## Saturday, December 08, 2007

### Choice - Transitive vs. Intransitive

This post is a continuation from the combox of this previous post (link).

Godismyjudge wrote: "I meant [by "diabling factor"] that which makes us unable to choose freely."
I answer: I was afraid of something like that. I think we are talking past each other.
When I speak about the ability to choose, I'm speaking about choosing transitively - that is to say, choosing an object, making a selection, reaching a decision. Same as when I talk about the ability to lift (e.g. 10 lbs.) or run (e.g. 50 ft.). A transitive ability is the ability to do something. That something is the object of action.

Now, because of the level of abstraction we have when discussing this matter philosophically, the object of choice is "A."

Thus, I contend that it is compatible to assert that:
1. Man freely chooses A; and
2. Man was determined to choose A,
3. Because determination and choice are compatible concepts.

Just as I contend that it is compatible to assert that:
1. Man lifts A; and
2. Man was determined to lift A,
3. Because determination and lifting are compatible concepts.

And in general, it is compatible to assert that:
1. Man does A; and
2. Man was determined to do A,
3. Because determination and action are compatible concepts.

Now, when we add the term "ability" we providing a further level of abstraction.

Having the ability to lift is a different concept from actually lifting.
Even as
Having the ability to choose is a different concept from actually choosing.
and in general
Having the ability to do is a different concept from actually doing.

Of course, conventionally we recognize that:
1. Actually lifting A is evidence of ability to lift A;
2. Actually choosing A is evidence of ability to choose A; and
3. Actually doing A is evidence of ability to do A.

Indeed, "evidence" is an understatement. We view it as proof.

But, contrariwise, we would not consider that:
1. Actually lifting A is evidence of ability to lift B;
2. Actually choosing A is evidence of ability to choose B; and
3. Actually doing A is evidence of ability to do B.

At least, not in the same sense as above, and depending on what "B" is. If "B" is somehow a subset of A, then of course we would grant that doing the whole is evidence of being able to do the part.

Where does determination come in?

Determination is consistent with action. That is to say, it is possible for man both to act and to be determined to act. The nature of the action (whether physical or mental) is not important to that definition. Thus, as one example of acting, freely choosing is consistent with being determined to freely choose.

That's certainly the case if we consider the choice transitively, as above. In other words, there's nothing contradictory about saying that man freely chooses A and that man was determined to freely choose A.

As noted above, however, going from freely choosing to the ability to freely choose is further level of abstraction. Actually freely choosing A necessarily implies the ability to freely choose A.

If we go back to the illustrations above, and we recall that:

In general, it is compatible to assert that:
1. Man does A; and
2. Man was determined to do A,
3. Because determination and action are compatible concepts.

And we apply the necessary inference of ability to do from the fact of doing, we see that it is compatible to assert that:
1. Man is able to do A; and
2. Man was determined to do A,
3. Because determination and action are compatible concepts, and transitive ability to act is (at least) a subset of action.

Likewise, we see that it is compatible to assert that:
1. Man is able to lift A; and
2. Man was determined to lift A,
3. Because determination and lifting are compatible concepts, and transitive ability to lift is (at least) a subset of lifting.

And so, coming to "freely choosing," we see that it is compatible to assert that:
1. Man is able to freely choose A; and
2. Man was determined to freely choose A,
3. Because determination and freely choosing are compatible concepts, and transitive ability to freely choose is (at least) a subset of freely choosing.

Now, of course, that's not particularly objectionable (except for one matter, that will be addressed below). The matter that is objectionable is about the ability to do B if man is determined to do A (and assuming that B is not simply a subset of A).

As we noted above, the inference of ability from action only works if we maintain the object (or a subset of the objection). To give a clear contrary example, the action of lifting 10 lbs. does not say anything about the ability to lift 100 lbs., although it does say something about the ability to lift the sub-set of 5 lbs. (why that is, would make an interesting paper in itself, but for now we will take it as intuitive).

