I’ve been working on a write-up on and off for months, which I might or might not ever get around to finishing.
The basic gist is that, while Hume assumes you have sense-data and are learning structures like causation from this sense-data, Kant is saying you need concepts of causation to have sense-data at all.
The Transcendental Aesthetic is a pretty simple argument if applied to Solomonoff induction. Suppose you tried to write an AI to learn about time, which didn’t already have time. How would it structure its observations, so it could learn about time from these different observations? That seems pretty hard, perhaps not really possible, since “learning” implies past observations affecting how future observations are interpreted.
In Solomonoff induction there is a time-structure built in, which structures observations. That is, the inductor assumes a priori that its observations are structured in a sequence.
Kant argues that space is also a priori this way. This is a somewhat suspicious argument given that vanilla Solomonoff induction doesn’t need a priori space to structure its observations. But maybe it’s true in the case of humans, since our visual cortexes have a notion of spacial observation already built in. (That is, when we see things, we see them at particular locations)
Other than time and space to structuring observations, what else has to be there? To see the same object twice there has to be a notion that two observations could be of the same object. But that is more structure than simply spacetime, there’s also a structure of connection between different observations so they can be of the same object.
Solomonoff induction might learn this through compression. Kant, unfortunately, doesn’t explicitly discuss compression all that much. However, even Solomonoff induction makes a priori assumptions beyond spacetime, namely, that the universe is a Turing machine. This is a kind of causal assumption. You couldn’t get “this runs on a Turing machine” by just looking at a bunch of data, without having some kind of prior that already contains Turing machines. It is, instead, assumed a priori that there’s a Turing machine causing your observations.
The book is mostly a lot of stuff like this, what thought structures we must assume a priori to learn from data at all.
The basic gist is that, while Hume assumes you have sense-data and are learning structures like causation from this sense-data, Kant is saying you need concepts of causation to have sense-data at all.
Hmm. Both of these ideas seem very wrong (though Kant’s, perhaps, more so). Is there anything else of value? If this (and similar things) are all that there is, then maybe rationalists are right to mostly ignore Kant…
I’ve been working on a write-up on and off for months, which I might or might not ever get around to finishing.
The basic gist is that, while Hume assumes you have sense-data and are learning structures like causation from this sense-data, Kant is saying you need concepts of causation to have sense-data at all.
The Transcendental Aesthetic is a pretty simple argument if applied to Solomonoff induction. Suppose you tried to write an AI to learn about time, which didn’t already have time. How would it structure its observations, so it could learn about time from these different observations? That seems pretty hard, perhaps not really possible, since “learning” implies past observations affecting how future observations are interpreted.
In Solomonoff induction there is a time-structure built in, which structures observations. That is, the inductor assumes a priori that its observations are structured in a sequence.
Kant argues that space is also a priori this way. This is a somewhat suspicious argument given that vanilla Solomonoff induction doesn’t need a priori space to structure its observations. But maybe it’s true in the case of humans, since our visual cortexes have a notion of spacial observation already built in. (That is, when we see things, we see them at particular locations)
Other than time and space to structuring observations, what else has to be there? To see the same object twice there has to be a notion that two observations could be of the same object. But that is more structure than simply spacetime, there’s also a structure of connection between different observations so they can be of the same object.
Solomonoff induction might learn this through compression. Kant, unfortunately, doesn’t explicitly discuss compression all that much. However, even Solomonoff induction makes a priori assumptions beyond spacetime, namely, that the universe is a Turing machine. This is a kind of causal assumption. You couldn’t get “this runs on a Turing machine” by just looking at a bunch of data, without having some kind of prior that already contains Turing machines. It is, instead, assumed a priori that there’s a Turing machine causing your observations.
The book is mostly a lot of stuff like this, what thought structures we must assume a priori to learn from data at all.
Hmm. Both of these ideas seem very wrong (though Kant’s, perhaps, more so). Is there anything else of value? If this (and similar things) are all that there is, then maybe rationalists are right to mostly ignore Kant…