Paula asked:

I know that Kant and Hume were influential concerning a priori knowledge, but why exactly have
philosophers held that all necessary truths are knowable a priori if they're knowable at all?

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I will give you a basic example. Take a look around your room and count a few objects. As you do,
say to yourself: all this is unreliable knowledge, because I could be dreaming or hallucinating or
looking into mirror, or the light might fall into the room in at a certain angle and what looks like a doll is
just the shadow cast from the chandelier. Happens all the time. Or you might look at a coin and
decide that it describes a circle, but if you took a photo and traced the shape, you'd find it to be an
ellipse. Or you pick up a piece of wood and find that it just plastic. And so on. Out in the world at large
we negotiate our way through all the objects by heaps of half-conscious guesses, most of the time
without taking in what they are, other than obstacles. Okay, so far so good. You might begin to realise
(I hope) that half-guessing and knowledge are not the same. But now consider this: how come I know
that these are objects at all? Even if I'm dreaming, even when I'm on autopilot, I must still negotiate
objects; I must recognise them as objects, because not to do so might be fatal. How then can we
define what an object is?

You might like to try this yourself before reading on. The answer, of course is that objects occupy
space— that's why I need to navigate them, for ultimately I am also an object. And now the cruncher:
try and define space.What is this 'container' where objects clutter the landscape?

Resist the temptation (if it is one for you) of loading the argument with scientific mumbo jumbo. We
want a simple, clear-cut idea of space. What is it? Where is it? Why is it? Do you think you can
answer this? Feel like trying?

Now the answer to this question, and the reason why I warned you about science, is that we can
have no knowledge of space either. If there is such a thing at all, we cannot know what it is (or where
it is) because we are in it.And if you pursue this thought to its logical conclusion, you will find that
there is only one answer: that space is the possibility for objects to exist.This entails no claim that
either space or the objects really do exist. It cannot assert any more than a possibility. But it does say
that ifthere are objects, then they mustoccupy space. So that the beginning of all genuine
(=necessary) knowledge concerning objects is that space precedes objects as an organising
principle, that without space no objects could be perceived; and that since we are objects ourselves,
we could not exist in the absence of any space. So space "comes before" (=a priori) all objects and
we are thus led to the conclusion that our intuition of space is the bedrock of the very possibility of
experience. And this is where I'm going to leave you to your own devices. I hope, though, that you will
now feel somewhat encouraged to get to the bottom of it yourself.

Jürgen Lawrenz

Sydney