On the Foundations of Geometry by Henri Poincaré (1898)(archive.org)
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On the Foundations of Geometry by Henri Poincaré (1898)
https://archive.org/stream/jstor-27899007/27899007_djvu.txt
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> Our sensations cannot give us the notion of space. That notion is built up by the mind from elements which pre-exist in it,
and external experience is simply the occasion for its exercising
this power, or at most a means of determining the best mode of
exercising it.
Can somebody explain what is meant here?
Can somebody explain what is meant here?
The premise that space is an a priori condition of all human experience of the empirical world flows undisstilled from Kant [Critique of Pure Reason]. The skeptic's argument for idealism, that we cannot deduce that things are as they appear based on there appearance, is taken seriously. Kant's solution to the problem of an independent empirical reality is that we have a schema[0] for experiencing the world.
The gist of the argument is:
1. The idealist's argument assumes each of us experiences the world in the same way: as appearances.
2. Kant deduces the boundaries of our mechanism by distinguishing between inner experience parsed into a temporal schema and outer experience parsed into a spatial schema. The fact that we can talk about idealized space as geometry supports this claim without bogging down in a Platonic realm of Pure ideas.
3. The upside is that empirical knowledge if the external world is possible. The downside is that deductive knowledge of it is not. We cannot know the ding an sich.
It's a powerful enough abstraction that it actually disappears in modern culture to the point that people arguing against it will cite statistical or probabilistic evidence in making their case, i.e. arguing for an absolute truth based on a confidence interval.
[0]: "schema" as in a database analogy, not in the way Kant's argument is traditionally translated to English.
The gist of the argument is:
1. The idealist's argument assumes each of us experiences the world in the same way: as appearances.
2. Kant deduces the boundaries of our mechanism by distinguishing between inner experience parsed into a temporal schema and outer experience parsed into a spatial schema. The fact that we can talk about idealized space as geometry supports this claim without bogging down in a Platonic realm of Pure ideas.
3. The upside is that empirical knowledge if the external world is possible. The downside is that deductive knowledge of it is not. We cannot know the ding an sich.
It's a powerful enough abstraction that it actually disappears in modern culture to the point that people arguing against it will cite statistical or probabilistic evidence in making their case, i.e. arguing for an absolute truth based on a confidence interval.
[0]: "schema" as in a database analogy, not in the way Kant's argument is traditionally translated to English.
You need two eyes for depth perception. Neither individually can tell you location, your mind figures that out by combining inputs. If you move your arms and feel something near you, you still don't know where it is until your mind relates it to other things your mind knows are near (or other parts of your body). The sensation itself only provides information on existence, the mind pieces together location. On the other side of experience, external actions are entirely an effect of internal processes. Essentially, the mind is a black box puppet master and the body is the puppet.
(I haven't read the passage, but that is my interpretation of your quote. I always enjoy Poincaire's musings on the mind, they resonate strongly with my own.)
(I haven't read the passage, but that is my interpretation of your quote. I always enjoy Poincaire's musings on the mind, they resonate strongly with my own.)
You need two eyes for depth perception.
This is false, you can get plenty of depth information from a picture or even better a movie which is not stereoscopic.
This is false, you can get plenty of depth information from a picture or even better a movie which is not stereoscopic.
Is that because the movie or picture are similar enough to the experiences we previously had with our eyes?
People born with one good eye still generally develop depth perception. There is a lot of research into this topic, https://en.wikipedia.org/wiki/Depth_perception#Monocular_cue... has a good list of things that work just fine with one eye. But, it's not obvious how much of these are learned vs instinctive.
Fair enough :)
Sounds a whole lot like Kant's synthetic a priori judgements.
It is - this is pretty much the argument of the Transcendental Aesthetic in the First Critique.
What is meant here is an ordinary empirical claim that is false, which is unsurprising because it is made independently of any empirical investigation into how we form our notion of space.
Observational studies in developmental psychology--which didn't exist in Poincare's day, much less Kant's--tell us that our notions of space are developed interactively, not observationally. We are not passive recipients of sensation trapped in Plato's cave, but active intervenors in the world who learn about the universe by being causes.
