We’ll have to familiarize ourselves with a number of background issues, to prepare for studying and discussing Davidson’s paper. Some of these had to do with the notion of laws. Examples of the kind of thing we’re thinking of here are Newton’s Law of Gravitation, or biological laws like these.
A generalization is a claim of the form “All/Most Fs are G,” or “Fs are always/usually G.” Some generalizations are true, but not for any deep systematic reason. For instance, it may be that every family on my street owns a Pitbull. Not because it’s a dangerous neighborhood, it just turned out that way. Maybe one or two of them bought Pitbulls because they liked their neighbor’s dog. But others already owned Pitbulls when they moved onto the street. In this case, “Every family on Street So-and-So owns a Pitbull” would be a true generalization, but it’s not a lawlike truth. It didn’t have to be true. If your family moved onto tbe street, nobody would make you go buy a Pitbull.
Generalizations like these we call accidentally true. That label can be misleading: it doesn’t have to be a complete accident in the everyday sense of that term. As I said, some of the families might have bought Pitbulls because their neighbors had them and they kind of liked them. Maybe some people decided to live there because they liked that there’d be other Pitbulls for their Petunia to play with. What philosophers mean by calling these generalizations “accidentally” true is just that they’re not natural laws or consequences of any such law.
There’s a lot of discussion and unsettled issues about what it is to be a natural law. But two criteria that philosophers often accept are that:
These are each meant as necessary conditions for being a law. Perhaps there are further conditions that laws have to satisfy too. What’s meant by the first criterion is that, if it is a law that All Fs are G, then it should also be true that if something that isn’t now F were to become (or have been) F, then it also would be G. Since in our example, we said that if you moved onto the street, you wouldn’t have to own a Pitbull, this condition is not satisfied for the generalization “Every family on Street So-and-So owns a Pitbull.”
We’ll spend more time discussing the second criterion in a moment. But the basic idea is that, if you find an example of something that’s F, and confirm that it’s also G, that should count as evidence for the claim that All Fs are G, if that generalization really is an appropriate candidate to be a law. This doesn’t help us much in the present example, for it’s also the case that if you find another family on Street So-and-So and they turn out to own a Pitbull too, that counts as evidence for the generalization “Every family on Street So-and-So owns a Pitbull.” Even though that generalization is not a law. So condition 2 is not only satisfied by laws; at least some other regularities can satisfy it too. We’ll meet some regularities that don’t seem to satisfy it below.
Sometimes philosophers talk of generalizations being “lawful” or “lawlike” instead of calling them laws. Some of this may just be different vocabulary for the same thing. But there’s a tendency when using the label “law” to understand this as meaning “true law,” or “something that really is a law.” Whereas if you use the other labels, you may be allowing that what you’re talking about has the right shape or character to be a law, but you’re leaving it open in the discussion whether it really is a law or not.
There’s also a tendency to use the label “law” as a special honorific, so that ideally only a few simple axioms count as laws. On the other hand, if you have a couple such laws, they will have all sorts of complex logical consequences. Some of those will be about what happens to particular objects, but others will also be generalizations. For instance, Newton’s Third Law of Motion says:
When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.
One consequence of that is this claim, which is more specific but which is also a generalization:
When any Pitbull exerts a force on a leash, that leash simultaneously exerts a force equal in magnitude and opposite in direction on the Pitbull.
Many philosophers wouldn’t want to call the second generalization a “law,” even though it will have some properties in common with things they do call “laws.” They might call the second one “lawlike.”
Some laws (or lawlike generalizations) are strict, in that they don’t allow for any exceptions. Newton’s Laws of Motion are strict in this sense. Other laws merely hold “for the most part,” or “usually,” or “other things being equal.” The biological laws I linked to above are of this sort. One of them says that within a broadly distributed species (or larger taxonomic group), populations of larger sized animals are in the colder regions. Of course there can be exceptions to this law. But it still tends to hold for the most part; it’s an interesting and reliable biological tendency. Philosophers call these hedged laws or ceteris paribus laws. (“Ceteris paribus” is just the Latin for “other things being equal.”)
