Long story: Some of it may (unpredictably) meander downstream through the hands of science and engineering. From there on the question becomes: Do science or engineering matter? For both mathematics and science, usefulness is ultimately harnessed by engineering. — alcontali

I think there's truth in that these days, but we know that historically it was the reverse. Math was purified from its immersion in applications--by Greeks as I understand it.

Without purification, however, it would be substantially less interesting to use in science or engineering. We also cannot know during the discovery process of mathematics if science or engineering will ever be able to do anything with it. That could take decades, if not, centuries. — alcontali

Fair enough. My primary point is that philosophy isn't like pure math and yet is what we have for dealing with the world strategically. Computation only gets us so far.

One last comment. Already Democritus and later Epicurus thought that atoms affected the human body so as to generate consciousness. True, they didn't doubt the existence of space and time. But the rest of experience was a kind of dream thrown up by the human sense organs and body in general in response to its interactions with atoms. When the body dies, that person's dream of the world ceases.

If one has this view, then obviously the objects of experience have to conform to the sense organs. What I non-expertly take as new in Kant is the focus on all of the linguistic-conceptual processing that goes into experience. After Kant, one can question whether the shared dream corresponds in any way to what is really going on. Yet Kant doesn't go into the 'sharedness' of this dream much, AFIK. How does one person trapped in his mindbox create the true metaphysics of all human mindboxes? Kant knew the structure and possibilities of my experience long before I was born. What assumptions go into that? Human reason is one and universal, a veritable Enlightenment brand 'Holy Ghost.'

The leading theme of [the story of Continental philosophy after 1750] is the rise and fall of an extraordinary concept of the self. The self in question is no ordinary self, no individual personality, nor even one of the many heroic or mock-heroic personalities of the early nineteenth century. The self that becomes the star performer in modern European philosophy is the transcendental self, or transcendental ego, whose nature and ambitions were unprecedentedly arrogant, presumptuously cosmic, and consequently mysterious. The transcendental self was the self ---timeless, universal, and in each one of us around the globe and throughout history. Distinguished from our individual idiosyncracies, this was the self we shared. In modest and ordinary terms it was called 'human nature.' In must less modest, extraordinary terminology, the transcendental self was nothing less than God, the Absolute Self, the World Soul. — Solomon

This next quote is from a dead link. Not sure who the author is, maybe also Solomon.

The exalted sense of the importance of the self arose from the subtle shift Kant introduced into Descartes's proposal. In the Kantian system, the Cartesian self became not just the focus of philosophical attention but the entire subject matter of philosophy. Rather than viewing the self as one of several entities in the world, Kant envisioned the thinking self in a sense "creating" the world - that is, the world of its own knowledge. The focus of philosophical reflection ever since has been this world-creating self.
The universalizing of the self readily followed. Underlying Kant's philosophy was the presumption that in all essential matters every person everywhere is the same. When Kant's self reflected on itself, it came to know not only itself, but all selves, as well as the structure of any and every possible self.
The transcendental pretense evident in Kant's philosophy helped produce "the white philosopher's burden." Kant's presumption that all selves resemble each other led some philosophers to conclude that they should be able to construct a universal human nature. Even thinkers (like Kant) who never left their hometowns should be able to make authoritative pronouncements on human nature and morality. — unknown

I'm not even against this 'transcendental pretense.' But it's worth point out, I think. And of course Locke and just about every philosopher needs it.

The idea of the universality of mathematics had to be abandoned with non-Euclidean alternative mathematics. — David Mo

I know that it was a revolution. These days math is all symbols, so it's no longer a problem (roughly speaking.)

Otherwise, Kant was right about knowledge a priori. Just it is not so much a priori than he thought. — David Mo

Yeah, I pretty much agree with you. Kant took certain distinctions as absolute that have since been brought down a notch. But he could hardly do everything at once, I guess. Maybe another reason I like Locke is because he writes in English and has a less grandiose personality.

Of course, Kant is a man of his time, and the debate of his time was between empiricists and rationalists. But to equate his starting point with Locke seems risky to me. In empiricism the concept of object is formed empirically (whether it is mathematical or not). In Kant it predates sensations. Without a previous concept of cause the game with the data of the senses would be chaotic. — David Mo

I think I know what you mean. As I understand him, Kant went into serious detail about our cognitive hardware. Locke does think about the operations of the mind, but he didn't cook up such a rigid system.

If I remember correctly, Locke introduces some rationalism in his empiricism when he considers the mathematical world of things universally factual by giving them a material body: atoms. This is another matter, but it is also contrary to the Kantian starting point. — David Mo

I understand what you mean here too. Locke had a plausible theory of the the stuff that caused sensation, as did Hobbes. Kant did a wilder thing and made it an X. But how can the X cause sensation? If causation is just a structure within experience?

If you want present the case for Locke, I would like to read it. — David Mo

I'll drop a few quotes.
http://www.gutenberg.org/files/10615/10615-h/10615-h.htm#link2HCH0004

I see no reason, therefore, to believe that the soul thinks before the senses have furnished it with ideas to think on; and as those are increased and retained, so it comes, by exercise, to improve its faculty of thinking in the several parts of it; as well as, afterwards, by compounding those ideas, and reflecting on its own operations, it increases its stock, as well as facility in remembering, imagining, reasoning, and other modes of thinking. — Locke

Later in the work he tackles language.
https://www.gutenberg.org/files/10616/10616.txt

Secondly, That though the proper and immediate signification of words
are ideas in the mind of the speaker, yet, because by familiar use from
our cradles, we come to learn certain articulate sounds very perfectly,
and have them readily on our tongues, and always at hand in our
memories, but yet are not always careful to examine or settle their
significations perfectly; it often happens that men, even when they
would apply themselves to an attentive consideration, do set their
thoughts more on words than things. Nay, because words are many of them
learned before the ideas are known for which they stand: therefore some,
not only children but men, speak several words no otherwise than parrots
do, only because they have learned them, and have been accustomed to
those sounds. But so far as words are of use and signification, so far
is there a constant connexion between the sound and the idea, and a
designation that the one stands for the other; without which application
of them, they are nothing but so much insignificant noise.

Words, by long and familiar use, as has been said, come to excite in men
certain ideas so constantly and readily, that they are apt to suppose
a natural connexion between them. But that they signify only men's
peculiar ideas, and that BY A PERFECT ARBITRARY IMPOSITION, is evident,
in that they often fail to excite in others (even that use the same
language) the same ideas we take them to be signs of: and every man has
so inviolable a liberty to make words stand for what ideas he pleases,
that no one hath the power to make others have the same ideas in their
minds that he has, when they use the same words that he does. And
therefore the great Augustus himself, in the possession of that power
which ruled the world, acknowledged he could not make a new Latin word:
which was as much as to say, that he could not arbitrarily appoint what
idea any sound should be a sign of, in the mouths and common language of
his subjects. It is true, common use, by a tacit consent, appropriates
certain sounds to certain ideas in all languages, which so far limits
the signification of that sound, that unless a man applies it to the
same idea, he does not speak properly — Locke

I like his awareness that language is a social convention. To me one of the big 20th century insights was just how 'exterior' and social meaning and thinking are. Sometimes you'll see troubled solipsists appearing on forums either arguing their position or asking to be argued out of it. What in the tradition made such absurdity possible? Descartes and/or watching The Matrix too many times. But my point is that the language of solipsism is directed outward from the get-go and was learned through interaction in the first place. What I like about The Concept of Time and Philosophical Investigations is (among other things) the quashing of an entrenched assumption of private language in the single soul.

