At what point do we say that the problem lies in the definition of a category? Since ordinary people have no especial use for the category “bird,” it’s unsurprising that they haven’t nailed down characteristics that would allow such a use.
Categories that we need—that must reliably possess some characteristic(s) such that they are useful—tend to have strict necessary and sufficient conditions for inclusion. Categories that we use purely to simplify speech can get away with fuzzier definitions.
Is the dolphin really a fish? That depends: is that thing over there really a blegg?
If a fuzzy definition becomes a massive problem, then that definition clearly wasn’t in existence merely to simplify speech.
Regarding mammals, is there a use for the term that requires its inclusion of dolphins? Does the existence of sweat glands usefully separate mammals from other animals? After all, mammals in general share a variety of properties: most give live birth, most have hair, most are warm-blooded, etc.--but we admit to the category of mammals many animals that fail one or more of these criteria.
A well-defined but useless category (I am not arguing that “mammal” is such a category, as there may well be a biological use for it) may be pedagogically interesting but otherwise may merely confuse our understanding of thingspace.
The definition of a mammal is simple: descent from the most recent common ancestor of all mammals. In practice, to avoid circularity, it is sufficient to take the MRCA of a few indisputable mammalian groups such as primates, rodents, carnivorans, ungulates, etc. to include all mammals.
This definition is useful because it turns out that there are many traits unique to mammals, and any given mammal will have almost all these traits. Many such traits are anatomical/biochemical/etc. (Many outwards traits like live birth or so-called “warm blood” aren’t unique to mammals.)
However, even if this definition wasn’t useful to us, the group Mammalia would still exist. It’s a natural evolutionary group (clade) in phylogenetics, to which we merely give a name. (Edit: and cladistics is a natural way of classifying species (among other ways). By natural I mean a classification that tends to match common and unique traits of species in the same clade, and which is causally linked to the history of of the species and to predictions for their future, so that I would expect aliens to have a relatively high probability of using similar classifications.)
The precise clade referred to by the word Mammalia can change depending on context. It makes sense to ask whether borderline species like platypuses are mammals or a sister group of mammals. That’s the fuzzy nature of any classification of real things. But the natural limits of the category “mammals” lie somewhere around the monotremes. A group which doesn’t include dolphins is definitely not the group of all mammals.
to avoid circularity, it is sufficient to take the MRCA of a few indisputable mammalian groups such as primates, rodents, carnivores, ungulates, etc. to include all mammals
But the MRCA of “indisputable” groups won’t be an ancestor of basal groups like the monotremes or marsupials.
However, there’s no dispute about including monotremes. The clade that excludes them is called the Theria. Likewise with the marsupials: the clade that excludes both them and the monotremes is the Eutheria. Every clade potentially has a name; Mammalia is just a particularly well known one.
Things get dicey if the evolutionary relationships are unclear, of course, or if some conventional group is recognised as not being a true clade.
You’re right, of course. I was just pointing out that clades nest nicely. Whether you talk about Theria or Eutheria, the species included or excluded by the differences will be the most distantly related ones such as monotremes; but no clade anywhere similar in scope to Eutheria would be able to exclude dolphins. In that sense, it doesn’t matter much which “indisputably” mammalian groups you take, their MRCA will be an ancestors of dolphins as well. For instance, the MRCA of humans and of cats is also an ancestor of dolphins.
Recursive definitions are possible, but they must still be founded on a base level that does not reference itself. Each other level can then be defined in a way that is not self-referential.
I believe usually it is also required that the number of steps (levels) to reach the non-recursive base should always be finite (e.g. recursion via a countable set).
Yeah, but in this case Annoyance is right. You need to find two extensional mammals such that their last common ancestor is the LCA of everything you want to call a mammal, then the definition is complete. As it stands it’s like a factorial without the base case.
EDIT: Stupid me.. I should have remembered that I was dealing with Annoyance, and been a bit more incredulous at the prospect of him being right, since Annoyance actually does use his intelligence in order to deliberately arrive at wrong answers.
You have to be careful—the LCA of those is not the LCA of all mammals, because those all happen to be placental mammals—and the splits leading to marsupial mammals and monotremes came before then.
That’s true. I addressed that originally by saying all monophyletic clades were natural groups, and they have a natural sequence (in order of increasing exclusivity).