Some ceteris paribus laws can be made more exact and accurate, by adding further restrictions or clauses. Sometimes it’s possible to do this while still staying inside the scientific vocabulary that the original law is formulated in terms of. For instance, Newton’s Law of Gravitation wasn’t strictly accurate, but could be improved by adding more physics. The new laws explained why Newton’s Law held in the cases we ordinarily interacted with, but became less and less accurate in the exceptional cases. On the other hand, the law that populations of larger sized animals are in colder regions also has exceptions. One exception is that Texas’s Circus of Big Tents and Bigger Animals has larger bears in it than can be found anywhere in Canada. If we wanted to rule out exceptions like this, we couldn’t just use the vocabulary of the population biologist and so on. We’d have to talk about Circuses, or human interventions more generally. We might also have to talk about earthquakes that caused some buffalo populations to migrate southward. And so on. There might be no way to make the original generalization more exact while both staying within the original vocabulary (and still getting a generalization that’s lawful and true).
Thus we could arrange true generalizations on a kind of spectrum:
We said above that when something is a law, it should “support counterfactuals.” So if it’s a law that All Fs are G, then it’s not just all actual Fs that are G, but also if something else had been F, it would also have to be G. So the laws have some kind of necessity to them. At the same time, many philosophers think it would have been possible for the world to have been fundamentally different, so that different laws of nature were in force. (Maybe in our world, faster-than-light travel isn’t possible, but that’s something that the universe could, in some sense, have permitted.) These philosophers will say that the kind of necessity that goes with laws isn’t the strongest kind of necessity. They’ll call the kind of necessity that goes with laws “natural” or “physical” or nomological necessity. (“Nomos” is just the Greek for “law”.) They’ll call the strongest kind of necessity “logical” or metaphysical necessity. Some philosophers think these categories coincide, because they think that whatever laws hold of our world, hold with the strongest kind of necessity there is. But as I said, many philosophers don’t think that. Hence there is a fifth kind of true generalization:
It’s hard to agree on uncontroversial examples of this last category, because philosophers have different views about what properties are essential. But a materialist might for example say that “All creatures with minds have a body” is an example of this, if they think that having a body is an essential property of a creature with a mind. (Not every materialist thinks this: remember that Smart thought it was only contingently true.) Another example might be “All mortal creatures eventually die.”
The question of whether laws are only in category 4, or also in category 5, is interesting but we can set it aside for the present discussion.
Nowadays, many philosophers think that physics is the only science that can give us lawful generalizations of categories 3 and 4. Sciences like biology, and chemistry, and economics, and so on — what philosophers call special sciences because they’re not about all of reality but only special parts of it — arguably can at best give us generalizations of category 2. One reason to think this might be, well if there are “better” generalizations to be found, what are they? Nobody seems to have come up with them yet. (Or if they seemed to, we eventually learned that those generalizations are false.) We can call that a modest reason for thinking the special sciences can’t give us strict laws. As we’ll see in a few days, Davidson thinks in the case of psychology we can go further and give a principled argument that there can’t be strict psychological laws of certain kinds.
Philosophers use the term “deduction” in a special way. They use this only for arguments that hold because of their logical form. Hence, a philosopher would count “My coin is metal and shiny. Therefore my coin is shiny.” as a deductive argument. They wouldn’t count the kind of thing that Sherlock Holmes or Hercule Poirot did “deduction.” That’s not to say that what Holmes and Poirot did wasn’t good reasoning. Philosophers just reserve the term “deduction” for a more specific kind of reasoning, that has special interest.
Reasoning that’s good but not deductive goes by a variety of names. You may see the labels “inductive” or “abductive” reasoning, or “inference to the best explanation.” Some philosophers reserve the term “induction” for a different specific kind of reasoning; another label for it is enumerative or statistical induction. It’s not what Holmes and Poirot did either. But it is what we want to consider now.
