Four-bit microcomputer trainer in Scratch

When I was a kid, I had a Radio Shack Microcomputer Trainer. This device was programmable in machine code, and was a 4-bit system with 112 nibbles(!) of RAM. It actually ran as a virtual machine on a more powerful TMS-1x00 4-bit processor. These days, kids learn coding with much higher level languages than machine code, including graphical languages like Scratch. So I had some fun over the break and bridged the gap between then and now by making an emulator (or maybe more precisely simulator) of the trainer in Scratch. For computations (though probably not for I/O) it runs in the browser (shift click the flag to get Turbo Mode, though) faster than the original did according to my benchmark.

[Scratch link.]

[Instructables link with usage instructions.]

A multiple faculty solution to the problem of conscience

I used to be quite averse to multiplying types of normativity until I realized that in an Aristotelian framework it makes perfect sense to multiply them by their subject. Thus, I should think that 1 = 1, I should look both ways before crossing the street, and I should have a heart-rate of no more than 100. But the norms underlying these claims have different subjects: my intellect, my will and my circulatory system (or perhaps better: I as thinking, I as willing and I as circulating).

In this post I want to offer two solutions to the problem of mistaken conscience that proceed by multiplying norms. The problem of mistaken conscience is two-fold as there are two kinds of mistakes of conscience. A strong mistake is when I judge something is required when it is forbidden. A weak mistake is when I judge something is permissible when it is forbidden.

Given that I should follow my conscience, a strong mistake of conscience seems to lead to two conflicting obligations: I should ϕ, because my conscience says so, and I should refrain from ϕing, because ϕing is forbidden. Call the claim that strong mistakes of conscience lead to conflicting obligations the Dilemma Thesis. The Dilemma Thesis is perhaps somewhat implausible on its face, but can be swallowed (as Mark Murphy does). However, more seriously, the Dilemma Thesis has the unfortunate result that strong mistakes of conscience are not, as such, mistakes. For the mistake was supposed to be that I judge ϕing as required when it is forbidden. But that is only a mistake when ϕing is not required. But according to the Conflict Thesis, it is required. So there is no mistake. (There may be a mistake about why it is required, and perhaps one can use that to defuse the problem, but I want to try something else in this post.) Moreover, a view that embraces the Dilemma Thesis needs to explain the blame asymmetry between the obligation to ϕ and the obligation not to ϕ: I am to blame if I go against conscience, but not if I follow conscience.

Weak mistakes are less of a problem, but they still raise the puzzle of why I am not blameworthy if I do what is forbidden when conscience says it’s permissible.

Moving towards a solution, or actually a pair of solution, start with this thought. When I follow a mistaken conscience, my will does nothing wrong but the practical intellect has made a mistake. In other words, we have two sets of norms: norms of practical intellect and norms of will. In these cases I judged badly but willed well. And it is clear why I am not blameworthy: for I become blameworthy by virtue of a fault of the will, not a fault of the intellect.

But there is still a problem analogous to the problem with the Dilemma Thesis. For it seems that:

1. In a mistake of conscience, my judgment was bad because it made a false claim as to what I should will.

In the case of a strong mistake, say, I judged that I should will my ϕing whereas is in fact I should have nilled my ϕing. But I can’t say that and say that the will did what it should in ϕing.

This means that if we are to say that the will did nothing wrong and the problem was with the intellect, we need to reject (1). There are two ways of doing this, leading to different solutions to the problem of conscience.

Claim (1) is based on two claims about practical judgment:

2. The practical intellect’s judgments are truth claims.

3. These truth claims are claims about what I should will.

We can get out of (1) by denying (2) (with (3) then becoming moot) or by holding on to (2) but rejecting (3).

Anscombe denies (2), for reasons having nothing to do with mistakes of conscience. There is good precedent for denying (2), then.

