This approach [2-formality] starts with the idea that what makes content specific is its concern with particular individuals. It is clear that the concept ‘horse’, the relation ‘is taller than’, and the quantifier ‘every animal’ have specific content, because they all distinguish between Lucky Feet, on the one hand, and the Statue of Liberty, on the other. - “Lucky Feet is a horse” is true; “The Statue of Liberty is a horse” is false. - “The Statue of Liberty is taller than Lucky Feet” is true; “Lucky Feet is taller than the Statue of Liberty” is false. - The truth that “Every animal is healthy” depends on whether Lucky Feet is healthy, but not on whether the Statue of Liberty is healthy. On the other hand, the concept ‘is a thing’, the relation ‘is identical with’, and the quantifier ‘everything’ do not distinguish between Lucky Feet and the Statue of Liberty. In fact, they do not distinguish between any particular objects. As far as they are concerned, one object is as good as another and might just as well be switched with it. MacFarlane, What does it mean to say that Logic is Formal?, p.56-57

Notions with […] indifference to the particular identities of objects might reasonably be said to abstract from specific content - to be “formal”. Tarski seems to have something like this in mind when he says: “since we are concerned here with the concept of the logical, i.e., formal, consequence, and thus with a relation which is to be determined by the form of the sentences between which it holds, this relation cannot be influenced in any way by empirical knowledge, and in particular by knowledge of the objects to which the sentence X or the sentences of the class K refer. The consequence relation cannot be affected by replacing the designations of the objects referred to in these sentences by the designations of any other objects” (Tarski 1936: 414-5) Call this notion of formality “2-formality”. MacFarlane, What does it mean to say that Logic is Formal?, p.57

One can capture the indifference of logical notions to the particular identities of objects by demanding that they be invariant under the group of all transformations of the objects in a domain. […] For present purposes, this approach can best be illustrated through examples. Unary first-order quantifiers can be modeled semantically as functions from sets (predicate extensions) to truth values. Now consider the quantifier “all chickens”, which takes every set that contains all the chickens in the domain to True and every other set to False. Suppose the domain of objects includes two chickens and two cows. Let K be a set containing two chickens, so that “all chickens” takes the value True on K. If we permute the objects in the domain by switching the chickens for the cows, so that K is now a set containing two cows, then “all chickens” takes the value False on K. Since the truth of sentences containing “all chickens” is sensitive to permutations of the domain, “all chickens” is not permutation-invariant. On the other hand, the numerical quantifier “at least three things”, which takes every set with three or more members to True and every other to False, is permutation-invariant. Permutation invariance can be regarded as a precise technical gloss on the idea of indifference to the particular identities of objects. Whereas “all chickens” is sensitive to the difference between chickens and cows, permutation-invariant notions - like quantifiers and identity - are insensitive to particular identities of the objects to which they apply. […] MacFarlane, What does it mean to say that Logic is Formal?, p.58-59

We motivated 2-formality as a way of thinking about abstraction from specific content. Thus the claim that logic is 2-formal leaves open the possibility that logic is concerned with general content and very general facts about the world. 3-formality […] precludes any concern with content. […] a logic that abstracts from the contents of some concepts (“specific” ones, like “horse” or “red”), but not from the contents of others (“general” or logical ones, like existence, identity, and conjunction), does not count as 3-formal. MacFarlane, What does it mean to say that Logic is Formal?, p.60