It's very much like learning the history of mathematics without being able to e.g. solve an integral, or model a problem in the real world and make meaningful observations about the model and its relation to the subject. History is fine if it's what you're into, but the other is not taught in any widely disseminated fashion and I believe people and society are deprived as a result.
There are entire sub-disciplines of philosophy that are useful and practical for everyday decision making. Here I would disagree that you need a formal background in mathematics. Game theory, statistics and the like are certainly valuable, but they are still more a part of the engineer's or mathematician's toolkit and will be glossed over due to their rigorous technical underpinnings that are simply out of reach for many individuals. Rhetoric, critical thinking, stoicism, ethics, and the like are pretty approachable topics that have somehow been elided from the educational system in any established fashion in the US - and they used to be at the core of a liberal arts education. Great religious thinkers, politicians, and intellectuals have left a legacy of work that speaks across time and space to a modern reader.
A lot of 'continental' philosophy seems to be a mix of historical analysis, and cult-of-personality/lit-crit...
In PTAFM 13, Kant is arguing that neither space nor time are intrinsic properties of things in themselves, and basically making the point that properties like position and congruence are relational, not intrinsic. Spatial relations fit with the intuition of space, which is the form of external experience (and one should think of this as the abstract form of any space whatsoever - people tend to think that Kant is undermined by the development of non-euclidean geometries, but I think one can push the abstraction so it fits equally well). Experience of- and reasoning about spatial objects involves both intuition that corresponds with the forms of space and time (which applies to any experience whatsoever, outer or inner), and the operation of the understanding through concepts. Now, reasoning from principles which might apply to spatial objects (in the case of algebra, geometry and topology) can go through concepts alone as long as it is logical. But those principles would be meaningless for us if we didn't have experience of any spatial objects whatsoever (if we didn't have the pure intuition of space).
"Thoughts without content are empty, intuitions without concepts are blind. The understanding can intuit nothing, the senses can think nothing. Only through their unison can knowledge arise." (KrV A51).
In philosophy you get this all the time because people refuse to agree on definitions like truth, consciousness, goodness, evidence etc. So debates generally involve people talking past each other until someone gets bored. If we're lucky spectators will judge by popular acclamation which side won or lost. Participants rarely concede their position.
No, in this case he was mistaken in some basic assumptions about what Kant is doing in that text. The paragraph he mentioned starts with: "Those who cannot yet rid themselves of the notion that space and time are actual qualities inherent in things in themselves, may exercise their acumen on the following paradox." So in this case it isn't even the case that he is proposing something about Kant one can reasonably disagree on (like my suggestion that Kant is not undermined by the development of non-euclidean geometry, something which I would be willing to concede given evidence against it).
On the other hand, in my experience, actual debates on philosophy usually revolve around conceding some initial assumptions and then debating on what follows from them. Of course, one can always move from the internal questions about what follows from those assumptions to external questions about what follows if we rejected those assumptions, but this move is usually well motivated by internal conflicts. One might, for example, find some dilemma for which no option is acceptable, and thus be forced to retreat to discussing the assumptions. And it is not a given from the outset whether no such conflicts will arise.
The problem I got with philosophy is that it's supposed to be applied knowledge. But it's always consumed as an intellectual one.
As a result, the smartest philosophy lovers that I know are incredibly unhappy. They know so many things. But knowing something doesn't mean you are able to do anything about it.
Some becomes cynical. Other become depressed. Other procrastinate to hell.
But only those who actually take the knowledge and try to act on it, improving themself in the process, ends up happy. And once they get there, they usually don't quote much philosophy anymore, except for humorous purpose or make someone feel better.
Bottom line: it's interesting to look for the meaning of life. But it's necessary to actually stop and live your life unless you want to have the joy of Sartre, the energy of Rilke, the sense of purpose of Kant and drive of Schopenhauer. Hint: you really don't.
Can you elaborate on that? On why it's supposed to be applied knowledge I mean?
To me philosophy is one of the most abstract forms of thought available, and to me abstract is the antithesis of "applied". Maybe the furthest I would go is to state that philosophy is knowledge applied recursively on itself. But that already seems an abstract formulation to me.
However, if you use your knowledge of philosophy to actually do something in your life instead of trying to think your way into the abyss of infinite dissection, it becomes a powerful tool.
This is the main difference between very old philosophers (Seneca, Gautama, Epicurus...) and more recent ones (Kant, Sartre, Schopenhauer...). The first ones try actively to make something out of their thinking. They derive a way of life out of it. The second ones try to understand more deeply, categorize more things, raise more difficult questions.
In the end, by reading the active ones, you can feel the joy, the sense of purpose and solutions arising. If you read the other ones, you can almost picture them trying to kill themself.
I firmly believe that philosophy without mathematically oriented thinking at the core is limiting. Teaching and studying of formal logic has been traditionally part of philosophy. In practice there is no real border between philosophy and formal sciences (logic, mathematics, statistics and theoretical computer science).
Consider the problem Kant faced in Prolegomena to Any Future Metaphysics, §13. Two objects that are intrinsically alike must be interchangeable. But there are objects that are intrinsically alike and you can't exchange them. Kant was incredible philosopher but he was thrown off by looking at his hands. Left hand and right hand seem to be intrinsically same, but you can't replace one with another. Kant concluded that things like chirality and mirror images could not be understood with intellect and reasoning using concepts. Time and space were part of sense intuition. Mathematics would disagree. Spatial intuition is not fundamental building block for reasoning about time and space. Algebra, geometry and topology are.
Many modern day problems facing humanity can be understood only as systems thinking using, probability, mechanism design, games, incentives, equilibrium, trade-off, hysteresis, etc. But many schools of philosopy still try to use tools and concepts that can't describe the system.
edit: Several important contemporary philosophers and schools of philosophy are not are in fact limiting themselves. Saul Kripke for example.
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I think philosophy should be part of curriculum in school. But it should be live philosophy centered in problem solving and rational thought. The traditional history oriented curriculum should be part of history. History of science, technology, philosophy, economics and ideas in general is more important than the narrative trough kings and power cliques.