I find the solution that denies (2) a bit murky, but I can kind of see how one would go about it. Oversimplifying, the intellect presents actions to the will on balance positively or negatively. This presentation does not make a truth claim. The polarity of the presentation by the intellect to the will should not be seen as a judgment that an action has a certain character, but simply as a certain way of presenting the judgment—with propathy or antipathy, one might say. Nonetheless there are norms of presentation built into the nature of the practical intellect. These norms are not truth norms, like the norms of the theoretical intellect, but are more like the norms of the functioning of the body’s thermal regulation system, which should warm up the body in some circumstances and cool it down in others, but does not make truth claims. There are actions that should be positively presented and actions that should be negatively presented. We can say that the actions that should be positively presented are right, but the practical intellect’s positive presentation of an action is not a presentation that the action is right, for that would be an odd circularity: to present ϕing positively would be to present ϕing as something that should be presented positively.

(In reality, the “on balance” positive and negative presentations typically have a thick richness to them, a richness corresponding “in flavor” to words like “courageous”, “pleasant”, etc. However, we need to be careful on this view not to think of the presentation corresponding “in flavor” to these words as constituting a truth claim that a certain concept applies. I am somewhat dubious whether this can all be worked out satisfactorily, and so I worry that the no-truth-claim picture of the practical intellect falls afoul of the thickness of the practical intellect’s deliverances.)

There is a second solution which, pace Anscombe, holds on to the idea that the practical intellect’s judgments are truth claims, but denies that they are claims about what I should will. Here is one way to develop this solution. There are times when an animal’s subsystem is functioning properly but it would be better if it did something else. For instance, when we are sick, our thermal regulation system raises our temperature in order to kill invading bacteria or viruses. But sometimes the best medical judgment will be that we will on the whole be better off not raising the temperature given a particular kind of invader, in which case we take fever-reducing medication. We have two norms here: a local norm of the thermal regulation system and a holistic norm of the organism.

Similarly, there are local norms of the will—to will what the intellect presents to it overall in a positive light, say. And there are local norms of the intellect—to present the truth or maybe that which the evidence points to as true. But there are holistic norms of the acting person (to borrow Wojtyla’s useful phrase), such as not to kill innocents. The practical intellect discerns these holistic norms, and presents them to the will. The intellect can err in its discernment. The will can fail to follow the intellect’s discernment.

The second solution is rather profligate with norms, having three different kinds of norms: norms of the will, norms of the intellect, and norms of the acting person, who comprises at least the will, the intellect and the body.

In a strong mistake of conscience, where we judge that we should ϕ but ϕing is forbidden, and we follow conscience and ϕ, here is what happens. The will rightly follows the intellect’s presentation by willing to ϕ. The acting person, however, goes wrong by ϕing. We genuinely have a mistake of the intellect: the intellect misrepresented what the acting person should do. The acting person went wrong, and did so simpliciter. However, the will did right, and so one is not to blame. We can say that in this case, the ϕing was wrong, but the willing to ϕ was right. And we can say how the pro-ϕing norm takes priority: the norm to will one’s ϕing is a norm of the will, so naturally it is what governs the will.

In a weak mistake of conscience, where we judge that it is permissible to ϕ but it’s not, again the solution is that under the circumstances it was permissible to will to ϕ, but not permissible to ϕ.

There is, however, a puzzle in connecting this story with failed actions. Consider either kind of mistake of conscience, and suppose I will to ϕ but I fail to ϕ due to some non-moral systemic failure. Maybe I will to press a forbidden button, but it turns out I am paralyzed. In that case, it seems that the only thing I did was willing to ϕ, and so we cannot say that I did anything wrong. I think there are two ways out of this. The first is to bite the bullet and say that this is just a case where I got lucky and did nothing wrong. The second is to say that my willing to ϕ can be seen as a trying to ϕ, and it is bad as an action of the acting person but not bad as an action of the will.

A proof that ought implies can

Some actions are are things I can do immediately: for instance, I can immediately raise my hand. Others require that I do something to enable myself to do the action: for instance, to teach in person, I have to go to the classroom, or to feed my children, I need to obtain food. So, here is a very plausible axiom of deontic logic:

1. If I ought to do A, and A is not an action I can do immediately, then I ought to bring it about that I can immediately do A.

Now, say that I remotely can do an action provided that I can immediately do it, or I can immediately bring it about that I can immediately do it, or I can immediately bring it about that I can immediately bring it about that I can immediately do it, or ….

