My Logical Discovery

Ok, this is how I beat the teacher/author (depending on who actually screwed up the proof)...

Here is the proof as shown by my teacher:

Key Terms -

• Op: a fact or condition about the world that would be true in all possible worlds(for instance, the laws of logic and mathematics)
• Np: a fact or condition about the world that no human(s) could even remotely be morally responsible for (for instance, the state of the universe before humanity existed)
• S: Any single moment in history. (for the purposes of this proof, we'll take one before humanity existed)
• L: The laws of nature
• T: Any truth
• ->: this is an "if, then" modifier. It means "this, therefore that"

Logical Rules -

• Rule A: Op -> Np (If something is true in all possible worlds, then no human can be held morally responsible for it)
• Rule B: Np + N(p -> q) -> Nq (If no human can be held responsible for some fact p, and if p is true, then q must be true too, then no human can be held responsible for q either)

Proof -

• O((S + L) -> T) (this is the definition of what determinism is, as the author describes it. "Any one moment in history, plus the laws of nature, can reveal the truth about any other time or place." The O in front is controversial, in that it might be possible for other worlds to exist where determinism is not true.)
• O(S -> (L -> T)) (this is just logical rearrangement. All you need to know is that it means the same thing as the first statement. Essentially the first one is allowing either S or L to change, causing T to be true. The second, however, is saying that if we fix S, then only L can change to cause T to be true)
• N(S -> (L -> T)) (Using Rule A, I can change the O to an N)
• Ns (This is a premise. This represents a moment for which no human is responsible. An instance of this would be a time before humans existed. Humans cannot be responsible for something that happened before they existed. There obviously was a time before humans existed, so this is a valid premise.)
• N(L -> T) (Using Rule B, I can say that no human is responsible for the fact that the laws of nature entail what is true. I can do this, because the above premise states that there is a time for which no human is responsible.)
• Nl (Another premise. This says that no human is responsible for the laws of nature. I think it is relatively obvious that this is true.)
• Nt (This is the conclusion. Using Rule B again, we can say that no human is morally responsible for any truth. That would include any actions, thoughts, facts, etc about the world. I can do this because the above premise states that no human is responsible for the laws of nature.)

I found this to be a very powerful argument, that on the surface, beyond the logical figures, makes great sense. If the past and the laws of nature determine our future, and we cannot control the past or the laws of nature, how can be be held responsible for what we do in our futures?

There still was that problem with that first statement though. As we were discussing the matter, however, it occurred to me that if determinism is true, that no human would be responsible for its being true. Furthermore, it would seem that the very process of determinism is in itself a law of nature! Since we cannot be held responsible for the laws of nature, we cannot be held responsible for determinism!

I raised my hand. When the teacher called on me, I pointed out that it would be easier to just say "

N((S + L) -> T)" in the first statement. He looked that over, figured out where the argument would go from there, and after a moment, agreed with me. Not only did this solve the original problem, but it also removed the need for rule A completely, and simplified the argument to look like this:

• N((S + L) -> T)
• N(S -> (L -> T))
• Ns
• N(L -> T)
• Nl
• Nt

Thus, I defeated the author/teacher in discovering the best possible proof. The person in front of me told me that I should write a book. I think this blog entry will do. On Tuesday, we will discuss other objections to this argument, and I'm sure I will discover that my findings about this argument are pointless because the whole argument is wrong somehow. For now, however, I will enjoy my moment of triumph!

I hope you were all able to understand the proof I laid out above. Please comment if there is anything that is unclear, and I will try to remedy the confusion. Thanks everyone!