So while we can debate which group should be called “mammals”—whether placentals, or placentals+marsupials, or something bigger yet—we can all agree that “mammals” is a group whose border lies somewhere near the placentals-marsupials joining point in the evolutionary sequence. Dolphins are nestled very deeply in the group, and so dolphins are definitely mammals by any definition you may use. (That’s what the original debate was about: I argued that “mammals without dolphins” is not a natural group.)
It’s not a question of fact, but of definition—to what group do we refer as “mammals”? So it makes little sense to argue over it.
All groups of animals defined via shared characteristics have fuzzy borders. The fact that all extant species either clearly do or clearly don’t lactate is purely an evolutionary accident, since all the intermediaries once existed. Even today we have species that lactate but don’t have localized nipples (the platypus exudes milk from a wide area of skin). Farther out, we have various fishes, amphibians, etc. that exude specialized non-milk substances from their skin for their young to eat. If you throw away the categories, “feeding the young on substances released from skin pores” is a wider category than just mammals.
Also, this whole thread started with people saying that “common people” wouldn’t know if dolphins are mammals, even though they do lactate.
Yeah, but in this case Annoyance is right. You need to find two extensional mammals such that their last common ancestor is the LCA of everything you want to call a mammal, then the definition is complete. As it stands it’s like a factorial without the base case.
In what way does your comment differ from Dan Armak’s original comment? how is Annoyance right in this case?
Which is why the next sentence after the one you quoted explained: “In practice, to avoid circularity, it is sufficient to take the MRCA of a few indisputable mammalian groups such as primates, rodents, carnivorans, ungulates, etc. to include all mammals.”
IOW, start from a few groups everyone agrees on calling mammals, and you have a precise rule stating whether any given animal is a mammal or not.
Monotremes are mammals, yet do not share the property of giving live birth.
“Hair… may be greatly reduced in the Cetacea (i.e. dolphins), where it is found as a few scattered bristles about the lips or often present only in the young.” W. J. Hamilton, American Mammals.
Heterocephalus glaber, the naked mole rat, is a mammal despite being poikilothermic.
As DanArmak notes, mammals are explicitly not the set of all species fulfilling a particular set of (external) criteria. They are defined by descent.
To the extent that this is useful, great. My point was merely that there is no external fact of the matter that requires drawing the boundaries where they currently are.
So when “ordinary people…get it wrong” by believing that dolphins are fish, it’s a little hard to blame them.
Monotremes are mammals, yet do not share the property of giving live birth.
And many decidedly non-mammal animals do give live birth. Wikipedia lists “scorpions, some sharks, some snakes, [...] velvet worms [and] certain lizards”.
What exactly do you mean when you say they believe that dolphins are fish? The question isn’t about what to call a fish.
If they believe dolphins are like tuna in that they live entirely in the sea, have no hands and feet, swim with a thrashing tail, and eat other fish, then they are right.
And if they believe dolphins are like tuna in that they breath through gills and lay single-cell eggs into the water which grow into baby fish, then they are wrong. And I’d happily blame them for being wrong, because these are things that would be easy to get right with a little observation.
I’m suggesting that people see dolphins sharing the (easily-observable) characteristics they do with tuna and aren’t especially interested in the respiratory or reproductive aspects—particularly because the category of “air-breathing fish” is wrong in some sense by construction.
They are also wrong on the biochemical differences, but insofar as fish are pretty much just “all the animals in the sea” to the general public, I’d say the scientific and the popular use of the word probably diverge.
Perhaps I’m being too much of an economist, but I figure that the actual need for most people to know most of these biological details is limited, and the fuzziness in the popular use of the word arises from a low-effort sweep of the observables.
For people who don’t care in the least about dolphins (or fish), it makes sense. I shouldn’t have assumed everyone shares a minimal interest in zoology.
At what point do we say that the problem lies in the definition of a category? Since ordinary people have no especial use for the category “bird,” it’s unsurprising that they haven’t nailed down characteristics that would allow such a use.
Categories that we need—that must reliably possess some characteristic(s) such that they are useful—tend to have strict necessary and sufficient conditions for inclusion. Categories that we use purely to simplify speech can get away with fuzzier definitions.
Is the dolphin really a fish? That depends: is that thing over there really a blegg?
The biological category of ‘mammal’ is quite well-defined, thank you.
And fuzzy definitions are fine until you’re dealing with a case that lies in the penumbra, at which time it becomes a massive problem.