It follows from (1) and a bit of reasoning that:

2. If I ought to do A, then I remotely can do A, or I have an infinite regress of prerequisite obligations.

But:

3. It is false that I have an infinite regress of prerequisite obligations.

So:

4. If I ought to do A, then I remotely can do A.

God and Beauty

Here is my talk from the Cracow philosophy of religion conference in September:

The possibility test for intentions

This test for whether one is intending some effect E of an action is often employed (e.g., by Germain Grisez) in the Double Effect literature:

1. If it is logically possible for an action with an intention J to be fully successful even though E does not happen, then E is not included in J.

Claim (1) follows in standard modal logic (with no need for anything fancy like S5) from:

2. If an intention J includes E, then the inclusion of E is an essential property of J.

3. Necessarily, if an action is done with an intention that includes E and E does not occur, then the action is not fully successful.

For suppose that E is included in J. Then in every possible world where an action is done with J, the action is done with an intention that includes E by (2)) and so in every possible world where an action is done with J, the action is not fully successful if E does not occur, by (3). Hence, there is no possible world where an action is done with J and is fully successful even though E does not happen. Thus, we have (1).

At the same time, (1) sounds awfully strong. Even if the possible world where the action is successful despite the lack of E requires a miracle, E is not included in J. For instance, suppose God is able to keep the soul of a human being bound to a single atom. That means that someone whose intention was to blow the man blocking the mouth of the cave literally to single atoms was not intending death, since there is a possible world where the person’s soul remains bound to a single atom, and in that world the action is clearly successful.

To deny (1), one needs to deny (2) or (3). I think the best route to denying (2) is a strong dose of semantic externalism: the content of an intention is dependent in part on things outside the individual. Perhaps on Earth the very same intention may be an intention to drink water, while on Twin-Earth the very same intention may be an intention to drink XYZ. I am sceptical of this: it seems to me that the best way to understand the water-XYZ issue is that intentions are partly grounded in facts outside the individual, and so it is a different intention on Twin-Earth than on Earth, even if it is partly grounded in the same facts in the individual.

But even if one is impressed by the water-XYZ issue, it seems one should be willing to accept the following variant on 2:

4. If an intention J includes E and occurs at t, then in any possible world that exactly matches the actual world up to an including t the intention J includes E at t.

The argument for (1) can now be modified to yield an argument for:

5. If an action with an intention J occurs at t, and if there is a possible world that matches the actual world up to and including t and where the action with J is fully successful but where E does not happen, then E is not included in J.

And if one’s motivation for denying (1) is to avoid the conclusion that intending to blow the man in the mouth of the cave to single atoms does not include intending death, then (5) is just as bad. For God could miraculously keep the soul bound to a single atom without anything being any different up to and including the time of the action.

If we don’t want (1), we won’t want (5), either.

So a better bet is to deny (3). A start towards a denial of (3) would be to talk of something like “stretch goals”. It seems that an action may have a stretch goal and yet be successful even if that stretch goal is unachieved. However, the stretch goal is surely intended.

I am not sure. If the stretch goal is intended, then it seems that the right thing to say is that the action is successful but not fully successful if the stretch goal is not met.

In any case, we might grant the claim about stretch goals, and introduce the concept of an intention being perfectly satisfied, which includes the satisfaction of all stretch goals, and then replace “fully successful” with “perfectly successful” in (1) and (5). And I think this will still generate the result about blowing the fat man to atoms, because the death of the fat man—the separation of soul from body—is not a stretch goal either. (If anything, one might imagine that his survival is a stretch goal.)

All this makes me want to say that (3) really is true, and we cannot avoid the conclusion that it is possible to intend to blow the man in the mouth of the cave to single atoms without intending to kill him. But I am now inclined to think that an intention to kill is not a necessary condition for murder, and so the action could still be a murder.

Independence, spinners and infinitesimals

Say that a “spinner” is a process whose output is an angle from 0^∘ (inclusive) to 360^∘ (exclusive). Take as primitive a notion of uniform spinner. I don’t know how to define it. A necessary condition for uniformity is that every angle has the same probability, but this necessary condition is not sufficient.

Consider two uniform and independent spinners, generating angles X and Y. Consider a third “virtual spinner”, which generates the angle Z obtained by adding X and Y and wrapping to be in the 0^∘ to 360^∘ range (thus, if X = 350^∘ and Y = 20^∘, then Z = 10^∘). This virtual spinner is intuitively statistically independent of each of X and Y on its own but not of both.

