The Nose Dive of Philosophy

[Simon Adams]

That makes me think the spiritual connection is vital. I get the same feeling you do - we read/hear about all of these big name 20th century philosophers who inspired generations of thinkers after them and whose ideas permeated every scientific and cultural sphere, but if we were to survey the average Westerner under 40 (especially in the U.S.), I am sure very few people could identify these philosophers or any of their key insights. Perhaps it's because many of them went so far out of their way to "de-spiritualize" their philosophies when the deep meaning provided by spirituality is exactly what's lacking right now. And that only leaves recognizable the philosophers with explicitly political overtones and agendas, because everything is seen as a political issue from start to finish.

Yes I agree completely. I think this is why you see Marxism underlying so many of these modern philosophies. When you’ve stripped away all the natural sense of meaning in the subject, the only place left to find meaning is in politics.

[SanteriSatama]

I notice there are a couple of interesting papers on this subject here. Not your work by any chance?

If only folks realised how completely they are being misled by the philosophy department.

Excellent!: https://philpapers.org/archive/JONTCE.pdf

Some comments, if I may.

We have every right to define the continuum for mathematics as we currently do, and if our idea is paradoxical then it is only a problem when we investigate the foundations of analysis.

Well not every right, at least from the point of view of intuitionist philosophy of mathematics, which requires 1) constructibility of mathematical languages and 2) linguistics constructions are in some sort of harmony with intuitive/idealist ontology of mathematics. Arbitrary language games of formalism can have heuristic value, but for foundational thinking of pure mathematics, nope.

Danzig gets very close to the answer:

The notion of equal-greater-less precedes the number concept. We learn to compare before we lean to evaluate. Arithmetic does not begin with numbers; it begins with criteria.

Equal is not on same foundational level as relational operators < >, which precede the notion of equality. Already the theory of Surreal Numbers, at least Knuth's presentation of it, makes this very explicit. If A is neither more nor less than B, then A = B.

Bergson's notion of duration gives another hint: a duration is neither unity nor multiplicity. And so does undecidability of Halting problem.

***

Re Weyl's claim, an interlude:

The fact that single points in a true continuum “cannot be exhibited” arises,

This is very qualified argument, and there is an intuitive way to exhibit a single point to the eye of the mind. Let's imagine continuous flat plane, and a straight line on the plane. Let's make a cut in the line. Taking a flat-lander point of view at the other end of the cut, we can see a point where the other part of the line ends. If the plane is not flat, or if other lines are allowed and they are not parallel, the point disappears as we can see only a line. The point does not exist and exhibit itself independently from the plane and the line and the cut (cf. "transition"), and here Bohm's notions of explicate and implicate orders can be useful. Defining an explicate view to see a point, implicates lots of structure, but nothing beyond imagination in this case. In this case, the relation of implicate and explicate orders supports Whiteheadian planar instead of pointy approach to geometry and mathematics.

***

Brouwer's First Act of Intuitionism, namely 'two-ity', is a relation of codependent arising, according to [ur=https://cosmosandhistory.org/index.php/ ... ile/30/59l]this article[/url]. On the other hand Brouwer considered relational operators "negative", apparently because they are something else than a discrete quantity. As an empirical science instead of formal speculation, intuitionism is evolutionary, also on the M@L level, where other intuitionists expanded the idealism of intuitionism after Brouwer's solipsism.

To bridge the "deep chasm" that Weyl speaks of, foundational mathematics needs to simply ask: is there a way to mathematically describe continuum, so that also discrete phenomena can be coherently derived and constructed from the foundation? Yes there is. Let's redefine relational operators as asubjective verbs denoting continuous processes. E.g. dynamic tetralemma of increases - decreases:

1) increases <
2) decreases >
3) both increases and decreases <>
4) neither increases nor decreases ><

A short for speaking such class of verbs is more-less. Form <> corresponds with notions of 'open interval' and Bergson duration. Negation/halting of process in the 4th lemma allows to define equivalence relations >=< and closed intervals aka finite sets >[]<. As we know, already finite set allows to construct discrete numbers in the style of von Neumann, but there can be also much better and interesting ways to bridge that "gap", for example the basic number-antinumber scheme of e.g. integers, which Relop language of relational operators allows to write as palindromes. Yet another possibility is to generate Stern-Brocot trees in Relop language.

