# Does the word 'And' refer?

The word 'house' and the word 'shed' refer - they are physical things we can point to (their referent).

Now consider the word 'and' - this at first appears to not refer to anything. If one is trained in formal logic, one could say that it acts as a logical operator.

However, conventionally, it is seen as grouping: say, A house and a shed. Here we can say it has been suggested we consider these two things together; and in fact we do have a referent - there is a house and a shed I can point to.

So, in that phrase not all words need to refer, but the sentence does; that is this sentence builds up what our referent is.

So the word 'and' doesn't directly refer like the word 'house' does; but it allows us to refer to groups of things.

Is this correct?

• Questions from a philosophy amateur. Does "Captain Ahab" refer? Does "3" refer? Of course "and" doesn't refer. It's a logical connective. Just like P & Q has a truth value solely dependent on the truth values of P and Q. '&' doesn't have a truth value. I would imagine it's the same thing for "referring," which I find to be a pretty nebulous concept. Does "rock" refer? To what? The collection of quarks that make up the rock? There's no rock there, you know. Commented Jun 6, 2014 at 3:41
• @user4894 Note that the property of having a truth value is the property of referring to elements of some set of truth-values. Having a truth-value is thus a type of a referring relation. I do wonder why you find having a truth-value unproblematic but referring in general 'nebulous'.. Commented Jun 6, 2014 at 3:53
• @user4894:'Captain ahab' refers to the fictional captain Ahab of Mody Dick; 3 refers if you believe in Platonic forms, or if you're talking about conventional language and so on. The point about reference is not that is 'nebulous' but that its complicated. Commented Jun 6, 2014 at 3:54

Neither 'house' nor 'shed' nor 'and' refer to any physical things. Your house (that is, the referent of the expression "my house" as uttered by you; if you have a unique house) is a physical thing, which may have a shed in it, which is also a physical thing. But the expression/term 'house' refers to an abstract entity, which we take to be the plurality/class/set of all houses. Similarly for 'shed', 'dog', and so on. A particular house, a particular shed, a particular dog, may be referred to by 'house', 'shed', and 'dog', but only if the context of utterance is such that it unambiguously determines the connection between the general term and the particular individual in the domain of discourse. That much about terms.

§1 And1 : Sentence × Sentence → Sentence

The word 'and' is usually introduced as a sentential connective: a function on the sentences of some underlying language. E.g. "p and q" is taken to be the sentence r which is true just in case p and q are true. This means that 'and' can be taken to be referring, with respect to some language L, to the set consisting of all triples (P, Q, R) s.t. R is true iff P and Q both are. From the category-theoretic point of view this explication of functions is certainly problematic, but that's an issue for another occasion.

The conclusion then is that 'and', like 'house' and 'shed', both refer to sets of entities: in the case of 'house' and 'shed' we're dealing with a set of physical entities; in the case of 'and' we're dealing with a set of linguistic and thus abstract entities. I.e., those terms are similar in that they both refer to abstract entities, but different in that those abstract entities they refer to contain entities of different kinds.

§2 And2 : Term × Term → Term

It's worth noting that in some logico-mathematical settings 'and' is overloaded: 'and1' is the usual and that connects two sentences, and 'and2' is a function between not sentences but terms. For example, "a and b" is taken to be the plurality that consists of individual a and individual b. That's the logical explication of the grouping idea Mozibur mentioned. To illustrate my earlier point about 'and' referring to an object, let's look at the referent of 'and2'. It's a function from a pair of terms to another term, so set-theoretically, 'and2' refers to the set of triples (a, b, c) s.t. c is the unique term s.t. for all properties φ, we have φ(c) iff φ(a) and φ(b). For example, if a is a red rose and b is a red lobster, then 'a and b' is their 'group term' of which we can truly predicate 'is red'. That's the general, informal, idea of this second, grouping sense of 'and'. If I find any appropriate readings on that I'll append to this post later.

• +1: for a good answer. I'm intrigued to see that you see some category theoretical perspective on this. I'd suggest that in many contexts, a pointed set, rather than just a set is possibly more appropriate (pointed sets are naturally found in Algebraic Topology) - this is a set with some distinguished element. I make this suggestion thinking that an indefinite sentence like 'a house' refers to a some house in the set of houses. Commented Jun 6, 2014 at 4:10
• @MoziburUllah ah! That's an interesting proposal. I'm a Russellian about descriptions, so I must stay faithful to the idea that 'a house' is meaningless on its own (and only obtains meaning in a context). I only said that the view of functions as deterministic relations => as sets of tuples of objects is category-theoretically problematic because functions have a dynamic side to them where we look at their behavior instead of their constitution as their characteristic feature. But open sets and indefinite descriptions...that's an excellent paper topic :) Commented Jun 6, 2014 at 4:22