But more Locke:

The next thing to be considered is,--How general words come to be made.
For, since all things that exist are only particulars, how come we by
general terms; or where find we those general natures they are supposed
to stand for? Words become general by being made the signs of
general ideas: and ideas become general, by separating from them the
circumstances of time and place, and any other ideas that may determine
them to this or that particular existence. By this way of abstraction
they are made capable of representing more individuals than one; each of
which having in it a conformity to that abstract idea, is (as we call
it) of that sort. — Locke

We get abstract ideas from experience, by erasing unimportant differences.

To return to general words: it is plain, by what has been said, that
GENERAL and UNIVERSAL belong not to the real existence of things; but
are the inventions and creatures of the understanding, made by it for
its own use, and concern only signs, whether words or ideas. Words are
general, as has been said, when used for signs of general ideas, and so
are applicable indifferently to many particular things; and ideas are
general when they are set up as the representatives of many particular
things: but universality belongs not to things themselves, which are all
of them particular in their existence, even those words and ideas which
in their signification are general. When therefore we quit particulars,
the generals that rest are only creatures of our own making; their
general nature being nothing but the capacity they are put into, by the
understanding, of signifying or representing many particulars. For the
signification they have is nothing but a relation that, by the mind of
man, is added to them. — Locke

General ideas are 'creatures of our own making,' which is a strong anti-metaphysical point.

I would not here be thought to forget, much less to deny, that Nature,
in the production of things, makes several of them alike: there is
nothing more obvious, especially in the races of animals, and all things
propagated by seed. But yet I think we may say, THE SORTING OF THEM
UNDER NAMES IS THE WORKMANSHIP OF THE UNDERSTANDING, TAKING OCCASION,
FROM THE SIMILITUDE IT OBSERVES AMONGST THEM, TO MAKE ABSTRACT GENERAL
IDEAS, and set them up in the mind, with names annexed to them, as
patterns or forms, (for, in that sense, the word FORM has a very proper
signification,) to which as particular things existing are found to
agree, so they come to be of that species, have that denomination, or
are put into that CLASSIS. For when we say this is a man, that a horse;
this justice, that cruelty; this a watch, that a jack; what do we else
but rank things under different specific names, as agreeing to those
abstract ideas, of which we have made those names the signs? And what
are the essences of those species set out and marked by names, but those
abstract ideas in the mind; which are, as it were, the bonds between
particular things that exist, and the names they are to be ranked under?
And when general names have any connexion with particular beings, these
abstract ideas are the medium that unites them: so that the essences of
species, as distinguished and denominated by us, neither are nor can
be anything but those precise abstract ideas we have in our minds. And
therefore the supposed real essences of substances, if different from
our abstract ideas, cannot be the essences of the species WE rank
things into. — Locke

It's we who sort the world into this kind of thing and that kind of thing. This is against the notion of those 'supposed real essences.'

Those are just some samples. I just mentioned Locke because I overlooked him for a long time. When I finally read him in an anthology of empiricists, I was impressed.

Formal proof is never about the real world. Furthermore, mathematics is not directly applicable. It first has to go through a framework of empirical rules and regulations, such a science or engineering. In that sense, there is no act of informal interpretation of mathematics. — alcontali

I think I do understand this idealization of ultra-pure math, which I like in some ways. But if it's just chess, then why should we expect it to matter in the real world?

Natural language is primarily used for non-knowledge which is the overwhelming majority of what is being expressed. In fact, we do not use that much epistemically-sound knowledge. It is not the main purpose of language (or communication in general) anyway. — alcontali

Which supports my point, I think. If 'pure knowledge' is just formalism, how could it be important for us? I've occasionally bumped into people (not you) who think that formal logic can somehow save the world. But real logic (applied logic) is entangled with ordinary language. Ultra pure math is something like language purified of all ambiguity but also therefore any reference to the world we live in.

I couldn't do calculus integrals for beans, but I took naturally to Zorn's lemma. Did you know that the proposition that every vector space has a basis, is fully equivalent to the axiom of choice? Isn't that wild? — fishfry

I had heard that, but never studied the proof. It is indeed wild.

At my school we only had to learn the set theory that comes with analysis and algebra. I did look into ordinals on my own. I remain impressed by the usual Von Neumann constuction. I used it in visual art and I also think it has a philosophical relevance. It's a nice analogy for consciousness constantly taking a distance from its history. 'This' moment or configuration is all previous moments or configurations grasped as a unity. It works technically but also aesthetically.

It's very doubtful to me that such a structure has an analog in the physical world. And if it did, it would be quite a surprise. — fishfry

That would be surprising indeed. I think we agree on the gap between math and nature. As you mention, our measurement devices don't live up to our intuition and/or formalism. I have a soft spot for instrumentalism as an interpretation of physical science.

Mathematicians have a tongue-in-cheek saying: The imaginary numbers are real; and the real numbers aren't! — fishfry

I haven't heard that one. But I know a graph theory guy who thinks the continuum is a fiction and an analyst who believes reality is actually continuous. Another mathematician I know just dislikes philosophy altogether. I like philosophy more than math when I'm not occasionally on fire with mathematically inspired, though I have spent weeks at a time in math books, obsessed. (At one point I was working on different models of computation, alternatives to the Turing machine, etc. Fun stuff, especially with a computer at hand.)

It's an extremely widely held false belief that pi encodes an infinite amount of information, when it of course does no such thing. Bad teaching of the real numbers in high school is the root cause of this problem. Whether there is a solution that would serve the mathematical kids without totally losing everyone else, I don't know. — fishfry

Right! Because of the infinite decimal expansion. One of my earliest math teachers had lots of digits of pi up on the wall, wrapping around the room. Some of the problem may be in the teaching, but I've wrestled with student apathy. Math tends to be viewed as boring but useful, the kind of thing that must be endured on the path to riches. Its beauty is admittedly cold, while young people tend to want romance, music, fashion, fame, etc.

This is a strange digression, perhaps, but it connects with the intuitive beauty of mathematics. When I fell in love with math, I also fell in love with the idea of an objective knowledge, a knowledge of some transpersonal structure. It wasn't about me-me-me and some rationalized 'theology' justifying my current lifestyle. Math was 'sculpture.' It was cold as ice, austere. It was ancient stone. What is this eroticism of the mathematical?