If a fuzzy definition becomes a massive problem, then that definition clearly wasn’t in existence merely to simplify speech.
Regarding mammals, is there a use for the term that requires its inclusion of dolphins? Does the existence of sweat glands usefully separate mammals from other animals? After all, mammals in general share a variety of properties: most give live birth, most have hair, most are warm-blooded, etc.--but we admit to the category of mammals many animals that fail one or more of these criteria.
A well-defined but useless category (I am not arguing that “mammal” is such a category, as there may well be a biological use for it) may be pedagogically interesting but otherwise may merely confuse our understanding of thingspace.
″.--but we admit to the category of mammals many animals that fail one or more of these criteria.”
No, we don’t. Dolphins have all of the required attributes to be considered mammals. If they didn’t, we couldn’t call them mammals any longer.
The definition of a mammal is simple: descent from the most recent common ancestor of all mammals. In practice, to avoid circularity, it is sufficient to take the MRCA of a few indisputable mammalian groups such as primates, rodents, carnivorans, ungulates, etc. to include all mammals.
This definition is useful because it turns out that there are many traits unique to mammals, and any given mammal will have almost all these traits. Many such traits are anatomical/biochemical/etc. (Many outwards traits like live birth or so-called “warm blood” aren’t unique to mammals.)
However, even if this definition wasn’t useful to us, the group Mammalia would still exist. It’s a natural evolutionary group (clade) in phylogenetics, to which we merely give a name. (Edit: and cladistics is a natural way of classifying species (among other ways). By natural I mean a classification that tends to match common and unique traits of species in the same clade, and which is causally linked to the history of of the species and to predictions for their future, so that I would expect aliens to have a relatively high probability of using similar classifications.)
The precise clade referred to by the word Mammalia can change depending on context. It makes sense to ask whether borderline species like platypuses are mammals or a sister group of mammals. That’s the fuzzy nature of any classification of real things. But the natural limits of the category “mammals” lie somewhere around the monotremes. A group which doesn’t include dolphins is definitely not the group of all mammals.
But the MRCA of “indisputable” groups won’t be an ancestor of basal groups like the monotremes or marsupials.
However, there’s no dispute about including monotremes. The clade that excludes them is called the Theria. Likewise with the marsupials: the clade that excludes both them and the monotremes is the Eutheria. Every clade potentially has a name; Mammalia is just a particularly well known one.
Things get dicey if the evolutionary relationships are unclear, of course, or if some conventional group is recognised as not being a true clade.
You’re right, of course. I was just pointing out that clades nest nicely. Whether you talk about Theria or Eutheria, the species included or excluded by the differences will be the most distantly related ones such as monotremes; but no clade anywhere similar in scope to Eutheria would be able to exclude dolphins. In that sense, it doesn’t matter much which “indisputably” mammalian groups you take, their MRCA will be an ancestors of dolphins as well. For instance, the MRCA of humans and of cats is also an ancestor of dolphins.
carnivore- any animal that feeds on flesh; “Tyrannosaurus Rex was a large carnivore”
I suspect that “carnivore” there was meant to indicate “the order Carnivora”.
Yes, I meant “Carnivorans”, not “carnivores. Fixed and thanks :-)
“The definition of a mammal is simple: descent from the most recent common ancestor of all mammals.”
Valid definitions cannot reference themselves.
You need to be a little more careful about such absolute statements. The definition of factorial(.) as
factorial(n) = n*factorial(n-1)
factorial(0) = 1
references itself and is valid.
Recursive definitions are possible, but they must still be founded on a base level that does not reference itself. Each other level can then be defined in a way that is not self-referential.
I believe usually it is also required that the number of steps (levels) to reach the non-recursive base should always be finite (e.g. recursion via a countable set).
Indeed. I’m just asking for a little precision, e.g., valid definitions cannot just reference themselves.
Some definitions which reference themselves plus something else are also invalid. :P
I presume that’s why he said “e.g.”, not “i.e.”
Yeah, but in this case Annoyance is right. You need to find two extensional mammals such that their last common ancestor is the LCA of everything you want to call a mammal, then the definition is complete. As it stands it’s like a factorial without the base case.
EDIT: Stupid me.. I should have remembered that I was dealing with Annoyance, and been a bit more incredulous at the prospect of him being right, since Annoyance actually does use his intelligence in order to deliberately arrive at wrong answers.
