Hoffmann thinks we should not be interested of ideas just for their own sake, but because these ideas refer to things – either actual or merely possible things. Thus, clarity of ideas is not required just for the sake of distinguishing ideas, but because of distinguishing things through the ideas. Yet, the clarity of ideas is still not sufficient for distinguishing things. For instance, we might have a clear definition of fluids, which would still be unable to distinguish fluids properly from other things – say, the definition might apply to also to sand. It thus makes sense to separate from mere clarity the full distinctness of ideas, that is, their ability of letting properly distinguish things that they refer to.
Hoffmann does not so much consider what distinction means for ideas, but discusses more different ways to confuse distinctions. The mildest form of confusion occurs when we are in some level aware of a distinction, but in another respect fail to use this distinction properly. This happens particularly in two cases. Firstly, we might be well capable of distinguishing individual examples of certain ideas, but we might fail in explaining what this distinction consists of in abstraction from individual examples. Secondly, we might have the opposite problem, that is, we might abstractly differentiate between some ideas (e.g. virtue and vice), but be incapable of distinguishing concrete examples of such ideas (we might be unable to say whether an action was virtuous or vicious).
A more dire confusion occurs, when we are convinced of the existence of a distinction that does not actually exist. In some cases such a confusion might be merely verbal, and Hoffmann is quick to blame Wolff for raising such mere verbal distinctions: for instance, Wolff's definition of possibility cannot be even used to decide whether fictions like golden mountains are possible. A somewhat more substantial confusion happens when the distinction is ideal, that is, something we can think, but which doesn't occur in actual existence – Hoffmann mentions some medieval theories of blood circulation as an example of such distinction. Even a real distinction might be uncharacterised in the sense that one couldn't apply such a distinction in special cases.
Moving on, a false distinction might be inadequate in the sense that one might know only a genus or other abstract feature, which is not enough for making a proper distinction. Hoffmann mentions especially Wolffian definition of necessity as an opposite of impossibility: if the definition is taken to its extremes, one could then say that the sentence ”triangle has five angles” as a sort of opposite of impossible sentence ”triangle has four angles” would be necessary. Another type occurs when one tries to distinguish a genus from one of its species, like when Wolff distinguishes absolute and hypothetical necessity, although, Hoffmann thinks, Wolffian hypothetical necessity as a necessity dependent on some (previously necessary) thing is just a form of absolute necessity. Finally, a false distinction might be based on mere abstract mental opposition – like when we distinguish a person's desire for happy life and a person's desire for good life – or it might be based on some ambiguity of concepts – like when metaphysics is defined both as a study of most general features of all beings and as a study of primary entities behind all beings.
In addition to mild confusion and false distinction Hoffmann also points out the possibility of logical ambiguity, in which one fails to see distinction that truly exists. Such logical ambiguity differs from verbal ambiguity, in which one is quite well aware that one word is used in two different senses. Logical ambiguity can result from confusion of words – like when Wolff uses word ”necessity” both of the opposite of impossibility and of the final ground of all things – but it is always something we are not aware of.
Still, not all logical ambiguities are caused by verbal confusions, but the idea of some genus might truly be equivocal and refer to many different genera. A simple case of such equivocation happens when one is incapable of abstracting from individual instances when thinking of a genus. Thus, one might think virtue sometimes as virtue towards oneself, sometimes as virtue towards other people, without noticing their difference.
A more serious case of logical ambiguity arises when one fails to note that an idea is heterogenous, that is, when different species of same genus have slightly different essential structure – an example of such heterogenity was correspondence, which was different in the relation between picture and original and in the relation between text and author's intention. Hoffmann notes that Wolffian notion of complex things is such a heterogenous idea. Wolff thinks that the essence of all composite entities is based on the particular arrangement of the parts, but this is true only of such machines, like clocks, in which removal of one piece causes the destruction of whole clock, while a lump of clay remains a lump of clay, no matter how much you rearrange the parts. Similarly heterogenous is the notion of infinite division, in which people often confuse potentially infinite with actually infinite division. Further example is also provided by Leibnizian monadology, which doesn't notice that while physical units can be actually separated from one another, this need not hold of metaphysical units.
Finally, logical ambiguity might be caused by the subtlety of conditions, on which the distinction is based. Such conditions might be material abstractions, that is, they might be true part of the idea from which the abstraction is made (e.g. animality is a material abstraction in relation to humanity). Thus, one might deny that the existence of collision of laws, because one fails to recognise the difference between contradictions and collisions. Contradiction occurs when we try to think two opposite at the same time – thus, it would be contradictory that a law would explicitly deny what the other law commands. Then again, collision concerns forces or causes – two different laws might assign different motives for action, which might in particular cases pull to opposite directions.
The subtle conditions might also be reflective abstracts, that is, they might be more the result of the act of abstraction (e.g. genus is a reflective abstraction in relation to humanity). Thus, being in general might refer either to genus of all things whatsoever or to a vague entity that is supposedly identifiable with all individual entities and should thus be called God, and pantheistic thinkers might confuse the existence of the first with the existence of the second.
This concludes Hoffmann's investigation of confused distinctions and also his investigation of ideas in separation from one another. Next on the menu is his study of combinations of ideas.