[The] impossible synthesis of assimilation and an assimilated which maintains its integrity has deep-rooted connections with basic sexual drives. The idea of "carnal possession" offers us the irritating but seductive figure of a body perpetually possessed and perpetually new, on which possession leaves no trace. This is deeply symbolized in the quality of "smooth" or "polished." What is smooth can be taken and felt but remains no less impenetrable, does not give way in the least beneath the appropriative caress -- it is like water. This is the reason why erotic depictions insist on the smooth whiteness of a woman's body. Smooth --it is what reforms itself under the caress, as water reforms itself in its passage over the stone which has pierced it....It is at this point that we encounter the similarity to scientific research: the known object, like the stone in the stomach of the ostrich, is entirely within me, assimilated, transformed into my self, and is entirely me; but at the same time it is impenetrable, untransformable, entirely smooth, with the indifferent nudity of a body that is beloved and caressed in vain. — Sartre

I like to contrast the mathematician and the novelist. The novelist seeks a personal immortality. As a novelist, I want to crystallize my own precious experience of reality. As a mathematician, I lose myself in the inter-subjectively available object. I can't sign or claim this knowledge, or not in the same way. The ostrich swallows a stone that it cannot digest (as Sartre describes it in another passage of 'Existential Psychoanalysis.')

The philosopher is somewhere between the mathematician and the novelist. That Sartre quote tries to capture in words what he takes for a universal experience, a general structure of experience that is otherwise particular. This is basically the eternal 'behind' time, the invariant that is constantly present if we can grasp it.

In general I have found that working over formalisms is one necessary part of developing understanding for a topic; don't just read it, fight it. Follow enough syllogisms allowed by the syntax and you end up with a decent intuition of how to prove things in a structure; what a structure can do and how to visualise it. — fdrake

This is a good point to bring up. I'm tempted to call it formal intuition. I used it for all the epsilon-delta stuff in basic real analysis. A continuous function was (in that context) something associated roughly with a set of logical moves. It's almost like playing a guitar. A certain know-how kicks in. A person can sit in class and start imagining how something might be proved. This is kind of what I meant by symbol manipulation. In this mode, the stuff of the proof itself is the medium of thought.

Developing such anchors and being able to describe them seems a necessary part of learning mathematics in general; physical or Platonic grounding deflates this idea by replacing our ideas with actuality or actuality with our ideas respectively. In either case, this leaves the stipulated content of the actual to express the conceptual content of mathematics without considering how the practice of mathematics is grounded in people who use mathematics and whether that grounding has any conceptual structure. — fdrake

I like this. On of the experienced mathematicians I know liked the math is language metaphor. I find this metaphor deeper than might be apparent. What is it to know English? Perhaps to know math is just as complicated, even if epistemologically the situation is simpler. A stupid computer can check a formal proof, but the world of mathematics is certainly not just a set of formal proofs. Squishy Heideggerian insights are valuable even here. Knowing math is like knowing English is like knowing how to ride a bike. That knowledge is largely tacit. When I've taught math, I mumbled to my students something about intuition coming with practice. 'Keep calculating. Faith will come!' I liked Hersh's mathematical humanism: https://www.amazon.com/What-Mathematics-Really-Reuben-Hersh/dp/0195130871 Maybe you've read that. He gets that math is a kind of intersubjective human practice.

What it seems important as principle in Kant is the regulative use of the reason. That is to say: physics principles are a priori because they come from a priori conditions of our knowledge, not being things in themselves. This links with Kuhnian concept of paradigm and with quantum paradoxes of measurement, relativity, etc. We live a world mediated by the categories of our way of thinking. — David Mo

Here is the way I make sense of this. The key for me is here: https://en.wikipedia.org/wiki/Deductive-nomological_model

Because we come equipped with mathematical intuitions and the notion of causality, we can hypothesize that maybe nature is subject to a law of gravity, for instance, mathematically expressed. We dream up patterns that may or may not fit the data. From this perspective, the mind is clearly active, even if it is passive with respect to sensation.

To me Democritus had to work like this, though without the math that become dominant with Galileo. 'Perhaps nature is really made of microscopic pieces.' Guided by this work of creativity, he could interpret uncontroversial facts in the light of their possible conformity to this hidden structure. As others have noted, observation is theory-laden. How much of Kant is compressed in that idea? If we take the theory-laden-ness of observation to be something that evolves historically, then we get various post-Kantian thinkers. Yes, reality is mediated by the social lens of an impersonal conceptual scheme, but also this scheme changes --or most of it is subject to change.

Broader point: formal systems don't just have syntactic rules, don't just have formal semantics, they also have conceptual content. The conceptual content of mathematical objects and systems is what unites them over the varying degrees of formality of their presentation. — fdrake

I agree. What is the flight from conceptual content to a dead machine?

Yes, science is not algorithmic, and hence not certain. It's a human enterprise, subject to all sorts of politics and abuse. — Banno

Here's the answer, a flight from the uncertainty of everything stained by social human being.

There is proof for that, i.e. justification. Hence, "The MU puzzle cannot be solved" is a justified (true) belief, i.e. legitimate knowledge. — alcontali

In general, my problem with prioritizing strictly formal proofs is that we forget that moving from formal proof to the real world is an act of informal interpretation. I don't see how we can get 'behind' the 'throwness' of ordinary language. Yes, we can make games like chess, but the leap from chess kings to the present king of France is something unspecified by the rules of chess. In real language, we can't strictly control the meanings of our signs. They are caught up in history and context.

I also like this approach: https://en.wikipedia.org/wiki/Interval_arithmetic

Nevertheless, how you stipulate or construct the object lends a particular perspective on what it means; even when all the stipulations or constructions are formally equivalent. — fdrake

I very much agree. For someone who insists on math being beautiful, it has to sing for the intuition. For example, when learning group theory I really liked thinking of groups of permutations. Those were the anchor for my intuition. The operation on the group was 'really' functional composition, which is why groups weren't automatically commutative. The theory doesn't care. Epistemologically it's a non-issue. But it matters for motivation. Another approach is just to understand math as a chess of symbol manipulation. In some contexts this is satisfying enough. But one gets lost in real analysis without intuition guiding the construction of a semi-formal proof.

A worth endeavor perhaps, but the nature of human subjectivity seems to prohibit, or at least seriously impair, its possibility. — Mww

I agree. And yet to say so is to have established some kind of universal trans-subjective truth about the nature of human subjectivity. Somehow I reason privately and come to conclusions about the limitations of the private reasoning of others. The CPR presents itself as the true metaphysics, the only kind now possible. A grandiose assertion! Which isn't to say he isn't right in some important sense...

