That sounds both defeatist and strangely preposterous. — Olivier5

I like the squaring-the-circle metaphor. I can imagine passionate squarers hearing rumors of a proof of the impossibility of their mission and saying the same thing.

[The first of these two misguided visionaries filled me with a great ambition to do a feat I have never heard of as accomplished by man, namely to convince a circle squarer of his error! The value my friend selected for Pi was 3.2: the enormous error tempted me with the idea that it could be easily demonstrated to BE an error. More than a score of letters were interchanged before I became sadly convinced that I had no chance. — Carroll

https://en.wikipedia.org/wiki/Squaring_the_circle

Back to mind-matter talk: from my POV, the issue is not that so-and-so just got bored or tired and gave up and became a spoilsport. No. Instead so-and-so kept trying and trying to make sense of 'mind' and 'matter' and finally traced various difficulties back to the medium itself, to how language works. The absurdity of the project becomes sufficiently (but never perfectly) 'visible' to drop the game with confidence. To me it's one of the main lessons of 20th century philosophy, and I mean the big names, not obscure rebels. IMO, philosophy has actually figured a few things out, made some progress, though it can't shine like new Mars rover, and no one has any practical reason to study and accept the soft but substantial results.

A number is simply a concept. There's no difficulty that I can see here. — Olivier5

And a concept is simply a what? And so on, until the whole dictionary hovers without foundation.

I don't know why theists think "God" will guarantee the validity of science. — Gregory

What I tend to see in philosophical theist is something like a depersonalized god, perhaps a crystalline super-self. For some theists it seems that the epistemological issue is primary, a god who pins our concepts down so that they don't float away, something guaranteeing the certain and the definite, a kind of crystal ship against decay and birth.

Socrates went to his death asking those questions, and all should model his life in that regard. He never said, "I don't know the answer yet, so I guess I'll just stop asking the questions." That's laziness. That's a cop-out. That's what I'd call philosophical suicide. — Dharmi

The irony here is that you suggest that I'm a philosophical suicide because I'm serving as your gadfly. Socrates stung people by making it clear to them that they were unclear, that they didn't know what they were talking about, not really, despite their pride. His wisdom was knowing that he didn't know. Meanwhile you are eager to argue that there is a god, and that anyone doubting that and your method is corrupt, craven, or indolent. I really don't hold it against you. This place only works because/when people get fired up.

And a concept is simply a what? And so on, until the whole dictionary hovers without foundation. — norm

This applies to any concept, not just numbers, and thus it is irrelevant to the point I am making about Hacker's quote. To ask what sort of entity is a number is not any more pernicious than to ask what sort of entity is a chair.

n other words, the whole point of existence is that question. — Dharmi

I agree. Giving up on a specific method of questioning (because you've learned something about it by doing) isn't giving up on questioning altogether. For me it's about better getting to the heart of the issue. It's about not handling a hammer like a saw or not using a fork to eat soup.

Descartes, Leibniz, Giordano Bruno, Gassendi, Averroes, Avicenna...

Ari-fuckin-stotle. — Olivier5

So philosophers then? Yet it was somehow the height of illogic for me to suggests that scientists invented science?

the significant point is that the scientists are usually playing catch-up with the philosophers — Joshs

If you can show some general progress that philosophy has made you'd be in a very small minority. Even among its advocates, it's generally accepted that philosophy doesn't actually 'progress' in that way. So whilst I don't doubt that professional philosophers have widened the scope of enquiry into the philosophy of science, It's just personal bias to suggest that there's a direction of thought that they should be moving toward but aren't (or are doing so too slowly). It's not as if all the philosophers in the philosophy of science have all agreed on anything, there's no "Yep, we nailed that one - let's tell the scientists" on any issue at all.

Looking at your conversation with Olivier, I should add that there are no fixed boundaries between what constitutes science vs philosophy. There are more and less theoretical or applied sciences , and the same goes for philosophy( analytic vs continental) . I’m less interested in whether a particular set of ideas is labeled philosophy or science that how profound and useful
those ideas are. I should add that all other areas of
culture including poetry, literature , music and art , contribute to the shaping of theoretical ideas. That’s why I’m fascinated by the way a particular scientific theory belongs to a large cultural
movement. — Joshs

I agree with you here. It's the point I was making, only more so than you it seems. The biggest difference between philosophy/art and science (even in the loosest sense of 'science' to include some humanities) is that the sciences are, even when wholly speculative, based on a body of empirical knowledge acquired by testing that is usually too extensive or specialised for a single person to carry out. This may seem like a trivial difference, and it is, when it comes to the utility or social contribution of the work. The non-trivial difference is in exactly that which we're discussing here. Anyone can do what Kant did. I could write something similar tomorrow. His insights were gained entirely by introspection using his mind, and we all have one of those. Even the authors he may or may not have read (Wittgenstein had famously read very little philosophy) he has simply chosen to agree or disagree with using nothing but introspection.

