It is as if one were to look at the shapes that crystals grow into and ask not, “What mechanisms produce these shapes?” (a question answered in the laboratory, not the armchair, by discovering that atoms bind to each other in ways that form orderly lattices), but “What is a shape?”
Why aren’t both questions valuable to ask? The latter one must have contributed to the eventual formation of the mathematical field of geometry.
I find it difficult to see any trace of the idea in Euclid. Circles and straight lines, yes, but any abstract idea of shape in general, if it can be read into geometry at all, would only be in the modern axiomatisation. And done by mathematicians finding actual theorems, not by philosophers assuming there is an actual thing behind our use of the word, that it is their task to discover.
And done by mathematicians finding actual theorems, not by philosophers assuming there is an actual thing behind our use of the word, that it is their task to discover.
I don’t mean to pick just on you, but I think philosophy is often unfairly criticized for being less productive than other fields, when the problem is just that philosophy is damned hard, and whenever we do discover, via philosophy, some good method for solving a particular class of problems, then people no longer consider that class of problems to belong to the realm of philosophy, and forget that philosophy is what allowed us to get started in the first place. For example, without philosophy, how would one have known that proving theorems using logic might be a good way to understand things like circles, lines, and shapes (or even came up with the idea of “logic”)?
(Which isn’t to say that there might not be wrong ways to do philosophy. I just think we should cut philosophers some slack for doing things that turn out to be unproductive in retrospect, and appreciate more the genuine progress they have made.)
For example, without philosophy, how would one have known that proving theorems using logic might be a good way to understand things like circles, lines, and shapes (or even came up with the idea of “logic”)?
How people like Euclid came up with the methods they did is, I suppose, lost in the mists of history. Were Euclid and his predecessors doing “philosophy”? That’s just a definitional question.
The problem is that there is no such thing as philosophy. You cannot go and “do philosophy”, in the way that you can “do mathematics” or “do skiing”. There are only people thinking, some well and some badly. The less they get out of their armchairs, the more their activity is likely to be called philosophy, and in general, the less useful their activity is likely to be. Mathematics is the only exception, and only superficially, because mathematical objects are clearly outside your head, just as much as physical ones are. You bang up against them, in a way that never happens in philosophy.
When philosophy works, it isn’t philosophy any more, so the study of philosophy is the study of what didn’t work. It’s a subject defined by negation, like the biology of non-elephants. It’s like a small town in which you cannot achieve anything of substance except by leaving it. Philosophers are the ones who stay there all their lives.
I realise that I’m doing whatever the opposite is of cutting them some slack. Maybe trussing them up and dumping them in the trash.
I just think we should cut philosophers some slack for doing things that turn out to be unproductive in retrospect, and appreciate more the genuine progress they have made.
What has philosophy ever done for us? :-) I just googled that exact phrase, and the same without the “ever”, but none of the hits gave a satisfactory defence. In fact, I turned up this quote from the philosopher Austin, characterising philosophy much as I did above:
“It’s the dumping ground for all the leftovers from other sciences, where everything turns up which we don’t know quite how to take. As soon as someone discovers a reputable and reliable method of handling some portion of these residual problems, a new science is set up, which tends to break away from philosophy.”
Responding to the sibling comment here as it’s one train of thought:
How might one know, a priori, that “What is a circle?” is a valid question to ask, but not “What is a shape?”
By knowing this without knowing why. That’s all that a priori knowledge is: stuff you know without knowing why. Or to make the levels of abstraction more explicit, a priori beliefs are beliefs you have without knowing why. Once you start thinking about them, asking why you believe something and finding reasons to accept or reject it, it’s no longer a priori. The way to discover whether either of those questons is sensible is to try answering them and see where that leads you.
That activity is called “philosophy”, but only until the process gets traction and goes somewhere. Then it’s something else.
That’s all that a priori knowledge is: stuff you know without knowing why. Or to make the levels of abstraction more explicit, a priori beliefs are beliefs you have without knowing why. Once you start thinking about them, asking why you believe something and finding reasons to accept or reject it, it’s no longer a priori.
The problem is that there is no such thing as philosophy. You cannot go and “do philosophy”, in the way that you can “do mathematics” or “do skiing”. There are only people thinking, some well and some badly. The less they get out of their armchairs, the more their activity is likely to be called philosophy, and in general, the less useful their activity is likely to be. [...]
When philosophy works, it isn’t philosophy any more, so the study of philosophy is the study of what didn’t work. It’s a subject defined by negation, like the biology of non-elephants.