What he adds to this:

The cause of Sense, is the Externall Body, or Object, which presseth the organ proper to each Sense — Hobbes

is perhaps lots of detail about how our concepts manage and organize this pressing of our sense organs.

This version of Leviathan has a great introduction:

http://files.libertyfund.org/files/869/0161_Bk.pdf

This is exactly the geometric interpretation that got me into trouble. :) It assumes that rays have points corresponding to every non-negative real number (or lines have points corresponding to all real numbers.) To which, I remember my brain screamed, how do you know? — simeonz

Good point. The rays I mentioned have 'melting tips.' In some ways we are just sweeping the problem under the rug. What I like about the Cauchy sequence approach is that the real number is like a program that spits out rationals (closer and closer together in the long run.) There's another version where positive real numbers are increasing sequences of rationals that are bounded above. These have their advantages. If we hobble ourselves and just think in terms of computable functions from N to Q (whose outputs get closer together), we get maximum clarity but lose most of the line. (And we have no more reals than rationals cardinality-wise.)

But maybe there's no perfectly satisfying way to capture our intuition of the line. And sometimes I'm tempted to just enjoy the axioms of R as descriptive of intuitions of space.

I started to question what was the goal - were numbers lexical entities or geometric properties? What was that we were trying to define - quantities, computations, geometrical facts? How could we validate them? At this point I didn't know much about algebraic structures and axiomatic systems. I went completely on a pseudo-philosophical tangent and refused to learn anything whose methodological grounds I did not understand completely. — simeonz

Ah, the curse of being a philosopher! I feel you. For me it was slightly different. I read a boatload of philosophy of math before studying math. I was vaguely anti-foundationalist by the time I was learning real analysis. With basic real analysis (pre-measure theory and Riemann integral), my intuition felt more or less satisfied. As I learned measure theory, all the sets of measure zero were a bit of a turnoff. More and more equivalence classes. Blah. I don't mind them in algebra, but in analysis there like film on a bathtub that needs cleaning. I'm a lapsed intuitionist. Math only has beauty to the degree that it corresponds (at some anchored point) to intuition. 'God intuition created the integers. The rest is the work of man.'

They could be, or they might not be, but how would a mathematical textbook use something like that, that we know very little about (i.e. space), and which is not axiomatic in nature, and use it to define a mathematical concept. At least for me, it didn't work, and caused me some difficulty. — simeonz

It does seem to depend on an intuition of space, a space independent of physics' space (an ideal space.) We can prove (for the intuition) the commutative law for multiplication by turning a rectangle 90 degrees. At some point I'd like to see how many of the axioms of the real number system can be intuitively supported this way.

but those rationalities wouldn’t be the same as ours. — Mww

Here's the crux: our rationality. Being-with-others, a universal-transcendental subject. Not just me. At the base of the I as its most truthful-accurate version is an ideal we. I must manage my bias (my unreason) in order to see from and with the ideal we (our reason).

I am only stating this, because rationals are looked upon so favorably, but I find that their simplicity is somewhat overstated. — simeonz

IMV, the rationals are quite difficult. We know how students hate fractions. But I like the idea of 1/n as a kind of flexible unit. Then m/n is just m of those units. We can adjust n to increase or decrease resolution. And we can do various conversions. So it's difficult but still (after much work and thinking) ultimately intuitive. At least for me.

Actually, yes. Dedekind cuts are another constructive approach. Not too different in spirit, I would say. — simeonz

One can construct the positive real numbers as a simpler version of the cuts. In the version I like we have a ray of rational numbers that starts from zero (a subset of Q that is closed downward with no maximum.) I like this for its intuitive connection to magnitude/length. The square root of 2 in this system of positive reals is just the rationals whose square is less than 2. The analogy is strong. We hold up some piece of Q^+ as a ruler, and we get all that Q itself leaves out. (I'm sure you already know this, so I'm just hyping the charms of this construction for the intuition. )

That may all well be, but it bears keeping in mind that peope don’t think qua think, in language; people think, meaning the private subjective rational activity, in images. — Mww

I find it plausible that people think with words and images but not that thinking is essentially imagistic. How does Kant exist for us? And even if you thought what you posted in pure image somehow, it's only a beetle-in-the-box that I can never see. I can't compare my internal images to yours to grasp whether or not I comprehend you. I can only trade words with you. This 'sociality of reason' seems crucial to me, and I aim it against Descartes too. 'I' don't doubt. The 'we' doubts in me as me, with this 'we' serving as a metaphor for our possession of language as the condition of the possibility for doubting the external world.

What I think Heidegger gets right independent of all the death stuff is a grasp of world as fundamental.

According to Heidegger, Descartes presents the world to us “with its skin off” (Being and Time 20: 132), i.e., as a collection of present-at-hand entities to be encountered by subjects. The consequence of this prioritizing of the present-at-hand is that the subject needs to claw itself into a world of equipmental meaning by adding what Heidegger calls ‘value-predicates’ (context-dependent meanings) to the present-at-hand. In stark contrast, Heidegger's own view is that Dasein is in primary epistemic contact not with context-independent present-at-hand primitives (e.g., raw sense data, such as a ‘pure’ experience of a patch of red), to which context-dependent meaning would need to be added via value-predicates, but rather with equipment, the kind of entity whose mode of Being is readiness-to-hand and which therefore comes already laden with context-dependent significance. — link

The world is not a set of objects but the 'stage' or 'background' on which or against which all things exist. IMV we learn the distinction of self and non-self. The individual mindspace is a product of social language use, though obviously it's not simply a fiction.

The system is complete in itself; the content of the system is predicated on experience, yes. And it really doesn’t matter what name a theory subsumes the system under, as long as they all agree we as humans all have the same faculties. — Mww

There's a line in Bennington's Derrida:

[T]he empirical is the transcendental of the transcendental (of the empirical). — Bennington page 278

For context, I'm with Kant 100% that we get reality 'filtered.' I'm just not sure that his particular system is stable or eternally correct. What Heidegger, Wittgenstein, and Derrida have to say about language makes the situation more complicated, IMV.

Cool. Thanks. I admit to not thumbing far enough, or thumbing right over it. I lost my place in answering your question. Are you ok with the responses you got, or is there anything you’re still unsatisfied with? — Mww

I thought they were good responses. I guess I'd like to hear what you have to say about the transcendental pretense (the assumption that we all have the same rational system.) Or in general what you think Kant had to take for granted in order to write CPR. Given that Kant is obviously a great philosopher, what did he not see? Do you have any criticisms of Kant?

Was it Cantor who said the rational numbers are like the stars in the night sky and the irrationals are like the darkness in the background? Perhaps this has been posted before. — jgill

I don't know, but I'm familiar with that excellent analogy.

