I’m late to this debate; it’s been well analyzed on the meta level but I want to add something on the object level. The question of ‘were coins of Alexander minted?’, which you want as your input data, sounds like a very simple one, but it may not be. The analysis of ancient coins in large part assumes a known history and dating.
The coins called ‘Alexander coins’ today didn’t carry the image of Alexander, but of Herakles. They had Alexander’s name on them, and sometimes the title ‘King’, but that’s just two words; not strong evidence of who exactly the coin-minters thought Alexander was and what he was supposed to have accomplished. So you have to separate ‘some Greek King named Alexander existed’ at one extreme, from ‘he did what’s commonly ascribed to him and is the person we think of as Alexander the Great’ at the other.
These coins were minted in many countries for hundreds of years, becoming something of a common coinage. People probably kept minting them because they were a standard coin, not because they really wanted to honor Alexander 300 years after his death. So the existence of most coins isn’t independent evidence.
When comparing coins minted of other people, you need to factor in the the different amounts of coins minted due to different technology and economy, the differential survival of the coins over time, and the probability of us finding them.
How do we identify a coin as being Alexandrian? Usually by matching it to other coins we’ve already identified. How do we identify the first Alexandrian coin we’ve ever seen? By noticing the name Alexander on it. What’s the probability coins were minted of Alexander, perhaps bearing his likeness (and not that of Herakles), but without his name? Putting the name of a king on a coin (whether or not he was pictured) became common (but not universal) somewhat after Alexander.
There were five kings of ancient Macedonia named Alexander, the third of them being the Great. Not to mention some non-Macedonian Alexanders. Coins with the name Alexander don’t specify which one is meant, or even ‘of Macedonia’. (A minority was actually minted in Macedonia, but if lots of other countries were minting coins of a foreign monarch, who’s to say Macedonia didn’t as well?) So the dating of the coins has to be precise enough (to within 50 years or so), which can be really hard (by the time you’ve found a coin who knows where it’s been?)
Clarification: I don’t seriously doubt the historicity of Alexander, but I’m also not versed in the subject, so I’m just going by expert opinion. My point is more that coins are really complex and/or weak as a source of evidence, and handling P(Alexander existed|Coins of Alexander) is really hard.
The issues you raised are interesting but actually make this a pretty good example of my problem—how do you account for weak evidence and assign it a proper likelihood. One way i am testing this is by taking an example which i think is agreed to be ‘most likely’ (that he existed as opposed to not existing). Then i want to work backwards and see if we there is a method for assessing probability that seems to work well on small scale questions, like probability’s of minted coins and give me the expected answer when i add it all together.
At this point i am still trying to work out the objective priors issue. The method either needs to be immediately agreeable by all potential critics or have an open and fair way of arguing over how to formulate the answer. When i work that out i will move to the next stages although no guarantee i keep using the Alexander example.
My point was that ‘probability of minted coins’ isn’t a much “smaller-scale” question than ‘probability of Alexander’, that is, it isn’t much simpler and easier to decide.
In our model of the world, P(coins) doesn’t serve as a a simple ‘input’ to P(Alexander). Rather, we use P(Alexander) to judge the meaning of the coins we find. This is true not only on the Bayesian level, where all links are bidirectional, but in our high-level conscious model of the world, where we can’t assign meaning to a coin with the single word Alexander on it without already believing that Alexander did all the things we think he did.
There’s very little you can say about these coins if you don’t already believe in Alexander.
I’m late to this debate; it’s been well analyzed on the meta level but I want to add something on the object level. The question of ‘were coins of Alexander minted?’, which you want as your input data, sounds like a very simple one, but it may not be. The analysis of ancient coins in large part assumes a known history and dating.
The coins called ‘Alexander coins’ today didn’t carry the image of Alexander, but of Herakles. They had Alexander’s name on them, and sometimes the title ‘King’, but that’s just two words; not strong evidence of who exactly the coin-minters thought Alexander was and what he was supposed to have accomplished. So you have to separate ‘some Greek King named Alexander existed’ at one extreme, from ‘he did what’s commonly ascribed to him and is the person we think of as Alexander the Great’ at the other.
These coins were minted in many countries for hundreds of years, becoming something of a common coinage. People probably kept minting them because they were a standard coin, not because they really wanted to honor Alexander 300 years after his death. So the existence of most coins isn’t independent evidence.
When comparing coins minted of other people, you need to factor in the the different amounts of coins minted due to different technology and economy, the differential survival of the coins over time, and the probability of us finding them.
How do we identify a coin as being Alexandrian? Usually by matching it to other coins we’ve already identified. How do we identify the first Alexandrian coin we’ve ever seen? By noticing the name Alexander on it. What’s the probability coins were minted of Alexander, perhaps bearing his likeness (and not that of Herakles), but without his name? Putting the name of a king on a coin (whether or not he was pictured) became common (but not universal) somewhat after Alexander.
There were five kings of ancient Macedonia named Alexander, the third of them being the Great. Not to mention some non-Macedonian Alexanders. Coins with the name Alexander don’t specify which one is meant, or even ‘of Macedonia’. (A minority was actually minted in Macedonia, but if lots of other countries were minting coins of a foreign monarch, who’s to say Macedonia didn’t as well?) So the dating of the coins has to be precise enough (to within 50 years or so), which can be really hard (by the time you’ve found a coin who knows where it’s been?)
Clarification: I don’t seriously doubt the historicity of Alexander, but I’m also not versed in the subject, so I’m just going by expert opinion. My point is more that coins are really complex and/or weak as a source of evidence, and handling P(Alexander existed|Coins of Alexander) is really hard.
The issues you raised are interesting but actually make this a pretty good example of my problem—how do you account for weak evidence and assign it a proper likelihood. One way i am testing this is by taking an example which i think is agreed to be ‘most likely’ (that he existed as opposed to not existing). Then i want to work backwards and see if we there is a method for assessing probability that seems to work well on small scale questions, like probability’s of minted coins and give me the expected answer when i add it all together.
At this point i am still trying to work out the objective priors issue. The method either needs to be immediately agreeable by all potential critics or have an open and fair way of arguing over how to formulate the answer. When i work that out i will move to the next stages although no guarantee i keep using the Alexander example.
My point was that ‘probability of minted coins’ isn’t a much “smaller-scale” question than ‘probability of Alexander’, that is, it isn’t much simpler and easier to decide.
In our model of the world, P(coins) doesn’t serve as a a simple ‘input’ to P(Alexander). Rather, we use P(Alexander) to judge the meaning of the coins we find. This is true not only on the Bayesian level, where all links are bidirectional, but in our high-level conscious model of the world, where we can’t assign meaning to a coin with the single word Alexander on it without already believing that Alexander did all the things we think he did.
There’s very little you can say about these coins if you don’t already believe in Alexander.