Comments on “Fixation and denial”
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Abstraction
Hmm. I am not sure I understand your comment… I think your point that philosophy ought to be grounded in specifics is a very good one. (My sometime colleague Phil Agre and I, frustrated by the abstractions of mainstream phenomenology, started a “phenomenology of breakfast” project. We learned some useful things.)
The page you commented on is from the introductory overview to the book. The introductory overview is general and abstract (as is common for introductory overviews). Later the book gets more specific. (Maybe it won’t be as specific as you’d like.)
The underlying problem is that I’m dribbling out the introduction over a period of months, when the whole of it ought to be read in a half hour. The individual pages of the introduction don’t stand well alone. They aren’t like blog posts.
The web really may not be the right format, after all… Or I should concentrate on writing just one thing at a time, rather than trying to interleave four sites.
Gian-Carlo Rota on phenomenology
Purely by coincidence, I just came across something relevant and funny, from an amusing talk about mathematical careers by one of my professors, Gian-Carlo Rota:
I sometimes publish in a branch of philosophy called phenomenology. After publishing my first paper in this subject, I felt deeply hurt when, at a meeting of the Society for Phenomenology and Existential Philosophy, I was rudely told in no uncertain terms that everything I wrote in my paper was well known. This scenario occurred more than once, and I was eventually forced to reconsider my publishing standards in phenomenology.
It so happens that the fundamental treatises of phenomenology are written in thick, heavy, philosophical German. Tradition demands that no examples ever be given of what one is talking about. One day I decided, not without serious misgivings, to publish a paper that was essentially an updating of some paragraphs from a book by Edmund Husserl, with a few examples added. While I was waiting for the worst at the next meeting of the Society for Phenomenology and Existential Philosophy, a prominent phenomenologist rushed towards me with a smile on his face. He was full of praise for my paper, and he strongly encouraged me to further develop the novel and original ideas presented in it.
Rota was, in striking ways, similar to a Tantric Vajra Master (only, of course, with respect to discrete mathematics and Husserlian phenomenology). There are many remarkable stories about him. I have a vague intention of writing something about him someday.
Abstract nonsense
It occurs to me that I studied category theory with Rota. Category theory is often described as the most abstract discipline there is—more abstract than any other branch of mathematics, and possibly even than phenomenology…
In fact, it is referred to humorously as “generalized abstract nonsense.”
As you can see, I’m reminiscing, instead of working on the next page of the introduction, like I should be. On the other hand, you said you wanted autobiographical details, so—there you are!
A New Kind of Science
That was fascinating and ironic. Thanx for the personal element. Very interesting.
I have always wanted to study discrete mathematics more after reading Wolfram’s
“A New Kind of Science”.
Isn't mathematics an example of successful fixation?
Or are mathematical truths out-of-context somehow in the discussion of “meaningness”?
I suppose another way of putting my question is, is meaningness always grounded in the concrete and so not relevant to (abstract) mathematics?
Mathematics and nebulosity
An excellent question!
Yes, math definitely seems to be an exception. The book outline says so somewhere-or-other.
There are hard philosophical questions about the nature of mathematics, and the relationship between mathematics and the concrete world. I don’t have strong opinions about them.
One thing I do believe strongly is that there is no straightforward or correct mapping of mathematics onto the macroscopic world; and that is exactly because the world is nebulous and mathematics is not. Some flavors of rationalist eternalism insist that there is a correct mapping, and I think that’s wrong and harmful.
Mathematics is certainly experienced as highly meaningful by some few weirdos (including me). The sense of “meaningful” is approximately aesthetic, although probably not quite the same.
Basically, I don’t think math has much (if anything) to do with “meaningness” as I’m discussing it in this book. But my mind might change about that in some way at some point!
Hmm… On re-reading, I see you are asking the converse of the question I expected: not, what does math imply about meaningness, but what does meaningness imply about math.
Some philosophers of mathematics think it is more nebulous than most working mathematicians believe. Is that what you had in mind?
the relationship between math and meaningness
I think that find both responses interesting. I wasn’t really thinking about the question from one perspective or the other, but rather as a question of relationship. If that makes any sense.
What does "negation" mean in the context of the last section?
I found most of this section really interesting and useful, but I’m not sure I quite follow “Each fixation denies the negation of what it fixates.” since I’m not sure what negation means in this context. Maybe “complement” would get at the meaning better than
“negation”?
“Negation” might be misleading in that it suggests only two possibilities (which then seems to be directly contradicted by the proceeding claim that ethical eternalism denies both its two-valued negation “ethical ambiguity” and the rest of its complement “freedom”).