[Peter Jones]

That makes me think the spiritual connection is vital. I get the same feeling you do - we read/hear about all of these big name 20th century philosophers who inspired generations of thinkers after them and whose ideas permeated every scientific and cultural sphere, but if we were to survey the average Westerner under 40 (especially in the U.S.), I am sure very few people could identify these philosophers or any of their key insights. Perhaps it's because many of them went so far out of their way to "de-spiritualize" their philosophies when the deep meaning provided by spirituality is exactly what's lacking right now. And that only leaves recognizable the philosophers with explicitly political overtones and agendas, because everything is seen as a political issue from start to finish.

Spot on, I would say. If we reject the philosophy of the Upanishads or refuse to study it then we can never understand philosophy. We will be reduced to producing endless sophistry to no purpose.

By 'de-spiritualising' philosophy we render it incomprehensible. Thus 20th century academic philosophy is a waste of time. Departments are closing as we speak. In its current form academic philosophy is indefensible, and universities in the US are beginning to vote with their feet. .

This is the price of not studying all of philosophy but just trying to reinforce ones own prejudices and pet theories.

There is no reason for any of us to fall into this trap. Today we have the internet and open access to all the literature.

.

[Peter Jones]

Excellent!: https://philpapers.org/archive/JONTCE.pdf

Some comments, if I may.

We have every right to define the continuum for mathematics as we currently do, and if our idea is paradoxical then it is only a problem when we investigate the foundations of analysis.

Well not every right, at least from the point of view of intuitionist philosophy of mathematics, which requires 1) constructibility of mathematical languages and 2) linguistics constructions are in some sort of harmony with intuitive/idealist ontology of mathematics. Arbitrary language games of formalism can have heuristic value, but for foundational thinking of pure mathematics, nope.

ETC...

You make some excellent points. Unfortunately some are over my head, but I'd agree with those I can understand. .

The central issue for me is the absurdity of the idea of an extended continuum. Once we accept that an extended continuum is a conceptual construction, not a truly real phenomenon, then the paradoxes associated with it evaporate.

I wonder whether you'd agree.

[SanteriSatama]

You make some excellent points. Unfortunately some are over my head, but I'd agree with those I can understand. .

The central issue for me is the absurdity of the idea of an extended continuum. Once we accept that an extended continuum is a conceptual construction, not a truly real phenomenon, then the paradoxes associated with it evaporate.

I wonder whether you'd agree.

Not sure what you mean by extended continuum. Something to do with "completed infinity", as in "infinite set"? Or immutable eternity? Those are concepts I don't agree with.

[AshvinP]

That makes me think the spiritual connection is vital. I get the same feeling you do - we read/hear about all of these big name 20th century philosophers who inspired generations of thinkers after them and whose ideas permeated every scientific and cultural sphere, but if we were to survey the average Westerner under 40 (especially in the U.S.), I am sure very few people could identify these philosophers or any of their key insights. Perhaps it's because many of them went so far out of their way to "de-spiritualize" their philosophies when the deep meaning provided by spirituality is exactly what's lacking right now. And that only leaves recognizable the philosophers with explicitly political overtones and agendas, because everything is seen as a political issue from start to finish.

Spot on, I would say. If we reject the philosophy of the Upanishads or refuse to study it then we can never understand philosophy. We will be reduced to producing endless sophistry to no purpose.

By 'de-spiritualising' philosophy we render it incomprehensible. Thus 20th century academic philosophy is a waste of time. Departments are closing as we speak. In its current form academic philosophy is indefensible, and universities in the US are beginning to vote with their feet. .

This is the price of not studying all of philosophy but just trying to reinforce ones own prejudices and pet theories.

There is no reason for any of us to fall into this trap. Today we have the internet and open access to all the literature. .