So, we recognize that it would not necessarily (not a matter of logical deduction) be compatible to assert that:
1. Man is able to do A; and
2. Man was determined to do B,
3. Because although determination and action are compatible concepts, and the transitive ability to act inferrable from (2) points to an ability to do B, not A, whereas (1) is asserting an ability to do A.

In other words, the two abilities to act are not aligned. (1) points to an ability to do A, whereas (2) points to an ability to do (B).

Perhaps a question should be posed:
Is
1. Ability to do A
compatible with
2. Ability to do B
where A&B are not identical to each other or in a subset relation?

The answer is that conventionally they are compatible. A man can be able both to walk to work and to carry his lunch. A man having more than one ability is not an incompatibility per se.

So then, where is the problem?

1. A first problem is that ability can be phrased uncertainly, indefinitely, or intransitively.
Thus, rather than addressing "the ability to freely choose A," an incompatibilist may wish to discuss "the ability to freely choose A OR B." That latter statement is hard to parse logically, because it is indefinite.

It's not saying that man either has the ability to freely choose A or the ability to freely choose B, which would seem to be one way to interpret it. Likewise, it is not saying that man has the ability to choose both A and B (at the same time and in the same way).

What it seems to be saying is that man has the ability to freely choose A and the ability to freely choose B, and that the man has both such abilities at the same time. As we noted above, that is not necessarily problematic, as man can be possessed of multiple abilities at the same time.

It also adds a twist, though. The two abilities are incompatible with simultaneity. In other, the advocate seems to be saying that man has the ability to freely choose A and the ability to freely choose B, and that the man has both such abilities at the same time, but that the abilities are interrelated such that if one ability is exercised, the other cannot be.

In other words, the man have two abilities, but (unlike our man who walks to work while carrying his lunch) the man is only able to exercise one of the two abilities at any given time.

This creates a sort of meta-ability. There is the underlying ability to transitively select A, the underlying ability to transitively select B, and a overlying ability to intransitively select only one option.

And frankly, this is the sort of perspective where the differences between compatibilism and incompatibilism can be more clearly seen.

If we divide out, for example, this restriction on simultaneity we can say that the man has the ability to do A and the man has the ability do B. But the restriction on simultaneity is a real restriction. When add it back in, we cannot unqualifiedly say that both the man has the ability to do A and the man has the ability do B. The restriction on simultaneity is a qualification, a restriction on ability, though - from the wording of the issue - it is an indefinite and uncertain restriction.

We can phrase the matter another way:
Something converts one of the abilities into a reality. If we ignore that something, we are speaking in a divided sense about ability. This is fairly normal.
On the other hand, if we consider the "something" and the restriction on simultaneity, it becomes quite odd to continue to assert an ability, the exercise of which would violate the restriction on simultaneity.
In other words, the restriction on simultaneity and the "something" that converts one of the two abilities to actuality have to be divided out in order to refer to the other of the two abilities as an ability.
That seems to follow fairly straightforwardly.

What objections can I immediately think of?

1. How about the ability to abstain? Some might suppose that actually doing A also implies an ability to abstain from doing A. The answer to that is to consider things that we know have the power to act (such as the Sun, to illumine the Earth) but which do not have he power of abstention from action. In fact, the ability to abstain relates to choice. Thus, humans and animals have the power of abstention from action. We understand this power of abstention to be in a divided sense, such that a dog cannot abstain from action A and do action A at the same time and in the same way.

2. But aren't determination and free choice definitionally opposed? The answer to this objection is that they are not within compatibilism. Of course, if you bring loaded definitions to the table, compatibilism will become incoherent.

Thus, within compatibilism, the restriction on simultaneity and the fact that "something" actualizes ability are recognized as compatible with free choice, because free choice is expressed with division to those things.

That there is restriction on simultaneity seems to be admitted by our LFW opponents, and that "something" actualizes ability seems to be uncontestable.