Even the most trivial scientific theory, by contrast, is based on a set of empirical findings which a non-scientists would be usually prevented from replicating or testing, simply for pragmatic reasons - the sample size is too large or the equipment too technical. There is a body of such empirical knowledge which, if you haven't read it, you will be unable, no matter how hard you try, to replicate it.

So I agree, in the Quinean sense, with the non-binary definitions of science and philosophy as regards their method of theorising, but there is a difference as to who can rightly claim to be carrying out such theorising. If you don't have the empirical data on which scientific theories are based, then you're not doing science (and yes, before the inevitable question, I am one of those people who thinks some theoretical physics is philosophy, not science).

What I objected to in the line of argument here is a kind of opposite framing, that anyone could do science, but only philosophers could do philosophy. That's just obviously wrong given that the sole source of data for philosophy is the mind and we all have one of those, whereas at least a partial source of data for science is a previous body of empirical test results and one may or may not have access to that.

OK, but you said 'a number is simply a concept.' That's linking one controversial word to an even more controversial word. There's no question that we can use both words in practical life with no problem, but when we play the game of metaphysics and try to make some concept (whatever those are exactly supposed to be) absolute, [fizzle, endless confusion].

So philosophers then? — Isaac

Science is indeed a by-product of philosophy.

Go back to Hacker's quote. This idea that numbers are some sort of magical thing that defies typologies is just absurd. It's all part of the pretense that 'minds are spooky'. Minds are pretty much the only thing we know. Matter defies understanding alright, numbers not so much.

Science is indeed a by-product of philosophy. — Olivier5

It doesn't just get truer if you keep repeating it.

It's a historical fact. You should study history of science, it's fascinating.

And a concept is simply a what? And so on, until the whole dictionary hovers without foundation. — norm

Until you ask the grocer for six bananas, and he gives you five, protesting that 'six is only a concept'.
'Concept, schmoncept', you say, storming out, without paying.

It's a historical fact. — Olivier5

Hence my accusation of historicism. That science did develop from philosophy tells us nothing at all about the necessary relationship between the two.

That a sequence of events happened to take place is not evidence that they are causally connected even, let alone necessarily so.

the sciences are, even when wholly speculative, based on a body of empirical knowledge acquired by testing that is usually too extensive or specialised for a single person to carry out. — Isaac

Empiricism is not necessarily science. Or, put another way, empiricism is one of the facets of modern science. Empiricism insists that what is proposed must be able to be validated by sense data, including data acquired by instruments.

Anyone can do what Kant did. — Isaac

:grin:

The mind is not an entity that could stand in a relationship to anything. All talk of the mind that a human being has and of its characteristics is talk of the intellectual and volitional powers that he has, and of their exercise. — Human Beings – The Mind and the Body: Wittgensteinian-Aristotelian Reflections - Peter M.S. Hacker, 2007

That is true, but so what? 'The mind is not an object'. Nevertheless we all possess one, or are one. So, 'the mind', which is not an object, is the ground of everything we know, including objects.

OK, but you said 'a number is simply a concept.' That's linking one controversial word to an even more controversial word. There's no question that we can use both words in practical life with no problem, but when we play the game of metaphysics and try to make some concept (whatever those are exactly supposed to be) absolute, [fizzle, endless confusion]. — norm

There's a current Smithsonian Institute essay on what is math that is worth perusing. I'm *still* with the Platonists. The metaphysical impact of 'the reality of number' is that 'number is real but not materially existent'. Therefore, there is an important class of things, that is real but not materially existent. Therefore, materialism is false.

Empiricism insists that what is proposed must be able to be validated by sense data, including data acquired by instruments. — Wayfarer

Yep. And?

I'm not sure what point you're making here. It's still the case that science is based on a corpus of such data.

