fwiw, i think this sort of picture gets somewhat better at what happens in your mind when you grasp a sentence involving “a dog” or “the dog” than the canonical proposal by russell involving quantifiers. this probably deserves a long essay but i’ll try to communicate the idea quickly:
as the first sentence of a novel, i claim that “porthos the dog crossed the street” and “the dog crossed the street” basically do the same thing in your head (except in the former case the object tracker/representer that is created has the name “porthos” attached to it[1])
there are many languages in which the 4 sentences “a/the dog crossed a/the street” are[2] literally the same string, namely “dog crossed street” in word-by-word translation. this is related to the thoughts being very similar
more speculative: roughly i think that “a” tells you to create a new object tracker/representer and “the” tells you to add to an old one. except that it’s fine to start a novel with “the dog was tired” even though the reader doesn’t already have an object tracker initialized beforehand, but i’d guess in that case you can still as if add to an old tracker (like, you imagine already being familiar with that dog)
roughly i think russell’s view of determiners (at least insofar as it is trying to get at what it is to grasp a sentence involving a determiner, which it needn’t be trying to get at) confuses a [frame/model]-internal proposition which doesn’t really have a quantifier with a statement capturing the adequacy of applying the frame/model which has a quantifier. like, in my view: we really think of “the round square” as some sort of ordinary object inside a frame/model, but then that frame/model turns out not to hang together or refer, and that can be seen from “there is a (unique) round square” being false. (this is related to wittgenstein’s hinge vs free belief distinction.)
this view has an easier time making sense of “a dog has four legs” usually communicating that dogs have four legs
this view coheres better with how “a/the dog” sits in the syntax tree of a sentence
(i haven’t thought this through carefully. an interesting challenge here is to spell this picture out much better and to [explain why]/[ascertain whether] this sort of thought-syntax “works” when doing eg mathematical thinking)
and also except for properties created by other associations like “porthos” being a name used for male dogs and maybe being used by such and such a person and reminding you of a particular porthos you knew and whatever
Is “The dog” in “The dog crossed the street” perhaps similar to “this dog”? “This” is often conceptualized logically as a constant/name. I guess “Porthos the dog” could also be analyzed as a name. Though one would have to ensure that “Porthos the dog is a dog” is a logical truth. Usually “a dog” would be formalized as “some dog”, “there is at least one dog such that”, which is usually plausible but not the intended meaning of “A dog has four legs” (in that intended meaning “A dog has three legs” would be false).
One underappreciated fact (which in my opinion clearly invalidates Russell’s analysis of the definite article) is that several languages use the definite article in front of names. So e.g. “The porthos crossed the street” rather than “porthos crossed the street.” Even English does that sometimes, e.g. “the Eiffel Tower”, “the NSA” (but not “the NASA”). Which suggests there is no fundamental logical difference between proper nouns (or “proper names”, as philosophers like to call them) and common nouns. Which suggests that names (parthos) are not logical constants, but predicates, just like common nouns (dog).
fwiw, i think this sort of picture gets somewhat better at what happens in your mind when you grasp a sentence involving “a dog” or “the dog” than the canonical proposal by russell involving quantifiers. this probably deserves a long essay but i’ll try to communicate the idea quickly:
as the first sentence of a novel, i claim that “porthos the dog crossed the street” and “the dog crossed the street” basically do the same thing in your head (except in the former case the object tracker/representer that is created has the name “porthos” attached to it [1] )
there are many languages in which the 4 sentences “a/the dog crossed a/the street” are [2] literally the same string, namely “dog crossed street” in word-by-word translation. this is related to the thoughts being very similar
more speculative: roughly i think that “a” tells you to create a new object tracker/representer and “the” tells you to add to an old one. except that it’s fine to start a novel with “the dog was tired” even though the reader doesn’t already have an object tracker initialized beforehand, but i’d guess in that case you can still as if add to an old tracker (like, you imagine already being familiar with that dog)
roughly i think russell’s view of determiners (at least insofar as it is trying to get at what it is to grasp a sentence involving a determiner, which it needn’t be trying to get at) confuses a [frame/model]-internal proposition which doesn’t really have a quantifier with a statement capturing the adequacy of applying the frame/model which has a quantifier. like, in my view: we really think of “the round square” as some sort of ordinary object inside a frame/model, but then that frame/model turns out not to hang together or refer, and that can be seen from “there is a (unique) round square” being false. (this is related to wittgenstein’s hinge vs free belief distinction.)
this view has an easier time making sense of “a dog has four legs” usually communicating that dogs have four legs
this view coheres better with how “a/the dog” sits in the syntax tree of a sentence
(i haven’t thought this through carefully. an interesting challenge here is to spell this picture out much better and to [explain why]/[ascertain whether] this sort of thought-syntax “works” when doing eg mathematical thinking)
and also except for properties created by other associations like “porthos” being a name used for male dogs and maybe being used by such and such a person and reminding you of a particular porthos you knew and whatever
or i mean: can naturally be
Is “The dog” in “The dog crossed the street” perhaps similar to “this dog”? “This” is often conceptualized logically as a constant/name. I guess “Porthos the dog” could also be analyzed as a name. Though one would have to ensure that “Porthos the dog is a dog” is a logical truth. Usually “a dog” would be formalized as “some dog”, “there is at least one dog such that”, which is usually plausible but not the intended meaning of “A dog has four legs” (in that intended meaning “A dog has three legs” would be false).
One underappreciated fact (which in my opinion clearly invalidates Russell’s analysis of the definite article) is that several languages use the definite article in front of names. So e.g. “The porthos crossed the street” rather than “porthos crossed the street.” Even English does that sometimes, e.g. “the Eiffel Tower”, “the NSA” (but not “the NASA”). Which suggests there is no fundamental logical difference between proper nouns (or “proper names”, as philosophers like to call them) and common nouns. Which suggests that names (parthos) are not logical constants, but predicates, just like common nouns (dog).