********* Continuing with the next chunk of dialog ****************

The present author had previously stated: "The ability to choose freely A in a divided sense, excluding the cause why A is not actually chosen, is compatible with there being a cause why A is not actually chosen. In a compound sense, including the determining cause, A will not be chosen."

Godismyjudge replied: "I notice you said “will not be chosen” rather than can not be chosen."
I answer: Yes. Let's see what significance you draw from that:

Godismyjudge continued: "Thus we are still able to do otherwise, despite the determining cause."
I answer: That does not seem to follow, unless one divides out the restriction on simultaneity, discussed above.

Godismyjudge continued: "I see no reason for a divided sense for being able to do otherwise."
I answer: Hopefully the above explanation helps. If not, is there really a restriction on simultaneity?

Godismyjudge continued: "It seems you providing the term in an absolute sense. I am not sure how dividing out or including in the determining cause alters the sense."
I answer: I'm not sure what you meant by that. Perhaps you could elaborate.

Godismyjudge continued: "Perhaps you intended (or implied) that A cannot be chosen, in the sense that we are unable to freely choose A?"
I answer: No, as noted above, I think that when we are talking ability to choose counterfactual options we are speaking in a divided sense, ignoring the "something" that actualizes the other ability and the restriction on simultaneity. Thus, to say that we are "unable to freely choose A" would be equivocal (within the discussion), because I would have moved from the divided sense of free choice (the ordinary sense) to a compound sense of free choice (an unusual sense, to say the least).

-Turretinfan

UPDATE: This recent article from Triablogue is close to the point being discussed here, but is from a little different perspective and part of a different dialog (link).
Further UPDATE: Steve Hays has now also provided a further post that goes into additional depth (while generalizing) on the subject (link).

Godismyjudge said...

Dear Turretin,

Sorry for the delay, I just watched to Cowboys get away with one on Detroit.

To avoid the subset relation (ie the ability to lift 10 lbs entails the ability to lift 5 lbs) and to avoid specifying the alternative as “B”(the alternative could be C or D…) I plan on substituting A or B with A or NonA. If you think it makes a material difference, please let me know.

When add it back in [the restriction on simultaneity] , we cannot unqualifiedly say that both the man has the ability to do A and the man has the ability do B.

Why not? The two abilities are not imcompossible, but rather the two actions are. Perhaps you confuse the ability to choose A and nonA, with the ability to choose A and the ability to choose nonA?

we would not consider that:
1. Actually lifting A is evidence of ability to lift B;
2. Actually choosing A is evidence of ability to choose B; and
3. Actually doing A is evidence of ability to do B.

I disagree with 2. Choice is in relation to opposites. Thus actually choosing A is evidence that a person had the ability to choose nonA. Elsecase the choice is not choice.

In other words, the restriction on simultaneity and the "something" that converts one of the two abilities to actuality have to be divided out in order to refer to the other of the two abilities as an ability.

Only the “something” would need to be divided out. It 1) removes the ability to choose nonA, 2) it’s causal and 3) it precedes the ability to choose A. In contrast, the restriction on simultaneity 1) doesn’t need to be divided out to assert the ability to do nonA, 2) it’s logical not causal, and 3) it’s subsequent to, not prior to the ability.

God be with you,
Dan

Godismyjudge said...

Dear Turretin,

You had explained the divided and compound sense of ability to choose freely as:

"The ability to choose freely A in a divided sense, excluding the cause why A is not actually chosen, is compatible with there being a cause why A is not actually chosen. In a compound sense, including the determining cause, A will not be chosen."

I had responded: I notice you said “will not be chosen” rather than can not be chosen."
Thus we are still able to do otherwise, despite the determining cause.

To which you responded: That does not seem to follow, unless one divides out the restriction on simultaneity, discussed above.

Are you saying that given the determining cause, we are unable to do otherwise? If so, could you please reformulate your divided and compound senses into one that includes the fact that in the compound sense, we can’t choose nonA?

