): you are allowed to color each edge either blue or red. whatever you want! So far so good. Now the theorem says that no matter how you decide to color the edges, there will be always a triangle whose edges are either blue or red. Meaning that, any two-coloring of this graph has a triangle that is either blue or red. I attached an example. there are 2 rise to the power of 15 possible coloring. All of them has three vertices that are connected by edges of the same color

So what's the takeaway if you expand this finding? you are free to choose whatever color you want, but no matter what you chose, you will get a triangle whose edges are of the same color . Our lives could be like this too. We could have free will. Yet we are also bound to causality which makes the world determined. There is no reason to believe that free will and determinism are mutually exclusive

• Good observation- At first it sounds like an outright contradiction in terms to place, free and determinism together. But Spinoza maintained that freedom and necessity are linked. He maintained that free-will is an illusion that occurs because people do not recognize the causation which drives their actions. At the same time he maintained that recognizing that our choices do clearly exist, but they do so in a limited sense due to the experiences which fundamentally shape our lives. Understanding this arrangement enables us to make better choices. Google Spinoza and free-necessity.
– user37981
Sep 12, 2020 at 4:08
• You are confusing free will with absolute power. Yes, laws of logic and mathematics would hold no matter what we do, indeed, even laws of physics would, energy will be conserved no matter what we do as well. This is not what free will is about, it is about whether mathematical and physical constraints leave room for non-unique choices that are undetermined by them, see SEP, Free Will. And there are plenty of distinct graph colorings, so this analogy is moot, but the answer remains controversial for other reasons. Sep 12, 2020 at 7:41
• This is just a more complicated example of the old rule imposed by an Oxford University college to protect the moral behaviour of its students: "If any student has two or more visitors in his room after 8pm, at least two of the people present must be of the same sex." Sep 12, 2020 at 15:21
• As with almost every philosophical argument, this one depends very sensitively on what your precise definition of "free will" is. Without providing such a definition, any discussion is bound to be misunderstood by one party or the other. Sep 12, 2020 at 21:36
• Virtually everyone who disagrees with your conclusion will concede that you can't violate the laws of mathematics. Most will even agree that you can't violate the laws of physics, by, say, flapping your arms to fly through the air, which is the usual example of a limitation on free will that isn't in any dispute. How does your K₆ argument extend to the fact that you couldn't have eaten your hash browns first this morning because initial conditions set before you were born entail that you ate the eggs first? If it doesn't, then whose view of free will are you arguing against? Sep 13, 2020 at 3:18

There is no short and easy answer which is uncontroversial. Metaphysical presumptions lead to different answers with different levels of sophistication of theory based on such perspectives as compatibilists and non-compatibilists and variants thereof. The nature of causality and events is also controversial.

Take a step back and parse what's really happening here. Ramsey's Theorem is a combinatorial theorem which essentially says that there exists a class of mathematical objects under the right conditions such that the freedom regarding the variables of edge-labeling is independent of the existence of a particular type of a monochromatic subgraph. That means, if given all permutations possible of the sufficiently large complete graph, no matter which permutation one pulls out of the metaphorical bag of choices, one is bound to get a graph with a monochromatic clique (in the general case).

If one uses a typical definition of free will, one is presented with:

Free will is the ability to choose between different possible courses of action unimpeded.

What you are asking has a few things that require unpacking first.

The theorem in question is a product of deduction. A deduction by definition says that if the hypothesis is true, than the conclusion is true, and in this case, the theorem says more specifically that any hypothesis chosen (a distinct permutation), the conclusion is the same (a monochromatic clique). But the question springs to mind, if every choice leads to the same consequence, is it really a choice? Henry Ford is quoted as saying that "A customer can have a car painted any color he wants as long as it’s black”. This is known eponymously as Hobson's choice. But what does it mean to make a choice? One interesting finding in cognitive science is that the brain reflects a choice before an individual's phenomenological awareness thereof.

What can be taken from this intuitionally is that there is and is not an element of free will involved depending on context of theory. A person can choose not to choose, and that is a choice; and in your example, if a person chooses a permutation, she will wind up with a unique graph by definition; but that that graph also contains some commonality with all graphs means that the person is not free to choose a graph from the set without a monochromatic clique. So, whether or not one views this as an act of free will is contingent upon how the situation is framed AND one's metaphysical presumptions about the definitions and relationships of and between free will and determinism.

Part of the consideration you need give to the question is that the essence of determinism is up for grabs too! The immaterialist George Berkeley and eliminative materialist Daniel Dennett all have very different views on what constitutes determinism to begin with.

One simple example of how complicated things might be that if you accept Cartesian dualism, there is no causality between the material and mental. Can one say that the mental choice (if it really is a choice) to roll a dice (a physical object) leads to an outcome which requires apprehension of the abstract? Is the dice roll predetermined, and how would you know? A theologian would argue divine revelation makes it part of God's predetermination. Would someone who rejects supernaturalism accept that?

This issue has been without consensus since time barely memorial; it will likely stay active and vigorously debated.

• wow! I need sometime to understand your response. It's not easy for a Non-philosophy major student to grasp this. Much appreciated for your time. Sep 13, 2020 at 3:33
• @navid No problem. I'm afriad my answer is more a morass of questions to help you find your own answer to the problem. If you need any clarifications or guidance, hit me up and I'll do my best. We're all on the same journey.
– J D
Sep 13, 2020 at 5:54

Once you be precise about what each of those terms mean, you would not be asking this question. Standard notions of determinism state that everything is determined, not just that some things are determined... For a better example than Ramsey's theorem, notice that whether you have free will or not, it always is the case in our world that something exists.