After much contemplation I have discovered, what I believe to be, a fundamental truth of the human experience. You cannot have true Peace or objectivity so long as Happiness and Misery exist in your life. I do not see peace as the balancing of happiness and misery, but the absence of both. I see peace and objectivity as one because for me to believe that I know something, but not objectively, causes great dissonance. — PoorAt99

if you find something that I have overlooked or that you would like to add/challenge, let me know. — PoorAt99

What I'd politely challenge is the implicit identification of virtue with objective knowledge. Why should not knowing objectively be so painful, cause such dissonance?

Continual Successe in obtaining those things which a man from time to time desireth, that is to say, continual prospering, is that men call FELICITY; I mean the Felicity of this life. For there is no such thing as perpetual Tranquillity of mind, while we live here; because Life itself is but Motion, and can never be without Desire, nor without Feare, no more than without Sense.
...
No Discourse whatsoever, can End in absolute knowledge of Fact, past, or to come. For, as for the knowledge of Fact, it is originally, Sense; and ever after, Memory. And for the knowledge of consequence, which I have said before is called Science, it is not Absolute, but Conditionall. No man can know by Discourse, that this, or that, is, has been, or will be; which is to know absolutely: but onely, that if This be, That is; if This has been, That has been; if This shall be, That shall be: which is to know conditionally; and that not the consequence of one thing to another; but of one name of a thing, to another name of the same thing.
...
Anxiety for the future time, disposeth men to enquire into the causes of things: because the knowledge of them, maketh men the better able to order the present to their best advantage. — Hobbes

As mortal, flesh-and-blood beings, we are thrown into our animal appetites. And into the more abstract appetite for knowledge and transcendence through knowledge. Objectivity seems valuable first as just a prudent theory of causes that allows us to thrive as social animals in the world. But the spiritualization of objectivity is like a flight from individual mortality into the relative immortality of a shared cultural heritage, the mind of the species being. As we lose our faith in God, 'He' gets transformed into Knowledge that's not just knowledge.

IMO it's the especially thoughtful people who suffer and react to this situation:

For being assured that there be causes of all things that have arrived hitherto, or shall arrive hereafter; it is impossible for a man, who continually endeavoureth to secure himselfe against the evill he feares, and procure the good he desireth, not to be in a perpetuall solicitude of the time to come; So that every man, especially those that are over provident, are in an estate like to that of Prometheus. For as Prometheus, (which interpreted, is, The Prudent Man,) was bound to the hill Caucasus, a place of large prospect, where, an Eagle feeding on his liver, devoured in the day, as much as was repayred in the night: So that man, which looks too far before him, in the care of future time, hath his heart all the day long, gnawed on by feare of death, poverty, or other calamity; and has no repose, nor pause of his anxiety, but in sleep. — Hobbes

So these thoughtful people create spiritual traditions that help them learn how to die (or learn how to live with a future that can only be disaster for the mortal individual.)

The ego, in this context, is the lens through which we view the objective world. It is the culmination of all that we have experienced, everything that we consider Me. This includes your opinions, fears, joys, desires, biases, purpose, passion, and even what is right or wrong. — PoorAt99

I pretty much agree. We can sum this up as mask is lens. What I experience is --without my consent and beyond my control --first filtered through my 'ego,' which includes who I pretend to be for mirror or my ideal self-image (my 'mask').

When it comes to others, it's easy to see bias. And so we can distinguish between what's really going on and the distorted version that the other mistakenly takes (mis-takes) for the situation. As we mature, we also (hopefully) evolve our vision of the world so that we can see our own past self as biased in the same way. We develop a healthy suspicion of our own current understanding. We can postulate the filter mentioned in the first paragraph. 'I, too, am wishful thinking, distorted by hope and fear.'

As a result of our attachment we see this as bad, it hurts, and we either give into that or desperately seek to find some optimistic way of viewing it. — PoorAt99

But whatsoever is the object of any mans Appetite or Desire; that is it, which he for his part calleth Good: And the object of his Hate, and Aversion, evill; And of his contempt, Vile, and Inconsiderable. For these words of Good, evill, and Contemptible, are ever used with relation to the person that useth them: There being nothing simply and absolutely so.
...
The names of such things as affect us, that is, which please, and displease us, because all men be not alike affected with the same thing, nor the same man at all times, are in the common discourses of men, of Inconstant signification. For seeing all names are imposed to signifie our conceptions; and all our affections are but conceptions; when we conceive the same things differently, we can hardly avoyd different naming of them. For though the nature of that we conceive, be the same; yet the diversity of our reception of it, in respect of different constitutions of body, and prejudices of opinion, gives everything a tincture of our different passions. And therefore in reasoning, a man bust take heed of words; which besides the signification of what we imagine of their nature, disposition, and interest of the speaker; such as are the names of Vertues, and Vices; For one man calleth Wisdome, what another calleth Feare; and one Cruelty, what another Justice; one Prodigality, what another Magnanimity; one Gravity, what another Stupidity, &c. And therefore such names can never be true grounds of any ratiocination. No more can Metaphors, and Tropes of speech: but these are less dangerous, because they profess their inconstancy; which the other do not. — Hobbes

https://www.gutenberg.org/files/3207/3207-h/3207-h.htm

I have decided to try and rid myself of my ego entirely, in hopes that I can see the world with true objectivity and experience peace.The cost for this is giving up all that I am and any notions of happiness in my future, though I am quite content with the decision. Initially I worried that this would mean losing everything that made me human, but I'm beginning to see that even what it is to be human is a construct of my ego. I simply want to be and learn, no more and no less. — PoorAt99

This reminds me of Schopenhauer. Becoming a kind of still lake that mirrors reality correctly via its passivity is a classic theme. But pointing that out doesn't subtract from the interest of the project. In my own way, I'm on the same page. For me the petty person has to continually die in order to make a colder more accurate knowledge possible. We learn to take the impersonal personally. To me this is still a mask, but it's the mask that strives beyond all idiosyncrasy (the transparent mask, the well-ground lens that lets the truth come through unmolested --or at least molested in a universally human and rational way.)

I think of them as the "dark matter" of the real number line. We can't name them, we can't compute them, we can't use them for anything. But without them, there aren't enough reals to be Cauchy-complete. — fishfry

I first read about them in Chaitin, before I had the training in math to really understand. It was clear even then that the real numbers had a certain magnificent unreality or ideality. When I studied some basic theoretical computer science (Sipser level), I saw the 'finitude' of now relatively innocent computable numbers like pi, which are of course countable. The measure of R is 0 without those unnameable numbers. Each is an oracle answering an infinite number of yes/no questions unpredictably. So does one believe in them? Within the mainstream game, of course! As pieces of the game that are one of its strangest features.

There are more things in heaven and Earth, Horatio, / Than are dreamt of in your philosophy -- — fishfry

Right! And there are more things in mathematics that are dreamed of by outsiders. I have taught math, and I occasionally hint at a world of strangeness awaiting those who wade in more deeply. It's a poetic enterprise, though one has to learn the grammar and spelling before one can understand the poetry.