God be with you,
Dan

Godismyjudge said...

Dear Turretin,

From the quick response to Godismyjudge post...

me: "I think I could demonstrate that what I mean by a divided is self canceling when stated overtly within the context of what is divided out."
thee: If that's true (let's suppose arguendo that it is), isn't that always true of the divided sense (and not limited to our discussion)? If so, then isn't the argument really non-unique?

Yes, it‘s non-unique. This was never intended as an argument against compatiblism per say. It's just an argument as to why people wouldn't use an implied divided sense at the same time explicitly stating what has been divided out. This goes for any divided sense, including the compatibility thesis.

But we can still hold up on bottoming this point out till we get past other issues.

God bless,
Dan

Turretinfan said...

Dan,

You wrote: "Yes, it‘s non-unique. This was never intended as an argument against compatiblism per [se]. It's just an argument as to why people wouldn't use an implied divided sense at the same time explicitly stating what has been divided out. This goes for any divided sense, including the compatibility thesis."
I answer: I'm not sure I agree, but as you go on to note, this is presumably something that can be tabled for later.

-Turretinfan

Turretinfan said...

Dan,

You wrote: Are you saying that given the determining cause, we are unable to do otherwise?

I answer: Not exactly. I am saying that it does not make much sense to talk about ability while including something that absolutely prevents the exercise of ability.
It may be true that, given the determining cause, we are "unable to do otherwise," but that's not using ability in its ordinary (divided) sense.

You wrote: "If so, could you please reformulate your divided and compound senses into one that includes the fact that in the compound sense, we can’t choose nonA?"

-Turretinfan

Turretinfan said...

Dan:

You wrote: "To avoid the subset relation (ie the ability to lift 10 lbs entails the ability to lift 5 lbs) and to avoid specifying the alternative as “B”(the alternative could be C or D…) I plan on substituting A or B with A or NonA. If you think it makes a material difference, please let me know."
I answer: NonA doesn't really solve that problem, as NonA can be a subset of A (5 lbs is not 10lbs.), and the alternative of "B" is generic (thus, mooting the need for C or D). The same qualifications, therefore, are necessary with nonA as B, except (I suppose) that one might think that B could be identical with A.

I had written: "When add it back in [the restriction on simultaneity] , we cannot unqualifiedly say that both the man has the ability to do A and the man has the ability do B."

You wrote: "Why not?"
I answer: Because we must qualify that by the fact that man cannot do both in the same way at the same time.

You continued: "The two abilities are not imcompossible [sic], but rather the two actions are."
I answer: An unactualizable ability is not a "real" ability. Don't you agree? If so, the impossibility of their simultaneous exercise (as action) is a real conflict between them.

You continued: "Perhaps you confuse the ability to choose A and nonA, with the ability to choose A and the ability to choose nonA?"
I answer: Not at all. Read my original post, where I explain the difference.

I had written: "we would not consider that:
1. Actually lifting A is evidence of ability to lift B;
2. Actually choosing A is evidence of ability to choose B; and
3. Actually doing A is evidence of ability to do B."
You answer: "I disagree with 2."
I answer: That is telling. What it tells me is that you treat choice differently from other actions. What I call this, in terms of fallacies, is "special pleading." But you do make some argument why:

You wrote: "Choice is in relation to opposites."
I answer: Not really, but it doesn't matter. Choice is primarily in relation to a single object (the object chosen), and not in relation to any object unchosen. Just as lifting is in relation to the object lifted (and not to an object that is not lifted).

You continued: "Thus actually choosing A is evidence that a person had the ability to choose nonA. Elsecase the choice is not choice."
I answer: That's simply you bringing in a libertarian definition of choice. It's pure ipse dixit. It explains why you object to (2), but it does not provide a basis for your objection. In other words, the basis for your objection has to be something more than just your say-so.

I had written: "In other words, the restriction on simultaneity and the "something" that converts one of the two abilities to actuality have to be divided out in order to refer to the other of the two abilities as an ability."