Suppose we take the intuitive statistical independence at face value. Then:

• P(Z = 0^∘)P(X = 0^∘)=P(Z = X = 0^∘)=P(Y = X = 0^∘)=P(Y = 0^∘)P(X = 0^∘),

where the second equality followed from the fact that if X = 0^∘ then Z = 0^∘ if and only if Y = 0^∘. Suppose now that P(X = 0^∘) is an infinitesimal α. Then we can divide both sides by α, and we get

• P(Z = 0^∘)=P(Y = 0^∘).

By the same reasoning with X and Y swapped:

• P(Z = 0^∘)=P(X = 0^∘).

We conclude that

• P(X = 0^∘)=P(Y = 0^∘).

We thus now have an argument for a seemingly innocent thesis:

1. Any two independent uniform spinners have the same probability of landing at 0^∘.

But if we accept that uniform spinners have infinitesimal probabilities of landing at a particular value, then (1) is false. For suppose that X and Y are angles from two independent uniform spinners for which (1) is true. Consider a spinner whose angle is 2Y (wrapped to the [0^∘, 360^∘) range). This doubled spinner is clearly uniform, and independent of X. But its probability of yielding 0^∘ is equal to the probability of Y being 0^∘ or 180^∘, which is twice the probability of Y being 0^∘, and hence twice the probability of X being 0^∘, in violation of (1) if P(X = 0^∘)>0.

So, something has gone wrong for friends of infinitesimal probabilities. I see the following options available for them:

2. Deny that Z = 0^∘ has non-zero probability.

3. Deny that Z is statistically independent of X as well as being statisticlaly independent of Y.

I think (3) is probably the better option, though it strikes me as unintuitive. This option has the interesting consequence: we cannot independently rerandomize a spinner by giving it another spin.

The careful reader will notice that this is basically the same argument as the one here.

More on the side-effect harm/help asymmetry

Wright and Bengson note an apparent intuitive asymmetry in our side-effect judgments. We blame people for not avoiding bad effects, even when these bad effects are not intended, but we do not praise people for not avoiding good effects when these good effects are not intended.

I wonder if the explanation for this asymmetry isn’t this:

1. Typical good people strive to avoid bad side-effects to others

2. Typical bad people don’t strive to avoid good side-effects to others.

The reason for (2) is that typical bad people are selfish rather than malevolent: their badness consists in the fact that they put themselves before others, not in their going out of their way to deprive others of goods as such. But typical good people are positively benevolent, so we have (1).

Now, given (1), if you fail to avoid a bad side-effect, that makes you be worse than a typical good person. And that calls for significant castigation. But given (2), if you fail to avoid a good side-effect, that doesn’t make you better than a typical bad person. Granted, you could still be praised for being better than a very bad person, but that would be damning with faint praise. So, (1) and (2) neatly predicts the asymmetry in our practices of praise and blame.

But now imagine that we lived in a more polarized society, where typical bad people were actually malevolent rather than selfish. Against that background, it would make sense to praise someone for not avoiding a good effect to another. This is similar to the way that we would not praise a 21st-century upper-class man for refraining from duelling, but we would praise a 19th-century one for the same thing. For the vice of duelling is no longer rampant like it was, and to say that someone never engages in duels is damning with faint praise. Praise is comparative, and comparisons depend on reference class.

Sometimes that reference class is the person’s past and present. And that provides cases where we would praise someone for not striving to avoid good side-effects. If out of hatred someone previously strove to avoid good effects to a particular other, and then stopped such striving, then praise would be in order.

We thus need to be careful in drawing conclusions from praise and blame practices, because these practices depend on statistical facts. If the above is right, the side-effect asymmetry may simply be due to reference class issues rather than any deeper facts about intentions, side-effects and value.

But I think there is probably a further asymmetry between praise and blame. While, as noted, we do not praise people for doing going things most people in the reference class do, we do in fact blame people for doing bad things that most people in the reference class do. While we do not praise our 21st century contemporaries for refraining from dueling, we would have been right to castigate our 19th century contemporaries for that vice. That “everybody is doing it” often makes praise feel nearly completely inappropriate, but it only somewhat decreases the degree of blame rather than eliminating it.