"According to Piaget, the origin of spatial representation coincides with the origin of drawing, language and representational thinking in general. In spite of their common development, drawing soon falls behind the mental conception of space (especially in the case of complex and three-dimensional constructions). Yet, in its simplest and earliest appearances, drawing should be conceived as the representation or even the motor of spatial conception, because—here Piaget quotes his teacher, the philosopher of mathematics Léon Brunschvicg—drawing is not founded on geometry, but on the contrary, geometry is founded on the practice of drawing. If one explains the origins of geometry as arising from drawing, the child’s drawing can indeed be operationalized as a reconstruction apparatus of the psychogenesis of space. If one understands drawing in this way, it does not record an independent process of development, rather it documents and reflects its own developmental conditions—and thereby furthers mental ontogeny. Children’s drawings are able to visualize geometric conceptions because they are one of its main motors. The drawing child constitutes a veritable machine that works on the production of a Euclidean future, because—as Piaget detected in his experiments—it helps to complete and partly to conceal the infant’s older tacit topological knowledge." (emphasis added) -- http://www.mpiwg-berlin.mpg.de/en/news/features/feature11
I am not in any sense a strict Piagetian, and I realized there has been a lot of work done on this topic since, but I use this as an example simply because his empirical investigations were foundational and should have brought us to the point where everyone recognizes that philosophical imaginings are not a useful way to approach any question whatsoever regarding the development of ideas, even when they are the imaginings of someone as clever as Kant, whom as others here have pointed out, Poincare' was channeling.
The imagination is a terrible guide to what is real: we can imagine all kinds of things that can't exist (the god of the Bible, for example) and can't imagine all kinds of things that do exist (whatever lies behind quantum phenomena, say).
Philosophers (and at times mathematicians) like to sweep away the messy empirical realities that actually give rise to our ideas of geometry and everything else. It's a fun game to play. It just tells us far more about the human imagination than the rest of reality.
Observational studies in developmental psychology--which didn't exist in Poincare's day, much less Kant's--tell us that our notions of space are developed interactively, not observationally. We are not passive recipients of sensation trapped in Plato's cave, but active intervenors in the world who learn about the universe by being causes.
"According to Piaget, the origin of spatial representation coincides with the origin of drawing, language and representational thinking in general. In spite of their common development, drawing soon falls behind the mental conception of space (especially in the case of complex and three-dimensional constructions). Yet, in its simplest and earliest appearances, drawing should be conceived as the representation or even the motor of spatial conception, because—here Piaget quotes his teacher, the philosopher of mathematics Léon Brunschvicg—drawing is not founded on geometry, but on the contrary, geometry is founded on the practice of drawing. If one explains the origins of geometry as arising from drawing, the child’s drawing can indeed be operationalized as a reconstruction apparatus of the psychogenesis of space. If one understands drawing in this way, it does not record an independent process of development, rather it documents and reflects its own developmental conditions—and thereby furthers mental ontogeny. Children’s drawings are able to visualize geometric conceptions because they are one of its main motors. The drawing child constitutes a veritable machine that works on the production of a Euclidean future, because—as Piaget detected in his experiments—it helps to complete and partly to conceal the infant’s older tacit topological knowledge." (emphasis added) -- http://www.mpiwg-berlin.mpg.de/en/news/features/feature11
I am not in any sense a strict Piagetian, and I realized there has been a lot of work done on this topic since, but I use this as an example simply because his empirical investigations were foundational and should have brought us to the point where everyone recognizes that philosophical imaginings are not a useful way to approach any question whatsoever regarding the development of ideas, even when they are the imaginings of someone as clever as Kant, whom as others here have pointed out, Poincare' was channeling.
The imagination is a terrible guide to what is real: we can imagine all kinds of things that can't exist (the god of the Bible, for example) and can't imagine all kinds of things that do exist (whatever lies behind quantum phenomena, say).
Philosophers (and at times mathematicians) like to sweep away the messy empirical realities that actually give rise to our ideas of geometry and everything else. It's a fun game to play. It just tells us far more about the human imagination than the rest of reality.
Why are you linking to an OCR of a scan? Link to the main page, where multiple formats are on offer:
https://archive.org/details/jstor-27899007
The main page even has a rather nice viewer to view the document in your browser.
https://archive.org/details/jstor-27899007
The main page even has a rather nice viewer to view the document in your browser.
Oftentimes stuff on the front page is posted as part of a recognizable cluster of activity, but if that's the case with this submission I can't figure it out. Can anyone help?
EDIT: Meaning, there's a theme; or one post comments on another post, or provides background with which to interpret it.
EDIT: Meaning, there's a theme; or one post comments on another post, or provides background with which to interpret it.
http://www-history.mcs.st-and.ac.uk/Extras/Poincare_Intuitio...