bd-from-kg

Taffy Lewis:

Against stupidity the very gods
Themselves contend in vain.

- Friedrich von Schiller

tronvillain

As bd-from-kg has pointed out, C3 is plainly false, so one or more of P1, P2, or P3 has to be false:

We have accepted that P3 is true by definition, meaning that even if determinism is in fact false, it is true that "If determinism is true, then whatever can be done, is done", so we can eliminate P3 as a candidate for being false.

Now, in order to combine P3 with P2, they must mean the same thing by "can be done." We have accepted P3 as true by definition and it uses the phrase to mean something like "has a probability of one." So, P2 must use the phrase to mean the same thing, making it "Whatever should be done has a probability of one." Now, we can stop in our search for a false premise now, or we can accept this new version of premise two while also admitting that we are often completely wrong in using the word "should."

Combining the two premises gives us C1, or "If determinism is true, then whatever should be done, is done." Now, in order to combine C1 with P1 they must mean the same thing by "should." Since in getting to this point we have accepted C1 as true, and it requires anything that should be done to have a probability of one. Now, since P1 states that "Everyone should always refrain from believing falsehoods" and everyone obviously does does not have a probability of one of refraining from believing falsehoods, we have found our false premise.

So, either P1 or P2 is false - take your pick.

tronvillain

Now, find a hole in our analysis of the argument, or shut the hell up.

Taffy Lewis

tronvillain:

The author is claiming that each premise considered on its own is highly plausible.

1. We should refrain from believing falsehoods.

2. Whatever should be done, can be done. OR

2'. Whatever should be done has a "nonzero probability" of being done.

3. If determinism is true, then whatever can be done, is done. OR

3'. If determinism is true, then whatever has a "nonzero probability" of being done, is done.

4. I believe in free will.


Premise 3 is a necessary truth. It cannot be false. However, the claim that "determinism is true" is NOT a necessary truth. The author is claiming that if you accept 1,2 (or 2'),3 (or 3'), and 4 along with the claim that determinism is true then you will have a contradictory set of beliefs (ie. the beliefs that determinism is true and false).

You have confused the claim that "determinism is true" with the 3rd premise. They are not the same.

In your next to last post, your confusion becomes evident when you say:

The term "can" means "has a nonzero probability of being done". Premise 3 says that IF determinism is true then every event that actually occurs has a probability of 1. It does not say that determinism is true.

So premise 3 reads "If determinism is true, then whatever has a nonzero probability of being done, has a probability of one that it will be done."

And premise 2 will read as 2'.

You ended your post with:

That should read "Either P1, P2, or determinism is false"

Again, premise 3 merely defines determinism. Combining it with 1, 2 and the claim that determinism is true yields the conclusion that "if you believe determinism is true then you are correct if you believe it is false". That's why the author claims determinism is self refuting.

Taffy Lewis

tronvillain:

Do you think that I should accept your arguments? Clearly you do.

The author claims that if you do then you must presuppose that I can (ie. there is some nonzero probability that I will).

So if I wish to be reasonable should I accept your arguments?

tronvillain

Taffy Lewis:
Yes, that is how he is attempting to sneak in the conclusion. You see, it is not enough that premises be plausible on their own - the argument must also follow from them.

And yes, if you wish to be reasonable, you should accept my arguments.

tronvillain

Further analysis of your "reply" will follow later.

tronvillain

Taffy Lewis:
That is not something I really wish to dispute - each premise can be interpreted in such as way as to make it seem plausible.

The author may be claiming that, but as bd-from-kg and I have shown, that claim is totally unfounded.

I am perfectly aware that they are not the same, and fortunately my analysis of the argument does not confuse them. My argument depends on the different meanings of the words "can" and "should."

It is amazing how much you are willing to torture your premises in an effort to have them confess the conclusion you want. By saying that "If determinism is true, then whatever has a nonzero probability of being done, has a probabilty of one that it will be done" you admit that the premise uses "nonzero probability" to mean "probability one."

Oh, you did it in an effort to distance one from the other so that you wouldn't have to have it mean the same thing in the second premise, but it just doesn't work. If determinism is true, then there is no other nonzero probability than probability one! As a result, any mention of "nonzero probability" following "if determinism is true" is the same as saying "probability one." Extending your premise to state what is already implicit won't save the argument.

bd-from-kg

Taffy Lewis:

OK, I’m going to through this one more time. This is absolutely, positively my last attempt to get you to (literally) see reason.

As I have pointed out several times, all of the first three premises are intended, not as factual claims about this world, but as necessary truths – i.e., statements that would be true in all possible worlds. (Note that “possible” means “logically possible” in this context.)

