Until now we have seen Hoffmann investigate merely ideas abstracted from other ideas, but this is a good time to reverse the process and start to combine ideas back. Hoffmann notes that when we are doing this combination for abstract ideas, we are still using our judgement – remember that combinations of non-abstract ideas were effected by ingenuity.
Hoffmann's division of the classifications of these combinations are rather familiar: we have combined ideas, propositions or judgements and deductions or proofs. Intriguing is his manner of explaining the difference between ideas like ”blue house” and propositions like ”house is blue”, which, he says, depends only on the mode of cognition: in the former case one is thinking merely about the combination, while in the second case one is also taking note of the existence of such a combination. Hoffmann is then one of the few philosophers before Frege and Husserl to note the importance of assertion in judgements, which are then something else than mere combinations of concepts.
What I am especially investigating in this post is Hoffman's notion of combined ideas, and I shall look at judgements and proofs in later posts. In fact, Hoffmann has here rather little to say about combined ideas. Sometimes ideas are at least partially subordinated, that is, they refer to some common entities. Then combining two ideas simply means finding an idea that shares with properties of both and that refers to these entities that belong to the extension of both ideas – just like red balls are a subset of both balls and red things. Such a combination Hoffmann calls definition, well knowing that it is more something that could be defined, instead of a literal definition.
Sometimes ideas are not subordinated at all, but completely diverse. Then we cannot combine them in a similar manner as subordinated ideas. We might still combine them under another idea, that is, as divisions of a more extensive class, like shirts and socks can be combined as a division of some type of clothes.
An important aspect of combinations of ideas is relating them to individuals. Hoffmann describes the notion of an individual through various means. Firstly, he notes that individuals can exist only once in the whole universe. This does not really help define individuals logically, but Hoffmann has another suggestion: individuals are the smallest parts of logical wholes. The second definition might sound rather weird, but it does have its point. A peculiar feature of logical parthood is that it is a transitive relation, that is, every logical part of a logical part is also a logical part of the original – subspecies of a species is also a logical part of the respective genus. All parts of an individual, though, are not its logical parts – parts of Aristotle cannot be human beings, but are instead things like feet and hair.
Now ideas of individuals can be related to abstract ideas in various ways. An idea of an individual can be a proximate individual of an abstract idea, that is, it might add to the abstraction only individuality, just like the idea of this triangle is related to the notion of triangularity. Then again, thought of an individual might have lot more in it, just like the idea of Aristotle contains something else than individuality and notion of being a scholar. Finally, an idea of an individual might have less content than some abstract idea, i.e. when we think that some individual figure is a triangle.
A special question is then the possible relation of combinations of at least partially subordinated ideas or definitions with actual individuals. We do know there are at least possible individuals connected with these combinations, since the ideas combined are at least partially subordinated. Sometimes the combination is real in a quite strong fashion, when one of the ideas is a ground for the other, such as when rationality is strongly dependent on the animality of something. Even here one can have various levels of naturalness. Rational animal or human being is in a sense most natural combination, since we cannot add any idea that would add to the essential features of the individual referred to with this combination of ideas. Then again, we might have a combined idea of such a level, that the combination of features is not similarly complete, for instance, on level of animality in general.
Combination might also be more arbitrary, if neither of the ideas were a ground for the other, although in some cases like these one idea might be grounded on the genus of the other idea. For instance, in a black hat, blackness is not an essential possibility of hats, but it might be an essential possibility of the material of the hat.
In the case of the black hat there is some real entity corresponding to the combined idea. Black hat is also something that can be physically produced, while some combinations corresponds to entities that exist only through human decisions, like kings. Even more arbitrary would be cases where the combination corresponds only to some ideal entities, like star signs.
All the natural and especially the arbitrary combinations multiply the number of ideas indefinitely. One thus needs a new means for thinking these multifarious ideas in a quick manner – words are used to that effect, Hoffmann notes, but instantly adds that words by themselves are not enough and that we must be able to think something without words, in order to avoid an infinite regress. Hoffmann knows that it is quite arbitrary which words refer to which ideas, but hopes that the hierarchy of words would somehow mirror the hierarchy of ideas.
So much for Hoffmann's notes on simple combinations of ideas and words. Next time I shall take a look at his classification of judgements.