Another problem for infinitesimal probabilities

Here’s another problem with independence for friends of infinitesimal probabilities.

Let ..., X₋₂, X₋₁, X₀, X₁, X₂, ... be an infinite sequence of independent fair coin tosses. For i = 0, 1, 2, ..., define E_i to be heads if X_i and X_{−1 − i} are the same and tails otherwise.

Now define these three events:

• L: X₋₁, X₋₂, ... are all heads

• R: X₀, X₁, ... are all heads

• E: E₀, E₁, ... are all heads.

Friends of infinitesimal probabilities insist that P(R) and P(L) are positive infinitesimals.

I now claim that E is independent of R, and the same argument will show that E is independent of L. This is because of this principle:

1. If Y₀, Y₁, ... is a sequence of independent random variables, and f and g are functions such that f(Y_i) and g(Y_i) are independent of each other for each fixed i, then the sequences f(Y₀),f(Y₁),... and g(Y₀),g(Y₁),... are independent of each other.

But now let Y_i = (X_i, X_{−1 − i}). Then Y₀, Y₁, ... is a sequence of independent random variables. Let f(x, y)=x and let g(x, y) be heads if x = y and tails otherwise. Then it is easy to check that f(Y_i) and g(Y_i) are independent of each other for each fixed i. Thus, by (1), f(Y₀),f(Y₁),... and g(Y₀),g(Y₁),... are independent of each other. But f(Y_i)=X_i and g(Y_i)=E_i. So, X₀, X₁, ... and E₀, E₁, ... are independent of each other, and hence so are E and R.

The same argument shows that E and L are independent.

Write AB for the conjunction of A and B and note that EL, ER and RL are the same event—namely, the event of all the coins being heads. Then:

2. P(E)P(L)=P(EL)=P(RL)=P(R)P(L)

Since friends of positive infinitesimals insist that P(R) and P(L) are positive infinitesimals, we can divide both sides by P(L) and get P(E)=P(R). The same argument with L and R swapped shows that P(E)=P(L). So, P(L)=P(R).

But now let X_i^* = X_i + 1, and define L^* to be the event of X₋₁^*, X₋₂^* being all heads, and R^* the event of X₀^*, X₁^*,… being all heads. The exact same argument as above will show that P(L^*)=P(R^*). But friends of infinitesimal probabilities have to say that P(R^*)>P(R) and P(L^*)<P(L), and so we have a contradiction if P(L)=P(R) and P(L^*)=P(R^*).

I think the crucial question is whether (1) is still true in settings with infinitesimal probabilities. I don’t have a great argument for it. It is, of course, true in classical probabilistic settings.

Independence, uniformity and infinitesimals

Suppose that a random variable X is uniformly distributed (in some intuitive sense) over some space. Then :

1. P(X = y)=P(X = z) for any y and z in that space.

But I think something stronger should also be true:

2. Let Y and Z be any random variables taking values in the same space as X, and suppose each variable is independent of X. Then P(X = Y)=P(X = Z).

Fixed constants are independent of X, so (1) follows from (2).

But if we have (2), and the plausible assumption:

3. If X and Y are independent, then X and f(Y) are independent for any function f,

we cannot have infinitesimal probabilities. Here’s why. Suppose X and Y are independent random variables uniformly distributed over the interval [0, 1). Assume P(X = a) is infinitesimal for a in [0, 1). Then, so is P(X = Y).

Let f(x)=2x for x < 1/2 and f(x)=2x − 1 for 1/2 ≤ x. Then if X and Y are independent, so are X and f(Y). Thus:

4. P(X = Y)=P(X = f(Y)).

Let g(x)=x/2 and let h(x)=(1 + x)/2. Then:

5. P(Y = g(X)) = P(Y = X)

and

6. P(Y = h(X)) = P(Y = X).

But now notice that:

7. Y = g(X) if and only if X = f(Y) and Y < 1/2

and

8. Y = h(X) if and only if X = f(Y) and 1/2 ≤ Y.

Thus:

9. (Y = g(X) or Y = h(X)) if and only if X = f(Y)

and note that we cannot have both Y = g(X) and Y = h(X). Hence:

10. P(X = Y)=P(X = f(Y)) = P(Y = g(X)) + P(Y = h(X)) = P(Y = X)+P(Y = X)=2P(X = Y).

Therefore:

11. P(X = Y)=0,

which contradicts the infinitesimality of P(X = Y).