I think there are useful kinds of thought that are best categorized as “philosophy” (even if it’s just “philosophy of the gaps”, i.e. not clear enough to fall into an existing field); mostly around the area of how we should adapt our behavior or values in light of learning about game theory, evolutionary biology, neuroscience etc. - for example, “We are the product of evolution, therefore it’s every man for himself” is the product of bad philosophy, and should be fixed with better philosophy rather than with arguments from evolutionary biology or sociology.
A lot of what we discuss here on LessWrong falls more easily under the heading of “philosophy” than that of any other specific field.
(Note that whether most academic philosophers are producing any valuable intellectual contributions is a different question, I’m only arguing “some valuable contributions are philosophy”)
Why aren’t both questions valuable to ask? The latter one must have contributed to the eventual formation of the mathematical field of geometry.
I find it difficult to see any trace of the idea in Euclid. Circles and straight lines, yes, but any abstract idea of shape in general, if it can be read into geometry at all, would only be in the modern axiomatisation. And done by mathematicians finding actual theorems, not by philosophers assuming there is an actual thing behind our use of the word, that it is their task to discover.
I don’t mean to pick just on you, but I think philosophy is often unfairly criticized for being less productive than other fields, when the problem is just that philosophy is damned hard, and whenever we do discover, via philosophy, some good method for solving a particular class of problems, then people no longer consider that class of problems to belong to the realm of philosophy, and forget that philosophy is what allowed us to get started in the first place. For example, without philosophy, how would one have known that proving theorems using logic might be a good way to understand things like circles, lines, and shapes (or even came up with the idea of “logic”)?
(Which isn’t to say that there might not be wrong ways to do philosophy. I just think we should cut philosophers some slack for doing things that turn out to be unproductive in retrospect, and appreciate more the genuine progress they have made.)
How people like Euclid came up with the methods they did is, I suppose, lost in the mists of history. Were Euclid and his predecessors doing “philosophy”? That’s just a definitional question.
The problem is that there is no such thing as philosophy. You cannot go and “do philosophy”, in the way that you can “do mathematics” or “do skiing”. There are only people thinking, some well and some badly. The less they get out of their armchairs, the more their activity is likely to be called philosophy, and in general, the less useful their activity is likely to be. Mathematics is the only exception, and only superficially, because mathematical objects are clearly outside your head, just as much as physical ones are. You bang up against them, in a way that never happens in philosophy.
When philosophy works, it isn’t philosophy any more, so the study of philosophy is the study of what didn’t work. It’s a subject defined by negation, like the biology of non-elephants. It’s like a small town in which you cannot achieve anything of substance except by leaving it. Philosophers are the ones who stay there all their lives.
I realise that I’m doing whatever the opposite is of cutting them some slack. Maybe trussing them up and dumping them in the trash.
What has philosophy ever done for us? :-) I just googled that exact phrase, and the same without the “ever”, but none of the hits gave a satisfactory defence. In fact, I turned up this quote from the philosopher Austin, characterising philosophy much as I did above:
“It’s the dumping ground for all the leftovers from other sciences, where everything turns up which we don’t know quite how to take. As soon as someone discovers a reputable and reliable method of handling some portion of these residual problems, a new science is set up, which tends to break away from philosophy.”
Responding to the sibling comment here as it’s one train of thought:
By knowing this without knowing why. That’s all that a priori knowledge is: stuff you know without knowing why. Or to make the levels of abstraction more explicit, a priori beliefs are beliefs you have without knowing why. Once you start thinking about them, asking why you believe something and finding reasons to accept or reject it, it’s no longer a priori. The way to discover whether either of those questons is sensible is to try answering them and see where that leads you.
That activity is called “philosophy”, but only until the process gets traction and goes somewhere. Then it’s something else.
This is a nice concise statement of the idea that didn’t easily get across through the posts A Priori and How to Convince Me That 2 + 2 = 3.
I think there are useful kinds of thought that are best categorized as “philosophy” (even if it’s just “philosophy of the gaps”, i.e. not clear enough to fall into an existing field); mostly around the area of how we should adapt our behavior or values in light of learning about game theory, evolutionary biology, neuroscience etc. - for example, “We are the product of evolution, therefore it’s every man for himself” is the product of bad philosophy, and should be fixed with better philosophy rather than with arguments from evolutionary biology or sociology.
A lot of what we discuss here on LessWrong falls more easily under the heading of “philosophy” than that of any other specific field.
(Note that whether most academic philosophers are producing any valuable intellectual contributions is a different question, I’m only arguing “some valuable contributions are philosophy”)
How might one know, a priori, that “What is a circle?” is a valid question to ask, but not “What is a shape?”