Footnote on Otto Weininger

4 posts



I have a bit of time today so I will just briefly elaborate on what my difference with Weininger. It does not involve the unimportance of the very concept of "genius", but the way that his approach seems to block several "better" ways of approaching it:

You can definitely distinguish between different levels of genius (or else just merit) even if you cannot impose a linear order on it. One way is by the poset or partially ordered set:


More formally then, not every element is comparable (like how every number has to be either "greater than or equal to", or else "less than", any other number), but the binary relation is reflexive, antisymmetric and transitive. The analogy can be with various sets of numbers, with the ordering of inclusion: {1, 2} is "greater than (contains)" {1}, but {1, 2} and {2, 5} are not comparable. (I repeat: this is in direct contrast to any kind of linear or total ordering, which is what most people have in mind when they "rank" this or that.)

Now, this analogy is a bit imperfect since a poset is much more general than what I am referring to, but it draws attention to the fact that any order is not a total order. Also it draws attention to transitivity, and the fact that it is always possible to imagine a single greatest (or highest) element.

We would then subdivide every single element of our set (of people) by their "rank". Now, the rank is simply a set of individuals, and correspond to the row that its members take on the Hasse diagram. Every single member of every rank, is "greater than" every single member of the rank that is immediately below it, although no members within a rank are comparable.

* End of trivial discussion

The real question, however, is how these "ranks" are to be interpreted. The interpretation is thus: if we had to choose only one person to "actualize" (i.e., to "have" rather than not have), then it would be the one at the top rank (or just choosing randomly within a rank). If we had to choose just two , however, it would not be the next person in the first rank, but a person chosen from the second "rank". That is, let us say that Leibniz is a higher genius than Newton (and I think this is true, for reasons that are somewhat involved). But the sort of genius that Newton represents is very different, and there are diminishing marginal returns once you consider a group of people who have highly similar abilities. Another example - Beethoven is higher than J. M. W. Turner , but after a few slots, it is necessary to get someone who represents the particular richness of experience that (representational) painting involves. And although the first-rank musical composers are better than paraphrasers (like Art Tatum) or detailed performers like Casals, great performers are clearly much more important than second-rank composers (like Berlioz).

This is all qualified by degrees - that is, perhaps we would open 6 slots for those of rank two, before taking any single person from rank 3 - but then we would then repeat by another 6 slots for the second rank, etc. There has to be a balance between the "height" and the diversity of the sort of genius represented.

And this is in distinction to when something is rendered superfluous by another. For example, there's no reason to place Herbart, or Oersted (or even Ampere), since they are clearly surpassed in every respect by others. Also, I think chess (even in the hands of Morphy or Steinitz) is a pointless activity compared to pure mathematics - pure mathematics has everything that chess has, and more. The case is a bit different with musical composition vs. detailed performance - the first involves making more involuted analogies between different aspects of musical structure (gradually evolving a new set of melodic devices), and the second does not involve seeing relations between various elements, but making a gradual and minute comparison between how various aspects of a piece might be conceived, if some part of it slightly changes. The second is slightly lower than the first - for the same reason that Karl Menger once spoke of, that seeing straightforward relations (like "difference") is of lower order than fruitful analogies. But in any case, the sheer scale of formalized music requires that the first activity actually depends on (or at least "involves") the second, since one cannot banish the way the texture and the rest enter into a direct relation with the other aspects of music.


Now among other things, this renders Weininger's entire discussion potentially trivial, or at least very confused. Whereas we would simply call rank 1 the highest order of genius (rather than simply "genius"), Weininger would prefer to call it simply "genius", and the rest of them - not genius. The basis for doing so is supposedly that there is a qualitative distinction running along the graph above. Now, whether there is or not, it's not the kind characterized by Weininger (but see the next paragraph) - but even this fact is ultimately of little relevance. The real point is, if you agree with my interpretation of the "rankings" above - of the precise way in which we say that something is of "lower rank" - then it's a purely verbal question of whether to call certain people non-geniuses, or else just belonging to a lower rank of genius. The point is that their abilities are still intrinsically important enough that one would occasionally allow them a place in a slot (even if we were not constricted to finitely many individuals) - i.e., the graph is the same , we have simply re-labeled the various subsets. Weininger would of course deny this - he says painting is completely irrelevant (and not just inferior), etc. compared to sculpture (I won't even explain why this is wrong), but notice that his "argument" otherwise has to fall back on his assertion that genius can only consist of what he distinguished it as. His brilliant argument: "this person (e.g., da Vinci) is not a genius, because genius is defined in the specific way that I defined it. And.. the reason why my definition of genius is the only thing of value [i.e., a fact not about my category of genius, but everything that falls outside of it], is because... these people are not geniuses."

Anyway, the point is moot because Weininger did not succeed in his monistic definition of "genius". If there is a single, qualitative distinction that separates "genius" from what is not, then it is the fact that however "complex" and involuted are one's actual reasonings, analogies and general mode of thought, one always senses that there is something more - and that "more" is something that cannot be articulated at all. The great philosopher does not, therefore, ever entirely dismiss any hypothesis or "possibility" as being completely silly or having no sound basis whatsoever, however wrong he might think it is - he is never fully complacent in anything (like Weininger is in his absolutely confident definition of "genius"). And the constructive artist, like a musical composer, must always know that he is not merely playing around with purely musical materials, but that all music reflects or is ultimately an analogy with experience that is outside of it (this is how it begins - the simplest kind of music is an imitation of phenomena within nature, like periodicity, or else within the self - how the self imposes order on its surroundings). Chopin, for example, lacked this ability; however complex and "charming" are the analogies between different musical ideas within a piece, it is "second hand" - it lacks the phenomenal character of the "first", or the monadic - the pure freshness of experience in itself, unrelated to any second. But (more importantly) it also lacks the sense that there might be anything like that richness of experience at all. It is purely content with itself - never moving outward and beyond. So I define genius (if I had to "define" it) as the ultimate sense that enables one to think clearly without thinking distinctly; or else (which is the same thing) not merely the fact that what one feels is infinitely more than what can be expressed (this is the case with Tolstoy, as much as Beethoven), but that what one "reaches for" is much more, than what one can even directly feel. It is some sort of the sense of something beyond, the sense of the "infinite". This is not perfect definition, but it seems much more plausible than those puerilities about "personality" that Weininger manages to "define" (and in any case it illustrates how one can just slightly change his characterization of "genius" to get something a bit more general, and Weininger doesn't have any kind of basis for why his own "definition" is somehow preferable to the modified one).


