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Hume applying rationality to causality showed that it could not exist - the question is then how does it exist. Kants reply was to place it in the mind. Popper discusses this in his *Conjectures & Refutations

Thus Kant’s reply to Hume came near to being right; for the distinction between an a priori valid expectation and one which is both genetically and logically prior to observation, but not a priori valid, is really somewhat subtle.

So Popper appears to agree with Kant here.

But Kant proved too much. In trying to show how knowledge is possible, he proposed a theory which had the unavoidable consequence that our quest for knowledge must necessarily succeed, which is clearly mistaken.

What does he mean by this? I read this first meaning the quest for all knowledge; but this cannot be right; I suspect given his theory of falsifiability one cannot attain proven knowledge of the world - there can always be new evidence that fails it. However, given Kants starting point I think Kant means knowledge of a more basic kind - measuring a metre, measuring a second, that there are two bottles there; or taking that this has caused that. But perhaps, and probably more likely, he means more. What was Kants 'quest for knowledge'?

When Kant said "Our intellect does not draw its laws from nature but imposes its laws upon nature", he was right.

Again he agrees with Kant on how nature is ordered by the mind.

But in thinking that these laws are necessarily true, or that we necessarily succeed in imposing them upon nature, he was wrong. Nature very often resists quite successfully, forcing us to discard our laws as refuted; but if we live we may try again.

But then what does he mean by this? If Nature 'resists' our laws forcing us to 'discard' them; then it appears he is describing the scientific laws - those of chemistry or physics, say. Surely he cannot mean the laws grounding experience - those of space, time, causality & quantity?

One might suppose that these laws are distorted in the hallucinations or dreams - but I suspect that these states of the mind is not what Kant was discussing; that is he took it as implicitly read he was talking about the human conscious when it is awake and functioning normally.

Kant believed that Newton’s dynamics was a priori valid (See his Metaphysical Foundations of Natural Science, published between the first and the second editions of the Critique of Pure Reason.) But if, as he thought, we can explain the validity of Newton’s theory by the fact that our intellect imposes its laws upon nature, it follows, I think, that our intellect must succeed in this; which makes it hard to understand why a priori knowledge such as Newton’s should be so hard to come by.

Is Popper just grumbling here - or is his attack serious?

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I should preface this by saying I haven't read Kant and this is just an account of Popper's position, including his position on Kant and not an account of Kant's position in its own right.

Popper's position on how knowledge is created goes like this. You start with your current ideas and look for problems with them: clashes among those ideas, or clashes with results of experiments. You then propose ideas that might solve those problems. You criticise the proposals until only one is left, at which point you have solved the problem. The criticism might include doing an experiment for which your chosen idea predicts a particular result, or looking for clashes or whatever. But the criticism is aimed at eliminating some proposed solution and that helps you decide what to do. If you didn't have any such standard you couldn't make a decision about what to test or why. Then you look for new problems.

In the first paragraph you quoted, what Popper is saying is that Kant is right that you need to have an idea before you can do an observation. In the second paragraph you quoted Popper is saying Kant was wrong to think that the idea you had before the observation must be correct. So what observations you do are determined by what ideas you have but the results are not. (I think it's a bad idea to describe this as imposing our ideas on nature.)

Now you say

However, given Kants starting point I think Kant means knowledge of a more basic kind - measuring a metre, measuring a second, that there are two bottles there; or taking that this has caused that.

You can measure a metre while having a bad idea about what should count as a metre. The standard for what counts as a metre has changed over time. It used to be defined in terms of a special type of metal bar under suitable conditions and is now set in terms of the speed of light. The metal bar standard was good enough for a lot of measurements but not good enough for some more recent measurements, see

http://www.nist.gov/calibrations/upload/4998.pdf.

The only question to ask about measurements in terms of the old standard is whether they require the accuracy of the new standard or not to test the ideas they were supposed to test. For example, if a biologist measures the length of a dolphin to presumably does not care about the length down to the last angstrom so then he shouldn't care about the change.

Next you write:

But then what does he mean by this? If Nature 'resists' our laws forcing us to 'discard' them; then it appears he is describing the scientific laws - those of chemistry or physics, say. Surely he cannot mean the laws grounding experience - those of space, time, causality & quantity?

I don't understand what "laws grounding experience" might be. Knowledge is not grounded on anything: it consists of guesses controlled by criticism. Our ideas about how to measure quantities have changed. Ideas about space, time and causality have also changed, e.g. - relativity of simultaneity.

Now, with respect to the last paragraph you quote from Popper, what he is saying is this. Suppose that we can impose our ideas on the world, in the sense that those ideas actually have to be true. Then why is it not the case that every idea we come up with is true? This makes sense as an objection to the idea that Popper attributed to Kant.

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