Keith Douglas
Two months ago we discussed classical computationalism. I sort of gave the game away when I said implementation. It should draw attention to the fact that I can program a computer to use any number of logical theories or nonclassical arithmetic. In fact, some people would argue that at the most basic level many computers do not use classical arithmetic either. Registers are only a fixed size and so adding 1 to a maxed-out register either produces “wrap around” (perhaps also with a flag set) or in some architectures an exception condition. Neither of these happen “in math world.”
This is illustrative of a more general principle: One should only criticize AI when one understands computers and humans without AI in the picture. The reason that we may have to learn arithmetic is independent of what arithmetic our “hardware” uses, for the same reason we need to learn how we metabolize proteins, how we form social groups, and even how we play the cello or hit a tennis ball. There are emergent effects in both computer systems and animals — and so, Dennett and I would say, the parts of animals happen also to be computer systems.
Last month, I encouraged us to reflect on the arbitrariness of names. One of the things I deliberately elided is the fact that names seem to have an arbitrary sound or series of marks. Nothing in that rules out having a systematic meaning. Yet are the meanings also arbitrary at a certain point?
It might appear arbitrary that we pick out one aspect of the world with the ane in (1S,3R)-1-bromo-3-chlorocyclohexane, for instance. After all, the colour of this molecule is not recorded. Some would adopt a “perspectival realism” here. I think that taken in one way this view is too hasty. There is no perspective in the actual patterns in nature. So if we attempt to name according to those patterns, those names are not arbitrary. Of course the sound produced by saying ane is. But not the sound produced by saying “cyclohexane” once one has the arbitrary cyclo and hex and ane.
So the lesson seems to be that only some sounds are arbitrary — that the semantics of some words dictate that the pronunciation and spelling are not arbitrary. So the answer to the first puzzle — whether names are based on configuration — is that we’re tempted to commit a fallacy of composition. The second puzzle — whether names can be unsystematic — can be answered in the same way the bonus question can be. Not all goals are met by one naming scheme. And all such naming schemes have to be some degree useful to creatures such as we are. Maybe creatures with more memory or patience would be able to name proteins with their IUPAC name, but a creature who could do the same for (each individual’s) DNA would be very different from us. (It is an interesting question to think about whether such a creature would be intelligent.)
The third puzzle — whether one can give exhaustive systematic names for any domain at all — can be answered: Yes, if the domain is well known enough and only one pattern of interest is selected. In formal arithmetic, a number’s position in the sequence of natural numbers is often used. Call the first number 0. Then the next is called 0’ (as the next after X is called X’). There might be a puzzle here about numbers and numerals I am eliding (more later), but note that this system of names is not available to us in other domains because some other domains, despite using numbers as part of names, use other, nonsystematic names of numbers.
For example, consider parts of the names of alkanes: methane, ethane, propane, butane, pentane, hexane, heptane. It looks at first glance that as of pentane we are using systematic names. But that’s only because you know from memory what the next Greek-origin prefix is. That’s unlike the first situation, because I gave a rule.
Peirce’s Paradox
Criminal Jacques Laroque runs out of his home near the Louisiana/Texas border to exact revenge against his rival Big Tex Mexi. Larouque stands on the state line with a small pistol and shoots Mexi, who falls from where he stands on the state line. A local Korean grocer witnesses the crime from the Louisiana side and calls the police in Texas because he knows they are closer.
Where should Laroque be charged with a crime? Does it matter if it turns out that Big Tex Mexi survived the initial shooting but was dead from his wounds a few days later in hospital?
This is a combination of two traditional paradoxes, the so-called “paradox of jurisdiction” and what I will call Peirce’s paradox. I am unsure if it has another name.
The only state line I am familiar with from having been there divides the town of Texarkana into jurisdictions belonging to (obviously) Texas and Arkansas. The main drag in Texarkana is State Line Road (not surprisingly) and each state is responsible for maintaining that road up to the center white line on their respective side. So, in practice, the actual state line is arguably one millimeter wide.
So, in the conundrum here, Laroque would likely have his feet more on one side of the state line than the other. In hockey, off-side is called by an official when any part of one’s skate precedes the puck over the blue line. So to call the jurisdiction responsible for charging Laroque with a crime, we may need to know what percentage of his feet were in each state at the time of the shooting, assuming a razor-thin state line of one millimeter.
As for Pierce’s Paradox, I presume, where Big Tex Mexi dies not die directly from being shot, but only later from related gunshot wounds, we might have to know 1) in which state is the hospital and 2) which state has jurisdiction based on state line foot placement.
That is the best I can do, not having much philosophy background.
I read somewhere, sometime, that there is a concept of overlapping jurisdiction, under which anything within something like 100m of the border can be tried in either jurisdiction. This prevents lawyers from trying stall the process by raising the question of exactly which side of the line the crime occurred on.