I have until now just assumed that what Hoffmann calls idea is what we might call representation and now this reading is verified: idea is for Hoffmann a state of understanding, in which a possible object is represented through a similarity of such state with the object or through the effect of such object to understanding. What is striking is Hoffmann's rather cavalier assumption that representation will surely correspond to what it represents. Of course, he admits that all ideas do not represent their objects as perfectly – an idea which shows all important properties of its object, as it were, in one glance, is more perfect than an idea that shows them only successively.
Just like one would expect, Hoffmann thinks there are as many ideas as there are powers of understanding. Thus, we have purely sensuous ideas (sensation of a bike I am seeing), memorised ideas (memory of a bike I have seen), ideas of ingenuity (say, an idea of a bike with a different shape from usual) and finally, abstract ideas (idea of a general structure of bikes). Of these, all ideas in which abstraction has been complete and all the parts are distinguished are non-concrete. Non-concrete ideas then consist of ideas with no parts to abstract any more (simple ideas, such as the idea of a certain colour) and of ideas which are combinations of abstracted ideas. Concrete ideas then are ideas in which parts are not distinguished from one another. Such concrete ideas could be of sensed individuals (like an idea of an apple I am seeing), but they might also be abstractions, albeit unclear abstractions (in this case we are presenting e.g. virtue through a concrete example, but we cannot say what makes this particular example an instance of virtue). Both sensuous and abstract concrete ideas can then either represent only an individual object or a group of such objects.
Hoffmann leaves the discussion of concrete ideas here, since it is especially abstract ideas that interest in discussion of logic. Abstract ideas can, Hoffmann continues, be more or less undetermined depending on how many characteristics one is thinking them to have. Of more undetermined ideas we cannot say whether any individuals correspond to it – it is difficult to say what counts as a good action, if goodness of an action is defined only as an agreement with good maxims. Then again, mere determination is also not an assured sign for finding individuals instantiating the idea – it might be that existence of something corresponding to the idea is dependent on some external circumstances that cannot be deduced out of the idea itself. Furthermore, some abstract ideas or transcendentals could be used in all possible worlds (all concepts of metaphysics would apply here), while others describe only the actual world.
Abstraction means for Hoffmann making distinctions, and an important consideration from an epistemological point of view is whether what is abstracted can truly exist in the manner it has been abstracted, that is, whether distinctions made have some basis in something external to understanding. Hoffmann points out that there are actually four different questions one must consider. Firstly, we should ask whether such distinction can be made at the level of essences, that is, whether it is something that we can even think about. In other words, when we abstract human will from the notion of freedom, we can think of the two apart, because it is possible to think that will might be deterministic. Then again, when we try to abstract such notions like force and substance from one another, we quickly note that force cannot even be thought without some substance, although the distinction appears to suggest otherwise.
Secondly, we could ask whether the distinction concerns real existence. We might abstract good understanding from virtue and the distinction is truly real, since there are people who have good understanding, but are not virtuous. Then again, we might abstract human understanding from its various powers and we might even think that understanding could come without these powers, but the distinction would still be just possible – understanding does not actually exist without these powers.
Thirdly, we could ask whether the abstracted thing does exist within those limits we assign to it in our thought. Thus, we can be fairly certain that limbs of an animal do have those limits they appear to have, but to separate a cylinder of water from ocean in our heads does not indicate any natural distinction, even though the cylinder of water could exist without the ocean. Hoffmann makes a passing suggestion that this is where Leibnizian monadology goes astray. The point appears to be that Leibniz leaps from thought of some ultimate units of existence to the notion that these units would actually describe natural division of reality, although it might well be that there are no ultimate units naturally distinct from their surroundings.
Fourthly, we could ask whether the supposed distinction does not merely indicate the same object from different perspectives. Thus, we can objectively abstract understanding from will, because these things are different objects, while when we start to abstract different perfections of God from one another, the distinction is merely ideal, since all these perfections are merely different perspectives to God himself. Hoffmann is especially keen to attack Aristotelians and disparage the notion of different types of souls – there are no separate vegetative, animal and rational soul in human beings, but they all indicate merely different aspects of the same soul.
