I don’t see Eliezer on a rampage against all definitions. He even admits that argument “by definition” has some limited usefulness.
I think key is when we say X is-a Y “by definition”, we are invoking a formal system which contains that definition. The further inferences which we can then make as a result of this are limited to statements about category Y which are provable within the formal system that contains that definition.
Once we define something by definition, we’ve restricted ourselves to the realm bounded by that formal definition. But in practice many people invoke some formal system in order to make a statement “by definition” and then go on to infer things about X, because it is-a Y, based on understandings/connotations of Y that have no basis in the formal system that was used to define X as a Y.
So let’s say we have a locus of points X in a euclidian plain equidistant from some other point C in the plane. Well in euclidian geometry, that’s a circle by definition, and we can now make a bunch of geometric statements about X that legitimately derive from that definition. But we can’t go on to say that because it is “by definition” a circle, that it represents “a protected area in which ritual work takes place or the boundary of a sphere of personal power cast by Wiccans”, or “a social group” or “The competition area for the shot put” or “an experimental rock-music band, founded in Pori, Finland in 1991” to throw out just things that are “circle”s by some definition I was able to find on the web.
In this case, the inference problem is terribly obvious, but often it is much less so, as Eliezer has described for “sound”.
The problem with arguing “by definition” from a typical natural language dictionary, is that such dictionaries are not formal systems at all, even though some of their definitions may be based on those in formal systems. It is quite common for a word to have two different and conflicting common definitions, and both of them will end up in a dictionary. I’m pretty sure that you could argue that a horse is a spoon, or that pretty much any X is equal to any Y “by definition” with some creative chaining up of dictionary “definitions”.
I don’t see Eliezer on a rampage against all definitions. He even admits that argument “by definition” has some limited usefulness.
I think key is when we say X is-a Y “by definition”, we are invoking a formal system which contains that definition. The further inferences which we can then make as a result of this are limited to statements about category Y which are provable within the formal system that contains that definition.
Once we define something by definition, we’ve restricted ourselves to the realm bounded by that formal definition. But in practice many people invoke some formal system in order to make a statement “by definition” and then go on to infer things about X, because it is-a Y, based on understandings/connotations of Y that have no basis in the formal system that was used to define X as a Y.
So let’s say we have a locus of points X in a euclidian plain equidistant from some other point C in the plane. Well in euclidian geometry, that’s a circle by definition, and we can now make a bunch of geometric statements about X that legitimately derive from that definition. But we can’t go on to say that because it is “by definition” a circle, that it represents “a protected area in which ritual work takes place or the boundary of a sphere of personal power cast by Wiccans”, or “a social group” or “The competition area for the shot put” or “an experimental rock-music band, founded in Pori, Finland in 1991” to throw out just things that are “circle”s by some definition I was able to find on the web.
In this case, the inference problem is terribly obvious, but often it is much less so, as Eliezer has described for “sound”.
The problem with arguing “by definition” from a typical natural language dictionary, is that such dictionaries are not formal systems at all, even though some of their definitions may be based on those in formal systems. It is quite common for a word to have two different and conflicting common definitions, and both of them will end up in a dictionary. I’m pretty sure that you could argue that a horse is a spoon, or that pretty much any X is equal to any Y “by definition” with some creative chaining up of dictionary “definitions”.