It's still the case that such data cannot be acquired by any other means than direct technical experiment or reading of such.

Whatever non-empirical data you want to include as 'knowledge' it is acquired with a mind, something we all have access to.

Whatever non-empirical data you want to include as 'knowledge' it is acquired with a mind, something we all have access to. — Isaac

Yeah, as we're all Kant, that is likely true.

There's a current Smithsonian Institute essay on what is math that is worth perusing. I'm *still* with the Platonists. The metaphysical impact of 'the reality of number' is that 'number is real but not materially existent'. Therefore, there is an important class of things, that is real but not materially existent. Therefore, materialism is false. — Wayfarer

I will agree that something that might be called 'metaphysical materialism' is false or unintelligible. I'm just as 'against' rigid materialism as against rigid mentalism.

FWIW, I grant that some kind of 'ideality' is 'obviously' going on in math and language. At the same time I do not have an intuition of 2,343,546,343,454,654,765. I can't see it in my mind. I am confident that it can be handled with calculations, that we can make objective statements about such integers. And that's extremely simple math! Already beyond our intuition. I could quote some proofs that take hours to work through. I remember expanding one terse proof, and I never had all of it in my intuition at once. I could only check individual links in the logic. Another issue: are non-computable numbers in Platonic heaven? Who's the authority when it comes to philosophical controversies? Personally I have a vague intuition of what's meant by math platonism, but that's it.

A theory that can't explain a fundamental aspect of reality like conscious awareness is a theory that's already in trouble. — RogueAI

to me that is the definition of mysticism: embracing the fact that you don't know what you don't know

Until you ask the grocer for six bananas, and he gives you five, protesting that 'six is only a concept'.
'Concept, schmoncept', you say, storming out, without paying. — Wayfarer

That's supposed to be a refutation, I think, but instead or also points to the dependence of meaning on social interaction. I can peel a banana but not a concept. If I claim to peel a concept, more charitable listeners will look for a metaphor. Others will think I don't know English that well.

IMO, the temptation is to think of our minds all having separate access to the same platonic essence, and that's why we can coordinate our behavior. This is not an absurd temptation in the context of a heritage of egocentric, private-mind assumptions. But it's been shown to be faulty. The beetle in the box, the secret peepshow, cancels out, does not bear weight. The private mind, however convenient and plausible in ordinary language, falls apart as a foundation upon close examination.

The problem or comedy is that philosophical realizations (breakthroughs, revolutions) don't necessarily provide wonder-working technical power. No one needs to (always imperfectly) grasp later Wittgenstein and others to live a happy life, be good person. No one will be convinced who doesn't want to be, which is fine.

At the same time I do not have an intuition of 2,343,546,343,454,654,765. I can't see it in my mind. I am confident that it can be handled with calculations, that we can make objective statements about such integers — norm

But here your confusing conception and imagination. A concept is different to what you can imagine. Descartes gave the example of a chilliagon, a thousand-sided polygon. You can’t reliably imagine such a thing, but if I tell you what it is, you can understand the concept and even reproduce it, albeit painstakingly. Therefore the chilliagon is a concept, not a mental image, a distinction modernity has generally forgotten.

‘Platonic heaven’ is also a misconception. There is a ‘domain of natural numbers’, right? Where is it? Obviously no place. It’s not some ‘ethereal ghostly domain’. It’s not ‘out there somewhere’. Nevertheless it’s real, because 2 is ‘in’ it, while the square root of 2 is not.

Platonic realism regarding numbers does not mean that imaginary number systems are real. They’re imaginary, by definition. Given the ability to grasp number, then we have the ability to invent such things. But that doesn’t undermine platonic realism.

The problem or comedy is that philosophical realizations (breakthroughs, revolutions) don't necessarily provide wonder-working technical power. — norm

The philosophical realisation that underlies our world began with Descartes’ algebraic geometry combined with Newton’s and Galileo’s science. That philosophical revolution certainly provided wonder-working technical power. You’re looking at it.

But here your confusing conception and imagination. A concept is different to what you can imagine. Descartes gave the example of a chilliagon, a thousand-sided polygon. You can’t reliably imagine such a thing, but if I tell you what it is, you can understand the concept and even reproduce it, albeit painstakingly. — Wayfarer

I agree that there are shades of meaning between the words, but what is it to 'understand' a concept? Call it 'grasping' (a metaphor) or whatever. The point is that some kind of 'having' of some private experience is invoked. I 'understand' what is meant in the usual way. My objection is pushing these ambiguous havings into something impossible sharp. We can't mind meld. We are stuck debating English usage, and yet the temptation is to think it's a kind of science of immaterial realms.