Now let’s write these premises so that their status as necessary truths is explicit:

1''. In all possible worlds, for all A, for every falsehood F, A should disbelieve F.

[Here I use “disbelieve” to mean simply “not believe”, not “believe to be false”.]

2''. In all possible worlds, for all X, if X should be done, X can be done.

[Here I use “can” in the sense of “having a nonzero probability”.]

3''. In all possible deterministic worlds, for all X, if X can be done, it is done.

Now combining 1'' and 2'' yields:

C1'': In all possible worlds, for all A, for every falsehood F, A can disbelieve F.

Now this is already manifestly false. It is simply not the case that there is no individual in any possible world who is certain to believe a particular falsehood.

So one of the first two premises if false. And we haven’t even mentioned determinism at this point.

The problem is simply brought out more starkly by considering deterministic worlds, as defined by 3'. Combining C1'' with 3'' yields:

C2'': In all possible deterministic worlds, for all A, for every falsehood F, A disbelieves F.

Far from showing that there is a problem with determinism, this is simply a formal way of pointing out that the most obvious counterexamples to C1'' are deterministic worlds in which there are any false beliefs. But since C1'' is false in lots of nondeterministic worlds as well, this is just “icing on the cake”.

Yes, and the author is right about this. The problem is that the first two premises yield a conclusion which is manifestly false. So all that the author has shown is that a certain set of premises of which at least one is false lead to a contradiction. Not a very interesting result.

It’s not good enough to point out that the first two premises are plausible. The problem is that they are logically incompatible. So if both seem plausible to you, it can only be because you’re interpreting the terms in them in different ways. Two logically incompatible statements cannot both be true in the same sense.

Now as to what’s “wrong” with the first two premises, here’s a good way of looking at it. The plausibility of the second premise, “Whatever should be done, can be done” comes from the fact that appears on its face to be logically equivalent to the generally accepted moral principle “It cannot properly be said that a thing should be done unless it can be done.” But this is not a statement about what can be done. Any statement that a “should” entails a “can” is absurd: a moral principle cannot entail a fact about the real world. It is intended to qualify other moral principles: to say that their validity is limited to cases in which it is actually possible to do what they say “should” be done. Thus the appropriate way to “combine” the first two premises is not to “derive” the absurd conclusion that it is always possible for everyone, in all possible worlds, to avoid believing falsehoods, but to modify the first premise to read:

1M''. In all possible worlds, for all A, for every falsehood F, if A can disbelieve F, he should.

In other words, one should always avoid believing falsehoods whenever there is a nonzero probability of doing so.

Now I don’t consider even 1M'' to be a valid moral principle, but that’s neither here nor there. At least it’s more plausible than the original first premise, because it takes into account the principle expressed by the second premise. Unfortunately for the author’s argument, it does not lead to the desired conclusion. Instead, it yields rather boring results like “If determinism is true, everyone disbelieves falsehoods whenever there is a nonzero probability of their doing so.”

P.S.: Your last post offers such a fat target that I can’t resist. I think that I can safely claim to be speaking for tronvillain on this one:

It is irrational not to accept our arguments. As to whether your moral code says that you “should” be rational, how would I know?

If you’re in Texarkana and wish to go to Chicago you “should” head north. If you wish to know something you “should” try to find it out. If you wish to be rich you “should” try to get lots of money. If you wish to be reasonable you “should” accept the results of sound, valid logical arguments. This has nothing to do with morality.

Now please take that course in Logic 101 before posting any more nonsense like this.

[ June 04, 2002: Message edited by: bd-from-kg ]</p>

Taffy Lewis

tronvillain:

I don't agree with you when you say :

It is evident that they cannot mean the same thing. "Can" means "has a nonzero probability of being done". A probability of 1 is a special case of "a nonzero probability". Another example would be "0.25". If "a nonzero probability" means "has a probability of one" then it must be the case that 1 equals 0.25. So "a nonzero probability" cannot mean "a probability of one". It means exactly what it says---"a NONZERO probability". By saying :

the third premise simply means that all probabilities are either zero or one. It also means that any probability that is not zero (or "nonzero") is a probability of one. In addition, it can read :

So all of my formulations of premise 3 are perfectly consistent and "can" still means "has a nonzero probability of being done".

If determinism is true then whichever events actually occur have a probability of one and any alternatives have a probability of zero.

Later you say:

You are mistaken. In premise 2, the term "can" still means "has a nonzero probability of being done".

However, the author's intent is to demonstrate that there is an inconsistency here. He thinks that you cannot accept premises 1,2,3, and 4 along with the claim that determinism is true. So you are right that there is a conflict. It just doesn't occur where you think it does.