"We could have free will. Yet we are also bound to causality which makes the world determined. There is no reason to believe that free will and determinism are mutually exclusive"

Good observation- At first it sounds like an outright contradiction in terms to place, free and determinism together. But Spinoza maintained that freedom and necessity are linked. He maintained that free-will is an illusion that occurs because people do not recognize the causation which drives their actions. At the same time he maintained that recognizing that our choices do clearly exist, but they do so in a limited sense due to the experiences which fundamentally shape our lives. Understanding this arrangement enables us to make better choices. Google Spinoza and free-necessity. – Charles M Saunders 10 hours ago

• Thanks for your opinion, much appreciated. Will definitely read some Spinoza. Sep 13, 2020 at 3:34

Even given:

• physicalism / existence monism;
• computationalism; and
• determinism,

free will can still be shown to exist. (Relaxing these constraints should preserve the conclusion, though this is left as an exercise for the reader.) The argument goes like this:

1. You have a brain.
2. The process going on in your brain is what makes you you.
4. Therefore, you make your decisions.

If the process in your brain was different, then the decisions made would be different – but also, there would be a different you. Determinism, then, does not restrict your actions; only the bounds on the kinds of people that can exist. (You didn't choose to exist, did you? That's true regardless of whether determinism holds; if that's your standard for free will, you're going to have some problems with it (see the bit about Author* control).)

In fact, non-determinism might be said to have more free will problems; with non-determinism your decisions are not entirely due to you, because they're being randomised as you're trying to make them. (Then again, all non-deterministic computations can be modelled as deterministic computations with additional, random input, so perhaps this isn't a concern within computationalism.)

If you want your decisions to come from somewhere outside of reality, but you've accepted physicalism, then you're out of luck. But if you're satisfied with your decisions taking place in your own head, such that you are a necessary part of the decision-making process, and a different decision being made if you wanted a different decision to be made, then determinism implies free will.

• Do you have a brain, or are you a brain? Also, if you are not free from causation, what are you free from? Causation is the only thing to be free from. This seems to just say that "there is will" not that the will is "free". On the other hand, the same argument could be made to any entity that makes a decision, so a computer program would have "will", which here is argued to be "free" Sep 15, 2020 at 3:42
• @GettnDer If you are in prison and cannot escape, forced to do what somebody else wants you to, do you have free will? What about when drugged out of your mind? Those are both things to be free from. Sep 15, 2020 at 6:19
• Freedom from causality means freedom from your actions following from your decisions; I don't think I'd call that free. A deterministic universe universe technically has constraints on what actions will be taken, but that's because it has constraints too on what kinds of people would exist. Different people would take different decisions; that's a counterfactual, but it's a true counterfactual. You didn't choose to exist, but you are still determining your decisions. (What else would be? It's not as if someone else is writing in my writing style in this comment box.) Sep 15, 2020 at 6:24
• As far as free will is concerned, freedom from causation is the only relevant part. If you are in a prison, you remain free to do as you will within the constrains of the prison (not unlike the constraints of determinism). What I am specifically trying to get at, what is the difference between a human and an automaton with this definition of free will? I fail to understand why this "free will" would not apply to any computer. e.g.: In a Cartesian world, the physical could be bound by determinism and the "pineal gland" being affected by something non-physical (mind) would be indeed free. Sep 15, 2020 at 22:19
• Well, technically you could simulate the entire rest of the universe, including the other people… but I rarely see anyone proposing that (and Yudkowsky would argue that that's equivalent to being causally linked to the universe). Sep 16, 2020 at 19:39

Your question falls apart with "you are free to choose whatever color you want,". This is basically an assumption of free will. You go on to point out all coloring schemes are constrained by your example to always have a blue or red triangle.

Such examples are endless. If you have five balls to put in six boxes you will always have a box without a ball in it. Even better if you have one ball and two boxes you'll always have one without a ball in it. The inevitable conclusion has nothing to do with free will. Your argument shows that even if we have free will we can't avoid logical constraints.

Perhaps you have an emotional interest in believing in free will.

If the many worlds theory of quantum mechanics is true, then each possible timeline for the universe exists as a parallel world. Free will selects which parallel world you live in; but it is predetermined that world will exist.

• That's not what Many Worlds says – at least, not alone. You also have to posit dualism and that the soul-essence is torn away from certain evolutions of the Schrödinger equation, which necessarily implies that ≈everyone around you is a soulless husk – the whole thing is revealed to be absurd if you think about it. Sep 13, 2020 at 8:32
• Einstein also thought quantum mechanics was absurd, especially “spooky action at a distance”. It breaks credibility with how we view the universe. That said, Einstein was eventually proven wrong by the Bell test... Now we have satellites using entangled particles for quantum key distribution, which is a direct application of quantum mechanic’s spooky action at a distance. Sep 13, 2020 at 16:46
• Einstein wasn't proven wrong by the Bell test, though. Einstein was convinced that the universe didn't work the way he and his contemporaries thought quantum mechanics worked, and ultimately he was right; quantum mechanics doesn't work how they thought it did. Sep 13, 2020 at 17:12
• To address this answer more specifically, Einstein would not have thought MWI absurd – at least, it succeeds on the counts that Einstein criticised contemporary QM for. You, however, are claiming something that implies that quantum mechanics claims that everyone around you is a philosophical zombie; I call that absurd. Sep 13, 2020 at 17:13
• Are you disagreeing that in the MWI, all possible outcomes are realized? Sep 13, 2020 at 17:26