Taffy Lewis

bd-from-kg:

Thanks for your time.

The author would agree with you that the claim "If determinism is true then all beliefs are true." follows from the three premises. His whole point is that determinism has self contradictory consequences. "Yes...all beliefs are true...even those that affirm free will."

You suggest that one sense of the word "can" is "a nonzero probability" that an action will be performed. Consider the author's second formulation of his argument:

1'. We should believe only propositions for which we have adequate justification.

Premises 2-7 remain the same and 8 becomes:

8'. I have adequate justification for MFT.

It seems as though your sense of "can" would work in premises 2 and 3 and yield the conclusion that if determinism is true then anyone who believes in free will is justified in believing it. Pointing out that there is more than one sense of "can" would only undermine the argument if the author couldn't use the same sense in premises 2 and 3 in the same argument.

Consider this famous argument:

1. All men are mortal.
2. Socrates is a man.
3. Therefore Socrates is mortal.

If you accept that the term "man" can be used in the same sense in the same argument (as above) then the argument will work. It makes no difference to the argument above that there are different meanings of the word "man" that would yield another argument which has false or improbable premises.

So if there are other senses of the word "can" that seems to make little difference. And I see no reason why the author cannot use one sense of "can" in both premises 2 and 3 that would yield premises that are highly plausible.

Consider premise 3: If determinism is true in the actual world then there is "a nonzero probability" that some people will believe in free will (since some people obviously do believe in it and the probability of any event in the real world given determinism is 1).

Now consider premise 2: It claims that if you think someone "should" or "ought" to do something then you must presuppose that they can do it. The "should" here is "believe only propositions for which we have adequate justification". And the "can" would be "there is a nonzero probability that we will believe only propositions for which we have adequate justification".

So we have:

1. We should believe only propositions for which we have adequate justification.
2. Whatever should be done, has a nonzero probability of being done.
3. If determinism is true, then whatever has a nonzero probability of being done, is done.

What is objectionable about these premises?

Premise 2 seems the one most likely to attract attention. But surely, if I tell you that you SHOULD do something I must presuppose that you CAN do it. Or I must presuppose that there is "a nonzero probability" that you will do it.

tronvillain

Those premises are attempting to sneak the conclusion in again.

Look at premise two:
When we say something should be done, it is because we think it has a nonzero probability of being done, but if determinism its probability is either zero or one. This will be true unless we are averaging over many cases.

Now, look at premise three:
As previously mentioned, unless we are averaging over many cases the probability is either zero or one. If we are simply averaging, the whatever has a nonzero probability of being done, is done sometimes and not others so obviously this premise is not about averaging.

Using those premises, presumably you are going to construct something like this:

In order to combine premise two with premise three, premise two cannot be talking about simply averaging over events since premise three is incompatible with that. As a result, premise two requires that something have a probability of one if it should be done. In other words, we are frequently wrong in saying that something should be done, since in retrospect it had a probability of zero.

So, finally we look at premise one:
In order for this premise to eventually be combined with the others, it has to be interpreted as saying that the probability of us only believing proposition for which we have adequate justification is one! Since this is simply not true, the argument with these revised premises fails.

Now, the argument can be taken apart in other ways, such as by accepting the first premise and second premises as using "should" in the conventional sense and combining them. In that case, the third premise will either be unable to be combined or be false.

Ierrellus

Taffy,

If determinism and free will are polar opposites, as you seem to express them, then one could come up with numerous arguments about their relationship simply because interpretations of either word suggest what the final arugument must be. In opposition, they define each other. Now, if you can see determinism and free will from an evolutionary perpective, since you see these abstractions as somehow a human dilemma, you would find no polarization, no deterministic outcome and no problem defining free will.

Ierrellus

[ June 02, 2002: Message edited by: Ierrellus ]</p>

bd-from-kg

Taffy Lewis:

By now tronvillain has pretty well demolished this argument, but (since I had almost finished this anyway) here’s my take from a slightly different angle.

OK, you are clearly a beginner in formal logic, so I’ll walk you through it slowly.

