“But I get a sense that “lattice” involves order in some way, and I am not seeing how order fits in to the question of how specific a concept is.”
Sounds to me like you’re on the right track. The claim made is that concepts can be ordered in terms of their abstractness. For example, the concept day would be taken to be more abstract than the concept sunny day in that day abstracts from the weather by admitting both sunny and cloudy days.
The order of concepts is ‘partial’ in that not all concepts can be compared by abstraction: for example, neither sunny nor day by themselves is more abstract than the other. So, unlike the familiar ‘total’ orderings that we see with, say, numbers, in which any two numbers can be compared/ordered by ‘less than’, the abstraction ordering on concepts is only ‘partial’ in that some pairs of concepts cannot be compared.
Now I’m wondering whether specificity can be measured in a sort of absolute sense rather than in a relative sense.
You mention that sunny day is more specific than day because it adds weather. Or as others have mentioned, because the set of points it includes is a subset of the set of points that day includes.
But what about the concept of “pizza that is warm, has an exterior that is thin and crispy, an interior that is warm, chewy, and fresh, a thin layer of tomato sauce that is mildly sweet and acidic, and small dollups of fresh mozzarella cheese that is cool and soft”? Can we say that this pizza concept is specific? That it’s more specific than day or even sunny day, despite being distant in Thingspace from the day and sunny day concepts?
Intuitively the answers to those questions seem to be “yes”, but I’m not sure why, at least not formally.
Maybe it’s about “potential for confusion”. If I said “the pizza was good”, the good pizza concept is it’s easy to be confused about what the concept is pointing too (thick or thin crust? red or white sauce?). I suppose this is because there are a lot points clustered together in the good pizza concept.
Alternatively, if I said “last weekend”, I used a lot less words than I did in my “pizza that is warm...” ramble, but I still think “last weekend” is quite specific. I suppose because even though I’m only specifying two “things”—“last” and “weekend”—the potential for confusion is low. There are only two days “last weekend” can be referring to.
One point I’d make is that I tried to limit my discussion to ‘abstraction’ as it relates to concepts, as that seemed most pertinent to the quote you cited. The opposite of abstract is concrete. I’m not entirely sure that we should confound the abstract/concrete comparison with that of general/specific.
“pizza that is warm, has an exterior that is thin and crispy, an interior that is warm, chewy, and fresh, a thin layer of tomato sauce that is mildly sweet and acidic, and small dollups of fresh mozzarella cheese that is cool and soft” Let’s say you’ve just described a ‘Napolitana’ pizza. Is “large Napolitana” specific in your sense? I can see a definitional regression emerging. For this reason, I suspect that specificity/generality might be best kept to comparisons relative to some ‘basis’ concepts, rather than made in some absolute sense.
“Last weekend” has its own issues, being relative to the day it is uttered. Indeed, to account for any day of utterance, it might be a difficult concept to articulate precisely. As a ‘relative’ (or ‘relational’) concept, it might be general in that it ranges over many instances.
There is the further issue of vagueness. Many of the concepts you use (eg, warm,thin, etc.) are not precise. This issue is exacerbated with good, which is, in addition, inherently subjective.
Adding to @TsviBT.
“But I get a sense that “lattice” involves order in some way, and I am not seeing how order fits in to the question of how specific a concept is.”
Sounds to me like you’re on the right track. The claim made is that concepts can be ordered in terms of their abstractness. For example, the concept day would be taken to be more abstract than the concept sunny day in that day abstracts from the weather by admitting both sunny and cloudy days.
The order of concepts is ‘partial’ in that not all concepts can be compared by abstraction: for example, neither sunny nor day by themselves is more abstract than the other. So, unlike the familiar ‘total’ orderings that we see with, say, numbers, in which any two numbers can be compared/ordered by ‘less than’, the abstraction ordering on concepts is only ‘partial’ in that some pairs of concepts cannot be compared.
Hm. I think that all makes sense.
Now I’m wondering whether specificity can be measured in a sort of absolute sense rather than in a relative sense.
You mention that sunny day is more specific than day because it adds weather. Or as others have mentioned, because the set of points it includes is a subset of the set of points that day includes.
But what about the concept of “pizza that is warm, has an exterior that is thin and crispy, an interior that is warm, chewy, and fresh, a thin layer of tomato sauce that is mildly sweet and acidic, and small dollups of fresh mozzarella cheese that is cool and soft”? Can we say that this pizza concept is specific? That it’s more specific than day or even sunny day, despite being distant in Thingspace from the day and sunny day concepts?
Intuitively the answers to those questions seem to be “yes”, but I’m not sure why, at least not formally.
Maybe it’s about “potential for confusion”. If I said “the pizza was good”, the good pizza concept is it’s easy to be confused about what the concept is pointing too (thick or thin crust? red or white sauce?). I suppose this is because there are a lot points clustered together in the good pizza concept.
Alternatively, if I said “last weekend”, I used a lot less words than I did in my “pizza that is warm...” ramble, but I still think “last weekend” is quite specific. I suppose because even though I’m only specifying two “things”—“last” and “weekend”—the potential for confusion is low. There are only two days “last weekend” can be referring to.
They’re all interesting questions.
One point I’d make is that I tried to limit my discussion to ‘abstraction’ as it relates to concepts, as that seemed most pertinent to the quote you cited. The opposite of abstract is concrete. I’m not entirely sure that we should confound the abstract/concrete comparison with that of general/specific.
“pizza that is warm, has an exterior that is thin and crispy, an interior that is warm, chewy, and fresh, a thin layer of tomato sauce that is mildly sweet and acidic, and small dollups of fresh mozzarella cheese that is cool and soft”
Let’s say you’ve just described a ‘Napolitana’ pizza. Is “large Napolitana” specific in your sense? I can see a definitional regression emerging. For this reason, I suspect that specificity/generality might be best kept to comparisons relative to some ‘basis’ concepts, rather than made in some absolute sense.
“Last weekend” has its own issues, being relative to the day it is uttered. Indeed, to account for any day of utterance, it might be a difficult concept to articulate precisely. As a ‘relative’ (or ‘relational’) concept, it might be general in that it ranges over many instances.
There is the further issue of vagueness. Many of the concepts you use (eg, warm, thin, etc.) are not precise. This issue is exacerbated with good, which is, in addition, inherently subjective.