‘Platonic heaven’ is also a misconception. There is a ‘domain of natural numbers’, right? Where is it? Obviously no place. It’s not some ‘ethereal ghostly domain’. It’s not ‘out there somewhere’. Nevertheless it’s real, because 2 is ‘in’ it, while the square root of 2 is not. — Wayfarer

Of course I understand something like a shared space of meanings. If that's all that's meant, then of course! But what is meaning? What is mentality? We don't exactly know. We just know how to use the words in practical life, and we've learned to use them in certain vague ways in a philosophical context. Anyway, a domain is what a function is defined on, set of 'inputs' that work, while natural numbers are often thought of as a set. But if you are being metaphorical, a domain is a place or a region. Or a space. Not arguing against some kind of space of meanings that's 'immaterial' in some ambiguous sense.

Platonic realism regarding numbers does not mean that imaginary number systems are real. They’re imaginary, by definition. Given the ability to grasp number, then we have the ability to invent such things. But that doesn’t undermine platonic realism. — Wayfarer

Which numbers are imaginary? Do you just mean complex numbers? Why are they kicked out? Who decides which number systems are merely inventions? Guassian integers are far simpler to think about than real numbers. The real numbers still give people headaches and were a matter of huge controversy before one side emerged victorious (very roughly speaking.)

The philosophical realisation that underlies our world began with Descartes’ algebraic geometry combined with Newton’s and Galileo’s science. That philosophical revolution certainly provided wonder-working technical power. You’re looking at it. — Wayfarer

I'm well aware that science & math do get results. That's why I get paid for math and programming skills and not for studying Wittgenstein. I'm saying that classical metaphysical arguments don't have obvious winners in the real world. And if I give reasons for their futility, I'm also just wasting my time in practical terms, because in general people don't take such things seriously to begin with, and those who like metaphysics are often religiously-politically motivated or just still captured by the notion that they are doing some kind of higher Science. It's a harmless vice, as is critiquing it.

For me the larger point is just to point my attention to the stuff that matters more. It's good to have wrestled with certain confusions so I could move beyond them to still better confusions.

I agree that there are shades of meaning between the words, but what is it to 'understand' a concept? Call it 'grasping' (a metaphor) or whatever. The point is that some kind of 'having' of some private experience is invoked. I 'understand' what is meant in the usual way. My objection is pushing these ambiguous havings into something impossible sharp. We can't mind meld. We are stuck debating English usage, and yet the temptation is to think it's a kind of science of immaterial realms. — norm

The Euro mission's Mars Rover crashed because of a confusion between Metric and Imperial in some table. The requirements for such a mission are indeed 'impossibly sharp', get it wrong and there are consequences in the real world.

Man is the interface between the imaginal and the material domains, the prejudices of our age notwithstanding.

There's something i haven't run by you, but you in particular might appreciate. I've discovered a peculiar article on the Internet Encyclopedia of Philosophy on 'the indispensability argument for mathematics'. This is all a response to some geezer called Paul Benacerraf whom I think the mathematical gurus on the site, like @Fishfry and @fdrake, will be familiar with.

Anyway, it starts with this: 'Standard readings of mathematical claims entail the existence of mathematical objects. But, our best epistemic theories seem to debar any knowledge of mathematical objects. ' What are 'our best theories' and why do they 'debar' such knowledge?

Sets are abstract objects, lacking any spatio-temporal location. Their existence is not contingent on our existence. They lack causal efficacy. Our question, then, given that we lack sense experience of sets, is how we can justify our beliefs about sets and set theory.

There are a variety of distinct answers to our question. Some philosophers, called rationalists, claim that we have a special, non-sensory capacity for understanding mathematical truths, a rational insight arising from pure thought. But, the rationalist’s claims appear incompatible with an understanding of human beings as physical creatures whose capacities for learning are exhausted by our physical bodies.

(I love the phrase 'some philosophers, called rationalists' - I always imagine David Attenborough intoning this, whilst peering into a laboratory - 'there they are, stooped over their books, in that characteristic state of absorption in abstractions....').