This argument works for any uniform distribution on an infinite set U. Just let A and B be a partition of U into two subsets of the same cardinality as U (this uses the Axiom of Choice). Let g be a bijection from U onto A and h a bijection from U onto B. Let f(x)=g⁻¹(x) for x ∈ A and f(x)=h⁻¹(x) for x ∈ B.

Note: We may wish to restrict (3) to intuitively “nice” functions, ones that don’t introduce non-measurability. The functions in the initial argument are “nice”.

Incompatible reasons for the same action

While writing an earlier post, I came across a curious phenomenon. It is, of course, quite familiar that we have incompatible reasons that we cannot act on all of: reasons of convenience often conflict with reasons of morality, say. This familiar incompatibility is due to the fact that the reasons support mutually incompatible actions. But what is really interesting is that there seem to be incompatible reasons for the same action.

The clearest cases involve probabilities. Let’s say that Alice has a grudge against Bob. Now consider an action that has a chance of bestowing an overall benefit on Bob and a chance of bestowing an overall harm on Bob. Alice can perform the action for the sake of the chance of overall harm out of some immoral motive opposed to Bob’s good, such as revenge, or she can perform the action for the sake of the chance of overall benefit out of some moral motive favoring Bob’s good. But it would make no sense to act on both kinds of reasons at once.

One might object as follows: The expected utility of the action, once both the chance of benefit and the chance of harm are taken into account, is either negative, neutral or positive. If it’s negative, only the harm-driven action makes sense; if it’s positive, only the benefit-driven action makes sense; if it’s neutral, neither makes sense. But this neglects the richness of possible rational attitudes to risk. Expected utilities are not the only rational way to make decisions. Moreover, the chances may be interval-valued in such a way that the expected utility is an interval that has both negative and positie components.

Another objection is that perhaps it is possible to act on both reasons at once. Alice could say to herself: “Either the good thing happens to Bob, which is objectively good, or the bad thing happens, or I am avenged, which is good for me.” Sometimes such disjunctive reasoning does make sense. Thus, one might play a game with a good friend and think happily: “Either I will win, which will be nice for me, or my friend will win, and that’ll be nice, too, since he’s my friend.” But the Alice case is different. The revenge reason depends on endorsing a negative attitude towards Bob, while one cannot do while seeking to benefit Bob.

Or suppose that Carl read in what he took to be holy text that God had something to say about ϕing, but Carl cannot remember if the text said that God commanded ϕing or that God forbade ϕing—it was one of the two. Carl thinks there is a 30% chance it was a prohibition and a 70% chance that it was a command. Carl can now ϕ out of a demonic hope to disobey God or he can ϕ because ϕing was likely commanded by God.

In the most compelling cases, one set of motives is wicked. I wonder if there are such cases where both sets of motives are morally upright. If there are such cases, and if they can occur for God, then we may have a serious problem for divine omnirationality which holds that God always acts for all the unexcluded reasons that favor an action.

One way to argue that such cases cannot occur for God is by arguing that the most compelling cases are all probabilistic, and that on the right view of divine providence, God never has to engage in probabilistic reasoning. But what if we think the right view of providence involves probabilistic reasoning?

We might then try to construct a morally upright version of the Alice case, by supposing that Alice is in a position of authority over Bob, and instead of being moved by revenge, she is moved to impose a harm on Bob for the sake of justice or to impose a good on him out of benevolent mercy. But now I think the case becomes less clearly one where the reasons are incompatible. It seems that Alice can reasonably say:

1. Either justice will be served or mercy will be served, and I am happy with both.

I don’t exactly know why it is that (1) makes rational sense but the following does not:

2. Either vengeance on Bob will be saved or kindness to Bob will be served, and I am happy with both.

But it does seem that (1) makes sense in a way in which (2) does not. Maybe the difference is this: to avenge requires setting one’s will against the other’s overall good; just punishment does not.