Please explain this to Metaphysician Undercover! I've had no luck. — fishfry

I know! I've followed your conversation. We human beings are sometimes stubborn as mules. We don't always want to know. Sometimes we'd prefer to 'win' an argument, however alone we are with that sense of victory. It's basically ridiculous to do philosophy of math without training in math: sex advice from virgins, marital advice from bachelors.

I always follow your posts. You know much more set theory than me, so I learn something. Though I agree that the rational numbers are synthetic, I find them intuitively satisfying enough to function as a foundation from the which the reals can be built as cuts or Cauchy sequences. I like cuts for not being equivalence classes. It's an aesthetic preference. Cuts are beautiful ('liquid crystal ladders').

This is extremely hard to explain without saying ‘read Kant’. He is careful with he words - too careful perhaps - and asks a lot of his reader.

The most simplistic way to view all this is, as I previously said, by regarding a priori as the canvas and a posteriori as the paint - either alone produce no picture and it is only through the former (a priori) that we make this deduction. — I like sushi

Read (more) Kant is of course good advice. I love his introductions, but I haven't studied all of the details. Kant is not always a pleasure to read. And then debates about Kant are like lots of classical metaphysical debates, which are haunted by a kind of futility perhaps.

Recently I found a philosopher who articulated my vague misgivings about Kant.

Whereas Locke’s ‘things themselves’ are objects of scientific investigations (especially by the corpuscular hypothesis), Kant’s ‘things in themselves’ are thoroughly unknowable. But despite their unknowability, Kant affirms the existence of things in themselves, and this has been viewed for a long time as one of the serious problems in Kant’s philosophy. According to Kant, things in space (and their properties) are nothing but representations ‘in us’, and appearances qua representations necessarily demand the existence of things in themselves (though these are unknowable). From an historical point of view, however, if Descartes’ and Locke’s theories of ideas do not precede it, such a view must be unintelligible. If I may limit my consideration to Locke and Kant, perhaps we can say that Kant’s ‘things in themselves’ are the product of a degeneration of Lockean ‘things themselves’. In other words, Kant’s concept of ‘things in themselves’ would not make sense without the model of Locke’s naturalistic theory of ideas,[4] and as a result of its degeneration, the framework of his transcendental idealism seems to have a distorted logic.
...
As already mentioned, Locke’s ‘things themselves’ are single corpuscles or aggregates of corpuscles that possess only primary qualities (and powers based on them). They affect our sense organs qua aggregates of corpuscles, and accordingly a sort of motion is communicated to the brain. As a result, sensible ideas are produced in the mind. By contrast, in Kant’s case, ‘things in themselves’ are not known to us, and since space is a form of our sensibility, the idea that things in themselves are in space does not make sense. But though he has such a view, Kant repeatedly emphasizes that sensible representations are given to us by ‘things in themselves’ affecting our minds or senses.

Why does Kant assert the existence of the unknown ‘things in themselves’? — Tomida

https://sites.google.com/site/diogenesphil/lk

One answer is that we 'obviously' share a single world. Humans are born, humans die. The world remains. This vaguely suggests a substratum that is independent of any particular-mortal human mind.

Another problem I have with my imperfect understanding of Kant is:

Kant’s things in themselves, which correspond to Locke’s things themselves, affect our senses and in this sense they certainly bear a quasi-causal character. However, the concept of cause that Kant regards as one of the pure concepts of understanding is applicable only to appearances qua representations.

...
Hegelians and Kantians often say that Kant synthesizes empiricism and rationalism. Indeed, on the one hand, he acknowledges the affection by things in themselves and regards the objects of our experience as mental; on the other hand, he acknowledges various a priori items in the mind and regards their rational consequences as important. However, his synthesis is performed by tacitly accepting the naturalistic logic of ideas that Locke shares with Descartes, and at the same time distorting it. In this sense, Kant’s antinaturalistic, transcendental idealism rests on a tacit naturalistic basis. — Tomida

Correct. Given that all humans incorporate the same rational system, all reality in general should be consistent among them. A basketball is such for me as it is such for you. Even if I have no experience of them, if you tell me about one, I should understand what you’re talking about and form a representation of it a priori for myself. This is for the most part because of the categories, which permits conception of an object in general without all the the necessary intuitions given from perception. — Mww

Thank you. This matches what I grasped from my own reading. This idea of the same rational system is what Solomon called the 'transcendental pretense.' I think we do have the same rational system, more or less, but believing this seems to depend on experience, on being socialized. To me the deep subject looks plural rather than singular, even though consciousness is founded in the individual brain.
Solomon also talks of methodological solipsism, which is basically starting from Descartes' individual doubting mind. To me this is like trying to understand the internet by studying only laptops. Our brains have evolved to be networked and are only understood in the highest functioning as such a network. (That's my rough position at the moment.)

I’m not sure what geometry is having to be saved from, unless you meant illusory appearance. — Mww

Some kind of corrosive Humean relativism?

The science of relativity is grounded in Galileo’s mind alone, isn’t it? Einstein may or may not have thought SR and GR on his own, even if there never was a Galileo, but he didn’t. — Mww

Deep question. If the 'I' is a modification of the 'we' --if intersubjectivity is primary and not secondary-- what then? The hardware is individual, but the software is networked.

If I say of myself that it is only from my own case that I know what the word "pain" means - must I not say the same of other people too? And how can I generalize the one case so irresponsibly?

Now someone tells me that he knows what pain is only from his own case! --Suppose everyone had a box with something in it: we call it a "beetle". No one can look into anyone else's box, and everyone says he knows what a beetle is only by looking at his beetle. --Here it would be quite possible for everyone to have something different in his box. One might even imagine such a thing constantly changing. --But suppose the word "beetle" had a use in these people's language? --If so it would not be used as the name of a thing. The thing in the box has no place in the language-game at all; not even as a something: for the box might even be empty. --No, one can 'divide through' by the thing in the box; it cancels out, whatever it is.

That is to say: if we construe the grammar of the expression of sensation on the model of 'object and designation' the object drops out of consideration as irrelevant. — Wittgenstein

If the language that the individual thinks in and with is forged socially, then Heidegger has a point with his being-in-the-world and being-with-others as a deeper layer than the epistemological theory of the individual mind processing sensation with an innate set of concepts.

can’t find this passage. To tell the truth, I don’t even recognize it, my keyword searches don’t lead me to it, and because I’m too lazy to peruse all my literature even after thumbing through some of it, would you please refer me to its source? — Mww

Sure. PFM, section 13, remark 2: http://www.gutenberg.org/files/52821/52821-h/52821-h.htm

his phenomenological analysis of "average everydayness" has always beens striking to me. His Introduction to Metaphysics should be read by anyone serious about Heidegger, and would be my recommendation to you if you haven't already. — Xtrix

Great recommendation! I have read it, but I agree that it's great. And we seem to agree that the analysis of average everydayness has value independently of what one makes of the death theme & authenticity theme. I think we can also phrase this as the phenomenon of the world. So forgetfullness of being is forgetfulness of the worldliness of world, of the network of significance that we mostly glide on and through without noticing it. This would be forgetfulness or ignorance of 'tool being' or equipment as ready to hand but not 'present.'

