Wolfgang Schwarz

Reliability

What does it take for something to be a perfectly reliable indicator of something else?

I'm not really familiar with discussions of reliability in epistemology, and I'd be grateful for pointers. Anyway, here is my own suggestion.

First, we need a mapping from (possible) states of the indicator to the indicated facts (or states or propositions). Let's say that the indicator displays that p, for short: I(p), if its state is mapped to p by that mapping. The mapping may be any old function (but the 'states' may not be any old Cambridge states): there is a good sense in which a clock that consistently runs 8 minutes fast is reliable; the tricky bit is only to read what it says, to figure out the mapping. This is the sense of "reliable" I'm interested in.

A perfectly reliable indicator never misrepresents -- not actually and not in nearby counterfactual situations. A thermometer that displays the correct temperature but would have malfunctioned had things been only slightly different is not perfectly reliable.

On the other hand, a perfectly reliable thermometer need not display the correct temperature in all counterfactual situations: not, for example, in situations where it is broken, or where it does not exist, or where the temperature is out of the thermometer's range.

Suppose the range of our thermometer goes from -40°C to 80°C. If it is perfectly reliable, it will presumably satisfy this condition: for all t between -40°C and 80°C, if the temperature actually were t, the thermometer would display that it is t.

R1) .

(R1) comes close to what it means to be reliable. But unless we impose some unusual interpretation on the counterfactal, it's not quite correct.

Consider an otherwise reliable thermometer that is heavily disturbed by planes passing above it (or nearby): whenever that happens, it displays a random temperature. Suppose right now there's no plane around. Then condition (R1) is satisfied: why should nearby worlds where the temperature is different be worlds where planes pass by? Still, the thermometer is not reliable, at least not if it's used in an area with many planes.

This case might be ruled out by adding the inverse of (R1):

R2) .

That looks sort of plausible anyway: a reliable thermometer should allow us to safely draw inferences from what it displays to the actual temperature. This is just what we can't do with the plane-disturbed device: if that thermometer were to display 67°C now, most likely a plane would be passing by; it wouldn't be 67°C (on this 3rd of November in this unheated flat in Berlin).

But we need a rather special reading of the counterfactual here, one that becomes quite artificial for less extreme thermometer readings, or when we take the plane-disturbed thermometer to some other place where the temperature varies a lot and where it is unlikely that there are ever any planes nearby: is it then still true that if the thermometer displayed, say, 28°C, a plane would be passing by? Maybe not. Then (R2) doesn't suffice to rule out the plane-disturbed thermometer.

On the other hand, it isn't clear that perfectly reliable thermometers must satisfy (R2). Can't we say of a perfectly reliable thermometer that if it now displayed 67°C, it would be broken (given that it's only 18°C)?

So I think we better not add (R2) as a condition on reliability. (We certainly shouldn't replace (R1) by (R2). Suppose our thermometer randomly switches between a state in which it traces the current temperature and one in which it always displays 18°C. Then if by coincidence it is 18°C and the thermometer is in 'always display 18°C' mode, it satisfies (R2) even though it is not reliable.)

At any rate, (R2) doesn't really do justice to the initial problem with (R1), which was that we want a reliable indicator to display the correct value in counterfactual situations where all kinds of other things besides the indicator and what it indicates -- the weather, the time, the traffic, etc -- are different than they actually are.

We should rather extend the range R to cover differences in these respects. For example, one of the propositions p in R might be that it's 17°C and a plane is passing by, another that it's 12°C and it's raining and the moon is full. Any such p must still determine the temperature (up to the relevant degree of precision). Let t(p) be that temperature: the temperature at all the p-worlds. Then we can improve on (R1):

R1') ,

where R is still some suitable range of propositions. What exactly counts as suitable depends on the indicator and its purpose or use. The same device can be reliable relative to one range but not relative to another.

(R1') is my proposed analysis of reliability.

(R2) looked plausible because we want to rule out indicators that misrepresent in nearby counterfactual situations. As far as I can see, (R1') also rules out these cases, and does so much better than (R2).

One might also think about adding the contrapositions of (R1) and (R2):

R1C)

R2C)

(R2C) looks as suspicious as (R2) to me, but (R1C) certainly looks right: if my thermometer would display 18°C if it wasn't 18°C, it wouldn't be very reliable.

(R1C) is logically independent of (R1) and (R1'). But we don't need to add it as a separate clause: in nearby worlds where it isn't 18°C, it is probably something like 19°C or 17°C, and such worlds will most likely fall under some of the conditions in R. So (R1) already ensures that the thermometer doesn't display 18°C there. (Note that displaying is a function: if the thermometer displays 19°C, it cannot also display 18°C.) In genereal, (R1) entails (R1C) unless either the actual temperature or the temperature at the closest world where the temperature is not the actual one is out of range. For what it's worth, (R2C) is related in the same way to (R2).

So in all reasonable cases, (R1) and (R1') entail (R1C). (The converse is clearly not true, for (R1C) by itself is a very weak condition: if a thermometer actually displays the correct temperature, (R1C) is trivially satisfied for all non-actual p: for those p, the closest world where not-p is the actual world. Hence all it takes to satisfy (R1C) is to actually display the correct temperature and to display something else at the closest worlds where the temperature is different.)