I conjecture that there are no morally upright cases of rationally incompatible reasons for the same action. That conjecture would provide an interesting formal constraint on rationality and morality.

An improvement on the objective tendency interpretation of probability

I am very much drawn to the objective causal tendency interpretation of chances. What makes a quantum die have chance 1/6 of giving any of its six results is that there is an equal causal tendency towards each result.

However, objective tendency interpretations have a serious problem: not every conditional chance fact is an objective tendency. After all, if P(A|B) represents an objective causal tendency of the system in state B to have state A, to avoid causal circularity, we don’t want to say that P(B|A) represents an objective causal tendency of the system in state A to have state B.

There is a solution to this: a more complex objective tendency interpretation somewhat in the spirit of David Lewis’s best-fit interpretation. Specifically:

• the conditional chance of A on B is r if and only if Q(A|B)=r for every probability function Q such that (a) Q satisfies the axioms of probability and (b) Q(C|D)=q whenever r is the degree of tendency of the system in state D to have state C.

There are variants of this depending on the choice of formalism and axioms for Q (e.g., one can make Q be a classical countably additive probability, or a Popper function, etc.). One can presumably even extend this to handle lower and upper chances of nonmeasurable events.

Scratch coding in Minecraft

Years ago, for my older kids' coding education, I made a Minecraft mod that lets you program in Python. Now I made a Scratch extension that works with that mod for block-based programming, that I am hoping to get my youngest into. Instructions and links are here.

Intending as a means or as an end

I used to think that it is trivial and uncontroversial that if one intends something, one intends it as an end or as a means.

Some people (e.g., Aquinas, Anscombe, O’Brian and Koons, etc.) have a broad view of intention. On such views, if something is known to inevitably and directly follow from something that one intends, then one intends that, too. This rules out sophistical Double Effect justifications, such as a Procrustes who cuts off the heads of people who are too tall to fit the bed claiming that he intends to shorten rather than kill.

But if one has a broad view of intention, then I think one cannot hold that everything intended is intended as an end or as a means. The death of Procrustes’ victim is not a means: for it does nothing to help the victim fit the bed. But it’s not an end either: it is the fit for the bed that is the end (or something else downstream of that, such as satisfaction at the fit). So on broad views of intention, one has to say that Procrustes intends death, but does not intend it either as a means or as an end.

While this is a real cost of the broad theory of intention, I think it is something that the advocates of that theory should simply embrace. They should say there are at least three ways of intending something: as a means, as an end, and as an inevitable known side-effect (or however they exactly want to formulate that).

On the other hand, if we want to keep the intuition that to intend is to intend as a means or as an end, then we need to reject broad theories of intentions. In that case, I think, we should broaden the target of the intention instead.

In any case, the lesson is that the characterization of intending as intending-as-a-means-or-as-an-end is a substantive and important question.

Reasons as construals

Scanlon argues that intentions do not affect the permissibility of non-expressive actions because our intentions come from our reasons, and our reasons are like beliefs in that they are not something we choose.

In this argument, our reasons are the reasons we take ourselves to have for action. Scanlon’s argument can be put as follows (my wording, not his):

1. I do not have a choice of which reasons I take myself to have.

2. If I rationally do A, I do it for all the reasons for A that I take myself to have for doing A.

And the analogy with beliefs supports (1). However, when formulated like this, there is something like an equivocation on “reasons I take myself to have” between (1) and (2).

On its face reasons I take myself to have are belief-like: indeed, one might even analyze “I take myself to have reason R for A” as “I believe that R supports A”. But if they are belief-like in this way, I think we can argue that (2) is false.

Beliefs come in occurrent and non-occurrent varieties. It is only the occurrent beliefs that are fit to ground or even be analogous to the reasons on the basis of which we act. Suppose I am a shady used car dealer. I have a nice-looking car. I actually tried it out and found that it really runs great. You ask me what the car is like. I am well-practiced at answering questions like that, and I don’t think about how it runs: I just say what I say about all my cars, namely that it runs great. In this case, my belief that the car runs great doesn’t inform my assertion to you. I do not even in part speak on the basis of the belief, because I haven’t bothered to even call to mind what I think about how this car runs.