But, anyway, I hope you see the point. The fact that rationlism says that we have certain knowledge of mathematical truths arising from pure thought, actually conflicts with 'an understanding of human beings as physical creatures whose capacities for learning are exhausted by our physical bodies.' But rather than throw out the belief in the fact that 'we're physical creatures', Quine et al go into an intricate argument that we must 'save' or 'respect' maths anyway, whilst still not preparted to acknowlege the fact that we have such faculties throws into doubt our station as 'purely physical beings'. The dogma must be maintained at all costs!

That just says so much about the current state of philosophy, in my view. As you're a bit of a math whiz yourself, and one of the all-around best read people on the site, thought I'd run it by you. :-)

I'm saying that classical metaphysical arguments don't have obvious winners in the real world. And if I give reasons for their futility, I'm also just wasting my time in practical terms, because in general people don't take such things seriously to begin with, and those who like metaphysics are often religiously-politically motivated or just still captured by the notion that they are doing some kind of higher Science. It's a harmless vice, as is critiquing it. — norm

Possibly the most elegant summary of the situation I've yet read.

I get that people like to feel part of a special group of initiated outliers who challenge the mainstream and embrace a numinous reality outside of conventional lifestyles and the ostensible limitations of crass science. I get the attractions of wanting to be one with a higher consciousness through the contemplative life.

What I don't get is the lack of joy in the communication of these ideas. It seems most of what I read is a thick soup of quotes, name dropping and terminology, with the requisite 'my reality is better than theirs' powerplay. I expect that from some atheists. There's almost nothing explaining the benefits or bliss found through the spiritual path and what it actually achieves. Is there somewhere here where this comes up or do we never get past the pissing competition?

Hence my accusation of historicism. That science did develop from philosophy tells us nothing at all about the necessary relationship between the two.

That a sequence of events happened to take place is not evidence that they are causally connected even, let alone necessarily so. — Isaac

There is a difference between historicism (the idea that history follows determinist laws à la Marx) and recognizing established historical facts.

That science as we know it grew historically out of a branch of philosophy (natural philosophy as it was called) is simply a fact, just like it's a fact that Homo sapiens evolved from earlier primates. We share a lot of DNA with our ancestors, and science still shares a lot of concepts with philosophy. And this should encourage you to respect your predecessors a little more, simian or not.

They can do it again, too. In fact they have. There are two broad types of sciences: the natural sciences and the social (or human) sciences, and they were not born at the same time. As is well known, the first to assert their independence from philosophy were natural sciences. This process was complete by the 18th century roughly. Social sciences came later, end 19th-early 20th century. In both cases they carved out a domain that was previously dealt with by philosophers, a set of empirical questions that science could answer. Sociology, psychology, history etc. emerged as sciences historically, and in doing so they tried to take a distance with philosophy (metaphysics) by stressing empiricism and the "laws of history". This led to exciting new theories such as social darwinism and scientific racism... :-\

That is where Popper disagreed and demonstrated (in the Poverty of Historicism) that social sciences ought not to ape natural sciences, and in particular ought not to try and discern immutable laws as historicists wrongly do. Social sciences are not determinist, not anymore -- far less in fact -- than QM. Man makes history, not vice versa.

This provides an example that the divorce was never complete. Philosophers can still tell us useful things about how scientists should go about their business.

There is a difference between historicism (the idea that history follows determinist laws à la Marx) and recognizing established historical facts. — Olivier5

I know. That's why I'm accusing you of historicism and not of pointing out historical facts.

You've just repeated more historical facts, none of which have any bearing on the matter of whether science is necessarily dependant on philosophy. The question is not whether it just so happened to have emerged from it.

At what point does the framing of a question cease to be philosophy and start to be science?

I don’t think philosophy is about who wins the argument. The practical value of philosophical thinking and discussion is in the distribution of human effort and attention.

While I don’t think metaphysics is necessarily a higher science, I do think it frames scientific endeavour, and as such is prone to religious and political motivations, among others. You can try to dismiss metaphysical discussion as a ‘harmless vice’, but all human endeavour nevertheless occurs under a variable framework of distributable effort and attention, and metaphysics is part of that, however it’s described. Learning how to map it, make predictions from it and alter it requires science to somehow accommodate quantitative uncertainty, intersubjectivity and qualitative structure. Until then, I think the distributed effort and attention of science will continue to be determined by those with religious, ideological, political and especially commercial motivations.