First, to eliminate a possible red herring, the statement “’determinism is true’ implies ‘all beliefs are true’” could well be true if “implies” is used in the sense of standard logical implication. In this sense of “implies”, “A implies B” is true if and only if A is false or B is true. And of course it may well be that “determinism is true” is false. This is often called “weak implication”.

But we’re talking here about logical entailment, not weak implication. To say that A entails B is to say that B is true in all possible worlds in which A is true.

But obviously there are possible worlds in which determinism is true but not all beliefs are true. Surely you don’t dispute this?

So determinism does not entail that all beliefs are true, which means that one of the author’s first three premises is false. End of story.

[By the way, the point is not that determinism has self-contradictory consequences, but that the premises entail obviously false propositions. If you’re right in believing that the author understands that his first three premises entail that “‘determinism is true” entails ‘all beliefs are true’” yet still believes that his argument is sound, it’s a waste of time to read anything he writes (unless for entertainment).]

To show that the problem here has nothing to do with determinism, let’s dispense with the third premise and consider only the generalized version of the first premise and the second premise. That is:

(1) We should always refrain from believing falsehoods.
(2) Whatever should be done can be done.

Now what is the nature of these premises? In what sense are they being claimed to be true? Clearly they are not meant to be statements about the real world; that is, there are no possible observations that would tend to confirm or falsify them. Thus the only possible interpretation is that the author takes these premises to be necessary truths – statements which are true in all possible worlds. If they are not necessary truths, there is no reason whatever to suppose that they are true at all; in fact, it is impossible to assign them any intelligible meaning except as necessary truths.

But now observe that these two premises yield:

(3) We can always refrain from believing falsehoods.

And this is clearly not a necessary truth: it is not true in all possible worlds. Plainly one can imagine without self-contradiction a world in which there is at least one person who is certain to have at least one false belief.

But (3) is rigorously entailed by (1) and (2), and necessary truths entail only necessary truths. So one of the premises is not a necessary truth, which is to say (since it is not a statement about the real world) that it is false or meaningless.

This makes no difference. Again the only intelligible way to construe this premise is that it is claimed to be a necessary truth. But combining it with (2) yields:

(3') We can believe only propositions for which we have adequate justification.

Once again, this is clearly not a necessary truth: there are obviously possible worlds in which there is zero probability that no one will have any beliefs for which he lacks adequate justification. So one of the premises is not a necessary truth. Etc.

I never said that he couldn’t.

I’ve already explained that the first two premises are logically incompatible. The reason that it’s not possible to say which one is false is simply that it is not clear what sense of “should” is intended. Some people use the word “should” in a sense such that it can be true that a person “should” do something even if there is a zero probability that he will actually do it. If “should” is used in this sense, the first premise is plausible but the second is false. Others use “should” in a sense such that it cannot be true that one “should” do something unless there is a nonzero probability of doing it. If “should” is used in this sense the second premise is true but the first is plainly false, because there are possible worlds in which there is at least one person who is certain to have at least one belief which is not adequately justified.

Thus if you are using “should” in a sense that makes your second premise true, the first premise must be modified to read “It is desirable to believe only propositions for which we have adequate justification.” This modification makes the first premise plausible, but it does not allow the argument to go through.

In any case, although this is an amusing academic exercise, it is self-evident that if a conclusion about the real world cannot be validly derived from true premises about the real world, it cannot be validly derived by adding moral premises. Thus the entire proof is in the same category as a proof that all triangles are isosceles (or better yet, a proof to this effect using moral premises). It is obvious at the outset that the proof must be fallacious; the interesting question is not whether all triangles are indeed isosceles, but where the fallacy lies.

Taffy Lewis

tronvillain:

You claim that the author is attempting to sneak the conclusion of the argument into one or more of his premises. You quote premise 2 then comment:


Premise 2 says nothing about determinism. The author believes that if you combine this premise with the thesis of determinism you can yield an argument that if determinism is true then it will yield its own contradiction given other plausible premises.

