I recently read a book called Freedom Evolves by the philosopher Daniel Dennett. In it, he puts forward the idea that free will is compatible with a deterministic view of the universe.

Determinism is the idea that everything that happens has been determined by a previous state of affairs. Imagine a beaker of liquid. If we know all the positions of the molecules in the liquid at time T we also know their positions at time T + 1 because they will all move in accordance with the laws of physics and we can calculate what their new positions will be. This idea can be applied to the universe as a whole. Theoretically, by knowing the position of every particle at the beginning of the universe and knowing the laws of physics governing those particles you can extrapolate everything that will ever happen.

At face value the idea of determinism seems to contradict the idea of free will. If everything is determined by what has gone before then how can any individual make a free choice? This has caused many thinkers to imagine there is some kind of non-material substance (e.g. mind, soul, spirit) that is not subject to the laws of physics. This supernatural substance is supposedly the seat of our free will and interacts with our brain to freely cause our actions. The philosopher Rene Descartes believed this interaction occurred at the pineal gland (source). I am not comfortable with supernatural entities at the best of times but even less so when they can interact with the natural world (i.e. our brain). Therefore I do not subscribe to dualism and have to account for all our actions from our material brain.

Dennett explains that some people have tried to use quantum indeterminancy to resolve the issue. The trick is to have some form of genuine randomness (through quantum particles) involved in our decision making process such that strict determinism is avoided. I do not know enough about quantum theory to confidently speak about it but I understand that in some way quantum-level randomness is different from the sort of pseudo-randomness you get from a computer algorithm. A computer algorithm will give you a bunch of numbers that seem random to us but they are actually predictable (since a set of deterministic computer instructions creates them). Quantum randomness is supposed to be genuinely random (completely unpredictable).

Dennett does not hold with the quantum explanation though. He states that, even if it were true that quantum level events occur as part of our thought processes, this does not provide us with the free will we seek because by definition we do not control this randomness. Therefore we are just slave to a different kind of process that happens to be random rather than determined. This does not make you any more free in his opinion, and I agree with him.

So what is Dennett's approach? Obviously condensing a large and complex book down to a few paragraphs does not do it justice but there was a particular example he used which I think illustrates his point. Imagine two computers that are designed to play chess. The first is a rather crudely written program which uses a sort of trial and error approach. It will analyse the result of a potential move and according to some basic rules work out whether this move puts it in a better position or not. It may even consider two, or three moves ahead depending on the computing power available. The number of possible moves in chess is so vast that the computer must be constrained in some way to keep it practical. A computer designed in this way will play a serviceable game of chess.

Now consider the second computer. Instead of trial and error it has been equipped with a database of previous chess games by grand-masters, along with a framework for understanding more complex strategies such as protecting the queen, or sacrificing pawns. Due to the superior design this computer plays chess at a much higher level than the first computer.

If you present these two computers with the same chessboard configuration the second computer, due to its design, has more useful options available to it than the first computer. A useful option is defined as one that increases the chances of the computer winning. This gives the second computer more freedom, according to Dennett. The level of freedom is defined by the amount of benefit-enhancing potential moves available. This is despite the fact that both computers are entirely deterministic (because they are running a predictable set of algorithms). Dennett claims that it is the same with humans. Our cognitive equipment presents us with a myriad of potential moves at any point in time and this gives us our freedom even though all the atoms composing our brains follow a deterministic course.

It's an interesting idea and I am drawn to it. It does imply that humans have more free will than, say, a fly because humans are more cognitively equipped. I am comfortable with this notion. However, an extension of this argument is that adult humans have more free will than baby humans. It also implies that the more knowledgeable one gets, the more free will one has. This is because the knowledge one gains presents more options for actions than were previously available. I'm not sure I can get on board with this idea.

What do others think? Can we be free in a deterministic universe?

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Yes. Most modern accounts on free will that I've read are not at all religious or spiritual and agree that with brain death comes eternal oblivion. I agree with you. If there is any free will (in whatever form) that does not automatically mean we have an immortal consciousness.

Free will, as most people think of it, because they don't really think about the ramifications, is a kind of omnipotence, whereby the mind operates in a realm quite apart from the electrochemical processes going on in the brain. This is the realm of the soul. The question then becomes: do you believe in souls? Mortal souls, perhaps, but a kind of soul nonetheless.

I agree, and have always agreed, with this point. That is what most people think of when they consider free will.

I agree also that free will is one of those terms that means something different to everyone who uses it.

I don't know. What they all seem to mean (the common ingredient, if you like) is that people have a type of agency related to their actions/behavior which makes them morally/ethically responsible for all of their conscious decisions and damnable for those deemed to be bad. 

Disagree?

Your common definition isn't bad but of course contains a set of terms that are themselves ambiguous (agency, morally/ethically responsible, conscious). I don't mean to get bogged down in define this/define that discussions because I hate those so instead I will clarify my statement to say that I think that the definition of free will by thinkers like Dennett is non-trivially different from that of most people's use of the term. I don't actually think there is common ground between how most people view free will and how someone like Dennett who has examined it rigorously understand the term.

If they discuss a so-called "free will" that differs from common usage, that kind of makes their discussion irrelevant.

Any solution to a philosophical issue, to be meaningful and relevant, can't get bogged down in jargon, unique definitions or re-definitions of terms, and shouldn't require hours, days, weeks, months, or years of study to understand.

Einstein was able explain his Theory of Relativity in everyday terms, after all so that any person of normal intelligence could understand what he was saying even if they didn't believe it.

Didn't Einey say "If you can't explain it to a six year old, you don't understand it yourself"?

Yes and the quote is referenced in “The Unbelievers” with Krauss and Dawkins.

Chaim Weizmann, a brilliant chemist and the future president of Israel, once accompanied Einstein on a trans-Atlantic sea voyage. After the voyage was over, Weizmann reported:

Einstein explained his theory to me every day, and on my arrival I was fully convinced that he understood it.

The theory of relativity cannot be explained in two sentences. A very vague statement on the implications of the theory yes...the theory itself NO.

Einstein obviously never tried to explain about sharing and taking turns to my six year old niece ;-)

Davis, the theory can be explained simply: Matter and energy are the same thing. Transformations of each other. Simple as that. 

What is hard is a) believing it and b) understanding and b) understanding and believing some of the implications.(e.g., that how quickly you age depends on how fast you are going relative to someone not moving at that speed).

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