Distinctions and Differences
There is distinction in the world and distinction in the mind: things differ and so do concepts. States of affairs differ and thoughts about them differ. But how are these distinctions related? Are they dependent or independent? Clearly there can be objective distinctions that are not mirrored by cognitive distinctions—where thought fails to capture distinctions in reality (consider reality before the onset of thought). But can there be distinctions in thought that are not mirrored by distinctions in reality? Of course, distinctions in thought are real distinctions, but the question is whether distinctions in thought always reflect distinctions in what thought is about. Can two thoughts be distinct even if what they are about is not distinct? Can thoughts differ while the states of affairs they represent are identical?
The orthodox view is that they can, but on closer analysis this is wrong. It is generally agreed that in the vast majority of cases cognitive distinctions are matched by objective distinctions—it isn’t that reality is a homogeneous lump that we insist in thinking about in different ways—but it is supposed that there is a special subclass of cases in which no worldly distinction can be found that corresponds to a cognitive distinction. I speak, of course, of classic sense-reference cases: the reference is the same but the sense differs. But this is confused thinking: identity of reference does not entail identity of state of affairs expressed, because of the different properties that can be connoted by a singular term. The name “Hesperus” connotes the property of being the evening star while the name “Phosphorous” connotes the property of bring the morning star—and morning and evening are not the same thing. Appearing in the evening is a different worldly state of affairs from appearing in the morning. Similarly for “water is H2O”: here the word “water” connotes the property of appearing in a certain way to human subjects while “H2O” does not; the way water looks is a different property from the property of having a certain molecular structure. In these kinds of cases the cognitive difference is not independent of distinctions in the world; it corresponds precisely to such distinctions. No cognitive difference without objective difference. The content of thought cannot vary without the subject matter of the thought varying, i.e. without a distinction at the level of objective reality.
This is as it should be: for what would be the point of conceptual distinctions that fail to map onto worldly distinctions? The aim of concepts is to make discriminations among things beyond the mind (sometimes within the mind): a distinction between concepts that concern exactly the same objects and properties is a pointless distinction—why distinguish what is not distinct? Our minds track distinctions in reality; they don’t invent distinctions that don’t exist in reality. Internal distinctions without external differences are not real distinctions. Do not multiply distinctions beyond necessity! That is, thought should track only objective distinctions, of which there are many and subtle. There is more than enough fine structure in the world to occupy the discriminating thinker; anything else is redundant and pointless. Indeed impossible: concepts can’t differ without the aid of distinct states of affairs–that is their nature (this is a variant of Brentano’s thesis). A distinct concept is always a concept ofsomething itself distinct. Externalism about conceptual distinctions is true: no concept is distinct but reality makes it so. Distinctions supervene on differences.
You might think that concepts could differ in their dispositional properties while corresponding to identical states of affairs, thus counting as distinct concepts. But (a) the same concept could have different dispositions in different cognitive beings as a result of their different cognitive architecture, and (b) such dispositions would be pointless as means of discrimination. What is the point of discriminating what cannot be discriminated? You might say that different beings could have different needs with respect to the same objective world, so they might differ in how they conceptualize external things; but then the different states of affairs involve states of the organism itself—their varying needs ground the distinction in the concepts. The concept edible may apply to the same thing for one creature as inedible does for another, but that is only because of different properties of the different creature’s digestive systems (the concept is relational). Concepts differ only in virtue of objective differences that they represent or correlate with—there is no separate dimension of variation capable of individuating concepts. This is not to say that connotation reduces to denotation, still less that connotation doesn’t exist; it is just to say that connotation always cashes out as objective worldly difference—since what is connoted is always a property of things. Even in the case of semantic tone (dog versus cur) there is always an underlying distinction at the level of facts: different emotions are aroused by the different concepts. There are no conceptual differences that are “purely cognitive”, that exist independently of non-conceptual facts. The world is the ultimate dictator of conceptual distinctions. Conceptual distinctions are never “in the head”. 
The right picture is this: the world consists of the totality of objective distinctions—different ways that things can be. The aim of thought is to latch onto and exploit these distinctions, and it has nothing to work with other than the distinctions that exist in reality. Thoughts divide up according to the states of affairs that form their content. It is certainly not that concepts acquire their distinctness from some source other than objective reality and then foist this distinctness onto reality whether it likes it or not. There is nothing to constitute a difference of concepts other than distinctness in what they represent—objects and properties,
 In the case of indexical expressions we always have differences in spatiotemporal context that correspond to different indexical concepts, as with “here” and “there” and “now” and “then”. But this is a complex subject I won’t pursue here.