What about premise 2 presupposes determinism? You have confused this premise with what one gets when one combines this premise with determinism.

Next, you say:

You make the same mistake here that you made above. Premise 1 says nothing about determinism. The author claims that when you combine premise 1 with the thesis of determinism and the "should-implies-can" premise then you can formulate an argument that determinism is self refuting.

How does premise 1 presuppose determinism? What does it say that entails determinism or is entailed by determinism? It only entails the denial of determinism when it is combined with other premises.

Think of it this way. The author is saying that of the 4 premises you must reject at least one of them. He believes this because when they are combined the argument yields determinism and its denial. He thinks that premises 1,2, and 4 are much more plausible than the premise which states determinism.

[ June 02, 2002: Message edited by: Taffy Lewis ]</p>

Taffy Lewis

bd-from-kg:

You make essentially the same mistake as tronvillain so this post will basically repeat the comments of my last post.

You say:

Again, the author does not say that determinism entails that all beliefs are true. One only gets that conclusion when it is combined with other premises.

So the author thinks that one gets a contradictory result when one combines determinism with the other premises. That's what the author means when he says that determinism is self defeating. You almost see the point when you say:

The author does not dispute this. His point is that determinism combined with the other premises "disputes" this.

tronvillain

Taffy Lewis:
Ah, but you are missing the necessity of looking ahead in the argument! In order to combine premise two with premise three, they must mean the same thing by "nonzero probability."

Again, let us look at premise three:
This is true by definition, but it is obvious that "nonzero probability" means "probability one." The only exception would be if we were talking about probablistic determinism rather than strict determinism, but in that case there is the possibility that something having a nonzero probability of being done would not be done.

Now, let us again look at premise two:
Now, in order to say that something should be done, it must at least have a nonzero probability of being done, though there are likely to be many additional requirements. In order to be combined with premise three, this premise must intend "nonzero probability" to mean "probability one." In other words, premise two rewritten to be combined with premise three would be:
Now, if we accept that premise (which seems unlikely in that it implies that we are often completely wrong to say that someone "should" do something), we will obtain this:

The next step is to combine the premise we have just obtained with premise one:

In order to combine these two premises they must mean the same thing by the word "should" just as we originally required the two premises to mean the same thing by "nonzero probability."

So, do they mean the same thing by "should"? Apparently not, unless we wish to propose that it is probability one that we will believe only propositions for which we have adequate justification! So, the argument does not follow.

END OF STORY.

You can make almost any one of the premises false, depending on which ones you start with and what interpretations you are forced to take as a result.

[ June 02, 2002: Message edited by: tronvillain ]</p>

tronvillain

bd-from-kg

Taffy Lewis:

OK, one last time. We have:

(P1) Everyone should always refrain from believing falsehoods.
(P2) Whatever should be done can be done.
(P3) If determinism is true, then whatever can be done, is done.

The third is true by definition, so it is a necessary truth. In other words, these premises can be written as follows:

(1*) (for all P)((P is false) implies (for all A)(A should disbelieve P))
(2*) (for all X)((X should be done) implies (X can be done))
(3*) (Determinism is true) entails (for all X) ((X can be done) implies (X is done))

Now let’s see what these premises logically entail.

First, combining (2*) and (3*) yields:

(C1) (Determinism is true) entails (for all X)(X should be done) implies (X is done))

Next, combining (1*) and (C1) yields:

(C2) (Determinism is true) entails (for all P)((P is false) implies (for all A)(A disbelieves P))

C2 can be restated in plain English as: “Determinism entails that all beliefs are true”.

C2 is rigorously entailed by P1, P2, and P3. But it is plainly false. If a false statement is entailed by a set of premises, one of the premises must be false. Therefore either P1, P2, or P3 is false.

If this is still to hard for you, I can only recommend a course in Logic 101.

Taffy Lewis

bd-from-kg:

Determinism combined with 3 other premises does in fact yield the conclusion that "All belief are true"--even the belief that determinism is false. So if you accept determinism and the other 3 premises then your set of beliefs are self-refuting.