2 added 108 characters in body
source | link

Kant supposes that certain ideas are "a priori, but synthetic". They reference the outside world, and we experience them only in response to it, but they come from within us. They arise from the context we lay upon our experience, instead of from the experience itself. We are more certain of them not because they are somehow any truer than other things, but because we assume them automatically by virtue of being ourselves. They are still phenomena, but they are part of our structure of understanding. We find them very difficult to question.

The structure of space and time are among those things. Kant describes those as 'forms of our intuition' rather than facts or basic ideas. Brouwer later elaborated the idea that mathematics is entirely based upon our perceptions of space and time, and therefore is entirely interior to human thought, and not part of external reality. It is a creative activity of the human mind, giving structure to things, and not a part of external reality, learned by exposure.

By that theory. whatever violates our deepest intuitions about space and time, we can not really comprehend. We can only allude to it, or form abstruse models that adapt our real understanding in artificial ways that provide them leverage over what we cannot really grasp. So we are not certain that these intuitions are true, only that to the degree they fail to be true, we have no chance of understanding the things to which they do not apply. Some humility regarding our own ability to grasp deeper truth is in order.

That is very different from saying they are really more certainly true of reality.

Kant supposes that certain ideas are "a priori, but synthetic". They reference the outside world, but they come from the context we lay upon our experience, instead of from the experience itself. We are more certain of them not because they are somehow any truer than other things, but because we assume them automatically by virtue of being ourselves. They are still phenomena, but they are part of our structure of understanding. We find them very difficult to question.

The structure of space and time are among those things. Kant describes those as 'forms of our intuition'. Brouwer later elaborated the idea that mathematics is entirely based upon our perceptions of space and time, and therefore is entirely interior to human thought, and not part of external reality. It is a creative activity of the human mind, giving structure to things, and not a part of external reality, learned by exposure.

By that theory. whatever violates our deepest intuitions about space and time, we can not really comprehend. We can only allude to it, or form abstruse models that adapt our real understanding in artificial ways that provide them leverage over what we cannot really grasp. So we are not certain that these intuitions are true, only that to the degree they fail to be true, we have no chance of understanding the things to which they do not apply. Some humility regarding our own ability to grasp deeper truth is in order.

That is very different from saying they are really more certainly true of reality.

Kant supposes that certain ideas are "a priori, but synthetic". They reference the outside world, and we experience them only in response to it, but they come from within us. They arise from the context we lay upon our experience, instead of from the experience itself. We are more certain of them not because they are somehow any truer than other things, but because we assume them automatically by virtue of being ourselves. They are still phenomena, but they are part of our structure of understanding. We find them very difficult to question.

The structure of space and time are among those things. Kant describes those as 'forms of our intuition' rather than facts or basic ideas. Brouwer later elaborated the idea that mathematics is entirely based upon our perceptions of space and time, and therefore is entirely interior to human thought, and not part of external reality. It is a creative activity of the human mind, giving structure to things, and not a part of external reality, learned by exposure.

By that theory. whatever violates our deepest intuitions about space and time, we can not really comprehend. We can only allude to it, or form abstruse models that adapt our real understanding in artificial ways that provide them leverage over what we cannot really grasp. So we are not certain that these intuitions are true, only that to the degree they fail to be true, we have no chance of understanding the things to which they do not apply. Some humility regarding our own ability to grasp deeper truth is in order.

That is very different from saying they are really more certainly true of reality.

1
source | link

Kant supposes that certain ideas are "a priori, but synthetic". They reference the outside world, but they come from the context we lay upon our experience, instead of from the experience itself. We are more certain of them not because they are somehow any truer than other things, but because we assume them automatically by virtue of being ourselves. They are still phenomena, but they are part of our structure of understanding. We find them very difficult to question.

The structure of space and time are among those things. Kant describes those as 'forms of our intuition'. Brouwer later elaborated the idea that mathematics is entirely based upon our perceptions of space and time, and therefore is entirely interior to human thought, and not part of external reality. It is a creative activity of the human mind, giving structure to things, and not a part of external reality, learned by exposure.

By that theory. whatever violates our deepest intuitions about space and time, we can not really comprehend. We can only allude to it, or form abstruse models that adapt our real understanding in artificial ways that provide them leverage over what we cannot really grasp. So we are not certain that these intuitions are true, only that to the degree they fail to be true, we have no chance of understanding the things to which they do not apply. Some humility regarding our own ability to grasp deeper truth is in order.

That is very different from saying they are really more certainly true of reality.