Aug 26, 2011

Free Will and Determinism, part 3

Part 2:
Part 3:
Part 4:
Part 5:
Part 6:
Part 7:

One interpretation of Free Will attributes the people power over facts of the future, which is addressed by the incompatibilist argument:

  • No one has power over the facts of the past and the laws of nature.

  • No one has power over the fact that the facts of the past and the laws of nature entail every fact of the future (i.e., determinism is true).

  • Therefore, no one has power over the facts of the future.
Issues with this have primarily come in the form over differences in "facts of the past" and "the laws of nature" with regards to Free Will and Determinism. Clearly we do not have direct control over the facts of the past, nor do we have direct control over the laws of nature. On the surface it would seem that this argument holds.

Some compatabilists contend that applying these definitions to Free Will is nonsensical and not required. For example, even if I don't have control over the facts of the past, and even if the facts of the past determine the facts of the future, it is still possible for me to choose other than I did because it is possible for the facts of the past to have been other than what they were to lead to a future where I chose otherwise.

Another way to state this is if some version of the past, P1, entails some version of the future F1, then the fact that P1 entails F1 (P1 -> F1) doesn't negate the possibility of another future, say F2, it's just that if F2 were the case, then it would have been entailed by a different past, say, P2. That only one past and one future actually happen is immaterial. That we can't alter what actually happens is also immaterial. What matters is that, if multiple pasts are possible, then so are the futures they entail. Since there are multiple possible futures with regards to our choices, we have Free Will.

This reasoning also applies to the "laws of nature" aspect. Instead of the past entailing the future, the laws of nature entail it. Since other laws of nature are possible, then so are other futures and we still have Free Will. Ultimately, the manner in which the past and the laws of nature entail the future do not forbid us from having Free Will.

This invokes a conception of Free Will using what is known as modal logic. Without getting too in depth, modal logic involves possibilities, actualities, and necessities and is often visualized through the concept of "possible worlds." Something is actually true if it actually happened, something is possibly true if it could have happened in some possible world, and something necessarily happened if it must happen in all possible worlds.

The terms "possibly" and "necessity" are related to each other. If something is necessary, then it is not possible for it not to happen, and if something is possible, then it is not necessary for it not to happen. In short, we can consider something as "possible" if there are some possible starting conditions which could logically result in it and we can consider something "necessary" if there are not possible conditions which wouldn't result in it.

In this sense, we are judged as having Free Will if any action is possible, whether or not the conditions required to bring about the alternate possibility happened. If P1 entails F1 and P2 entails F2, and both P1 and P2 are possible, then so are F1 and F2.* Since F1 and F2 are possibilities in the modal sense, then we have Free Will, even if they arise from drastically different past conditions.

A more in depth analysis shows that this definition of Free Will is lacking in two ways. First, there are scenarios which meet these requirements that defy our application of Free Will and, two, it contradicts with determinism at a more fundamental level.

First, consider this scenario:

I come to a narrow bridge and see a person on the other side that is hurt and needs my help. I can choose to cross the bridge or not. So I have Free Will in this decision.

However, what if there is a storm that has knocked a tree down across the bridge, preventing from me getting to the person. Do I still have Free Will in helping the person? According to the modal interpretation of Free Will: Yes.

Take P1 to mean a past where the bridge is open and accessible, and F1 to be a future arising from that past where I help the person.

Take P2 to mean a past where the bridge is closed off and F2 to be a future arising from that past where I don't help the person.

Since both pasts are possible, so are both futures and, therefore, I have Free Will. I freely chose not to help the person even if a tree blocks my path.

Clearly this is absurd and indicates something lacking in this depiction of Free Will.

The error comes in how to resolve this depiction of Free Will with determinism. We are taking for granted the possibility of other pasts or other laws of nature. If determinism is true then any past and any set of the laws of nature must be determined. So, on what are they determined?

If something is determined, then it is determined by some preexisting state. If there are two possible laws of nature, and determinism is true, then they must each be determined by mutually exclusive preexisting states, each of which themselves must be determined.

We can avoid infinite regression only be accepting some initial state which is determined, not by some temporally prior preexisting state, but by simply being necessary. That is, it is not possible for it to be any other way; it is determined by its own necessity. But mutually exclusive laws of nature can't be necessary; there can only be one necessary set of the laws of nature. Through this, we eliminate the other possibilities as illogical.

This applies to the facts of the past as well. We must start at some initial set of conditions that are necessary. Since we have reduced reality to a single set of the facts of the past, and a single set of the laws of the nature, only one unique sequence of future events can be determined from that, precluding us from claiming Free Will on the basis of possible pasts or possible alternates to the actual laws of nature.

Some may conclude from this reasoning that determinism is therefore false, which may be the case. It nevertheless shows that it is incompatible with Free Will.

* the argument here may not be obvious. Essentially I have argued that if P1 -> F1 and P1 is possible, then so is F1. We can demonstrate this via contradiction:

Assume that F1 is not possible. If F1 is not possible then anything that entails F1 is also not possible. P1 entails F1, but is possible, given our premises. This is a contradiction, thefore F1 is possible.

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