As I already mentioned in the previous post, Hoffmann thinks abstraction can be either causal or existential, that is, it might concern either processes and e.g. separate cause from its effect, or it might concern some wholes and divide it into its parts or constituents. Of these two types, existential abstraction is in a sense more fundamental, since all causal abstractions could be thought as existential – we might ignore that we are dealing with a process and consider e.g. a relationship of clouds and rain as a whole from which both are abstracted. In this case we could speak of an accidentally existential abstraction, in which the existentiality depends only on the arbitrary whim of the abstracting cogniton. This is an important distinction for the logic of judgements, since existential abstractions reveal relations that can be expressed with the form ”A is B”. Thus, Hoffmann is noting that even if we could bring a sentence describing causal relations into such a form – say, as in ”cloud IS the cause of rain” – this would just hide the true form ”cloud causes rain” indicating the peculiarity of causal relations.
Hoffmann further divides existential abstraction into external and internal abstraction. In external abstraction, what is abstracted doesn't really inhere in the starting point or ground of abstraction, for example, it indicates merely relations of a thing to other things or is just a certain time and place in which the thing exists. In internal abstraction, then, what is abstracted inheres in the ground of abstraction, like figures, quantities and forces of a thing. Internal abstraction is then divided into logical and properly existential abstraction. In logical abstraction, what is abstracted inheres in the whole abstracting ground, somewhat like animality concerns the whole of human being, while in properly existential abstraction, what is abstracted could exist apart from the other parts of the whole, somewhat like soul and body could be separated in a human being.
We just mentioned the notion of the ground of abstraction, by which Hoffmann apparently refers to the idea from which the abstraction begins. Hoffmann notes that there always is some connection between the ground of abstraction and that which is abstracted from it – later, we shall see that this connection is the basis of our ability to make judgements. Hoffmann notes that this connection might be either a posteriori and contingent or a priori and necessary. This sounds suspiciously like Kant's division of judgements into a posteriori and a priori types, and Hoffmann's definitions appear to correspond with the Kantian notions. Thus, a contingent connection between ground of abstraction and what is abstracted is something we know based on experience, for instance, just like we know human beings have blood circulation only through observations. On the contrary, a necessary connection is something we know based just on both of the ideas, for instance, when we know that triangle is a figure.
What is even more striking is that Hoffmann then divides the necessary connection into two types that closely resemble the Kantian notions of analytical and synthetic a priori judgements. In fact, Hoffmann notes that the necessary connection might be either identical – or as Hoffmann also calls it, hypothetical – or then absolutely a priori. In an identical connection, the abstraction is completely based on the ground of abstraction, that is, what is abstracted is already thought with the idea from which abstraction begins. Hoffmann notes as an example a connection of rational animal with an animal, which could clearly be expressed in a Kantian analytic judgement, but also the mathematical relation of number 12 and its part 6. Then again, an absolutely a priori connection is not completely based on the ground of abstraction or what is abstracted is not expressly thought with the idea from which the abstraction begins, but instead, the abstracted element is somehow connected to the ground of abstraction, although it is essential to that ground. As a special example of such a connection, Hoffmann mentions causal relations, but also the relation of a figure to matter embodying it, which somewhat resembles Kant's first analogy of experience.
We are already seeing Hoffmann's enthusiasm with divisions. We have also seen that these divisions are not meant to be mere empty scholasticism, but important tools in making cognition more certain and in avoiding faulty reasoning. Indeed, we have seen Hoffmann engaging with Leibnizian and Aristotelian philosophies and emphasising the importance and distinct nature of causality that cannot be reduced to mere logical relations. We shall see more of Hoffmann's careful analysis next time, when we start with the relations of ideas.