Especially considering the algebraic approach that you presented. I find it intuitively satisfying without considering set theoretic foundations. And the Dedekind cut is satisfying if one can admit sets of rational numbers (intuitively self-supporting, IMO).

Now if you want to say, "Yes but you admit numbers aren't real, they're only an abstraction!" I respond: Yes exactly. And traffic lights aren't real either, they're only an abstraction. Law is an abstraction. Government is an abstraction. Science is an abstraction. The Internet is an abstraction. Humans have the power of abstraction. It's how we crawled out of caves and built all this. — fishfry

Indeed, and one needs the abstraction of itself abstraction in order to complain about abstraction in the first place.

It's those pesky noncomputable numbers again, one of my favorite topics. — fishfry

Now those are strange entities, unlike the essentially finite square root of 2 (as you've already noted.) A dark ocean of infinitely informative numbers that can't be named is far more poetic and disturbing than little old $\sqrt 2.$

In my opinion what makes Kant attractive is that he stands between subjective idealism and dogmatic realism. The world of phenomena is somewhere between pure subjectivity and pure reality. It exists outside the mind, but it does not exist apart from the mind. — David Mo

I also like indirect realism, which is what I think you are getting at. But why not Locke? Locke should get more play. And then Hobbes is one of the great writers in English. The fact that he doesn't dwell very long on this or that detail is perhaps to his credit. He steams ahead to the social nature of the human being. He also anticipates Heidegger by emphasizing that human beings are future oriented, in terms of fear and hope, and that they want to understand in order to predict and control.

There is a part of Kant's theory of mathematics that is fully valid: mathematics are constructions that are imposed a priori and then justified by experience. — David Mo

Have you considered that Kant (seems to) implicitly assume that all human subjects have some kind of core structure of cognition in common? Let's say that I am convinced by a mathematical proof, but that no one else finds the proof convincing. Where is mathematics then? It seems to me that as a matter of experience mathematics is relatively uncontroversial. We all agree that there are an infinity of primes. It seems we infer a shared hard-wired mathematical faculty from this consensus.

I would like the debate to shift to Heidegger. I tried to read Being and Time and found it too cumbersome, so I stopped. I only know about him through third parties too involved in controversies against or in favour of him. — David Mo

Being and Time is cumbersome indeed. I recommend the first draft, which is less than 100 pages and written in a much friendlier style:
https://www.amazon.com/Concept-Time-Contemporary-European-Thinkers-dp-144110562X/dp/144110562X/ref=mt_paperback?_encoding=UTF8&me=&qid=

That one will cost you.

Or you can read for free an even shorter lecture here that has (confusingly) the same name: https://grattoncourses.files.wordpress.com/2012/11/pages-from-21501-the_concept_of_time.pdf

That shorter lecture is nice, but it is so short that it's more of an appetizer than the thing itself. As someone who hesitated about Heidegger for a long time and ended up thinking he was great, I insist that you just gotta read some more Heidegger. He was famous among those in the know for 10 years before B&T came out. B&T is to Heidegger like Nevermind is to Nirvana (made him famous for outsiders). And also over-produced.

Here's a free anthology of his earlier stuff. The style is plain Jane accessible. About half way through I start to recognize the exciting Heidegger.

https://religiousstudies.stanford.edu/sites/g/files/sbiybj5946/f/1_becoming_heidegger_2nd_revised_edition.pdf

In a way, the introduction of the distinction (b/t subject and object) into philosophy ought to be seen as a kind of abberation, a wrong turn taken that we've had to devote entire generations of philosophy in order to get over. Hopefully sooner rather than later. — StreetlightX

There is perhaps a reasonable version of it. Already in Democritus, we have a theory of the substratum of atoms and void and a (crude) theory of sensation/appearance. Feynman said that he would choose “atomic hypothesis” among all others if all scientific knowledge were to be lost in a cataclysm and he could only save one idea. Democritus had to consider that his sense organs weren't sensitive enough to see the atoms that were plausibly there due to more abstract considerations.

For me the problem with the subject-object distinction is about private language. Certain philosophers forget the social-historical nature of talking-thinking, that self-consciousness depends on the other, etc.

Heidegger was entirely right to inject time into any analysis of things, even though he tethered that injection to (a certain conception of) death in a way I find problematic. — StreetlightX

I agree that the death theme is a distraction. It's as if Heidegger was trying to work his home-grown religion into an otherwise neutral analysis. A better approach to authenticity is perhaps in contrast to chatter or idle talk in the sense of pre-interpretedness that blocks access to a genuine grasp of a text, for instance. Gadamer's Truth and Method strikes me as sober and impressive application of Heidegger's insights on time.

Interesting. It does seem he's getting at that when speaking of "de-worlding." But yes, that the subject-object dichotomy is just a "founded" mode of seeing the world I get out of him as well. And I have to say that prior to reading Heidegger, I never had quite considered things in this way, despite reading Freud and Schopenhauer and all our contemporary talk of automaticity. — Xtrix

I also never encountered the notion of 'deworlding' in the same way as in Heidegger. Maybe what really brings it home is the analytic of everyday dasein, the usually ignored network of equipment, Dreydegger's 'one', 'interpretedness,' etc. Inherited frameworks of interpretation, a past that leaps ahead!

And then there's the gap between 'science space' (geometric space) and 'lived' space --the familiar path down the stairs or around the block. And in The Concept of Time he imaginatively reconstructs the public time of the clock that we all take for granted. For me, grasping being-in-the-world and being-with-others and (what I call ) being-in-language as 'phenomena' just obliterated certain epistemological issues that I could once take more seriously.

So even if a person jettisons the death and authenticity stuff, the unveiling description of all the structure of the mundane that we usually ignore as too close to us is a game changer. Being-with-others is primary. Can't start with the beetle in the box.

Yes I've read his lectures on Aristotle and Hegel. I didn't find Blattner's book all that convincing. I haven't heard of "The Young Heidegger." — Xtrix

Nice. I like The Concept of Time, first draft of B&T, if I had to pick just one. The big picture is squeezed into < 100 pages. I have the red & white little paperback translated by Farin and Skinner. Thankfully they don't capitalize 'being,' which used to put me off of Heidegger. It's more clearly an extension of Dilthey and Von Wartenberg (and about the historicity of human existence as opposed to more general questions about being --while including the classic analytic in abbreviated form.)