My comment did provide a base case (primates, rodents, carnivorans, ungulates). Annoyance didn’t quote it.
You have to be careful—the LCA of those is not the LCA of all mammals, because those all happen to be placental mammals—and the splits leading to marsupial mammals and monotremes came before then.
That’s true. I addressed that originally by saying all monophyletic clades were natural groups, and they have a natural sequence (in order of increasing exclusivity).
So while we can debate which group should be called “mammals”—whether placentals, or placentals+marsupials, or something bigger yet—we can all agree that “mammals” is a group whose border lies somewhere near the placentals-marsupials joining point in the evolutionary sequence. Dolphins are nestled very deeply in the group, and so dolphins are definitely mammals by any definition you may use. (That’s what the original debate was about: I argued that “mammals without dolphins” is not a natural group.)
I don’t think anyone debates whether monotremes and marsupials are mammals.
Both groups produce milk through mammary glands to feed their young—and both groups have long been recognised as being mammals.
It’s not a question of fact, but of definition—to what group do we refer as “mammals”? So it makes little sense to argue over it.
All groups of animals defined via shared characteristics have fuzzy borders. The fact that all extant species either clearly do or clearly don’t lactate is purely an evolutionary accident, since all the intermediaries once existed. Even today we have species that lactate but don’t have localized nipples (the platypus exudes milk from a wide area of skin). Farther out, we have various fishes, amphibians, etc. that exude specialized non-milk substances from their skin for their young to eat. If you throw away the categories, “feeding the young on substances released from skin pores” is a wider category than just mammals.
Also, this whole thread started with people saying that “common people” wouldn’t know if dolphins are mammals, even though they do lactate.
Oh, I didn’t see that.
Voted down Annoyance’s original, then. (Argh! Can’t believe I fell for his old tricks!)
In what way does your comment differ from Dan Armak’s original comment? how is Annoyance right in this case?
Annoyance is almost right—his criticism is just a little too inclusive, that’s all.
Which is why the next sentence after the one you quoted explained: “In practice, to avoid circularity, it is sufficient to take the MRCA of a few indisputable mammalian groups such as primates, rodents, carnivorans, ungulates, etc. to include all mammals.”
IOW, start from a few groups everyone agrees on calling mammals, and you have a precise rule stating whether any given animal is a mammal or not.
Monotremes are mammals, yet do not share the property of giving live birth.
“Hair… may be greatly reduced in the Cetacea (i.e. dolphins), where it is found as a few scattered bristles about the lips or often present only in the young.” W. J. Hamilton, American Mammals.
Heterocephalus glaber, the naked mole rat, is a mammal despite being poikilothermic.
As DanArmak notes, mammals are explicitly not the set of all species fulfilling a particular set of (external) criteria. They are defined by descent.
To the extent that this is useful, great. My point was merely that there is no external fact of the matter that requires drawing the boundaries where they currently are.
So when “ordinary people…get it wrong” by believing that dolphins are fish, it’s a little hard to blame them.
And many decidedly non-mammal animals do give live birth. Wikipedia lists “scorpions, some sharks, some snakes, [...] velvet worms [and] certain lizards”.
What exactly do you mean when you say they believe that dolphins are fish? The question isn’t about what to call a fish.
If they believe dolphins are like tuna in that they live entirely in the sea, have no hands and feet, swim with a thrashing tail, and eat other fish, then they are right.
And if they believe dolphins are like tuna in that they breath through gills and lay single-cell eggs into the water which grow into baby fish, then they are wrong. And I’d happily blame them for being wrong, because these are things that would be easy to get right with a little observation.
I’m suggesting that people see dolphins sharing the (easily-observable) characteristics they do with tuna and aren’t especially interested in the respiratory or reproductive aspects—particularly because the category of “air-breathing fish” is wrong in some sense by construction.
They are also wrong on the biochemical differences, but insofar as fish are pretty much just “all the animals in the sea” to the general public, I’d say the scientific and the popular use of the word probably diverge.
Perhaps I’m being too much of an economist, but I figure that the actual need for most people to know most of these biological details is limited, and the fuzziness in the popular use of the word arises from a low-effort sweep of the observables.
For people who don’t care in the least about dolphins (or fish), it makes sense. I shouldn’t have assumed everyone shares a minimal interest in zoology.