So, (2) can only be true when the “take myself to have” is occurrent. For consistency, it has to be occurrent in (1). But (1) is only plausible in the non-occurrent sense of “take”. In the occurrent sense, it is not supported by the belief analogy. For we often do have a choice over which beliefs are occurrent. We have, for instance, the phenomenon of rummaging through our minds to find out what we think about something. In doing so, we are trying to make occurrent our beliefs about the matter. By rummaging through our minds, we do so. And so what beliefs are occurrent then is up to us.

This can be of moral significance. Suppose that I once figured out the moral value of some action, and now that action would be very convenient to engage in. I have a real choice: do I rummage through my mind to make occurrent my belief about the moral value of the action or not? I might choose to just do the convenient action without searching out what it is I believe about the action’s morality because I am afraid that I will realize that I believe the action to be wrong. In such a case, I am culpable for not making a belief occurrent.

While the phenomenon of mental rummaging is enough to refute (1), I think the occurrent belief model of taking myself to have a reason is itself inadequate. A better model is a construal model, a seeing-as model. It’s up to me whether I see the duck-rabbit as a duck or as a rabbit. I can switch between them at will. Similarly, I can switch between seeing an action as supported by R₁ and seeing it as supported by R₂. Moreover, there is typically a fact of the matter whether I am seeing the duck-rabbit as a duck or as a rabbit at any given time. And similarly, there may be a fact of the matter as to how I construed the action when I finally settled on it, though I may not know what that fact is (for instance, because I don’t know when I settled on it).

In some cases I can also switch to seeing the action as supported by both R₁ and R₂, unlike in the case of the duck-rabbit. But in some cases, I can only see it as supported by one of the reasons at a time. Suppose Alice is a doctor treating a patient with a disease that when untreated will kill the patient in a month. There is an experimental drug available. In 90% of the cases, the drug results in instant death. In 10% of the cases, the drug extends the remaining lifetime to a year. Alice happens to know that this patient once did something really terrible to her best friend. Alice now has two reasons to recommend the drug to the patient:

• the drug may avenge the evil done to her friend by killing the patient, and

• the drug may save the life of the patient thereby helping Alice fulfill her medical duties of care.

Both reasons are available for Alice to act on. Unless Alice has far above average powers of compartmentalization (in a way in which some people perhaps can manage to see the duck-rabbit as both a duck and a rabbit at once), it is impossible for Alice to act on both reasons. She can construe the recommending of the pill as revenge on an enemy or she can construe it as a last-ditch effort to give her patient a year of life, but not both. And it is very plausible that she can flip between these. (It is also likely that after the fact, she may be unsure of which reason she chose the action for.)

In fact, we can imagine Alice as deliberating between four options:

• to recommend the drug in the hope of killing her enemy instantly

• to recommend the drug in the hope of giving her patient a year of life

• to recommend against the drug in order that her enemy should die in a month

• to recommend against the drug in order that her patient have at least a month of life.

The first two options involve the same physical activity—the same words, say—and the last two options do as well. But when she considers the first two options, she construes them differently, and similarly with the last two.

Intention doesn't transfer to inevitable consequences

Some people, maybe as part of a response to the closeness problem for Double Effect, think:

1. Whenever I intend A while knowing that A inevitably causes B, I intend B.

This is false. Suppose I play a game late at night in order to have late night fun, knowing that late night fun will inevitably lead to my being tired in the morning. Now, if I intend something, I intend it as a means or as an end. I clearly don’t intend to be tired in the morning as a means to having had fun in the evening: there is no backwards causation. But I also don’t intend being tired in the morning as an end: the end was my late night fun, which led to being tired. So if I don’t intend it as a means or as an end, I don’t intend it at all, contrary to 1.

More precisely:

2. I intend E as my end and know that E inevitably causes F.

3. If I intend something, I intend it as a means or as an end.

4. If I know that something is caused by my end, then I do not intend it as an end.

5. If I know that something is caused by my end, then I do not intend it as a means.

6. So, I do not intend F as an end or as a means. (2, 4, 5)

7. So, I do not intend F. (3, 6)

8. So, sometimes I act intending E and knowing that E inevitably causes some effect F without intending F. (2, 7)

9. So, (1) is false.