Negation
Good point, thanks! I’ve changed it to “opposite,” which is imprecise, but might be easier to for many readers to understand than “complement” (which might be more accurate).
Symbols of fixation and denial in Christianity
I couldn’t resist to point two things:
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According the Bible, Jesus proclaimed himself as “the truth” and he ended up “fixated” in the cross and at the same time “denied” even by his Apostles. One of our most solid believe systems, with 2000 years of antiquity and still 2000 million believers is based in fixation and denial as basic mechanism.
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Peter, the first of the Apostles, who “denies” Jesus 3 times, and his Church are depicted as a ship. The ship became one of the earliest Christian symbols and means the Church tossed on the sea of disbelief, worldliness, and persecution. I found interesting that you also chose the analogy of the ship: “In fixation, you cling to relatively solid fragments of meaningness and try to lash them together into a raft.”
Love and meaningness
Hi David,
How does love play into meaningless?
Thanks.
… or sorry meaningness.
… or sorry meaningness. Meaning that love is the distribution of power. So how does distribution of power play with meaningness?
Laws of Thought in classical logic
Hello, David. What do you think about Laws of Thought in classical logic? It seems that they’re not doing good for understanding meaningness, at least in an unconditional manner of their use.
For example, the Law of identity states that every time you should think of precisely the same thing as being denoted by a certain symbol, which seems like a struggle to get rid of nebulosity and fluency of meaning. Probably that is another reason why certain rationalists I talked to were insisting on a certain, defined meaning of words - it looks like a fixation of meaning accompanied by denial (but here I use the word in a sense a bit different from yours: I mean denial of meaning I try to convey them. I think the denial of certain meaning is connected to the denial of nebulosity and consequently meaning at large).
The Law of excluded middle seems to be also entangled with the observations above. By itself, it seems like fixating the way of thinking about the thing forcing one into interpretation when “either A is X, or A is not X”. In other words, I suppose it makes sense to say that “the meaning of A to us is fixated, thus the way of interpretation is fixated”. It is interesting, that logicians have already known it at least since 1925. Citing A. Kolmogorov in a paper “On ‘tertium non datum’ principle”:
“However, the basis of the formalistic point of view in mathematical logic lies in the negation of the real meaning of mathematical propositions. Indeed, no one would suggest applying to reality formulas of the logic of no real meaning. <…> Thus this separation between mathematical logic and general logic, since the latter is concerned with the applicability of propositions to reality. <…>
But here we do not separate some special “mathematical logic” from general logic, but only admit that specificity of mathematics as science creates problems for [general] logic which are to be solved by special “logic of mathematics” science. Only there occur doubts about the unconditional application of ‘tertium non datum’ principle.”
Math and meaningness
I’ve re-read some comments above and noticed that the relationship between mathematics and meaningness was touched already. Thus I decided to clarify the point of view behind my previous comment: I’m not separating mathematical thought from other kinds of thought entirely, that is I think mathematics is also nebulous. Thus mathematical logic is not clearly separable from standard (general) logic. And probably trends from standard logic also influenced the general public.
I observed some mathematicians, one of them talked about, say, metric spaces as being a part of ‘hard mathematics’, groups as being a part of ‘soft mathematics’, and this way he separated mathematics into hard-hard, hard-soft, soft-hard, and soft-soft parts. He said it is ‘intuitively understandable’ if you can deformate space or another mathematical object as much as you want, depending on certain restrictions. So he seemed to associate nebulous concepts (vague image of what is hard or soft) with properties of mathematical concepts and doing so helped him to reason. I don’t think that such an act can be separated from his mathematical reasoning completely.
It seems to me like there is a whole spectrum of intensity of nebulosity across areas of thought, and mathematics excels at lowering this intensity, not being able to obliterate it completely. More than that, I’d think that complete obliteration, if possible at all, would make mathematics inapplicable to the real world.
We all are engaged in many
We all are engaged in many activities:
- Building an addition to your house
- Raising animals
- Working as a chemist
- Raising children
- Nurturing friendships
- Playing in a band
The above abstract post is global. So it is tempting, at any given moment, to think of a different activity when reading your post with its analogies to apply them to a particular activity. And as you can see by the list, they invite, I think different judgments. For me, it has always been hard listening to someones abstractions of deeply personal insights – they aren’t my abstractions, they aren’t how I feel and experience them. I see pitfalls uncovered when applied to the particulars of my life. It is difficult to talk about these things. Grounding philosophy with particulars helps me a great deal.