So: monistic definitions of genius do have their place, although it's still a purely verbal question as to whether they define "genius", or simply the highest rank of genius. But notice that any single qualitative distinction (like Weininger's, or the one I just made above) would be too broad - Weininger lumps into the category all manner of people that simply aren't, at least in terms of actual attainments. Ultimately, one has to also succeed to be a genius - and that is most definitely the simple combination of different elements, although finding what those elements are is a bit tricky:

For the really more important issue is not the underlying basis for genius in terms of either "personality" or else an underlying "sense", but how these combine with other matters of circumstance - that are themselves necessary conditions for success (that is, for "genius" to bear fruit - for that is the line between genius and insanity). One thing that you will never hear from Weininger, is that the necessary condition for the success of Beethoven (this is his favorite example) is not something psychological at all, but the mere fact that he is ignorant of certain things. (This is a necessary condition for success.) Beethoven was shielded and protected from the excessive influence of someone as powerful and original as himself - and this cannot be said for any of those who followed him (it's impossible to even imagine how Schubert or Brahms would have sounded like, without Beethoven). This is why "erudition" and education is the death of art - the originality of the great ones is primarily owed to the fact that they were not overly educated. They did not allow themselves to be influenced by others. (I simply cringe when people casually speak of "education" as though it were always a good thing. The entire point is that success is often due to not knowing - and not being negatively influenced - by something.)

If you want to be a "genius" composer, the best thing to do is to never listen to Beethoven. Instead, listen only to the kind of second-rate, very incomplete (and yet for that reason, technically transparent) kind of pieces that Beethoven himself was exposed to - e.g., Hummel, Albrechtsberger, Salieri even. Learn to despise it, to make partial demolitions of the structure and create another edifice on top of it - which is what Beethoven seems to have done.


nobody knows what the fuck you're talking about

The Rambler

I don't think it's necessary to avoid different ideas in order to keep them from affecting ones originality. It's possible to be educated while still being out of step with everyone else enough to make new things.


A footnote to a footnote:

To simplify: Otto Weininger makes a big deal in his book about how he distinguishes a level of merit above the others, that he calls "genius". We might not even disagree with that sort of distinction (although we do), but the point is that there is no material difference between his position and one such as the following: that Weininger did not at all distinguish "genius" (in contrast to non-genius), but perhaps a higher sub-level within a broader category of genius - although even this fails to be true, as I pointed out above.

In the same way, you can simply make further subdivisions within his scheme, and distinguish a level within that which is the "highest level" within the group of geniuses. You can then out-Weininger Weininger, and say that he hasn't distinguished the "true" category of genius either (i.e., he wasn't being restrictive enough). Weininger himself even provides the very means by sub-levels can be distinguished within his own category of "genius" - for example, he casually and incomprehensibly says that Bruno is a "greater" genius than Leibnitz.

This point is that this (the sort of thing above) is a purely verbal sort of disagreement - it involves puerilities about words rather than a matter of actual fact. The real question is not which of our categories (however you keep on subdividing them) is called genius or not, but the material significance of the categories. Now re-read the first paragraph after the "trivial discussion" in the original post - this carefully distinguishes the particular sense in which we interpret various "ranks" of genius.) (Seriously, the actual notation that I mentioned (that of a partially ordered set ) is so completely trivial that it's probably easier than trigonometry)

This significance of my definition of ranking can be illustrated by what it is distinct from: the idea that since certain individuals are superior to others, they can replace those others. (This notion does not apply to all comparisons, but it does to some.) On the opposite end, we have the idea that if two things are qualitatively different, there is no way to even "compare" them. Now, the second notion is the province of extremely indolent and often feeble minds - for example, it's a fallacy to think that because we can't order (compare) two things, that we cannot order a set of things greater than two. (In fact we can, by a partial ordering - see above.) And the point is that he actually have a model for the precise sense in which A is "superior" to B although B has "its place", and the precise nature of that "place" which is even distinguished in degrees.


The other part of the argument is logically independent - it involves how Weininger's argument isn't decisive, since you can easily make several others that are slightly more general and which seem to be just as plausible - he never "argues" for anything since he believes that simply pointing something out will render it plausible.

But anyway, I just wrote the original post to kill time - it is just clear enough, although it could have been clearer. I have much better things to do than think about Weininger. And I touch on component points that are much more important - like how the lack of influence by others is often a necessary condition for a kind of originality (such as that in musical composition) that involves the direct association of ideas ("association", I think, in the sense used by J. S. Mill).

(Of course, the entire discussion requires knowledge of what Weininger said, and actually having read his book - either the German original, or one of the semi-tolerable translations of it.)

( Edit: it occurs to me that partial ordering diagrams are a clumsy and roundabout way to express the point, but still a simple way to visualize it.)