The problem with Blattner is maybe that he intentionally ignored the early stuff, as he says in the intro. You mentioned Dreyfus, whose Being-in-the-world is great. Maybe Dreyfus and others downplay the early stuff because it's inspired by Christian thinkers and also morbid-angsty. Anyway, what Dermot Moran writes in the essay linked to agrees with the much more detailed treatment in Van Buren.

https://www.ucd.ie/t4cms/Choosing%20a%20Hero%20Heidegger%20on%20Authentic%20Life%202010.pdf

Although Heidegger is aware of Rudolf Otto’s analysis of religion as centred on the idea of the “holy” or the “numinous”, in fact, for Heidegger, the key to an understanding of religion in general and the Christian religion in particular is not so much the numinous as what he calls “the historical” (das Historsiche) (GA60: 323). The “core phenomeon” (Kernphänomen) (GA60: 31) or “founding sense-element” (GA60: 323) of religion is “the historical” (GA60: 31) : “Factical life 13 emerges out of a genesis and becomes in an entirely special way historical (enacted)” (GA60: 141). The religious way of being in the world is as a kind of historical consciousness. Unfortunately, in his 1920-21 Phenomenology of Religious Life course, Heidegger is not particularly forthcoming about what precisely he means by “the historical”. For Heidegger, history is not something that can simply be made an object of study. Rather, we are cast in history, we live it: “History hits us, and we are history itself” (Die Geschichte trifft uns, und wir sind sie selbst) (GA60: 173). Factical life and the experience of the historical add up to being the same thing; the manner human beings are concerned, worried or preoccupied by time and by the temporal aspects of their lives. In later lecture courses Heidegger will be more explicit about the manner that Dasein occupies history and is highly critical of inauthentic ways of understanding the process of history. — link

For context, I'm an atheist, but I like what Heidegger cooked up.

There are basketballs out there, there are no basketballs in my head. Therefore it is absolutely impossible that the basketball I know, in whatever way, shape or form I know it, can be the basketball out there. — Mww

I think you know Kant better than me, so perhaps you can clear this up. Does Kant really think there are basketballs out there? Isn't our division of experience into a system of 'law'-obeying objects the work of our minds? As I understand it, what is 'really' out there (according to Kant) is utterly unknowable, and not even in space or time or the causal nexus. So we can't even say that our intuitions/sensations are 'caused' by it. My rough understanding of Kant (I'm willing to be schooled) is that ordinary reality is a kind of intersubjective representation of a represented that only exist theoretically as a '?.' Kant is fascinating for taking such an extreme position. Even space and time are just modes of representation. (!?)

In the same way, if I consider all the representations of the senses, together with their form, space and time, to be nothing but appearances, and space and time to be a mere form of the sensibility, which is not to be met with in objects out of it, and if I make use of these representations in reference to possible experience only, there is nothing in my regarding them as appearances that can lead astray or cause illusion. For all that they can correctly cohere according to rules of truth in experience. Thus all the propositions of geometry hold good of space as well as of all the objects of the senses, consequently of all possible experience, whether I consider space as a mere form of the sensibility, or as something cleaving to the things themselves. In the former case however I comprehend how I can know a priori these propositions concerning all the objects of external intuition. Otherwise, everything else as regards all possible experience remains just as if I had not departed from the vulgar view.
...
My doctrine of the ideality of space and of time, therefore, far from reducing the whole sensible world to mere illusion, is the only means of securing the application of one of the most important cognitions (that which mathematics propounds a priori) to actual objects, and of preventing its being regarded as mere illusion. For without this observation it would be quite impossible to make out whether the intuitions of space and time, which we borrow from no experience, and which yet lie in our representation a priori, are not mere phantasms of our brain, to which objects do not correspond, at least not adequately, and consequently, whether we have been able to show its unquestionable validity with regard to all the objects of the sensible world just because they are mere appearances. — Kant

A small point. Can geometry really be saved this way? Does Kant not need to assume that we all intuit space the same way? And how can he see anyone's beetle in their box? The truths of Euclid seem to depend on shared practices. Trying to ground science on an individual mind seems iffy. What does Kant assume without realizing it? I still think Kant is great.

is anyone very familiar with Heidegger's take on the subject/object distinction? I myself have read a great deal and am not in the camp that he's a deliberately obfuscating charlatan, as many of my friends claim.

Nevertheless, if anyone has bothered I'd like their interpretation. — Xtrix

I like Heidegger, especially the lectures that made him famous among students well before Being and Time. Have you read any of the early stuff or perhaps The Young Heidegger by Van Buren? Having looked at the early stuff, it's clear to me that Blattner's Heidegger's Temporal Idealism gets 'death' wrong. It's nothing so complicated. It's just the possibility of our own death, certain but indeterminate. Memento mori!

To answer your question, what I take from Heidegger is that the subject/object paradigm is artificial, which is to say founded on something primary that just 'worlds' or 'events.' I am the there itself, caught up in time or even as time that runs out, having started without my permission in the middle of situations and habits I did not choose. Theory's subject-object device is part of an epistemological project that neglects our primary, non-theoretical kind of existence --the same experience of sharing a world of tools and words that makes such a theory possible in the first place.

At the same time, the subject-object device is used well by the empiricists (including Kant).

Idealism consists in the assertion, that there are none but thinking beings, all other things, which we think are perceived in intuition, being nothing but representations in the thinking beings, to which no object external to them corresponds in fact. Whereas I say, that things as objects of our senses existing outside us are given, but we know nothing of what they may be in themselves, knowing only their appearances, i.e., the representations which they cause in us by affecting our senses. Consequently I grant by all means that there are bodies without us, that is, things which, though quite unknown to us as to what they are in themselves, we yet know by the representations which their influence on our sensibility procures us, and which we call bodies, a term signifying merely the appearance of the thing which is unknown to us, but not therefore less actual. Can this be termed idealism? It is the very contrary.

Long before Locke's time, but assuredly since him, it has been generally assumed and granted without detriment to the actual existence of external things, that many of their predicates may be said to belong not to the things in themselves, but to their appearances, and to have no proper existence outside our representation. Heat, color, and taste, for instance, are of this kind. Now, if I go farther, and for weighty reasons rank as mere appearances the remaining qualities of bodies also, which are called primary, such as extension, place, and in general space, with all that which belongs to it (impenetrability or materiality, space, etc.)—no one in the least can adduce the reason of its being inadmissible. As little as the man who admits colors not to be properties of the object in itself, but only as modifications of the sense of sight, should on that account be called an idealist, so little can my system be named idealistic, merely because I find that more, nay,

All the properties which constitute the intuition of a body belong merely to its appearance.

The existence of the thing that appears is thereby not destroyed, as in genuine idealism, but it is only shown, that we cannot possibly know it by the senses as it is in itself. — Kant

Kant just radicalizes Locke, and yet, as others have noted, he goes so far that we no longer have a plurality of things, for this imposes too much structure on whatever causes sensation. Small wonder that Kant is so controversial; he's on the edge of absurdity.