You wrote: "Only the “something” would need to be divided out. It 1) removes the ability to choose nonA, 2) it’s causal and 3) it precedes the ability to choose A. In contrast, the restriction on simultaneity 1) doesn’t need to be divided out to assert the ability to do nonA, 2) it’s logical not causal, and 3) it’s subsequent to, not prior to the ability."
First) Even if it were only the "something," that would be enough for my point to stand.
Second)
1) The restriction on simultaneity does need to be presented as a qualifcation.
2) The fact that something is logical is not preclusive of it being also causal. Furthermore, a logical restriction is more not less disabling than a merely causal restriction. The latter kind of restriction can be overcome by miracle, the former cannot.
3) Your comment that: "it’s subsequent to, not prior to the ability," is a bit odd. It's obviously logically subsequent, but so is every restriction, by virtue of being a restriction, namely because a restriction must have an object (the object, therefore, being logically prior). Thus, if you are referring to logical subsequence, your point is not particularly significant.
If you are asserting chronological subsequence, your assertion is clearly wrong, and I don't think you are trying to do so.

So, in fact, the restriction on simultaneity remains a real and important restriction.

-Turretinfan

Godismyjudge said...

Dear Turretin,

Me:"The two abilities are not imcompossible [sic], but rather the two actions are."
Thee: An unactualizable ability is not a "real" ability. Don't you agree? If so, the impossibility of their simultaneous exercise (as action) is a real conflict between them.

Yes, we are unable to do the impossible. That leads me to think we are unable to choose A and nonA. It doesn’t lead me to think that we can’t be able to choose A and able to choose nonA. It’s good that you don’t mix the two, but it leaves me wondering where you are coming from.

Me: "Choice is in relation to opposites."
Thee: Not really, but it doesn't matter. Choice is primarily in relation to a single object (the object chosen), and not in relation to any object unchosen. Just as lifting is in relation to the object lifted (and not to an object that is not lifted).

Hum… If I had said that the “ability to choose” is in relation to opposites would you have agreed? Or are you saying choice has nothing at all to do with opposites?

Thee: Even if it were only the "something,"[the determining cause] that would be enough for my point to stand [without the restriction on simultaneity].

I think this might shift the discussion a bit, if we can get passed the restriction on simultaneity.

God bless,
Dan

Turretinfan said...

GIMJ: I think it might be helpful, down the road, so if you could please do reformulate.

Given that I answered in the negative, how would the reformulation be helpful?

GIMJ (first):"The two abilities are not imcompossible [sic], but rather the two actions are."
TF (second): An unactualizable ability is not a "real" ability. Don't you agree? If so, the impossibility of their simultaneous exercise (as action) is a real conflict between them.
GIMJ (third): Yes, we are unable to do the impossible. That leads me to think we are unable to choose A and nonA. It doesn’t lead me to think that we can’t be able to choose A and able to choose nonA. It’s good that you don’t mix the two, but it leaves me wondering where you are coming from.
I answer: I'm not sure what's unclear to you.

GIMJ: "Choice is in relation to opposites."
TF: Not really, but it doesn't matter. Choice is primarily in relation to a single object (the object chosen), and not in relation to any object unchosen. Just as lifting is in relation to the object lifted (and not to an object that is not lifted).
GIMJ: "Hum… If I had said that the “ability to choose” is in relation to opposites would you have agreed? Or are you saying choice has nothing at all to do with opposites?"

I answer: The ability to choose is in relation to the act of choosing. It's just one step from choice itself. Choice can have something to do with opposites, but it has a selective relation. That is, an actual choice relates to one item, and by the choice (usually) distinguishes that item from another.

TF: Even if it were only the "something,"[the determining cause] that would be enough for my point to stand [without the restriction on simultaneity].
GIMJ: I think this might shift the discussion a bit, if we can get passed the restriction on simultaneity.