I wouldn't go quite that far. 20th century philosophy, academic or otherwise, has been tremendously insightful and important, as long as we keep in mind that many of the philosophers are only approaching from one angle and there are many other angles out there to consider. The insights which can be confirmed from a variety of different angles, i.e. philosophical, religious and scientific 'fields' of inquiry, are the ones which we should have the most confidence in. So if analytic idealism, pragmatism, phenomenology, depth psychology, and "spiritual science" are all pointing towards the same insights, and those insights also align with ancient mythological and religious traditions, then we can have a lot of confidence in them. Ultimately, though, we also have to experience those insights within ourselves.

[Lou Gold]

That makes me think the spiritual connection is vital. I get the same feeling you do - we read/hear about all of these big name 20th century philosophers who inspired generations of thinkers after them and whose ideas permeated every scientific and cultural sphere, but if we were to survey the average Westerner under 40 (especially in the U.S.), I am sure very few people could identify these philosophers or any of their key insights. Perhaps it's because many of them went so far out of their way to "de-spiritualize" their philosophies when the deep meaning provided by spirituality is exactly what's lacking right now. And that only leaves recognizable the philosophers with explicitly political overtones and agendas, because everything is seen as a political issue from start to finish.

Spot on, I would say. If we reject the philosophy of the Upanishads or refuse to study it then we can never understand philosophy. We will be reduced to producing endless sophistry to no purpose.

By 'de-spiritualising' philosophy we render it incomprehensible. Thus 20th century academic philosophy is a waste of time. Departments are closing as we speak. In its current form academic philosophy is indefensible, and universities in the US are beginning to vote with their feet. .

This is the price of not studying all of philosophy but just trying to reinforce ones own prejudices and pet theories.

There is no reason for any of us to fall into this trap. Today we have the internet and open access to all the literature. .

I wouldn't go quite that far. 20th century philosophy, academic or otherwise, has been tremendously insightful and important, as long as we keep in mind that many of the philosophers are only approaching from one angle and there are many other angles out there to consider. The insights which can be confirmed from a variety of different angles, i.e. philosophical, religious and scientific 'fields' of inquiry, are the ones which we should have the most confidence in. So if analytic idealism, pragmatism, phenomenology, depth psychology, and "spiritual science" are all pointing towards the same insights, and those insights also align with ancient mythological and religious traditions, then we can have a lot of confidence in them. Ultimately, though, we also have to experience those insights within ourselves.

I agree Ashvin and would add that transformations abound when might and right align. It's harder for me to align with Peter's scholarly privileging because I've never studied philosophy.

[SanteriSatama]

The central issue for me is the absurdity of the idea of an extended continuum. Once we accept that an extended continuum is a conceptual construction, not a truly real phenomenon, then the paradoxes associated with it evaporate.

I wonder whether you'd agree.

The meaning that this day of discussions has given to "extended continuum" is the Myth of Sisyphos as told by Camus. Yes, the task is intellectually absurd. It can be also spiritually very real.

[Peter Jones]

I wouldn't go quite that far. 20th century philosophy, academic or otherwise, has been tremendously insightful and important, as long as we keep in mind that many of the philosophers are only approaching from one angle and there are many other angles out there to consider. The insights which can be confirmed from a variety of different angles, i.e. philosophical, religious and scientific 'fields' of inquiry, are the ones which we should have the most confidence in. So if analytic idealism, pragmatism, phenomenology, depth psychology, and "spiritual science" are all pointing towards the same insights, and those insights also align with ancient mythological and religious traditions, then we can have a lot of confidence in them. Ultimately, though, we also have to experience those insights within ourselves.

Well okay, although I'm not aware of any significant progress in academic philosophy since it began.

We don't have to experience anything much in order to calculate the answers to philosophical problems. If 'non-ordinary' experience was required I would not be complaining. Unlike mathematicians philosophers seem reluctant to just shut up and calculate.

[SanteriSatama]

Unlike mathematicians philosophers seem reluctant to just shut up and calculate.

Calculus has been a sick infant from it's birth. We do need medicine of philosophy to heal the baby, so that it can grow strong and wise.