This is reasoning where we start with premises like “Here’s an F that’s G; here’s another F that’s G; here’s another…” Or the premises may have the form “The past 100 Fs have all been G” or “More than 90% of the past Fs have been G.”
Those are the premises we begin with. The reasoning then continues either by drawing a generalization, like “All Fs are G” or “(At least) most Fs are G.” Or it may continue by applying that to a specific new case, as in “Here’s another F; so it will be G too,” or “The next F we find will also be G.”
This is the kind of thing we had in mind before when we said that laws are supported by their instances. Part of the evidence for Newton’s Laws were that everything we’ve seen so far matched what they said. So that gives us some reason to believe that his Laws were at least true generalizations — that we could expect future cases also to conform to them. (Having reason to believe that they’re not just true generalizations, but also laws, probably requires more evidence than this; but this is at least part of the story.)
Now there have been philosophical challenges to how we can be justified in relying on this kind of reasoning. Some famous challenges came from Hume in the mid-1700s. Another famous challenge came from Goodman in the 1950s. Goodman’s challenge had to do with a property he called “grue.”
Some philosophers understand “grue” to be defined like this:
Other philosophers define “grue” like this:
The first definition has the consequence that an emerald that you hold in your hand on the stroke of midnight as 2030 ends — assuming nothing funny happens, and it stays green — would change from being grue to not being grue anymore. (Instead it would be “bleen,” which is defined in terms of blue/green the way “grue” is defined in terms of green/blue.) Whereas with the second definition, the emerald would continue to be grue, since you first observed it in 2030 or earlier. But a green emerald that’s first discovered after 2030, both definitions would agree is then grue.
Goodman himself understood “grue” in the second way, and we’ll follow him here; though that defintion is in some ways more complex. (You have to consider two times: both the time at which the object does/doesn’t exemplify grueness, and also the time at which the object was first observed. Also: observed by who?)
Philosophers call words like “grue” and “bleen” gruelike or gruesome. Other examples of such words would be “gred” (defined in terms of green/red) and “emeroses” (defined in terms of emerald/roses). Thus:
The ordinary, non-gruesome words we instead call natural. Now one issue here is just figuring out what makes a word gruesome. You might say, well the gruesome words are defined in terms of a time and the more natural words. But as Goodman pointed out, we could also define “green” in terms of “grue” and “bleen.” That is, this is also true:
So somehow we have to be able to figure out which of these properties or concepts is more basic that the others: should we think that really grue and bleen are defined in terms of green, blue, and what time something was observed, or is it the other way?
Another part of the challenge here is what inductive reasoning we’re justified in engaging in. For notice that all of the emeralds we’ve observed up until now, that have been green, have also been grue. We’re tempted to say that the emeralds we observe in the future (and more specifically in 2031) will also be green, because all the past ones have been. But one could also argue, we should expect them to be grue, because all the past ones have also been grue.
In 2031, new emeralds won’t be both green and grue. If they’re green they’ll be bleen, and if they’re grue they’ll be blue. So these two lines of reasoning lead to different expectations about what future emeralds will look like.
Of course, everyone thinks that the green reasoning is somehow preferable to the grue reasoning. The challenge is to explain why that is. Different philosophers have different views about this, and we can’t explore the options here. You can study that more in a Philosophy of Science class.
We just needed to familiarize ourselves with this background issue to be able to understand some of what Davidson will be talking about in his article.
He has the idea that words like “gred” and “emerose” go together, and words like “green” and “emerald” go together, and that you could have laws like “All emeroses are gred,” but you can’t have laws that mix the groups, like “All emeralds are gred” or “All emeroses are green.” He’ll argue that laws that try to link psychological and physical properties will be like trying to mix “emerose” with “green.”
One detail here is that Davidson is willing to count “All emeroses are gred” as a law, because it follows from what everyone would agree are the lawful truths that “All emeralds are green” and “All roses are red.” (Actually, I guess that’s only true for some kinds of roses.) As I mentioned before, though, not every philosopher agrees that every generalization that follows from a law should also be called a “law.” I think many would not want to follow Davidson in calling “All emeroses are gred” a law.