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

What is left to consider when we abstract entirely from semantic content of a thought? Some philosophers would say “nothing”. But some have held that there is more to thought than the concepts it employs: there is also the way they are put together. On Kant’s view, for example, “... all judgements are functions of unity among our representations”, and the various modes of unity determine the possible forms of judgements. “The matter of the judgement consists in the given representations that are combined in the unity of consciousness in the judgement, the form in the determination of the way that the various representations belong, as such, to one consciousness”. General logic, in Kant’s view, abstracts from the matter and considers only the form of judgements: it considers only the way in which concepts are united in judgements. “General logic … abstracts from all content of knowledge, that is, from all relation of knowledge to the object, and considers only the logical form in the relation of any knowledge to any other knowledge; that is, it treats of the form of thought in general.” For example, general logic treats “all horses are mammals” simply as the unification of two concepts in a universal, affirmative, categorical, and assertoric judgement. It abstracts entirely from the content of concepts. The way in which the concepts are united in thought is not, for Kant, a further constituent of the thought (a “binding” concept), but a feature of the thought’s form. MacFarlane, What does it mean to say that Logic is Formal?, p.60-61

To claim that logic is 3-formal presupposes that we can distinguish between the constituents and the form of thought, in such a way that the latter can be understood apart from the former. […] Many twentieth century philosophers accept the distinction, demarcate logic by its concern with the form of thought or conceptual inquiry, and draw the same consequences as Kant: 1. that logic alone tells us nothing about the world; 2. that the world does not constrain logic, so that logical knowledge and knowledge about the world are fundamentally different; and 3. that “logical truths”, if there are such things, do not state facts. MacFarlane, What does it mean to say that Logic is Formal?, p.62

“In this distinction we [The Vienna Circle] had seen the way out of the difficulty which had prevented the older empiricism from giving a satisfactory account of the nature of knowledge in logic and mathematics. ... Our solution, based on Wittgenstein’s conception, consisted in asserting the thesis of empiricism only for factual truth. By contrast, the truths in logic and mathematics are not in need of confirmation by observations, because they do not state anything about the world of facts, they hold for any possible combination of facts” (Schilpp, 1963, The Philosophy of Rudolf Carnap). Carnap acknowledges the influence of Wittgenstein’s Tractatus here, and Wittgenstein does seem to be advocating for a version of the view that logic is 3-formal: “The propositions of logic are tautologies... The propositions of logic therefore say nothing… Theories which make a proposition of logic appear substantial are always false” (TLP, §6.1, 6.11, 6.111) MacFarlane, What does it mean to say that Logic is Formal?, p.63-64

I am not persuaded that 3-formality does not imply 2-formality. It seems to me a stronger version of it as it abstracts entirely from semantic content. (See MacFarlane, What does it mean to say that Logic is Formal?, p.67-68 for a relevant argument).

Although Kant thinks that logic can be formal, he does not take formality to be part of the essence of logic. That a general logic must also be formal is a substantive claim that requires justification, not a matter of semantics. I call this claim Kant’s Thesis: General (i.e., 1-formal) logic must also be formal (i.e. 3-formal). That is, “the universal, and necessary rules of thought in general can concern merely its form and not in any way its matter” (Jasche Logic, p.12). MacFarlane, What does it mean to say that Logic is Formal?, p.91-92